Designed Metamagnetism in CoMnGe P 1−x x Z. Gercsi,1 K. Hono,2 and K.G. Sandeman1 1Dept. of Physics, Blackett Laboratory, Imperial College London, London SW7 2AZ UK 2Magnetic Materials Center, National Institute for Materials Science (NIMS), 1-2-1 Sengen, Tsukuba 305-0047, Japan We extend our previous theoretical study of Mn-based orthorhombic metamagnets to those that possess large nearest neighbour Mn-Mn separations (d (cid:38) 3.22 Å). Based on our calculations, we 1 designandsynthesizeaseriesofalloys,CoMnGe P ,toexperimentallydemonstratethevalidity 1−x x ofthemodel. Unusually,wepredictandprepareseveralmetamagnetsfromtwoferromagneticend- members, thus demonstrating a new example of how to vary crystal structure, within the Pnma symmetry group, to provide highly tunable metamagnetism. 1 PACSnumbers: 75.30.Sg,75.30.Kz,75.80.+q,75.30.Et 1 0 2 I. INTRODUCTION and NiMnGe1-xSix14 where the nearest-neighbour Mn- n Mndistancesareclosetoacriticalseparationof2.95Å(cid:46) a d (cid:46)3.05 Å. J Manganese-based orthorhombic (Pnma) binary and 1 Althoughthelattermodelwascomputedinalargein- 1 ternary alloys are of fundamental research interest as tervalof2.5Å(cid:46)d (cid:46)3.22Åtocovermanyoftherelevant 1 theyoftenexhibitcomplex,non-collinearmagneticstruc- 1 tures that can be tuned by temperature, pressure and compositions in the literature, it may lead to a misinter- ] pretationofatechnologicallyrelevantalloywithalarger i applied magnetic field. Some well-known examples are c the set of fan, helical and cycloidal spin structures found d1 = 3.4 Å spacing: CoMnGe. CoMnGe is a collinear s ferromagnetwithatendencytoformametastablehexag- - inthe(H,T)phasediagramofMnP1–3,thecycloidalan- trl taigfenrertoismmagonfeCtiosMmn(SAi3F,5M.)VoafriIoruMsntShie4oraentdicahleelixcpallamnaettiaomns- oexntaelnsdtrouucrtuprreevuipouonstrhaepoirdetciocoallinang1a5ly.sIisn11thtioswAarrdtiscllea,rgweer m Mn-Mn separations to explain the re-appearance of fer- have previously been suggested to describe the mecha- . romagnetism in alloys with d (cid:38)3.37 Å. The importance t nismsresponsibleforthenoncollinearmagnetismofsuch 1 a of the correct theoretical description of latter composi- materials. Somerefertocompetingsymmetricandasym- m tion is due its large magnetocaloric effect around room metric exchange interactions2,6; others to conduction- - mediated indirect (RKKY) exchange7. Another poten- temperature16–18. d InthisArticlewefirstshowthestrikingre-appearance n tial cause put forward is band crossing and appropriate o Fermi surface topology (nesting)4,8. ofaFMgroundstateatlargeinteratomicMnseparations c One of the most feature-rich materials of this kind is in Mn-based Pnma alloys where d1 (cid:38)3.37Å, thereby ac- [ counting for the magnetic properties of CoMnGe. Sec- CoMnSi on account of its pronounced magnetic field- ondly, andsignificantly, wehavedesignedanewalloyse- 1 induced tricritical metamagnetism and associated neg- ries, CoMn(P,Ge) based on our extended model in order v ative magnetocaloric effect (MCE)9. Our recent high- 9 resolutionneutrondiffraction(HRPD)study10uncovered totestanddemonstrateitsvalidityandinparticularthe 9 dominance of the (d ) Mn-Mn separation in determining agiantmagneto-elasticcouplingwithintheantiferromag- 1 0 the magnetic groundstate of the series of Mn-containing 2 neticgroundstateofthissystem. Itoccursasachangeof Pnma alloys. We show that metamagnetism can be de- 1. upto2%innearest-neighbourMn-Mnseparationsd1,d2 rived, unusually, by inter-doping two ferromagnetic end- onheating. Thefield-inducedtricriticalityofthissystem 0 compositions in order to bring d to the critical regime can thus be understood as the result of tuning the meta- 1 1 where antiferromagnetism and ferromagnetism are simi- 1 magnetic critical temperature with an applied magnetic lar in energy. : field to the point at which it coincides with this native v The remainder of the Article is organised as follows: giant magneto-elasticity. i first in Sec. II, the theoretical results calculated by ap- X Using Density Functional Theory (DFT) we recently plyingDFTtotheprototypeMnPalloyaregiven. Based r examined the importance of the same Mn-Mn separa- a on this model, we present the structural and metamag- tions in determining the occurrence of different mag- netic properties of purposefully designed CoMnGe P 1−x x netic groundstates across several Mn-based orthorhom- alloys in Sec. III. Finally, a summary is made and con- bic (Pnma) systems.11. By applying hydrostatic expan- clusions are drawn in Sec. IV. sion and compression to a prototype model MnP al- loy, we found a stability criterion for the appearance of an AFM groundstate, rather than the usual FM state seen in MnP. This direct relation between Mn-Mn sep- II. THEORETICAL aration and magnetic groundstate can explain the en- ergetic proximity of FM and AFM states in materi- In our previous work we considered what we term the als such as CoMnSi3,5, MnAs P 12, (Fe Co )MnP13 “prototype” binary MnP (Pnma) alloy and calculated 1-x x 1-x x 2 the effect of isotropic lattice expansion and compression onhypotheticalnon-magnetic(NM),ferromagnetic(FM) and antiferromagnetic (AFM) states by using the gen- eral gradient aproximation method (GGA-DFT) imple- mented in VASP Kresse and Furthmuller19. We found thecriticallatticeparameterswhereacrossoverfromone magnetic state to another can occur11. In that study, a singleunitcellconsistingof8atoms(4Mnand4P)was used, which allowed three different collinear antiferro- magneticconfigurations(AFM1, AFM2andAFM3)and acollinearferromagnetic(FM)onetobeconstructed. In theintervalof2.5Å(cid:46)d (cid:46)3.22Åwewereabletopredict 1 a transition in the zero temperature magnetic structure from NM to FM, and finally to AFM as a function of expanding lattice parameters. A detailed description of the DFT calculations is given in that work11. Here we extend our simple binary model to d >3.22 Å values by 1 further hydrostatic expansion in order to interpret ferro- Figure 1: (Color online) Stability of possible collinear mag- magnetism in CoMnGe where d1 = 3.4 Å in the current netic structures, relative to ferromagnetism, within a single model. unitcellofMnPasafunctionofd Mn-Mnseparation. AFM 1 Fig. 1 shows the difference in energy between the pos- configurations become stable where (cid:52)EAFM−FM < 0. The sible collinear AFM and FM magnetic states ((cid:52)E = vertical dashed line represents the experimental (strain-free, Tot ε=0)latticeofMnP.WeseethattheFMstateisfirstdesta- E −E )asafunctionofMn-Mnseparation. Using AFM FM bilised by lattice expansion, and then becomes stable again this comparison scheme a non-FM state becomes most at large d values: FM(2). favourablewhenithasthemostnegativevalueof(cid:52)E . 1 Tot On the left hand side of Fig. 1, the large compression causes a strong overlap of d-orbitals, and the broad d-d hybrid bands thus formed cannot support spontaneous thesubstantialchangesinmagneticgroundstate,wefirst magnetisation. Inagreementwithexperimentalfindings, calculatetheelectronicbandstructureandmagneticmo- the FM state is the groundstate of MnP and is stable ment of CoMnGe P alloys with x=0, 0.25, 0.5, 0.75 1−x x for intermediate deformations of the lattice. On fur- and 1 in a collinear FM state. The calculated magnetic ther expansion of the lattice parameters, first the AFM1 momentsaregiveninTableI.Themagneticmomentson typemagneticstructure(ataroundd ∼2.97Å)andthen Mn (2.68µ ) and Co (0.28µ ) sites in the CoMnP alloy 1 B B the AFM3-type ordering (at d ∼3.1 Å) become energet- agreeswellwithpreviouscalculationsbasedontheKKR 1 ically favorable. However the extended study presented method with coherent potential approximation (CPA) here shows that AFM3-type ordering ceases to be the by Zach and co-workers21. Furthermore, the partial re- most stable magnetic state for large lattice expansion, placement of P by Ge results in a progressive increase and eventually the collinear FM state is once again the of magnetic moment on both 3d elements, leading to an groundstate for d (cid:38)3.37 Å. increased M of up to 3.58 µ for CoMnGe. A small 1 Tot B In order to experimentally prove the validity of the negativemomentinducedonthep-blockelementsisalso model, we carefully selected two collinear FM compo- observed. sitions with lattice parameters from the different FM The FM total density of electronic states (DoS) of the regions of the stability plot in Figure 1. Our choices two end compositions, CoMnP and CoMnGe, are plot- were CoMnP from the FM(1) regime (d1∼2.95Å20) and ted, together with CoMnP0.5Ge0.5 in Fig. 2. Although CoMnGe(d1∼3.4Å3 )fromthelargerMn-Mnseparation the value of total density of states at the Fermi level, (FM2)zone. Ourhypothesisisthatprogressivesubstitu- NTot(EF) = N⇓(EF)+N⇑(EF) exhibits a large change tionofonepelementforanotherinCoMnGe1−xPx,with- withcomposition,eachtotalDoSpossessesthesamefea- outchangingthe3d-elementconcentration,cancausethe tures over a large extent of energy range. The main dif- appearanceofmetamagnetisminparticularcompositions ferenceisthelocationofthesefeatures,andinparticular oftheseries. Thisreplacementoflargegermaniumatoms the location of a pseudogap-like feature in the DoS. Us- by the much smaller phosphor atoms should result in a ingCoMnPasreference,iftheenergyscaleoftheminor- shrinkage of lattice. From Figure 1 we expect that the ity DoS is shifted by about +0.25 eV for CoMnGe and decreasing d1 separation will lead to the destabilization about -0.3 eV for CoMnP0.5Ge0.5, not only would the of FM state in competition with the AFM one at a cer- pseudogap fall at EF but most of the exchange-split DoS tainP/Geratio. Itshouldthenbepossibletomanipulate peaks of Mn and Co would line up at around the same the magnetic state of the energetically metastable alloys position. The large NTot(EF) in CoMnP0.5Ge0.5 (Table by changing temperature or applied magnetic field. I) suggests the instability of the collinear FM state in In order to identify the key factors that can lead to this composition. A possible scenario that stabilizes the 3 Figure2: (Coloronline)CollinearFMtotaldensityofstates for CoMnGe P with x=0, 0.5 and 1. The Fermi energy 1−x x fallsintothehybridizationgapforbothCoMnPandCoMnGe, Figure3: RepresentativeSEMmicrographandcorresponding butshiftedforCoMnP0.5Ge0.5 resultinginalargeNTot(EF). elemental mapping from EDX of CoMnGe P . 0.75 0.25 x MMn MCo MSi/Ge MTotal NTot(EF) 0 3.05 0.6 -0.07 3.58 5.0 in quartz tube under protective He atmosphere and a homogenization at 10000C for 24 hours and annealing 0.25 2.83 0.45 -0.06 3.22 10.0 treatment at 8000C for 72 hours then followed. The 0.5 2.89 0.47 -0.07 3.29 9.5 samples thus obtained were crushed into fine powder in 0.75 2.71 0.33 -0.07 2.97 7.5 order to determine their crystal structure using X-ray 1 2.68 0.28 -0.07 2.89 1.7 diffraction (XRD) with Cu Kα radiation. Structural (Rietveld) refinement of the data was carried out the Table I: Calculated magnetic moments (µB) and NTot(EF) using the Fullprof22 program. A microstructural and (states/eV/f.u.) for CoMnGe P . 1−x x compositionalanalysiswascarriedoutusingaCarlZeiss 1540EsB scanning electron microscope (SEM). Magnetic properties of the samples were studied in a Quantum noncollinearstatethroughtheformationofhybridization Design MPMS system. gapattheFermienergyisdescribedbyLizárragaetal.8. We recently showed the relevance of this mechanism in a noncollinear DFT study on the metamagnet CoMnSi10. B. Crystal Structure In the following sections, we are going to demonstrate the validity of our theoretical prediction of metamag- BothCoMnGeandCoMnPalloyscrystallizeintheor- netismintheseMn-basedPnma alloysthroughmagnetic thorhombic (Pnma, 62) structure in which the elements and structural results on an experimentally synthesized occupy general 4c (x,1,z) crystallographic positions. CoMnGe1−xPx series of alloys. 4 XRD analysis of the CoMn(Ge,P) samples revealed the formation of this orthorhombic structure in all composi- tions. Furthermore,inthesampleswithx=0.25,0.4,0.5 III. EXPERIMENTAL and 0.75, extra reflections in the diffraction pattern also appearthatcanbeascribedtothehexagonalNi In-type 2 A. Experimental details (P6 /mmc, 194) lattice structure. The appearance of 3 the higher symmetry hexagonal phase is often observed Samples of CoMnGe P with x = in similar alloy systems because the orthorhombic struc- 1−x x 0.25,0.4,0.5,0.55,0.6 and 0.75 were prepared in a ture can be regarded as a distortion from this hexagonal quartz nozzle by an induction melting technique, using structure and the two structures ca√n be interrelated as Co P (99.9%) and Mn P (99.9%) master alloys mixed follows: b =a and c = 3×a . 2 3 2 ortho hex ortho hex together with high purity Co (99.97%), Mn (99.99%) The importance of this latter correlation has and Ge (99.9999%) elements in the required propor- been exploited in several Mn-based Pnma sys- tions. The alloys were cast into a copper mold under tems. In the pseudo-binary Mn Fe As alloys the 1-x x protective Ar atmosphere. The ingots were then sealed sharp, first order type magnetostructural transforma- 4 ference between the two structures. These findings are direct evidence for a compositional phase separation of the quaternary alloy rather than for a second-order type transformationofthesinglequaternarycompositionwith temperature. TheresultsofthequantitativeRietveldanalysisinFig. 4(top)revealtheformationofsinglephaseorthorhombic structures in the alloys rich in P (x>0.5). Fig. 4 (bot- tom)summarizesthelatticeparameteroftheorthorhom- bic structure as a function P content. (The composition values (x(cid:48)) given in the lower figure are corrected based on the quantitative analysis.) The b and c lattice con- stantsshowdecreasecontinuouslywithGeadditionwhile the a parameter stays nearly constant and until the lat- tice parameters with x∼0.5 become close to those of the metamagnet CoMnSi. Inthenextsection,wewilldemonstratetheoccurrence Figure4: (Coloronline)Volumefractionoftheorthorhombic of metamagnetism in these Mn-based alloys that have CoMnGe P andhexagonalCoMnGephasesasafunction 1−x x appropriately designed lattice parameters. of nominal composition (top) and lattice parameters of the mainorthorhombicphaseasafunctionofcorrectedphosphor concentration (bottom). The lattice parameters of CoMnSi, a metamagnet, are added (star symbols) for comparison. C. Magnetic properties As we demonstrated in Sec. IIIB, the lattice param- tion (orthorhombic⇐⇒hexagonal)23 is also accompanied eters of the CoMnP Ge alloy can be tuned towards 1−x x by a “colossal” MCE24. The magnitude of the use- those of the CoMnSi metamagnet. In the present sec- ful magnetic entropy change is, however, now strongly tion, we will show that this structural engineering allows contested25.A similar magnetostructural transition in us to prepare metamagnetic quaternaries, even though CoMnGe-based ternary compositions was reported by the end alloys (CoMnP and CoMnGe) are ordinary fer- Kanomata and co-workers who observed a large, ∼5.3%, romagnets. Basedonthea,b andc latticeparametersof volume change26,27. Theoretical calculations also re- the CoMnGe P alloys, one would expect progressive 1−x x vealed that the Co vacancy-induced phase transforma- change from collinear ferromagnetism to non-collinear tion is due to a high moment to low moment magnetic anti-ferromagnetism with the replacement of P by Ge in transition accompanied by a large magnetovolume effect thesystem. Ataroundx∼0.5thestructureshouldresem- originating from the change of the coupling distance be- blethatoftheCoMnSimetamagnetandoncethecompo- tweentheprincipalmagneticatoms28. Asanextensionof sition is on the P-rich end of the series, ferromagnetism thisstudy, bothHamer16andTrung17,18 recentlydemon- should re-appear. Indeed, we have found this scenario to stratedthatthetransitionscanbefine-tunedbypseudo- be fulfilled; however the structural phase separation into ternary additives (Sn, B or Cr elements) around room a ternary CoMnGe and a residual CoMn(Ge,P) phase in temperature for an enhanced magnetocaloric effect. The compositions that are rich in Ge hinders a simple inter- appearance of the hexagonal structure at room temper- pretation. ature in our samples can therefore be understood as a The composition dependence of magnetisation loops first order transformation from the low temperature or- takenat10KisshowninFig.5. Metamagnetismismost thorhombic structure to a high temperature hexagonal visibleinthesinglephasecompositionswithx=0.55and one. 0.6. In these samples, the initial magnetisation varies al- In order to clarify the composition of the hexagonal mostlinearlywithappliedfieldbelowtheinflectionpoint phase,arepresentativesecondaryelectron(SE)SEMmi- thatoccursatacriticalfieldvalue. Althoughthiscritical crograph was taken from the CoMnGe P alloy and behaviourisalsovisibleinallcompositionswithx≤0.6, 0.75 0.25 is shown in Fig. 3a. The two different structural regions the increasing volume of ferromagnetic CoMnGe phase are identified in accordance with the XRD results. EDX at low x suppresses the sharpness of the upturn in mag- elemental mapping revealed that the two phases have netisation. A distinct shift of the peak of ∂M, seen in ∂H substantially different atomic compositions. Our inves- Fig. 5b shows that the critical field decreases sharply as tigations show that the orthorhombic phase is poor in more Ge is replaced by P (towards small x). Ge (and consequently enriched in P) whereas the second The composition dependence of the critical field in a phaseisenrichedinGeandisthereforecloseincomposi- field of 1 Tesla is shown in Fig. 6 and is consistent with tion to stoichiometric CoMnGe. An atomic composition the magnetisation loops collected at 10 K. The lower the profile taken along the direction of the arrow indicated critical field that is observed at 10 K (Fig. 5), the lower in Fig. 3b shows quantitatively the compositional dif- thecriticaltemperatureisatwhichthe1Tappliedmag- 5 Figure 5: (Color online) Magnetisation loops of Figure 6: (Color online) Iso-field magnetisation of CoMnGe P at 10K. 1−x x CoMnGe P as a function of temperature, measured in a 1−x x 1 Tesla applied field. We observe metamagnetism in almost all samples, and a sharp change in the metamagnetic critical netic field is sufficiently large to bring the sample to the temperature with composition in the range x=0.4 to 0.6. high magnetic state. A strong dependence of the meta- magnetic transition temperature on crystal structure is evident from this Figure, when compared with Fig. 4. Although samples with x ≤ 0.5 contain a minor sec- d1 =3.4Å. ond phase, they all show a characteristic increase in the Based solely on the deduced magnetic stability plot magnetisationasafunctionoftemperature,indicativeof (Fig. 1), we designed a series of pseudo-ternary CoMn- native metamagnetism. In the high Ge (low x) side of based alloys in order to experimentally prove the valid- the series, with x=0.25, although the substantial ferro- ity of our theoretical concept. Taking two collinear FM magnetic volume (from the CoMnGe phase) largely sup- ternaries: one, CoMnP with a low d from the FM1 re- 1 presses the metamagnetic transition, it still appears at gion ; the other, CoMnGe with a high d from the FM2 1 around room temperature (RT). region we attempted to drive the alloy magnetism to- As the samples become richer in phosphor, the criti- wardsthemetamagnetic/AFMzonebycarefulstructural cal temperature decreases sharply from ∼300K to ∼80K design. and it eventually disappears for x=0.75. The highest The experimental investigation of CoMnGe P has 1−x x magnetisation values in a 1 T applied field show an in- indeed revealed an AFM ground state for compositions crease with x (except for x=0.25) as the result of a bal- x ≈ 0.5. The appearance of a magnetic field- and anceofseveraleffects. Firstly,itiseasilyforeseeablethat temperature-dependent metamagnetic transition in sev- at lower transition temperatures ferromagnetic configu- eral samples also suggests the existence of complex non- rationswillexhibitlargeroverallnet momentscompared collinear spin structure in most of them , and in par- to those of the higher temperature ones. Secondly, the ticular in the range x=0.4 to 0.6. The large predicted presence of the hexagonal CoMnGe lifts the low temper- NTot(EF) for x = 0.5 (in Sec. II) in a hypothetical ature “baseline” of magnetisation in Fig. 6. FM state is because of a shift in the energy of the hybridisation-derived pseudogap as the lattice parame- ters expand upon Ge substitution for phosphor. IV. SUMMARY AND CONCLUSIONS Althoughthecomplexmagneticspinstructureofthese new samples is to be determined, the system is an ex- Using DFT calculations based on a “prototype” bi- ample of the stabilization of non-collinear magnetism nary MnP composition, we have investigated the occur- through the formation of hybridization gap at the Fermi rence of AFM and FM states in Mn-based orthorhombic energy as described by Lizárraga et al.8 and as recently (Pnma, 62) alloys. As the result of isotropic expansion, found in the ternary CoMnSi10. The Mn-containing the FM(1) ground state is no longer stable but instead Pnma structure is extremely versatile with regard to AFMcouplingofthespinsontheMnatomsispredicted elemental substitution. The above demonstration of a above d (cid:38)2.95 Å11. In this work, we have extended our structurally-directedtuningofmagneticpropertiesthere- 1 theoreticalinvestigationtohigherhydrostaticexpansions fore provides a potential direction for future tailoring of and found the re-occurrence of ferromagnetism (FM2) metamagnetic phase transitions towards their use in ap- at large Mn-Mn separations over d (cid:38)3.37 Å that also plications such as those that rely on the magnetocaloric 1 explains the collinear ferromagnetism in CoMnGe with effect. 6 Acknowledgments sis. The research leading to these results has received funding from the European Community’s 7th Frame- Z.G.isgratefulfortheinvitationandfinancialsupport work Programme under grant agreement No. 214864 of NIMS through the Open Research Institute Program. (“SSEEC”). Computing resources provided by Darwin K.G.S. acknowledges financial support from The Royal HPC and Camgrid facilities at The University of Cam- Society. Furthermore, the authors thank H. S. 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