Characterization of the Spin-1/2 Linear-Chain Ferromagnet CuAs 2 O 4
K. Caslin, R. K. Kremer, F. S. Razavi, A. Schulz, A. Muñoz, F. Pertlik, J. Liu, M.-H. Whangbo, J. M. Law
aa r X i v : . [ c ond - m a t . m t r l - s c i ] J a n Characterization of the Spin-1/2 Linear-Chain Ferromagnet CuAs O K. Caslin,
1, 2, ∗ R. K. Kremer, F. S. Razavi, A. Schulz, A.Mu˜noz, F. Pertlik, J. Liu, M.-H. Whangbo, and J. M. Law Max-Planck-Institut f¨ur Festk¨orperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany Brock University, 500 Glenridge Ave., St. Catharines, Ontario L2S-3A1, Canada MALTA Consolider Team, Departamento de F´ısica Fundamental II,and Instituto de Materiales y Nanotecnolog´ıa, Universidad de La Laguna, La Laguna 38205, Tenerife, Spain Vienna University of Technology, Institute of Mineralogy and Crystallography, Althanstr. 14, A-1090 Wien, Austria Department of Chemistry, North Carolina State University, Raleigh, North Carolina 27695-8204, U.S.A. Hochfeld-Magnetlabor Dresden, Helmholtz-Zentrum Dresden-Rossendorf, D-01314 Dresden, Germany (Dated: May 27, 2018)The magnetic and lattice properties of the S =1/2 quantum-spin-chain ferromagnet, CuAs O ,mineral name trippkeite, were investigated. The crystal structure of CuAs O is characterizedby the presence of corrugated CuO ribbon chains. Measurements of the magnetic susceptibility,heat capacity, electron paramagnetic resonance and Raman spectroscopy were performed. Ourexperiments conclusively show that a ferromagnetic transition occurs at ∼ Ab initio
DFTcalculations reveal dominant ferromagnetic nearest-neighbor and weaker antiferromagnetic next-nearest-neighbor spin exchange interactions along the ribbon chains. The ratio of J nn / J nnn is near-4, placing CuAs O in close proximity to a quantum critical point in the J nn - J nnn phase diagram.TMRG simulations used to analyze the magnetic susceptibility confirm this ratio. Single-crystalmagnetization measurements indicate that a magnetic anisotropy forces the Cu spins to lie inan easy plane perpendicular to the c -axis. An analysis of the field and temperature dependentmagnetization by modified Arrott plots reveals a 3d-XY critical behavior. Lattice perturbationsinduced by quasi-hydrostatic pressure and temperature were mapped via magnetization and Ramanspectroscopy. PACS numbers: 61.50.Ks, 75.40.-s, 75.30.Et, 75.40.Cx, 75.50.Dd, 76.30.-v, 78.30.-j
I. INTRODUCTION
Low dimensional magnetic Cu systems containingCuX ribbon chains have attracted a great deal of at-tention because of their unusual intrachain nearest- andnext-nearest neighbor spin exchange relations. In suchcompounds it is frequently found that the spin exchangeinteractions between the Cu ( S =1/2) ions are suchthat the next-nearest-neighbor (NNN) exchange is an-tiferromagnetic (AFM), the nearest-neighbor (NN) ex-change is ferromagnetic (FM), and the NNN spin ex-change is often considerably stronger than the NN spinexchange. Due to the inherent competition of the NNand NNN spin exchange interactions, the CuX ribbonchains tend to develop unusual AFM incommensuratespiral spin structures and sometimes concomitantlymultiferroic behavior. These CuX ribbon chains areformed by linking CuX basal-square-planes of axiallyelongated CuX (X = O, Cl, Br,...) octahedra togethervia their trans-edges.The magnetic properties of the CuX ribbon chainsare primarily determined by the ratio of the NN toNNN spin exchange parameters, J nn and J nnn , with α = J nn / J nnn . However, at low temperatures additionalinteractions (e.g., smaller interchain spin exchange in-teractions) also become important. Interchain interac-tions usually drive the systems to long-range magneticorder, the exact details of which are often determinedby additional weak magnetic anisotropies. Over the last decade, much interest has been devoted to such rib-bon chain systems with spin exchange parameters lyingwithin the so-called frustrated regime, i.e., between theMajumdar-Ghosh point, α = 2, and the ’FM point’, α = -4. A first-order phase transition to a FM ground isexpected at α = -4 and hence, it constitutes a quantumcritical point (QCP) in the vicinity of which small per-turbations, such as interchain exchange and anisotropicexchange couplings, may induce a pronounced responseof the system. Several CuO ribbon chain systems with α ∼ -4 havebeen investigated, none of which undergoes long-rangeFM ordering at low temperatures. Some systems, suchas Li ZrCuO and PbCuSO (OH) (linarite), preventlong-range FM ordering since they exhibit an AFMincommensurate spin-spiral structure along the ribbonchains. Other systems, such as Ca Y Cu O and Li CuO , do contain FM ribbon chains, how-ever, weak interchain interactions force the FM-ribbonchains to align antiparallel, resulting in long-range AFMordering. In the case of Li CuO , the absence of aspiral magnetic order in the ribbon chains is understoodto be a consequence of order by disorder arising from in-terchain interactions. In all these cases, it appears thateither magnetic spiral ordering or weak interchain inter-actions drive the systems to long-range AFM ordering.It also appears to be possible for such systems not toexhibit a magnetic long-range ordering at all. For exam-ple, the system Rb Cu Mo O , with α ∼ -2.7, does notundergo long-range magnetic ordering down to 2 K eventhough magnetic field induced ferroelectricity is observedbelow 8 K. Here we describe the magnetic and lattice propertiesof a new system, trippkeite, featuring edge-sharing CuO ribbon chains. Trippkeite is an exceptional ribbon chainsystem because it shows a FM ground state below ∼ O . A first investigation and descriptionof the crystal structure of natural trippkeite, by Zemannin 1951, was based on the assumption that trippkeite isisotypic to schafarzikite, FeSb O . In 1975, Pertlik em-ployed hydrothermal synthesis to prepare small crystalsof synthetic trippkeite and performed a full crystal struc-ture determination which confirmed Zemann’s earlier re-sults (see Figure 1).
This investigation showed thattrippkeite is isostructural to the family of compoundswith the general composition MT O (M = Mg, Mn,Fe, Co, Ni, Zn; T = As, Sb, Bi), with schafarzikite,FeSb O , being the most popular member. Trippkeite crystallizes in a tetragonal structure (spacegroup P / mbc ) with lattice parameters a = b = 8.592(4)˚A and c = 5.573(4) ˚A. The Cu atoms are located onWyckoff sites 4 d and the As atoms on sites 8 h . The Oatoms occupy Wyckoff sites 8 g (O1) and 8 h (O2). The Cuatoms are coordinated by elongated oxygen octahedra(Cu - O distances: 4 × × ribbons.The O1 and O2 atoms are located at the apical and basalpositions of the octahedra, respectively. The As atomsform AsO pyramids, which link the oxygen atoms in thebasal planes with the apical oxygen atoms of neighboringchains such that the basal planes of neighboring chainsare perpendicular to each other. The 4 s electrons ofthe As atoms act as pseudo-ligands and extend into thechannels enclosed by four neighboring chains. Similarspacious structures are known to have a high suscepti-bility to structural phase transitions that can be inducedby external pressure. II. EXPERIMENTAL DETAILS
Small wine-bottle-green crystals of CuAs O , approx-imately 1 × − mm in size, were prepared by hy-drothermal synthesis as described in detail by Pertlik. Some of the crystals showed brownish impurity ap-pendages, such crystals were discarded. Sample puritywas checked by X-ray powder diffraction on crushed crys-tals. A STOE STADI-P diffractometer with Mo Kα radiation, λ = 0.7093 ˚A, was used.Temperature and magnetic field dependent magneti-zations were measured with a Quantum Design, super-conducting quantum interference device magnetometer(MPMS). A selection of randomly oriented crystals (mass ∼ FIG. 1: (color online) (a) Projection along the [001] directionof the trippkeite crystal structure . The Cu atoms are repre-sented by the large (green) spheres, the oxygen atoms by small(red) spheres, and the As atoms by (grey) medium spheres.(b) A corrugated chain of trans-edge connected CuO octa-hedra highlighting the twisted basal planes of the octahedrain CuAs O , which lead to a corrugation of the CuO ribbonchains. collected on a well defined large single crystal (mass 8 ± µ g), oriented by x-ray diffraction with the c -axis par-allel and perpendicular to the magnetic field.Magnetization measurements under pressure were per-formed in a copper-beryllium pressure clamp cell provid-ing hydrostatic pressure up to 1.2 GPa and using siliconoil as a pressure medium. The pressure was determinedfrom the superconducting critical temperature of a highpurity (99.999%) Sn sample located next to the CuAs O sample within the pressure cell. Heat capacity measurements were performed in aQuantum Design, physical property measurement systemcalorimeter (PPMS). A collection of randomly orientedcrystals (mass ∼ ∼ − spectral resolution. The spectrometer setup wasequipped with a double super razor edge filter, Peltiercooled CCD camera and a Mikrocryo cryostat with acopper cold finger. Measurements were performed withlinearly polarized He/Ne gas laser light of 632.817 nmwith < µ m spot on the top surface of the sample using a mi-croscope. Orientated measurements were taken paralleland perpendicular to the c -axis in temperatures rangingbetween 4 K and 325 K.Electron paramagnetic resonance (EPR) measure-ments were carried out with a Bruker ER040XK X-band microwave spectrometer and Bruker BE25 mag-net controlled by a BH15 field controller calibrated withDiphenylpicrylhydrazyl (DPPH). The spectra of a selec-tion of non-oriented crystals (mass ∼ ∼ III. THEORETICAL DETAILSA. Spin Exchange Interactions
The intrachain spin exchange interactions, J nn and J nnn , of CuAs O were evaluated by performing energy-mapping analyses based on first principles DFT cal-culations for the three ordered spin states depicted inFigure 2. The energies of the three order states can bewritten in terms of the Heisenberg spin Hamiltonian; H = − X J ij ~ S i ~ S j , (1)where J ij are the exchange parameters for the couplingbetween spin sites i and j . According to the energy ex-pressions for spin dimers with N (= 1 in this case) un-paired spins per spin site , the total spin exchange en-ergies of the three ordered spin states, per eight formulaunits (FUs), are expressed as summarized in Figure 2.We calculated the electronic energies of the three orderedspin states by employing the projected augmented-wave(PAW) method encoded in the Vienna ab initio sim-ulation package (VASP) and the generalized gradientapproximation (GGA) for the exchange and correlationfunctional. The plane-wave cut-off energy was set to400 eV and a set of 18 k -points for the irreducible Bril-louin zone was used. To probe the effect of electron cor-relations associated with the Cu 3 d state, we performedDFT plus on-site repulsion (DFT+ U ) calculations with U eff = 0, 4, 6 and 8 eV for Cu. By mapping the rel-ative energies of the three ordered spin states obtainedfrom our DFT+ U calculations onto the correspondingHeisenberg Hamiltonian (Eq. (1)), we obtain the valuesof the nearest- and next-nearest neighbor spin exchangeparameters, J nn ( ≡ J ) and J nnn ( ≡ J ).The results summarized in Table I show that the FM-NN spin exchange dominates over the AFM-NNN spinexchange. As shown in Figure 3, the ratio of the NNover the NNN spin exchanges increases with increasing U eff values used in the DFT+ U calculations. In general,the spin exchange J between two spin sites (say, 1 and 2represented by the magnetic orbitals Φ and Φ , respec-tively) is written as J = J F + J AF . The FM component J F increases when increasing the overlap density Φ Φ C FIG. 2: (color online) Three order spin states of CuAs O used to determine the values of J nn ( ≡ J ) and J nnn ( ≡ J )by DFT+ U calculations. Only the Cu sites are shown forsimplicity. The unfilled and filled circles represent up-spinand down-spin Cu sites, respectively.TABLE I: Values of the NN and NNN spin exchange con-stants, J nn and J nnn , respectively, obtained from the DFT+ U calculations along with the Curie-Weiss temperatures calcu-lated using Eq. (2). U eff (eV) J nn (K) J nnn (K) Θ CW (K)0 42.3 -25.9 8.24 38.8 -13.5 12.76 34.0 -10.0 12.08 27.5 -7.1 10.2 while the AFM component J AF is proportional to t andinversely proportional to U eff . The magnetic orbital, x - y orbital, of the Cu ion has large O 2 p contri-butions. The strong FM-NN interaction in CuAs O istraced to the fact that the bond angle of the Cu-O-Cusuperexchange path is close to 90 ◦ ( ∼ ◦ ) and the mag-netic orbitals of the NN Cu ions lead to a large overlapdensity around the bridging oxygen atoms. The weakerAFM-NNN interaction is a consequence of the twistingof the CuO ribbon chains since it reduces the hoppingintegral between the NNN Cu ions.The Curie Weiss temperatures listed in Table I werecalculated with the equation,Θ CW = 13 S ( S + 1) X i z i J i . (2)The J i ’s represent the NN and the NNN spin exchange in-teractions along the ribbon chains, J nn and J nnn , respec-tively. z i is the number of neighbors with spin exchange J i in the NN and NNN shell, z nn = z nnn = 2 for CuAs O .Θ CW is positive if the spin exchange is predominantlyFM. The calculated Curie-Weiss temperatures are posi-tive, consistent with the experimental findings (see be-low). The U eff values of 6 and 8 eV, most appropriatefor Cu , indicate -3.9 < α < -3.4 (see Fig. 3), close tothe FM-QCP at α = -4. Since the x - y magnetic or-bitals of neighboring ribbon chains are largely orthogonalto each other, the interchain spin exchange interactionsare expected to be small and not easily accessible withDFT calculations. J nn / J nnn U eff (eV) FIG. 3: (color online) The ratio of the NN to NNN spin ex-change constants of CuAs O calculated from the DFT+ U calculations as a function of U eff . The plot displays the dom-inance of the FM J nn term over the AFM J nnn term. B. TMRG Calculations
The temperature dependent magnetic susceptibili-ties, χ ∗ (see Figure 4), of a NN–NNN spin exchange,Heisenberg S =1/2 spin-chain was simulated via transfer-matrix density-matrix renormalization group (TMRG)calculations, as implemented by Wang et al . A con-sistent set of parameters was used for the simulations of χ ∗ in the reduced temperature range 0.1 ≤ T /J nnn ≤ α range -4.50 ≤ J nn /J nnn ≤ -3.50. 150 stateswere kept with H/J nnn =0.001, J nnn = 1 and a maximumtrotter number of 4000. No difference was seen between250 and 150 states down to T /J nnn =0.1 (not shown here),as such, 150 states were retained. J nn /J nnn = -3.50 J nn /J nnn = -3.75 J nn /J nnn = -4.00 J nn /J nnn = -4.25 J nn /J nnn = -4.50 * T/J nnn
FIG. 4: (Color online) TMRG spin susceptibilities, χ ∗ ,versus temperature for various ratios of the NN to NNNspin exchange interactions as indicated in the inset. χ ∗ = χ mol J nnn / N A µ g . C. Lattice Properties
The lattice properties were obtained from DFT calcu-lations using the VASP code combined with the phononpackage. The PAW scheme within the VASP packageaccommodates the full nodal character of an all-electroncharge density in the core region. To achieve highly con-verged results with an accurate description of the elec-tronic and dynamical properties, basis sets with planewaves up to a 520 eV cut-off energy were used. A GGAwith PBEsol prescription was utilized to describe theexchange-correlation energy. In order to obtain highlyconverged energies and forces, a dense special k -pointsampling for the integration of the Brillouin zone wasperformed. At each selected volume, the structures werefully relaxed to their equilibrium configurations throughthe calculation of the forces on the atoms and stresstensor. Lattice-dynamic calculations of phonon modeswere performed at the zone center (Γ-point) of the Bril-louin zone using the direct force-constant approach (orthe supercell method). These calculations provide in-formation about the symmetry of the modes and their po-larization vectors, and also allowed us to identify the irre-ducible representations and the character of the phononmodes at the Γ-point. The calculated Raman frequencieswith their assigned symmetries are listed in Table II incomparison to the experimental observations.To gain more insight on the lattice properties ofCuAs O , DFT-GGA and LDA calculations were per-formed for a hypothetical, diamagnetic compoundZnAs O , discarding any magnetic contributions. Figure5 displays the total and partial phonon densities of statesof the hypothetical compound ZnAs O . The phononspectrum is characterized by a set of rather sharp bandsindicating nearly localized lattice vibrations extendingup to ∼
800 cm − . The set of phonon bands decomposesinto three subgroups, one group below ∼
300 cm − , cor-responding mainly to Zn and As vibrations with littlecontribution from O vibrations. Above ∼
300 cm − twogroups of phonon bands corresponding mainly to O vi-brations with almost no contribution from the heavierZn and As atoms. Vibrations related to O atoms in thebasal plane of the distorted octahedra (O2) exhibit thehighest vibrational frequencies. IV. RESULTS AND DISCUSSIONA. Raman Scattering
Raman spectroscopy is a sensitive technique which canbe used to search for structural transformations. Ramanspectra with light polarized along the crystal c -axis weremeasured for various temperatures between 4 K and 325K, see Figure 6. Our spectra are similar to that takenat room temperature by Kharbish with the exceptionof two additional peaks detected. Table II lists the re-sults of the CuAs O Raman spectra in comparison with
FIG. 5: (color online) Total and partial phonon densities ofstates of a hypothetical compound ZnAs O per unit cell. data from Kharbish. The peak positions and symmetryassignments according to the GGA-LDA calculations arealso given. As frequently observed for GGA and LDAcalculations, the difference between the calculated andexperimental wavenumbers is ∼ ∼ − (marked by arrows in Figure 6) becomenarrower and better resolved with decreasing tempera-ture. I n t en s i t y ( c oun t s / s ) Raman Shift (cm -1 ) R a m an S h i ft ( c m - ) T (K)
FIG. 6: (color online) Raman spectra of CuAs O at varioustemperatures as indicated. The spectra have been shifted forclarity. The inset shows a typical down shift with increasingtemperature of the 371.3 cm − peak, attributed to latticeexpansion. A contraction of the lattice will shorten the spin ex-change paths, r i , between Cu spins and also alter the TABLE II: Comparison of the Raman peak positions withthose found by Kharbish and those obtained from GGA-LDA calculations. The notation n.o. indicates a peak whichwas not observed. Kharbish reported two peaks at 359 and461 cm − which were not found in the current study.Symmetry 295 K Kharbish(RT) GGA LDA(GGA-LDA) (cm − ) (cm − ) (cm − ) (cm − ) B g n.o. n.o. 23.2 28.9 E g n.o. n.o. 32.5 35.3 E g n.o. n.o. 98.9 105.3 E g A g n.o. n.o. 123.6 128.6 B g B g E g A g B g B g E g B g A g n.o. n.o. 364.3 370.9 E g B g B g E g A g n.o. n.o. 477.4 481.3 E g B g n.o. n.o. 509.9 514.2 E g B g A g B g B g bonding angles, possibly differently for J nn and J nnn ,which may lead to a small alteration of α . However, asevidenced by the low-temperature bulk properties shownbelow, the ferromagnetic spin exchange remains domi-nant leading to long-range FM ordering. B. Electron Paramagnetic Resonance
A typical EPR spectrum of a polycrystalline CuAs O sample collected at 15 K and at a microwave frequencyof 9.48 GHz is displayed in Figure 7. The spectrum canbe very well modeled by a field derivative of a Lorentzianabsorption resonance line taking into account ± ω reso-nances. The equation used to fit the spectra is as follows dP abs dH ∝ ddH ( ∆ H + δ ( H − H res )( H − H res ) + ∆ H + ∆ H + δ ( H + H res )( H + H res ) + ∆ H ) , (3)where P abs is the absorbed microwave power, ∆ H is thehalf-width at half-maximum (HWHM), H res is the reso-nance field, and δ measures the degree of admixture ofdispersion to the signal. Additionally, a background off-set and a linear variation of the background signal withthe field were taken into account for the fits. Very goodagreement to Eq. (3) with the data could be achieved for δ = 0, as seen in Figure 7. The addition of a dispersionterm ( δ = 0) was not beneficial to the fits. The insetin Figure 7 shows how the g -factor varies with temper-ature. Towards room-temperature the averaged g -factorwas calculated to be g = 2 . ± . . This value is close to the expected average g -factor for aCu, S = 1/2 system in an elongated octahedral environ-ment and gives an effective magnetic moment of µ eff =1.82 µ B . An analysis of the inverse EPR intensity ver-sus temperature ( T &
150 K), shown in Figure 8, with aCurie-Weiss type temperature of Θ
EPR ∼
40 K. The pos-itive Θ
EPR indicates a predominant FM spin exchangein accordance with the positive magnetic susceptibilityCurie-Weiss temperature (see below) and the DFT cal-culations. Below ∼
150 K the inverse integrated intensitybends upwards, away from the Curie-Weiss type fit. Asimilar behavior is also seen in the inverse susceptibilitydata and discussed in detail below. The temperature de-pendence of the linewidth, shown in the Figure 8 inset,displays a broadening with temperatures above ∼
50 K.Below ∼
50 K the linewidth decreases which we attributeto a build-up of internal fields caused by magnetic shortrange ordering. These can also be a source of the temper-ature variation of the g -factor along with minute changesof the crystal field due to the lattice contractions. EP R ab s . de r i v a t i v e ( a r b . un i t s ) H (T) g - F a c t o r T (K) FIG. 7: (color online) An EPR spectrum of a polycrystallineCuAs O sample collected at 15 K with a microwave fre-quency of 9.48 GHz. The (red) solid line is a fit of the fieldderivative of the microwave power absorption with a singleLorentzian resonance line according to Eq. (3). The insetdisplays the g -factor variation with temperature. C. Magnetization and Magnetic Susceptibility
The magnetic susceptibility as a function of tempera-ture of a randomly oriented selection of CuAs O crystals FIG. 8: (color online) Reciprocal intensities of the EPR res-onance lines of a polycrystalline CuAs O sample obtainedfrom the fits. The (red) solid line is a linear fit of the in-tensity with a Curie-Weiss like temperature dependence. Theinset displays the resonance linewidth (FWHM) broadeningwith temperature. is displayed in Figure 9. At high temperatures the mag-netic susceptibility follows a Curie-Weiss law accordingto χ mol = CT − Θ CW + χ . (4)The Curie constant, C , depends on the Avogadro num-ber N A , the spin of the system S =1/2, the Boltzmannconstant k B , the g -factor g , and the Bohr magneton µ B according to C = N A g µ B2 S ( S + 1) / k B . (5)The temperature independent term in Eq. (4), χ , repre-sents a sum of the diamagnetic contributions, χ dia , fromthe closed electron shells and the van Vleck susceptibility, χ VV , arising from admixtures of the ground state wavefunctions into excited Cu electronic levels. χ = χ dia + χ VV . (6)From the tabulated diamagnetic increments for individ-ual ions, χ dia can be estimated to contribute -77 × − cm /mol. The van Vleck susceptibility depends onthe direction of the external field with respect to thecrystal axes and the energy level separation. For apolycrystalline Cu system, it typically amounts tovalues between +100 × − cm /mol and +120 × − cm /mol, resulting in a χ of approximately +43 × − cm /mol. The (red) solid line in Figure 9 shows a fit of the ex-perimental inverse susceptibility to Eq. (4) obtained byvarying the g -factor and the Curie-Weiss temperature.The best fit to the data above ∼
150 K was found with g = 2 . ± . . The Curie-Weiss temperature from the fit wasΘ CW = 39 ± , indicating predominant FM spin exchange interactions,as also found by the EPR measurement.The slight difference in the g -factor obtained by themagnetic susceptibility measurement to that derivedfrom the EPR measurement (see above) may be causedby unavoidable experimental errors and/or a minor g -factor anisotropy . FIG. 9: (color online) Reciprocal magnetic susceptibility of apolycrystalline CuAs O sample measured in a field of 1 T.The solid (red) line is a fit of the Curie-Weiss law (Eq. (4)) tothe data above 150 K. The lower inset shows the data below20 K, collected at 0.01 T, in an enlarged scale. The upperinset displays the magnetization versus field collected at 1.85K. Below ∼ T C , obtained from the inflection pointof the susceptibility curve amounts to T C = 7 . ± . . An isothermal magnetization measured at 1.85 K, plot-ted in the upper inset of Figure 9, reveals saturation ofthe magnetization above a field of ∼ ± µ B . This saturation moment is in good agree-ment with the expected ∼ µ B value for a S =1/2 system.Below ∼
150 K the inverse susceptibility noticeablybends upwards from the high-temperature Curie-Weisslaw, similar to what has also been observed in the inte-grated signal intensity gained from the EPR spectroscopyexperiment. The temperature dependence of the suscep-tibility over the whole temperature range, including theupward deviation from the high-temperature Curie-Weisslaw, can be well modeled by the magnetic susceptibility of a Heisenberg chain with NN and NNN spin exchangeinteractions calculated with the TMRG code as describedin detail above. Figure 10 displays our experimental datain comparison with the TMRG susceptibility results cal-culated for ratios -4.5 ≤ J nn /J nnn ≤ -3.5, a ferromagneticNN spin exchange constant of J nnn ∼ -38 K and a g -factorof g TMRG =2.155, very close to the g -factor obtained fromthe Curie-Weiss fit of the high-temperature susceptibilitydata. FIG. 10: (color online) The inverse experimental suscepti-bility shown in Figure 9 (corrected by a temperature inde-pendent part χ = 43 × − cm /mol) compared with theresults of the TMRG calculations, solid (red) line, for the ra-tio J nn / J nnn = -4.25 (main frame). The inset displays theTMRG results, solid (red) lines, for J nn / J nnn = -3.5, -3.75,-4, -4.25, -4.5 (from top to bottom). For all theoretical curves J nnn = -38 K and a g -factor of 2.155 was used. For furtherdetails see text. Figure 11 displays the magnetization at 1.85 K of asingle crystal (8 ± µ g) oriented with the c -axis paralleland perpendicular to the magnetic field. With the fieldperpendicular to the c -axis, saturation is readily achievedabove ∼ c -axis,saturation is not obtained at 1 T indicating the c -axisto be a magnetic hard axis. The saturation moment isin fair agreement with an expected value of ∼ µ B , theslight excess can be attributed to errors in the mass de-termination of the crystal. D. Modified Arrott plots
An Arrott plot analysis of magnetization isotherms of aFM is a well-established method to determine the Curietemperature, T C , and the zero-field magnetic polariza-tion. Arrott and Noakes proposed a modified equationof state which takes into account the critical exponents, β and γ , of the magnetization and the magnetic suscepti-bility, respectively. The Arrott-Noakes equation of state FIG. 11: (color online) Magnetization of an oriented CuAs O single crystal measured at 1.85 K with the magnetic field H k c -axis and H ⊥ c -axis. is given by ( µ H/M ) /γ = ( T − T C ) /T + ( M/M ) /β . (7) T and M are material constants which for CuAs O amount to T = 0.04 ± M = 1.42 ± M /β versus ( µ H/M ) /γ , with the criticalexponents adjusted such that the isotherms close to theCurie temperature follow a linear behavior. Such a mod-ified Arrott-Noakes plot of CuAs O is shown in Figure12. The critical isotherm, which extrapolates to the ori-gin of the graph, lies between the isotherms measuredat 7.00 K and 7.50 K. The best agreement with linearbehavior for the isotherms near T C was obtained by ad-justing the critical exponents to β = 0 . ± . , and γ = 1 . ± . . The critical exponent β for the magnetization is con-sistent with values for standard universality classes 3d-Heisenberg and 3d-XY, but within the experimental er-ror does not allow for a differentiation between the twocases. γ is clearly lower than the value expected fora 3d-Heisenberg model but is close to the value expectedfor a 3d-XY class. This finding is consistent with theanisotropy seen in the single-crystal magnetization mea-surement indicating an easy-plane perpendicular to the c -axis (see above).Figure 13 displays the temperature dependence of thezero-field polarization as obtained by extrapolating thehigh-field data in the modified Arrott plot to H →
0. Byfitting a critical power law according to M ( T ) = M (1 − T /T C ) β , (8) FIG. 12: (color online) Modified Arrott plot of the isother-mal magnetization of a CuAs O polycrystalline sample. Thetwo solid (red) lines mark the magnetization curves measuredat 7.00 K and at 7.50 K. The dashed (blue) lines mark theisotherms used to extract the zero-field magnetic polarizationplot. with β fixed to 0.35 as shown in the Modified Arrott plot,a Curie temperature of T C = 7 . ± . FIG. 13: (color online) Temperature dependence of the zero-field magnetic polarization of CuAs O . The data points wereobtained from the intersections with the ordinate of the lin-early extrapolated high-field branches in the modified Arrottplot (i.e. H → T C with a fixedcritical exponent β = 0.35. E. Pressure Dependence of T C Pressure measurements of schafarzikite, FeSb O , ini-tially showed the cell lattice parameters to decrease lin-early for pressures below 3.5 GPa. At approximately3.5 GPa and 7 GPa, structural phase transitions oc-curred, inducing a symmetry reduction from spacegroups P / mbc via P / c to P / m . Figure 14 displays the pressure dependence of the T C of CuAs O . The T C increases linearly with pressure ata rate of 1 . ± . / GPa . Evidence for pressure induced phase transitions has notbeen found up to 1.2 GPa. T c ( K ) Pressure (GPa) M / M s a t Temperature (K)
FIG. 14: (color online) Pressure dependence of the Curie tem-perature, T C , of CuAs O . The inset shows the shift of themagnetization with increasing pressures. Applying the pressure induced decrease of the latticeparameters observed for FeSb O similarly to CuAs O ,we expect apart from the reduction of the atomic dis-tances, a decrease of the NN Cu - O - Cu bonding an-gle towards 90 o . The effect of pressure on the O - O- O ’buckling’ angle, enclosed by the O atoms at theedge of the basal planes running along the c -axis, is lesspronounced. The decrease of atomic distances and thereduction of NN bonding angles will favor the FM-NNspin exchange which explains the increase of the Curietemperature observed experimentally. Applying pres-sure decreases the spin exchange ratio α , thus pushingthe system further into the ferromagnetic regime. F. Heat Capacity
The results of the heat capacity measurements per-formed on a sample of randomly oriented CuAs O crys-tals versus temperature and magnetic field are shown inFigure 15. In zero-field, a λ -shaped anomaly is clearlyexhibited at 7.4 ± O Phonon C p / T ( J / m o l K ) T (K) FIG. 15: (color online) Heat capacity of a randomly orientedensemble of CuAs O crystals versus temperature and ex-ternal magnetic field. The solid lines represent the scaledheat capacity of the hypothetical compound ZnAs O anda phonon contribution to the heat capacity as obtained byextrapolating the Debye-Einstein fit to low temperatures. heat capacity and extract the magnetic heat capacity, C mag ( T ), we proceeded in two ways: i. We approxi-mated the lattice contribution to the heat capacity ofCuAs O by fitting a superposition of a Debye-type andtwo Einstein-type heat capacity terms according to C P ( T ) = f D C Deb (Θ Deb , T )+ X i g i C Ein ,i (Θ Ein ,i , T ) . (9)The Debye-type heat capacity is given by C Deb ( T ) = 9 R ( T / Θ Deb ) Deb /T Z x exp( x )(exp( x ) − dx. (10)In order to simplify the fit procedure, a Pad´e approxima-tion for the Debye-type heat capacity proposed recentlyby Goetsch et al. was utilized. The Einstein-type heatcapacities, C Ein ,i ( T ), were calculated according to C Ein ,i ( T ) = 3 R ( E i k B T ) exp( E i /k B T )(exp( E i /k B T ) − . (11)The weights, f D , g and g , were conditioned such thatat sufficiently high temperatures the Petit-Dulong valueof 7 × R ( R is the molar gas constant) was satisfied.By fitting the weights, the Debye-temperature and twoEinstein-temperatures, the experimental heat capacityabove 20 K could be well approximated and extrapolatedto T → TABLE III: Weights and characteristic temperatures used toapproximate the lattice contribution to the heat capacity ofCuAs O according to Eq. (9).contribution weight T (K)Debye 1.5 136.59(7)Einstein, i =1 2.25 284.5(3)Einstein, i =2 3.25 789(1) ii. Alternatively, the heat capacity of the hypotheti-cal compound ZnAs O was calculated from the phonondensity of states obtained by ab initio calculations (seeabove, Figure 5) and the second derivative of the freeenergy, F ( T ). The relation is as follows C V ( T ) ≈ C P ( T ) = − T (cid:18) ∂ F ( T ) ∂T (cid:19) V , (12)where C V ( T ) and C P ( T ) are the heat capacities at con-stant volume and at constant pressure (accessible by theexperiment), respectively. F ( T ) is the free energy givenby F ( T ) = − Z ∞ ( ~ ω k B T ln[2 n B ( ω )]) ρ ( ω ) dω. (13)In Eq. (13), k B represents the Boltzmann constant, n B the Bose-Einstein factor, and ρ ( ω ) the phonon density ofstates. The high frequency cut-off of the latter definesthe upper limit of integration in Eq. (13).The extracted magnetic contribution to the specificheat was obtained by subtracting the lattice contribu-tion from the experimental results. A plot of C mag ( T ) /T versus T is shown in the Figure 16. At low temperaturesthe magnetic heat capacity follows a power law C mag ( T ) ∝ T n , (14)with n ∼ n = 3/2) contributions. Above ∼
20 K, a shoul-der becomes visible which we attribute to short-rangeordering contributions.By integrating C mag ( T ) /T , the magnetic entropy re-moved by the magnetic ordering is obtained accordingto S mag ( T ) = Z T C mag ( T ′ ) /T ′ dT ′ . (15)The magnetic entropy amounts to S mag = 4 . / molK , which is ∼
70% of the entropy expected for a S = 1/2system, S mag = R ln(2 S + 1) = R ln(2) . (16)The largest fraction of the entropy is contained in the λ -anomaly and only a minor fraction is removed by shortrange ordering, the short range ordering effects were alsoseen in the g -factor temperature dependence (see above). FIG. 16: (color online) Magnetic contribution to the spe-cific heat of CuAs O ( H = 0 T). Different symbols (redand black) indicate two independent runs of a selection ofCuAs O crystals. The inset displays the temperature de-pendence of the magnetic entropy obtained according to Eq.(15). The straight (black) line indicates a T / power law. V. CONCLUSIONS
In summary, we have investigated the magnetic andlattice properties of CuAs O , a system characterized byaxially elongated CuO octahedra linking to form CuO ribbon chains. Ab initio
DFT calculations show that thenearest-neighbor intrachain spin exchange interaction isFM with a magnitude ∼ O in the ferromagnetic regimenext to a quantum critical point between frustrated in-commensurate spin-spiral and ferromagnetic order. Acomparison of our temperature dependent magnetic sus-ceptibility data with TMRG simulations supports the ab initio calculations. Long-range FM ordering due tosmaller interchain spin exchange interactions is found be-low ∼ ∼ T C and down to 4 K. GGA and LDAcalculations of the lattice dynamics have been performedand are found to be in good agreement with the Ramanspectra.1 Acknowledgments
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