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Magnetoelastic effects in doped Fe2P

Z. Gercsi,1 E. K. Delczeg-Czirjak,2 L. Vitos,3 A. S. Wills,4 A. Daoud-Aladine,5 and K.G. Sandeman1

1Dept. of Physics, Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom2Division of Materials Theory, Department of Physics and Astronomy,

Uppsala University, Box 516, SE 751210 Uppsala, Sweden3Applied Materials Physics, Department of Materials Science and Engineering,

Royal Institute of Technology, SE-100 44 Stockholm, Sweden4Department of Chemistry, University College London ,

20 Gordon Street, London WC1H 0AJ, United Kingdom5ISIS facility, Rutherford Appleton Laboratory, Chilton,

Didcot, Oxfordshire, OX11 0QX, United Kingdom

We use combine high resolution neutron diffraction (HRPD) with density functional theory (DFT)to investigate the exchange striction mechanism at the Curie temperature (TC) of Fe2P and toexamine the effect of boron and carbon doping on the P site. We find a significant contraction ofthe basal plane on heating through TC with a simultaneous increase of the c-axis that results ina small overall volume change of ∼ 0.01%. At the magnetic transition the FeI -FeI distance dropssignificantly and becomes shorter than FeI -FeII . The shortest metal-metalloid (FeI -PI) distancealso decreases sharply. Our DFT model reveals the importance of the latter as this structural changecauses a redistribution of the FeI moment along the c-axis (Fe-P chain). We are able to understandthe site preference of the dopants, the effect of which can be linked to the increased moment on theFeI -site, triggered by both valence electron and structural contributions.

PACS numbers: 75.30.Sg,75.30.Kz, 75.80.+q, 75.30.Et

I. INTRODUCTION

Fe2P-based magnetic alloys attract interest from manyareas of physics, materials science and geophysics re-search. They are found in meteorites and are consideredas a candidate minor phase present in the Earth’s core1,2.An understanding of the mechanism of formation of theseminerals can help to identify the histories of planetarybodies and the composition of the Earth’s outer core.In LiFePO4-based battery materials, a percolating nano-network of metal-rich phosphides including Fe2P can sig-nificantly enhance electrical conductivity3. Fe2P-basedalloys can furthermore be prepared as 1-dimensional (1D)nanowires and nanocables4. Of most relevance to this ar-ticle, however, is the prospect of hexagonal Fe2P-basedalloys being used as room temperature magnetic refrig-erants.

Fe2P exhibits a first order magnetic transition from aferromagnetic (FM) state to a paramagnetic one (PM)at 217 K5 accompanied by a significant change in thec/a-ratio of the hexagonal structure. The magnetisa-tion deviates from the Curie-Weiss law for temperaturesup to 700 K and net magnetism can be observed abovethe Curie temperature in fields of only a few Tesla. Innanocable form, the magnetic transition temperature isshifted 10-50 K higher compared to the parent composi-tion because of strong strain and/or carbon doping4. Theincrease in the Curie temperature, TC with only a small,partial replacement of phosphorus with other p-block ele-ments (B, Si or As) is remarkable. 10% replacement of Pby B leads to ∼120% change, while the same amount ofSi and As substitution also results in a ∼70% and ∼60%increase (Fig. 1) respectively, with a simultaneous change

in the nature of the transition from first order to secondorder6–8. Such large changes in TC are not restricted todoping by p-block elements. Partial replacement of Feby Mn results in a significant increase of the saturationmagnetisation, while the first order nature of the meta-magnetic transition is preserved up to and beyond roomtemperature and is tuned by magnetic field at a rate of∼3 KT−1 9,10.

The metamagnetism of Fe2P shares many featureswith the itinerant electron metamagnetism (IEM) ofLa(Fe,Si)1311. That material also has a PM to FM transi-tion, the temperature of which can be tuned from around190 K to well above 300 K. The high magnetisation statecan be induced by a magnetic field above TC , and themetamagnetic transition is tuned by field at a rate ofaround 4 KT−1. As in Fe2P the first or second ordernature of its metamagnetism depends on the substituent(e.g. Co or Mn) or intercolating atom (e.g. H or C)12,13.Fe2P-based and La(Fe,Si)13-based alloys are two of theleading contenders for scale-up as magnetic refrigerants,due to their tunable metamagnetism, their large roomtemperature magnetocaloric effect (MCE) and the factthat they are mostly composed of abundantly available3d and p-block elements14.

There has been a recent growth in theoretical inves-tigations of the origin and tuneability of metamagne-tim in Fe2P and of the appearance of a body centeredorthorhombic structure in substituted alloys. This ispartly motivated by the sensitivity to doping of the Curietemperature and any associated thermomagnetic hystere-sis, and given added impetus more recently by the in-vestigation of the MCE of industrially-scaled quantitiesof material where good compositional tolerance is re-

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quired. A Landau-Ginzburg free energy analysis basedon fixed-spin-moment (FSM) calculations that took intoaccount the effect of spin fluctuations revealed the meta-magnetic nature of the Fe-atoms at a particular crys-tallographic (3f) site in the parent alloy as well as inthe doped counterparts15,16. Using linear muffin tin or-bitals in the atomic sphere approximation (ASA), Severinet al.17 found that the magnetic moments in the inter-related hexagonal and orthorhombic structures are verysimilar and scale with the nearest-neighbour Fe-P dis-tances. We recently found that the phonon vibrationalfree energy stabilizes the hexagonal phase, whereas theelectronic and magnetic entropies favour a low symme-try orthorhombic structure in Si-substituted Fe2P1−xSixalloys18. An analysis of the exchange constants in thehexagonal structure of B-, Si- and As-doped Fe2P helpsto explain trends in Curie temperature. A principal in-terlayer Fe-Fe interaction was identified as controlling thestrength of ferromagnetism19.

In the present paper we employ a joint experimental-theoretical approach that we have used elsewhere to un-cover the microscopic mechanism of metamagnetism inMn-based antiferromagnets. By using density functionaltheory (DFT) in combination with structural informa-tion from high resolution neutron diffraction (HRPD)20

we have previously mapped the magnetic phase diagramof Mn-based metallic orthorhombic compounds in thePnma space group as a function of Mn-Mn distance21 andhave predicted new antiferromagnetic metamagnets22,23.Taking the same approach here, we first analyse and com-pare the peculiar magnetoelastic coupling of the metam-agnetic transition in Fe2P, in boron-doped Fe2(P,B) and,for the first time, carbon-doped Fe2(P,C) using HRPD.In the second part of the article, we use a simple DFTmodel to further interpret the large interatomic changesat the magnetic transition. Our aim is to provide clues asto how to control and optimise the structure-magnetismrelationship in this highly tuneable materials class.

II. PREVIOUS EXPERIMENTAL FINDINGS

Fe2P is the prototype structure of the hexagonal spacegroup 189 (P62m) with 9 atoms in the unit cell. The6 Fe atoms occupy two non-equivalent threefold symme-try sites (3f and 3g), while the phosphor atoms sit ona singlefold (1b) and on a twofold position (2c) in thecrystal lattice. Here we adopt the following establishednotation: FeI for the 3f (xI , 0, 0) positions, FeII for the3g (xII , 0, 1/2) positions, and PI and PII for the 2c(1/3, 2/3, 0) and 1b (0,0, 1/2) positions of the P atoms,respectively. The hexagonal cell is composed of trianglesin the ab plane as shown in Figure 2. The iron atomsthat alternate along the c-axis are surrounded either byfour P-atoms with tetrahedral symmetry (FeI) or byfive P-atoms forming a pyramid (FeII). It was reportedpreviously24 that the c-axis lattice parameter increaseswith temperature while the a- and b-axes (basal plane)

Figure 1: (Color online) The effect of boron, silicon and ar-senic doping in Fe2P1−xZx on the magnetic ordering temper-ature TC (top) and the room temperature lattice parameters(bottom)6–8.

Figure 2: (Color online) Atomic arrangement of the Fe2P inthe basal plane. Fe atoms occupy two non-equivalent three-fold symmetry sites, 3f (FeI) and 3g (FeII), and the phospho-rus atoms sit on a single-fold 1b (PI) and two-fold position,2c (PII) in the hexagonal crystal lattice. FeI (xI , 0, 0) atomsshare the same plane with PI (1/3, 2/3, 0) and FeII atoms(xII , 0, 1/2) with PII (0,0, 1/2), respectively.

exhibit negative thermal expansion. The same authorsused a strain gauge dilatometer to measure the linearthermal expansion (∆l/l) of a single crystal of Fe2P uponcooling through the first order type magnetic transitionand found a sharp increase of ∆a

a= 0.74× 10−3 with the

simultaneous decrease of the c-axis: (∆cc

= −0.84×10−3).

The coupling between the structure and magnetism isfurther manifested by the effect of doping shown in Fig. 1.A significant increase in Curie temperature upon partialreplacement of the P atoms by other p-block elementssuch as B, Si and As has been observed.6–8 Catalano etal.6 investigated the effect of isovalent substitution of Asfor P on the crystalline lattice and on magnetic proper-

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ties. The authors found that the larger atomic radiusAs can be continuously accommodated into the hexago-nal lattice between 0 ≤ x ≤ 0.65 in Fe2P1−xAsx with astrong site preference for the PI (2c) position. The mono-tonic increase of the lattice volume with As addition is acompromise of a moderate increase of a-axis and a simul-taneous contraction of the lattice along the c-direction.The same tendency was observed by the substitution oflarger atomic radius, non-isovalent Si for P by Jernberget al.8 Interestingly, Si atoms were also found to showsome site preference for the PI position with opposingtrends in the a and c lattice parameters and a signifi-cant increase in the magnetic ordering temperature. Sil-icon addition above x ≤ 0.1 results in a change from thehexagonal lattice structure into one with a body-centeredorthorhombic, Imm2 (44) symmetry.

Finally, the partial replacement of P by the substan-tially smaller atomic radius boron results in a formidableincrease of the Curie temperature. The solid solubilityof the B atoms in Fe2P1−xBx is, however, limited tox ≈ 0.15 due to the formation of other Fe5PB2, Fe3Band Fe2B refractory borides at higher B concentrations.Chandra et al. established by means of Mössbauer spec-troscopy that the small boron atoms, unlike the largerelements (As and Si), occupy the PII (1b) singlefold po-sition in the hexagonal lattice7. Another consequenceof the chemical pressure on the hexagonal lattice causedby boron addition as compared to the parent alloy orto the Si/As-doped compositions is decreased lattice vol-ume. Despite such differences, the monotonic increase ofthe a and decrease of the c lattice parameters of the unitcell is strikingly similar to the effect of larger p-elementdopants (Fig. 1). An additional consequence of borondoping is that the first-order PM-FM transition of un-doped Fe2P becomes second order.

III. METHODS

A. Experimental Methods

The samples used in this study were prepared from ul-tra high purity elements. The powders were mixed toweight ratios to according to nominal compositions ofFe2P and Fe2P0.96Z0.04 , (Z=B or C) and then thoroughlyground together in an agate mortar under protective at-mosphere. The initial powders were then pressed intopellets and sealed into quartz ampoules under protectiveargon atmosphere for solid state reaction. The initialannealing temperature was raised slowly (0.5 K min−1)up to 673 K, where each sample was kept for 4 hoursfor an initial reaction. There was a subsequent heatingstep (at 1 K min−1) up to 1273 K where the temperaturewas held for a further 4 hours. An additional heat treat-ment at 973 K for 4 hours was applied before the samplewas oven-cooled to room temperature. X-ray diffractom-etry (XRD) was used to evaluate the structural prop-erties of the prepared samples. Single phase hexagonal

compositions were found in all specimens by this method.Neutron diffraction was carried out at the time-of-flighthigh resolution powder diffractometer (HRPD) at ISIS,UK. This instrument has a resolution of ∆d

dof 10−4 and

was used at temperatures between 4.2 and 550 K. Neu-tron diffraction found some traces of unreacted carbon inFe2P0.96C0.04 which we here refer to as a nominal compo-sition since the actual carbon concentration of the mainphase will be somewhat smaller. Magnetic propertieswere measured between 10 and 400 K in a QuantumDesign Physical Properties Measurement System (QD-PPMS).

B. Computational model

The electronic structure calculations were performedusing the Vienna ab initio simulation package (VASP)code, based on DFT within projector augmented wave(PAW) method25 with Perdew-Burke-Ernzerhof (PBE)parameterization26. Site-based magnetic moments werecalculated using the Vosko-Wilk-Nusair interpolation27

within the general gradient approximation (GGA) for theexchange-correlation potential. A k-point grid of 11 × 11× 13 was used to discretize the first Brillouin zone andthe energy convergence criterion was set 10−7 eV duringthe energy minimization process. The density of states(DOS) plots presented in this work were calculated on adense (19 × 19 × 21) k-grid for high accuracy. The spin-orbit interaction was turned off during the calculationsand only collinear ferromagnetic (FM) and non-magnetic(NM) configurations were considered.

The minimal, nine-atom basis cell (six Fe atoms andthree P atoms) was used to evaluate the total energiesand magnetic properties of the alloys. Using this sim-ple model, the effect of doping was simulated by thereplacement of a single phosphorous atom by anotherp-block element (Z) that represents an x=1/3 compo-sitional change in the Fe2P1−xZx formula. Although thisapproach is undoubtedly oversimplified in respect of ex-act compositions provided in the experimental section,we believe it is still a suitable model to capture the rel-evant changes in the electronic structure caused by thedoping elements. In order to be consistent with the ex-perimental results, we only considered changes along thea- and c-axis by the individual expansion and compres-sion of the a- and c-lattice parameters, without allow-ing any relaxation of the strained structure. In prac-tice, we varied the lattice parameters using a stepsizeof ±0.5%, calculating the self-consistent electronic struc-tures at each step.

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Figure 3: (Color online) Thermomagnetic curves of the parentFe2P alloy with the C and B doped counterparts (top, leftaxis) in the field of µ0M=0.01T. Derivatives ( dM

dH) are linked

to the right axis (top). Bottom figure shows the change ofthe lattice parameters (a, c) for comparision, obtained usingHRPD.

IV. RESULTS

A. Magnetometry

The samples were first cooled to 10 K, where mag-netisation curves were collected at fields up to 5 T, afterwhich thermo-magnetic curves were collected on heat-ing to 400 K in an applied field of 0.01 T. The resultsare plotted in Fig. 3. The parent alloy shows a sharp,first order transition at T ≈215 K in accordance withvalues reported previously. The strong effect of dopingon the magnetic order temperature is apparent. As ex-pected, the partial replacement of P by the much smalleratomic radius B significantly increases TC . In this study,we also partially replaced P by C atoms for the firsttime. The empirical atomic radius of carbon is muchsmaller (70 pm) than that of the phosphorus (100 pm)and boron (85 pm) elements. On the other hand, in termsof valence electrons the sequence B(p1) <C(p2) <P(p3)stands. In practice, carbon doping shows a very sim-ilar effect to that of the other p-block substituents asit also clearly increases the magnetic order tempera-ture. Furthermore, the Curie transition is heavily broad-ened by doping as demonstrated by the smearing out ofthe temperature derivative of the magnetisation (∂M

∂H)

(Fig. 3). Finally, the saturation magnetisation (MS) in-creases slightly with doping; MS=112 , 113 and 116 Am2

kg

was obtained for Fe2P, Fe2P0.96C0.04 and Fe2P0.96B0.04,respectivelly at 10 K in 9 T applied magnetic field. Thisslight increase of MS is in line with the expectations fromDFT calculations (see sec. VB). However, the sampleswere not fully saturated due to the large magnetocrys-talline anisotropy5.

Figure 4: (Color online) Temperature evolution of the latticeparameters of the parent Fe2P compound together with thatof the C- and B-doped samples. The strong magnetoelasticresponse is especially apparent around the magnetic orderingtemperature (∼215 K).

B. High resolution neutron diffraction

Fig. 4 shows the anisotropic lattice expansion of thea- and c-axes of Fe2P and the doped compounds. Inthe magnetically ordered state (T .200 K) the basalplane exhibits negative lattice expansion with increas-ing temperature. When the temperature reaches TC , asharp contraction of the lattice in the ab plane is ob-served. The a-lattice expansion only looks Debye-like athigher temperatures (T &240 K) in the paramagneticphase. On the other hand, the thermal expansion of thec-axis is found to be positive over the entire investigatedtemperature range. The magnetic ordering temperatureis also strongly reflected in the lattice response along c.The consequence of these counteracting lattice parameterchanges over the magnetic transition is a volume changeat TC which is as small as 0.01%.

The effect of doping on the lattice parameters is clear;the basal plane of the hexagonal lattice expands whilstthe c-axis shows contraction. At first glance, the anoma-lous thermal lattice expansion resembles that of the par-ent alloy. However, temperature derivatives of thesequantities (∂a/∂T , ∂c/∂T ) reveal characteristic differ-ences between the parent and doped alloys in Fig. 3. Thesharpness of the derivatives demonstrates the first ordernature of the magnetoelastic transition of stoichiometricFe2P. Although ∂a/∂T and ∂c/∂T are of opposite sign,they both have sharp peaks at temperature Tp=209 K.Both B and C doping cause a shift of Tp to higher tem-peratures with broader ∂a/∂T and ∂c/∂T . These effectson the lattice properties correspond very well to the ob-served changes in the magnetic properties. The temper-ature derivative of the magnetisation in Fig. 3 (top), re-veals similar broadening of the ferromagnetic transitionwith B or C doping.

HRPD is capable of tracking the change in the inter-

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Figure 5: (Color online) The shortest FeI -2FeI and FeI -2FeII distances as a function of temperature for all inves-tigated samples. Inset depicts the temperature region of thecrossover.

atomic distances, thus providing vital information aboutthe magnetoelastic coupling in these materials. The evo-lution of the lattice parameters through the magnetoe-lastic transition is already a clear indication of the sig-nificant changes of the atomic distances. Both the 3f and3g positions of the iron atoms are low symmetry posi-tions described by the positional parameters xI and xII ,respectively. Iron atoms on the 3f-site (FeI) are con-nected to 2 other iron atoms of the same type, denotedas FeI -2FeI . There are also two distinctive FeI -2FeIIand FeI -4FeII connections to iron atoms located at the3g-site (FeII). Finally, there exists a relatively close FeII -4FeII distance above 3 Å. In Fig. 5, we only plot the twoshortest distances, FeI -2FeI and FeI -2FeII , as a functionof temperature, evaluated from Rietveld refinements ofthe HRPD data. In all of the investigated samples, theFeI -2FeII distance is the shortest Fe-Fe separation at lowtemperatures(<200 K). The latter increases with tem-perature, eventually becoming larger than the FeI -FeIdistance, which is strongly reduced in the vicinity of themagnetic transition temperature. The point in tempera-ture above which FeI -FeI is the shortest Fe-Fe distanceis between 190 and 220 K for all samples.

In addition we can distinguish two groups of metal-metalloid distances: FeI -(PI ,PII) and FeII -(PI ,PII).The shortest one is FeI -2PI , followed by FeI -2PII , FeII -PII and FeII -4PI . Fig. 6 contains the two shortest dis-tances only. The separation of FeII -PII and FeII -4PI

atoms is in the range of ∼2.37 Å and ∼2.49 Å, respec-tively. It is worth noting that both FeI -2PI and FeII -PII distances only have components within the ab-planewhich explains the resemblance of their temperature evo-lution to that of the a lattice parameter in Fig. 4: theshortest FeI -2PI distance decreases sharply around themagnetic transition temperature in the parent alloy and

Figure 6: (Color online) The shortest metal-metalloid dis-tances, FeI - 2PI and FeI - 2PII as a function of temperaturein Fe2P together with the doped counterparts. Both distancesrelate to the metamagnetic 3f (FeI) site.

Figure 7: Total magnetisation as a function of lattice param-eter of Fe2P. Magnetisation is strongly linked to the changein a-lattice parameter.

the doped compounds. The larger a lattice parameterin the doped compounds means that the metal-metalloiddistance is largest in those samples.

V. THEORETICAL RESULTS

A. Stoicheometric Fe2P

The variation of total magnetisation with lattice pa-rameters expected from our DFT calculations is plottedin Figure 7. A change in the lattice can have a very strongeffect on the magnetic properties. The lattice expansion

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Figure 8: (Color online) Comparision of the densitiy of statesof a high magnetisation state (red) and a low magnetisationstate (black) in Fe2P.

within the basal plane causes the total magnetisation toincrease abruptly from ∼ 1.3 µB to 3.1 µB around a crit-ical value of a ≈ 5.7 Å, and stays practically constantabove it. The magnetisation varies very little with c, re-flecting the greater importance of the atomic distanceswithin the basal plane, where the atoms are packed moredensely. In order to depict the changes related to theelectronic structure that are most relevant to such ananisotropic magneto-elastic coupling, we compare the to-tal electronic density of states (DOS) of the high and lowmagnetisation states, at (a, c) values indicated by red andblack dots in Figure 7. The lattice structure in the highmagnetic state has a high and sharp DOS at EF with∼80% spin polarisation, dominated by minority spins(Figure 8, red line). This signature is typical of a mag-netic instablility. When the lattice is compressed withinthe basal plane, the magnetic ground state is significantlydifferent, as shown in black in Figure 8. The filled bandsin the bottom contain the phosphorus 3s states. Theconduction band is formed by the 3d states of Fe and the3p states of P as is typical of strong p-d hybridization.The hybridized states are also present near the Fermilevel, influencing the exchange splitting of the 3d statesof Fe. The effect of the smaller a-lattice parameter (lowmagnetisation state) is to reduce the exchange splittingconsiderably. The high peaks in the majority density ofstates located around -0.5 eV are shifted to -0.2 eV. Inthe minority DOS, the opposite trend is observed as thetriple peak feature between 0 and 0.25 eV is lowered toaround -0.25 eV.

The relationship between the DOS at the Fermi En-ergy, D(EF ) and the strength of magnetic exchange, I,can be expressed as the Stoner criteria I × D(EF ) > 1for an itinerant ferromagnet. Such an analysis has beenextensively discussed by Eriksson et al.28. They inves-

tigated site-related magnetic stability and also found amagnetic instability with decreasing cell volume. In ourstudy we concentrate on comparing the differences in spindensities of the high and low magnetic configurations,plotted in Fig. 9. As a consequence of the lattice symme-try, the shortest metal-metalloid distance, FeI -PII , aswell as the shortest metal-metal separation, FeI -FeII ,have projections along both the a- and c-axes, and sothis is the most suitable cross-section for our analysis.

We can ascribe three competing effects to the mag-netoelastic transition. Firstly, with increasing tempera-ture the separation between FeI and FeII atoms increasesmonotonously as observed experimentally (see Fig. 5).This is linked to our recent investigations of the exchangecoupling mechanism among the magnetic sites using theexact muffin-tin orbital (EMTO) method. Our exchangecoupling analysis19 found that the largest contributionto the decrease in the c/a ratio to the total magneticexchange interaction is the weakened magnetic interac-tion between the Fe atoms on 3f and 3g sites. Secondly,at the magnetic transition the FeI -FeI distance is also al-tered and it becomes comparably to the FeI and FeII butthe exchange constant between these atoms is only thefraction of the FeI and FeII exchange, and has a less pro-nounced dependence on distance. Thirdly, the shortestFeI -PI distance, located in the ab plane also dips aroundthe transition temperature. This results in a significantlystronger hybridisation that can explain the decrease inmagnetisation and alternation of these bonds, and hencetrigger a lattice distortion in the first place. A similarscenario was also drawn from the comparison of the totalelectronic charge density in the FM and PM states of Mnand Si doped Fe2P-type alloy by Dung et al.9

Our current DFT results provide further evidence foran understanding of the microscopics of the Curie tran-sition. The calculations reveal the unusual duality ofthe magnetic structure of Fe2P in which there is alarge magnetic moment of M(FeII)=2.16 µB on the 3g-site together that coexists with a significantly smaller,M(FeI)=0.85 µB, moment on the 3f crystallographic site.These findings are in full agreement with previous stud-ies (see Sec. II). If we consider solely the effect of thestructural changes that we know to occur at the Curietransition (Fig. 5), we find that there is a redistributionof magnetisation of the FeI -site. The large and localisedmagnetic moment on the FeII site is decreased in ampli-tude to ∼ 1.3µB above the transition and strong delocal-isation of the FeI magnetisation occurs simultaneously.Electrons from the FeI -site that have a magnetic con-tribution are redistributed along the c-axis in directionsthat link the FeI and PII sites. This strong coupling be-tween magnetism and lattice is the origin of the strongmagnetoelastic response and the highly field dependenttransition in these alloys. In the following section, wecompare the effect of doping on the structure and mag-netic properties obtained by means of DFT using struc-tural data from neutron diffraction (HRPD).

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Figure 9: (Color online) A comparison of the spin density ofthe high magnetisation state (right) and low magnetisationstate (left) of Fe2P. The large magnetic moment around theFeII site is only decreased in amplitude above the transition,when strong delocalisation of the FeI magnetisation occurssimultaneously.

B. The Effect of Doping

There exist two crystallographic sites where the metal-loid elements can be incorporated into the lattice, albeitwith strong site preference as described in Sec. II. Exper-imentally, elements with an atomic radius smaller than Pwere found to show a preference in the single-fold position(1b), whilst larger elements tends to occupy the twofoldsymmetry site (2c) in the hexagonal lattice. In order toestablish the site preference from DFT calculations, wecompare the difference in total energy for the differentelemental substitution. First of all, the calculated totalenergies of the FM solutions (at any (a, c) lattice param-eter value) were always found to be energetically morestable than that of the NM configurations by typically1.5-3 eV/f.u., yielding a strong tendency toward the for-mation of magnetic order in all the investigated alloys.The site preference of the dopants can be established bycalculating the difference in total energy (dE) betweenthe single-fold and two-fold site position occupancies us-ing the equilibrium lattice of the FM state. The calcula-tions find a clear trend with the size of the substituents:the energy difference is negative for elements that aresmaller than P (left hand side of Fig. 10), reflecting thepreference for singlefold occupation. On the other hand,a substituent with larger atomic radii (Si and As) prefersto occupy the twofold position of the hexagonal lattice.

This theoretically established site occupation of thedopant elements is in line with the experimental find-ings see Sec. II, suggesting the dominance of size effects.Therefore, we hereafter focus our magnetoelastic investi-gations on the effect of single-fold site occupation by the

Figure 10: (Color online) Site preference of the p-blockdopants as established from DFT. Negative total energy dif-ferences represent preference for the single-fold position. Pos-itive total energy differences suggest tendency for two-fold siteoccupancy.

Figure 11: (Color online) Equilibrium lattice parameters forNM and FM states as a result of DFT calculations as a func-tion of dopants in Fe2P2/3Z1/3, where Z=C, B, Si, or As,respectively.

small C and B elements and the two-fold site occupationof the large Si and As elements.

The effect of doping on the lattice parameters is shownin Fig. 11. The non-magnetic (NM) calculations (blackline) show an increasing trend in both the a- and c pa-rameters of the hexagonal structure with the inclusion oflarger atomic radius, anionic p-block elements. This be-haviour is easily anticipated in terms of chemical pressureas the lattice is expected to adapt according to the sizeof dopant. Examining Fig. 11, the steepest change inthe lattice is seen with the partial replacement of P by Batoms, due to the largest difference in atom size betweenthese elements. However, in the presence of ferromag-netic (FM) interactions, any monotonic relation of lattice

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Figure 12: (Color online) Total and site-projected magneticmoments in Fe2P2/3Z1/3, for Z=C,B,Si and As, respectively.

parameter to the atomic radius of the dopant is broken.The parent alloy has significantly smaller a and larger cparameters in the FM ground state than the doped com-pounds. The onset of ferromagnetism increases the sepa-ration of atoms within the basal plane (positive exchangestriction) while their separation along the c-axis is re-duced (negative exchange striction), regardless of the sizeor valence state of the dopant as compared to the parentcomposition (Fe2P). The overall volume change causedby the ferromagnetic exchange is positive, dominated bythe larger a parameter (Vhex = a2c sin(2π/3)). Basedon these calculations, one would expect the lattice to ex-pand along the a-axis with a simultaneous contraction ofthe c-axis in the vicinity of the magnetic ordering tem-perature. Indeed, experimental (HRPD) measurementsclearly reveal this sharp positive exchange striction in thebasal plane and the shrinkage of the c-axis upon coolingthe sample through the Curie temperature (see Fig. 4).

The significant coupling of the lattice dimensions tothe magnetism also becomes aparent from the analy-sis of the total and site-projected magnetic momentsas plotted in Fig. 12. The magnetic moment of FeIIatoms show very little variation with doping and staysat around 2.2 µB. Although the larger p-block dopantsincrease the separation of the FeII -FeII atoms, this dis-tance is typically above 3 Å, and so doping only slightlyalters the exchange-split states. In strong contrast, thesite-resolved magnetisation of the 3f site is found to bemuch more sensitive to the valence electron number ofthe anionic elements. Examining Fig. 12 there is astrong relation between added valence electron numberand magnetisation with Z=B (−2e−), C (−1e−), P(−),Si (−2e−), or As(−). This feature can be explained interms of charge transfer from FeI to the anionic Z elementin order to fill the electronegative p shell of the latter.The charge transfer is distance dependent and is stronglysupressed by the strong p-d interaction at smaller FeI -Zseparations, while lattice expansion suppresses p-d hy-

bridization and increases the degree of localisation andionic bonding in the system. With doping, the shortFeI -Z distances are strongly influenced, altering the bal-ance between magnetic moment formation (Fig. 9) andbond formation. The larger magnetic moments on theFeI atoms that result from doping account for the expan-sion of the basal plane as indicated by the comparison ofFigs. 11 and 7.

VI. SUMMARY AND CONCLUSION

We have used high resolution neutron diffraction(HRPD) as well as density functional theory to investi-gate the effect of p-block elements doping on the magne-toelastic properties of Fe2P. HRPD has revealed that thestrong coupling between the magnetism and the lattice ismanifested by the contraction of the basal plane and bya significant increase of the c-axis on heating through themagnetic transition, resulting in a small overall volumechange of the lattice (>0.01%). A simultaneous changein both the metal-metal and metal-metalloid distances isobserved.

DFT calculations reveal that the magnetic propertiesare strongly dependent on expansion in the basal (ab)plane, while they are almost invariant with regard tovariation of the c parameter. The strong dependenceof magnetic moments on the 3f site is related to the alattice parameter being on the verge of a metamagnetictransition. The closest metal-metal and metal-metalloiddistances - the latter ones also linked to the metamag-netic 3f site - are strongly altered by both the d-d andp-d hybridisation energies at the transition. As a result,the redistribution (delocalisation) of the magnetisationfrom the 3f site along the FeI -PII chains in the c-axisdirection occurs as shown in Fig. 9, implying its stronginfluence on bonding (also suggested by Dung et al.10).The magnetic moment on the 3g site is only slightly re-duced (to ∼ 1.3µB) above the transition, accounting forthe observed strong divergence of the Curie-Weiss law5.

Our theoretical investigations on the effect of dopingshow that elements with an atomic radius smaller thanphosphorus (e.g. C or B) occupy single-fold (1b) siteswhile larger elements such as Si or As prefer to occupythe two-fold symmetry site (2c) in the hexagonal lattice.The magnetism on the high magnetic site (3g) is not in-fluenced by the dopant and stays approximately constant(∼2.2µB). By contrast, the iron atoms on the metam-agnetic site develop larger magnetic moments, in directrelation to the valence electron number of the doping el-ement. As a result, the conditions for the metamagnetictransition of the 3f site are locally modified, resultingin a smearing of the transition as observed experimen-tally. Indeed, the larger exchange splitting on FeI resultsin increased exchange coupling parameters, significantlyincreasing the Curie temperature19.

The large difference in the lattice equilibrium betweenthe non-magnetic and ferromagnetic solutions in the par-

9

ent compound as well as in the doped materials as foundby DFT calculations suggests that the magnetic proper-ties are not only very sensitive to compositional inhomo-geneities but also to internal strains set by the prepa-ration conditions29. Therefore for applications (such asmagnetic refrigeration), where the transition tempera-ture needs to be set by the material to a high accuracy,elements such as Si and As are favorable but process con-trol will be crucial. Finally, as the remarkable change inmagnetic ordering of these alloys is linked to the latticeparameters within the basal plane, uniaxial thin films onflexible substrates could be exploited to electrically ma-nipulate the magnetic properties of this material system.

Acknowledgments

We thank L. Szunyogh for useful discussions and D.Boldrin for help with sample preparation. We also thankK.S. Knight for providing us with the 11B isotope used forthis study. Financial support is acknoweldged from TheRoyal Society (KGS) and EPSRC grant EP/G060940/1(KGS and ZG). Fig. 9 was prepared using VESTA open-source software.30 Computing resources provided by Dar-win HPC and Camgrid facilities at The University ofCambridge and the HPC Service at Imperial College Lon-don are gratefully acknowledged.

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