Low Temperature Giant Magnetocaloric Effect and Critical Behavior in Amorphous Co100−xErx (x = 55, 65) Alloys

DOI 10.1007/s10948-014-2773-z

ORIGINAL PAPER

Low Temperature Giant Magnetocaloric Effect and Critical Behavior in Amorphous Co _{100 − x} Er _x ( x = 55, 65) Alloys

A. Boutahar · H. Lassri · E. K. Hlil

Received: 15 August 2014 / Accepted: 2 September 2014 / Published online: 16 September 2014

© Springer Science+Business Media New York 2014

Abstract We report on the magnetic properties, magne- tocaloric effect (MCE) and critical exponents in amorphous Co

Er

( x = 55 and 65), prepared by liquid quenching technique. The transition temperature from ferromagnetic to paramagnetic state has been evaluated according to M(T ) measurements, and it is found to be 26 and 15 K for Co

Er

and Co

Er

, respectively. The magnetization dependence M(H , T ) on the temperature T and magnetic field H was measured carefully in the critical region. Mag- netic entropy change (–S

) allowing estimation of the MCE was determined based on thermodynamic Maxwell’s relation. The magnetocaloric study exposes a quite large value of the magnetic entropy change, which decreases when increasing Er concentration. For an applied magnetic field of 5 T,the values of (– S

) peak are about 10.8 and 9.8 J kg

K

for Co

Er

and Co

Er

, respec- tively. From the field dependence of the magnetic entropy S

(S

α H

) and the relative cooling power (RCP) (RCP α H

), it was possible to evaluate the critical exponents of the magnetic phase transitions. Their values are in good agreement with those obtained from the critical exponents using a modified Arrott method.

Keywords Amorphous alloys · Agnetization · Agnetocaloric effect · Hase transition

A. Boutahar ()·H. Lassri

LPMMAT, Facult´e des Sciences Ain Chock, Universit´e Hassan II Casablanca, BP 5366, Mˆaarif Casablanca, Morocco

e-mail: boutahar.fsac@gmail.com E. K. Hlil

InstitutN´eel, CNRS et Universit´e Joseph Fourier, BP 166, 38042 Grenoble Cedex 9, France

1 Introduction

Recently, magnetic refrigeration based on the magne- tocaloric effect (MCE) of a magnetic material has been attracted much attention due to its higher energy efficiency and friendly environment compared to conventional gas compression refrigeration [1–5]. The search of new mag- netocaloric materials is attracting considerable attention recently due to their potential application as refrigerants [6].

A large value of MCE is considered to be the most important

requirement of the industrial application near temperature

helium liquefaction [7]. In addition, it is known that mate-

rials exhibiting large MCE below 70 K can be used in

a magnetic refrigerator to liquefy hydrogen gas [8]. As a

result, based on this concept, it is highly desirable to develop

new magnetic materials applicable in a low temperature

range with large MCE. Recently, some magnetic materials,

in particular Er

Mn

O

[9], Er

In [10], ErCr

Si

[11], and

TbCo

B

[12] compounds have shown a large reversible

MCE in a low temperature range. Moreover, it has been

recently demonstrated that there exists a universal curve

for the magnetic entropy change for second-order transition

materials [13]. It can be constructed using a phenomeno-

logical procedure which does not require the knowledge of

either the equation of state or the critical exponents of the

material. Expressing the field dependence as S

versus

H

, this approach allows us to find a relationship between

the exponent n and the critical exponents of the material

and to propose a phenomenological universal curve for the

field dependence of S

, which was successfully tested for

series of soft magnetic amorphous alloys and lanthanide-

based crystalline materials. Up to now, very little attention

has been paid to the field dependence of RCP [14]. We

have studied previously the critical behavior of the amor-

phous Co

Er

(x = 55 and 65) using the modified

Arrott plot and the critical isotherm [15]. In this paper, we report the effect of substitution the Er on the magnetic properties, MCE, and critical phenomenal in amorphous Co

Er

(x = 55, 65) alloys. We anticipate that the addition of a small amount of Er atoms would lead to a decrease of the Curie temperature, without losing the large MCE.

2 Experimental

The amorphous Co

Er

alloys, with x = 55 and 65, were prepared by melt spinning technique, and the ribbons were about 1 mm wide and 30 µm thick and were all amor- phous as shown by the characteristic broad X-ray diffraction peak. The exact chemical composition of the samples was determined by electron probe microanalysis. The magneti- zation was measured by the extraction method with applied field up to 200 kOe.

3 Results and Discussion

3.1 Magnetic Properties

The investigation of the magnetic properties measured in a magnetic field of 10 kOe shows that the amorphous Co

Er

( x = 55 and 65) alloys exhibit a single magnetic transition and behave in a ferromagnetic manner at low temperatures (T < T

) and in paramagnetic man- ner above the Curie temperature T

(T > T

) as presented in Fig. 1a and b. This result confirms the good quality of our amorphous alloys. The temperature derivatives of the M–T curves are shown in the inset of Fig. 1a and b, from which the Curie temperature T

(T

= 26 and 15 K for x = 55 and 65, respectively) can be determined.

These values are very close the temperature range of helium liquefaction which is quite suitable for magnetic refrig- eration at low temperature. The isothermal magnetization curves of different temperatures near the vicinity of the Curie temperature are shown in Fig. 2a and b for differ- ent concentrations. These curves reveal a strong variation of magnetization around the Curie temperature, indicat- ing a possible large magnetic entropy change associated with the ferromagnetic-paramagnetic transition tempera- ture. To determine the type of magnetic phase transition near the Curie temperature in Co

Er

(x = 55 and 65), Loudghiri et al. [15] gave a detailed examination of the behavior of magnetic phase transitions using the modified Arrott plot and the critical isotherm. They con- clude that the amorphous Co

Er

(x = 35 and 45) alloys exhibit a second-order magnetic phase transition (SOMT).

0 30 60 90 120

0 50 100 150

-3 -2 -1 (a) 0

M (emu/g)

M (T)

TC=26 K Co45Er55

dM/dT (emu/g K)

T (K)

dM/dT (T)

0 50 100

0 50 100

-4 -2 0

TC=15 K Co35Er65

M (emu/g)

T (K)

M (T)

dM/dT (emu/g K)

dM/dT (T) (b)

Fig. 1 Variation of the magnetization and the dM/dT as a function of temperature (a, b) in an applied magnetic field of 10 kOe for amorphous Co100−xEr_x(x=55 and 65) alloys

3.2 Magnetocaloric Effect

The magnetocaloric effect (MCE) can be related to the magnetic properties of the material through the thermo- dynamics Maxwell’s relations, and it has been calculated in terms of isothermal magnetic entropy change using magnetization isotherms obtained at various temperatures (Fig. 2a and b). According to thermodynamically the- ory [16], the isothermal magnetic entropy changes asso- ciated with a magnetic field variation is given by the following:

SM(T , H ) = SM(T , H )−SM(T ,0) =

μ0HMax

0

∂S(T , H )

∂H

T

H (1)

From the Maxwell’s thermodynamic relation ∂S(H, T )

∂H

T

=

∂M(H, T )

∂T

H

(2)

0 100 200 0

30 60 90 120 150

Co

Er

M (emu/g)

µ

H (kOe)

10 K 20 K 30 K 60 K 80 K 100 K 120 K 150 K

(a)

0 100 200

0 80 160

Co

Er

65

M (emu/g)

µ

H (kOe)

8 10 20 25 35 60 100 120 150

(b)

Fig. 2 Magnetization versus applied magnetic field µ0H, measured at different temperatures, for amorphous Co100−xEr_x (x=55 and 65) alloys

One can obtain the following expression:

S

(T , H )

=

μ0

0

∂M(H, T )

∂T

H

dH (3) where µ

H

is the maximum external field.

Figure 3a and b shows the temperature dependence on the magnetic entropy change for different applied mag- netic field change interval for amorphous Co

Er

(x = 55 and 65) alloys up to 20 T. ( −S

) reaches a maximum value in the vicinity of T

. The value of ( −S

) peak increases with the field and the peak posi- tion remains nearly unaffected. At a magnetic field of 5 T, the maximum values of entropy change ( −S

) are found to be about 10.8 and 9.8 J kg

K

for Co

Er

and Co

Er

, respectively. The temperature at which maximum entropy change observed is in good agree- ment with the values of T

obtained from M versus T .

0 50 100

0 8

16

Co

Er

(a)

- S (J/Kg K)

T (K)

2T 3T 4T 5T 6T 8T 10T

0 25 50 75 100 125 150

0 10

20

Co

Er

(b)

T (K)

- S (J/Kg K)

2T 3T 4T 5T 6T 8T 10T

Fig. 3 Temperature dependence of the magnetic entropy change at different applied magnetic fields change interval for amorphous Co_100−xEr_x(x=55 and 65) alloys

Figure 4a and b shows the applied magnetic dependence on the magnetic entropy change for different concentra- tions. It can be seen that the magnetic-entropy change ( −S

) depends on both applied magnetic and tem- perature. To evaluate the potential of Co

Er

alloys for magnetic refrigeration, the (– S

) values determined in the present studies are compared with the other pop- ularly researched magnetic refrigerant materials DyCoAl ( − 16.3 J kg

K

) , GdPd

Si ( − 8.6 J kg

K

) , RNi

( − 8 J kg

K

) and ErRu

Si

( − 17.6 J kg

K

) in low temperature regime under the same field changes [17–20].

The magnetocaloric effect in amorphous alloys always

focus on a temperature window centered about the Curie

temperature, the critical exponents influences the nature

of magnetocaloric response [21]. In order to demonstrate

this coupling, the field dependence of the magnetic entropy

change is analyzed. According to Oesterreicher et al [22],

the field dependence of the magnetic entropy change (S

)

0 10 20 30

0 8 16 24

0 1000

Co 2000

45Er

55

-S

(J/Kg K)

(a)

µ0H (T)

RCP (J/kg)

0 5 10 15

0 400 800 1200

8 16

24 Co (b)

35Er

65

RCP (J/kg)

-S

(J/Kg K)

µ0H (T)

Fig. 4 Field dependence of entropy change and RCP (a, b) forx=55 and 65 respectively

of materials with a second-order phase transition can be expressed as

−S

αH

(4)

where the exponent n depends on the magnetic state of the compound. It can be locally calculated as follows:

n = d ln(−S

)

d ln(μ

H ) (5)

In the particular case of T = T

or at the temperature of the peak entropy change, the exponent n becomes field independent [23–26]. In this case

n(T c) = 1 + β − 1

β + γ (6)

where β and γ are the critical exponents.

With βδ = (β + γ ), relation (6) can be written as n(T

) = 1 + 1

δ (1 − 1

β ) (7)

Using the order parameters (β = 0.4

, γ = 1.35

, and δ = 4.8

at T

) obtained from the modified Arrott plot method [15], the values of n calculated from the above relations are found to be 0.6571 (from (6)) and 0.6875 (from

(7)) for Co

Er

(x = 55 and 65), respectively. Other- wise, the exponent n can be also calculated directly from the fitting of the linear plot of ln( −S

) versus ln(µ

H ) (from (5)) constructed at the transition temperature of the peak of the magnetic entropy change at T

which are shown in Fig. 5a and b. The values of n obtained from the slope are 0.6535 and 0.6837 for x = 55 and 65, respectively, which are in good agreement with those obtained from the critical exponents using the modified Arrott plot method (from (6) and (7)).

3.3 Relative Cooling Power

Another useful parameter which describes the efficiency of a magnetocaloric material is the RCP or the refriger- ant capacity. It is the heat transfer between the hot and the cold reservoirs during an ideal refrigeration cycle. This represents numerically the area under ( −S

) versus T curve:

RCP = −S

× δT

(8)

4 5 6 7

0.8 1.6 2.4 3.2

2.4 2.7 3.0 3.3

= 4.8343

Co

Er

55

ln (RCP)

ln ⁽ µ0H ⁾ ln (- S

)

n= 0.6537

(a)

0.8 1.6 2.4

1.8 2.4 3.0

5 6 7

ln (- S

) ^Co

^Er

ln (RCP)

ln ( µ0H ⁾

n= 0.6835

(b)

= 5.1859 δ

δ

Fig. 5 Field dependence of the−SMmaxand the RCP (a b) calcu- lated from the magnetic data, with the calculatednandδfor both slops for amorphous Co_100−xEr_x(x=55 and 65) alloys

where δT

is the full width at half maximum of the magnetic entropy change curve. The results of this estimation are shown in Fig. 4a and b. The RCP val- ues exhibit a nonlinear increase with increasing field for all alloys. For H = 5 T, the estimated val- ues of RCP are found to be 294.5 and 333.2 J kg

for Co

Er

and Co

Er

, respectively. The values of RCP are extended over a wide range of temperature around the Curie temperature in both the amorphous alloys, and hence, these materials are useful for helium liquefaction

The field dependence of RCP for our amorphous alloys is analyzed. It can be expressed as a power law by taking into account the field dependence of entropy change S

and reference temperature into consideration [14]:

RCP αH

(9)

where δ being the critical exponent of the magnetic transi- tion. Field dependence of RCP is depicted in Fig. 5a and b.

The values δ calculated from the exponent are 4.8343 and 5.1859 for amorphous Co

Er

and Co

Er

, respectively.

There are in agreement with those obtained using modified Arrott plot [15].

4 Conclusion

We prepared amorphous Co

Er

( x = 55 and 65) alloys and studied their magnetic properties, magne- tocaloric effect and critical behavior around T

. The nature of the phase transition for both amorphous alloys is of second-order. A study of the local expo- nent nand δ controlling the field dependence of S

and RCP (S

αH

andRCPαH

) were carried out.

The presen results indicated thatCo

Er

(x = 55 and 65) is a promising candidate for magnetic refrigera- tion at low temperature, particularly possibly for heliu liquefaction

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