Impact of the crystal electric field on magnetocaloric properties of CsGd(MoO_4)_2
aa r X i v : . [ c ond - m a t . o t h e r] S e p Impact of the crystal electric field on magnetocaloricproperties of CsGd(MoO ) a, ∗ , A. Orend´aˇcov´a a , R. Tarasenko a , M. Orend´aˇc a , A. Feher a a Institute of Physics, P. J. ˇSaf´arik University, Park Angelinum 9, 040 01 Koˇsice, SlovakRepublic
Abstract
Magnetocaloric effect (MCE) was investigated in the single crystal of CsGd(MoO ) in the temperature range from 2 to 30 K and fields up to 5 T applied along theeasy and hard magnetic axis. The analysis of specific heat and magnetizationprovided the refinement of crystal electric field (CEF) parameters supportingthe dominance of uniaxial symmetry. The knowledge of CEF energy levels en-abled the extrapolation of MCE parameters outside the experimental region.Consequently, maximum values of the isothermal entropy change, − ∆ S M , inmagnetic fields up to 5 T are expected to occur at temperatures between 1 and2 K. While − ∆ S M achieves 19.2 J/kgK already for the field 1 T, for the fieldchange 7 T, maximal − ∆ S M ≈ ) attractive for magnetic refrigeration at low temperatures. The possibilities offurther enhancement of MCE parameters are discussed. Keywords:
Magnetocaloric effect, Crystal electric field, Magnetic anisotropy,Specific heat, Rare-earth ion ∗ Corresponding author
Email address: [email protected] (V. Tk´aˇc)
Preprint submitted to arXiv.org November 5, 2018 . Introduction
Energy efficient and environmentally friendly technologies receive much at-tention to solve the energy crisis accompanied with a serious problem of a globalwarming phenomenon. In this context, refrigeration based on magnetocaloriceffect (MCE) has attracted much research interest because of its higher energyefficiency and the use of environmentally friendly materials [1, 2]. MCE resem-bles processes that occur in gas in response to the changing pressure. Isother-mal magnetizing of a magnetic refrigerant reduces magnetic part of the entropy,∆ S M , and corresponds to the isothermal compression of gas. Adiabatic demag-netizing (corresponding to adiabatic expansion of gas) is accompanied with theadiabatic temperature change, ∆ T ad . Both thermodynamic quantities describethe measure of MCE. The discovery of a giant MCE in Gd (Si Ge ) near aroom temperature [3], with − ∆ S M ≈
19 J/kg K, for the field change 0 - 5 Ttriggered flurry of research activities in a wide area of physics, chemistry andmaterial science.During last two decades, giant MCE associated with the occurrence of mag-netic phase transition of the first or second order has been reported for a broadvariety of materials [4, 5, 6, 7, 8, 9]. Besides the systems with magnetic phasetransition, more options are available for magnetic cryo-cooling. At low temper-atures, the vibrational specific heat decreases, consequently, also paramagnets[10, 11, 12, 13] and superparamagnets [14] under special conditions which en-hance MCE, can be employed. Superparamagnetic systems composed of 3d-4fintermetallic nanoparticles represent nanomagnets with large cryogenic MCE[15]. However, their application potential is limited due to large content ofMCE inactive matrix and in case of encapsulated nanoparticles, their shell haslow thermal conductivity [14]. Single molecule magnets or molecular nanomag-nets (MNs) represent another class of nanoscopic systems. MNs such as Mn ,Fe and Mn containing high-spin molecules (magnetic clusters) with vanish-ing magnetic anisotropy are particularly favorable due to large magnetic entropycontent and easy polarization of net molecular (cluster) spins in magnetic field2f low or moderate strength [16].Currently, much attention is devoted to other isotropic systems, namely Gd-based single-ion magnets (SIMs) [11, 12, 13]. Unlike aforementioned molecularnanomagnets, SIMs contain paramagnetic ions well separated from others bydiamagnetic ligands, thus suppressing the existence of magnetic transitions tovery low temperatures. Contrary to conventional bulk refrigerants with mag-netic transitions, in molecular nanomagnets, the entropy changes take placein the nanoscale range, thus micron and submicron-sized devices can be fabri-cated for exploiting the functionality of the molecular coolers [17]. Design ofeffective cryo-refrigerant requires optimization of diverse parameters as mag-netic anisotropy, spin value, type and strength of magnetic interactions andrelative amount of non-magnetic elements in the structure [18]. In this respect,molecular-based Gd(III) compounds are usually recognized as good candidatesfor magnetic refrigeration at low temperatures [19], because Gd(III) ion haszero orbital angular momentum and provides the largest entropy per single ionassociated with the highest spin value 7/2.Maximal usability of magnetic entropy for the magnetocaloric applicationis usually reduced by the effects of crystal electric field (CEF) splitting andmagnetic correlations characterized by parameters ∆ and J . At relatively hightemperatures ( k B T ≫ ∆, J ) all magnetic degrees of freedom can be used formagnetic cooling. While increasing of density of magnetic atoms enlarges theMCE, it can also reinforce magnetic correlations which lower the magnetic en-tropy and induce the magnetic ordered state. The solution of this dilemma canbe found in the competing effect of magnetic anisotropies from different sources.As was shown in ref. [20], CEF induced magnetic anisotropy can support theexchange anisotropy which results in the enhancement of the transition tem-perature T C to the magnetic ordered state and lowering MCE. On the otherhand, the competition of the aforementioned anisotropies can suppress the ef-fect of magnetic correlations and T C , which creates appropriate conditions foreffective usability of magnetic dense material with maximal magnetic entropyfor magnetic cooling. 3n this paper we present the study of the magnetocaloric effect in CsGd(MoO ) .The compound together with other materials from the series of rare-earth dou-ble molybdates MR(MoO ) (M + is an alkali-metal ion and R is a rare-earthion) belongs to laser active materials [21, 22, 23]. Besides their potential usein the optoelectronic devices at room-temperature applications, the compoundspossess interesting magnetic properties at low temperatures [24, 25]. Previouslow-temperature studies [26, 27, 28, 29, 30, 24] considered this material as aquasi-one dimensional dipolar magnet with a magnetic phase transition to theordered state at T C = 0.45 K. The effective strength of dipolar interactions wasestimated in the form of the effective intra-chain coupling parameter J/k B ≈ J ′ < ions, theoretical calcula-tions [29] suggest the presence of the magnetic anisotropy with the easy axisparallel to the crystallographic c axis. On the other hand, the symmetry ofthe crystal field should induce the anisotropy characterized by the easy axiscoinciding with the crystallographic a axis [25]. Thus, considering the com-petition between the aforementioned anisotropies, the weakness of magneticcorrelations and CEF splitting as well as the high spin value of Gd ion, themaximal usability of magnetic entropy for magnetic cooling can be expected inCsGd(MoO ) .The present study is focused at the response of the material to the appli-cation of magnetic field investigated in the paramagnetic phase. The analysisof the magnetization and specific heat allowed us to describe basic MCE prop-erties in the studied temperature region. What is more, the refinement of thecrystal-field parameters enabled to extrapolate the MCE predictions to a wideparametric region of temperatures and fields, which was not achieved in thecurrent experiment. Our study revealed that besides the aforementioned room-temperature optical applications, this material can be also used as an efficientcryo-refrigerant at helium temperatures already in relatively low magnetic fields ∼ . Crystal structure and experimental details CsGd(MoO ) is a transparent and soft material which was prepared by aflux method [31] at the Institute of Low Temperature Physics and Engineer-ing in Kharkov. The starting materials, Gd O , MoO and Cs O(Cs CO )in powder form were weighed according to the stoichiometric ratio and mixedhomogeneously. The solid-state synthesis was realized at 700 ◦ C. The systemcrystallizes in the
P ccm ( D ) space group with 2 formula units in the unit cellwith the parameters a = 5.07 ˚A, b = 9.25 ˚A and c = 8.05 ˚A [31, 32]. The co-ordination sphere of Gd ion consists of eight oxygen atoms forming a slightlydistorted square antiprism (Fig. 1a). The shortest distance between Gd ionsis along the c axis, and equals c /2. The Gd chains alternate with the chains of[MoO ] − groups in the ac plane which are separated by Cs + ions. Thus, onlya weak electrostatic coupling exists between the ac planes.Isothermal magnetization curves have been investigated in the temperaturerange from 2 to 30 K in magnetic fields up to 5 T in a commercial Quantum De-sign SQUID magnetometer. The measurements of the temperature dependenceof the specific heat have been performed in the temperature range between 2and 100 K in the zero magnetic field using commercial Quantum Design PPMSdevice. Two single crystals in the shape of a thin plate with the mass about 20mg and 5 mg were used for the magnetization and specific heat measurements,respectively.Several single crystals with approximate dimensions a ’ × b ’ × c ’ = 2 × × were used for a room-temperature x-ray study to determine the orientation ofthe crystallographic axes a , b and c with respect to the crystal edges a ’, b ’ and c ’. The longest crystal edge c ’ was identified with the crystallographic c axis,the shortest crystal edge b ’ is parallel to the b axis and the edge a ’ is parallel tothe a axis. Crystals grow in the form of thin plates parallel to ac layers with apronounced lamination within the [010] cleavage plane as a result of very weakcoupling between the layers along the b axis.5 . Results and discussion Gd ion has essentially isotropic ground state S / ( L = 0, S = 7/2, g J = 2), which means that no magnetic anisotropy is expected. Consequently,when neglecting dipolar interactions, the magnetocaloric response of the systemshould depend only on the number of spin degrees of freedom and the densityof Gd ions. However, a strong spin-orbit coupling of the 4f electrons mixesthe ground multiplet S / with the first excited state P / . Consequently, theground-state contains an admixture of nonzero L states resulting in the crystal-field splitting of the order of 1 K. As will be shown below, even such subtletiescan affect magnetization, and corresponding MCE, therefore a special attentionwas devoted to the crystal-field symmetry in CsGd(MoO ) . Considering only crystal electric field and magnetic field effects at sufficientlyhigh temperatures, the magnetic behavior of CsGd(MoO ) in the paramagneticphase can be described using Hamiltonian H = H CEF + g J µ B SB, (1)where µ B and S stands for the Bohr magneton and spin, respectively. Crystal-field effects are included in the term H CEF = P q =0 B q O q + P q =0 B q O q + P q =0 B q O q ,expressed in Abragam and Bleaney notation [33]. O qk represents equivalent op-erators and B qk are crystal-field parameters. Previous reports [24, 27] estimatedcrystal-field splitting of the ground state by considering the axial symmetry ofthe crystal field characterized by the parameter B = -0.089 K. Correspondingeasy axis is parallel to the crystallographic axis a [25].To verify the value of the parameter B , the corresponding energy levelscheme in Fig. 1b has been used for the calculation of the specific heat in zeromagnetic field. The obtained curve was compared with experimental specificheat depicted in Fig. 2a. The experimental data set comprises of previous6 (3) b) B = -0.0557 KB = -0.089 K E E E (2) E / k B ( K ) (1) E a) Figure 1: (a) The coordination sphere of the Gd ion (gray sphere) with eight oxygen atomsforming a slightly distorted square antiprism with the upper base (light blue spheres) andbottom base (dark blue spheres). (b) Splitting of the ground multiplet S / for differentcrystal-field symmetries. Energy schemes (1) and (3) correspond to the crystal field withuniaxial symmetry characterized by the parameter B . Energy scheme (2) corresponds to thelocal symmetry D with CEF parameters given in Table. 1 H CEF should be included.To exclude the effect of magnetic correlations which become significant be-low 1 K, the isothermal magnetization measurements were performed in theparamagnetic phase. The lowest temperature, T = 2 K, corresponds to 4 T C ,which is sufficiently high for neglecting the effect of the magnetic correlations.The magnetization curves obtained in the magnetic field applied along the crys-tallographic a and c axes are shown in Fig. 3.In accord with the aforementioned CEF induced magnetic anisotropy, themagnetization reflects the presence of a weak anisotropy with the easy axis par-allel to the a axis. No hysteresis effects were observed in the experimental data.The magnetization data were compared with the theoretical predictions for B = -0.089 K (Fig. 3a). Alike specific heat, the deviations between the magne-tization data and the predictions clearly indicate that the actual anisotropy inCsGd(MoO ) is weaker than expected.Considering the local symmetry D of Gd ion determined at room tem-perature, we realized simultaneous fitting of magnetization curves at varioustemperatures and for both orientations of magnetic field ( B k a and B k c ) us-ing 9 CEF parameters and much better agreement with experimental data wasachieved (Fig. 3b). The obtained CEF parameters (Table. 1) obey a generalrule, that a ratio of the rhombic anisotropy E = B to the axial anisotropy D = 3 × B , E/D is always positive and acquires values between 0 and 1/3. CEFvalues from the Table. 1 provide
E/D ∼ .1 1 10 100110100 0.1 110 -4 -4 -4 CsGd(MoO ) (present work) CsGd(MoO ) (Ref. 25) C T O T ( J / K m o l ) T (K) b) L ( m ) T(K) a) Internal surface T C Figure 2: (Color online) (a) Temperature dependence of the total specific heat ofCsGd(MoO ) involving data of present work (triangles) and data taken from Ref. [26] (cir-cles). The solid line represents the prediction for the CEF model with parameters from Table1. Dashed and dotted lines correspond to the CEF model with the axial symmetry for B = -0.089 K and B = -0.0557 K, respectively. The dashed-dotted line represents the latticecontribution 1.98 × − T [26]. (b) Temperature dependence of the phonon mean free path ofCsGd(MoO4)2 in zero magnetic field [24]. The dashed lines denote hypothetic temperaturescorresponding to dominant phonons with the CEF energies for B = -0.0557 K. b) M ( B / G d + ) B (T) B a B c B a B c
30 K2 K }} M ( B / G d + ) B (T) }
10 K a) KGd(WO ) , CsGd(MoO ) C T O T ( J / K m o l ) T (K)
Figure 3: (Color online) (a) Isothermal magnetization curves of CsGd(MoO ) for B k a (fulland open squares) and for B k c (full and open circles) measured at T = 2 K. The open symbolsrepresent data corrected for demagnetization effect with the average demagnetization factor N = 0.2. The lines correspond to theoretical predictions for the CEF model with the axialsymmetry for B = -0.089 K (dashed) and B = -0.0557 K (solid). Inset: Temperaturedependence of total specific heat. Open squares represent data of KGd(WO ) taken fromRef. [34], open circles and open triangles have the same meaning as in Fig. 2a. (b). Isothermalmagnetization curves of CsGd(MoO ) for B k a (open squares) and for B k c (open circles)shown at selected temperatures T = 2, 10, 30 K. The lines represent the simultaneous fitswith the CEF parameters from Table. 1. able 1: Effective CEF parameters obtained from the analysis of magnetization curves (inunits of Kelvin). B B B B B -0.0661 -0.0398 -0.0013 -0.0033 -0.0116 B B B B × − -0.0018 0.0017 7.6261 × − lower local symmetry, demagnetization effects and/or potential misalignment ofthe sample by a few degrees from the crystallographic axes. In accord withprevious susceptibility studies [27], the effective CEF parameters reflect thepredominance of the uniaxial anisotropy providing nearly identical magnetiza-tion values for hard (crystallographic axis b ) and medium (crystallographic axis c ) axes. In comparison with the previous estimate, B = -0.089 K [27], thelower value of the uniaxial term ( B = - 0.0661 K, Table. 1) indicates weakeruniaxial anisotropy in CsGd(MoO ) .The actual significance of low-symmetry CEF components was verified bythe simultaneous fitting of magnetization curves at T = 2 K in both orienta-tions with a CEF model considering only B parameter (Fig. 3a). The proce-dure yielded B = -0.0557 K suggesting even weaker CEF splitting (Fig. 1b).The agreement with magnetization curves does not achieve such quality as thedescription within the D symmetry, but it can be improved by consideringdemagnetization effects with the average demagnetizing factor N ∼ symmetry (Fig. 2a). Possibly, the weaklow-symmetry components can partially interfere with magnetic correlations ofcomparable strength.Moreover, the interplay of lattice vibrations and the CEF electronic stateswith the energies corresponding to the model with B = -0.0557 K can eluci-11ate anomalous behavior of the phonon mean free path, L , below 1 K (Fig. 2b).Unlike previous analysis [24], the existence of plateau below 1 K should resultfrom the scattering of phonons on the internal surfaces of this highly anisotropicmaterial with a layered structure. While the low-temperature end of the plateaunicely correlates with the magnetic phase transition at 0.45 K, further decreaseof L with a minimum appearing at 0.2 K can be attributed to the one-magnon-one-phonon resonance phonon scattering [35]. Within the Debye model, theacoustic phonons with the energies ~ ω ∼ k B T provide the greatest contri-bution to the phonon heat capacity. Accordingly, the phonons with the CEFenergies dominate the phonon spectrum at temperatures as denoted in Fig. 2b.The correlation between the hypothetic temperatures and the observed anoma-lies is apparent. Isothermal magnetization curves in the magnetic field oriented along the a and c axes are depicted in Fig. 4. The data were used for the calculation of theisothermal magnetic entropy change, ∆ S M , applying the Maxwell relation [36]∆ S M ( T, ∆ B ) = Z B f B i ∂M ( T, B ) ∂T dB, (2)where B i and B f represent initial and final magnetic field, respectively. Temper-ature dependence of -∆ S M derived from the experimental magnetization datafor B i = 0 and several values of B f applied along the a and c axes is shown inFig. 5.It is obvious, that for all magnetic field changes, the entropy change achievesmaximum out of the experimental temperature window. To complete the in-formation, theoretical -∆ S M values were calculated from the CEF model withuniaxial symmetry for B = -0.0557 K in a wide temperature range for thesame magnetic fields (Fig. 5). Excellent agreement with experimental datasupports the prevalence of the CEF with uniaxial symmetry affecting magne-tocaloric properties at temperatures far above T C . Theoretical -∆ S M curves12 T = 30 KT = 11 KT = 10 K M ( A m / k g ) B (T)
T = 2 K b) T = 10 KT = 2 K M ( A m / k g ) B (T)a)
Figure 4: (Color online) Isothermal magnetization curves of CsGd(MoO ) for (a) B k a , mea-sured with the temperature step 0.5 K and 1 K for the temperature interval 2-10 K and11-30 K, respectively (b) B k c , measured with the temperature step 0.5 K for the temperatureinterval 2-10 K. .1 1 10 1000510152025300.1 1 10 1000510152025300.1 1 10 100051015202530 S , - S M ( J / k g K ) T (K) S CEF (B=1T) S
C,TOT ) S C,TOT ) S CEF (B=0T) b) S , - S M ( J / k g K ) T (K) a) c) (1) B = 0 K (2) B = -0.0557 K (3) B = -0.089 K (4) B = -0.5 K (5,6) Table 1 S , - S M ( J / k g K ) T (K) B = 0-1 T igure 5: (Color online) (a) Temperature dependence of the entropy and isothermal entropychange in CsGd(MoO ) in different magnetic fields, B k a . Symbols represent − ∆ S M valuesobtained from experimental magnetization curves, dotted lines represent − ∆ S M values cal-culated from the CEF energies corresponding to B = -0.0557 K. A solid and long-dashedline represent a total entropy of CsGd(MoO ) and KGd(WO ) , respectively. For more de-tails, see text. Dashed-dotted and short-dashed line represent magnetic entropy in zero fieldand 1 T, respectively, calculated from the CEF energies corresponding to B = -0.0557 K.(b) Temperature dependence of the entropy and isothermal entropy change in CsGd(MoO ) in different magnetic fields, B k c . Symbols and lines have the same meaning as in (a). (c)Temperature dependence of the entropy in B = 0 T (dotted lines) and isothermal entropychange in the magnetic field ( B k a ) changing from zero to 1 T (solid lines) calculated for thedifferent strength of B . Dash-dotted lines (5) and (6) represent S and − ∆ S M , respectively,corresponding to the parameters in Table. 1. achieve maximum below 2 K, shifting towards low temperatures for decreas-ing magnetic field B f . Closer inspection revealed that at low temperatures,all theoretical -∆ S M curves merge into a universal curve with a nonzero value.This rather artificial behavior results from a two-fold degeneracy of the CEFground state in zero magnetic field. As can be seen, the universal curve en-veloping the low-temperature parts of the theoretical -∆ S M curves represents atheoretical entropy in zero magnetic field, S CEF , derived from the CEF modelwith the aforementioned uniaxial symmetry (Fig. 5). At high temperatures, thetheoretical entropy (in units of J/kg K) saturates to a maximum value S max = ln (2 S + 1) R/M ( R and M represent a gas constant and a molar mass, re-spectively). For CsGd(MoO ) parameters, S max achieves 28.34 J/kg K. At lowtemperatures S CEF attains minimum value, ln(2)
R/M = 9.45 J/kg K.Concerning the calculation of the experimental entropy in zero magneticfield, S c , tot ( B = 0 T), total specific heat data were used in a wide temperatureregion. Since the lowest temperature achieved in the low-temperature experi-ment [27] was 0.42 K i.e., 0.95 T C , unknown amount of magnetic entropy stillremained below a phase transition. To avoid large uncertainty introduced byany artificial extrapolation of the specific heat down to zero temperature, theexperimental data of a similar KGd(WO ) compound [34] were used for the15alculation of the missing entropy in the whole ordered region. The excellentagreement of both specific heat datasets suggests close similarity of dipolar in-teractions and CEF symmetry in both compounds (inset of Fig. 3a).The comparison of the experimental entropy (comprising lattice and mag-netic contribution) and S CEF in zero magnetic field (Fig. 5) point at the preva-lence of CEF contribution above 2 K. A deviation of the experimental entropyfrom S CEF gradually developing below 1 K indicates the onset of magnetic cor-relations resulting in a phase transition accompanied with a sudden drop of theexperimental entropy at T C . Concerning the S CEF in nonzero magnetic field, theapplication of external magnetic field removes the two-fold CEF ground-statedegeneracy. Corresponding energy gap projects to the exponential decrease of S CEF at lowest temperatures. As a consequence, S CEF calculated for B = 1 Tachieves nearly zero values at temperatures below 0.5 K (Fig. 5a). Increasingmagnetic field enforces the exponential decrease, shifting the region of nearlyzero S CEF ( B ) values towards higher temperatures. This result suggests, thatalike theoretical -∆ S M curves merge at low temperatures into a universal curve S CEF ( B = 0 T), all real -∆ S M vs. T dependencies are expected to merge into auniversal curve identical with the experimental entropy in zero magnetic field.As was shown in ref. [37], the experimental entropy forms an envelope of alow-temperature side of the experimental -∆ S M maxima. At higher tempera-tures, at least above 2 K, the contribution of crystal field prevails in all studiedmagnetic fields, leading to large conventional magnetocaloric effect. In the field5 T applied along the easy axis, ∆ S max = 26 J/kg K already achieves nearly 92% of S max .Concerning the isothermal entropy change in B k c , as expected from magne-tization data (Fig. 3), the values are comparable with those in the field appliedalong the easy axis (Fig. 5b).Noticeable differences between -∆ S M in B k a and B k c appearing in magneticfields lower than 2 T can be associated with the CEF effects. A closer examina-tion of the CEF impact on the magnetic entropy in zero magnetic field as wellas -∆ S M parameters in the relatively low magnetic field 1 T applied along the a B = 0 K) leads to the fullspin degeneracy in zero magnetic field while CEF with any symmetry partiallyremoves the spin degeneracy in Gd ion. Assuming uniaxial CEF symmetry,the strengthening of magnetic anisotropy (the increase of B parameter) leadsto lowering of maximal -∆ S M values. What is more, the maxima shift towardshigher temperatures. Analogical effect can be expected for CEF with lower sym-metry. As can be seen, despite the nearly isotropic nature of Gd ion, CEFplays important role in MCE parameters at temperatures comparable with thezero-field splitting (Fig. 1b).The refrigerant capacity, RC , was calculated from the experimental -∆ S max values [36], using a relation RC = R T hot T cold | ∆ S M ( T ) | dT , where T cold and T hot aworking temperature interval of the refrigerant (Fig. 6a inset). We used T cold = 0.4 K, while T hot is a temperature, at which the quantity -∆ S M reaches halfof the maximum value.In the field applied along the a (easy) axis, RC achieves 215 J/kg for 7 T,whereas for the same field applied along the c axis, RC ∼
200 J/kg.The relative independence of MCE on the orientation of magnetic field ( B & ) for practical applications in the formof powder. Unlike single crystals, this rather comfortable form of refrigerant isnot so sensitive to introducing strains or other imperfections.The adiabatic temperature change, − ∆ T ad is associated with the isentropicchange from nonzero initial magnetic field, B i , to the final zero value and rep-resents another important parameter of MCE. The procedure of the determina-tion of − ∆ T ad is depicted in Fig. 6a. Experimental entropy curves in nonzeromagnetic field, S ( B, T ), were constructed using the relation [37] S ( B, T ) = S C , TOT ( B = 0 , T )- | ∆ S M ( B, T ) | at temperatures down to 2 K. At lower tem-peratures, unknown experimental values | ∆ S M ( B, T ) | were approximated by∆ S CEF values. Corresponding estimations of − ∆ T ad values achieve maximumat temperatures around 10 K and the maximum shifts towards higher temper-atures for higher initial magnetic field (Fig. 6b). As can be seen, setting the17 S M S C,TOT (B = 0 T) S ( J / k g K ) T (K) T INIT B i T ad ( K ) T INIT (K) b) B a B c RC ( J / k g ) B (T) a) Figure 6: (a) Temperature dependence of the total entropy of CsGd(MoO ) comprisingmagnetic and lattice contribution. A thick solid line represents the experimental entropyin zero magnetic field. Thin solid lines represent experimental entropies in magnetic fieldapplied along the a axis. The dashed lines represent estimates using CEF theory (for moredetails, see text). The horizontal arrow shows how much the sample is cooled down from theinitial temperature, T INIT , in the isentropic process, while the vertical arrow demonstrates anexample of the isothermal entropy change. Inset: Field dependence of the refrigerant capacity RC . (b) Adiabatic temperature change as a function of the initial temperature during theisentropic change from nonzero initial magnetic field, B i , to zero B f . Vertical dashed linesdenote low-temperature and high-temperature interval in which the estimations of ∆ T ad werecalculated from CEF values (see text). T INIT = 15 K and field 5 T, the material iscooled down to 2 K during adiabatic change of magnetic field to zero value.Despite good MCE parameters achieved in CsGd(MoO ) , there still existsa possibility how to improve magnetocaloric properties of the double molyb-dates. Concerning the paramagnetic phase, large magnetocaloric effect givenby -∆ S M values, depends on the interplay of a few mechanisms. The high den-sity of magnetic moments (small molar mass M ) and high spin values enhancemaximum magnetic entropy S max = ln (2 S + 1) R/M which represents the upperlimit for -∆ S M . However, increasing density of the magnetic moments leadsto the enhancement of magnetic interactions between magnetic moments whichlower magnetic entropy as well as -∆ S M at temperatures where the magneticcorrelations dominate. As was already demonstrated in Fig. 5c, crystal electricfield has similar effect.Examples of magnetocaloric properties of selected Gd-based oxides with var-ious M parameters and the strength of magnetic correlations are given in theTable. 2. As can be seen, for some materials a large difference between S max and maximum -∆ S M is observed as a result of the aforementioned effects. Inthe majority of the systems (Table. 2) the maximal value of -∆ S M is achievedat temperatures T max . T C and it does not reach the value of S max . The sig-nificant reduction of -∆ S M can be ascribed to the influence of strong magneticcorrelations with corresponding large value of T C . Apparently, only few systemscan use full potential of the magnetic degrees of freedom.Thus, considering double molybdates, already a simple replacement of theCs + ion by other alkali-metal ions M + with smaller mass, as Li, Na, K or Rb,should provide for corresponding MGd(MoO ) compounds maximal magneticentropy S max = 35.7, 34.6, 33.5 and 30.7 J/kgK, respectively. As can be seenfrom the Table. 2, further increase of -∆ S M would require hypothetical com-pounds with higher number of Gd ions per formula and at the same time weakmagnetic correlations between Gd ions.19 able 2: Magnetocaloric properties of selected Gd-based oxides. S max is calculated for S =7/2. Compound -∆ S M T max B f T C S max = ln(2 S +1) R / M (J/kgK) (K) (T) (K) (J/kgK)GdMnO [38] 31 7 8 42, 23, 5.2 66.45Gd O [39] 10.7 2 ∗ Fe O [40] 2.45 35 3 90 55Gd Ga O [41] 24 2 ∗ Al O [41] 28 2 ∗ [42] 40.9 2 9 40, 25, 3.9 74.75GdVO [43] 41.1 3 5 2.4 63.52GdCrO [44] 28 20 7 20 63.28GdPO [20] 62 2.1 7 0.77 68.55 ∗ values obtained at lowest experimental temperature.
4. Conclusion
In conclusion, we studied magnetic and magnetocaloric properties of the sin-gle crystal of CsGd(MoO ) . The analysis of specific heat and magnetizationprovided refinement of CEF parameters indicating the dominance of uniaxialsymmetry of local crystal field. Maximum values of the isothermal entropychange in magnetic fields up to 5 T are expected to occur at temperaturesaround 2 K. It should be noted that -∆ S M achieves 18 J/kgK already for thefield 1 T, while for 7 T, maximal -∆ S M = 26.8 J/kgK with a refrigerant ca-pacity of 215 J/kg. The absence of thermal hysteresis and the losses due toeddy currents as well as good chemical stability and high thermal conductivitymakes the compound CsGd(MoO ) attractive for magnetic refrigeration at lowtemperatures.Last but not least, our simulations of crystal field effect showed that strongerCEF lowers the maximal value of -∆ S M , and shifts the position of the -∆ S M maximum towards higher temperatures. Thus, the strength of CEF can control20he size of MCE as well as a working temperature interval.
5. Acknowledgments
This work has been supported by VEGA grant 1/0269/17, projects APVV-0132-11, 14-0073 and ERDF EU project No. ITMS26220120047. Financialsupport of US Steel DZ Energetika is greatly acknowledged.
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