one dimension is not enough
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RAPID COMMUNICATIONS
PHYSICAL REVIEW B 1 JUNE 2000-IIVOLUME 61, NUMBER 22
Ordering wave vectors of metamagnetic states in HoNi2B2C: One dimension is not enough
C. DetlefsEuropean Synchrotron Radiation Facility, Boıˆte Postale 220, 38043 Grenoble Cedex, France
F. Bourdarot, P. Burlet, and P. DervenagasCommissariat a` l’Energie Atomique, De´partement de Recherche Fondamentale sur la Matie`re Condense´e,
SPSMS/MDN, 38054 Grenoble Cedex 9, France
S. L. Bud’ko and P. C. CanfieldAmes Laboratory and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011
~Received 14 January 2000!
Elastic neutron-diffraction measurements have been preformed in each of the metamagnetic states ofHoNi2B2C for an applied field applied in the tetragonal basal plane making an angle of approximately 15° withthe @110# axis. Whereas these data are in excellent quantitative agreement with earlier thermodynamic studiesof theHapp-u phase diagram of HoNi2B2C, the magnetic wave vector of the metamagnetic state,'4/7a!, is instark contradiction with the predictions of two, one-dimensional theoretical models developed for this system.On the other hand, simple energetic arguments which are consistent with the existence of thea! phase arepresented.
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TheRNi2B2C (R5Gd-Lu, Y! series is the host to a widrange of low-temperature ground states as well as a vaof magnetic-field and temperature-dependent phtransitions.1 Whereas YNi2B2C and LuNi2B2C are nonmag-netic, intermetallic superconductors with relatively high sperconducting transition temperatures (TC'16 K!, for R5Tm-Dy there is the coexistence of superconductivity alocal moment magnetism arising from the unfilled 4f shell ofthe rare-earth element. Most moment bearing members oRNi2B2C series also exhibit very well defined magnetic-fieinduced, metamagnetic, states forT,TN .
HoNi2B2C in particular has been studied extensively2–5 infive years since its discovery.6,7 HoNi2B2C is a particularlyclear example of a local moment system that manifeststreme basal plane anisotropy at low temperatures:3,8 for tem-peratures,T<100 K, the local moments in HoNi2B2C areconfined to the basal plane, and byT52 K the Ho momentsare confined to one of the four@110# directions.9,10 Uponcooling in zero applied magnetic field,Happ50, there are aseries of magnetic phase transitions between 6 K and 5 Kthat are clearly seen in thermodynamic3 and microscopic11–13
data. ForT52 K the magnetically ordered state can besualized as ferromagnetic basal planes aligned along@110# directions9,10which are rotated by 180° with respecteach other along thec axis, i.e., a@0,0,1# magnetic wavevector.11,12
The thermodynamic study of the angular dependencethe metamagnetic states9,10 leads to a rather simple undestanding of theHapp versusu ~the angle the field appliedwithin the basal plane makes with the nearest@110# easyaxis! phase diagram in terms of net distribution of momenUp to four different states can be observed with increasHapp with critical fields,H1 , H2, andH3, depending onu:the low-field ground state,↑↓, the first metamagnetic state↑↑↓, the second metamagnetic state,↑↑→, and finally thesaturated paramagnetic state,↑ ~see Ref. 9 for a detailed
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discussion!. The arrows↑, ↓, and → represent local mo-ments aligned along the@110# axes that are near parallenear antiparallel, and near perpendicular to the directionthe applied field. Based on these data two theoreticaltempts have been made to model this specific system.14,15
Both theoretical treatments of the system assumed thatordering of all the metamagnetic states could be viewedstacking of ferromagnetically aligned basal planes alongc axis: i.e., a particularly simple type of one-dimensionordering, conceptually similar to that found in the low temperature, zero-field state.
In this Rapid Communication we present experimentadetermined magnetic wave vectors,q, for each of the mag-netically ordered states. As will be shown in detail belothe predictions of the one-dimensional models14,15accuratelyaccount for the commensurate, low-field ordering,↑↓,11,12
the first metamagnetic state,↑↑↓, and the trivial, saturatedparamagnetic state,↑. The second metamagnetic sta↑↑→, on the other hand, has a magnetic wave vector ina! direction: a result in stark contrast to the assumptionstheory.14,15 This result, however, can be understoodsimple energetic arguments, comparisons to other memof the RNi2B2C series, and even the higher temperatumagnetically ordered state found in HoNi2B2C itself.
Elastic neutron-diffraction experiments were carried oon the diffractometer D15 of ILL. The diffractometer waoperated in the normal beam mode with a wavelength of 1Å. The sample was mounted in a vertical field cryomagwith a base temperature of 1.5 K and a maximum applfield of 5.0 T. Single crystals of HoNi2
11B2C were grownfrom Ni2
11B flux.1,16 A 35 mg single crystal of HoNi211B2C
was aligned such that the applied magnetic field was perpdicular to the crystallographicc axis withu'15°. This anglewas chosen because it allowed for each of the four metamnetic phases to be present and well separated in the avai
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PRB 61 R14 917ORDERING WAVE VECTORS OF METAMAGNETIC . . .
field range, and because it lifted the magnetic degenerabetween the possible@110# directions.
In Fig. 1 the longitudinal magnetization,M, and the mag-netic scattering amplitude,Fmag
(125), are plotted as a function oHapp. M (Happ) shows the metamagnetic transitions that wused to create theHapp-u phase diagram.9,10 Fmag
(125)(Happ)}AI (Happ)2I (Happ50), whereI is the integrated intensityof the (1,2,5) nuclear Bragg reflection, is approximately pportional to the ferromagnetic contribution to the Bragg peand shows quantitative agreement with values ofM (Happ) data.
Figure 2 presents scans along the@0,0,l # and @h,0,2# di-rections in reciprocal space for a selection ofHappafter zero-field cooling the sample. In Fig. 3,I (Happ) of several differ-ent peaks are plotted as a function of applied field. The lofield state (Happ,H1) has a magnetic wave vector,q↑↓51.0c! which is consistent with the earlier neutroscattering work11–13 and theoretical models.14,15 As the ap-plied field is increased the first metamagnetic state is stlized and~i! for H1,Happ, q↑↓51.0c! disappears and~ii !H1,Happ&H2 a new wave vectorq↑↑↓52/3c! appears. Thisis the wave vector that was predicted by theory and is atrivially consistent with the net distribution of moments dduced from the thermodynamic measurements.9,10 As the ap-plied field is further increased and approachesH2, the inte-grated intensity ofq↑↑↓ gradually disappears and forHapp>H2 there is no detectable magnetic wave vector alongc! direction. Instead, as can be seen in Fig. 2~b! for H'H2, peaks associated with several magnetic wave vecalonga!, the basal plane axis closer to the applied field, atheir harmonics appear. ForHapp59.5 kG the primary peakand harmonics associated with 3/5a! appear to be more intense, but by 11.5 kG the peaks associated with 4/7a! arestronger. Details of these states and this transition aresubject of ongoing research. In Fig. 3 the integrated intenof the primarya! peak is plotted as a function of appliefield. Because the 3/5a! and 4/7a! peaks overlap, these datin essence, represent the total integrated intensity of a m
FIG. 1. Longitudinal magnetization,M ~circles, left scale! andmagnetic scattering amplitude,Fmag
(125) ~squares, right scale! ~as de-scribed in text! of HoNi2B2C as a function of applied magnetifield. Inset:Happ-T phase diagram of HoNi2B2C for Happ appliedalong the@100# axis, i.e.,u545° ~from Fig. 10 of Ref. 5!. Thearrows denote the metamagnetic phases, as described in the t
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netic peak associated with an 0.58a! ordering. This penulti-mate metamagnetic state orders in a manner that is ruledby both theoretical models by fiat. Both models assumeromagnetic basal planes without modulation alonga! being
t.
FIG. 2. Reciprocal space scans for applied fieldHapp making anangle of approximately 15° to the@110# direction of HoNi2B2C forvarious values ofHapp. ~a! @0,0,l # scans,~b! @h,0,2# scans. Thecommensurate positions of fundamental and harmonic peak ltions are indicated by the dashed~4/7a!) and dot-dashed~3/5a!)lines.
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RAPID COMMUNICATIONS
R14 918 PRB 61C. DETLEFSet al.
allowed. Finally, as the field is increased andHapp.H3 thesaturated paramagnetic state is entered and only the fmagnetic contributions to the nuclear peaks are detectedordering with modulation along theb! direction was de-tected for 0,Happ,2T.
The most striking result of the diffraction experimentsthe presence ofa! modulation and lack of any detectedc!
modulation in the↑↑→ metamagnetic state. In order to uderstand the import of this finding, it is useful to review thistory of this state. In the original, zero-field, neutroscattering work11,12 there was general agreement aboutlow-temperature, commensurate state and both groupsfound the 0.9c! modulation in the temperature betweenand 6 K. On the other hand, the single-crystal study11 de-tected a 0.58a! modulation which was not detected in thpowder work.12 There ensued a debate in the literature abthe nature of the 0.58a! phase.17–20 Subsequent studies oother single crystals21 as well as (Ho12xYx)Ni2B2Cpowders22 have lent credence the hypothesis that thea!
phase is not only intrinsic, but responsible for the sharp mmum inHC2 near 5 K~Ref. 2, 3, and 5! as well as enhancevortex pinning.23 In addition it was found that there iswell-defined nesting feature in the Fermi surface that leada maximum inx(q)24 for q'0.6a!, and that many of themembers of theRNi2B2C family have magnetic orderingwave vectors1,20 as well as phonon softening anomalies25
near this wave vector.On the other hand, given the simple magnetic structur
Happ50 and T52 K, the appeal of an one-dimensionmodel is obvious from a theoretical point of view.14,15 Thedesire to create and solve a tractable theory led to the mginalization of the existing work that emphasized the extence of the zero-field 0.58a! phase. As a result, both theories are, by construction, unable to account for the 0.5a!
ordering wave vector. Two basic assumptions have bbuilt into the existing theories:~i! that at 2 K the momentsare extremely anisotropic and confined to one of the f@110# directions, and~ii ! that all of the metamagnetic statewere built from the ferromagnetic basal planes that makethe low-field ordered state. While the first assumptionpears to be valid and is supported by experiment,8–10 thesecond assumption is flawed. This can be seen by two sim
FIG. 3. Integrated intensity of various peaks as a functionapplied field.
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arguments. First, forHapp50 and T'5 K there is 0.58a!
ordering. By comparing energy scales, the differencetween 2 K and 5 K is notthat different fromHapp50 andHapp510 kG on the saturated moment of Ho. In other worby energetic arguments, there is no valid reason for excing the possibility of 0.58a! ordering in the metamagnetistates. The second argument is based on the knownHapp-Tphase diagram for the Ho sublattice whenHappi@100# ~seeinset to Fig. 1!. For T52 K this figure is consistent with theseries of metamagnetic transitions that are seen foru545°.It should be noted, though, that theHapp50, 5 K,T,6 Kregion is topologically part of the same phase space asT52 K, Happ.10 kG region.26 In other words, forHappi@100# the existingHapp-T phase diagram already suggests thatq↑↑→ might be 0.58a!.
A final point that may be important to note is that th0.58a! wave vector only manifests itself in the one noncolinear structure. One possible explanation for this is foundobserving that there are clear magnetostrictions observemembers of theRNi2B2C when they are cooled through thNeel temperatures.27,28,29 In the cases of ErNi2B2C andTbNi2B2C ~Ref. 10! the crystalline electric-field~CEF! splitlocal moments are along the@100# directions and the low-temperature magnetic ordering wave vector is close to0.58a!, whereas for HoNi2B2C and DyNi2B2C ~Refs. 9 and10! the CEF split local moments are along the@110# direc-tions and the low-temperature ordering wave vector@0,0,1#. By symmetry arguments, a distortion along t@110# direction is far more likely to disrupt a Fermi surfacnesting along the@100# direction24 than a distortion alongthe @100# direction is. This observation may indeed accoufor the curious change in low-temperature ordered wave vtor asR moves across the series,R5Er-Tb. If this hypothesisis carried further, into the finiteHapppart of theHapp-T phasediagram, then the one state in the HoNi2B2C phase diagramthat will have a reduction in the magnetostriction along t@110# direction will be the state, in which the net magnezation actually points 26° away from the@110# axis. Thisidea is rather compelling because it explains the absenca! ordering in low-temperature and low-field HoNi2B2C andDyNi2B2C, but it is currently just a hypothesis and will havto be examined and tested in detail.
In summary, in this paper we have presented neutrdiffraction data on all four magnetically ordered lowtemperature metamagnetic states of HoNi2B2C. The rela-tively simple, one-dimensional theories of local momemagnetism in HoNi2B2C ~Refs. 14 and 15! account for thethree states that are actually composed of ferromagnbasal plane sheets. The third state,↑↑→, has no magneticordering wave vector along thec axis and instead orders witq↑↑→50.58a!, the same wave vector that is commothrough out the heavyRNi2B2C series. Whereas this is noinconsistent with experimental data or empirical argumenthis discovery does requires that any theory attemptingaccount for the metamagnetic transitions in HoNi2B2C mustbe more complex than a one-dimensional model.
Recent work by Amici et al.30 extends their earliermodel15 to incorporate interactions with the superconductielectrons. Given that this paper, as well as a recent pape
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PRB 61 R14 919ORDERING WAVE VECTORS OF METAMAGNETIC . . .
Campbellet al.,31 refute one of the key assumptions of ththeory ~ferromagnetic basal planes! and emphasize the importance of the'0.58a! ordering wave vector, the conclusion of the recent work by Amiciet al.30 ~features inHc2 areuncorrelated with the zero field,a! ordering! must be criti-cally reexamined.
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Ames Laboratory is operated for the U.S. DepartmentEnergy by Iowa State University under Contract NW-7405-Eng-82. The work at Ames was supported byDirector of Energy Research, Office of Basic Energy Sences. P.C.C. is grateful to the CEA and UniversityGrenoble for supporting part of this research.
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