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Magnetocaloric effect and critical behaviors of R2NiMnO6 (R=Eu and Dy) double perovskite oxides
Journal of Alloys and Compounds 746 (2018) 594e600
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Magnetocaloric effect and critical behaviors of R2NiMnO6 (R¼Eu and Dy) double perovskite oxides Lei Su a, b, Xiang-Qun Zhang b, Qiao-Yan Dong c, **, Ya-Jiao Ke b, Kai-Yue Hou b, c, Cheng-Shi Liu a, Zhao-Hua Cheng b, * a
Key Laboratory for Microstructural Material Physics of Hebei Province, School of Science, Yanshan University, Qinhuangdao 066004, PR China Key Laboratory for Magnetism, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, PR China Center for Condensed Matter & Beijing Key Laboratory of Metamaterials and Devices, Department of Physics, Capital Normal University, Beijing 100048, PR China b c
a r t i c l e i n f o
a b s t r a c t
Article history: Received 5 January 2018 Received in revised form 26 February 2018 Accepted 27 February 2018 Available online 6 March 2018
We have investigated the magnetocaloric effects and critical behaviors of Eu2NiMnO6 and Dy2NiMnO6 double perovskite oxides. For a magnetic field varying from 0 to 7 T, the maximum values of the magnetic ) reach 4.0 J/kg K and 5.2 J/kg K, and the relative refrigeration capacity (RCP) entropy change (DSmax M values are 241.5 J/kg and 385.1 J/kg for Eu2NiMnO6 and Dy2NiMnO6, respectively. The relatively high values of jDSM j and RCP suggest that these double perovskite oxides can be used as candidates of magnetic refrigerants working in a wide temperature range. Various techniques such as modified Arrott plot, Kouvel-Fisher method and critical isotherm analysis are used to estimate the critical exponents (b, g and d) as well as TC for Eu2NiMnO6. These critical exponents not only obey the Widom scaling relation d ¼ 1 þ g=b, but also fulfill the scaling equation MðH; εÞ ¼ εb f± ðH=εbþg Þ where ε ¼ (T e TC)/TC, fþ (T > TC) and f- (T < TC) are the regular analytic functions. Therefore, the deduced critical exponents are reasonably accurate. Moreover, temperature variation in effective critical exponents resemble with those for disordered ferromagnet, which matches with the Griffiths-like phase behavior observed from inverse magnetic susceptibility just above TC. © 2018 Published by Elsevier B.V.
Keywords: Ceramics Magnetization Magnetocaloric Critical behavior
1. Introduction In recent years, with the constantly increasing need for powerful, clean, efficient, and miniaturized devices incorporating different physical properties, much attention has been attracted to double perovskite oxides as multifunctional materials because they simultaneously possess magnetic, dielectric, magnetodielectric and magnetocaloric (MC) properties [1e5]. This kind of oxides have general stoichiometric formula A2B0 B00 O6, where A is rare-earth, alkali or alkaline-earth ion and B0 , B00 are transition metal ions [6]. La2NiMnO6 is a typical one of them. There are abundant reports on its magnetic and magnetocaloric properties [7,8], magnetodielectric properties [9], magnetocapacitance and magnetoresistance [10].
* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (Z.-H. Cheng). https://doi.org/10.1016/j.jallcom.2018.02.327 0925-8388/© 2018 Published by Elsevier B.V.
(Q.-Y.
Dong),
[email protected]
La2NiMnO6 shows a ferromagnetic (FM)-paramagnetic (PM) phase transition around Curie temperature (TC) of 280 K [11]. Ni2þOMn4þ superexchange interaction leads to the appearance of FM state [12]. For magnetocaloric effect (MCE), Monte Carlo simulations have proved the temperature where the maximum of the magnetic entropy change locates is in accord with TC [13]. Furthermore, modulating the coupling between the spin and phonon have greatly enhanced the magnetic entropy change of polycrystalline La2NiMnO6 [7]. On the basic of the magnetocaloric effect, magnetic refrigeration as a promising technology compared with the traditional gascompression refrigeration because of its higher efficiency and environmentally friendly has attracted more attentions [14,15]. It is of great significance to explore new magnetic refrigeration materials. Recently, the double perovskite family of R2NiMnO6 (R ¼ Pr, Nd, Tb, Ho, and Y) have been found they possess considerably high values of jDSM j and RCP as the prospective magnetocaloric refrigerant around TC [4]. Subsequently, Dy2NiMnO6 is also thought as a promising magnetic refrigerant material because it shows amazing
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magnetocaloric effect in a wide temperature range [16]. In addition, many Eu-based oxides such as EuHo2O4 and EuDy2O4 [17], Eu1xBaxTiO3 (0.1 0.9) [18], EuTiO3 [19] have been reported to exhibit a large magnetic entropy change. Within this context, we report the magnetocaloric effect of R2NiMnO6 (R ¼ Eu and Dy) polycrystalline samples. At the same time, we also systematically investigate the critical behavior of Eu2NiMnO6 for a better understanding of its magnetic transition. 2. Experimental process Polycrystalline Eu2NiMnO6 and Dy2NiMnO6 were synthesized by standard solid-state reaction method. Stoichiometric amounts of R2O3 (R ¼ Eu or Dy) (purity of 99.99 wt %), NiO (purity of 99.998%) and MnO2 (purity of 99.9 wt %) were intensively mixed. The mixtures for Eu2NiMnO6 and Dy2NiMnO6 samples were calcined at 1000 C for 24 h and 1200 C for 24 h under the atmosphere of air, respectively. Then they were cooled down to room temperature in the furnace at the rate of 1 C/min. Consecutively, the resulting powders were reground, pressed into pellets and sintered at 1200 C for 24 h for Eu2NiMnO6 and at 1300 C for 24 h for Dy2NiMnO6. Powder X-ray diffractometer (Rigaku Ultima-IV diffractometer with combined Cu-Ka radiation) was performed to characterize the crystal structure of the samples. The dc magnetic measurements were carried out on a superconducting quantum interference device magnetometer (MPMS XL, Quantum Design) in magnetic fields up to 7 T at temperatures between 2 K and 300 K. 3. Results and discussion
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Table 1 Structural and reliability parameters obtained from the refinement for R2NiMnO6 (R ¼ Eu and Dy) as well as La2NiMnO6 [20,21]. La2NiMnO6 a (Å) 5.5115 b (Å) 5.4851 c (Å) 7.7387 3 V (Å ) 232.79 90.015(2) bð Þ Bond angles( ) NieO1eMn 157.6(1) NieO2eMn 163.5(9) 160.9(1) NieO3eMn 〈Ni-O-Mn〉 160.7(1) Average bond length(Å) 〈NieO〉 1.97(3) 〈MneO〉 1.96(2) R:x 0.0021(6) y 0.0171(2) z 0.2524(7) Ni:x y z 0 1/2 0 Mn:x y z 1/2 0 0 O1:x 0.218(5) y 0.191(5) z 0.019(4) O2:x 0.233(4) y 0.758(4) z 0.466(3) O3:x 0.559(2) y 0.001(1) z 0.265(3) Rp 7.93 Rwp 10.8 c2 3.47
Eu2NiMnO6
Dy2NiMnO6
5.3249 5.5282 7.5873 223.35 90.008(1)
5.2466 5.5500 7.5055 218.55 90.251(7)
149.4(2) 145.0(3) 150.8(2) 148.4(2)
143.2(7) 148.8(8) 149.4(6) 147.2(0)
2.01(2) 1.96(2) 0.5108(9) 0.5590(1) 0.2483(8) 1/2 0 0 0 1/2 0 0.2257(9) 0.2160(8) 0.9373(5) 0.3238(8) 0.6892(9) 0.9582(1) 0.4108(3) 0.9775(7) 0.2698(0) 1.90 2.95 7.99
1.95(5) 2.00(4) 0.5168(3) 0.5692(5) 0.2517(3) 1/2 0 0 0 1/2 0 0.1901(4) 0.1895(0) 0.9415(9) 0.3140(0) 0.7141(4) 0.9509(3) 0.4019(8) 0.9694(3) 0.2551(3) 1.48 2.04 5.14
3.1. Structural properties Rietveld refined powder X-ray diffraction (XRD) patterns of Eu2NiMnO6 and Dy2NiMnO6 polycrystalline samples at room temperature (See Fig. 1) show that the Eu2NiMnO6 sample is in pure phase with a monoclinic structure (space group P21/n), while Dy2NiMnO6 sample has the main phase with a monoclinic structure (space group P21/n) as well as a small amount of impurity phase Dy2O3 marked by “Y” in the pattern of Fig. 1. The obtained structural and reliability parameters of Eu2NiMnO6 and Dy2NiMnO6, as well as La2NiMnO6 [20,21], are shown in Table 1. The lattice parameters of Eu2NiMnO6 and Dy2NiMnO6 are in accord with the previous
works [22,23]. As summarized in Table 1, lattice parameters a and c, cell volume v, and 〈NieOeMn〉 bond angle j decrease, while lattice parameter b increases with decreasing the lanthanide ionic radius. Refinement parameter c2 is defined as Rwp/Rexp, where Rwp is the weighted-profile R value, Rexp is the statistically expected R value and reflects the quality of the data (i.e. the counting statistics) [24]. Ideally, c2 should approach 1. However, the c2 values of Eu2NiMnO6 and Dy2NiMnO6 polycrystalline samples are much larger than 1. There are two reasons. One is that the XRD data have been overcollected which results a small Rexp value. The other is a large Rwp value due to the level of background when collecting XRD data. 3.2. Magnetic properties
Fig. 1. Rietveld refined powder XRD patterns of Eu2NiMnO6 and Dy2NiMnO6 at room temperature. The experimental data are indicated by dots, and the calculated profile is shown by the solid line. The short vertical lines show the positions of the Bragg diffraction peak. The underneath curve shows the difference between the observed and calculated intensity. The inset shows the crystallographic structure of R2NiMnO6.
In order to confirm the magnetic properties of Eu2NiMnO6 and Dy2NiMnO6 oxides, the temperature (T)-dependence of magnetization (M) has been measured. Fig. 2(a)e(b) show the zero field cooling (ZFC) and field cooling (FC) magnetization vs. temperature curves of Eu2NiMnO6 and Dy2NiMnO6 from 2 K to 300 K under 0.01 T. With increasing the temperature, it is evident that the compounds undergo a ferromagnetic-paramagnetic phase transition. The Curie temperature TC, corresponding to the maximum slope of FC M-T curve (jdM=dTj) (See the insets of Fig. 2(a)e(b), is determined to be 145 K for Eu2NiMnO6 and 97 K for Dy2NiMnO6, respectively. They are in agreement with the result reported in the literatures [22,23]. The TC of La2NiMnO6 reported is 280 K [11]. Obviously, TC shifts towards low temperature with decreasing the lanthanide ionic radius. It also can be seen from Fig. 2(a)e(b) that the ZFC and FC curves are completely reversible around TC. However, a significant thermal magnetic irreversibility between the ZFC and FC branches is clearly observed below TC. This kind of bifurcation is also yielded in many other R2NiMnO6 compounds such as
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oxides are calculated to be 138.8 K and 39.5 K. The positive qP further confirms that the predominant exchange interaction is ferromagnetic [1], that originates from the ordered alignment Ni2þ and Mn4þ superexchange interaction [5,27,29]. However, the value of qP for Dy2NiMnO6 is much lower than that of TC. It further suggests the existence of antiferromagnetic interaction. In addition, it is worth mentioned that there is a sharp downturn deviation from Curie-Weiss law behavior on the 1/c-T curve just above TC for Dy2NiMnO6. The reason of deviation is Griffiths-like phase behavior, just like reported in Tb2NiMnO6 [29]. Raman scattering experiments demonstrated that the smaller size of the rare earth could generate a Griffiths phase in double perovskites [30]. 3.3. Magnetocaloric properties For a better understand of magnetic behavior and evaluating magnetocaloric effect of these two oxides within a wide temperature range, the isothermal magnetization curves were measured in applied magnetic fields up to 7 T with an interval of 0.2 T in the vicinity of Curie temperature with an interval of 2 K for Eu2NiMnO6 and Dy2NiMnO6 (See Fig. 3(a)e(b)). As shown in Fig. 3(a), the magnetization of Eu2NiMnO6 increases quickly at low fields and then increases slowly at higher field below TC, just like normal ferromagnetic material. While the magnetization of Dy2NiMnO6 exhibits a linear increment for fields from 0.5 T to 7 T below TC, showing strong antiferromagnetic interaction. According to the isothermal magnetization data, the magnetic entropy changes jDSM j for Eu2NiMnO6 and Dy2NiMnO6 are numerically calculated by using the Maxwell's relation [31]:
ZH Fig. 2. ZFC and FC magnetization (M) versus temperature (T) curves and the temperature variation of the ZFC inverse susceptibility fitted to the Curie-Weiss law under 0.01 T for (a) Eu2NiMnO6 and (b) Dy2NiMnO6. The inset of (a) and (b) shows the FC dM=dT-T curve of Eu2NiMnO6 and Dy2NiMnO6 under 0.01 T, respectively.
R ¼ Nd, Sm, Gd and Y [20,25,26]. The ordered alignment of Ni2þOMn4þ superexchange interaction contributes to the FM interaction, which is dominant in these compounds. Whereas, Ni2þO Ni2þ and Mn4þeOeMn4þ due to partial disorder of Ni and Mn leads to weak antiferromagnetic interaction [26,27]. Thus, this thermal irreversibility is likely attributed to the competition of FM and AFM interaction in Eu2NiMnO6 and Dy2NiMnO6. In addition, similar with previously reported results on Nd2CoMnO6 double perovskite, Dy2NiMnO6 exhibits a sharp drop of magnetization around 6 K, which originates from the anti-parallel alignment of rare earth moment with respect to the Ni/Mn moments [28]. Therefore, the appearance of two discrete phase transition temperatures for Dy2NiMnO6 stems from the order of transition metal and rare earth, respectively. Temperature dependences of inverse magnetic susceptibility (c) of Eu2NiMnO6 and Dy2NiMnO6 are also shown in Fig. 2(a)e(b). They obey the Curie-Weiss (CW) law above 250 K for Eu2NiMnO6 and 200 K for Dy2NiMnO6, respectively. The effective magnetic moments per molecule are ascertained to be 6.86 mB for Eu2NiMnO6 and 14.13 mB for Dy2NiMnO6, which resemble with the correlative theoretical effective magnetic moments value of 7.04 mB and 15.78 mB for two oxides. The theoretical effective magnetic moments are calculated by the following equation:
meff ðcalcÞ ¼ ½2mðR3þ Þ2 þ mðNi2þ Þ2 þ mðMn4þ Þ2 1=2 [1], where the effective paramagnetic moments are 3.65 mB for Eu3þ, 10.63 mB for Dy3þ, 2.83 mB for Ni2þ, 3.87 mB for Mn4þ. Meanwhile, the paramagnetic Curie temperature (qP ) for Eu2NiMnO6 and Dy2NiMnO6
DSM ðT; HÞ ¼ 0
vM vT
dH
(1)
H
Figs. 3(c)e4(d) show the temperature dependence of jDSM j for Eu2NiMnO6 and Dy2NiMnO6 under different field variations, respectively. The jDSM j peaks appear around 147 K for Eu2NiMnO6 and around 97 K for Dy2NiMnO6 compounds, which were induced by the FM-PM phase transition. The value of jDSM j gradually increases with the increase of the applied magnetic field for these two oxides. The maximum value of magnetic entropy change ) reaches to 4.0 J/kg K for Eu2NiMnO6 and 5.2 J/kg K for (DSmax M Dy2NiMnO6 for a field change of 0e7 T, respectively. They are much larger than that of La2NiMnO6 (1.5 J/kg K for 0e4.5 T) [7]. Although the value of magnetic entropy change peak is not very large, the peak is very broad and the full width at half peak of the jDSM j-T curve reaches ~60 K for Eu2NiMnO6 and ~74 K for Dy2NiMnO6 for the field change of 0e7 T. Not only the peak value of magnetic entropy change, but also its full width at half peak, are very useful to obtain a large refrigerant capacity. Besides the jDSM j value, the relative refrigerant capacity (RCP) is another significant factor for evaluating a magnetocaloric material, defined by the following expression [31]:
RCP ¼ DSmax dTFWHM M
(2)
where dTFWHM is the full width at half maximum of jDSM j. Obvi value but also the ously, the RCP depend on not only the DSmax M magnitude of dTFWHM . The inset of Fig. 3(a) exhibits the field dependence of RCP for the two oxides. The value of RCP reaches 241 J/kg for Eu2NiMnO6 and 385 J/kg for Dy2NiMnO6 for the field change of 0e7 T, respectively. They are comparable with or even much larger than those of some rare-earth-based oxides such as La0.67Ca0.33Mn0.9Fe0.1O3 (87 J/kg for 0e3 T) [32], LaMn0.9Fe0.1O3 (152 J/kg for 0e5 T) [33], SmCr0.85Mn0.15O3 (176 J/kg for 0e9 T) [34],
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Fig. 3. Isothermal magnetization curves in the vicinity of TC for (a) Eu2NiMnO6 and (b) Dy2NiMnO6 oxides. Magnetic entropy change curves as a function of temperature for (c) Eu2NiMnO6 and (d) Dy2NiMnO6 for different magnetic field changes. The inset of (a) shows the relative refrigeration capacity (RCP) vs. magnetic field curves of Eu2NiMnO6 and Dy2NiMnO6.
La0.85Zr0.15MnO3 (142.5 J/kg for 0e5 T) [35] and Nd0.55Sr0.45Ca0.98Mn0.02O3 (260 J/kg for 0e7 T) [36]. Therefore, they can be potential candidates for magnetic refrigerants working in a wide temperature range.
3.4. Critical behavior To get a deeper insight into the origin of magnetocaloric effect around TC, we further investigate the phase transition of Eu2NiMnO6 and Dy2NiMnO6 oxides by using the Banerjee criterion [37]. The Arrott plots of Eu2NiMnO6 and Dy2NiMnO6 oxides are shown in Fig. 4(a)e(b). According to the Banerjee criterion [37], a magnetic transition is expected to be of first order when the slope of M2 vs. H/M plot is negative, while it would be of second order when the slope is positive. It is very clear from Fig. 4(a) and (b) that the nature of the phase transition for both oxides is of second-order magnetic transition. In addition, it is evident that the Arrott-plot of Dy2NiMnO6 does not display any positive intercepts around TC. It manifests the nonexistence of long-range order. Therefore, we will
only investigate the critical behavior of Eu2NiMnO6 in the followings. Clarifying the nature of critical behavior is performed normally near the FM transition temperature. Based on the scaling hypothesis, a second-order magnetic phase transition around TC is described by a series of interrelated critical exponents, b; g; d and some magnetic equations of state [38] which are given by:
MS ðTÞ ¼ M0 jεjb ;
ε < 0;
g c1 0 ðTÞ ¼ ðh0 =M0 Þε ;
M ¼ DH1=d ;
ε ¼ 0;
T < TC
ε > 0; T ¼ TC
T > TC
(3) (4) (5)
where ε means the reduced temperature established as ε ¼ (T e TC)/ TC. MS ðTÞ is the spontaneous magnetization below TC and c1 0 ðTÞ is the inverse initial susceptibility above TC. M0, h0 and D are the respective critical amplitudes. Using scaling hypothesis the
Fig. 4. Arrott-plots of (a) Eu2NiMnO6 and (b) Dy2NiMnO6.
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magnetic equation of state can be expressed as:
.
MðH; εÞ ¼ εb f± H εbþg
MS ðTÞ½dMS ðTÞ=dT1 ¼ ðT TC Þ=b (6)
where fþ (T > TC) and f- (T < TC) are the regular analytic functions. In term of renormalized magnetization and field, Eq. (6) can be written as:
m ¼ f± ðhÞ
(7)
where m≡εb MðH; εÞ and h≡εðbþgÞ H. Eq. (7) suggests that for correct scaling relations and proper critical exponents, plots of m vs. h will fall on two universal curves: one below TC and another above TC. This is an important criterion for critical regime. Based on the above theories, we will analyze the critical behavior of Eu2NiMnO6 in detail. Ms ðTÞ and c1 0 ðTÞ can be obtained by linear extrapolation of a plot of M 1=b vs. ðH=MÞ1=g to the ordinate and abscissa axes, respectively. It is clear from Fig. 4(a) that all the curves of the Arrot-plot for Eu2NiMnO6 are almost linear in high fields. Therefore, we choose the critical exponents of the mean-field model (b ¼ 0:5; g ¼ 1:0) as a modified Arrott plot [39,40]. Based on Fig. 4(a), we obtain the Ms ðT; 0Þ-T curve and c1 0 ðTÞ-T curve, as shown in Fig. 5(a). They can be well fitted by Eq. (3) and Eq. (4), respectively. The critical exponents are obtained to be b ¼ 0.443 ± 0.005 with TC ¼ 147. 429 ± 0.045 and g ¼ 1.014 ± 0.013 with TC ¼ 147.559 ± 0.091. Obviously, the TC value is pretty in agreement with that determined from the dM/dT curve. To determine the critical exponents more accurately, we have further analyzed the Ms ðTÞ and c1 0 ðTÞ data of Eu2NiMnO6 by using the KouveleFisher (KF) method [41]. The KF equations are denoted as follow:
h
1 c1 0 ðTÞ dc0 ðTÞ=dT
i1
¼ ðT TC Þ=g
(9) 1
1 MS ðTÞ½dMS ðTÞ=dT1 vs. T and c1 vs. T curves of 0 ðTÞ½dc0 ðTÞ=dT Eu2NiMnO6 are plotted in Fig. 5(b). It is clear that 1
1 MS ðTÞ½dMS ðTÞ=dT1 and c1 change linearly 0 ðTÞ½dc0 ðTÞ=dT with the increment of temperature. They can be well fitted by Eq. (8) and Eq. (9). It illustrates that the values of Ms ðT; 0Þ and c1 0 ðTÞ obtained from Arrott-plot are reasonable. The critical exponents obtained from the KF method are b ¼ 0.463 ± 0.053 with TC ¼ 147.699 ± 0.213 and g ¼ 1.032 ± 0.016 with TC ¼ 147.449 ± 0.179. Table 2 lists the critical exponents values obtained from different methods. It is remarkable that the values of critical exponents based on both modified Arrott-plot method and KF method match reasonably well, suggesting that the estimated values are self-consistent and unambiguous. Meanwhile, the critical exponent d of Eu2NiMnO6 can be derived from the critical isotherm according to equation (5). Here, we use the isothermal M-H data at 148 K, as shown in Fig. 6. The value of d is determined to be 3.226. For clarity, the inset of Fig. 6 shows a loglog plot of field-dependent magnetization. Moreover, the critical exponents satisfy the Widom scaling relation [42]:
d ¼ 1 þ g=b
(10)
Using the critical exponents b and g calculated previously, we can get that d is 3.289 for modified Arrott method and d is 3.229 for K-F method. It is clear that these values are very close to the value obtained from critical isotherm. Therefore, estimated exponents in the present study are dependability. By using the values of critical exponents and TC ~148 K obtained from the KF method and following Eq. (7), we have plotted scaled m vs. scaled h curves of Eu2NiMnO6 in the vicinity of TC, as shown in Fig. 7(a). The inset of Fig. 7(a) shows the same plot on a log-log scale. All the points collapse into two independent branches: one for T < TC and the other for T > TC. In order to see clearly, Fig. 7(b) shows the m2 vs. h=m plot [43]. We can see from Fig. 7(b) that all the data still fall on two separate branches. These results confirm that these critical exponents can generate the scaling equation of state for Eu2NiMnO6. In addition, Table 2 also lists the values of critical exponents of Y2NiMnO6 [44] as well as the theoretical models [43] for comparison. It is obvious that the values of critical exponents for Eu2NiMnO6 and Y2NiMnO6 are in between those theoretically predicted for 3D Heisenberg and mean-field interaction models. However, the values of Eu2NiMnO6 are closer to those for meanfield interaction model. The values of Y2NiMnO6 are closer to those for 3D Heisenberg interaction model. This difference must be caused by the degree of short-range interaction due to the change of the rare earth ionic radium. The deduced critical exponents of Eu2NiMnO6 do not belong to any theoretical models, it is crucial to clarify whether they obey any universality class as they approach the asymptotic region. For this intention, effective exponents beff and geff are calculated following the equations [45]:
d½ln MS ðεÞ ; beff ðεÞ ¼ dðlnεÞ Fig. 5. (a) Temperature dependence of the spontaneous magnetization Ms ðT; 0Þ and the inverse initial susceptibility c1 0 ðTÞ for Eu2NiMnO6. (b) KouveleFisher plots for the spontaneous magnetization and the inverse initial susceptibility for Eu2NiMnO6.
(8)
d ln c1 0 ðεÞ geff ðεÞ dðlnεÞ
(11)
Fig. 8 show the ε dependence of effective critical exponents (beff and geff ). beff is decreased from beff z0:55 at εz0:014 to beff z0:46
L. Su et al. / Journal of Alloys and Compounds 746 (2018) 594e600
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Table 2 Values of the critical exponents determined from different theoretical models for Eu2NiMnO6. The theoretically predicted values of critical exponents for various universality classes as well as the critical exponents of Y2NiMnO6 are also listed for the sake of comparison. Abbreviation: PC, polycrystalline. Composition
Ref.
Technique
Eu2NiMnO6(PC)
This work
Mean Field Model 3D Heisenberg Model 3D Ising Model Y2NiMnO6(PC)
[43] [43] [43] [44]
Modified Arrrot plot Kouvel-Fisher method Critical isotherm Theory Theory Theory Kouvel-Fisher method
Fig. 6. Critical isotherm at TC ¼ 148 K (inset: logelog scale) for Eu2NiMnO6.
at εz0:095. Nevertheless, geff presents a nonmonotonic change with ε. It resembles with that for disordered ferromagnets such as amorphous ferromagnets [46]. Similar phenomenon has also been found in Pr0.5Sr0.5MnO3 [47]. Thus, this study shows the presence of disorder which influences the critical behavior in Eu2NiMnO6. This disorder FM property matches with the Griffiths-like phase behavior observed from the inverse magnetic susceptibility just above TC in Eu2NiMnO6.
4. Conclusion We have investigated the magnetocaloric effects and critical behaviors of ferromagnetic Eu2NiMnO6 and Dy2NiMnO6 double perovskite oxides. The Curie temperature shifts toward low
a
0.0 0.115 0.11
b
g
d
0.443 ± 0.005 0.463 ± 0.053
1.014 ± 0.013 1.032 ± 0.016
0.5 0.365 0.325 0.375 ± 0.033
1.0 1.386 1.241 1.331 ± 0.09
3.289 3.229 3.226 ± 0.002 3.0 4.8 4.82 4.31 ± 0.1
Fig. 8. Effective exponents beff below TC and geff above TC as a function of reduced temperature ε for Eu2NiMnO6.
temperature with the reduction of rare earth ionic radius. Curie temperature TC is 145 K for Eu2NiMnO6 and 97 K for Dy2NiMnO6, respectively. For a field change of 0e7 T, the maximum values of max DS reach 4.0 J/kg K for Eu2NiMnO6 and 5.2 J/kg K for M Dy2NiMnO6. RCP values as high as 241.5 J/kg and 385.1 J/kg are achieved for both oxides due to the large full width at half peak of the jDSM j-T curve. The high RCP values together with the broad magnetic entropy change peak indicate the applicability of Eu2NiMnO6 and Dy2NiMnO6 as magnetic refrigerants working in a wide temperature range, they are very promising magnetic refrigerants materials. The critical exponents estimated from various techniques match reasonably well and values are in between those theoretically predicted for 3D Heisenberg and mean-field interaction model. Effective critical exponents further confirmed the existence of disorder FM property, which matches with the Griffiths-
Fig. 7. (a) Magnetic equation of state of KF method below and above TC for Eu2NiMnO6. The inset shows the same plots on a logelog scale. (b) The renormalized magnetization m2 and field h=m for Eu2NiMnO6.
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like phase behavior observed from the inverse magnetic susceptibility just above TC. Author contribution statement L. S. and Z. H. C planned the experiment. L. S grew the polycrystalline samples, carried out the magnetic and magnetic entropy change measurement and calculation and critical behavior simulation. L. S., X. Q. Z., Y. J. K., C. S. L. and K. Y. H. contributed to the analysis and discussion for all the results. L. S., Z. H. C and Q. Y. D. wrote the paper with the input from all the co-authors. Competing financial interests The author declare no competing financial interests. Acknowledgements This work was supported by the National Key R&D Program of China (Grant Nos. 2017YFB0702702, 2016YFA0300701 and 2015CB921403), the National Natural Sciences Foundation of China (Grant Nos. 91622126, 51427801, and 51471111), and the Key Research Program of Frontier Sciences, CAS (Grant Nos. QYZDJSSW-JSC023). References [1] M. Retuerto, A. Munoz, M.J. Martinez-Lope, J.A. Alonso, F.J. Mompean, M.T. Fernandez-Diaz, J. Sanchez-Benitez, Magnetic interactions in the double perovskites R2NiMnO6 (R ¼ Tb, Ho, Er, Tm) investigated by neutron diffraction, Inorg. Chem. 54 (2015) 10890e10900. [2] H.J. Zhao, X.Q. Liu, X.M. Chen, L. Bellaiche, Effects of chemical and hydrostatic pressures on structural, magnetic, and electronic properties of R2NiMnO6 (R¼rareearthion) double perovskites, Phys. Rev. B 90 (2014), 195147. [3] S. Kumar, G. Giovannetti, J. van den Brink, S. Picozzi, Theoretical prediction of multiferroicity in double perovskite Y2NiMnO6, Phys. Rev. B 82 (2010), 134429. [4] T. Chakraborty, H. Nhalil, R. Yadav, A.A. Wagh, S. Elizabeth, Magnetocaloric properties of R2NiMnO6 (R¼Pr, Nd, Tb, Ho and Y) double perovskite family, J. Magn. Magn. Mater. 428 (2017) 59e63. [5] R.J. Booth, R. Fillman, H. Whitaker, A. Nag, R.M. Tiwari, K.V. Ramanujachary, J. Gopalakrishnan, S.E. Lofland, An investigation of structural, magnetic and dielectric properties of R2NiMnO6 (R¼rare earth, Y), Mater. Res. Bull. 44 (2009) 1559e1564. [6] M.T. Anderson, K.B. Greenwood, G.A. Taylor, K.R. Poeppelmeier, B-cation arrangements in double perovskites, Prog. Solid State Chem. 22 (1993) 197e233. [7] X. Luo, Y.P. Sun, B. Wang, X.B. Zhu, W.H. Song, Z.R. Yang, J.M. Dai, The magnetic entropy change in the double perovskite La2NiMnO6 with strong spinephonon coupling, Solid State Commun. 149 (2009) 810e813. [8] M. Balli, P. Fournier, S. Jandl, M.M. Gospodinov, A study of the phase transition and magnetocaloric effect in multiferroic La2MnNiO6 single crystals, J. Appl. Phys. 115 (2014) 173904. [9] P. Neenu Lekshmi, M. Raama Varma, Colossal magneto-dielectricity in La2NiMnO6 probed by Raman spectroscopy, Mater. Sci. Forum 830e831 (2015) 513e517. [10] N.S. Rogado, J. Li, A.W. Sleight, M.A. Subramanian, Magnetocapacitance and magnetoresistance near room temperature in a ferromagnetic semiconductor: La2NiMnO6, Adv. Mater. 17 (2005) 2225e2227. [11] S. Zhou, Y. Guo, J. Zhao, S. Zhao, L. Shi, Nature of short-range ferromagnetic ordered state above Tc in double perovskite La 2 NiMnO 6, Appl. Phys. Lett. 96 (2010), 262507. [12] G. Blasse, Ferromagnetic interactions in non-metallic perovskites, J. Phys. Chem. Solid. 26 (1965) 1969e1971. [13] R. Masrour, A. Jabar, Magnetocaloric and magnetic properties of La2NiMnO6double perovskite, Chin. Phys. B 25 (2016), 087502. [14] K.A. Gschneidner Jr., V.K. Pecharsky, A.O. Tsokol, Recent developments in magnetocaloric materials, Rep. Prog. Phys. 68 (2005) 1479e1539. [15] A.M. Tishin, Y.I. Spichkin, The Magnetocaloric Effect and its Applications, first ed., IOP Bristol, 2003. [16] Y. Jia, Q. Wang, Y. Qi, L. Li, Multiple magnetic phase transitions and magnetocaloric effect in double perovskites R 2 NiMnO 6 ( R ¼ Dy, Ho, and Er), J. Alloys Compd. 726 (2017) 1132e1137. [17] A. Midya, N. Khan, D. Bhoi, P. Mandal, Giant magnetocaloric effect in magnetically frustrated EuHo2O4 and EuDy2O4 compounds, Appl. Phys. Lett. 101 (2012), 132415.
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Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
Magnetocaloric effect and critical behaviors of R2NiMnO6 (R¼Eu and Dy) double perovskite oxides Lei Su a, b, Xiang-Qun Zhang b, Qiao-Yan Dong c, **, Ya-Jiao Ke b, Kai-Yue Hou b, c, Cheng-Shi Liu a, Zhao-Hua Cheng b, * a
Key Laboratory for Microstructural Material Physics of Hebei Province, School of Science, Yanshan University, Qinhuangdao 066004, PR China Key Laboratory for Magnetism, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, PR China Center for Condensed Matter & Beijing Key Laboratory of Metamaterials and Devices, Department of Physics, Capital Normal University, Beijing 100048, PR China b c
a r t i c l e i n f o
a b s t r a c t
Article history: Received 5 January 2018 Received in revised form 26 February 2018 Accepted 27 February 2018 Available online 6 March 2018
We have investigated the magnetocaloric effects and critical behaviors of Eu2NiMnO6 and Dy2NiMnO6 double perovskite oxides. For a magnetic field varying from 0 to 7 T, the maximum values of the magnetic ) reach 4.0 J/kg K and 5.2 J/kg K, and the relative refrigeration capacity (RCP) entropy change (DSmax M values are 241.5 J/kg and 385.1 J/kg for Eu2NiMnO6 and Dy2NiMnO6, respectively. The relatively high values of jDSM j and RCP suggest that these double perovskite oxides can be used as candidates of magnetic refrigerants working in a wide temperature range. Various techniques such as modified Arrott plot, Kouvel-Fisher method and critical isotherm analysis are used to estimate the critical exponents (b, g and d) as well as TC for Eu2NiMnO6. These critical exponents not only obey the Widom scaling relation d ¼ 1 þ g=b, but also fulfill the scaling equation MðH; εÞ ¼ εb f± ðH=εbþg Þ where ε ¼ (T e TC)/TC, fþ (T > TC) and f- (T < TC) are the regular analytic functions. Therefore, the deduced critical exponents are reasonably accurate. Moreover, temperature variation in effective critical exponents resemble with those for disordered ferromagnet, which matches with the Griffiths-like phase behavior observed from inverse magnetic susceptibility just above TC. © 2018 Published by Elsevier B.V.
Keywords: Ceramics Magnetization Magnetocaloric Critical behavior
1. Introduction In recent years, with the constantly increasing need for powerful, clean, efficient, and miniaturized devices incorporating different physical properties, much attention has been attracted to double perovskite oxides as multifunctional materials because they simultaneously possess magnetic, dielectric, magnetodielectric and magnetocaloric (MC) properties [1e5]. This kind of oxides have general stoichiometric formula A2B0 B00 O6, where A is rare-earth, alkali or alkaline-earth ion and B0 , B00 are transition metal ions [6]. La2NiMnO6 is a typical one of them. There are abundant reports on its magnetic and magnetocaloric properties [7,8], magnetodielectric properties [9], magnetocapacitance and magnetoresistance [10].
* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (Z.-H. Cheng). https://doi.org/10.1016/j.jallcom.2018.02.327 0925-8388/© 2018 Published by Elsevier B.V.
(Q.-Y.
Dong),
[email protected]
La2NiMnO6 shows a ferromagnetic (FM)-paramagnetic (PM) phase transition around Curie temperature (TC) of 280 K [11]. Ni2þOMn4þ superexchange interaction leads to the appearance of FM state [12]. For magnetocaloric effect (MCE), Monte Carlo simulations have proved the temperature where the maximum of the magnetic entropy change locates is in accord with TC [13]. Furthermore, modulating the coupling between the spin and phonon have greatly enhanced the magnetic entropy change of polycrystalline La2NiMnO6 [7]. On the basic of the magnetocaloric effect, magnetic refrigeration as a promising technology compared with the traditional gascompression refrigeration because of its higher efficiency and environmentally friendly has attracted more attentions [14,15]. It is of great significance to explore new magnetic refrigeration materials. Recently, the double perovskite family of R2NiMnO6 (R ¼ Pr, Nd, Tb, Ho, and Y) have been found they possess considerably high values of jDSM j and RCP as the prospective magnetocaloric refrigerant around TC [4]. Subsequently, Dy2NiMnO6 is also thought as a promising magnetic refrigerant material because it shows amazing
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magnetocaloric effect in a wide temperature range [16]. In addition, many Eu-based oxides such as EuHo2O4 and EuDy2O4 [17], Eu1xBaxTiO3 (0.1 0.9) [18], EuTiO3 [19] have been reported to exhibit a large magnetic entropy change. Within this context, we report the magnetocaloric effect of R2NiMnO6 (R ¼ Eu and Dy) polycrystalline samples. At the same time, we also systematically investigate the critical behavior of Eu2NiMnO6 for a better understanding of its magnetic transition. 2. Experimental process Polycrystalline Eu2NiMnO6 and Dy2NiMnO6 were synthesized by standard solid-state reaction method. Stoichiometric amounts of R2O3 (R ¼ Eu or Dy) (purity of 99.99 wt %), NiO (purity of 99.998%) and MnO2 (purity of 99.9 wt %) were intensively mixed. The mixtures for Eu2NiMnO6 and Dy2NiMnO6 samples were calcined at 1000 C for 24 h and 1200 C for 24 h under the atmosphere of air, respectively. Then they were cooled down to room temperature in the furnace at the rate of 1 C/min. Consecutively, the resulting powders were reground, pressed into pellets and sintered at 1200 C for 24 h for Eu2NiMnO6 and at 1300 C for 24 h for Dy2NiMnO6. Powder X-ray diffractometer (Rigaku Ultima-IV diffractometer with combined Cu-Ka radiation) was performed to characterize the crystal structure of the samples. The dc magnetic measurements were carried out on a superconducting quantum interference device magnetometer (MPMS XL, Quantum Design) in magnetic fields up to 7 T at temperatures between 2 K and 300 K. 3. Results and discussion
595
Table 1 Structural and reliability parameters obtained from the refinement for R2NiMnO6 (R ¼ Eu and Dy) as well as La2NiMnO6 [20,21]. La2NiMnO6 a (Å) 5.5115 b (Å) 5.4851 c (Å) 7.7387 3 V (Å ) 232.79 90.015(2) bð Þ Bond angles( ) NieO1eMn 157.6(1) NieO2eMn 163.5(9) 160.9(1) NieO3eMn 〈Ni-O-Mn〉 160.7(1) Average bond length(Å) 〈NieO〉 1.97(3) 〈MneO〉 1.96(2) R:x 0.0021(6) y 0.0171(2) z 0.2524(7) Ni:x y z 0 1/2 0 Mn:x y z 1/2 0 0 O1:x 0.218(5) y 0.191(5) z 0.019(4) O2:x 0.233(4) y 0.758(4) z 0.466(3) O3:x 0.559(2) y 0.001(1) z 0.265(3) Rp 7.93 Rwp 10.8 c2 3.47
Eu2NiMnO6
Dy2NiMnO6
5.3249 5.5282 7.5873 223.35 90.008(1)
5.2466 5.5500 7.5055 218.55 90.251(7)
149.4(2) 145.0(3) 150.8(2) 148.4(2)
143.2(7) 148.8(8) 149.4(6) 147.2(0)
2.01(2) 1.96(2) 0.5108(9) 0.5590(1) 0.2483(8) 1/2 0 0 0 1/2 0 0.2257(9) 0.2160(8) 0.9373(5) 0.3238(8) 0.6892(9) 0.9582(1) 0.4108(3) 0.9775(7) 0.2698(0) 1.90 2.95 7.99
1.95(5) 2.00(4) 0.5168(3) 0.5692(5) 0.2517(3) 1/2 0 0 0 1/2 0 0.1901(4) 0.1895(0) 0.9415(9) 0.3140(0) 0.7141(4) 0.9509(3) 0.4019(8) 0.9694(3) 0.2551(3) 1.48 2.04 5.14
3.1. Structural properties Rietveld refined powder X-ray diffraction (XRD) patterns of Eu2NiMnO6 and Dy2NiMnO6 polycrystalline samples at room temperature (See Fig. 1) show that the Eu2NiMnO6 sample is in pure phase with a monoclinic structure (space group P21/n), while Dy2NiMnO6 sample has the main phase with a monoclinic structure (space group P21/n) as well as a small amount of impurity phase Dy2O3 marked by “Y” in the pattern of Fig. 1. The obtained structural and reliability parameters of Eu2NiMnO6 and Dy2NiMnO6, as well as La2NiMnO6 [20,21], are shown in Table 1. The lattice parameters of Eu2NiMnO6 and Dy2NiMnO6 are in accord with the previous
works [22,23]. As summarized in Table 1, lattice parameters a and c, cell volume v, and 〈NieOeMn〉 bond angle j decrease, while lattice parameter b increases with decreasing the lanthanide ionic radius. Refinement parameter c2 is defined as Rwp/Rexp, where Rwp is the weighted-profile R value, Rexp is the statistically expected R value and reflects the quality of the data (i.e. the counting statistics) [24]. Ideally, c2 should approach 1. However, the c2 values of Eu2NiMnO6 and Dy2NiMnO6 polycrystalline samples are much larger than 1. There are two reasons. One is that the XRD data have been overcollected which results a small Rexp value. The other is a large Rwp value due to the level of background when collecting XRD data. 3.2. Magnetic properties
Fig. 1. Rietveld refined powder XRD patterns of Eu2NiMnO6 and Dy2NiMnO6 at room temperature. The experimental data are indicated by dots, and the calculated profile is shown by the solid line. The short vertical lines show the positions of the Bragg diffraction peak. The underneath curve shows the difference between the observed and calculated intensity. The inset shows the crystallographic structure of R2NiMnO6.
In order to confirm the magnetic properties of Eu2NiMnO6 and Dy2NiMnO6 oxides, the temperature (T)-dependence of magnetization (M) has been measured. Fig. 2(a)e(b) show the zero field cooling (ZFC) and field cooling (FC) magnetization vs. temperature curves of Eu2NiMnO6 and Dy2NiMnO6 from 2 K to 300 K under 0.01 T. With increasing the temperature, it is evident that the compounds undergo a ferromagnetic-paramagnetic phase transition. The Curie temperature TC, corresponding to the maximum slope of FC M-T curve (jdM=dTj) (See the insets of Fig. 2(a)e(b), is determined to be 145 K for Eu2NiMnO6 and 97 K for Dy2NiMnO6, respectively. They are in agreement with the result reported in the literatures [22,23]. The TC of La2NiMnO6 reported is 280 K [11]. Obviously, TC shifts towards low temperature with decreasing the lanthanide ionic radius. It also can be seen from Fig. 2(a)e(b) that the ZFC and FC curves are completely reversible around TC. However, a significant thermal magnetic irreversibility between the ZFC and FC branches is clearly observed below TC. This kind of bifurcation is also yielded in many other R2NiMnO6 compounds such as
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oxides are calculated to be 138.8 K and 39.5 K. The positive qP further confirms that the predominant exchange interaction is ferromagnetic [1], that originates from the ordered alignment Ni2þ and Mn4þ superexchange interaction [5,27,29]. However, the value of qP for Dy2NiMnO6 is much lower than that of TC. It further suggests the existence of antiferromagnetic interaction. In addition, it is worth mentioned that there is a sharp downturn deviation from Curie-Weiss law behavior on the 1/c-T curve just above TC for Dy2NiMnO6. The reason of deviation is Griffiths-like phase behavior, just like reported in Tb2NiMnO6 [29]. Raman scattering experiments demonstrated that the smaller size of the rare earth could generate a Griffiths phase in double perovskites [30]. 3.3. Magnetocaloric properties For a better understand of magnetic behavior and evaluating magnetocaloric effect of these two oxides within a wide temperature range, the isothermal magnetization curves were measured in applied magnetic fields up to 7 T with an interval of 0.2 T in the vicinity of Curie temperature with an interval of 2 K for Eu2NiMnO6 and Dy2NiMnO6 (See Fig. 3(a)e(b)). As shown in Fig. 3(a), the magnetization of Eu2NiMnO6 increases quickly at low fields and then increases slowly at higher field below TC, just like normal ferromagnetic material. While the magnetization of Dy2NiMnO6 exhibits a linear increment for fields from 0.5 T to 7 T below TC, showing strong antiferromagnetic interaction. According to the isothermal magnetization data, the magnetic entropy changes jDSM j for Eu2NiMnO6 and Dy2NiMnO6 are numerically calculated by using the Maxwell's relation [31]:
ZH Fig. 2. ZFC and FC magnetization (M) versus temperature (T) curves and the temperature variation of the ZFC inverse susceptibility fitted to the Curie-Weiss law under 0.01 T for (a) Eu2NiMnO6 and (b) Dy2NiMnO6. The inset of (a) and (b) shows the FC dM=dT-T curve of Eu2NiMnO6 and Dy2NiMnO6 under 0.01 T, respectively.
R ¼ Nd, Sm, Gd and Y [20,25,26]. The ordered alignment of Ni2þOMn4þ superexchange interaction contributes to the FM interaction, which is dominant in these compounds. Whereas, Ni2þO Ni2þ and Mn4þeOeMn4þ due to partial disorder of Ni and Mn leads to weak antiferromagnetic interaction [26,27]. Thus, this thermal irreversibility is likely attributed to the competition of FM and AFM interaction in Eu2NiMnO6 and Dy2NiMnO6. In addition, similar with previously reported results on Nd2CoMnO6 double perovskite, Dy2NiMnO6 exhibits a sharp drop of magnetization around 6 K, which originates from the anti-parallel alignment of rare earth moment with respect to the Ni/Mn moments [28]. Therefore, the appearance of two discrete phase transition temperatures for Dy2NiMnO6 stems from the order of transition metal and rare earth, respectively. Temperature dependences of inverse magnetic susceptibility (c) of Eu2NiMnO6 and Dy2NiMnO6 are also shown in Fig. 2(a)e(b). They obey the Curie-Weiss (CW) law above 250 K for Eu2NiMnO6 and 200 K for Dy2NiMnO6, respectively. The effective magnetic moments per molecule are ascertained to be 6.86 mB for Eu2NiMnO6 and 14.13 mB for Dy2NiMnO6, which resemble with the correlative theoretical effective magnetic moments value of 7.04 mB and 15.78 mB for two oxides. The theoretical effective magnetic moments are calculated by the following equation:
meff ðcalcÞ ¼ ½2mðR3þ Þ2 þ mðNi2þ Þ2 þ mðMn4þ Þ2 1=2 [1], where the effective paramagnetic moments are 3.65 mB for Eu3þ, 10.63 mB for Dy3þ, 2.83 mB for Ni2þ, 3.87 mB for Mn4þ. Meanwhile, the paramagnetic Curie temperature (qP ) for Eu2NiMnO6 and Dy2NiMnO6
DSM ðT; HÞ ¼ 0
vM vT
dH
(1)
H
Figs. 3(c)e4(d) show the temperature dependence of jDSM j for Eu2NiMnO6 and Dy2NiMnO6 under different field variations, respectively. The jDSM j peaks appear around 147 K for Eu2NiMnO6 and around 97 K for Dy2NiMnO6 compounds, which were induced by the FM-PM phase transition. The value of jDSM j gradually increases with the increase of the applied magnetic field for these two oxides. The maximum value of magnetic entropy change ) reaches to 4.0 J/kg K for Eu2NiMnO6 and 5.2 J/kg K for (DSmax M Dy2NiMnO6 for a field change of 0e7 T, respectively. They are much larger than that of La2NiMnO6 (1.5 J/kg K for 0e4.5 T) [7]. Although the value of magnetic entropy change peak is not very large, the peak is very broad and the full width at half peak of the jDSM j-T curve reaches ~60 K for Eu2NiMnO6 and ~74 K for Dy2NiMnO6 for the field change of 0e7 T. Not only the peak value of magnetic entropy change, but also its full width at half peak, are very useful to obtain a large refrigerant capacity. Besides the jDSM j value, the relative refrigerant capacity (RCP) is another significant factor for evaluating a magnetocaloric material, defined by the following expression [31]:
RCP ¼ DSmax dTFWHM M
(2)
where dTFWHM is the full width at half maximum of jDSM j. Obvi value but also the ously, the RCP depend on not only the DSmax M magnitude of dTFWHM . The inset of Fig. 3(a) exhibits the field dependence of RCP for the two oxides. The value of RCP reaches 241 J/kg for Eu2NiMnO6 and 385 J/kg for Dy2NiMnO6 for the field change of 0e7 T, respectively. They are comparable with or even much larger than those of some rare-earth-based oxides such as La0.67Ca0.33Mn0.9Fe0.1O3 (87 J/kg for 0e3 T) [32], LaMn0.9Fe0.1O3 (152 J/kg for 0e5 T) [33], SmCr0.85Mn0.15O3 (176 J/kg for 0e9 T) [34],
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597
Fig. 3. Isothermal magnetization curves in the vicinity of TC for (a) Eu2NiMnO6 and (b) Dy2NiMnO6 oxides. Magnetic entropy change curves as a function of temperature for (c) Eu2NiMnO6 and (d) Dy2NiMnO6 for different magnetic field changes. The inset of (a) shows the relative refrigeration capacity (RCP) vs. magnetic field curves of Eu2NiMnO6 and Dy2NiMnO6.
La0.85Zr0.15MnO3 (142.5 J/kg for 0e5 T) [35] and Nd0.55Sr0.45Ca0.98Mn0.02O3 (260 J/kg for 0e7 T) [36]. Therefore, they can be potential candidates for magnetic refrigerants working in a wide temperature range.
3.4. Critical behavior To get a deeper insight into the origin of magnetocaloric effect around TC, we further investigate the phase transition of Eu2NiMnO6 and Dy2NiMnO6 oxides by using the Banerjee criterion [37]. The Arrott plots of Eu2NiMnO6 and Dy2NiMnO6 oxides are shown in Fig. 4(a)e(b). According to the Banerjee criterion [37], a magnetic transition is expected to be of first order when the slope of M2 vs. H/M plot is negative, while it would be of second order when the slope is positive. It is very clear from Fig. 4(a) and (b) that the nature of the phase transition for both oxides is of second-order magnetic transition. In addition, it is evident that the Arrott-plot of Dy2NiMnO6 does not display any positive intercepts around TC. It manifests the nonexistence of long-range order. Therefore, we will
only investigate the critical behavior of Eu2NiMnO6 in the followings. Clarifying the nature of critical behavior is performed normally near the FM transition temperature. Based on the scaling hypothesis, a second-order magnetic phase transition around TC is described by a series of interrelated critical exponents, b; g; d and some magnetic equations of state [38] which are given by:
MS ðTÞ ¼ M0 jεjb ;
ε < 0;
g c1 0 ðTÞ ¼ ðh0 =M0 Þε ;
M ¼ DH1=d ;
ε ¼ 0;
T < TC
ε > 0; T ¼ TC
T > TC
(3) (4) (5)
where ε means the reduced temperature established as ε ¼ (T e TC)/ TC. MS ðTÞ is the spontaneous magnetization below TC and c1 0 ðTÞ is the inverse initial susceptibility above TC. M0, h0 and D are the respective critical amplitudes. Using scaling hypothesis the
Fig. 4. Arrott-plots of (a) Eu2NiMnO6 and (b) Dy2NiMnO6.
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L. Su et al. / Journal of Alloys and Compounds 746 (2018) 594e600
magnetic equation of state can be expressed as:
.
MðH; εÞ ¼ εb f± H εbþg
MS ðTÞ½dMS ðTÞ=dT1 ¼ ðT TC Þ=b (6)
where fþ (T > TC) and f- (T < TC) are the regular analytic functions. In term of renormalized magnetization and field, Eq. (6) can be written as:
m ¼ f± ðhÞ
(7)
where m≡εb MðH; εÞ and h≡εðbþgÞ H. Eq. (7) suggests that for correct scaling relations and proper critical exponents, plots of m vs. h will fall on two universal curves: one below TC and another above TC. This is an important criterion for critical regime. Based on the above theories, we will analyze the critical behavior of Eu2NiMnO6 in detail. Ms ðTÞ and c1 0 ðTÞ can be obtained by linear extrapolation of a plot of M 1=b vs. ðH=MÞ1=g to the ordinate and abscissa axes, respectively. It is clear from Fig. 4(a) that all the curves of the Arrot-plot for Eu2NiMnO6 are almost linear in high fields. Therefore, we choose the critical exponents of the mean-field model (b ¼ 0:5; g ¼ 1:0) as a modified Arrott plot [39,40]. Based on Fig. 4(a), we obtain the Ms ðT; 0Þ-T curve and c1 0 ðTÞ-T curve, as shown in Fig. 5(a). They can be well fitted by Eq. (3) and Eq. (4), respectively. The critical exponents are obtained to be b ¼ 0.443 ± 0.005 with TC ¼ 147. 429 ± 0.045 and g ¼ 1.014 ± 0.013 with TC ¼ 147.559 ± 0.091. Obviously, the TC value is pretty in agreement with that determined from the dM/dT curve. To determine the critical exponents more accurately, we have further analyzed the Ms ðTÞ and c1 0 ðTÞ data of Eu2NiMnO6 by using the KouveleFisher (KF) method [41]. The KF equations are denoted as follow:
h
1 c1 0 ðTÞ dc0 ðTÞ=dT
i1
¼ ðT TC Þ=g
(9) 1
1 MS ðTÞ½dMS ðTÞ=dT1 vs. T and c1 vs. T curves of 0 ðTÞ½dc0 ðTÞ=dT Eu2NiMnO6 are plotted in Fig. 5(b). It is clear that 1
1 MS ðTÞ½dMS ðTÞ=dT1 and c1 change linearly 0 ðTÞ½dc0 ðTÞ=dT with the increment of temperature. They can be well fitted by Eq. (8) and Eq. (9). It illustrates that the values of Ms ðT; 0Þ and c1 0 ðTÞ obtained from Arrott-plot are reasonable. The critical exponents obtained from the KF method are b ¼ 0.463 ± 0.053 with TC ¼ 147.699 ± 0.213 and g ¼ 1.032 ± 0.016 with TC ¼ 147.449 ± 0.179. Table 2 lists the critical exponents values obtained from different methods. It is remarkable that the values of critical exponents based on both modified Arrott-plot method and KF method match reasonably well, suggesting that the estimated values are self-consistent and unambiguous. Meanwhile, the critical exponent d of Eu2NiMnO6 can be derived from the critical isotherm according to equation (5). Here, we use the isothermal M-H data at 148 K, as shown in Fig. 6. The value of d is determined to be 3.226. For clarity, the inset of Fig. 6 shows a loglog plot of field-dependent magnetization. Moreover, the critical exponents satisfy the Widom scaling relation [42]:
d ¼ 1 þ g=b
(10)
Using the critical exponents b and g calculated previously, we can get that d is 3.289 for modified Arrott method and d is 3.229 for K-F method. It is clear that these values are very close to the value obtained from critical isotherm. Therefore, estimated exponents in the present study are dependability. By using the values of critical exponents and TC ~148 K obtained from the KF method and following Eq. (7), we have plotted scaled m vs. scaled h curves of Eu2NiMnO6 in the vicinity of TC, as shown in Fig. 7(a). The inset of Fig. 7(a) shows the same plot on a log-log scale. All the points collapse into two independent branches: one for T < TC and the other for T > TC. In order to see clearly, Fig. 7(b) shows the m2 vs. h=m plot [43]. We can see from Fig. 7(b) that all the data still fall on two separate branches. These results confirm that these critical exponents can generate the scaling equation of state for Eu2NiMnO6. In addition, Table 2 also lists the values of critical exponents of Y2NiMnO6 [44] as well as the theoretical models [43] for comparison. It is obvious that the values of critical exponents for Eu2NiMnO6 and Y2NiMnO6 are in between those theoretically predicted for 3D Heisenberg and mean-field interaction models. However, the values of Eu2NiMnO6 are closer to those for meanfield interaction model. The values of Y2NiMnO6 are closer to those for 3D Heisenberg interaction model. This difference must be caused by the degree of short-range interaction due to the change of the rare earth ionic radium. The deduced critical exponents of Eu2NiMnO6 do not belong to any theoretical models, it is crucial to clarify whether they obey any universality class as they approach the asymptotic region. For this intention, effective exponents beff and geff are calculated following the equations [45]:
d½ln MS ðεÞ ; beff ðεÞ ¼ dðlnεÞ Fig. 5. (a) Temperature dependence of the spontaneous magnetization Ms ðT; 0Þ and the inverse initial susceptibility c1 0 ðTÞ for Eu2NiMnO6. (b) KouveleFisher plots for the spontaneous magnetization and the inverse initial susceptibility for Eu2NiMnO6.
(8)
d ln c1 0 ðεÞ geff ðεÞ dðlnεÞ
(11)
Fig. 8 show the ε dependence of effective critical exponents (beff and geff ). beff is decreased from beff z0:55 at εz0:014 to beff z0:46
L. Su et al. / Journal of Alloys and Compounds 746 (2018) 594e600
599
Table 2 Values of the critical exponents determined from different theoretical models for Eu2NiMnO6. The theoretically predicted values of critical exponents for various universality classes as well as the critical exponents of Y2NiMnO6 are also listed for the sake of comparison. Abbreviation: PC, polycrystalline. Composition
Ref.
Technique
Eu2NiMnO6(PC)
This work
Mean Field Model 3D Heisenberg Model 3D Ising Model Y2NiMnO6(PC)
[43] [43] [43] [44]
Modified Arrrot plot Kouvel-Fisher method Critical isotherm Theory Theory Theory Kouvel-Fisher method
Fig. 6. Critical isotherm at TC ¼ 148 K (inset: logelog scale) for Eu2NiMnO6.
at εz0:095. Nevertheless, geff presents a nonmonotonic change with ε. It resembles with that for disordered ferromagnets such as amorphous ferromagnets [46]. Similar phenomenon has also been found in Pr0.5Sr0.5MnO3 [47]. Thus, this study shows the presence of disorder which influences the critical behavior in Eu2NiMnO6. This disorder FM property matches with the Griffiths-like phase behavior observed from the inverse magnetic susceptibility just above TC in Eu2NiMnO6.
4. Conclusion We have investigated the magnetocaloric effects and critical behaviors of ferromagnetic Eu2NiMnO6 and Dy2NiMnO6 double perovskite oxides. The Curie temperature shifts toward low
a
0.0 0.115 0.11
b
g
d
0.443 ± 0.005 0.463 ± 0.053
1.014 ± 0.013 1.032 ± 0.016
0.5 0.365 0.325 0.375 ± 0.033
1.0 1.386 1.241 1.331 ± 0.09
3.289 3.229 3.226 ± 0.002 3.0 4.8 4.82 4.31 ± 0.1
Fig. 8. Effective exponents beff below TC and geff above TC as a function of reduced temperature ε for Eu2NiMnO6.
temperature with the reduction of rare earth ionic radius. Curie temperature TC is 145 K for Eu2NiMnO6 and 97 K for Dy2NiMnO6, respectively. For a field change of 0e7 T, the maximum values of max DS reach 4.0 J/kg K for Eu2NiMnO6 and 5.2 J/kg K for M Dy2NiMnO6. RCP values as high as 241.5 J/kg and 385.1 J/kg are achieved for both oxides due to the large full width at half peak of the jDSM j-T curve. The high RCP values together with the broad magnetic entropy change peak indicate the applicability of Eu2NiMnO6 and Dy2NiMnO6 as magnetic refrigerants working in a wide temperature range, they are very promising magnetic refrigerants materials. The critical exponents estimated from various techniques match reasonably well and values are in between those theoretically predicted for 3D Heisenberg and mean-field interaction model. Effective critical exponents further confirmed the existence of disorder FM property, which matches with the Griffiths-
Fig. 7. (a) Magnetic equation of state of KF method below and above TC for Eu2NiMnO6. The inset shows the same plots on a logelog scale. (b) The renormalized magnetization m2 and field h=m for Eu2NiMnO6.
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like phase behavior observed from the inverse magnetic susceptibility just above TC. Author contribution statement L. S. and Z. H. C planned the experiment. L. S grew the polycrystalline samples, carried out the magnetic and magnetic entropy change measurement and calculation and critical behavior simulation. L. S., X. Q. Z., Y. J. K., C. S. L. and K. Y. H. contributed to the analysis and discussion for all the results. L. S., Z. H. C and Q. Y. D. wrote the paper with the input from all the co-authors. Competing financial interests The author declare no competing financial interests. Acknowledgements This work was supported by the National Key R&D Program of China (Grant Nos. 2017YFB0702702, 2016YFA0300701 and 2015CB921403), the National Natural Sciences Foundation of China (Grant Nos. 91622126, 51427801, and 51471111), and the Key Research Program of Frontier Sciences, CAS (Grant Nos. QYZDJSSW-JSC023). References [1] M. Retuerto, A. Munoz, M.J. Martinez-Lope, J.A. Alonso, F.J. Mompean, M.T. Fernandez-Diaz, J. Sanchez-Benitez, Magnetic interactions in the double perovskites R2NiMnO6 (R ¼ Tb, Ho, Er, Tm) investigated by neutron diffraction, Inorg. Chem. 54 (2015) 10890e10900. [2] H.J. Zhao, X.Q. Liu, X.M. Chen, L. Bellaiche, Effects of chemical and hydrostatic pressures on structural, magnetic, and electronic properties of R2NiMnO6 (R¼rareearthion) double perovskites, Phys. Rev. B 90 (2014), 195147. [3] S. Kumar, G. Giovannetti, J. van den Brink, S. Picozzi, Theoretical prediction of multiferroicity in double perovskite Y2NiMnO6, Phys. Rev. B 82 (2010), 134429. [4] T. Chakraborty, H. Nhalil, R. Yadav, A.A. Wagh, S. Elizabeth, Magnetocaloric properties of R2NiMnO6 (R¼Pr, Nd, Tb, Ho and Y) double perovskite family, J. Magn. Magn. Mater. 428 (2017) 59e63. [5] R.J. Booth, R. Fillman, H. Whitaker, A. Nag, R.M. Tiwari, K.V. Ramanujachary, J. Gopalakrishnan, S.E. Lofland, An investigation of structural, magnetic and dielectric properties of R2NiMnO6 (R¼rare earth, Y), Mater. Res. Bull. 44 (2009) 1559e1564. [6] M.T. Anderson, K.B. Greenwood, G.A. Taylor, K.R. Poeppelmeier, B-cation arrangements in double perovskites, Prog. Solid State Chem. 22 (1993) 197e233. [7] X. Luo, Y.P. Sun, B. Wang, X.B. Zhu, W.H. Song, Z.R. Yang, J.M. Dai, The magnetic entropy change in the double perovskite La2NiMnO6 with strong spinephonon coupling, Solid State Commun. 149 (2009) 810e813. [8] M. Balli, P. Fournier, S. Jandl, M.M. Gospodinov, A study of the phase transition and magnetocaloric effect in multiferroic La2MnNiO6 single crystals, J. Appl. Phys. 115 (2014) 173904. [9] P. Neenu Lekshmi, M. Raama Varma, Colossal magneto-dielectricity in La2NiMnO6 probed by Raman spectroscopy, Mater. Sci. Forum 830e831 (2015) 513e517. [10] N.S. Rogado, J. Li, A.W. Sleight, M.A. Subramanian, Magnetocapacitance and magnetoresistance near room temperature in a ferromagnetic semiconductor: La2NiMnO6, Adv. Mater. 17 (2005) 2225e2227. [11] S. Zhou, Y. Guo, J. Zhao, S. Zhao, L. Shi, Nature of short-range ferromagnetic ordered state above Tc in double perovskite La 2 NiMnO 6, Appl. Phys. Lett. 96 (2010), 262507. [12] G. Blasse, Ferromagnetic interactions in non-metallic perovskites, J. Phys. Chem. Solid. 26 (1965) 1969e1971. [13] R. Masrour, A. Jabar, Magnetocaloric and magnetic properties of La2NiMnO6double perovskite, Chin. Phys. B 25 (2016), 087502. [14] K.A. Gschneidner Jr., V.K. Pecharsky, A.O. Tsokol, Recent developments in magnetocaloric materials, Rep. Prog. Phys. 68 (2005) 1479e1539. [15] A.M. Tishin, Y.I. Spichkin, The Magnetocaloric Effect and its Applications, first ed., IOP Bristol, 2003. [16] Y. Jia, Q. Wang, Y. Qi, L. Li, Multiple magnetic phase transitions and magnetocaloric effect in double perovskites R 2 NiMnO 6 ( R ¼ Dy, Ho, and Er), J. Alloys Compd. 726 (2017) 1132e1137. [17] A. Midya, N. Khan, D. Bhoi, P. Mandal, Giant magnetocaloric effect in magnetically frustrated EuHo2O4 and EuDy2O4 compounds, Appl. Phys. Lett. 101 (2012), 132415.
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