Hyperfine and crystal field interactions in multiferroic HoCrO 3
C M N Kumar, Y Xiao, H S Nair, J Voigt, B Schmitz, T Chatterji, N H Jalarvo, Th Brückel
aa r X i v : . [ c ond - m a t . s t r- e l ] S e p Hyperfine and crystal field interactions in multiferroicHoCrO C M N Kumar , , , † , Y Xiao , ‡ , H S Nair , J Voigt , B Schmitz ,T Chatterji , N H Jalarvo , , Th Brückel Jülich Centre for Neutron Science JCNS and Peter Grünberg Institut PGI,JARA-FIT, Forschungszentrum Jülich, 52425 Jülich, Germany Jülich Centre for Neutron Science JCNS, Forschungszentrum Jülich GmbH,Outstation at SNS, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831,United States Chemical and Engineering Materials Division, Spallation Neutron Source, OakRidge National Laboratory, Oak Ridge, Tennessee 37831, United States Department of Physics, Colorado State University, Fort Collins, CO 80523, USA Institut Laue–Langevin, BP 156, F–38042 Grenoble Cedex 9, FranceE-mail: † [email protected]; [email protected], ‡ [email protected] Abstract.
We report a comprehensive specific heat and inelastic neutron scatteringstudy to explore the possible origin of multiferroicity in HoCrO . We have performedspecific heat measurements in the temperature range 100 mK–290 K and inelasticneutron scattering measurements were performed in the temperature range 1.5–200 K. From the specific heat data we determined hyperfine splitting at 22.5(2) µ eVand crystal field transitions at 1.379(5) meV, 10.37(4) meV, 15.49(9) meV and23.44(9) meV, indicating the existence of strong hyperfine and crystal field interactionsin HoCrO . Further, an effective hyperfine field is determined to be 600(3) T. Thequasielastic scattering observed in the inelastic scattering data and a large linear term γ = 6 . mJmol − K − in the specific heat is attributed to the presence of shortrange exchange interactions, which is understood to be contributing to the observedferroelectricity. Further the nuclear and magnetic entropies were computed to be, ∼ . Jmol − K − and ∼
34 Jmol − K − , respectively. The entropy values are inexcellent agreement with the limiting theoretical values. An anomaly is observed inpeak position of the temperature dependent crystal field spectra around 60 K, at thesame temperature an anomaly in the pyroelectric current is reported. From this wecould elucidate a direct correlation between the crystal electric field excitations of Ho and ferroelectricity in HoCrO . Our present study along with recent reports confirmthat HoCrO , and R CrO ( R = Rare earth) in general, possess more than one drivingforce for the ferroelectricity and multiferroicity.PACS numbers: 75.40.-s, 31.30.Gs, 71.70.Ch, 28.20.Cz yperfine and crystal field interactions in multiferroic HoCrO
1. Introduction
Perovskite chromites R CrO , where R is a rare earth element or yttrium are revisited inthe recent years as possible multiferroic materials in which multiple ferroic orders such asferroelectricity and antiferromagnetism coexist as discussed below [1–8]. Compared toperovskite manganites, which are well studied in light of multiferroicity, the microscopicphysical properties of chromites are not explored in detail and the mechanism formultiferroicity in HoCrO is still under debate. The coexistence of ferroelectric andmagnetic orders in rare-earth orthochromites was first suggested by Subba Rao et al. [9].Based on dielectric studies it is reported that the heavy rare earth chromites, R CrO ( R =Ho, Er, Yb, Lu) undergo a ferroelectric transition in the temperature range − K [2]. In a recent article, electrical polarization and magnetodielectric effectstudies are reported for polycrystalline LuCrO and ErCrO [6]. Although both LuCrO and ErCrO showed the presence of a polar state induced by magnetic ordering below T N , polarization was not affected by applied magnetic fields, so that the magnetoelectriccoupling was not evident in these compounds. Further, the magnetodielectric effectobserved in the case of ErCrO is one order of magnitude higher compared with LuCrO reflecting the role of different magnetism of rare-earth cations in ferroelectricity [6].Recently, Ghosh et al ., have studied the ferroelectric properties of polycrystallineHoCrO by measuring the thermal variation of pyroelectric current [8]. It was foundthat pyroelectric current exhibits its maximum value around the antiferromagnetictransition temperature T N = 140 K, nevertheless, the ferroelectric order temperaturewhich associated with the emergence of spontaneous electric polarization is observedat a higher temperature of T ≈ K. The atypical multiferroic behavior observed inHoCrO is argued to be a result of Ho displacements and oxygen octahedral rotationsin the non–centrosymmetric P na space group [4, 8, 10, 11]. The role of the rare earthion in determining the physical properties of chromites R CrO was revealed in a recentcommunication where the origin of ferroelectricity in orthochromites has been attributedto the instability of the symmetric position of the rare earth ion [5]. The interactionbetween magnetic rare earth and week ferromagnetic Cr ions is the driving force forthe breaking of symmetry, and thus the emergence of multiferroic behavior in thesesystems [5, 7]. Despite a debatable multiferriocity, orthochromites possess a plethoraof physical phenomena, providing excellent opportunities to study and understand thebasic interactions in materials. The detailed knowledge on the properties of rare earthion is of particular importance to understand the multiferroicity in rare earth chromites R CrO .The rare earth orthochromites crystallize in a distorted orthorhombic perovskitestructure with four formula units per unit cell [12–14]. In HoCrO the exchange couplingbetween the Cr nearest neighbors is predominantly antiferromagnetic and they ordermagnetically below the Néel temperature of T N = 140 K [15]. On the other hand, earlierreports differ on the aspect of Ho-ordering. Cooperatively induced ordering of Ho inHoCrO was reported at 12 K [15, 16] whereas no ordering was observed by Hornreich yperfine and crystal field interactions in multiferroic HoCrO et.al. , down to . K [17]. Ferroelectricity is observed in R CrO systems only when the R ion is magnetic. This directly suggests the exchange interaction between Cr and R is very important in inducing polarization and warrants the study of the local distortionsaround the R ion as well as its magnetic properties. Hence, we have chosen HoCrO as our subject to investigate the role of rare earth in the magnetic and thermodynamicproperties of chromites.
2. Experimental details
Polycrystalline HoCrO was synthesized by solid state reaction of Ho O (3N) and Cr O (4N) in stoichiometric ratio. The precursors were mixed intimately and subsequentlyheat treated at 1100 ◦ C for h. Then, the material was reground and annealed againat ◦ C for h. The phase purity of the synthesized powder sample was confirmedby powder x-ray diffraction (PXRD) with Cu- K α ( λ = 1 . Å) radiation, usinga Huber x-ray diffractometer (Huber G ) in transmission Guinier geometry. Theprofiles of the PXRD data were analyzed using the Rietveld method [18] implementedin the
F ullP rof software suit [19]. This confirmed the formation of orthorhombic singlephase. The powder was then pressed into pellets and sintered at ◦ C for h forfurther magnetic and thermal characterization. The heat capacity was measured in thetemperature range from mK to K using a commercial Quantum Design PhysicalProperty Measurement System equipped with a dilution insert. The heat capacity valueswere extracted using the relaxation method [20]. The background heat capacity of themicrocalorimeter and the Apiezon N grease used for thermal conduction was measuredbefore the sample measurement and subtracted from the raw data to obtain the absoluteheat capacity of the sample.Inelastic neutron scattering (INS) measurements were carried out on the BASISbackscattering spectrometer of the Spallation Neutron Source (SNS), Oak RidgeNational Laboratory, USA [21]. More details of this measurement is presented inreference [22]. Inelastic neutron scattering experiments were also carried out on thehigh–resolution time–of–flight spectrometer FOCUS at the Spallation Neutron SourceSINQ at PSI, Villigen in Switzerland. The polycrystalline sample was enclosed in analuminum cylinder ( mm diameter, ∼ mm height) and placed into a He – cryostatand the spectrum was collected using an incident energy of . meV. Additionalexperiments were performed for the empty container as well as for vanadium to allow thecorrection of the raw data with respect to background, detector efficiency, absorptionand detailed balance according to standard procedures. Inelastic data reduction andanalysis was carried out using the software DAVE [23]. yperfine and crystal field interactions in multiferroic HoCrO
20 30 40 50 60 70 80 90-2-10123121314 (b) I n t en s i t y ( a r b . un i t s )
2 (degree)
ObservedCalculatedDifferenceBragg position (a)
Figure 1: (Color online) Observed (black circle) and calculated (red curve) PXRDpatterns and their difference (blue curve) at
K. The vertical bars denote the positionof Bragg reflections. A spurious peak indicated by asterisk symbol could not be indexed.(b) Graphical representation of the crystal structure of HoCrO with Cr-O octahedrain P bnm space group. Blue, gray and red spheres indicate Ho, Cr and O atoms,respectively.
3. Results and discussion
The Rietveld refinement of room temperature PXRD data is presented in Fig. 1(a), andthe results are tabulated in table 1. Using Shannon–radii values for the ions [24] the valueof the tolerance factor t G for HoCrO is found to be ∼ . . Accordingly HoCrO is anorthorhombically distorted perovskite with the space group P bnm [12–14]. The crystalstructure at
K is in good agreement with the previously determined orthorhombicstructure with similar lattice parameters [8, 25]. The unit cell parameters obey therelationship, a < c/ √ < b which is characteristic of O –type orthorhombic structures.A buckling of the network of octahedra corresponding to cooperative rotation about a [110] –axis leads to the O –type orthorhombic structure. The clinographic view of theCrO octahedra in HoCrO is presented in Fig. 1(b). In perovskite manganites R MnO ( R = La, Pr, Nd, Sm, Eu, Gd, Tb and Dy), in addition to the distortion due tobuckling of the MnO octahedron, a second distortion also arises because of the Jahn–Teller effect. This is because the Mn in R MnO with four unpaired electrons the d –shell in high spin state is Jahn–Teller active. On the other hand Cr in chromiteswith three unpaired electrons in d -orbitals is Jahn–Teller inactive. Thus a contributionto the lattice distortion in R CrO due to the Jahn–Teller effect is ruled out. yperfine and crystal field interactions in multiferroic HoCrO obtained from the Rietveld refinement of the PXRD pattern at K. The values insidethe brackets are the standard deviations.Atoms x y z B iso (Å )Cr . − . . . . . . − . . . a = 5 . Å b = 5 . Å c = 7 . Å V = 218 . Å Discrepancy Factors R p = 3 . R wp = 5 . R exp = 3 . χ = 3 . The variation of the specific heat ( C P ) of HoCrO with temperature is presented inFig. 2. The low temperature features in C P can be visualized clearly in a log-log plot asshown in the inset of Fig. 2. The direct inspection of the specific heat curve evidencesthe presence of three main contributions or features: (1) a sharp increase in specific heatbelow K with a maximum at ∼ . K due to anomalously large hyperfine interactionbetween the electronic and nuclear spins of Ho leading to a nuclear-Schottky specificheat ( C N ); (2) the electronic Schottky contribution ( C e ) from thermal depopulation ofthe I ground state multiplet of Ho with a maximum at ∼ K; and (3) the λ –likeanomaly with a peak at T ≈
142 K due to the magnetic ordering of the Cr moments.To determine different contributions to C P , a detailed analysis was performed in twosteps, first C P was modeled in the temperature range . T K and then T K. . K T K The specific heat below K has two broad features with maxima around ∼ . K and ∼ K. From the low temperature specific heat measurements of Ho metal it was foundthat anomalously large hyperfine interaction between the electronic and nuclear spinsof Ho commonly leads to a nuclear Schottky anomaly with a maximum at ≈ . K [26].The Hamiltonian for hyperfine interactions can be written in the form [27]: H k B = a ′ I z + P (cid:20) I z − I ( I + 1) (cid:21) (1)where, a ′ is the magnetic hyperfine constant, which is a measure of the strength of thehyperfine interaction between the nuclear moment and the magnetic moment associatedwith the 4 f electrons. P is the quadrupolar coupling constant. The field is applied in yperfine and crystal field interactions in multiferroic HoCrO z direction. Since the projection I z can take I + 1 values, i.e. − I, − I + 1 , ...I ,the hyperfine specific heat C P will be a Schottky type specific heat, associated withthe I + 1 hyperfine levels. The nuclear spin of Ho with 100% natural abundance is I = 7 / , while Cr with I = 3 / has a natural abundance of 9.5%. One can calculatethe mean square of effective nuclear moment for the natural abundance of active isotopesof Ho and Cr, µ eff , yielding . µ for Ho and . µ for Cr. With these effectivenuclear moments one can conclude that the Cr hyperfine contribution is about threeorders of magnitude smaller than the Ho one. Thus only the Ho contribution is takeninto account in the calculation of nuclear hyperfine contribution to the specific heat.Due to the hyperfine interaction the holmium nucleus has I + 1 = 8 possible spinorientations relative to an effective field H eff . The energies ε i /k B of various nuclearspin states, i.e. the eigenvalues of the Hamiltonian in equation (1) are ε i k B = a ′ i + P (cid:20) i − I ( I + 1) (cid:21) (2)where, i = − / , − / , ...., / , / . Information about a ′ and P can be obtainedby measuring the heat capacity at sufficiently low temperatures. In case of holmium,the quadrupolar coupling contribution is small and can be neglected [28]. Therefore for P ≈ the equation (2) reduces to, ε i k B ≈ a ′ i (3)The specific heat in the temperature range . − K is modeled by taking intoconsideration the contributions from nuclear specific heat C N , an electronic Schottkyterm C e and a lattice term C L . Thus at low temperatures the C P of HoCrO is givenby, C P = C N + C e + C L (4) T (K) C P ( J m o l - K - ) C P ( J m o l - K - ) Temperature (K)
Figure 2: (Color online) The temperature dependence of specific heat C P of HoCrO .Three distinct features in the C P are clearly visible in the inset. yperfine and crystal field interactions in multiferroic HoCrO C P ( J m o l - K - ) Temperature (K)
Data total fit Nuclear Electronic Lattice (a) (b) C N / T ( J m o l - K - ) R ln(8)=17.29
Jmol -1 K -1 S N ( J m o l - K - ) Temperature (K)
Figure 3: (Color online) (a) Double logarithmic plot of specific heat C P measured atzero magnetic field plotted along with the refined model using equation 4. Differentcontributions to the total specific heat C P are also shown. (b) A plot of C N /T vs. Tand the entropy associated with the nuclear specific heat S N obtained by the numericalintegration of C N /T (shaded region) using equation 8. The horizontal dashed-linecorresponds to the theoretical limiting value of the entropy.where, C N and C e are given by the general expression for an n-level Schottky specificheat term given by [29]: C Schottky = RT P i P j (∆ i − ∆ i ∆ j ) exp [ − (∆ i + ∆ j ) /T ] P i P j exp [ − (∆ i + ∆ j ) /T ] (5)In this expression, ∆ i = ε i /k B and R = 8 . Jmol − K − is universal gas constant.To calculate the nuclear specific heat C N , a Schottky curve for Ho with I =7/2,eight equally spaced energy levels with splitting energy, ε i / k B ≈ a ′ i , where i = − / , − / , ... / , / , is used. To calculate the electronic Schottky specific heat C e , asimple two level Schottky term with energy splitting ε s / k B is used, as the contributionfrom higher energy terms is negligible in the temperature range . − K. In thistemperature range the lattice contribution is expressed by a single Debye term. At lowtemperatures, when
T << Θ D , the Debye temperature, the Debye specific heat can berepresented by well-known Debye T –law as [29], C Debye = R r D T Θ = β T (6)where, r D is the number of atoms per molecule.The fit results to equation (4) are given in Fig. 3 (a). From the fit the valuesof electronic Schottky splitting energy ε s and the Debye temperature Θ D are foundto be, 1.379(5) meV and K, respectively. The Schottky energy 1.379(5) meVis consistent with earlier reports based on specific heat measurements [16] and opticalabsorption Zeeman spectroscopy [30]. The value of a ′ from our analysis is found to yperfine and crystal field interactions in multiferroic HoCrO a ′ ≈ . − . K [26, 31, 32], in inter-metallic HoCo , a ′ ≈ . K [33] and inparamagnetic salts, a ′ ≈ . K [31]. The energy difference between two adjacent nuclearlevels due to hyperfine field thus calculated from equation (3) is . µ eV. Frominelastic neutron scattering measurements it is possible to observe these energy levelsdirectly, as an inelastic peak centered at ∼ . µ eV. Similar observations were madein spin–ice compound Ho Ti O which shows a nuclear Schottky peak around . Kin the specific heat data [34], which was later observed in inelastic neutron scatteringmeasurements as a peak at ∼ µ eV [35]. The effective magnetic (hyperfine) field atthe holmium nuclei can be computed by writing [32], a ′ = µH eff k B I (7)where, µ = 4 . µ N for Ho and µ N is the nuclear magneton ( µ N = 5 . × − JT − ).Using the value of a ′ in equation (7) the hyperfine field, H eff is found to be T.This value is comparable to the values reported for Ho Ti O (720 T) [34], metallic Ho(770 T) [32] based on specific heat data and in ErCrO (530 T) [36] based on Mössbauerspectroscopy.The nuclear specific heat C N was obtained by subtracting the lattice and electroniccontributions from C P . The entropy S N associated with the nuclear specific heat wascalculated by the numerical integration of C N /T . S N is given by the expression, S N ( T ) = T Z (cid:18) C N T (cid:19) dT (8)The C N /T versus T and the computed S N are presented in Fig. 3(b). The nuclear entropy S N reaches a maximum value of ∼ . Jmol − K − at ∼ K. The theoretical limitingvalue of entropy for
Ho with nuclear spin I = 7 / is calculated as Rln (2 I + 1) = Rln (8) ≃ . Jmol − K − . It is shown as an horizontal dashed line in Fig. 3(b). Anexcellent agreement between the experimental S N with the theoretical value suggeststhat only contribution to the low temperature peak in the specific heat is from thenuclear Schottky term due to hyperfine interactions. K T K. The non-magnetic contribution to the specific heat C nm in the temperature region − K is fitted assuming the contributions from an electronic Schottky term C Schottky ,lattice term C Lattice and a linear term C Linear . HoCrO has 5 atoms per formula unit,which implies that 15 vibrational modes to the phononic specific heat exist. Taking into account this constraint, we approximate the lattice contribution to the specific heat( C Lattice ) as sum of a Debye term ( C Debye ) and two distinct Einstein terms C Einstein . Thespecific heat associated with the magnetic ordering, ( C m ) results in a λ –like transitionwith a maximum at ∼ K. C m is obtained by subtracting C nm from the experimentaldata ( C P ). The magnetic entropy S m associated with C m is obtained by the numerical yperfine and crystal field interactions in multiferroic HoCrO C m /T . The C nm and C m in the temperature range − K can bewritten as [29, 37], C nm = C Schottky + C Lattice + C Linear (9) C Lattice = C Debye + C Einstein (10) C m = C P − C nm (11)Here C Schottky is purely electronic Schottky term as we are fitting only above 2 K, wherethe nuclear contribution is negligible. The non-magnetic contribution to the specificheat in this temperature is obtained by equations (5), (9), (10) and, C Debye = 9 rR/x Z x D x e x / ( e x − dx (12) C Einstein = 3 rR X i a i (cid:2) x i e x i (cid:14) ( e x i − (cid:3) (13) C Linear = γT (14)In these expressions, R is the gas constant, x D = ~ ω D /k B T , x i = ~ ω E /k B T , k B isBoltzmann constant, γ is the coefficient of the linear term and r is the number ofatoms per molecule. The fitting was performed excluding the data in the temperaturerange 60–200 K. The different contributions to the measured specific heat obtained fromfitting are presented in Fig. 4(a). The values of Debye temperature Θ D and two Einsteintemperatures ( Θ E , Θ E ) obtained from the fit are K (46(1) meV) and
K(67(1) meV) and
K (15.17(2) meV), respectively. This contribution to C Lattice wasparametrized by using 3 Debye modes with Debye temperature ( Θ D ), 7 Einstein modeswith Einstein temperature Θ E , and another 5 Einstein modes with Θ E . Although theused parametrization over simplify the phonon spectrum, the obtained key results arenot influenced by subtleties in the choice of the modeled lattice contribution, i.e., bythe number of Debye and Einstein contribution or by the used absolute values withinreasonable error bars [38].Based on optical absorption spectroscopy [30], magnetization and magneticsusceptibility [17], specific heat [39], elastic neutron diffraction [40] and inelastic neutronscattering (INS) [41] experiments five electronic Schottky levels were observed in HoCrO with the fifth level being at ∼ K (23.4 meV). To calculate C Schottky , a Schottky curvefor five energy levels is used which contribute to C Schottky below
K. The ground stateenergy level is assumed to be zero i.e., ε /k B = 0 . From the low temperature specificheat analysis, where a simple two level Schottky model was used to calculate C Schottky ,the energy splitting is found to be 1.379(5) meV. We fixed this value as ε in the presentcalculations. The higher energy levels are determined from the fit as ε = . meV, ε = . meV and ε = . meV. These values are in excellent agreement withthe reported crystal field energy values in HoCrO (within 0.5 % ).After subtracting the contributions, C Schottky , C Lattice and C Linear from the totalspecific heat C P , the magnetic specific heat C m is obtained, which can be seen as thedeviation from the total fit in Fig. 4(a) in the temperature range − K. Themagnetic entropy, S m was calculated by the numerical integration of C m /T analogous yperfine and crystal field interactions in multiferroic HoCrO
75 100 125 150 175 200 225 2500102030400.0000.0250.0500.0750.1000.1250 50 100 150 200 250 300020406080100 (b) S m ( J m o l - K - ) Rln(17)+Rln(4) = 35.08 Jmol -1 K -1 C m / T ( J m o l - K - ) Temperature (K) (a) C P ( J m o l - K - ) Temperature (K) data total-fit Schottky Lattice Linear
Figure 4: (Color online) (a) Specific heat, C P measured at zero magnetic field plottedalong with the fitted results using the equation (9). Different contributions to the totalspecific heat C P are also shown. (b) The C m /T vs. T and the magnetic entropy S m ,obtained by the numerical integration of C m /T (shaded region). The horizontal dashed-line corresponds to the theoretical limiting value of the entropy.to the expression (8), by replacing C N by C m . The C m /T versus T and computed S m ispresented in Fig. 4(b). The experimental magnetic entropy value reaches a maximumvalue of ∼
34 Jmol − K − around 180 K, above T N . The theoretical limiting value of S m was calculated by adding the contributions due to ordering of both Ho ( J = 8 )and Cr ( S = 3 / ) moments, i.e., R ln(17) + R ln(4) ≃ . Jmol − K − , indicatedas a horizontal dotted line in Fig. 4(b). The experimental magnetic entropy is veryclose to the theoretical magnetic entropy around 180 K ( ∼ . The good agreementbetween the experimentally found value for the magnetic entropy and that calculatedfor the spin only component of Cr ions and orbital magnetic moment of Ho ions,allows for concluding the following: first, the orbital moments of Cr ions appear to bequenched while keeping the full spin moment. Second, the lattice contribution seems tobe described sufficiently well by the Debye and Einstein models.The value of linear coefficient γ from the fit is found to be . mJmol − K − .This value of γ is comparable to the reported values, − mJmol − K − which isassociated with conduction electrons in some doped manganites [42–45]. The linearcoefficient is usually attributed to charge carriers, and is proportional to the density ofstates at the Fermi level. However, HoCrO is an electrical insulator, thus the origin oflinear term should be interpreted with caution. Several electrical insulators have beenreported with large values of γ , viz., LaMnO δ ( γ ≈ mJmol − K − ) [46], BaVS ( γ = 15 . mJmol − K − ) [47] and La . YCa . Mn O ( γ = 41 . mJmol − K − ) [48].The origin of a linear contribution in these electrical insulators was attributed to avariety of magnetic phenomena. The most plausible explanation for the appearance ofa linear term in the heat capacity in HoCrO is due to disordered Ho as in the caseof insulating Ho − x Y x MnO . For this compound it was observed that with increasingY content γ is reduced and drops to zero at x = 0 . , indicating the dependence of γ on yperfine and crystal field interactions in multiferroic HoCrO spins above the ordering temperature. From highresolution neutron spectroscopy a huge quasielastic scattering was observed in HoCrO ,which was understood as due to fluctuating disordered Ho electronic moments [22].This supports our interpretation of disordered Ho electronic moments as a possiblesource of a linear term in the observed specific heat. It is worth noting at this pointthat, to model the low temperature specific heat data using equation (4), a linear termwas not required which can be understood due to spin ordering of Ho at these lowtemperatures [50]. These observations confirm that the main origin of the linear termin HoCrO is disordered Ho spins. Inelastic neutron scattering spectra measured at the BASIS back–scatteringspectrometer are presented in Fig. 5(a). At low temperatures two clear inelastic signalsare observed on both energy gain and energy loss sides. A detailed study of the hyperfinespectra of HoCrO is published elsewhere [22]. The inelastic spectra was modeled withthe equation, S ( ω ) = [ xδ el ( ω ) + p δ ins ( − ω ) + p δ ins (+ ω )] ⊗ R ( ω ) + B (15)where, delta function δ el and δ ins represent elastic and inelastic peaks, respectively.These terms are convoluted numerically with the experimentally determined resolutionfunction, R ( ω ) , which is asymmetric due to the neutron pulse shape. B is a flatbackground term and x, p and p are scaling factors. The average energies of theinelastic peaks as obtained from the fits are E = ± . µ eV, this is in excellentagreement with the hyperfine splitting energy, . µ eV determined from our lowtemperature specific heat data. The fitting result to the 1.5 K data is presented inFig. 5(b). As can be seen from Fig. 5(a) a strong quasielastic scattering signal arises withincreasing temperatures, broadening the elastic peak. An additional Lorentzian termwas required to describe this intensity. The temperature evolution of the quasielasticterm was attributed to fluctuating electronic moments of the Ho ions, which getincreasingly disordered at higher temperatures. This reassures the validity of the largelinear coefficient obtained by fitting the specific heat data at higher temperatures.From our earlier detailed report on the temperature dependence quasielastic scatteringin HoCrO [22] we found that the intensity decreases sharply below 40 K. Furtherthe temperature dependence of ordered magnetic moment of Ho obtained from ourrecent neutron powder diffraction measurements [50], varies inversely as the temperaturedependence of quasielastic scattering intensity and shows a sharp increase below 40 K.This confirms that the origin of quasielastic scattering is indeed fluctuating Ho momentswhich are short range in nature. A similar phenomenon was also observed in Ho Ti O ,the authors have interpreted it as being due to the fluctuating electronic moments of theHo [35]. Wan et al ., [51] showed both analytically and numerically that indirect magneticexchange, which is short-range in nature is another driving force for the off-center atomic yperfine and crystal field interactions in multiferroic HoCrO -40 -20 0 20 400.00.51.01.52.02.5 -40 -20 0 20 40 I n t en s i t y ( a r b . un i t s ) Energy ( eV)
100 K (a) (b) I n t en s i t y ( a r b . un i t s ) Energy ( eV)1.5 K data S( ) el ins1 ins2 B (c) I n t en s i t y ( a r b . un i t s ) Data
Energy transfer (meV)
Elastic ( ) T=1.5 KE i =19.61 meV Total fit Figure 5: (Color online) (a) INS spectra of HoCrO collected on the instrument BASIS,spectral lines are shifted along y-axis for clarity. (b) Fits to the 1.5 K INS data asdescribed in the main text using equation (15). The inelastic peaks at both energyloss and energy gain sides are fitted by convoluting the instrument resolution functiondetermined from vanadium with two delta functions for two inelastic peaks (magenta andgreen lines) plus one delta function for the elastic peak (blue line). The horizontal line isthe flat background term [22]. (c) INS spectra collected on the instrument FOCUS, withneutrons of incident energy E i = 19 . meV at temperature 1.5 K. Three well–resolvedpeaks at ε , ε and ε are fitted using a Gaussian peak function.motion and ferroelectricity. In the present case, proposed short-range magnetic exchangeinteractions could cause the off-center atomic motion leading to ferroelectricity. We willreport a detailed nuclear and magnetic structure studies as a function of temperatureelsewhere, which should shed more light on atomic displacements and short rangemagnetic order in HoCrO .A typical inelastic spectrum measured at the time–of–flight instrument FOCUS ispresented in Fig. 5(c). The non-Kramer’s Ho ions in HoCrO are at sites of pointgroup symmetry m (C ), which typically leads to a singlet ground state. Thus theground multiplet of the Ho ion, I , split into J + 1 = 17 singlets by the crystalline yperfine and crystal field interactions in multiferroic HoCrO Energy (meV) I n t en s i t y ( a r b . un i t s ) T e m p e r a t u r e ( K ) (a) (c) (b) Temperature (K) I n t eg r a t ed I n t. ( a r b . un i t s ) P ea k po s i t i on ( m e V ) Temperature (K)
Figure 6: (a) Temperature dependence of Crystalline electric field excitations with theenergy range 7–13 meV. (b) Temperature dependence of integrated intensity of peakcorresponding to CEF excitation ε and (c) Temperature dependence of peak position,for the inelastic peak corresponding to crystal electric field excitation ε . Vertical dashedline at 140 K indicates the magnetic ordering temperature and the dashed line at 60 Kcorresponds to the peak in pyroelectric current curve, reported in reference [8].field generated by surrounding ions. The energy range of our inelastic data, limitedto only three crystal field levels, makes a crystal field calculation inadequate using apoint–charge model. Despite that, the observed inelastic peaks, fitted with Gaussianpeak functions as shown in Fig. 5(c), are centered at energies, ε = 1 . meV, ε = 10 . meV and ε = 15 . meV are in excellent agreement with thosedetermined from heat capacity data and reported values [41].The hyperfine excitation signal which is masked gradually by quasielastic scatteringupon increasing temperature, in contrast, the Crystal Electric Field (CEF) excitationsignal is still visible in high temperature range. The temperature evolution of inelasticpeak associated with the CEF excitation between ground state ( ε ) and the secondexcitation level ( ε ) is presented in Fig. 6(a). The inelastic peak due to transitionsbetween first excitation level ( ε ) and the second excitation level ( ε ) can also beseen (above 10 K). Two inelastic peaks were simultaneously fitted with Gaussian peakfunction, both the peaks are well separated in all temperatures below 100 K abovewhich the peak due to the transition between first excitation level ( ε ) and the secondexcitation level ( ε ) vanishes. The integrated peak intensity as a function of temperaturefor the peak corresponding to crystal field excitation ε is plotted in Fig. 6(b). Itexhibits a typical behavior of Van Vleck contribution below T N and a clear anomaly at T N = 140 K. Given the fact that the CEF interaction reflects directly the electrical and yperfine and crystal field interactions in multiferroic HoCrO T N indicated the change of local environment surrounding the Ho ion in HoCrO . Becauseboth Cr and Ho moments order below T N , the anomaly on peak intensity can be mainlyattributed to the effect of exchange field on the Ho ion from the long range orderof Cr magnetic sublattice. Rajeswaran et al ., [5] proposed that the multiferroicity in R CrO is caused by the interaction between magnetic rare earth and weak ferromagneticCr ions following the breaking of symmetry. The observed anomaly in CEF signalstrengthens the importance of Ho-Cr exchange striction. The anomaly in 6(b) alsoimplies the possible distortion of Ho ions and their surroundings since the pyroelectriccurrent exhibits its maximal at the same temperature [8].The temperature dependence of ε peak position is shown in Fig. 6(c). In thetemperature range 1.5 – 60 K, the peak position remains unchanged at 10.1 meV andstarts moving gradually to lower energy, above ∼
60 K, which is well below T N . Thechange of peak position of CEF excitation at ∼
60 K hints at the shift of CEF levelsaccompanied with the change of local crystallographic symmetry of Ho ion. However,so far there is no report on the observation of structural distortion for HoCrO at 60 K.It is noticed that a tiny peak is observed at the same temperature in pyroelectric currentcurve, as shown in Fig. 5(a) in the ref. [8]. Therefore, the change of CEF peak positionat 60 K is related to the change of ferroelectric properties. A detailed study on thetemperature–dependent crystal structure is needed to understand the unusual behaviorof CEF excitation and thus the mechanism of multiferroicity in HoCrO .
4. Summary and conclusions
High quality polycrystalline HoCrO was prepared by solid state reaction methodand characterized by means of x-ray powder diffraction, heat capacity and inelasticneutron scattering measurements. From the structural analysis we could establishthe consistency of the observed crystal structure and theoretical predictions based onGoldschimdt’s tolerance factor rule. From the low temperature nuclear contributionto the specific heat results we obtained the first CEF excitation energy for Ho ,1.379(5) meV and hyperfine field of 600(3) T with a hyperfine splitting energy,22.5(2) µ eV for Ho with I = / . The entropy ( S N ) associated with nuclear hyperfinespecific heat ( C N ) was also estimated from the low temperature specific heat, whichis in excellent agreement with theory. The hyperfine splitting energy determined fromspecific heat data is then confirmed from the peak observed in inelastic back scatteringdata. The large linear term γ = 6 . mJmol − K − in the specific heat was understoodas due to disordered Ho spins, which is further supported by strong quasielasticscattering observed in inelastic backscattering data at high temperatures. From theanalysis of high temperature specific heat, by fixing the first CEF excitation level to1.379(5) meV, obtained from low temperature specific heat analysis, we determinedthree more crystal field transitions at 10.37(4) meV, 15.49(9) meV and 23.44(8) meV.The lower energy crystal field levels observed from the inelastic neutron scattering yperfine and crystal field interactions in multiferroic HoCrO S m ) associated with the magnetic specific heat ( C m )is obtained, which is consistent with the theoretical prediction. The linear term inspecific heat and also quasielastic scattering observed in inelastic neutron spectra,further adds another possible driving force for the observed ferroelectricity in the formof short range exchange interactions in this compound as proposed by Wan et al ., [51].Further, from the temperature evolution of crystal field spectra we confirm a directcorrelation between the magnetic ordering and the ferroelectricity in this compound,as predicted by Rajeswaran et al . [5]. In addition to aforementioned mechanisms,the asymmetry driven ferroelectricity as proposed by Ghosh et al . [8, 10] and Indra et al ., [11] should also be considered as one of the driving force for ferroelectricity.More detailed temperature dependent structural studies are required for the quantitativeanalysis of distortions induced ferroelectricity. Thus our study and recent reports onthe ferroelectricity confirm that HoCrO and R CrO in general, possesses more thanone ingredient which can drive ferroelectricity, suggesting that these materials arepotential multiferroic candidates for device applications. Our study warrants, moredetailed temperature dependent nuclear and magnetic structure studies to establish amost favorable mechanism for multiferroicity in HoCrO and rare-earth orthochromitesin general. Acknowledgments
We thank the expert assistance of T. Strässle, SINQ, Paul Scherrer Institute. Part of theresearch conducted at SNS was sponsored by the Scientific User Facilities Division, Officeof Basic Energy Sciences, US Department of Energy. This work is partially based onthe experiments performed at the Swiss Spallation Neutron Source SINQ, instrumentFOCUS (Proposal ID 20090536). Financial support from the European Project EUNMI3 is acknowledged.
References [1] Serrao C R, Kundu A K, Krupanidhi S B, Waghmare U V and Rao C N R 2005
Phys. Rev. B J. Mater. Chem. J. Rare Earths J. Solid State Chem.
Phys. Rev. B (21) 214409[6] Preethi Meher K R S, Wahl A, Maignan A, Martin C and Lebedev O I 2014 Phys. Rev. B (14)144401[7] Apostolov A T, Apostolova I N and Wesselinowa J M 2015 Mod. Phys. Lett. B J. Mater. Chem. C (16) 4162[9] Subba Rao G V, Chandrashekhar G V and Rao C N R 1968 Solid State Commun. EPL yperfine and crystal field interactions in multiferroic HoCrO [11] Indra A, Dey K, Midya A, Mandal P, Gutowski O, Rütt U, Majumdar S and Giri S 2016 J. Phys.:Condens. Matter Acta Crystallogr. J. Chem. Phys. J. Phys. (Paris) IEEE Trans. Magn. J. de Phys. Int. J. Magn. J. Appl. Crystallogr. Physica B
Rev. Sci. Instrum. Rev. Sci. Instrum. J. Phys. Condens. Matter J. Res.Natl. Inst. Stand. Technol.
Acta Crystallogr., Sect. A: Found. Crystallogr. Bull. Soc. Fr. Mineral. Crystallogr. Physica Proc. Phys. Soc. London Phys. Status Solidi B The specific heat of matter at low temperatures (Imperial College Press, London)[30] Courths R and Hüfner S 1976
Zeitschrift für Physik B Condensed Matter Phys. Rev.
Phys. Rev.
Solid State Commun. Phys. Rev. B Phys. Rev. B
Phys. Rev
Specific heats at low temperatures (Heywood books London)[38] Schäpers M, Wolter A U B, Drechsler S L, Nishimoto S, Müller K H, Abdel-Hafiez M,Schottenhamel W, Büchner B, Richter J, Ouladdiaf B, Uhlarz M, Beyer R, Skourski Y, WosnitzaJ, Rule K C, Ryll H, Klemke B, Kiefer K, Reehuis M, Willenberg B and Süllow S 2013
Phys.Rev. B (18) 184410[39] Pataud P and Sivardière J 1970 J. de Phys. Physica B+C Physica B J. Magn. Magn. Mater.
Phys. Rev. B (21) 14926[44] Coey J M D, Viret M, Ranno L and Ounadjela K 1995 Phys. Rev. Lett. (21) 3910[45] Woodfield B F, Wilson M L and Byers J M 1997 Phys. Rev. Lett. (16) 3201[46] Ghivelder L, Abrego Castillo I, Gusmao M A, Alonso J A and Cohen L F 1999 Phys. Rev. B J. Phys. Soc. Jpn. J. Phys.Condens. Matter L191[49] Zhou H D, Lu J, Vasic R, Vogt B W, Janik J A, Brooks J S and Wiebe C R 2007
Phys. Rev. B yperfine and crystal field interactions in multiferroic HoCrO [50] Kumar C M N, Xiao Y, Nandi S, Senyshyn A, Su Y, Brückel T Magnetic ordering andmagnetoelastic effect in HoCrO , manuscript in preparation[51] Wan X, Ding H C, Savrasov S Y and Duan C G 2016 Scientific reports6