Universal behavior of magnetocaloric effect in a layered perovskite La1.2Sr1.8Mn2O7 single crystal

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Universal behavior of magnetocaloric effect in a layered perovskite La1.2Sr1.8Mn2O7 single crystal Tran Dang Thanh a,n, T.V. Manh b, T.A. Ho b, Andrey Telegin c, T.L. Phan d, S.C. Yu b,n a

Institute of Materials Science, Vietnam Academy of Science and Technology, 18-Hoang Quoc Viet, Hanoi, Vietnam Department of Physics, Chungbuk National University, Cheongju 361-763, South Korea c Department of Magnetic Semiconductors, Institute of Metal Physics, RAS, Russia d Department of Physics and Oxide Research Center, Hankuk University of Foreign Studies, Yongin 449-791, South Korea b

art ic l e i nf o

a b s t r a c t

Article history: Received 9 May 2015 Accepted 6 September 2015

In this paper, we present a detailed analysis on temperature and magnetic field dependences of the magnetic entropy change (ΔSm) near the ferromagnetic (FM)–paramagnetic (PM) phase transition of a La1.2Sr1.8Mn2O7 single crystal. Experimental results reveal the material exhibiting a FM–PM phase transition at TC ¼ 85 K, and belongs to a second-order phase transition (SOPT). Around TC,  ΔSm reaches the maximum value (|ΔSmax|), which increases with increasing an applied magnetic field change, ΔH. The |ΔSmax| values found are about 0.93, 1.73, 2.38, 2.91, and 3.33 J kg  1 K  1 for ΔH ¼10, 20, 30, 40, and 50 kOe, respectively. However, the peak position of the  ΔSm(T) curves is effectively shifted to higher temperatures when ΔH increases. Additionally, the ΔSm(T) curves measured at different ΔH values do not collapse into a universal curve when they are normalized to their respective ΔSmax value, and Prod. Type: rescaled the temperature axis with θ1 ¼ (T  TC)/(Tr  TC) for a reference temperature Tr 4TC or Tr oTC. Nevertheless, they can be collapsed into a unique curve in the whole temperature range if using two separated reference temperatures, Tr1 and Tr2, with θ2 ¼  (T  TC)/(Tr1  TC) for T r TC and θ2 ¼(T  TC) /(Tr2  TC) for T 4TC. & 2015 Elsevier B.V. All rights reserved.

Keywords: Perovskite manganites Magnetocaloric effect Magnetic phase transformation

1. Introduction Perovskite-type manganese oxides Lnn þ 1MnnO3n þ 1 (Ln is lanthanide or alkaline-earth metal, n is the dimension), the member of the Ruddlesden–Popper series [1], are ones of most fascinating materials in the condensed-matter research. A renewed interest in these compounds has recently been aroused because their interesting phenomena related to the ferromagnetic (FM)–paramagnetic (PM) transition, such as colossal magnetoresistance (CMR) [2], magnetocaloric effect (MCE) [3], and complex magnetic and electrical properties [4–6]. Many previous reports have revealed a strong dependence of phase transitions, CMR, MCE, and magneto-transport properties of doped perovskite manganites on crystal structure, stoichiometry and dopant types. Basically, these effects and properties have been explained by means of Mn3 þ –Mn4 þ FM double-exchange (DE) interactions, and anti-FM super-exchange (SE) interactions of Mn3 þ –Mn3 þ and Mn4 þ –Mn4 þ pairs [7]. Their interaction strength is strongly affected by Mn3 þ and Mn4 þ concentrations and the structural n

Corresponding authors. E-mail addresses: [email protected] (T.D. Thanh), [email protected] (S.C. Yu).

parameters (such as the Mn–O bond length, Mn–O–Mn bond angle, and tolerance factor t). Among these, the microstructure of the Mn–O networks plays a crucial role in spin-change dynamics, which is responsible for the magneto-transport properties of perovskite manganites. Accordingly, the scientists have paid much attention to the effect of the dimensionality of Mn–O networks on the magneto-transport properties of materials. Experimental studies indicated that perovskite manganites with n ¼1 (such as, La1  xSrxMnO4) have a layered perovskite structure, and aretwo-dimensional anti-FM materials [8]. Meanwhile, Ln2  2xA1 þ 2xMn2O7 type manganites (with n ¼2, A ¼Sr or Ca) have a double layered perovskite structure, and are considered as twodimensional FM materials. Their structures are a stack of FM metal sheets composed of MnO2 bilayers separated by a (Ln, A)2O2 rocksalt layer, and thus form a natural array of FM-insulator-FM junction. Their physical properties become strongly anisotropic and complex [9–12]. Recently, the MCE in La2 2xSr1 þ 2xMn2O7 compounds has been studied upon the magnetic entropy change (ΔSm) [13, 14]. A maximum of  ΔSm (denoted as |ΔSmax|) was found at around TC. However, the peak position of the  ΔSm(T) curves of La2 2xSr1 þ 2xMn2O7 compounds is effectively shifted towards higher temperatures by increasing the applied field change (ΔH)

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second order phase transition (SOPT), according to the criteria suggested by Banerjee [17]. According to the mean-field theory for FM long-range order [16], the M2 versus H/M isotherms give a set of parallel straight lines, and the line at TC passes through the origin. However, the absence of the linearity in Fig. 2(a) proves that our sample exhibit FM short-range order rather than longrange FM one. We have also used different values of β and γ of the 3D-Heisenberg model (β ¼0.365 and γ ¼ 1.336), the 3D-Ising model (β ¼0.325 and γ ¼1.241), and the tricritical mean field (β ¼ 0.25 and γ ¼1.0) [16] as trial exponents to perform the β γ modified Arrott plots, M1/ versus (H/M)1/ , as can be seen in Fig. 2 γ (b–d). According to the Arrott–Noakes equation of state, (H/M)1/ 1/β ¼a(T  TC)/T þbM (a and b are constants) [18], the magnetic system with a nonmean-field critical behavior requires the modified Arrott plots, in which spanning TC will generate a set of β parallel straight lines when the M–H–T data are plotted as M1/ 1/γ versus (H/M) . The critical isotherm passes through the origin for β appropriate values of β and γ [18]. Unfortunately, the M1/ versus 1/γ curves in Fig. 2(b–d) do not exhibit the mentioned (H/M) features. This proves that our sample does not follow any model. This could be related to a magnetic anisotropic property and an existence of complex FM interactions in layered perovskite La1.2Sr1.8Mn2O7 [9–12,14]. Fig. 3(a) shows the  ΔSm(T) curves with different ΔH values for La1.2Sr1.8Mn2O7. As a function of temperature,  ΔSm reaches a maximum value around TC, corresponding to FM–PM phase transition. Its value increases with increasing ΔH, |ΔSmax| ¼0.93, 1.73, 2.38, 2.91, and 3.33 J kg  1 K  1 for ΔH¼10, 20, 30, 40, and 50 kOe, respectively. These values are slightly smaller than those obtained by Wang et al. (|ΔSmax| ¼ 3.7 J kg  1 K  1 for ΔH¼50 kOe) [14]. Besides, the peak position of the  ΔSm(T) curves is remarkably shifted towards higher temperatures as increasing ΔH, which is similar to the case observed in Ref. [14]. To understand more thoughtfully the magnetic field and temperature dependences of ΔSm, we analyzed in detail the ΔSm(T, ΔH) data. According to Franco et al. [19, 20], the magnetic field dependence of ΔSm in SOPT materials can be expressed as a power law |ΔSm| ¼a  ΔHm, where a and m are the coefficient and the field exponent, respectively. This expression is in a good correspondence with experimental results related to soft-magnetic alloys and rare-earth-based MCE materials. Here, the field exponent m can be locally calculated through the following expression:

[14]. To get a clear idea about the performance of materials used in magnetic refrigeration devices, it is necessary to understand how their MCE evolves in desired temperature and magnetic-field ranges. A detailed analyses for ΔSm(T, ΔH) data provides important information about magnetocaloric properties of materials. In this work, we analyze the ΔSm(T, ΔH) data of a La1.2Sr1.8Mn2O7 single crystal. Our results point out that the field dependences of |ΔSmax| and the refrigerant-capacity (RC) can be described by the power laws |ΔSmax|¼ a  ΔHm and RC¼b  ΔHN, respectively. Also, by normalizing ΔSm(T, ΔH) data to their respective ΔSmax value, we indicate that all these curves are collapsed onto a universal curve.

2. Experimental details A single crystal of La1.2Sr1.8Mn2O7 was grown by the floatingzone method. The magnetic measurements versus temperature and magnetic field were performed on a superconducting quantum interference device (SQUID) magnetometer. Temperature dependences of magnetization, M(T), under an applied field H ¼100 Oe were recorded during the warming protocol after zerofield cooling (ZFC) and field cooling (FC), see Fig. 1(a). The Curie temperature (TC) of the material obtained from the flexion point in of the M(T) curves is about 85 K. The isothermal magnetization, M (H), curves were measured around TC (with a temperature interval of 2 K) in the field range of 0–50 kOe, Fig. 1(b). The MCE is assessed by means of ΔSm (dependent on both the temperature and magnetic field), which can be calculated by the following equation:

∫0

Hmax

⎛ ∂M (T , H ) ⎞ ⎜ ⎟ dH , ⎝ ⎠H ∂T

(1)

3. Results and discussion To assess the nature of magnetic phase transition in the layered perovskite La1.2Sr1.8Mn2O7, we have performed the Arrott plots [15] for the M(H) data, as shown in Fig. 2(a). It is well known that the Arrott plots assume the critical exponents β ¼ 0.5 and γ ¼ 1.0, as a consequence of the mean-field theory [16]. One can see from Fig. 2(a) that the nonlinear parts in the low field region at temperatures below and above TC are driven toward two opposite directions, revealing the FM–PM phase separation. Positive slopes of the H/M versus M2 curves (not shown, the coordinate axes are inversed of the Arrott plots) reflect the material undergoing the

m (T , H ) =

d ln |ΔSm (T , H )| , d ln H

(2)

8

70

FC ZFC

M (emu/g)

6

60

60 K

50

H = 100 Oe

40

4

98 K T=2K

2 0

0

50

100 150 200 T (K)

0

4

2 10

4 10 H (Oe)

4

30 20

M (emu/g)

ΔSm (T , ΔH ) =

10 0 4 6 10

Fig. 1. (a) Temperature dependences of magnetization taken both ZFC and FC protocols for H¼ 100 Oe. (b) Isotherm magnetization curves measured at different temperatures around TC.

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2 1

x 10 (Oe.g/emu)

1/

T=2K 60 K

1

1/

M

98 K

0 0 0.5 1 1.5 2 2.5 3 1/

2 98 K

0

0

1.5

= 0.325 = 1.241

(H/M)

4

2

0.5

(H/M)

7

2

T=2K 60 K

1/

1/

1/

5

3

3

x 10 (emu/g)

1/

4

M

0 0.2 0.4 0.6 0.8 1 1.2 1/

6

1/

98 K T=2K

M

M

0

= 0.365 = 1.336

1/

60 K

(H/M)

x 10 (emu/g)

x 10 (emu/g)

3

8

= 0.5 = 1.0

1/

3

x 10 (emu/g)

1/

4

3

1/

x 10 (Oe.g/emu)

1.2 0.9

1

1.5

2 1/

2

x 10 (Oe.g/emu)

= 0.25 = 1.0 T=2K 60 K

0.6 0.3

98 K

0 0 0.2 0.4 0.6 0.8 1 1.2 (H/M)

1/

3

1/

x 10 (Oe.g/emu)

Fig. 2. (a) Arrott plots (isotherm M2 versus H/M), and modified Arrott plots, M1/β versus (H/M)1/γ, corresponding to the critical exponents expected for the (b) 3D-Heisenberg, (c) 3D-Ising, and (d) tricritical mean-field models.

where the value of m approaches to 2 in the PM range with T c TC, and approaches to 1 in the FM range with T { TC. Fig. 3(b) shows the temperature dependence of m calculated from Eq. (2) for La1.2Sr1.8Mn2O7 at several ΔH values. One can see that the value of m strongly depends on both the magnetic field and temperature. For each ΔH value, m reaches the minimum around TC, and approaches to 1 at low temperatures (T{ TC), and approaches to 2 at high temperatures (T c TC). The minimum position of the m(T) curve is shifted towards high temperatures when ΔH increases. Although Franco et al. [19, 20] have reported that in the case of single magnetic phase transition materials, the value of m is field independent at T¼ TC, or is the temperature of the peak position (TP) of the  ΔSm(T) curves. However, our

1

1

50 kOe 10 kOe

60

80 100 120 T (K)

0.5

60

80

100 120

T (K)

| S

max

10 kOe

m

2

250 200 150 100 | Smax| 50 RC

0 10 20 30 40 50 H (kOe)

-1

1.5

3.5 3 2.5 2 1.5 1 0.5 0

RC (J.kg )

-1 -1

50 kOe

3

0

| (J.kg .K )

2

-1

-1

- S m (J.kg .K )

4

experiment results show that the value of m obtained at TP of the  ΔSm(T) curves (denoted as m(Tp)) strongly depends on both magnetic field and temperature. Namely, m(Tp) decreases from 0.80 (at 80 K and ΔH¼ 10 kOe) to 0.61 (at 87 K and ΔH ¼50 kOe). This contrast could be related to the magnetic anisotropy in the material. As mentioned above, the field dependence of ΔSm in SOPT materials follows a power law of the field. In this work, the | ΔSmax| versus ΔH is plotted in Fig. 3(c). Interestingly, it can be described well by the power law of |ΔSmax| ¼a  ΔHm with m ¼0.75, see the solid line in Fig. 3(c). This value is located in the range of m(Tp) values obtained from Eq. (2) and Fig. 3(b). However m ¼0.75 is much different from the value of m(TC) ¼2/3 expected for the mean-field theory [20]. This is an additional confirmation that the

0

Fig. 3. (a) Temperature dependences of the magnetic-entropy change under different applied field changes. (b) The local exponent m with ΔH¼ 10–50 kOe (with step of 10 kOe). (c) Magnetic field dependences of |ΔSmax| and RC data are fitted to the power law, |ΔSmax| ΔHm and RC  ΔHN, respectively (the solid lines).

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1

m

0.4

10 kOe

0.2 T < T 0 -2

r

C

-1

0

1

2

3

max

0.6 0.4

50 kOe

0.2 T > T r C 0 -3 -2 -1 0 1 2 3 4

1

m

50 kOe

0.6

1

0.8 10 kOe

S / S

max

0.8

S / S

m

S / S

max

1

0.8 0.6 0.4 0.2

T
50 kOe 40 kOe 30 kOe 20 kOe 10 kOe

0 -2 -1 0

1

C

T >T r2

1

2

C

3

4

2

Fig. 4. Normalized magnetic entropy change as a function of the rescaled temperature θ1 with (a) Tr o TC, (b) Tr 4TC, and (c) θ2 with two separated reference temperatures Tr1 o TC and Tr2 4TC.

mean-field theory for FM long-range order is not suitable to describe magnetic interactions of the layered perovskite La1.2Sr1.8Mn2O7. On the other hand, the magnetic cooling efficiency of refrigerants can be, in simple cases, evaluated by considering the magnitude of | ΔSmax| and its full width at half maximum (δTFWHM). It is easy to establish the refrigerant-capacity (RC) as RC¼|ΔSmax|  δTFWHM. Depending on ΔH, δTFWHM obtained for La1.2Sr1.8Mn2O7 increases from 40 to 64 K, corresponding to the value of RC increases from 37 to 213 J kg  1 when ΔH increases from 10 to 50 kOe, respectively. The magnetic field dependence of RC is also shown in Fig. 3(c). Based on the obtained data, we have fitted the RC values to the power law, RC¼b  ΔHN (where b and N are the coefficient and the field exponent, respectively). One can see that the magnetic field dependence of RC can be described well by the power law of RC¼b  ΔHN with N¼ 1.09, see the solid line in Fig. 3(c). More recently, a new criterion for determining the nature of a transition has been proposed upon the re-scaling of entropy change curves [20]. Universal behavior manifested in the collapse of ΔSm(T) data points measured under different ΔH values after a scaling procedure has been established for SOPT materials. In contrast, when applied to a first-order phase transition, this behavior is broken down. According to entropy scaling method, if a material exhibits a single magnetic phase transition, all ΔSm(T) data measured under different ΔH values are constructed by plotting ΔSm(T)/ΔSmax versus θ, where θ is the temperature variable defined by

θ1 = (T − TC )/(Tr − TC ),

(3)

where Tr is the reference temperature corresponding to a certain fraction f that fulfils ΔSm(Tr)/ΔSmax ¼ f. However, if a material consists of multiple phase transitions, two reference temperatures, Tr1 and Tr2, are selected for each of the curves (one below and another above TC), and the temperature axis is rescaled as:

⎧ − (T − TC )/(Tr1 − TC ) T ≤ TC θ2 = ⎨ T > TC ⎩ (T − TC )/(Tr2 − TC )

(4)

The choice of f, and using either TC or TP in Eqs. (3) and (4) do not affect the actual construction of the universal curve [20]. In this work, we identified TC as the value of TP, and selected f ¼0.6 when constructing the universal curve for the layered perovskite La1.2Sr1.8Mn2O7 at several values of ΔH ¼10–50 kOe with step of 10 kOe. Fig. 4(a) and (b) shows the normalized magnetic entropy change as a function of the rescaled temperature θ1, ΔSm(T)/ΔSmax versus θ1, for La1.2Sr1.8Mn2O7 measured at different ΔH values, with the unique selection of the reference temperature Tr o TC (Fig. 4(a)) or Tr 4TC (Fig. 4(b)). Clearly, the ΔSm(T)/ΔSmax versus θ1

curves do not collapse into a unique curve in the whole temperature range in spite of the M(T) curves of La1.2Sr1.8Mn2O7 exhibited a single magnetic phase transition as shown in Fig. 1(a). It suggests that the ΔSm(T) data of La1.2Sr1.8Mn2O7 do not follow a universal curve for the magnetic entropy change with using the unique reference temperature Tr. However, if using Eq. (4) with two separated reference temperatures, Tr1 o TC and Tr2 4 TC, to construct the universal curve, we obtained the collapse of all the ΔSm(T) data points into a unique curve in the whole temperature range as can be seen in Fig. 4(c). It means that the ΔSm(T) behavior of La1.2Sr1.8Mn2O7 is followed a universal curve when using two separated reference temperatures, one below and another above TC, which is similar in the case consisting of multi magnetic phase transitions. This feature once again demonstrates the existence of complex FM interactions and magnetic anisotropic property in the layered perovskite La1.2Sr1.8Mn2O7.

4. Conclusion We have presented detailed analyses on temperature and magnetic field dependences of ΔSm for a La1.2Sr1.8Mn2O7 single crystal. Experimental results demonstrated the existence of magnetic anisotropic property and complex FM interactions in the sample. The value of |ΔSmax| in the  ΔSm(T) curves has been observed, which corresponds to FM–PM phase transition. With increasing ΔH, the peak position of the  ΔSm(T) curves is shifted towards higher temperatures, while the |ΔSmax|, δTFWHM, and RC values strongly increase. The magnetic field dependence of |ΔSmax| and RC were fitted following the power laws, |ΔSm| ¼ a  ΔHm and RC ¼ b  ΔHN, respectively, with m and N found to be 0.75 and 1.09, respectively. Additionally, the universal curves of all ΔSm(T) data points measured with different ΔH values were constructed by plotting ΔSm(T)/ΔSmax versus θ. We pointed out that if using the unique reference temperature Tr, the ΔSm(T) data do not follow a universal curve. However, it becomes suitable if using two separated reference temperatures, Tr1 and Tr2, for each of the curves, one below and another above TC, to construct the universal curve. This feature is similar to the case of a material exhibiting multi magnetic phase transitions, which is an additional confirmation related to the existence of complex FM interactions and magnetic anisotropic property in the layered perovskite La1.2Sr1.8Mn2O7.

Acknowledgments This research was supported by the Converging Research Center Program through the Ministry of Science, ICT and Future

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Planning, Korea (2015055808). The first author is also thankful to the Institute of Materials Science, Vietnam Academy of Science and Technology.

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