Structural, magnetic, thermodynamic and electrical transport properties of a new compound \mbox{Pr}_2\mbox{Rh}_{2}\mbox{Ga}
SStructural, magnetic, thermal and electrical properties of a new compoundPr Rh Ga Baidyanath Sahu, a) Sindisiwe P. Xhakaza, and Andr´e M. Strydom Highly Correlated Matter Research Group, Physics Department, University of Johannesburg, PO Box 524,Auckland Park 2006, South Africa
A new ternary intermetallic compound Pr Rh Ga was synthesized by arc-melting and was characterizedby powder X-ray diffraction (PXRD), magnetization, heat capacity C p ( T ), and electrical resistivity ρ ( T )measurements. PXRD patterns revealed that Pr Rh Ga crystallizes in the La Ni -type of orthorhombicstructure with the space group Cmca . The temperature variation of magnetic susceptibility, C p ( T ) and ρ ( T ) confirmed that Pr Rh Ga exhibits a ferromagnetic behavior with the transition temperature of 18 K.The estimated Sommerfeld coefficient γ = 640 mJ/(Pr . mole . K ) from the C p ( T ) results in the paramagneticregion just above T C was large in comparison to ordinary metals. In the paramagnetic region ρ ( T ) datashowed a metallic behavior characteristic of electron - phonon scattering. The maximum negative magneto-resistance at high field occurs in the region near the magnetic phase transition temperature. The maximumvalue of magnetic entropy change ( − ∆ S M ) and adiabatic temperature change (∆ T ad ) are 8 . / kg . K and3 . / kg, and 135 J / kg for a change of magnetic field 0–5 T and 0–9 T, respectively.Arrott plot derived from isothermal magnetization and the universal scaling plot by normalizing − ∆ S M confirm that the compound undergoes a second order ferromagnetic to paramagnetic phase transition.Keywords: Ferromagnet; Spin wave; Heat capacity; Electrical resistivity; Magnetoresistance; Magnetocaloric A. Introduction
The Praseodymium (Pr) based ternary compoundspresent interesting magnetic, electric and thermal trans-port properties such as non–magnetic ordering, ferro andantiferromagnetic behavior, heavy fermion , Kondobehavior and superconductivity . The magnetic andtransport properties of Pr-compounds are strongly in-fluenced by the crystal electric field (CEF). Pr-basedternary compounds are also attractive for the heavyfermion superconductivity properties. Bauer et. al. ,observed the occurrence of a heavy-fermion supercon-ductivity state in the PrOs Pb compound. Similarly,Zhang et. al. , have reported multiband superconduc-tivity in PrPt Ge compound with critical temperatureof 8 K. Additionally, Pr–compounds such as PrCu In ,PrCo B C , and PrNi B C show large Sommerfeldcoefficient values.Recently RE T X (RE = rare earth metal, T = tran-sitions metal and and X = p-block elements) series ofcompounds are of interest for attractive structural andphysical properties. RE T X compounds are known toform in a small number different structure type, whichdepends on the composition. Most of RE T X com-pounds crystallize in Mo FeB – type of tetragonal struc-ture with space group P /mbm . A small number ofcompounds form a superstructure of Mo FeB and crys-tallize in U Pt Sn-type of tetragonal structure . Someof the compounds crystallize in W CoB and Mn B Al –type of orthorhombic structure with space group
Immm and
Cmmm , respectively . Some RE T X com- a) Corresponding author pounds show structural transformation, which dependson the rare-earth size, external pressure and also on pro-cessed temperature. For example, a tetragonal to or-thorhombic is found in RE Ni Sn compounds by vary-ing rare-earth elements and external pressure on a par-ticular sample. Pr T X (T = Cu, Ni and Pd, X =In, Sn) crystallize in the tetragonal Mo FeB − typestructure . Pr Ni Ga, Pr Ni Al and Pr Co Alcrystallize in W CoB – type of orthorhombic struc-ture with space group Immm . Pr Co Al shows a struc-tural transformation from orthorhombic to monoclinic athigher temperatures .Very recently, a new variant of the 2:2:1 formula typewas reported, namely Ce Rh Ga which crystallizes inmonoclinic (space group C /c ) at low temperature andshows an ordered version of the orthorhombic La Ni –structure type with space group Cmca (no-64) at highertemperature. Surprisingly, this orthorhombic compoundwas found to exhibit a phase transition at 130 K that isunusually high among Ce compounds . In this paper, wehave investigated whether other rare-earth elements areamenable to the new 2:2:1 type structure, and report onthe synthesis, structure, and physical properties of a newcompound Pr Rh Ga. The magnetocaloric effect (MCE)of this compound has also been studied from isothermalmagnetization and heat capacity measurements.
B. Experimental Set-up
A stoichiometric mixture of the elements Pr (99.85wt.% purity) Rh (99.85 wt.% purity), and Ga (99.999wt.% purity) with the ratio Pr:Rh:Ga = 2:2:1 and to-tal mass of 1 g for this compound was arc-melted ona water-cooled copper hearth using an Edmund B¨uhler a r X i v : . [ c ond - m a t . m t r l - s c i ] F e b GmbH MAM-1 commercial arc furnace. The sample wasmelted under ultra-high purity argon (Ar) atmosphere,where the gas bottle was connected to a Monotorr high-temperature gas getterer. The sample was melted severaltimes to ensure homogeneity. The weight losses after themelting process were confirmed to be less than 1.0 wt.%. The as-cast sample was wrapped in tantalum foil andannealed for one week at 1073 K in an evacuated silicaampoule. Finally the sample was quenched in cold water.In order to study the phase purity of the annealed sam-ple Pr Rh Ga was characterized by powder X-ray diffrac-tion (PXRD) using a Rigaku diffractometer with Cu-K α radiation. Magnetic, heat capacity ( C P ) and electricaltransport ( ρ ) properties measurements were performedon a Quantum Design commercial Dynacool PhysicalProperty Measurement System (PPMS) in the temper-ature range of 1.8 - 300 K, with applied magnetic fieldup to 9 T. Heat capacity was measured by employingthe two- τ relaxation method. The sample is stacked andthermally coupled to the sample platform using ApiezonN grease. Electrical resistivity measurements were per-formed by a standard four probe contact method andusing an ac-current excitation. C. Results and Discussions1. X-ray Diffraction
Fig. 1a depicts PXRD pattern measured at room tem-perature. For investigating the crystal structure andphase purity, the data was processes with a Rietveldrefinement method using the FULLPROF software .The PXRD pattern of Pr Rh Ga along with the refine-ment fitting is shown in Fig. 1a. The refinement resultsrevealed that this compound crystallizes in the La Ni -type of orthorhombic structure belonging to the Cmca space group. In the structure of La Ni , the rare-earthatom Pr occupies La site, whereas Rh and Ga occupy thetwo sites of Ni . The obtained refinement parametersare listed in Table1. A schematic diagram for the crys-tal structure was generated from the refinement data byusing VESTA software and is shown in Fig. 1b . Thedetails arrangement of atoms in crystal structure is de-scribed for the compound of Ce Rh Ga .The obtained Pr-Pr distances are ranging from 3.431 to3.710 ˚A, which is approximately twice the metallic radiusof Pr element (r Pr = 1.810 ˚A) . The short interatomicdistances of Pr-Rh is 2.978 ˚A, Pr-Ga is 3.334 ˚A and Rh-Ga is 2.547 ˚A, which is significantly smaller than thesum of the metallic radius (r Rh = 1.345 ˚A) and Ga (r Ga = 1.411 ˚A) of two atoms. These results suggest thatthere is a strong bonding between these elements. TABLE I. The lattice parameters and unit cell volumesPr Rh Ga compounds obtained from the Rietveld refine-ments of XRD patterns for Orthorhombic phase along withthe atomic coordinate positions.a 5.869(3) ˚Ab 9.607(2) ˚Ac 7.464(2) ˚AV 420.80(3) ˚A Atomic coordinates for Pr Rh GaAtom Wyckoff x y z
Pr 8 f e a
2. Magnetic properties
The temperature variation of dc–magnetization( M ( T )) was carried out in both zero-field-cooled (ZFC)and field cooled (FC) protocol in the applied externalapplied magnetic fields of 0.2 T and 0.5 T. In the ZFCprocess, the sample was cooled down to 2 K in zero field.Thereafter, a field was applied and data were recordedwhile warming the sample to high temperature. In FCprocess, the sample was cooled down in presence of mag-netic field to 2 K, thereafter data was recorded uponwarming from 2 K. Fig. 2 shows the temperature depen-dence of dc–magnetic susceptibility χ ( T ) = M ( T ) /H , forPr Rh Ga. χ ( T ) shows that the sample exhibits ferro-magnetic behavior. The Curie temperature T C was esti-mated from the peak of the d M ( T )/d T of the FC magne-tization curve for 0.5 T, and was found to be T C = 18 K,which is shown in inset (a) of Fig. 2. The ferro- magnetictransition temperature deduced for Pr Rh Ga is higherthan the reported for Ce Rh Ga . The Pr Rh Ga com-pound does not show any high temperature transition likeCe Rh Ga. However, Ce Rh Ga exhibits an additionalantiferromagnetic transitions above 125 K . It is alsonoteworthy that the ZFC and FC curves start to divergebelow T C , which is known as irreversibility behavior. Thedifference between ZFC and FC magnetization becomesnegligible for the applied field of 0.5 T. This irreversibilitybehavior at small value of applied magnetic field proba-bly arises due to the presence of uniaxial anisotropy as-sociated with 4f-electron cations, short-range magneticordering or the domain wall pinning effect . However,in this case, the ZFC magnetization decreases with de-crease in temperature far below T C , which causes theirreversibility behavior. This point towards domain wallpinning due to the magnetocrystalline anisotropy of thePr ions, as a probable cause of the irreversibility be-havior in the compound .The temperature variation of inverse dc-magnetic sus-ceptibility, χ − ( T ) for H = 0.2 T is depicted in inset FIG. 1. (a) PXRD patterns along with the Rietveld refine-ment profile for Pr Rh Ga. The red open circles representthe experimental data and black solid line stands for the cal-culated pattern from the model structure used in the Rietveldrefinement to fit the experimental data. The difference curveis shown as a blue line and the allowed Bragg peaks as verticalbars. (b) Schematic diagram for the crystal structure of thePr Rh Ga compound. (b) of Fig. 2. The χ − ( T ) graph shows a linear behav-ior at temperatures above 20 K, which follows the Curie– Weiss law; χ ( T ) = C / ( T − θ p ), where C is the Curieconstant and is defined as C = N µ / B . θ p is the para-magnetic Weiss temperature. A linear fit to the inversesusceptibility in the data yields θ p = 17.1 K. The positivevalue of θ p indicates the presence of a strong ferromag-netic exchange interaction in the system. The calculatedvalues of the effective moment ( µ eff ) range µ eff = 3.57 µ B /Pr , which is very close to theoretical value for afree trivalent Pr , g J [J(J + 1)] / = 3.58 µ B for J = 4.This result indicates that 4f shell electrons of Pr ionsare the predominant magnetic species.Fig. 3 shows the field-dependent isothermal magnetiza-tion of Pr Rh Ga compound. A set of isothermal magne-tization M ( H ) curves were measured with magnetic fieldas high as 9 T. The measurements were carried out atdifferent temperatures from 2 to 30 K ( for both aboveand below T C ). As seen from Fig. 3, the sample exhibitsferromagnetic behavior below the ordering temperature T = 18 K. Above T C , M ( H ) shows a typical paramag-netic behavior. It is also observed that the magnetizationdoes not reach saturated value even at high field of H = FIG. 2. Temperature dependence of the dc-magnetic suscep-tibility χ ( T ) of Pr Rh Ga in the field-cooled (FC) and zero-field-cooled (ZFC) process. Inset (a) shows the d M ( T )/d T ofFC curve under 0.2 T to estimate the transition temperature.Inset (b) temperature variation inverse magnetic susceptibil-ity of FC curve under 0.2 T.FIG. 3. Isothermal magnetization at different temperatures. µ B /Pr. Theobtained magnetization of Pr Rh Ga is smaller than thetheoretical value of Pr free ions, gJ = 3.2 µ B /Pr. Themagnetic moment per Pr ions at 9 T for 2 K, is found tobe 1.65 µ B /Pr, which is also two times less than the sat-urated moment value expected for parallel alignment offree Pr . The low saturation value may be attributed tothe influence of anisotropy due to the CEF surroundingPr ions .
3. Heat capacity
Fig. 4a depicts the C p ( T ) for Pr Rh Ga in solidblack symbols and non-magnetic reference compound,La Rh Ga in solid red symbols. At room temperature, C p ( T ) is found to reach a value of 128 J/(mole . K). Thesevalues deviate only 3% from the Dulong-Petit value un-der the formula C p = 3nR = 124.7 J/(mole . K), where nis the number of atoms per formula unit (in this case n= 5) and R is the universal gas constant. At low temper-atures, C p ( T ) shows a λ -type anomaly, which marks theferromagnetic ordering in the compound. The discontin-uous jump with λ -shape anomaly of heat capacity resultindicates that the compound undergoes second order fer-romagnetic phase transition .At low temperature, the heat capacity of the metalis contributed by both electronic and phononic contri-bution, i.e C p = C el + C ph . The free electron na-ture of the quasi-particle interactions in an electronicsystem is indicated by the Sommerfeld coefficient( γ ) .The value of γ can be obtained from the linear fitof the C p / T vs. T plot by assuming the general ex-pression C p = γ T + β T . In order to perform thefit, the lowest available paramagnetic temperature re-gion was used and is shown in Fig. 4b along with thefitted line (red line). The best fit data yields γ =640 mJ/(Pr . mole . K ). The obtained γ value is com-pared with other heavy fermions Pr-based ternary com-pounds viz.,
286 mJ/(Pr . mole . K ) for PrRhSn , 315mJ/(Pr . mole . K ) for Pr Rh Ge , 716 mJ/(Pr . mole . K )for Pr Rh Sn , 300 mJ/(Pr . mole . K ) Pr Ru Ge and 300 mJ/(Pr . mole . K ) for PrV Al . The value ob-tained here is enhanced as compared to the reportedvalue for the Pr-based ternary compounds. The Debye-temperature( θ D ) was also extracted using the fitted valueof β and yield θ D = 313 K.The inset to Fig. 4a present the low-temperature C p ( T )data in the range between 2 K and 30 K, which wasmeasured under the different values of magnetic field viz.,
0, 1 and 5 T. One can see that the peak associated withthe phase transition shifts towards higher temperatureswith applied magnetic field and also suppresses at highmagnetic field of 5 T. This feature is commonly seen inferromagnetic compounds . Below T C , the C p ( T ) datacan be described with the following formula; C p ( T ) = γ e T + BT / exp ( − ∆ T ) , (1)where γ e is the electronic contribution to the heat capac-ity in the ordered state. The second term BT / exp ( − ∆ T ) represents the spinwave contribution for a ferromagnetwith an energy gap ∆ = E g /K B in the magnon spec-trum of the heat capacity. The best fit on the experi-mental data is shown in inset of Fig. 4a with solid linesand yielded parameters: γ e = 0.029(3) J/(mole- K ), B =0.794(3) J/(mole- K ), ∆ = 8.47(3) K in zero field, and γ e = 0.053(4) J/(mole- K ), B = 0.616(3) J/(mole- K ), ∆ FIG. 4. (a) Temperature dependence of the heat capacity C P ( T ) of Pr Rh Ga measured in zero field. C P ( T ) data ofthe non-magnetic reference compound La Rh Ga . Inset:temperature dependent heat capacity under different mag-netic field. (b) The low-T part of C P ( T )/ T as a function of T together with fitting for evaluating the Sommerfeld coeffi-cient and Debye temperature. (c) The calculated 4f-electronentropy as a function of temperature. = 7.16(2) K in 1 T. The values of ∆ are smaller than T C ,which is in good agreement with the previously reportedRE T X system .The magnetic entropy S m has been estimated by inte-grating ( C m ( T ) / T ) as a function of T and is shown inFig. 4c. The S m released at T C is very close to the valueof Rln2. This reflects that the Pr-has doublet magneticground state. It is also noticed that the S m graduallyincreases with increasing temperature and fully saturateat 100 K, which is much higher than the phase transitiontemperature. The obtained saturation S m value at 200 Kis only about 71 % of the full Rln(2J+1), J = 4 entropy.
4. Electrical resistivity
The ρ ( T ) of Pr Rh Ga is presented in Fig. 5. It isobserved from Fig. 5 that the resistivity gradually de-creases with decreasing temperature and shows well de-fined kink at the magnetic transition. The compound
FIG. 5. Temperature dependence of resistivity under zeromagnetic field and the red solid line represents the fit ofEq. (2) to the experimental data.. The upper inset (a) d ρ /dTas a function of temperature. The arrow indicates the criticaltemperature T C associated with ρ . Inset (b) solid symbols arelow-temperature ρ ( T ) measured under field of 0 and 1 T andthe solid line represents the fit of Eq. (3) to the experimentaldata. shows overall metallic behavior. It is also noticed thatthe resistivity data shows a strong curvature in the para-magnetic region (above 50 K), which is associated withthe substantial electron-phonon interaction strength athigh temperature and also the scattering effects of theconduction electrons on disordered magnetic moments incombination with the CEF effect . At low temperature,s-d interband scattering of the conduction electrons is re-lated to a Mott term. In the paramagnetic region T >
50 K, experimental data of ρ ( T ) was derived using thefollowing the Bloch - Gr¨uneisen - Mott formula . ρ ( T ) = ρ + 4 A θ R (cid:18) Tθ R (cid:19) θ R /T (cid:90) x dx ( e x − − e x ) − KT , (2)where ρ is the residual resistivity typically associatedwith metallurgical defects. A is the electron-phononcoupling constant. θ R is the Debye temperature, whichrepresents the characteristic energy scale of lattice vi-brations. In the last term, K of Eq.(2) is known as theMott coefficient, which is a characteristic of s–d inter-band scattering. The best fits of Eq. (2) with solid line tothe experimental ρ ( T ) vs T data yielded: ρ = 51.29(2) µ. Ω .cm ; θ R = 102 . K ; A = 9 . µ. Ω .cm.K − and K = 2 . × − µ. Ω .cm.K − .The inset (b) of Fig. 5 depicts an expanded view of ρ ( T ) data at low temperature. The resistivity decreasessharply below the phase transition which is due to spin FIG. 6. Field dependence of the magnetoresistance isothermsof Pr Rh Ga at different temperature near T C . disorder scattering of the conduction electrons have beenquenched by the magnetic ordering of the spins. Themagnetic transition temperature was also evaluated from ρ ( T ) result by taking the derivative of ρ with respect to T . The expanded region of d ρ /d T curve at low tempera-ture is presented in inset (a) of Fig. 5. According to Satocriterion , the value of T C = 18 K was estimated fromthe midpoint of the anomaly in the d ρ /d T curve, and ismarked with an arrow inside of the figure. The magneticphase transition temperature in ρ is consistent with theresults of χ ( T ) and C p ( T ) data.In order to analyse the characteristic features for re-sistivity associated with the magnetic ordered state, thetemperature dependence ρ ( T ) was measured at low tem-perature under magnetic field value of 1 T and is plottedin the inset (b) of Fig. 5. As seen from the inset (b)of Fig. 5, the anomaly at the transition temperature issuppressed with the application of magnetic field, whichis generally seen in a ferromagnetically ordered system.The scattering of the conduction electrons in terms ofmagnons can be explained though the spin-wave excita-tion. Below T C , the temperature variation of ρ underzero-magnetic field data was described by using spin-wave excitation of Eq. (3) . ρ ( T ) = ρ F M + A ∆ R T (cid:20) T ∆ R (cid:21) exp (cid:20) − ∆ R T (cid:21) , (3)where ρ F M represents the residual resistivity of the mag-netic ordered state, A is a material constant which de-pends on the spinwave stiffness, and ∆ R is associatedwith the energy gap in the ferromagnetic magnon spec-trum. A best fit of Eq.(3) on the experimental resultwith solid line yields fitting parameters: ρ F M = 26.6(3) µ Ω . cm , A = 0.015(2) µ Ω . cm . K − and ∆ R = 9.01(3) K.In order to investigate the magnetoresistance (MR) be-havior of Pr Rh Ga, isothermal magnetic field depen-dence of resistivity was measured at different tempera-tures for both below and above T C . MR was calculatedfrom the isothermal magnetic field dependence of resis-tivity curve using the following formula of Eq.(4). Theobatined MR variation with magnetic field was plottedin Fig. 6. M R = ρ ( H, T ) − ρ (0 , T ) ρ (0 , T ) 100% (4)It is seen from Fig. 6 that isothermal MR shows bothpositive and negative values at high fields of 9 T depend-ing on the temperature. As seen the data for lowest tem-perature of 2 K, the magnitude of MR is positive above H = 3 T and gradually increases with increasing field.However, negative MR is seen for T = 15 K and higher.This result indicates that both positive and negative MRcan exists below the transition temperature. The neg-ative MR in ferromagnetic region can be attributed toreduction in spin-disorder resistivity. However, the posi-tive MR in ferromagnetic compound can be understoodin-terms of the Lorentz’s force, which causes the classicalmodification of the electron trajectory . The MR at 20K just above the T C shows negative behavior, which maysuggest the presence of weak ferromagnetic correlationsat 20 K. Similar behavior of MR properties below andabove T C was also reported in the case of Pr Rh Ge andCeIr B compounds . D. Magnetocaloric effect
The magnetocaloric effect of the Pr Rh Ga is ex-plored through isothermal magnetization and heat ca-pacity measurements. The order of the phase transi-tion is also confirmed from Arrott plots. Arrott plots( M vs. H/M ) were performed from the M ( H ) curves.Fig. 7 shows the isotherms of M vs. H/M plot in thetemperature range of 12 K to 25 K (near the transitiontemperature region). According to Banerjee criterion, apositive slope in the M vs. H/M plot implies that thesystem possesses a second order magnetic transition .Arrott plots are commonly used to determine the na-ture of a magnetic phase transition based on the isother-mal magnetization data. However, determining the mag-netic phase transition from Arrott plot has also somelimitation for the shortcomings such as meta-magnetictransition, demagnetization field and domain wall pin-ning effect . Therefore, Bonilla and Franco have sug-gested one more method to determine the second order ofphase transition by employing − ∆ S M vs . T curve, whichwill be discussed for this Pr Rh Ga compound.The ∆ S M was calculated from isothermal magnetiza-tion curve using the following Maxwell relation : FIG. 7. Arrott plots ( M vs. H/M ) derived from the magne-tization isotherms in the temperature range of 12 - 25 K witha step of 1 K. ∆ S M ( T,H ) = H (cid:90) (cid:18) ∂ M ∂ T (cid:19) d H . (5)Fig. 8 shows the variation of − ∆ S M as a function oftemperature for different values of magnetic field. It isseen that there is no tendency of saturation in − ∆ S M values even at applied magnetic field strength of 9 T. Itis found that the maximum values of − ∆ S M are 6 . , . . / kg . K for the change of magnetic field of 0–5 T,0–7 T, and the 0–9 T, respectively. The obtained − ∆ S M values are comparable with the reported value of otherPr based ternary compounds viz. , − ∆ S M = 5 . / kg . Kfor 7 T of Pr Pt In and − ∆ S M = 6 . / kg . K for 5 T ofPr Co Si . The observed values are also comparedwith the some other reported RE T X compound in Ta-ble. II. As seen from the Table. II, the obtained value ofPr Rh Ga is also quite large and comparable to those ofthe reported refrigerant materials around correspondingtransition temperature. From this comparison, one cansay that the present Pr Rh Ga compound is in a mate-rials class that may profitably be exploited from MCE.Another important parameter to determine potentialof a MCE material is the ∆ T ad . The ∆ T ad was calcu-lated from temperature dependent zero-field heat capac-ity data (is shown in Fig. 4) and obtained − ∆ S M , usingMaxwell’s relation by the following formula :∆ T ad ≈ T C p | ∆ S M | . (6)Fig. 9 shows the temperature variation of ∆ T ad for thechange of magnetic field up to 9 T. The maximum value FIG. 8. Temperature variation magnetic entropy changes(∆ S M ) for different values of changing magnetic fieldTABLE II. The transition temperature, the maximum valuesof magnetic entropy change (∆ S M ), and refrigeration capacity(RC) under the field change of 0–5 T for some rare-earthcompounds of RE T X.Method T N / T C − ∆ S M RC Ref(K) (J/kg.K) (J/kg)Nd Pt In 16 5.01 — Gd Ni Sn 75 4.6 — Er Co Al 32 5.9 120 Gd Cu Cd 120 7.8 234 Dy Co Ga 55 6.2 114 Pr Rh Ga 18 6.1 70 This work of ∆ T ad was found to be 3.5 K for the change of field0–9 T. This estimated value of ∆ T ad is quite good ascompared to some of RE T X ternary compounds formagneto-refrigerant application .Additionally, the quality factor of MCE materials isthe refrigeration capacity (RC) which evaluates the mag-netic cooling efficiency. RC is an indirect measurementof heat transfer in an ideal MCE cycle between the coldand hot reservoirs. The RC of Pr Rh Ga was estimatedfrom − ∆ S M vs . T curve. As suggested by Pecharskyaand Gschneidner , the RC value is estimated from thearea under the curve by integration using following theformula: RC = T (cid:90) T ( − ∆ S M ) d T , (7) FIG. 9. Temperature variation of the adiabatic temperaturechange (∆ T ad ) for different values of magnetic field. where T and T are the temperatures corresponding toboth sides of the half-maximum value of the − ∆ S M (T)peak. It is found that the RC values gradually increasewith increasing field. The values of RC are 70 J/kg, 100J/kg and 135 J/kg for a change of field 0–5 T, 0–7 T and0–9 T respectively. As seen from Table. II, our observedvalues for the present Pr Rh Ga compound is compa-rable even larger than those of some reported magneticcaloric materialsMagnetocaloric effect of a magnetic material also de-pends on the order of its magnetic phase transition. Inorder to get more confirmation for the second order mag-netic phase transtion of Pr Rh Ga, we have used uni-versal scaling plots for the magnetic entropy changes .The universal scaling plot is derived from the − ∆ S M vs. T curve. The normalized entropy change ∆ S M /∆ S max M (where ∆ S max M is the maximum entropy change) againstrescaled temperature ( θ ) for below and above T C is plot-ted for different fields and is shown in Fig. 10. Therescaled temperature θ below and above T C as definedin the following equation θ = − ( T − T C) ) / ( T r − T C) ( T − T C) ) / ( T r − T C) ) , (8)where T r1 and T r2 is the temperature corresponding tohalf of the value of ∆ S M /∆ S max M at T < T C and T > T C ,respectively. As seen from Fig. 10, the normalized en-tropy change with respect to rescaled temperature con-verge to a single universal curve for both below and above T C for different values of magnetic field. This merging tosingle universal curve indicates that the compound un- FIG. 10. Normalized entropy change (∆ S M /∆ S max M ) as afunction of the rescaled temperature( θ ) for the selected valuesof applied field dergo second order ferromagnetic to paramagnetic tran-sition. E. Summary
In summary, we have successfully synthesized a newpolycrystalline compound Pr Rh Ga. This compoundcrystallizes in the orthorhombic, La Ni -type of struc-ture. Magnetic, heat capacity measurements and resistiv-ity results revealed that the present compound undergoesferromagnetic behavior with the Curie temperature T C =18 K. We found that Pr Rh Ga does not have structuralphase transition like Ce Rh Ga. The Sommerfeld coeffi-cient value derived from heat capacity shows, a significantenhancement, which gives an indication of a heavy elec-tron ground state in Pr Rh Ga. Resistivity results con-firmed that the compound has a metallic-like conductiv-ity character, where the curvature paramagnetic region isobserved due to strong electron-phonon scattering. Be-low T C , the temperature dependence of heat capacity andresistivity data were well described with the ferromag-netic spin-wave relation. Ferromagnetic spin-wave rela-tion below T C yields an energy gap value of 8.47(3) K and9.01(3) K from temperature dependent heat capacity andresistivity data, respectively. This compound exhibitsboth positive and negative magnetoresistance in the mag-netically order state. Arrot plot ( H/M vs. M ) and theuniversal scaling plot of − ∆ S max M vs. rescaled tempera-ture ( θ ) confirm that this compound undergoes a secondorder paramagnetic to ferromagnetic phase transition.The maximum − ∆ S max M value of 8 . / kg . K and max-imum ∆ T ad value of 3.6 K are obtained for Pr Rh Ga under change of field 0–9 T. The corresponding valuesof RCP is 121 J/kg at 9 T. These obtained values areconsiderable as compare to the reported MCE materials.
Acknowledgements
This work is supported by Global Excellence andStature (UJ-GES) fellowship, University of Johannes-burg, South Africa. AMS thanks the URC/FRC of UJfor assistance of financial support.
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