24 Magnetism

By S. T. BRAMWELL University College London, Department of Chemistry, Christopher Ingold

Laboratories, 20 Gordon Street, London WCIH OAJ, UK

1 Introduction

Magnetism forms a gigantic field of research of which magnetochemistry is a small part. It is an exceedingly rich subject, which does not fit easiIy into the traditional disciplines of science. This report strives to d o justice to the richness and diversity of the subject, whilst concentrating on developments of direct reIevance to chemistry. In no sense is an attempt made to give an exhaustive account of the literature; this is clearly unfeasible when the 1996 literature contains over twenty thousand references that allude to magnetic properties.

The report is divided into four sections. The introductory section will try to identify the major highjigbts and trends in magnetochemistry, and will mention some of the more interesting developments across diverse fields that may give inspiration to the magnetochemist. Some books and general reviews will also be described. Section 2 is devoted to a more detailed summary of the year’s literature in several selected topics. The remaining sections, 3 and 4, group work according to the type of materia1 under investigation. Section 3 describes work on ionic, covalent and metallic materials, particularly oxides and halides which are the traditional interest of solid state chemists. Section 4 describes work on metal complexes and molecular solids, more traditionally the domain of coordination chemists. In this section the materials are cfassified by dimensionality of the complex, which from the magnetic point of view seems to provide a natural division. This report follows on from the excelIent series by Harrison and colleagues,’ their policy of not reporting on the simple characterisation of magnetic materials has been adopted, apart from in cases that this is relevant to a more general problem in magnetism.

Perhaps the highlight of the year is the discovery by several groups of dramatic quantum tunnelling effects in molecular clusters. These results, which are described in detail in Section 2, raise hopes that one day such effects can be harnessed to make nanoscale magnetic memory devices. They provide a clear motive for the mag- netochemist to synthesize and study such cIusters, and open up exciting prospects for future research. I t is to be hoped that coordination chemists wilI rise to this challenge, as it is clear from this survey of the literature that the huge amount of work on small magnetic clusters, although worthy, has little scientific motive beyond basic character- ization. A rather more focused, and equally popular subject of research is ‘molecu1ar

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458 S. T. Bramwell

ferromagnetism’, but unfortunately progress in this field is slow, with transition temperatures largely rooted to liquid helium levels. In solid state chemistry giant magnetoresistance is the most popular current topic of study, and is again motivated by a commercial goaI. Progress in this field is much faster than in the rather ailing ‘high-T,’ industry, although there are stiH many chemists involved in studying magnet- ic oxides related to the superconducting cuprates. From the point of view of pure science, frustrated magnets are the main focus of attention, and although only a relatively modest number of researchers are involved in this field, the collaboration of chemists and physicists ensures steady progress.

The research areas described above form the main subject of the forthcoming sections of this report. Also selected are some topics which are really physics, but are of genera1 relevance to magnetochemistry. These include new magneto-optic effects, nucIear magnets and various theoretical studies. It is interesting to put all these subjects into a wider context by examining the magnetic research that has made it into the pages of the semi-popular scientific journals. Both Nature2 and Science3 have devoted editorial space to discussing the quantum mechanical tunnelling phenomena described in section 2, giant rnagnetoresi~tance,~~~ and the new magneto-optic effects described in section 3.6*7 Science also carried an editorial article on the effect of ‘negative viscosity’ in magnetic fluids.8 This topic is so fascinating that it would seem worthy of a brief description. Negative viscosity refers to the reduction in viscosity of a magnetic fluid-a colloidal suspension of single-domain magnetic partictes-when subject to changing magnetic fields. Almost magical effects can be observed, for exampie, if a drop of magnetic fluid is suspended in another fluid in a rotating magnetic field: the drop develops starfish-like spiny arms, and, depending on the frequency, weird eel-like structures. Although magnetic fluids are widely used in hard disk drives, audio speakers, printing and magnetic resonance imaging, there is as yet no practical use for these effects.

Other magnetic headlines in these journals have concentrated on magnetic fields in space. Nature has reported an interesting result from the Galileo space probe, that Jupiter’s moon Ganymede is the first moon to be discovered that has a magnetic field, possibly arising from convection in a layer of salty water below the ~ u r f a c e . ~ On a more popular leveI, New Scientist described how PobelI and colleagues at Bayreuth Univer- sity have made the ‘coldest lump of metal ever’, a 32g piece of Pt cooled to 3 pK by adiabatic demagnetization of the nuclear spins.”

A number of magnetic devices have been reported in engineering magazines. Profes- sional Engineering describes a torque magnetometer that traveIs along the 17 000 krn of Britain’s steel gas pipelines, detecting flux Ieakage into corroded regions on the exterior of the pipe.” Insight magazine noted that Oxford Instruments have an- nounced the successful operation of the world’s first cryogen-free superconducting magnet; the work required to cool the magnet to 5 K being provided entirely by the externaI power Electronics Today reported an ingenious new type of mag- netometer designed by Givens el a[+:’ based on a xylophone resonator, i t is sensitive to a wide range of fields and Iends itself to miniaturization.

This introductory section is concluded by noting a number of books and reviews that have appeared this year. Aharoni has pubIished a book on the theory of feromag- netism that covers basic aspects of exchange, anisotropy and magne tostatics, as well as giving a more comprehensive coverage of the theory of rnicr~magnetics.’~ Although

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Magnetism 459

mainly intended for physicists and engineers, magnetochemists may find this book a useful guide to the more mysterious aspects of ferromagnetism. At a much more popular level, Livingstone’s book, Driving Force-The Natural Magic of Magnets,’ has been reviewed very favourably by Grantx6

Volume 544 of the American Chemical Society Symposium Series, the published proceedings of the 1995 International Chemical Congress of the Pacific Basin Societies at Honolulu, is devoted to molecular-based magnetic materials. l 7 It contains 22 reviews and research papers on theory, technique and applications in molecular magnetism.

Gatteschi el a!.” have reviewed the magnetism of large iron-oxo clusters. Giant magnetoresistance in layered and granular alloy systems has been reviewed by Levy.I9 The giant or coIossal magnetoresistance of the Ianthanide manganates has been reviewed by Rao et aL2” Several reviews on molecular ferromagnetism have ap- peared.’ lS2 ’ Kirchmayr has reviewed permanent magnets, with an emphasis on hard magnetic materials based on rare-earth inter metallic^.^^ Mydosh has reviewed dis- ordered magnetism and spin gIasses, and suggested that future avenues of research will concentrate on the changes of magnetic behaviour caused by nanostructuring such material^.^^ Govord et have reviewed the magnetism of intermetallics with non-magnetic constituent elements, such as weakly ferromagnetic PdTiAl.

There have been several rather less general reviews, concentrating on work from particulargroups. Khan et al. have reviewed their work on the magnetism ofmolecular based bimetdlic species,26 and Day has reviewed work at the Royai Institution of Great Britain on organic-inorganic layer corn pound^.^^ Broholm et at. have published a short review of the magnetism of transition metal oxides in which there are strong magnetic fluctuations at low temperature.28 They discuss frustration, the Haldane effect in one-dimensional chains, and the unusua1 case of (V, -xCr,),O, in which orbital fluctuations limit spin correlations to small ciusters. Some other reviews are mentioned in the forthcoming test.

2 Selected topics

Quantum mechanical tunnelling As mentioned above, one of the highlights of the magnetic year is the demonstration by several groups of quantum tunnelling effects in moIecular magnets. Physicists have for a number of years being trying to make an ensemble of identical nanometer scale magnets. This is of interest both for theoretical reasons, as a probe of the ‘grey area’ between quantum and classical mechanics, and for practicaI reasons, as a development in the nanomolecular engineering of magnetic memory elements. It is well known that small magnetic clusters behave quantum mechanically with the projection of the magnetic moment on the field direction adopting a series of discrete values labelled by the quantum number M,. Much larger assembhes of magnetic ions, however, behave as classical monodomain particles, that is, as tiny ‘compass needles’, with statistical averaging masking all evidence of discreteness in the magnetization. In the presence of uniaxial magnetic anistropy, a cIassical cIuster will not be able to ‘flip’ its magnetiz- ation if the temperature is much lower than the anisotropy barrier which prevents rotation of the particle’s magnetization; but a quantum mechanical cluster may

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460

n S. T. Brnmweli

Fig. 1 Mn3’ (open)

Structure of Mn,,0,,(CW,C0,),6fH,0), showing Mn4’ (shaded) and

support resonant tunnelling of the magnetization through the potential barrier, an effect that should be Iargest when ‘spin up’ and ‘spin down’ states are degenerate in energy. In order to measure the tunnelling, an assembly of identical nanopartides is required, as all particles will have identical tunnelling rates. Large molecular clusters can be crystallized easily into such an ensemble.

used the sample [Mn,,O l,(CH,C0,),6(H20)4] the structure of which is illustrated in Fig. 1. It has a tetrahedral core of four Mn4+ ions, each with spin 3/2, which are strongly exchange-coupled ferromagneticall y to one another. These are surrounded by eight Mn3 + ions, with their spins (S = 2) coupled ferromagnetically to each other, but antiferromagnetically to the central core. This gives the complex an overall spin S = 10, which behaves at low temperature as a single ‘super spin’. Anisotropy, arising from spin-orbit coupling, gives the complex an easy axis of magnetization and causes the M, = -t 10 states to lie lowest in energy, with M , = f 9 Iying next lowest and so on. The anisotropy axis corresponds to the crystaIline c-axis; Friedman et at. have exploited this to magnetically align a polycrystalline sample which is then immobiiized in epoxy resin, obviating the need for large single crystals. Experimentally, the sample is found to have a stepped hysteresis loop, illustrated in Fig. 2; but more remarkably the rate of approach to equilibrium of the magnetization at a given external field depends sensitively on the magnitude of the field, with maxima in the rate at fields corresponding to the steps in the hysteresis curve (Fig. 3).

To appreciate just how remarkable this result is, consider the following: if the sarnpIe is initially magnetized in say the M , = + 10 state and the field is switched off, then individual complexes will occasionally ff ip their spins and the bulk magnetization will decay slowIy. However, if a weak field is applied opposite to the magnetization direction, the rate of decay is suppressed, rather than enhanced, as would be intuitively supposed. These remarkable observations provide clear evidence for quantum mech- anical tunnelling between the different M , states on either side of the potential barrier.

Friedman et

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Magnetism 46 1

0.15

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5 0.0 \

z -0.05

- 0 10

1 I t I I - 0.15 -3 -2 -1 0 1 2 3

H / Tesla

Fig. 2 Magnetization-v-field isotherms for Mn,,O 12(CH3C0,)4(H20),

Fig. 3 Relaxation of the magnetization in Mn,,O,,(CH,CO,),,(H,0),: the differ- ence between the magnetization ( M ) and its asymptopic value ( M , ) as a function of time for two different fields

As the applied field is increased, states with negative M , are stabilized with respect to states with positive M,, which become increasingly metastable. At regular intervals of the fietd, accidental degeneracies occur between states of positive and negative M,, and resonant quantum mechanical tunnelling through the potential barrier is greatIy enhanced. Thus the magnetization is more prone to ‘flipping’ at every field at which such a degeneracy occurs, leading to the steps in the hysteresis Ioop and the oscillating

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462 S. T. BramwelI

Fig. 4 Schematic representation of tunnelling in Mn,,U, 2(CH,C0,),6(H,0),: tun- neHing from the metastable state M, = S to M, = - S + 2 followed by thermaIly assisted decay to the ground state M , = - S

relaxation times. This process is illustrated schematically in Fig. 4, at the field which brings the M, = S state degenerate with M, = - S + 2. The magnetization tunnels from M , = S to M , = - S + 2 and then decays to the ground state M , = - S by losing quanta of energy to the lattice vibrations. There is evidence that the main tunnelling processes are in fact from excited states on the left hand side of the potential barrier, which gives rise to a concise description of the phenomenon as ‘thermally assisted quantum tunnelling’. Similar effects have been observed in the closely reIated complex [Mn, ,(CH3C0,),6(H:20)40121. 2CH,C02H-4H,0.30*31 A comprehensive theory of tunnelling effects has been published,32 which is relevant to zero tempera- ture. However, the theory does not immediately support the experimental findings, and the authors discuss possible reasons for this.

Giant and colossal magne toresis tance Among solid state chemists, giant magnetoresistance in magnetic oxides continues to be a very popular subject of research. In private, however, some do not see what a11 the fuss is about, as such effects have been known for years. It is therefore interesting to identify the factors that motivate the current research. Magnetoresistance is the change in resistivity with magnetic field. Doped ferromagnetic semiconductors such as the chromium chalcogenide spinels (e.9. HgCr,S,) have Iong been known to show particularIy large magnetoresistance. This can be thought of as arising from the scattering of conduction electrons by spin deviations in much the same way as normal metaIlic resistivity arises from the scattering by lattice vibrations or impurities. Just Iike the scattering of light or neutrons, this spin disorder scattering reaches a maximum at the magnetic critical point. The appIication of a field in this region suppresses the spin disorder and hence reduces the resistivity, leading to large, negative rnagnetoresis- tance. Similar effects in doped LaMnO, have also been known for many years; for exampIe Searle and Wang reported it in La, -,Pb,MnO, as long ago as 1969.j3 The origin of the effect in these magnets has traditionally been ascribed to the Zener double exchange mechanism of ferromagnetic interaction between Mn3 + and Mn4+. This mechanism arises because it is particularly easy for Mn3+ and Mn4+ to exchange an electron. In reality the ‘excess’ electrons become delocalized over several Mn4’ sites, forcing the remaining IocaIized spins on Mn4+ to align parallel by Hund’s rules. When

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Magnetism 463

these ‘magnetic polarons’ form a percolating cluster, a transition occurs to a ferromag- netic metal. The appIication of a magnetic field not only reduces spin disorder, but also encourages delocalization, which is generally competing with antiferromagnetism, and hence can precipitate the transition to the metallic state. However the doping of LaMnU, also reduces the concentration of the Jahn-Teller ion Mn3+ and so leads to structural changes. At the time of the discovery of the giant magnetoresistance in the doped lanthanum manganates, the complex magnetic and structural properties of these materials had already been extensively characterized by the pioneering work of, among others, Wollan and Koehler and Goodenough. Harrison, in last year’s AnnuaI Report, has given a detailed account of this early work, and has emphasized that the ‘rediscovery’ of the lanthanum manganates is due in part to the improvements in experimental diffraction techniques allowing a more detailed analysis of the complex phases that exist in this system. To that can be added several other factors, including the widespread availability of commercial magnetometers with magnetoresistance probes, the renewed interest in magnetoresistance among the physics community arising largely from the discovery of giant magnetoresistance in metallic mu1 tilayers, and the modern emphasis of research funding bodies on research with an applied aspect. However perhaps the most important single factor motivating the research is the genuine increase in the importance of magnetoresistance as a commercially ex- ploitable magnetic property. As described by Brug et magnetoresistive recording heads have recently been introduced into the magnetic recording industry, and there is a direct relationship between the magnitude of the magnetoresistance and the final storage capacity of the disk drive. Magnetoresistance thus clearly has a role to play in the computer age, and the rediscovery of magnetoresistance in the manganates is timely. On the other hand only time wilI tell if the rewards justify the magnitude of the effort.

A question of current interest is whether the simple double exchange mechanism described above does indeed account for the ‘coIossaI’ magnetoresistance in Ln, -,B,MnO, (Ln = lanthanide; B = alkaline earth metal). Field-induced antifer- romagnetic insulator to ferromagnetic metaI transitions have been observed in Nd, - xCaxMn03,35 Pr, -,Ca,Mn0336 and La0,96Mno.960337 emphasizing the corre- lation between magnetic ordering and resistivity. Other work has emphasised the importance of Jahn-Teller induced strains leading to charge ordering.38 M i l k et al.39 have presented a theory that incorporates the effects of both double exchange and the Jahn-Teller effect. Experimental work by Ramirez et al. on La, -,Ca,MnO, has lent support to this picture.40 It is undoubtedly the case that electron-phonon coupling is as important as double exchange in determining the electronic properties of these sysfems. Zhou et at. have gone as far as suggesting that the strong coupling between conduction eIectrons and cooperative local lattice distortions leads to a new type of electronic Fontcuberta et at.42 have shown that the coIossal magnetoresistance in Ln, -,Ca,MnO, is correlated with the size of the Ln ion; this is aIso equivalent to the effect of hydrostatic pressure.43

The occurrence of giant magnetoresistance in the mixed vaience manganates does not seem to depend too crucially on the crystal structure, and there are a growing number of examples of giant magnetoresistance materials that adopt structures differ- ent to varying degrees from the cubic perovskite structure of LnMnO,. The series Ln, +,B2-,Mn20, (Ln = lanthanide; B = alkaline earth) have crysta1 structures of

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._.__.._.......__. ........ ..

Magnetic field I T

Fig. 5 Colossal magnetoresistance in Lal.2Srl.BMn,0, (adapted from ref. 43). In- plane resistivity (upper panel) and magnetization (lower panel) as a function of magnetic field

the Ruddlesdon-Popper type which consist of layers formed of alternating perovskite and rock-sah-type blocks. Moritomo et have reported coIossal negative mag- netoresistance in La,.,Sr,.,Mn,O, over a wide range of temperatures above the ferromagnetic Curie temperature of 124 K. These results are illustrated in Fig. 5. The authors suggest that the large spin fluctuations associated with two dimensionality enhance the magnetoresistance in this range of temperature.

The closely related La,.,Ca,.,Mn,O,, is a ferromagnetic metal below 215K and shows large resistivity and magnetoresistance (60%) over a wide temperature range below the Curie point.45 There is a peak in the resistivity at 100K, and the mag- netoresistance rises as the temperature falls in this region. Battle et al. have made a detailed study of Sr,NdMn,O, and Sr,~9Ndl.1Mn207.46-48 These compounds ex- hibit colossaI magnetoresistance of more than lo4% at 14T, in the temperature range 4.2-100K. Both have low resistivity, and neither are bulk ferromagnets, which the authors interpret as casting doubt on the involvement of double exchange. However both Sr,NdMn,O, and Sr,.,Nd,.,Mn,O, show a difference between the field cooled and zero field cooled susceptibility, which could be interpreted as evidence of the competing ferromagnetic and an tiferromagne tic interactions that are in heren t to the double exchange mechanism. It appears that both compounds are biphasic, with each phase adopting the Ruddlesdon-Popper structure, and having very similar lattice

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Magnetism 465

parameters. Another series of oxides showing giant magnetoresistance are TI, -,In,Mn,O,, which adopt the cubic pyrochlore s t r~c ture ;~’ the pressure behav- iour of these materials is different to that of the p e r ~ v s k i t e s . ~ ~

Frustrated antiferrornagnets Frustrated antiferromagnets continue to provide the major themes in magnetic re- search. As described in last year’s report, most interest currently centres on those systems, which as a consequence of frustration, have an infinite number of degenerate spin structures at zero temperature. The prototypical examples are the Heisenberg model on the two-dimensional kagomC: lattice, in which the spins occupy the vertices of an infinite network of corner-linked triangles, and on the three-dimensional pyro- chlore lattice, in which the spins occupy the vertices of an infinite network of corner- linked tetrahedra. The relationship between these two lattices is illustrated in Fig. 6. In zero magnetic field these systems do not order even at temperatures well below the Curie-Weiss constant (which is a measure of the near-neighbour exchange), but rather adopt a ‘spin liquid’ ground state, in which oniy near neighbours are strongly corre- lated. Competing with the spin liquid are spin glass, and long-range ordered ground states. The ordered ground states may be stabilized by weak terms in the spin Harniltonian, or, more remarkably, by thermal or quantum fluctuations, a phenom- enon referred to as ’order by disorder’. It may sound surprising that entropy can favour ordered arrangements in this way, but in magnetism it is certainly a powerful ordering force.

SrCr,Ga,, -xO19 (x z 41, with the magnetoplumbite structure, has for several years been considered to approximate to a kagome lattice antiferromagnetic, and has been the subject of numerous studies. However, it is probably fair to say that progress in understanding this interesting material is rather slow owing to the compiexity of its structure, and the lack of chemically ordered single crystals. The most important property of SrCr,Ga,,-,O,, is its apparent spin glass transition at T = 3.3 K, a temperature far below the Curie-Weiss temperature of 500K. Lee et aL5I have characterized the spectrum of magnetic excitations in the low temperature phase and shown that this has more structure than that of a conventional spin glass.

In an effort to characterize more suitable model materials than SrCr,Ga,, -x019, attention has turned to the jarosite series, with general formula AM3(OH)6(S0,),, where A is a monopositive cation and M = Fe or Cr. In these materials, which bear more chemical similarity to hydroxides that to sulfates, the M 3 + ions occupy a kagome lattice in layers formed by the O H - and SO,,- ions. A particularly interesting representative of this series is hydronium jarosite, an important mineral, which has been synthesized by Harrison el by direct hydrolysis in an autoclave of Fe,(SO,), solutions. The full crystal structure of the synthetic material was determined by powder neutron diffraction, and showed a surface coverage of Fe3’ on the kagome lattice of97% in the best samples. Despite a huge Curie-Weiss constant of - 1200 K, the material does not adopt a long range ordered state down to at least l S K , but rather has an apparent spin glass freezing transition at 17.2 K, and is thus comparable to SrCr,Ga, , __ .O 19- Iron jarosite, KFe,(OH),(SO,),, and chromium jarosite, KCr,(OH),(SO,),, have been carefully investigated by the muon spin rotation tech- n i q ~ e - ~ ~ The Curie-Weiss constants in these materials are 600 K and 67.5 K respect- ively. The iron compound was observed to order magnetically at 55 K in agreement

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466 S. T. Brurnwell

Fig. 6 Relationship between the two-dimensionaI kagome lattice (a) and the three- dimensional pyrochiore lattice (b). Figure (b) represents a siice of cubic pyrochlore lattice perpendicular to (1, 2, l), showing a kagome plane (medium circles) decorated by lattice points above and below the plane (large and small circles respectively), to form a network of corner-linked tetrahedra

with previous measurements, but in the chromium compound spin fluctuations were found to persist even at T = 25 mK, a temperature well below that at which history dependence of the bulk susceptibility sets in (T = 2 K). This result again lends support to the idea that the Iow-temperature phase of the kagornt: lattice antiferrornagnet bears a certain resemblance to that of a conventional spin glass, but is far more fluctuating.

A susceptibility and nuclear magnetic resonance study of the jarosite RFe,(UH),(SU,), with R = NH,, Na and K5* has reveafed successive phase transi- tions to long range order around 60 K, which have been ascribed to the effect of weak

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Ising-like anisotropy in the Heisen berg Hamiltonian. Jarosite-type materials currently offer the best prospects for future experimental study of the kagomk lattice antifer- romagnet, although a number of alternative systems are available. These include the RCuO,.,, delafossite-type oxides, which have been the subject of a theoretical study this year,55 and fluormica days intercalated with magnetic Ni2 ' ions.56 Although an imaginative chemical approach to the problem of preparing kagome lattice magnets, there is no evidence that the Ni2+ ions lie on a kagome lattice, rather than a partially filled triangular lattice. The compound is nevertheless interesting on its own right. It exhibits a spin glass-like transition at Tg = 4.5 K, which is close to the Curie-Weiss constant of 8 K, suggesting IittIe relationship with the kagomk lattice antiferrornagnets discussed above.

The pyrochlore lattice antiferrornagnet has received if anything more attention than its two-dimensional counterpart, the kagome lattice. The pyrochlore lattice is much more common in nature than the kagome Iattice, occurring, for example in the pyrochlore oxides A,B,U,, the B-sublattice of the spinels A3,0,, various fluorides (e.g. FeF, and CsNiCrF,) and in interrnetallics with the C15 structure (e-g. YMn,). Work on the oxide pyrochlores has been pioneered by Greedan and co-workers in Canada, while the fluoride pyrochlores have mainly been studied in Europe. Harris and Zinkin5, have reviewed experimental and theoretical work on these systems. A striking generality is that the oxide pyrochlores A,B,U, are chemicaIly ordered but thought to form conventional spin glasses, whilst the fluoride pyrochlores ABCF, are chemicalIy disordered yet do not. This is contrary to the received wisdom that a spin glass requires both frustration and disorder.

This year Greedan et a!. have investigated the pyrochIore oxides Ho,Mn,O, and Yb,Mn,O, by dc and ac susceptibility, heat capacity and neutron diffraction, and compared the results with those of the previously studied Y,Mn,0,.58 In these materials both the Ianthanide and Mn4+ ions occupy interpenetrating pyrochlore lattices. In Y,Mn,O, only the Mn4+ sublattice with spin S = 3/2 is magnetic, and the predominant coupling is ferromagnetic. Y 2Mn2U, displays conventional spin glass behaviour below 7 K, preceeded by an apparent ferromagnetic transition at 17 K. It is thus like a 're-entrant' spin glass. The Ho and Yb homologues, in which the lanthanide ion is also magnetic, display similar behaviour, but at a higher temperature. The ferromagnetic transition is at about 40 K in both cases, but the divergence of the field cooled and zero field cooied susceptibility occurs at about 33 K for Ho,Mn,O,, and 23 K for Yb,Mn,O,. The spin glass transition in the oxide pyrochlores YZMo,U, has been studied by nun-linear susceptibility measurementss9 and the spin dynamics of Y,Mo,O,, Y,Mo,.6Ti0L407 and Tb,Mo20, have been investigated by muon spin

In general the results show that the low temperature state of these magnets is like a conventional spin glass, but with a large density of states for magnetic excitations near zero energy.

Zinkin et a!. have reported susceptibility and neutron inelastic scattering measure- ments on the pyrochlore compound Tm2Ti207, in which only the rare earth ion Tm3+ may be magnetic. However the crystal-field ground state of the Tm3+ ion has zero magnetization, and it was found that the crystal-field interaction dominates any superexchange between the Tm ions, leading to a non-magnetic ground state in the

As mentioned above, in the spinels, the B sites occupy a pyrochIore lattice, but the magnetism is compIicated by the possibility of the A site being

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magnetic, as we11 as by the well-known inversion properties of spinels. In ZnFe,U, the Zn ions are nonmagnetic and the Fe3' ions with spin 5/2 occupy the pyrochlore lattice, with negligible inversion, making this compound closely analogous to the p yrochlores.

ZnFe,O, has been the subject of a thorough investigation, using neutron diffrac- tion, m u m spin rotation and relaxation, and 57Fe Mossbauer ~pectroscopy.'~ The samples were prepared by ceramic techniques, involving slow cooling from 1500 OK. The spinel was found to exhibit magnetic order at TN = 10SK, an unusually Iow temperature scale for magnetic ordering in a spinel. Most intriguingly, the short range magnetic order observed at temperatures as high as N 10 T, was observed to coexist with the long range order below TN- This study may provide's link between pure research on the pyrochlores and appIied research on the spinel ferrites, which are technologically important magnetic materials. Further reports of frustrated magnet- ism in spinel oxides are described in Section 3.

The intermetallic C15 Laves phase compound Y0.97S~0.03Mn2, in which the Mn ions occupy a pyrochlore lattice, has been studied by inelastic neutr~n-scattering.~~ It was found that the spins on individual tetrahedra were strongly correlated as a spin singlet over short tirnescales, but uncorrelated over long timescales. A theoretical study of the effect of lattice distortion on the spin structure of YMn, has been d e s ~ r i b e d , ~ ~ and Plumier has calculated magnetic structures as a function of exchange couplings in C15 and spinel structures.66

Another important class of frustrated antiferromagnet is the triangular lattice antiferrornagnet (Fig. 7). This, and its three-dimensional relative, the stacked triangu- lar tattice antiferrornagnet, have long been of interest in connection with unusual modes of ordering, unconventional phase transitions and critical exponents, and the possibility of formation of a Pauling-Anderson resonating valence bond (RVB) solid. The previous five years' reports by Harrison and co-authors should be referred to for a detailed overview of recent work in these systems. The stacked triangular lattice is well-represented by the ABX, hexagonal perovskite type halides (e.g., CsMnBr,), but there are relativeiy few reaIizations of essentidly two-dimensionaI systems. In particu- lar the onIy known examples of the interesting S = 1/2 triangular lattice antiferromag- net, which according to Anderson is a candidate for RVB behaviour, are LiNiO, and NaTiO,. However the latter is a poor model compound, and a high resolution powder diffraction study pubIished this year shows that Na,TiO, (x E 1) has previously

Fig. 7 Regular triangular lattice with all magnetic bonds equal

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Fig. 8 The ‘row’ model for frustrated triangular lattice antiferrornagnets, with hori- zontal bonds (double lines) of different strength to other bonds (single lines)

unsuspected multiple-phase behaviour, which casts doubt on the validity of Na,TiO, as a model S = 1/2 material.67

A new series of essentially two-dimensional triangular lattice antiferrornagnets has been identified, in which the spin value can be varied from S = 5/2 to S = 1/2. They are an extensive series of compounds related to the mineral yavapaiite, KFe(SO,),. The structure type is such that magnetic ions (e.g., Fe3 *) occupy a regular or very slightly distorted triangular lattice in we11 separated layers. Bramwell et reported a susceptibility study of RbFe(SO,),, which has an equilateral triangular lattice, and KFe(SO,), and KTi(S0J2 which both have isosceles triangular lattices. RbFe(SO,), appears to be a good example of an S = 5/2 two-dimensional Heisenberg lattice antiferrornagnet, with a weak cusp in the magnetic susceptibility at T = 4.2K. KFe(SO,),, also with S = 5/2, has a more rounded susceptibility curve, reflecting the relief of frustration which results from the orthorhombic distortion, and can be thought of as a realization of the so-called ‘row model’, described in Fig. 8.

The susceptibiIity us. temperature for these two compounds are plotted in terms of reduced units in Fig. 9. KTi SO,),, which was made for the first time, has S = €/2, and is a realization of the quantum row model. Zhitomirsky69 has published an analysis of the phase diagram of the classical stacked row modei as a function of the various magnetic couplings involved; it will be interesting to compare the behaviour of KFe(SO,), and its relatives with these predictions. Inarni et a!. have extended work on the yavapaiite compounds to the anaIogous molybdates, and have published a high field magnetization study of CsFe(SO,), and CSF~(MOO,),.~* Another frustrated triangular lattice system is 3He adsorbed on graphite, as described below.

New magneto-optic effects Magneto-optical effects provide some of the most sensitive methods of investigating magnetic materials, as well as being of practical use in the optical industry. It is therefore always of interest when new effects are discovered. Rikken and van Tig- gelen” reported the observation of a new magneto-optic effect which they had previously predicted theoretically. It is to some extent analogous to the Hall effect, in which an electrical current, when subject to a transverse magnetic field, develops a component perpendicular to both the current direction nd the field. In a non-scatter-

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3 x

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Fig. 9 Reduced susceptibility us. reduced temperature for RbFe(SO,), (upper curve) and KFe(SO,), (lower curve). The former approximates to the model in Fig. 7, the latter to Fig. 8

ing, non-absorbing medium there is no analogous effect on a flux of photons. Such 'beam walk off can be caused by absorption, and Rikken and vanTiggelen have now shown that scattering can have the same effect. The experiments were performed using fine (2 pm) CeF, powder suspended in glycerol, which has a different refractive index. The effect observed may be compared to the well-known Faraday effect in which a magnetic field applied longitudinally to a sample causes rotation of the plane of polarization. A perhaps more dramatic magneto-optic effect was discovered by Pittini et When light is reflected from the surface of a ferromagnet its polarization rotates, the so-called Kerr effect, which arises from spin-dependent transitions. Normally the effect is rather small, typically only a few degrees, but Pittini et a!. have shown that a crystal of CeSb at 1.5 K and in a field of 5 T has a giant Kerr effect of90". This is 6.5 times more than the previous record rotation of 14" and it is the absolute maximum observable rotation in a single reflection. The authors suggest that the effect is caused by the proximity of the band edge to an optical transition involving the paramagnetic f electron of Ce.

following on from earlier work by Reiem et

Langmuir-Biodgett films Following the pioneering work of P~rnerantz '~ the subject of magnetic Lang- muir-Blodgett films lay dormant for several years, probably as a result of the difficulty in making magnetic measurements on such systems. In recent years magnetochemists have shown renewed interest in such systems.

on a monolayer Langmuir-Biodgett film of manganese octadecylphosphonate, Mn(0,PC,8H,,)-H,U. The authors show that in-plane antiferromagnetic coupling, J = - 2.8 K, is similar to that observed in bulk samples of manganese octadecyl- phosphonate. The latter order magnetically at about 15 K, but the resonance signal

This year sees an electron paramagnetic resonance study by Seip et

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Magnet ism 471

was too weak, below 17 K, to probe this effect in the film. Ando et ~ 2 1 . ' ~ reported the formation of Langmuir-Blodgett films of stearates of Mn, Fe, Co and Ni. The Ni film has ferromagnetic interactions.

Nuclear magnets Although nuclear magnetism piays a decisive role in chemistry uia nucIear magnetic resonance, the role of nuclear spins in bulk magnetism is usually ignored. This is acceptable because the magnitude of the nuclear contribution to the paramagnetic susceptibility is usually only about loA6 that of the electronic susceptibility, and the temperature scale for ordering of the nuclear moments is of the order of mK or even pK. NevertheIess, advances in instrumentation have in recent years allowed physicists to observe nuclear magnetism. Gross et have described a SQUID ac suscep- tometer which has been tested by measuring the nuclear susceptibility of HoVO, in the range 15 mK-130mK. In this materia1 the nuclear paramagnetism of Ho is enhanced by hyperfine coupling to the electronic spin system. Nuclear magnetic ordering has been observed in AuIn, at 35 pK, and has been shown to affect the superconductivity of the sample.78 Other nuclear ordering phenomena reported this year include hexag- onal dose packed solid 3He which is ordered ferromagnetically at 0.6mK,78 The nuclear magnetism of 3He has been exploited as a method of making truly two- dimensional magnets. The results have been reviewed by Godfrin and Rapp,80 and may be compared to the behaviour of other truly two-dimensional systems such as Langmuir-Blodgett films74 and ultrathin metallic films." In 3He absorbed on graph- ite three partjde exchange Ieads to ferromagnetic coupling and two particle exchange to antiferromagnetic coupling: the result is a two-dimensional frustrated Heisenberg magnet with a triangular lattice.**

Theoretical work A small selection of theoretical studies that are of relevance to magnetic materials are listed here.

The question of quantum disordered ground states in low dimensional frustrated magnets has been of interest to theorists for a number of years. This year Schulz et aLS3 report exact diagonalization of clusters of up to 36 spins of the Heisenberg antifer- romagnet on the square lattice with competing antiferromagnetic ( J I ) and ferromag- netic (JJ bonds. They find that for 0.34 < J J J , < 0.68 fhere is a region of no magnetic order. Albrech t and MilaS4 have investigated the transition between valence bond order and magnetic order in a two-dimensionaI frustrated Heisenberg modeI. Deaven and R o k h ~ a r * ~ have used variational methods to investigate the ground states of the quantum spin S = 1/2 magnet on various two-dimensional lattices. For the square, honeycomb and triangular lattice they find evidence of order, while for the kagome lattice they do not. A problem of direct relevance to cuprate superconductors is the annealed positions adopted by ferromagnetic bonds when doped into a two-dimen- sional antiferromagnet. Salem and GoodingS6 have determined the ground state of such a system in both the classical and quantum cases. In the classical case there are an infinite number of degenerate arrangements of the ferromagnetic bonds, but quantum fluctuations lift this degeneracy leading to phase separated ground states, such as stripes of ferromagnetic bonds.

The ferromagnetic order-disorder transition in the classical Heisenberg model in a

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fluid has been and it is claimed that the critical exponents differ by a small but significant amount from the ones for the lattice Heisenberg model. The random field Ising model, relevant to Co,Zn, -xF2, has been investigated by reaI space renor- rndization group techniques, and all three critical exponents have been calculated in arbitrary dimension for the first time." In three dimensions the exponent ,8 has the value 0.02. The spin dynamics of the classical two-dimensional XY model, which is of relevance to many ul trathin films'' and layered magnets,89 has been investigated n u m e r i ~ a l i y . ~ ~ Both spin waves and central peak are found below the Koster- Iitz-Thouless transition temperature, in agreement with e~per iment .~ '

3 Ionic, covalent and metallic materials

Halides Halides with the layered perovskite K,NiF,-type crystal structure are classic quasi two-dimensional magnetic model materials. The magnetic ions (e.g., Ni2 +) occupy a square Iattice in well-separated Iayers formed by the haIide ions. In K,CuF,, the Cu2 +

moments with S = 1/2 order ferromagnetically below T, = 6.25 K. K,CuF, is a prototypical two-dimensional easy-plane ionic ferromagnet, but is also of interest as an example of a compound in which a cooperative antiferrodistortive ordering of the partly filled Cu e, orbitals gives rise to ferromagnetism by enforcing orthogona1 overlap. The distortion associated with the orbital ordering can be thought of as a cooperative Jahn-Teller effect. The question then arises as to why isostructural La,CuO,, the parent compound of the high temperature superconductors, has fer- rodistortive orbital ordering and concomitant antiferromagnetism? Ishizuka et have shed light on this question by characterizing the magnetism of K,CuF, at pressures of up to 13GPa. They have observed a pressure induced change from ferromagnetism to antiferromagnetism at 8-9 GPa, which was interpreted in terms of a change from antiferrodistortive to ferrodistortive orbital order. Sekine et aLg3 have studied the magnetism of the related compound [CuCl,(p-cyan~anilinium)~] under hydrostatic pressure, but have found that in this case the ferromagnetic exchange increases with increasing pressure, presumably because of the shrinkage of Cu-C1-Cu exchange pathway. Ferromagnetic exchange arising from a cooperative Jahn-Teller distortion also occurs in related cornpounds with the Jahn Teller ions Cr2 ' and Mn3 *, of which a well known exampIe is Rb,CrCI,.

Moron et a / . have recently demonstrated that the series AMnF, (A = Na, K, Rb, Cs) has a particularly rich magneto-structural hemi is try.'^ The structure type can be thought of as derived from K2NiF, by removing half the K ions and shifting the layers relative to one another. The isolated A ions induce small structural distortions in the MnF, layers which have a significant effect on the magnetism. Thus there is a gradual crossover in magnetic behaviour between tetragonal CsMnF,, a collinear ferromagnet which orders at 18.9 K, to monochic NaMnF,, a canted antiferrornagnet which orders at 13.0K. The K and Rb compounds are respectively a monoclinic canted antiferrornagnet and an orthorhombic collinear antiferrornagnet, which order at 5.2 K and at 3.7 K respectively. This year Moron et al. report a pressure study of the crystal structures of the series,95 with the main result that increasing the external pressure to the order of GPa has a similar effect to decreasing the size of the A ion, in that it

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Magnetism 473

induces a series of distortions from tetragonal to orthorhombic to monoclinic. It would be of evident interest to study the magnetism of the pressure-induced phases.

The hexagonal perovskite halides AMX, (A = alkah metal, M = transition metal, X = halide) form another classic series of model magnets. The crystaI structure con- sists of linear chains of magnetic M ions stacked in a triangular array, such that the inter chain interactions in the ab plane are frustrated. They might therefore be regarded as either one-dimensional or as triangular lattice magnets, depending on the phenomenon being investigated. CsCoX, (X = CI, Br) are Ising-like, while CsFeX, (X = C1, Br), are so-called 'singlet ground state' systems, as the ground term of Fe2 ' in the absence of an applied field has M , = 0. Visser et aLg6 have described pressure- induced changes in the magnetic ordering of AFeX, arising from structural phase transitions.

The compounds AMnBr, (A = Cs, Rb) are XY-like. The anisotropy of their magnet- ization at high magnetic fields has been ascribed to quantum effects, but Santini et al." have shown that the anisotropy occurs at a cIassical level provided thermaI fluctu- ations are accounted for. CsMnI, and CsNiC1, are nearly Heisenberg systems with weak king anisotropy. The magnetic phase diagram of the mixed crystals CsNi, -,Fe,Cl, have been investigated by Takeuchi et ~ 2 1 . ~ ' ~ and the results interpreted in terms of a crossover from king-Iike to XY-like anisotropy with substitution of Fe2 +

ions. KNiC1, has the complication of small structural distortions. This year Petrenko et

af.99 have reported neutron scattering measurements to reveal an unusual effect in a seemingly perfect crystal of KNiCl,. It segregates into two phases with different lattice distortions in the basal ab plane at temperatures below T z 270 K. These two phases have different magnetic structures with T, = 12.5 K and 8.6 K.

Cs,CuCl,, although of the same stoichiometry as R,CuF, (mentioned above), forms a different crystaI structure with CuZ+ spin chains running parallel to the orthorhombic b-axis. Coldea el a1.'O0 have solved the magnetic structure of this compound using elastic neutron scattering. They find that below the ordering tem- perature TN = 0.62 K, the Cu2' spins ( S = 1/2) form an incommensurate structure, with a temperature-independent ordering wavevector (0, 0.472, 0). The proposed magnetic structure at 0.3 K is cycloidal with the spins rotating in a plane that contains the b-axis, and arises as a result of the frustrated inter-chain interactions.

Oxides As well as for their magnetoresistance described in Section 2, oxides with the perov- skite structure continue to be of interest for other reasons. Kawasaki et a!."' have investigated the magnetic properties of the cubic perovskite solid solutions SrFe, -xC~x03-g, which were prepared by pressure treatment and high temperature oxidation of oxygen deficient samples prepared at ambient pressure. These phases contain Fe and Co in the rather unusual oxidation state of +4. SrFeO, is an antiferrornagnet with a Niel temperature of 134K. At x % 0.1 a change occurs to a ferromagneticstate with a high Curie temperature, which reaches a maximum of 240 K at x = 0.6; it would seem that the phase Sr,FeCoO, is responsible for the ferromag- netism. Amow and Greedan lo' have investigated the structural and magnetic proper- ties of the orthorhombic (almost tetragonal) perovskite-type phases Nd, - ,TiO, with x = 0,0.5 and 0.1. With x = 0, the Ti ions have spin S = 1/2 and the Nd3+ ions have

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J = 9/2. Antiferromagnetic ordering of the Ti3+ sublattice was observed at TN = 90 K and 75 K for the x = 0 and x = 0.05 samples respectively; and low temperature neutron diffraction on these samples indicated that both the Nd and Ti sublattices were ordered. However for the phase with x = 0.1 no antiferromagnetic transition was found above 4K. Eylem et have investigated the isostructural series LaTi, -xV,03 . The end members LaTiO, and LaVO, are antiferromagnetic insula- tors with Neel temperatures of 148K and 140K respectively. As in the case of Nd, -xTiO,, increasing substitution of Ti decreases the ordering temperature, until at x = 0.1 a paramagnetic and poorly metallic phase is formed. For x > 0.25 antifer- romagnetism is restored. The x = 0.9 and x = 1.0 phases display negative magnetiz- ation, as previously discussed by Goodenough and N g ~ y e n . ' ~ ~

Ten years after the discovery of 'High-T,', cuprate oxides with the layered perovskite structure continue to command a great deal of interest. This section will concentrate on purely magnetic problems. Birgeneau et al. have reviewed their extensive studies of the static and dynamic magnetic fluctuations in La,CuO,-based phases. La,CuO,, with the K,NiF, structure, is a quasi two-dimensiona1 antiferrornagnet with a Neel temperature of 325 K. Between 340 K and 820 K the correlation length behaves exactly according to the predictions of the two-dimensionaI quantum non-iinear sigma mode1 (a continuum approximation to the Heisenberg model) in the renormalized classicai regime. Substitution of La in La,CuO, by isovalent ions does not have a strong effect on the magnetic or electronic properties. Thus La1.2Tb0.8Cu04, reported this year, has a similar magnetic structure to L ~ , C U U , , ' ~ ~ although short range order of the Tb3 moments is observed at low temperature. The substitution of aliovalent ions on the other hand, leads to hole doping with well known and extraordinary consequences. Thus the phase La,~,,Sro~,,Cu04 behaves as a spin glass, and the phase La,.,,Sr,. I ,CuU, as a superconductor with T, = 37.3 K.

The primary effect of hole doping in La,CuO, is believed to be the formation of ferromagnetic clusters or ferrons.'" Zakharov et a!. report a susceptibility study of La,CuO,+,, also hole doped, which lends support to this picture."' Substitution of La for Nd in otherwise superconducting lanthanum cuprate compositions causes an anomalous suppression of the superconductivity. Tranquada et al. log have described a neutron scattering study of the charge and spin order in the CuO, pIanes of La,.,,Nd,~,Sr,- 12Cu04, which establishes a remarkable coexistence of two-dimen- sional magnetic and charge order below 50 K. The dopant-induced holes collect in domain walls which separate antiferromagnetic antiphase domains, with the neodym- ium ions ordering magnetically below 3 K.

The sensitivity of superconductivity to lanthanide substitution is also well known in the '123' type superconductors LnBa,Cu,O, -, (Ln = lanthanide). In particular the compound YJ3a,Cu,O,-, has a T, of -9OK, but Y,~,Pr,~,Ba,Cu30,-, is non- superconducting. However onIy Pr among the lanthanides has this effect. Other evidence of the anomalous nature of Pr comes from the fact that the Pr moments in PrBa,Cu,O, -, order antiferromagnetically at the relatively high temperature of 17 K, while the homologous compounds of the other lanthanides only order at temperatures below 2.5 K. There is no fully accepted explanation of this anornaIy, but it is interesting to compare the behaviour of the related series LnSr,Cu,NbO, + d (Ln = Y, Pr, Gd) in which the Y cornpound is a superconductor with a transition at 13 K.'" The Pr and Gd compounds are found to be non-superconducting down to 1.8 K, but while the Gd

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moments order at 2.2K, the P r moments remain magnetically disordered at this temperature.

Other phases which illustrate the sensitivity of electronic properties to lanthanide substitution include the series Ln,Ba,Mn,Cu,O,,.'l' With Ln = Gd or Eu the behaviour is ferromagnetic below about 25 K, while with Ln = Sm there is a spin glass transition at about 15 K. The magnetic properties of the lanthanide ions themselves in high-T, related oxides are also a popular field of research. Staub and Ritter'" have investigated Ho13azCu,0, by neutron scattering and have observed two-dimensional short range ordering of the Ho3+ moments even at 1.6 K, a temperature far above the ordering temperature 0.19 K. Quasi two-dimensional ordering of Gd moments below 4 K is observed in CaCdCu0,CI and Ca4Gd,Cu,08C1, by susceptibility measure- ments.

Other cuprates of interest include the 'spin ladder' type compound LaCuU,.,. The spin ladder model was described in the 1994 Report, and consists of parallel, strongly antiferromagnetically coupled spin S = 1/2 chains. It is a candidate for a non-magnetic 'spin liquid' ground state. Matsumoto et have reported that although the susceptibility of LaCuO,., suggests a spin Iiquid, 63Cu NMR measurements indicate antiferromagnetic ordering at 110 K. However it is interesting to note that the doping of 5% holes by substituting La for Sr suppresses this transition. Another chain-like cuprate Ca,CuU, has antiferromagnetic interchain couphng. AbdeIgadir et a!. l1

have reported that sintering in oxygen produces a remarkable transition to room temperature ferromagnetisrn, apparently by introducing excess oxygen to form Ca,CuO, +a; one might tentativeIy suggest a similarity to oxygen excessive La,CuO, described above.

The fact that the high-T, superconductors contain magnetic ions with spin S = 1/2 means that any related magnetic oxides with S = 1/2 are immediately of interest. James and Attfield have described several new Ni3+ oxides with S = 1/2, although these are all paramagnetic down to 6 K. These include the series MSr,NiO, (M = Sc, In, Tm, Yb, Lu),'16 the solid solutions Ln,-,, SrxNi4kd (Ln = La, Nd, Sm, Gd; x > 1)'17 and the compound CeSr,Ni,01,.'18 The latter is a metallic compound adopting the K2NiF, type structure with Ce and Sr disordered over the K sites. The Ni3 * moments have a moment of 0.5 pLe per atom, a value which is much less than the spin only value of 1.73.

Oxides with the 'other' majority ternary oxide structure type, the AB,O, spinel structure, have Iong been popuIar subjects of research. The magnetostructural proper- ties of the spineIs are very complex with cation ordering, competing magnetic exchange and mixed valency all playing a role. Nowadays, most attention is focused on spinei solid solutions, a1 though results on the site-ordered frustrated antiferromagnetic ZnFe,O, are described in Section 2. The structure and frustrated magnetism of the mixed spinels Cu - ,Zn,TiO,,l LiCr - xAIxTiO,,l 2o CoFe, - .Cr,04,' 2 1

Mg, +,Fe,- 2,Ti,04122 and Li[Mn2_,Li,]0,-a'23 have also been investigated. The latter series is particularly interesting. The compounds are normal spinels with Li on the A-sites and Mn on the €3-sites of the spine1 structure. The x = 0 composition, LiMn,O,, has a formal oxidation state of + 3.5 for the Mn ion, and exists in both cubic and tetragonal forms. The dominant exchange coupling is antiferromagnetic, with Curie-Weiss temperatures of - 367 K for the tetragonal form and - 273 K for the cubic form. There is a spin freezing transition at 60 K for the tetragonal from and 55 K

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for the cubic form, reflecting the frustration of the 3-site spinel lattice, which is identicai to the pyrochIore lattice described in Section 2. The substitution of Li on to the B-sites increases the formal oxidation state of manganese and causes a progressive decrease of both the magnitude of the Curie-Weiss temperature and the spin freezing temperature. At x=O.33, which corresponds to an oxidation state of +4, the Curie-Weiss temperature is + 10 K, indicating ferromagnetic coupling, and the spin freezing temperature is also 10 K.

The Ti and V homologue of LiMn,O, have been the subject of an investigation by Kirchambare er These compounds are again both norma1 spinels, and form the full range of solid solutions. LiTi20, is a superconductor with a transition temperature of 13 K, while LiV,O, is metallic, apparently with localized magnetic moments. The compositions LiTi I rV,O, show a decrease in superconducting transition tempera- ture with increasing x, and the superconductivity is destroyed at x = 0.05. The V ions are found to have a moment of 1.7ps, indicative of V4+. These localized moments are believed to be responsible for the destruction of superconductivity.

Goya et af-1259126 have investigated the magnetic properties of the series of ortho- rhombic ternary rare earth oxides tn,BaZnO, with Ln = Sm, Eu, Dy, €30 and Gd mainly by susceptibility measurements. The Eu compound has a singlet ground state, and the Sm compound has negiigibIe magnetic coupling. The Dy and Ho compounds have quite large antiferromagnetic coupIing for rare earth compounds, with Curie-Weiss temperatures - 15 and - 11 K respectiveIy. The absence of magnetic ordering in these materials down to 1.8K was interpreted in terms of frustrated interactions. Gd,BaZnO,, which also has a large Curie-Weiss temperature of 15-9 K, shows an antiferromagnetic transition at 2.3 K; this is raised to 12.0 K in the analogous Cu compound Gd,BaCuO,.

Among other rare earth oxides, a new ternary samarium rhenium oxide, Sm,Re,U,, has been described.127 The Re ions appear to be in the + 5 oxidation state with S = I and the Sm ions show a very large temperature independent paramagnetism. There is, however, only very smaIl magnetic coupling between the Re ions, with a Curie-Weiss temperature of - 1.4 K.

Hydroxides and other hydroxy-salts Hydroxides often have very interesting magnetic properties, but have been rather neglected in the past, perhaps because of difficulty in obtaining good quality crystalline samples. Metal hydroxide layers are a common structural motif in later transition metal hydroxides and hydroxy-salts, and altering the interlayer separation can be used as the basis for chemical ‘tuning’ of the magnetic properties. Thus in Co(OH), the Iayers can be forced up to 25A apart by exchange of (OH) by organic or inorganic anions. The intralayer interactions are ferromagnetic. In the three-dimensional ordered magnetic phase, the ferromagnetic planes are stacked an tiferromagneticatly for ma11 interlayer spacing and ferromagneticaly for large interlayer spacing; for example tCo,(U~),(C,,H,,)SU,~.2H,U has a Curie temperature of 8 K. The com- pounds [Cu,(OH),(C,H,,+ ,)C02] with n = 0 and 1 similarly have ferromagnetic intralayer magnetic exchange, and show metamagnetic behaviour at 20 K.129 How- ever their homologues with n = 7, 8 and 9 appear to have an antiferromagnetic intralayer interaction, undoubtedly arising from structural changes with the layer on intercalation.

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Magnet ism 477

Ni(OH), is also a layered compound with Ferromagnetic intralayer interaction, exhibiting metamagnetism below TN = 25.8 K.l3O The series [Ni(OH), +,NO,), -,I (x = 0.64,0.74,1.14) however show spin gIass behaviour below 10 K, showing that the substitution of nitrate severely disrupts the magnetic long range order. Another nickel(I1) hydroxynitrate, [Ni(OH)(NO,)f*H,O, behaves as a double chain system, with two Ferromagnetic intrachain interactions between neighbouring S = 1 spins of magnitude + 26.9 K and + 6.9 K.I3*

Salts of oxy-anions: phosphates, perrhenates, silicates and carbonates Phosphates of the first row transition metals commonly adopt layered structure which can intercalate long chain alkylammonium cations. Such materials can be of interest magneticalIy as examples of quasi two-dimensional systems in which the magnetic coupling in the third dimension can be perturbed in a systematic way by intercalation. Goni et d.131 have prepared the new layered compound [NiH(PO,)]-H,O and its intercaIated derivatives [NiH(C,H,, + 1NH2),(P0,)].H,0 with n = 3-7. [NiH(PO,)] -H,O is antiferromagnetic, with a maximum in the susceptibility at 12 K. The magnetic behaviour is not strongly affected by intercahtion, reflecting two-dimensionality: [NiH(C,H,SNH,),.7,(P0,)]*H2U is aIso antiferromagnetic, with a maximum in the susceptibility 1 1 K. Another Iayered material, tFe(OHXH,NCH,CH,NH,),,,(PO,)], has a weak ferromagnetic transition at about 30K;'32 homologues with different alkyl chain lengths have not been reported. The perrhenates [M(ReU,),] (M = Ni, Fe, Co) again have a layered crystal structure, and order ferromagnetically at 12.5 K, 8.5 K and 4.7 K respec t i~e1y. l~~ The Ni compound exhibits substantial coercivity (-0.25T at 4.2 K). The pyrosilicate BaCo,Si,O, contain chains of distorted tetrahedral COO, groups interlinked by Si,O,. The compound has a weak ferromagnetic transition at 21 K. The magnetic critical exponents of FeCO,, an antiferrornagnet ordering at 38 K, have been determined by time-of-flight neutron diffraction techniques and have been found to be in good agreement with those of the three-dimensional Ising model.' 34

Pnictides and pnictide oxides The compounds CePdPn with Pn = As, Sb have been found to be quasi two-dimen- sional metals, with metallic conductivity perpendicular to the crystallographic c-axis, but semiconducting behaviour parallel to c.135 The magnetic behaviour is similarty anisotropic, with CePdAs and CePdSb showing paramagnetic susceptibility perpen- dicular to c, but apparently antiferromagnetic behaviour paralIel to c. The Nee1 temperatures are 4 K and 17 K respectively.

Brock et a!.136 have reported neutron diffraction results for the pnictide oxides Sr,Mn,Pn,O, with Pn = As, Sb. The crystal structure of these compounds consists of alternating tetragonal iayers of MnOZ2- and Mn,Pn,'-, separated by Sr2 + ions. The Mn occupy a centred tetragonal lattice in the pnictide layer and a primitive one in the oxide layer; however the symmetry of the structure is such that the layers are substan- tiaIly decoupled. Thus in both the Pn = As and Pn = Sb cdmpounds the manganese ions in the oxide layer order antiferromagnetically at ambient temperature (300 K Sb, 340K As), while ordering effects are not observed in the Pn layer until much tower temperature. In Sr,Mn,Sb,O, the Mn ions in the pnictide layer order antiferrornag- netically at 65K, while in Sr,Mn,As,O, they remain disordered until at least 4K, despite a build up in two-dimensional correlations.

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478 S. T. Bramwell

Chalcogenides and phosphide chalcogenides BaVS, has a hexagonal crystal structure consisting of chains of face-sharing VS, octahedra. At low temperatures it behaves like a semiconducting, one-dimensional antiferromagnet with spin S = 1/2; however at 70 K there is a transition to a metallic state. Imai et al. have determined the entropy change for this phase transition by specific heat measurements, and shown that is close to Rh2, the expected magnetic entropy for S = 1/2 spins of V4+ ions.'37 Wet1 known for their electronic and interca- lation properties are the layered transition metal dichalcogenides of Groups IV, V and VI. Miwa et reported the synthesis and magnetic properties of Mn,NbS2, with 0.19 < x < 0.52. The compounds show metallic behaviour, with paramagnetic Mn2+. However the Curie-Weiss temperature changed from positive to negative at x = 0.4.

MPS, type compounds (M = Ni, Mn) similarly consist of van der Waals bonded layers which may intercalate a variety of species. Qin et a!.139 report a new intercala- tion compound Mn,.,,PS,(2,2'-bipy),, which is ferromagnetic below the Curie tern- perature of 40 K. The Chevrel phase type cornpounds M,Mo,Ch, (M = metaI; x - 1; Ch = S, Se, Te) are also well known for their remarkable physica1 properties, which arise from the electron transfer from the A ion to the molybdenum chalcogenide host clusters. Daoudi et have reported the magnetic behaviour of UMo,S,, U,-,,Mo,Se, and Th,.,,Mo,Se,, which illustrate the sensitivity of the electronic properties to the A ion, Thus while UMo,S, is paramagnetic down to 2K, U J , , ~ ~ M O & ~ is weakly ferromagnetic below 25 K, and Th,,,,Mo,Se8 appears to have a superconducting transition at 3 K. Zhang el ~ 1 . ' ~ ' . reported the magnetic properties of amorphous Fe,(InTe,), which can be prepared by the metathesis reaction between FeCI, and the Zintl phase K5(XnTe4) in water; the compound has a spin glass-like transition at about 6 K.

Boron carbides The discovery in 1994 of superconductivity at 12 K in tetragonal YNi2B,C142 led to increased activity in the fieid of intermetallic superconductors. There is much interest in the magnetism of the members of the series LnNi,B,C (Ln = lanthanide) with magnetic Ln ions. With Ln = Tm, Er, Ho and Dy, superconductivity and magnetism coexist below typically 10 K, but with Ln = Th and Gd, the magnetic transitions occur at slightly higher temperatures (15.5 K and 19.4K respectively), and there is no superconductivity down to 2 K.

Among many other papers, this year sees magnetic structure determinations of TmNi,B,C by neutron d i f f r a ~ t i o n , ' ~ ~ and of GdNi,B2C by resonant and non-reson- ant X-ray ~ c a t t e r i n g . ' ~ ~ TmNi2B,C exhibits superconductivity below f 1 K and mag- netic ordering below 1.5 K; the magnetic structure consists of aligned ferromagnetic(1, 1, 0) planes of Tm moments, with the magnitude of the moments sinusoidally modulated along the crystalline (1, I, 0) direction. It is suggested that the modulated structure allows the coexistence of magnetism and superconductivity. GdNi,B,C, on the other hand, orders magnetically at 19.4 K with an incommensurately modulated antiferromagnetic spin structure, and there is a further magnetic transition at 13.5 K. Between these two temperatures the modulation wave vector increases with decreasing temperature. The use of X-ray techniques in this magnetic structure determination is noteworthy. Gadolinium has very large neutron absorption, which means that neu- tron investigations of Gd salts require expensive isotopic substitution.

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Magnetism 479

Metallic elements and intermetallic compounds Although not of immediate interest to many chemists, intermetallic compounds dis- play a huge wealth of magnetic phenomena, of which a small selection are illustrated here.

Plutonium is at the critical composition between the light actinides, which have itinerant 5f electrons, and the heavy actinides, which have localized 5f electrons. Meotreymond and Foucnier have argued that that the high temperature 6-Pu phase has far more localisation than the low temperature x-Pu phase.'45 There is a 24% votume expansion at the x-6 phase transition, which the authors argue is indicative of electron localization. They conclude that 'the delocalization-localization transition of the 5f electrons along the actinide series starts within the plutonium phase diagram', a conclusion which was previously predicted by Antropov et on the basis of band structure calcuiations. The alloys CeFe, -,Ru, (x = 0.07,0.08) show a rnetarnagnetic transition in which ferromagnetic sheets, aligned antiferromagnetically in zero field, are aligned ferromagnetically by the application of a field.i47*'48 In CeFe, -,Ru, the transition is accompanied by giant ( > 20%) magnetoresistance. Other metallic meta- magnets include EuPdIn and E U A U I ~ ' " ~ which order at 13 K and 21 K respectively.

Frustration effects are as common in intermetallics as they are in ionic and covalent soIids. As a result of frustrated interactions, the LnNiAl series (Ln = Tb, Dy, Ho) show successive ferromagnetic and antiferromagnetic transitions below 30 K, and the TbNiAl shows sinusoidal ~rdering. '~ ' FePt, is a frustrated antiferromagnet and when alloyed with ferromagnetic Copt, becomes a spin glass.' 5 1

have reported an interesting effect that occurs in the melting of Al, _,_,Pd,Mn,, quasicrystals, such as A1,,,,,Pdo.207Mno.,,,2' The Mn atoms, which are diamagnetic in the solid state, acquire a local moment of about 3pB in the liquid, which can possibly be explained in terms ofa different local environment. This agrees with the theoreticaI prediction of Srnirnov and Bratovsky, who considered AlMn liquids.

Micron thickness films of Ho have been used to probe the phenomenon of 'two length scales' observed in neutron and X-ray scattering experiment^.'^^ At a critical point one expects critical fluctuations on a11 length scales up to a 'cut-of, the correlation length <- In quasielastic neutron or X-ray scattering the criticai spin fluctuations give rise to a scattering function in reciprocal space, with a Lorentzian line shape, the width of which is equaI to l/& However, recent improvements in instrumenta1 resolution have reveaIed that the scattering is often described by two Lorentzian line shapes, the second with a width about 1/10 that of the first. In order to prove the possible involvement of surface effects, Gehring et 0 1 . ' ~ ~ have measured the critical scattering at the 131 K magnetic phase transition in 1 pm Ho films, and once again observed the two length scales. However the origin of the effect remains unclear.

Major improvements in nanotechnology in the last decade have meant that ultra- thin metallic films of one to three monolayers thickness can be deposited on non- magnetic metallic substrates. An exampIe of this is ferromagnetic Fe on the (1,0,0) surface of W.155 This material appears to be an almost ideal realization of a two- dimensional XY magnet showing the finite size critical exponent fi = 37c2/128 = 0.23 predicted by Bramwell and Holdsworth8' (see last year's report).' Shi et ~ 1 . ' ~ ~ have made submicron ferromagnets in GaAs semiconductors by the ion implantation of

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480 S. T. Bramweli

MnZ +, followed by annealing, which precipitates GaMn ferromagnetic clusters. The bulk behaves as a room-temperature ferromagnet.

Methods of a more chemical nature to nanoparticulate magnets include the reduc- tion of a metal halide using organic solvents in the presence of lithium. Leslie-Pelecky et al.'57 have used this technique to make ultrafine Co particles stabiIized in a polymer matrix; the materials show ferromagnetic properties at room temperature, with addi- tional spin-glass-like transitions at about 10 K. Another reported chemicai method to nanoparticulate magnets is the reduction of Fez' ions to Fe by KBH, in aqueous s o I u t i ~ n . ~ ~ ~

4 Coordination complexes and molecuIar compounds

Framework structures; three-dimensional systems The bimetallic complex, [CoCu(OH)(H,O),(pba)] [pbaOH = 2-hydroxy-I,2- propylenebis(oxamato)], is of interest as a three-dimensional ferromagnet, which orders at 38 K, and has rather a large coercive field of about 6 kOe at 2 K.159 The dilute ferromagnetic complexes [Fe, -,As,C~~S,CN(C,H,),J order magnetically below about 2K. They are expected to show critical exponents of the universality class predicted by K a ~ a r n u r a ' ~ ' which has a large positive specific heat exponent x. According to the Harris criterion, the positive r means that critical exponents will depend upon dilution. Careful susceptibility measurements by DeFotis et al. 16' show that the susceptibility exponent 7 does indeed depend OR x, although only slightly. It increases from 7 = 1.19 at x = 0&014 to y = 1.22 at x = 0.040. An unusual effect has been observed in the linear chain antiferrornagnet [MnC1,(CH,NH,)-H,0.162 A 1 % substitution of Mn for Cu or Cd leads to a remnant magnetization when samples are field cooled through the three-dimensional Nee1 temperature of 4.12 K.

There is continued interest in developing pureIy organic ferromagnets. The main problem is not to find a ferromagnet, but to find one with a reasonably high Curie temperature. Thus a report of interest is that by Ueda et who have found that the purely organic tetracyanoquinodimethane (TCNQ) charge-transfer salts R '(TCNQ),.,(TCNQ-') [R Cs' and N(CH,), '1 are room temperature ferromag- nets with coercive fields of 100 Oe and 300 Oe respectively. However the materials are not fully structurally characterized, and the saturation moments are onIy about 1/1000 that expected for full spin ordering. A metal-containing, room-temperature molecular ferrornagnet is the amorphous [V(tetracyanoethene),I.(solvent), the improved syn- thesis of which has been reviewed.164 A novel new molecular magnet is the suIfur- nitrogen radical p-NC-C,F,-CNSSN 1, which has a Curie-Weiss constant of - 107 K and a weak ferromagnetic transition at 34 K.165

The sensitivity of molecular magnetism to chemical substitution, crystal structure

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Magnetism 48 1

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and pressure effects has been demonstrated by several groups. Thus Togashi et al.166 studied 165 organic radicals of the type 4-arylmethyleneamino-2,2,4,6-tetramethyl- piperidin- I-yloxyls (and related compounds), and found that 52 compounds exhibited ferromagnetic coupling, but the highest Curie-Weiss temperature among these was only 0.75 K, for the compound 2. Interestingly, an antiferromagnetic Curie-Weiss temperature was found which was much higher than this: - 24 K for the compound 3.

The prototypical purely organic ferromagnet j3-nitrophenyl nitronylnitroxide has a Curie temperature of 0.6 K under ambient pressure, but this is lowered to 0.35 K under a pressure of 7 kbar.167*168 Different behaviour is observed for the compound [NH,] [Ni(male~nitrile),]-H,O.'.~~ The structure of this charge transfer salt consists of stacked planar metal Iigands separated by ammonium cations; the Ni(maleonitriIe), anion is 4. Coomber el found that the ferromagnetic Curie temperature in- creased from 4.5 K at ambient pressure to 7 K at 6 kbar, and ascribed this large change to a switch from dominant metal-sulfur to dominant metal-metaI interactions with increasing pressure. At 6.8 kbar the ferromagnetic order abruptly disappeared, prob- ably as a result of a structural phase change.

Polymorphism is always a possibility with molecular compounds, and this can affect the magnetic properties. Thus the charge-transfer salt Fe(C5(CH,),}2.TCNQ exists as three different structural phases which are respectively paramagnetic, metamagnetic and ferromagnetic at low temperature."'

4

Layered structures; two-dimensional systems The layered bimetallic oxalate complexes AM1iM11'(C204)3 (A = monovalent organic cation) show a wealth of interesting magnetic behaviour, which depends upon the metals M" and M1" and the nature of the A ion. Mathonikre et ~ 2 . ' ~ ' have character- ized an extensive series of cornpounds AM"Fe(C,O,), [MI' = Mn, Fe; A = alkyl- and aryl-ammonium, phosphonium, and arsonium ions J. In these compounds the metal ions occupy alternate sites in a two-dimensionai honeycomb lattice. The metals are coordinated by oxaiate, and neighbouring layers are separated by the organic cations. The M" = Fe series behave as ferrimagnets with Curie temperatures between 30 K and 50 K, but several exhibit an unusual crossover to negative magnetization at low temperature when cooled in a fieId of 10mT. In simple terms the ferrimagnetic behaviour can be thought of as arising from the imbalance in atomic magnetic moment between antiferromagnetically coupled Fe2 + and Fe3 ', but the origin of the negative

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magnetization is not yet understood. In the M” = Mn series, both ions have spin S = 5/2, and behave as low dimensional antiferromagnets, with a broad susceptibility maximum at about 50K, but an increase in the magnetization characteristic of spin canting at lower temperatures.

Bhattacharjee et d.’ 7 2 have investigated the series N(C,Hg),Fe”Fe’~’,Cr”l, - x-

(c&)4)3. The compound N(C,H9)3Fe”Cr’”(C,0~~~ has a ferromagnetic transition at 14 K, while N(C4H,),Fe”Fe”’(C,0,), has a ferrimagnetic transition at 35 K. For 0 -= x < 1, the transition temperature varies smoothly between these extremes. For x > 0.4 a spin glass-like transition is observed at a temperature just below the ferrimagnetic transition.

Another series of honeycomb layered magnets are the azides M,(N,),(bipyridinium) (M = Co” and Fe”). These compounds exhibit rnetarnagnetic behaviour below 60 K and 40 K respecti~ely.”~ The compound KMn(3-CH,0-~alen)Mn(CN),‘~~ is also a quasi two-dimensional metamagnet, and also exhibits negative magnetization below the Nee1 temperature of 16 K.

Layered charge-transfer salts based on bis(ethy1enedit hio)tetrathiofuIvalene (BEDT) are well known as ‘molecular metals’ and also show magnetic coupling with a quite high temperature scale, although so far only antiferromagnetic coupling has been observed. For example, Kurrnoo et have investigated the compounds MCl,(BEDT-TTF), (M = Ga, Fe). The magnetic susceptibility of the semiconducting Ga compound is well described by a model containing two antiferromagnetic spin dimers with couplings of 108 K and 212 K. That of the Fe compound is modelled by a single antiferromagnetic dimer with coupling 45 K in addition to an ahnost paramag- netic term arising from the Fe3+ moments. The exchange coupling between the magnetic moments on the Fe and those on the organic layer is apparently negligible.

Chain structures; one-dimensional systems From a theoretical point of view, one- and two-dimensional magnets are not expected to order magnetically. However, the one-dimensional Ising model and the two- dimensional Heisenberg and X Y models are all at their lower critical dimension, and order is easily restored by minor perturbations& From a practical point of view this means that the only systems that actually show a marked reluctance to order magneti- cally are one-dimensional magnets that approximate the Heisenberg or XY model. The one-dimensional Heisenberg antiferromagnet also has the unusual property of the magnetic ground state depending strongly on spin value. Thus while in general the grounds state is a singlet, only the even-spin chains have an energy gap to the first magnetic excited state, which makes them particularly resistant to magnetization. This so-called Haldane gap has been observed in several compounds, but mainly with spin S = 1. This year Granroth el a!. report evidence of the Hddane gap in a spin S = 2 chain, M r ~ C I ~ ( b i p y H ) . ’ ~ ~ The compound has exchange coupIing of about 30K, but no magnetic order at 30 mK, and at that temperature no magnetization in fields of up to 1 T. Several quasi one-dimensional Heisenberg ferromagnets have been reported. An example is the organic radica1 3-(4-chIorophenyI)-l,5-dimethyi-~-thioxoverdazyi, which has ferromagnetic exchange coupling of about 6K, and a transition to an ordered state at 0.68 K induced by inter-chain exchange of magnitude 0.21 K.177

The Iow ordering temperatures of ferromagnetic chains have not deterred workers from seeking chain-like molecuIar magnets. Lang er al. 7 8 have reported a magnetic

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Magnetism 483

characterization of the organic radical methy1-1,2,4-triazolenitronyl nitroxide, for which the authors claim ‘exceptionally strong’ magnetic interactions, although the Curie-Weiss temperature is only about 9 K. Bohm et a/ . 79 report a ferromagnetic Curie-Weiss constant of about 90 K and a Curie temperature of 15 K for the complex [meso- tetrakis( 3,5 -di-tert- bu t yl-4- hydroxypheny1)porphinatoj t et - racyanoethenide.

manganese@r)

Isolated complexes; ‘zero’ dimensional systems As well as being centre stage this year in terms of quantum mechanical tunnelling, there have been a huge number of reports of dimers, trimers, tetramers and so on. However in most cases the magnetic measurements stop at the characterization stage, and so there is little purpose in listing them all here. A handful of examples will suffice.

report spin crossover behaviour in an Fe” complex, tris(pyridy1 ben- zimidazole)iron(rI). The crossover between a low-temperature low spin state to a high-temperature high spin state occurs in the temperature range 9tr160K. Castro et dl” have described a complex of V’I’ with a butterfly structure, which exhibits magnetic frustration. It has formula [V,0,(0,CEt),(bipy)2(C104)] and contains both ferromagnetic and antiferromagnetic interactions. Cu2 ’ dimers are well known for being antiferromagnetically coupled, but Oshio et ~ ~ 1 . l ~ ~ have shown that with a GO,’ - bridge, ferromagnetic coupling can result. The Cu complex is [Cu(p- CrO,Xacpa), ]*4CH,OH.4H2O and the exchange coupling is about 10 K [Hacpa = N-( l-acetyl-2-propyridene)(2-pyridylmethyI)amineJ With CrO,’ - sub- stituted for MOO,’- to give the complex [Cu(p-MoO4)(acpa),]4H2O, there is antifer- romagnetic exchange coupling of magnitude about - 5 K.

Boca et a!.’

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