Magnetoelastic coupling in triangular lattice antiferromagnet CuCrS2
Julia C. E. Rasch, Martin Boehm, Clemens Ritter, Hannu Mutka, Jürg Schefer, Lukas Keller, Galina M. Abramova, Antonio Cervellino, Jörg F. Löffler
aa r X i v : . [ c ond - m a t . s t r- e l ] J u l Magnetoelastic coupling in triangular lattice antiferromagnet CuCrS Julia C. E. Rasch , , ∗ Martin Boehm , Clemens Ritter , Hannu Mutka , J¨urg Schefer ,Lukas Keller , Galina M. Abramova , Antonio Cervellino , and J¨org F. L¨offler Institut Laue-Langevin, 6 Rue Jules Horowitz, BP 156, 38042 Grenoble Cedex 9, France Laboratory for Neutron Scattering, ETH Zurich & Paul Scherrer Institut, CH-5232 Villigen, PSI, Switzerland L.V. Kirensky Institute of Physics, SB RAS, Krasnoyarsk 660036, Russia Swiss Light Source, Paul Scherrer Institut, CH-5232 Villigen, PSI, Switzerland Laboratory of Metal Physics and Technology, Department of Materials, ETH Zurich, 8093 Zurich, Switzerland (Dated: December 4, 2018)CuCrS is a triangular lattice Heisenberg antiferromagnet with a rhombohedral crystal structure.We report on neutron and synchrotron powder diffraction results which reveal a monoclinic latticedistortion at the magnetic transition and verify a magnetoelastic coupling. CuCrS is therefore aninteresting material to study the influence of magnetism on the relief of geometrical frustration. I. INTRODUCTION
Heisenberg antiferromagnets on a triangular latticeare subject to ongoing interest due to a strong cor-relation between lattice geometry, electronic and mag-netic properties. Geometrical frustration plays a keyrole in compounds with triangular arrangement of mag-netic moments and leads to particular characteristicsincluding incommensurate spin structures and multifer-roic properties. Ternary triangular lattice dioxides anddichalcogenides have in common to crystallize in a lay-ered structure with strong crystalline anisotropy perpen-dicular to the layers (mainly space group R m and R ¯3 m ).In chromium based dioxides the most commonly estab-lished magnetic structure is a quasi two-dimensional 120 ◦ spin structure, typical for Heisenberg exchange on a tri-angular lattice, with a weak interlayer coupling e.g. inAgCrO , PdCrO , NaCrO and CuCrO . The lattertwo also show a magnetoelectric coupling where the spinstructure induces ferroelectricity . Ternary chromiumdichalcogenides have been less intensively studied, andshow a variety of different magnetic structures rangingfrom a 120 ◦ spin structure in LiCrS over a commen-surate magnetic structure in KCrS to a helix with anin-plane spin orientation in NaCrS . The compound under investigation, CuCrS , has drawnattention as an ionic conductor and is assumedto exhibit a spin glass state under the substitutionof chromium ions by vanadium. A microscopictemperature-dependent investigation of magnetic andcrystallographic properties is, however, lacking. CuCrS crystallizes in space group R m at room temperature. The basic atomic structure consists of covalent-ionicbound S-Cr-S layers separated by a van der Waals gapcausing strong crystalline anisotropy perpendicular tothe layers. Isolated CrS is metastable and occursonly with an electron donor, therefore monovalent Cu + cations are intercalated between (CrS )-sandwiches. The magnetic Cr ions with spin S = 3 / , , ) and ( , , ),as shown in the inset of Fig. 1. The nearest-neighborintralayer Cr-Cr distance of 3 .
48 ˚A is small compared to the interlayer Cr-Cr distance of 6 .
55 ˚A. The mag-netic exchange within the layers over Cr-S-Cr pathwaysis expected to be much stronger than the interlayer ex-change via Cr-S-Cu-S-Cr bonds. Hence, one would ex-pect to find the crystalline anisotropy to be reflected inthe magnetic system, as described in the dioxides. Never-theless, early neutron powder diffraction experiments onCuCrS revealed a three-dimensional magnetic orderingbelow T N = 40 K into a complex helical structure withan incommensurate magnetic propagation vector. Thisphenomenon cannot be explained without interlayer ex-change interactions which must be of the same order ofmagnitude as the intralayer exchange. An estimation ofexchange constants is given in the discussion. The partic-ularity of CuCrS is a strong lattice effect exactly at T N .We assume that the lattice distortion provides a chan-nel for the system to escape the 2D triangular arrange-ment, usually leading to magnetic frustration. The conse-quences on the lattice and magnetic structure throughoutthe phase transition are subject of this paper. A similarlattice effect occurs in triangular lattice CuFeO , where acrystal symmetry lowering is found to lift the degeneracyof the frustrated spin system together with multiferroicproperties induced by a magnetic field or non magneticimpurities. Strong spin-lattice effects are also foundin 3D frustrated systems, as shown for the well-known py-rochlore spinel ZnCr O . The compound was found toundergo a Spin-Peierls-like phase transition which com-prises an energy lowering through a lattice distortion andthe opening of an energy gap. The origin of this gaphas been explained by clustering of the Cr moments intoweakly interacting antiferromagnetic loops. Althoughthe formation of spin cluster has been clarified, the mag-netic structure is not fully understood. We claim to seea similar effect on a triangular lattice and report in thispaper on the detailed magnetic structure.
II. EXPERIMENTAL DETAILS
The polycrystalline sample of CuCrS was synthesizedby solid state reaction of the pure elements. A de-tailed description is given elsewhere . Single crystals FIG. 1: (Color online) Magnetic susceptibility of CuCrS measured at H = 10 kOe as a function of temperature. Anantiferromagnetic anomaly at T N = 37 . at room temperature with space group R m . were grown by chemical vapor transport in an evacuatedquartz ampoule with p ≤ − mbar. A temperaturegradient was applied over 30 cm ampoule length between900 ◦ C and 950 ◦ C during three weeks. The furnace wasthen cooled at a cooling rate of 1 K/min to room tem-perature. The resulting single crystals are thin plateletswhich possess a black shiny surface with the [001] direc-tion perpendicular to it. The size of the surface rangesfrom 10 to 100 mm with a typical thickness of 0.2 mm.The stoichiometry of the samples was checked by energydispersive X-ray spectroscopy and verified in case of thepolycrystalline powder. The single crystals contain animpurity phase of not more than 10% CuCr S . System-atic variations of growth conditions in order to avoid theimpurity phase, produced crystals too thin ( < µ m)and unstable for use in neutron scattering experiments.Neutron powder diffraction measurements were carriedout on the cold diffractometer DMC at the neutron spal-lation source SINQ, Paul Scherrer Institut (PSI) andthe thermal diffractometer D1A at the Institut Laue-Langevin (ILL) with λ = 2 .
46 ˚A and λ = 1 .
91 ˚A , re-spectively, in a standard orange cryostat. Single crys-tal diffraction experiments were performed on the ther-mal instrument TriCS (SINQ) with λ = 1 .
18 ˚A in afour-circle Eulerian cradle and on the three-axis spec-trometer IN3 (ILL) with λ = 2 .
36 ˚A. High-resolutionsynchrotron radiation powder diffraction patterns werecollected at the powder diffraction station of the SwissLight Source Materials Science (SLS-MS) beamline at anincident photon energy of λ = 0 . θ scan to avoid preferred orientation. The collected FIG. 2: (Color online) Powder diffraction data taken on D1Aat 10 K (refined) and 44 K (raw data). The refinement ofthe 10 K data with a nuclear and magnetic phase is indicatedby a black solid line. The difference between refinement andobserved data at 10 K is shown in grey. (a) depicts the low 2 θ region where magnetic reflections are visible which disappearat 44 K and (b) shows the high 2 θ region where a splitting ofthe nuclear Bragg peaks below the transition is observable. neutron and X-ray diffraction data were refined using theprogram Fullprof based on Rietveld refinement.Magnetic susceptibility measurements were carried outon a physical properties measurement system over a tem-perature range of 4 −
300 K with an external field of10 kOe and on a SQUID magnetometer for temperaturesup to 400 K.
III. RESULTS
Figure 1 shows the temperature dependence of themagnetic susceptibility of the powder sample with an an-tiferromagnetic transition at T N = 37 . CW = − . µ exp =3 . µ B close to the spin-only value µ S / = 3 . µ B .The magnetisation curve of the single crystal, mea-sured up to 400 K (not shown), indicates a superpo- FIG. 3: (Color online) (a) Correlation of the rhombohedralunit cell in hexagonal description ( R m ) and the monoclinicunit cell ( Cm ). (b) Influence of the monoclinic angle β on thelayers. The angle is overdrawn to show the effect of distortion;actually β only deviates slightly from 90 ◦ . sition of the antiferromagnetic transition of CuCrS at T N = 37 . S at T c = 377 K. A good measure for the degree of frustration is the ra-tio | Θ CW | /T N which is in case of CuCrS only 3.16 andtherefore rather small to infer a strongly frustrated sys-tem with values usually larger than 10. Neutron powder diffraction data taken on D1A and DMCat different temperatures show strong magnetic Braggpeaks emerging below the magnetic transition, i.e. T N =37 . θ ,accessible on D1A, a splitting of nuclear Bragg peaks isalso observable, which indicates a symmetry lowering ofthe crystal structure. The pattern taken above and belowthe transition at 44 K and 10 K, respectively, are shownin Fig. 2. The pictures (a) and (b) show the refinementof the low temperature data at 10 K with two phases, nu-clear and magnetic, superimposed by the raw data pat-tern at 44 K. Above T N the Cr moments show no longrange order anymore, but localized Cr moments stillcause paramagnetic scattering. Therefore, the differencein background intensity between spectra taken at 10 Kand 44 K at low angles 2 θ (Fig. 2(a)) can be explainedby an angle dependence of the paramagnetic scatteringdue to the magnetic form factor. The effect is negligibleat higher angles 2 θ (Fig. 2(b)).The structural transition indicated by a splitting of thenuclear Bragg peaks in the low temperature phase couldbe identified as a symmetry lowering from rhombohe-dral space group R m (160) to monoclinic space group Cm (8). The relation between both unit cells is given inFig. 3, as well as a visualization of the monoclinic angle β .The introduction of a monoclinic angle β causes a slightshear movement of the layers in the ab -plane. Lattice pa-rameters and crystal symmetry at 300 K and 10 K takenat the SLS-MS beamline are listed in Table I. Refine-ments with space group Cm describe the splitting of theBragg peaks in the nuclear phase very well (see Fig. 2(b)).Above the phase transition all three lattice parameters,depicted in Figs. 4(a) to 4(c), decrease with tempera- FIG. 4: (Color online) Temperature evolution of the latticeparameters a, b and c corresponding to (a) to (c), extractedfrom synchrotron data, in monoclinic description Cm . Forbetter comparability the refinements for T >
37 K wereperformed in the monoclinic description with β = 90 ◦ and a = √ b . (d) shows the refined weight percentage of boththe high temperature R m phase and the low temperature Cm phase through the transition. The error bars are smallerthan the symbols. ture. Upon further cooling a and c show a discontinuousjump towards lower values, whereas b increases quickly.The complementarity of the in-plane lattice constants a and b will later be explained by a distortion of the Crhexagon. TABLE I: Lattice parameters of CuCrS , refined with spacegroup R m at 300 K and Cm at 10 K. Data were collectedat the SLS-MS beamline with wavelength λ = 0 . R m Cm Nr. 160 8rhombohedral monoclinic a [˚A] 3.484543(4) 5.99923(1) b [˚A] 3.484543(4) 3.491502(5) c [˚A] 18.71878(2) 18.64794(3) α [ ◦ ] 90 90 β [ ◦ ] 90 89.93727(8) γ [ ◦ ] 120 90 R Bragg [%] 4.13 3.83
The refinement of magnetic intensities was done with amagnetic propagation vector documented earlier whichwas redefined on the monoclinic lattice and fits well tothe magnetic Bragg peaks (see Fig. 2(a)). The propaga-tion vector k = ( − . , − . , .
25) in relative lengthunits (r.l.u.), describes a three-dimensional helical ar-rangement of magnetic moments originating from Cr FIG. 5: (Color online) Intensity of the strongest magneticBragg peak at 2 θ = 13 . ◦ (squares) and the monoclinic an-gle β (circles) as a function of temperature, extracted fromneutron powder diffraction data taken on D1A. While coolingthe sample, the ordering of magnetic moments and the latticedistortion set in simultaneously. ions. The best fitting results were obtained with nomagnetic moment on the Cu atoms, from which we con-clude that Cu is in oxidation state Cu + , correspondingto the stoichiometry of the sample. Neutron single crys-tal diffraction experiments were performed on IN3 (ILL)and TriCS (SINQ) to confirm the rather unusual mag-netic propagation vector and to avoid artifacts from thepowder refinement. Magnetic Bragg peaks were found atseveral positions in 3D reciprocal space, corresponding tothe propagation vector obtained from powder measure-ments and verified the incommensurate magnetic struc-ture. The intensity of all magnetic peaks, including thestrongest (003)- k , vanishes at T N = 37 . M s ∼ √ I closeto the phase transition. The values are 0.08(4) for thepowder compared to 0.5(1) for the single crystal. Thisis possibly due to an internal magnetic field in the singlecrystal caused by the ferromagnetic impurity CuCr S which slows down the transition. The magnetic inten-sity is saturated for T <
30 K. Since T N and k coin-cide for powder and single crystal in both susceptibilityand diffraction data, we conclude that the presence ofCuCr S does not disturb the measurement of the mag-netic structure in CuCrS at low temperatures.A detailed analysis of the D1A powder data revealedan interesting coupling between magnetic ordering andstructural distortion. The temperature dependencies ofthe magnetic intensity in the strongest Bragg peak at2 θ = 13 . ◦ and the monoclinic angle β show reversebehavior, depicted in Fig. 5. As the sample is cooledbelow T N the magnetic ordering sets in and a deforma-tion of the lattice develops simultaneously, expressed bya monoclinic angle β deviating from 90 ◦ . Although the FIG. 6: (Color online) Temperature dependence of in-planeCr-Cr bonds measured by synchrotron powder diffraction. In-set: Different kinds of chromium bonds and their influence onthe distortion. The deformation is overdrawn for better illus-tration. deviation of β from a higher symmetric value seems tobe tiny it is crucial to solve the low temperature crystalstructure. Figure 5 shows the mutual influence of latticedistortion and magnetic ordering.Additional to the interlayer shear movement, anothertype of intralayer structural distortion was identifiedfrom synchrotron powder measurements at the SLS-MSbeamline. At high temperatures the in-plane chromiumlattice describes a symmetric hexagon. Upon coolingthe symmetric chromium environment distorts, such thatfour of the six equal Cr-Cr bonds contract and two elon-gate. This causes a flattening of the hexagon, as schemat-ically shown in the inset of Fig. 6, and leads to nearest-neighbor ( d ) and next nearest-neighbor ( d ) Cr-bonds.The Cr-Cr distances d and d show the same tempera-ture evolution as the interlayer distortion (see Fig. 6). Inaddition, d coincides with the lattice parameter b , whichexplains its unconventional temperature dependence be-low T N .These two types of distortions, the interlayer shearmovement by an angle β and the intralayer hexagonalsymmetry breaking, seem to play an important role forthe magnetic ordering. The system is able to select amagnetic ground state due to the relief of geometricalfrustration. IV. DISCUSSION
The analysis of the diffraction pattern at different tem-peratures shows an abrupt change of Cr-Cu (lattice pa-rameter c ) and Cr-Cr distances ( d ) below the phase tran-sition. Usually a contraction causes strain in the latticewhich is proportional to the square of the atomic dis-placement u and increases elastic energy ∼ u . A phasetransition has to be energetically favorable, which meansthat the gain in elastic energy must be compensated. Us-ing the example of the phase transition in solid oxygen,Rastelli et al. state that a first-order transition is fea-sible when the ground-state energy of the rhombohedralphase equals the ground-state energy of the monoclinicphase. Synchrotron powder diffraction data confirm afirst-order transition in CuCrS identified from a resid-ual rhombohedral R m phase even at the lowest tem-perature, depicted in Fig. 4 (d). Mixed-phase regimesare characteristic for first-order phase transitions . Thismay explain the deviation of the critical exponent 0.08(4)from common models (Ising, XY or Heisenberg), since itis merely defined for second-order phase transitions. Areduction of the total free energy can only be achievedby a decrease in magnetic energy. For discussion we as-sume three different magnetic exchange paths in CuCrS comprising in-plane nearest-neighbors J (along d , seeFig. 6) and next nearest-neighbors J (along d ) andinter-plane exchange J .The intralayer exchange integrals J and J can have twoorigins, a direct antiferromagnetic interaction of neigh-boring Cr ions or an indirect superexchange interactionvia S − which would be ferromagnetic due to the Cr-S-Cr angle of 90 ◦ . The susceptibility curve shows antifer-romagnetic behavior, and we can therefore neglect theferromagnetic superexchange path. Interlayer exchangeis presumably mediated by Cu + ions through the pathCr-S-Cu-S-Cr. It needs to be taken into account to ex-plain the three-dimensional magnetic structure. The con-traction of Cr-Cu bonds through the transition seems toprovide evidence for the important role of the interlayerCr-Cu-Cr exchange path. The ratio between the in-planeand inter-plane exchange constants can be calculated fora rhombohedral antiferromagnet with a helical propaga-tion vector. For CuCrS we find a ratio J /J = 2,which would imply a very strong inter-plane coupling,but this value needs to be confirmed by inelastic neutronscattering.The in-plane distortion of the high temperature symmet-ric Cr -hexagon consists of a deformation where fournearest-neighbors move towards the central Cr ion and two nearest-neighbors move away. The transition takesplace in order to maximize magnetic energy, as was foundin solid oxygen . The two different kinds of intralayerCr-Cr distances d and d (Fig. 6) may be evidence forthe formation of magnetic clusters in CuCrS , which issupported by preliminary neutron scattering results. Ithas been found that localized magnetic excitations occuradditionally to standard spin waves branches in the spec-tra. To our knowledge the formation of magnetic clus-ters in triangular antiferromagnets with spin-lattice cou-pling has only been theoretically described so far. Thisphenomenon makes CuCrS an interesting candidate forstudying new magnetic effects on frustrated lattices. V. CONCLUSION
From the quasi two-dimensional layered structure ofCuCrS one would expect a low dimensional magneticordering due to the van der Waals gap between magneticCr layers. Nevertheless, our measurements show un-ambiguously that magnetic moments in CuCrS order ina fully three-dimensional manner with a helical magneticpropagation vector k = ( − . , − . , . R m to monoclinic Cm at T N = 37 . has been identified asmagnetoelastic material. The system is therefore an in-teresting candidate for studying spin-lattice effects on atriangular lattice. VI. ACKNOWLEDGMENT
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