J Supercond Nov MagnDOI 10.1007/s10948-014-2580-6

ORIGINAL PAPER

Investigation of Magnetocaloric Behavior of Sr-DopedEuMnO3

E. Sagar · N. Pavan Kumar · Jian Zhu · Yemin Hu ·P. Venugopal Reddy

Received: 21 March 2014 / Accepted: 13 May 2014© Springer Science+Business Media New York 2014

Abstract An effort has been made to calculate the mag-netocaloric behavior of Sr-doped EuMnO3 by theoreticallyusing the experimental magnetization data (at different mag-netic fields) available in the literature. Other importantparameters such as maximum entropy change, full width athalf maximum, relative cooling power, and maximum adi-abatic temperature change in 1 and 2 T magnetic fieldswere also computed. The observed behavior exhibited bythe samples has been explained qualitatively.

Keywords Magnetic materials · Magnetocaloric effect ·Magnetization · Thermal properties · Magnetic entropychange

1 Introduction

Magnetic refrigeration has attracted the attention of scien-tific community for the last few years due to its superiorityover gas refrigeration [1]. For this purpose, investigations

E. Sagar · N. Pavan Kumar · P. Venugopal ReddyDepartment of Physics, Osmania University,Hyderabad 500007, India

J. Zhu · Y. HuSchool of Materials Science and Engineering,Shanghai University, 200072 Shanghai, China

P. Venugopal Reddy (�)Vidya Jyothi Institute of Technology, Hyderabad, Indiae-mail: paduruvenugopalreddy@gmail.com

were carried out in a variety of materials such as inter-metallic compounds, metals, and rare earth alloys whichhave a high total angular momentum quantum number.Some of the compounds on which extensive work was car-ried are Gd [2], Gd5Si4 [3], and MnAs and MnP [4]. Infact, the largest reported value of the magnetic entropychange in these materials was 13.7 J/kg/K in the case ofundoped Gd at 293 K under a magnetic field change of 8 T[5]. In recent past, increasing attention has been focusedon large magnetocaloric effects in perovskite-type man-ganese oxide [6, 7]. It was reported that several materialsof this type have even larger magnetic entropy changesat Curie temperature than the undoped Gd. In fact, dueto strong coupling between spin and lattice, significantlattice change accompanying magnetic transition in per-ovskite manganites has also been observed [8, 9]. Thestructural change in Mn–O bond distance as well as Mn–O–Mn bond angle would, in turn, favor spin ordering,resulting in an abrupt reduction of magnetization near TC,which, in turn, leads to magnetic entropy change [10–12].Thus, a strong spin–lattice coupling at the magnetic tran-sition temperature leads to additional magnetic entropychange favoring magnetocaloric effect (MCE). Moreover,additional advantage with these materials is that theyare less expensive when compared with those based onGd.

In view of this, an effort has been made to investigate themagnetocaloric behavior of some of the manganites theoret-ically. In the present investigation, Sr-doped EuMnO3 andundoped EuMnO3 materials available in the literature [13]have been chosen, and the results of such an investigationare presented in this paper.

J Supercond Nov Magn

2 Experimental

2.1 MCE Studies

2.1.1 Theoretical Aspects of MCE

For the determination of magnetocaloric effect especially inmagnetic materials, both the experimental and theoreticalapproaches were adopted. For the experimental evalua-tion, heat capacity and/or magnetization data are required.However, for the theoretical investigation of MCE, severalapproaches were used using the models available in theliterature [14, 15]. In the present investigation, a simpleapproach has been adopted to evaluate the MCE.

From the fundamentals of thermodynamics, the entropyof a magnetic material can be written as

�SM =∫ Hmax

0

(∂S

∂H

)T

dH (1)

From Maxwell’s equations, the relationship betweenentropy and magnetization is given by(∂M

∂T

)H

=(∂S

∂H

)T

(2)

From (1) and (2), one may write as

�SM =∫ Hmax

0

(∂M

∂T

)H

dH (3)

According to molecular field theory of ferromagnetism,the variation of magnetization (M) of a magnetic materialwith temperature may be represented by the well-knownrelation [16]

M = NgμB tan h μ0gμBλm/kT (4)

In order to explain the variation of magnetization of sev-eral types of magnetic materials, two more terms, viz., BTand C, are added.

On simplification, (4) may be written as

M (T ) =(Mi −Mf

2

)tanh [A (TC − T )] + BT + C (5)

(Tf,Mf)

Mag

netiz

atio

n (a

.u.)

Temperature (K)

(Ti,Mi)

Tc

Fig. 1 Temperature dependence of magnetization in constant mag-netic field

where Mi and Mf are initial and final values of magneti-zation at ferromagnetic–paramagnetic transition (shown inFig. 1) and

A = 2 (B − SC)

Mi −Mf

B is magnetization sensitivity dM / dT in the ferromag-netic region before transition, Sc is magnetization sensitivitydM / dT at Curie temperature (TC) and

C =(Mi +Mf

2

)− BTC

In fact, Hamad [17] used the same equation to obtain theMCE values of some magnetic materials.

Now, (5) can be written as

dM

dT= −Ar sec h2 [A (TC − T )] + B (6)

where r = Mi −Mf/2Substituting (6) in (3), we have

�SM =∫ Hmax

0

(−Ar sec h2 [A (TC − T )] + B

)dH

=(−Ar sec h2 [A (TC − T )] + B

)Hmax (7)

Table 1 Model parameters for EuMnO3 and Sr-doped EuMnO3 in 1- and 2-T fields

Composition Field (T) Mi (emu/g) Mf (emu/g) B (emu/g/K) Sc (emu/g/K) TC (K)

EuMnO3 1 4.6 1.8 −0.01257 −0.209 36

2 6.5 3.3 −0.01466 −0.1678 39

Eu0.7Sr0.3MnO3 1 37 7 −0.0265 −0.52 82

2 48 8 −0.00234 −0.44 91

J Supercond Nov Magn

20 40 60 80 100

2

4

6

0 25 50 75 100 125

10

20

30

40

M(e

mu

/g)

T(K)

Mexp

at 2T

Mfit

at 2T

Mexp

at 1T

Mfit

at 1T

Eu0.7

Sr0.3

MnO3

Mexp at 2T Mfit at 2T Mexp at 1T Mfit at 1T

M(e

mu/

g)

T(K)

EuMnO3

Fig. 2 Temperature dependence of magnetization of EuMnO3 at 1-and 2-T magnetic fields. Inset represents temperature dependence ofmagnetization of Eu0.7Sr0.3MnO3 at 1- and 2-T magnetic fields

At T = TC, entropy change becomes maximum so that(7) may be written as

�Smax = (−Ar + B)Hmax (8)

Full width at half maximum (FWHM) is an expression ofthe extent of a function, given by the difference between thetwo extreme values of the independent variable at which thedependent variable is equal to half of its maximum value.

0.00

0.05

0.10

0.15

0.20

0.25

0 50 100 150

0.0

0.2

0.4

0.6

0.8

1.0

S(J/

Kg-

K)

T(K)

2T

1TEu0.7

Sr0.3

MnO3

S(J/Kg

-K)

2T1T

EuMnO3 (a)

0 50 100 150 200 250-0.02

0.00

0.02

0.04

0.06

0.08

0 50 100 150 200

0.00

0.25

T(K

)

T(K)

2T

1T

Eu0.7

Sr0.3

MnO3

T(K)

T(K)

2T1T

EuMnO3 (b)

Fig. 3 (a) Variation of �S with temperature of EuMnO3 at 1Tand 2T fields. Inset shows the variation of �S for Eu0.7Sr0.3MnO3sample. (b) Variation of �T with temperature of EuMnO3 at 1Tand 2T fields. Inset shows the variation of �T for Eu0.7Sr0.3MnO3sample

At a temperature half way between maximum and min-imum (T ∗) �SM becomes �Smax / 2, so that (7) may bewritten as

�Smax

2= −Ar sec h2 [

ATC − T ∗] + BHmax

On simplification, we may write as

−Ar + B

2Hmax = −Ar sec h2 [

ATC − T ∗] + BHmax

T ∗ =ATC ± cos h−1

√2AMi−Mf

AMi−Mf+2B

A

From (1), δTFWHM can be deduced as follows:

δTFWHM = T ∗2 − T ∗

1

δTFWHM =ATC + cos h−1

√2A(Mi−Mf)

A(Mi−Mf)+2B

A

−ATC − cos h−1

√2A(Mi−Mf)

A(Mi−Mf)+2B

A

δTFWHM = 2

Acos h−1

{√2A (Mi −Mf)

A (Mi −Mf)+ 2B

}(9)

Using this equation, full width at half maximum (δTFWHM)

of a given material can be obtained.Another important parameter for the magnetic refriger-

ators is the relative cooling power (RCP) defined as theproduct of −�Smax and δTFWHM.

0.0

0.2

0.4

0.6

0.8

1.0

0 50 100 150

0.0

0.1

0.2

0.3

0.4

0.5

S(J/

Kg-

K)

T(K)

EuMnO3

Eu0.7

Sr0.3

MnO31T

S(J/Kg

-K)

EuMnO3

Eu0.7Sr0.3MnO3

2T

0 50 100 150 200 250

0.0

0.1

0.2

0.3

0.4

0 50 100 150 200

0.00

0.05

0.10

0.15

0.20

T(K)

T(K)

EuMnO3

Eu0.7

Sr0.3

MnO3

1T

T(K)

T(K)

EuMnO3

Eu0.7Sr0.3MnO3

2T

Fig. 4 Comparison of MCE properties of EuMnO3 andEu0.7Sr0.3MnO3

J Supercond Nov Magn

Table 2 The predicted values of MCE properties of EuMnO3 and Sr-doped EuMnO3 in 1- and 2-T fields

Composition Field (T) |�Smax| (J/kg/K)� |�Tmax|(K)� RCP (J/kg) δTFWHM (K) |�S|max�H

× 102 (J/kg/K/KOe)

EuMnO3 1 0.19 0.062 3.08 22.45 1.86

2 0.24 0.082 4.53 45.22 1.2

Eu0.7Sr0.3MnO3 1 0.5 0.21 43.71 87.18 5

2 1.01 0.45 100.79 99.03 5.05

RCP = −�Smax (T ,Hmax)× δTFWHM

=(Mi −Mf − 2

B

A

)Hmax

× cos h−1

{√2A (Mi −Mf)

A (Mi −Mf)+ 2B

}(10)

From the basics of thermodynamics, the relation betweenspecific heat (Cp) and entropy (S) is

�S = (Cp/T)�T (11)

From (3) and (11), the adiabatic temperature change (�T )of a magnetic system, when the magnetic field is variedfrom 0 to Hmax, can be written as

�T = − T

Cp

∫ Hmax

0

(∂M

∂T

)H

dH (12)

where Cp is the heat capacity at constant magnetic field.By substituting the value of ∂M

∂Tfrom (6), we have

�T = AT (Mi −Mf)

2Cp

[sec h2 [A (TC − T )] + B

]Hmax

(13)

Thus, the values of δTFWHM, �Smax, RCP, and �Tfor a magnetic system can be calculated using the aboveequations.

3 Results and Discussions

In order to calculate the MCE of a given material, first, themagnetization values were computed using (5). For this pur-pose, the magnetization data available in the literature [13]were used as the starting data and are given in Table 1.Figure 2 shows the variation of magnetization with tempera-ture in 1- and 2-T magnetic fields (unfilled circles representthe experimental data). It can be seen from the figure thatthe magnetic transition temperature (TC) is increasing withincreasing magnetic field. It is interesting to note fromthe figure that the experimental data and theoretical val-ues obtained using (5) are found to fit well, indicating theaccuracy of the method adopted.

Now, one of the two important parameters in the eval-uation of MCE, viz., change in entropy (�SM) in thevicinity of magnetic transition temperature (TC), was cal-culated using (7). Later, the second important parameter,the adiabatic temperature change (�T ), was obtained byusing (13). For the computation of this parameter, the heatcapacity values of 102 and 190 J/kg/K for EuMnO3 andEu0.7Sr0.3MnO3, respectively, were taken from the liter-ature [13]. These values were chosen such that they liemidway between the peak and the baseline of the zero-fieldheat capacity. It can be seen from Fig. 3a,b that �Smax and�Tmax values are found to increase by doping Sr. By dop-ing Sr in place of Eu, ��max value is increased by almostfive times, compared with the undoped sample as shown inFig. 4a,b.

Later, the values of δTFWHM and RCP at both magneticfields were also calculated using (9) and (10), respectively,and the results are given in Table 2. One may observe that�Smax / �H values of the present investigation are com-parable with the reported data of Gd3Al2 [18] and Gd3In[19].

4 Conclusions

The magnetocaloric effect of Sr-doped EuMnO3 was evalu-ated using a theoretical model. As |�S|max

�H×102 is increasing

with Sr doping, it has been concluded that Sr doping maybe useful for as MCE is concerned. Based on these results,one may conclude that the theoretical model used in thepresent investigation for the evaluation of MCE is use-ful in predicting the probable material for refrigerationdevices.

Acknowledgments The first and second authors thank DRDO andCSIR for providing fellowships, respectively.

References

1. Zimm, C.B.,Jastrab, A.,Sternberg, A.,Pecharsky, V.,Gschneidner,K., Osborne, M., Anderson, I.: Adv. Cryog. Eng. 43, 1759 (1998)

2. Gschneidner, K.A. Jr., Pecharsky, V.K., Tsokol, A.O.: Rep. Prog.Phys. 68, 1479 (2005). and references therein

3. Pecharsky, V.K., Gschneidner, K.A.: Phys. Rev. Lett. 78, 4494(1997)

J Supercond Nov Magn

4. Booth, R.A., Majetich, S.A.: J. Appl. Phys. 105, 07A926 (2009)5. Dan’kov, S.Y., Tishin, A.M., Pecharsky, V.K., Gschneidner, K.A.:

Phys. Rev. B 57, 3478 (1998)6. Phan, M., Yu, S.: J. Magn. Magn. Mater. 308, 325 (2007). and

references therein7. Pavan Kumar, N., Venugopal Reddy, P.: Mater. Lett. 122, 292

(2014)8. Radaelli, P.G., Cox, D.E., Marezio, M., Cheong, S.-W., Schiffer,

P.E., Ramirez, A.P.: Phys. Rev. Lett. 75, 4488–4491 (1995)9. Kim, K.H., Gu, J.Y., Choi, H.S., Park, G.W., Noh, W.T.: Phys.

Rev. Lett. 77, 1877–1880 (1969)10. Tang, T., Gu, K.M., Cao, Q.Q., et al.: J. Magn. Magn. Mater. 222,

110–114 (2000)11. Phan, M.H., Tian, S.B., Yu, S.C., et al.: J. Magn. Magn. Mater.

256, 306–310 (2003)

12. Sun, Y., Tong, W., Zhang, Y.H.: J. Magn. Magn. Mater. 232, 205–208 (2001)

13. Mukovskiiet, Hilscher, G., Michor, H., Ionov, A.M.: J. Appl.Phys. 83, 11 (1998)

14. von Ranke, P.J., de Oliveira, N.A., Mello, C., Magnus, A.,Carvalho, G., Gama, S.: Phys. Rev. B. 71, 054410 (2005)

15. von Ranke, P.J., de Oliveira, N.A., Gama, S.: Phys. Lett. A 320,302–306 (2004)

16. Elementary Solid State Physics by Ali Omer17. Hamad, M.A.: Mater. Lett. 82, 181 (2012)18. Pecharsky, V.K., Gschneidner, K.A. .Jr., Dan’kov, S.Y.u., Tishin,

A.M.: Cryocoolers 10, 639 (1999)19. Ilyan, M.I., Tishin, A.M., Gschneidner, K.A.J.r., Pecharsky, V.K.,

Pecharsky, A.O.: In: 11th Proceedings of International CryocoolerConference. Colorado (2000)