Structural, magnetic and magnetocaloric properties of hexagonal multiferroic Yb_1−xSc_xMnO₃ (x = 0.1 and 0.2)

Abstract

We have studied the effect of Sc doping on the structural, magnetic and magnetocaloric properties of multiferroic Yb_1−xSc_xMnO₃ (x = 0.1 and 0.2). X-ray powder diffraction shows that both samples crystallize in the hexagonal phase with P6₃cm space group. The structural analysis shows a decrease in the lattice parameter a, a decrease in the cell volume of the hexagonal unit cell and a decrease in the average bond length between Mn–O, with Sc substitution. Magnetic measurements show that the Néel temperature (T_N) increases from 90 K for x = 0.1 to 94 K for x = 0.2 samples. Isothermal magnetic curves show that the field variation in magnetization generates a metamagnetic transition. The maximum entropy change −ΔS^max_M and the relative cooling power (RCP) of Yb_1−xSc_xMnO₃ are found to be 2.46 ± 0.40 J mol⁻¹ K⁻¹ and 38.5 ± 9 J mol⁻¹ for x = 0.1 and 1.87 ± 0.31 J mol⁻¹ K⁻¹ and, 30.1 ± 8 J mol⁻¹ for x = 0.2 with ΔH = 10 T. The rescaled magnetic entropy change curves for different applied fields collapse onto a single curve for materials with second-order phase transitions.

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1. Introduction

Materials with the simultaneous presence of more than one ferroic property (multiferroics) with a strong coupling between them have been the subject of tremendous research activity in recent years. Control of electric polarization by the application of a magnetic field and inducing magnetic ordering by the application of an electric field in these materials are expected to lead to next generation multifunctional devices for applications in information storage processes, spintronics, multiple-state memories, magnetoelectric sensors, etc.^1–4 One typical example of multiferroic materials is hexagonal manganites RMnO₃ with space group P6₃cm, for elements at the rare-earth R site with a relatively small ionic radius, e.g., Ho, Er, Tm, Yb, Lu, Y, and Sc which exhibit a strong coupling between electric and magnetic dipoles.^5–7 In these hexagonal manganites, Mn ions form a natural two dimensional edge-sharing triangular network, which becomes magnetically frustrated with an antiferromagnetic nearest–neighbor interaction.^8,9

Among rare earth hexagonal manganites YbMnO₃ has been studied only occasionally. The crystal structure of YbMnO₃ comprises layers of corner-sharing MnO₅ trigonal bipyramids with two apical (O1, O2) oxygen atoms and a triangular base of nonequivalent O3 and O4 oxygen atoms. Yb atom occupies two crystallographic sites (in Wyckoff notations), 2a and 4b of space group P6₃cm. The Yb–O displacements give rise to a ferroelectric moment along the c-axis (T_C = 990 K), the Mn³⁺ moments order at the Neel temperature (T_N = 85 K) and below T_C ∼ 5 K, the magnetic moments of the Yb³⁺ ions are completely ordered.^10,11 Most of the studies in such multiferroic manganites focus on their magnetic and ferroelectric behavior, but less work has been undertaken on exploring their magnetocaloric effect (MCE) properties.

MCE describes the reversible change in temperature of a material under adiabatic condition produced by the magnetic entropy change ΔS_M due to the variation in applied magnetic field.^12,13 The main aim in this field is to search for new materials that exhibit a large MCE and are capable of operating at different temperature ranges, depending on the intended applications. Large MCE close to room temperature would be useful for domestic and several technological applications while large MCE in the low-temperature region is important for specific technological applications such as space science and liquefaction of hydrogen in fuel industry.^12,14 The guidelines for the choice of an appropriate material are that it should have low heat capacity and exhibit a large entropy change at the ferromagnetic (FM) to paramagnetic (PM) transition or field-induced metamagnetic transition from antiferromagnetic (AFM) to FM states with a minimal hysteresis.

In the present report, effect of Sc substitution on structural, magnetic and magnetocaloric properties in the Yb_1−xSc_xMnO₃ (x = 0.1 and 0.2) system is studied. In order to successfully use multiferroic materials in practical applications, the most important criterion is that the coupling between the ferroelectric and magnetic ordering should occur close to room temperature. Thus, it is necessary to enhance the low antiferromagnetic ordering T_N of YbMnO₃ through chemical doping. In our previous paper¹⁰ on divalent Mg ion doped YbMnO₃, it is shown that T_N increases marginally with doping. The increase in T_N can be explained on the basis of smaller cell volume (Mg has small ionic radii), which may lead to strong exchange interactions and therefore higher ordering temperatures. Hence, it is of significance to search for other effective dopants. Hexagonal ScMnO₃ exhibits an antiferromagnetic (AFM) transition at 139 K (ref. 15) and Sc³⁺ has small ionic radius compare to that of Yb³⁺. The large field induced magnetization observed in Yb_1−xSc_xMnO₃ has motivated us to investigate the magnetocaloric behavior in this system.

2. Experimental details

Polycrystalline samples of Yb_1−xSc_xMnO₃ (x = 0.1 and 0.2) were synthesized by the conventional solid state reaction method. High-purity (purity better than 99.9%) Yb₂O₃, Sc₂O₃ and MnCO₃, powders are obtained from M/s Sigma-Aldrich. The precursors Yb₂O₃ and Sc₂O₃ powders are preheated at 500 K for 5 h to remove any absorbed moisture. Stoichiometric proportions of Yb₂O₃, Sc₂O₃ and MnCO₃ powders are thoroughly mixed, and then calcined in platinum crucibles at 1150 °C in air for 24 h with an intermediate grinding for homogenization. The calcined mixture is cold pressed into pellets at approximately 5 × 10⁷ Pa pressure and then sintered at 1350 °C in air for 20 hours. Finally, all samples are slowly cooled to room temperature for sufficient oxygenation. The phase purity of each sample is checked by powder X-ray diffraction (XRD) using a Bruker D8 Advance X-ray powder diffractometer operating with the Cu-Kα radiation. The magnetization measurements, performed in a Cryogenic Inc. (UK) make vibrating sample magnetometer operating at 20.4 Hz. The temperature dependence of magnetic moment was measured for zero-field cooled (ZFC) and field cooled (FC) conditions at a magnetic field of 1000 Oe. The magnetization isotherms in fields up to 10 T were measured, at different temperatures in the vicinity of low temperature ordering transition.

3. Results and discussion

3.1. Structural characterization

The X-ray diffraction patterns and the Rietveld refinement of polycrystalline samples Yb_1−xSc_xMnO₃ (x = 0.1 and 0.2) are shown in Fig. 1. Both samples are in single phase and the measured patterns can be indexed to the hexagonal phase with P6₃cm space group (JCPDS no. 38-1246) in agreement with a previous report.¹⁰ Refined values of lattice parameters and discrepancy factors for Yb_1−xSc_xMnO₃ (x = 0.1 and 0.2) are shown in Table 1 along with corresponding values for YbMnO₃. It is clearly seen that due to Sc substitution, the relative cell parameter c/a increases. Overall the cell volume decreases. The decrease in lattice constant a and cell volume is due to the smaller ionic radius of Sc³⁺ [Shannon radius = 0.87 Å for coordination number (CN) = 8] than Yb³⁺ (Shannon radius = 0.985 Å for CN = 8). As the average A-site (i.e., Yb site) radius changes with Sc content, it is expected that the tolerance factor will also change.

Fig. 1 Rietveld refinement of room temperature XRD pattern of Yb_1−xSc_xMnO₃ (x = 0.1 and 0.2) samples indexed in space group P6₃cm.

Table 1 Refined crystallographic parameters and reliability factors of Rietveld refinement for Yb_1−xSc_xMnO₃ (x = 0.1 & 0.2) samples at room temperature^a

Yb1−xScxMnO3	x = 0.1	x = 0.2	Reported values for YbMnO3 (ref. 10 and 16)
a ‘t’ is the tolerance factor, given as: t = ((rYb+Sc + ro)/√2(rMn + ro)).
a (Å)	6.0577 (4)	6.046 (4)	6.0671 (4)
c (Å)	11.362 (4)	11.3575 (4)	11.3519 (4)
V (Å^3)	361.07 (2)	359.542 (2)	361.886 (2)
c/a	1.8756	1.8785	1.8710
χ^2	4.12	5.97	—
RP (%)	6.55	6.67	5.06
Rwp (%)	8.28	8.86	6.82
RB (%)	4.05	5.34	4.50
t (Å)	0.846	0.842	0.850

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Some selected bond distances and bond angles of Yb_1−xSc_xMnO₃ (x = 0.1 & 0.2) as well as those of YbMnO₃ are given in Table 2. The value of a decreases in Sc doped sample when compared to that in YbMnO₃ sample. This change is ascribed to the decrease in the average ab-plane i.e., Mn–O3, Mn–O4 is on Sc doping. The Mn–O1 and Mn–O2 bond lengths are also decrease along the c axis on Sc doping The average Mn–O distances in MnO₅ units are significantly shorter in the doped samples compared to pure YbMnO₃. In the hexagonal phase the Mn³⁺ ion is fivefold coordinated, forming a trigonal bipyramid polyhedral environment. Polyhedral distortions Δ are calculated using the following formula,¹⁷

where N is the coordination number (N = 5), d_n is the individual distance between Mn and the n^th nearest oxygen neighbor, and 〈d〉 is the average distance value.

Table 2 Main bond distances (Å) and angles for MnO₅ polyhedra in Yb_1−xSc_xMnO₃ (x = 0.1 and 0.2)^a

Parameter	x = 0.1	x = 0.2	Reported values for YbMnO3 (ref. 7)
a Δ is the distortion of MnO5 polyhedra.
Mn–O1	1.8442	1.8434	1.8532
Mn–O2	1.8019	1.8011	1.8366
〈Mn–O1, O2〉	1.823	1.822	1.845
Mn–O3	1.9104	1.9067	1.9033
Mn–O4	2.0931	2.0891	2.1017
〈Mn–O3, O4〉	2.002	1.9979	2.0025
〈Mn–O〉	1.9125	1.9099	1.9237
∑Radii	2.00	2.00	2.00
Yb1–O1(X3)	2.3781	2.3745	—
Yb1–O2(X3)	2.4719	2.4676	—
Yb1–O3	2.3251	2.3242	—
Yb2–O1(X3)	2.1853	2.1816	—
Yb2–O2(X3)	2.2765	2.2733	—
Yb2–O4	2.4439	2.4729	—
〈Yb–O〉	2.3468	2.349	—
∑Radii	2.405	2.405	—
Mn–O3–Mn (°)	118.644 (3)	118.64 (6)	119.5 (7)
Mn–O4–Mn (°)	119.04 (3)	119.038 (5)	118.6 (2)
Δ(10^−4)	27	26.5	24.14

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The distortion parameter is nearly constant with the Sc content in the hexagonal phase. In general, the Sc doping does not notably affect the structure of the MnO₅ polyhedron, in agreement with the weak changes of the trigonal bipyramidal crystal field, which is proved by the fact that the Mn³⁺ ions (3d⁴) remain in the high spin state (S = 2) throughout the whole doping range. The Mn–O bond lengths are in agreement with the sum of the ionic radii.¹⁵ Moreover, in the YbO₇ polyhedron, the Yb–O distances are larger in x = 0.1 sample than in x = 0.2 sample, as expected due to the larger ionic radius of Yb³⁺ when compared to Sc³⁺. Also, the average Yb–O distances are close to the sum of the ionic radii.

3.2. Magnetic behaviors

Fig. 2 shows the temperature dependence of the susceptibility χ = M/H of Yb_1−xSc_xMnO₃ (x = 0.1 and 0.2) measured at a magnetic field H = 1000 Oe. The susceptibility strongly increases with the decrease in the temperature at about 5 K. In the upper inset, we have shown zero field cooled (ZFC) and field cooled (FC) curves in the low-temperature region below 10 K. Near about 5.5 K both the curves show an anomaly with a sudden increase in magnetization with decreasing T. This abrupt change corresponds to the ferromagnetic (FM) ordering of Yb³⁺ moments at the 2a crystallographic sites through Yb–Yb interactions.¹⁸ A second anomaly (a kink) is observed at 90 K for x = 0.1 and 94 K for x = 0.2, as shown in the lower inset of Fig. 2, which correspond to the AFM ordering of the Mn³⁺ moments and represent Neel temperatures (T_N) for these samples. Further, from the Rietveld refinement study it is observed that the average bond distance between the manganese and oxygen atoms decreases with increases in Sc content. This increases the covalence of Mn–O bonds and results stronger exchange interaction. It may be noted that lattice parameter a decreases with the Sc content and the magnetic interaction occurs in the a–b plane of the hexagonal manganites. Therefore, the increase in covalence of Mn–O accounts for both the increase in magnetic ordering temperature and the decrease in the lattice parameter a. The increase in T_N from 85 K for YbMnO₃ (ref. 16) to 94 K for Yb_0.8Sc_0.2MnO₃ sample also can be explained on the basis of smaller cell volume, which might lead to strong exchange interactions and therefore higher ordering temperatures.

Fig. 2 Temperature dependence of 1/χ with Curie–Weiss fit and χ (H = 1000 Oe) of Yb_1−xSc_xMnO₃ (x = 0.1 and 0.2): Upper inset: ZFC and FC curves of T near the FM transition of Yb³⁺. Lower inset: ZFC and FC curves of T near the AFM transition of Mn³⁺.

Temperature variation of inverse magnetic susceptibility is plotted in Fig. 2 which shows that the Curie–Weiss (CW) law is well obeyed in temperature interval between 200 and 300 K in paramagnetic phase. It fits well to the Curie–Weiss law χ = C/(T − θ_CW). The values of paramagnetic Curie temperature (θ_CW) and effective magnetic moment (μ_eff) are calculated from this Curie–Weiss fit which are listed in Table 3. The negative Weiss temperature indicates presence of the antiferromagnetic interaction in these compounds. The experimental effective magnetic moments of Yb_1−xSc_xMnO₃ (x = 0.1 and 0.2) samples are obtained from the relation μ_eff = (7.99C)^0.5, where C is the Curie–Weiss constant.¹⁰ It is seen that the effective moment (μ_eff) decreases with increases in nonmagnetic Sc content. The experimental values of μ_eff are in reasonable agreement with the calculated values using the following formula: μ_eff = ((1 − x)μ_Yb² + μ_Mn²)^1/2, where x is the Sc concentration while μ_Yb and μ_Mn are the effective magnetic moment of Yb³⁺ (μ_Yb = 4.53 μ_B), and Mn³⁺ (μ_Mn = 4.9 μ_B), respectively. The ratio f = |θ_CW/T_N|, which is a measure of geometric frustration, is around 2.05. It is smaller for Sc doped samples when compared to that of YbMnO₃ which indicates that the magnetic coupling between the Yb and the Mn moments in presence of Sc relieves the frustration effect as the magnitude of the magnetically coupling between Yb and Mn ions is the most important factors for the geometrical frustration.

Table 3 Values of magnetic parameter of Yb_1−xSc_xMnO₃ (x = 0.1 and 0.2). Also listed are magnetocaloric effect (MCE) parameters: ΔS^max_M and RCP with reported values

	From Curie–Wiess fit					MCE
	μ^expeff (μB)	μ^theoreff (μB)	θCW (K)	TN (K)	f = |θCW/TN|	ΔH(T)	ΔS^maxM (J mol^−1 K^−1)	RCP (J mol^−1)
x = 0.1	6.1	6.5	−182	90	2.02	5	1.32	13.8
						10	2.43	38.5
x = 0.2	5.6	6.3	−193	94	2.05	5	1.01	10.2
						10	1.88	30.1
Reported values for YbMnO3
Ref. 10	5.91	6.68	−219	85	2.57	8	2.3	26	Ref. 20
Ref. 18	6.1	6.68	−220	85	2.58	10	2	26	Ref. 16
Ref. 19	6.40	6.68	−166	82	2.02	—	—	—

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The isothermal magnetization (M–H) curves of Yb_1−xSc_xMnO₃ (x = 0.1 and 0.2) measured at 2.5 K are shown in Fig. 3. Both the samples show a small magnetic hysteresis loops in low fields indicating a weak ferromagnetic (FM) behavior due to Yb³⁺.^18,20 At 2.5 K, the ferromagnetic (FM) behavior is observed with corresponding coercivity (H_c) around 500 Oe. A change in Sc concentration slightly changes coercivity but retentivity decreases with increase in the Sc content as shown in the inset Fig. 3. The isothermal magnetization (M–H) at 2.5 K also shows a noticeable sudden increase in magnetization around 30 kOe, similar results are observed in RMnO₃ in general and is attributed due to a magnetically induced phase transition where the Mn³⁺ ions ordering changes from AFM to FM along the c-axis while along the ab-plane the ordering remains unchanged to AFM.^20–23 Further, M does not saturate up to 100 kOe. As for Yb_0.9Sc_0.1MnO₃ and Yb_0.8Sc_0.2MnO₃, the magnetization at 100 kOe is 1.6 μ_B and 1.3 μ_B, respectively. The magnetization of these samples decreases with increasing Sc concentration, which is nonmagnetic.

Fig. 3 The hysteresis loops of Yb_1−xSc_xMnO₃ (x = 0.1 and 0.2). Insert shows up to 1 tesla.

To explain the role of applied magnetic field on metamagnetic transition, the isothermal magnetization curves as a function of magnetic field for Yb_1−xSc_xMnO₃ (x = 0.1 and 0.2) were measured in applied fields of up to 10 T in the temperature range of 2–40 K. Fig. 4 shows the typical isothermal magnetization curves of Yb_1−xSc_xMnO₃ (x = 0.1 and 0.2), which upholds a field-induced metamagnetic transition.²⁴ The isotherms vary almost linearly in the low-field region and depending upon the temperature the slope changes at a critical field H_c without any indication of saturation. From these plots, below T_C, M increases slowly with H in the low field region the slope changes at a critical field H_c and then increases slowly with further increase of H.

Fig. 4 Field dependence of isothermal magnetization for Yb_1−xSc_xMnO₃ (x = 0.1 and 0.2) at some selective temperatures.

To understand the nature of the metamagnetic phase transitions, we have transformed the M(H) data into Arrott plots as shown in Fig. 5.²⁵ Banerjee²⁶ has given an experimental criterion, which allows the determination of the nature of the magnetic transition (first or second order). It consists in observing the slope of the isotherms plots M² versus H/M. Applying a regular approach, the straight line was constructed simply by extrapolating the high magnetization parts of the curves for each studied temperature. The negative slope of the Arrott plot indicates a first order nature of the transition, while the positive slope implies a second order transition. It is seen from Fig. 5 that the Arrott plots have positive slopes above and below T_C for Yb_1−xSc_xMnO₃ (x = 0.1 and 0.2) samples in the complete M² ranges, indicating that the system exhibits a second order AFM to FM phase transition.

Fig. 5 The Arrott plots of M² vs. H/M at various temperatures for Yb_1−xSc_xMnO₃ (x = 0.1 and 0.2) samples.

3.3. Magnetocaloric behaviors

In the isothermal process of magnetization, the MCE of the materials can be derived from Maxwell's thermodynamic relationship:²⁷

The magnetic-entropy change ΔS_M, which results from the spin ordering (i.e. ferromagnetic ordering) and is induced by the variation of the applied magnetic field from 0 to H is given by

for magnetization measured at discrete field and temperature intervals, the magnetic entropy change defined in eqn (3) can be approximated by the eqn (4):²⁸with the uncertainty in ΔS_M(T_av)_ΔH as
where, δT = T_u − T_l is the temperature difference between the two isotherms measured at T_u and T_l with the magnetic field varying from H₁ to H_n in constant steps of δH. δM_k = M(T_u)_k − M(T_l)_k is the difference in the magnetization at T_u and T_l for each magnetic field H_k. For the calculation of relative error in the entropy change, following,²⁸ the accuracy of magnetization measurements are taken as 0.5% and the accuracy of the magnetic field as 0.1%. The manufacturer quoted temperature stability of 0.25% is used as the error for temperatures. In general, the relative error in the calculated entropy change is 10–20% except at very high fields and low temperatures (H ∼ 10 T, T < 4 K).

The magnetic entropy changes, −ΔS_M of Yb_1−xSc_xMnO₃ (x = 0.1 and 0.2) samples, associated with the magnetic field variation (1 to 10 T) were calculated using eqn (4) and the data for selected fields are displayed in Fig. 6. These curves present a characteristic shape with a broad maximum in the vicinity of the FM transition of Yb moment. The magnitude of the peak increases with increasing the value of ΔH for each composition and the position of the maximum shifts from 5 to 7.5 K when the magnetic field change increases from 1 to 10 T. The maximum entropy change, −ΔS^max_M, corresponding to a magnetic field variation of 10 T is found to be 2.46 ± 0.40 J mol⁻¹ K⁻¹ and 1.87 ± 0.31 J mol⁻¹ K⁻¹ for x = 0.1 and 0.2, respectively. The magnitude of |ΔS^max_M| increases linearly with increasing magnetic field. The field induced metamagnetic transition contributes to the enhancement of ΔS_M.²⁹ These values are in agreement with the reported values in the literature which are ∼2.3 J mol⁻¹ K⁻¹ for H = 8 T for single crystal YbMnO₃.²⁴ For comparison, we list in data of various magnetic materials in Table 3 which could be used as magnetic refrigerants.

Fig. 6 Temperature variation of magnetic entropy change for selected field change for Yb_1−xSc_xMnO₃ (x = 0.1 and 0.2) samples.

When comparing different magneto-caloric materials, it is useful to calculate their relative cooling power (RCP) based on the magnetic entropy change. The relative cooling power is evaluated by considering the magnitude of ΔS_M and its full width at half-maximum δT_FWHM was expressed as follows:³⁰

RCP = |ΔS^max_M| × |δT_FWHM|, (5)

it is a measure of the quantity of heat transferred by the magnetic refrigerant between hot and cold sinks. The results of these calculations are shown in Fig. 7(b). We estimate a relative error of 15–30% for the RCP values (as field increases from low: 1 T to high: 10 T) considering the relative error of 10–20% in the value of |ΔS^max_M| and considering a 5–10% error in assigning the δT_FWHM values. The RCP values show increase with increasing field for both compounds. RCP values are 38.5 ± 9 J mol⁻¹, and 30.1 ± 8 J mol⁻¹ with ΔH = 10 T for samples with x = 0.1 and 0.2, respectively. These values are higher than those for single crystal YbMnO₃ (RCP = 26 J mol⁻¹ with ΔH = 8 T).²⁴ Thus, RCP values of these compounds indicate that these are potential candidates for applications at low temperatures.

Fig. 7 (a) Temperature dependence of magnetic entropy change ΔS^max_M versus h^2/3 (b) relative cooling power as a function of field for Yb_1−xSc_xMnO₃ (x = 0.1 and 0.2) samples.

Fig. 7(a) shows the dependence of the magnetic entropy change on the parameter h^2/3 (ref. 31 and 32) where h is the reduced field just around T_C and is given by [h = (μ_BH)/(K_BT_C)]. The mean-field theory predicts that in the vicinity of second-order phase transitions, ΔS^max_M = −kM_S(0)h^2/3 − S(0,0), here k is a constant, M_S(0) is the saturation magnetization at low temperatures and S(0, 0) is the reference parameter, which may not be equal to zero.^33,34 Fig. 7(a) shows the linear dependence of ΔS^max_M versus h^2/3 which implies the second order transition for Yb_1−xSc_xMnO₃ (x = 0.1 and 0.2). The fact that ΔS^max_M is estimated around T_C and in fields larger than the critical field required for the metamagnetic transition, the conclusion about the second order transition is justified.

3.4. Universal curve

The construction of the phenomenological universal curve is based on the collapse of the ΔS_M(T, H) points into one single point in the new curve corresponding to equivalent states of the system. Those equivalent states have the same height, in the (−ΔS_M/ΔS^max_M) curves. The collapse of the normalized entropy change curves can be then obtained by defining a new variable for the temperature axis, θ, given by the expressionwhere T_r1 and T_r2 are the temperature of the two reference points that, for the present study, have been selected as those corresponding to ΔS_M(T_r1,2) = 1/2ΔS^max_M.³⁵ Fig. 8 shows the dependence of ΔS* (−ΔS_M/ΔS^max_M) for Yb_1−xSc_xMnO₃ (x = 0.1 and 0.2) for typical field changes. It can be clearly seen that the experimental points of the samples distribute on one universal curve of the magnetic entropy change (ranging from 4 T up to 10 T). The universal curve can be well fitted by a Lorentz function³⁵where a, b, and c are the free parameters. A fit to this relation gives a = 1.0246, b = 1.01, and c = −0.05. According to eqn (7), only the position and magnitude of the peak, namely, T_C and ΔS^max_M, and two reference temperatures T_r1 and T_r2, are needed to characterize the entropy change, where T_r1 < T_C and T_r2 > T_C. That is to say, to translate S into the “real” ΔS_M(T), one needs only these values that are determined by the properties of the materials. Thus, incomplete ΔS_M(T) curves, which are experimentally determined from a small temperature span in the vicinity of T_C for the isothermal magnetization measurements, can be easily transformed into the complete curves, which is a helpful tool for the evaluation of material properties such as the refrigerant capacity RC.

Fig. 8 The universal curve behavior of the curves as a function of the rescaled temperature for different magnetic field for Yb_1−xSc_xMnO₃ (x = 0.1 and 0.2).

4. Conclusion

In conclusion, we report detailed investigations of structural, magnetic and magnetocaloric properties of Yb_1−xSc_xMnO₃ (x = 0.1 and 0.2) revealing the effect of Sc doping in YbMnO₃ on the structure (bond length, bond angles, unit cell volume, tolerance factor, distortion of MnO₅ polyhedra) and magnetism (increase in T_N, change in frustration parameter, f). From analysis of experimental data, we deduced RCP of Yb_1−xSc_xMnO₃, which are found to be 38.5 ± 9 J mol⁻¹, and 30.1 ± 8 J mol⁻¹ with ΔH = 10 T for x = 0.1 and 0.2 respectively. Thus, multiferroic manganites seem to be potential materials for magnetic refrigeration in the low temperature region. The behavior of ΔS^max_M vs. h^2/3 curve confirm that present materials exhibit a second order transition. The phenomenological construction of the universal curve for the studied Yb_1−xSc_xMnO₃ (x = 0.1 and 0.2) with a Lorentz function is a helpful tool for the evaluation of material properties such as the refrigerant capacity RC.

Acknowledgements

This work has been supported by UGC-DAE Consortium for Scientific Research, Mumbai Centre, India in the form of a collaborative research scheme (CRS) through project number CRS-M-199. BSB acknowledges UGC-DAE CSR, Mumbai Centre for project fellowship. AKB is thankful to the National Academy of Sciences, India for their support to this work through Senior Scientist Platinum Jubilee Fellowship Scheme. Thanks to Dr K Gireesan, IGCAR, Kalpakkam for providing help in part of this work and also thanks to Dr B. Koteswara Rao, DST-INSPIRE Faculty for fruitful discussions.

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