Magnetic magnetocaloric properties and phenomenological model in amorphous Fe<inf>60</inf>Ru<inf>20</inf>B<inf>20</inf> alloy

Author's Accepted Manuscript

Magnetic, magnetocaloric properties And phenomenological model in amorphous Fe60Ru20B20 alloy

A. Boutahar, H. Lassri, E.K. Hlil

PII: S0038-1098(15)00277-X

DOI: http://dx.doi.org/10.1016/j.ssc.2015.08.002 Reference: SSC12737

To appear in: Solid State Communications

Revised date: 28 June 2015 Accepted date: 12 August 2015

Cite this article as: A. Boutahar, H. Lassri, E.K. Hlil, Magnetic, magnetocaloric properties And phenomenological model in amorphous Fe₆₀Ru₂₀B₂₀ alloy, Solid State Communications, http://dx.doi.org/10.1016/j.ssc.2015.08.002

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Magnetic, magnetocaloric properties and

phenomenological model in amorphous Fe

Ru

B

alloy

A. Boutahar

, H. Lassri

, E.K. Hlil

1

LPMMAT, Université Hassan II-Casablanca, Faculté des Sciences Ain Chock, BP 5366, Mâarif - Casablanca, Morocco

2

Institue Néel, CNRS et Université Joseph Fourier, BP 166, F-38042 Grenoble Cedex 9, France.

Magnetic, magnetocaloric properties and

phenomenological model in amorphous Fe

Ru

B

alloy

B. Boutahar

, H. Lassri

, E.K. Hlil

1

LPMMAT, Université Hassan II-Casablanca, Faculté des Sciences Ain Chock, BP 5366, Mâarif - Casablanca, Morocco

2

Institue Néel, CNRS et Université Joseph Fourier, BP 166, F-38042 Grenoble Cedex 9, France.

Abstract

Magnetic, magnetocaloric properties and phenomenological model of

amorphous Fe

Ru

B

alloy are investigated in detail. The amorphous alloy has

been synthesized using melt spinning method. The magnetic transition nature

undergoes a second-order magnetic phase transition from ferromagnetic to

paramagnetic states with a Curie temperature of 254 K. Basis on the

thermodynamic Maxwell’s relation, magnetic entropy change (- ∆ S

) is

calculated. Further, we also report a theoretical investigation of the

magnetocaloric effect using a phenomenological model. The best model

parameters and their variation with temperature and the magnetic field were

determined. The theoretical predictions are found to agree closely with

experimental measurements.

Keywords: Amorphous Fe60Ru20B20 alloy; Magnetocaloric effect; Magnetic transition;

phenomenological model.

E-mail: boutahar.fsac@gmail.com (A. Boutahar)

1. Introduction

Fe–B based amorphous alloys have been widely studied because they combine excellent combination both mechanical and magnetic properties [1-5].

P. L. Paulose et al. [6] shown that amorphous Fe

Ru

B

alloys undergo interesting changes in magnetic behavior with Ru concentration and temperature. Furthermore, S. Lofland et al. [7] reported that Fe

Ru

B

is a concentrated spin glass while Fe

Ru

B

exhibits reentrant magnetism. To investigate the magnetocaloric effect MCE in such systems further the present work on Fe

Ru

B

alloy was under taken.

On the other hand, the giant magnetocaloric effect (MCE) was observed in materials with a first-order magnetic transition such as LaFe

Si

[8], Gd

(Si,Ge)

[9] and others [10]. However, it is difficult to use these materials for magnetic refrigeration mainly because they have very large thermal and magnetic-field hysteresis [11]. However, the positive characteristics of second order magnetic transition (SOMT) in amorphous materials are a low magnetic hysteresis, a high electrical resistivity, enhanced corrosion resistance, good mechanical properties, and a tunable T

by varying the composition [12-13]. From this point of view, magnetic studies reveal that the Fe

Ru

B

alloy undergoes a SOMT.

In this paper, we have performed magnetic and magnetoclaoric properties around SOMT of amorphous Fe

Ru

B

alloy. To investigate the magnetic transition nature, the magnetization behavior around T

was analyzed in terms of Landau theory and confirmed by Arrott plots curves. In addition, a phenomenological model is applied to predict the magnetocaloric properties.

2. Experimental

Amorphous Fe

Ru

B

alloy was prepared by the usual melt spinning technique using single roller quenching, in an atmosphere of argon. The resulting ribbons were typically 1 to 2 mm wide and 25 µm thick. X-ray diffraction was used to check the amorphous state of the alloy and no Bragg peaks were observed. The exact chemical composition was determined by electron probe microanalysis. The magnetization was measured by the extraction method with applied magnetic field up to 14 T. The Curie temperature (T

) is defined as the inflection point of the derivative of the temperature dependence of magnetization curve in a field of 0.05T.

3. Results and discussion 3.1 Magnetic properties

The temperature dependences of magnetization (M–T) for the Fe

Ru

B

alloy was measured under an applied field of 0.05T in a temperature range of

5-320 K as shown in Fig. 1. To have a precise determination of the Curie

temperature, the dM/dT versus T plot has been performed and reported in the

inset of Figure 1. The T

is defined as the inflection point of the dM/dT curve

and it is found to be around 254 K. We note that the Fe

B

has a T

of around

650 K, as reported by S. Lofland et al.[7]. Next, replacing Fe by Ru, causes a rearrangement of Fe-Fe distances promoting more antiferromagnetic (AFM) pairing which decreases significantly the Curie temperature. The competing interactions are also responsible for the disappearance of ferromagnetism (FM) in amorphous Ru

Fe

B

alloy with Ru concentration as reported by P. L. Paulose et al. [6].

We also note that the M (T) curve displays a tail at low temperatures, which can be attributed to the presence of a minor AFM contribution in this system. Fig. 2 confirms that the magnetization of this alloy does not saturate in an applied field of 8 kOe and consequently, the magnetic structure is not collinear at low temperature in Fe

Ru

B

alloy and that a very large applied field is needed to achieve total alignment of spins.

To investigate the type of the magnetic phase transition, we use the Inoue–Shimizu s-d model [14,15], which has been widely used to discuss behaviors of several types of magnetocaloric materials.

According to Landau theory [14,15], the magnetic free energy F (M, H) versus magnetization and temperature can be expressed as:

MH M

T c M

T b M T a

F ⁴ ( ) ⁶ ₀

6 ) 1

4 (

² 1 ) 2 (

1 + + − µ

= . (1)

The Landau coefficients are accessible through the equation of state linking M and the magnetic field:

H M

T c M T b M T

a( ) + ( ) ³ + ( ) ⁵ = µ₀ . (2)

The coefficients a (T), b (T) and c (T) depend on temperature with respect to the

thermal variation of spin fluctuations amplitude and can be determined by fitting

the isothermal magnetization data using the above equation. Examination of the

free energy demonstrates that the parameter a(T) is always positive and would

get a minimum value at the Curie temperature corresponding to a maximum of

susceptibility. On the other hand, the order of magnetic transition is governed by

the sign of b (T): the 1

order transition takes place if b (T

) < 0, while the 2

order transition occurs when b (T

) ≥ 0. Besides, c(T) is positive at T

and, in the other temperature regions, can be negative or positive. The values of Landau’s coefficients are determined by fitting the magnetization curves to Eq.

(2). Accordingly, b (T

) was found to be positive for Fe

Ru

B

alloy studied here, indicating a 2

character to the magnetic transition for the sample. Fig. 3 shows the temperature dependence of the Landau’s parameters for the Fe

Ru

B

alloy. As explained above, a (T) was found positive with a minimum close to T

and b (T

) was found positive indicating the occurrence of a SOMT. As shown in Fig. 3, the value of Curie temperature T

derived from thermomagnetic measurements is exactly that obtained from the a(T) behavior.

In order to confirm that present alloy showed second-order magnetic transitions, we have checked the Arrott plots (M

vs. H/M curves) at different temperatures in Fig. 4. For all isothermal curves, the slope of the Arrott plots is found to be positive confirming that the present alloy undergoes a second-order magnetic transition according to the Banerjee criterion [16].

3.2 Magnetocaloric effect

The magnetocaloric effect is an intrinsic property of magnetic materials. It consists of heating or cooling of magnetic solids in a varying magnetic field. In order to evaluate the MCE of this amorphous alloy, the isothermal magnetization curves of amorphous Fe

Ru

B

alloy were measured over a wide range of temperatures at regular intervals from 5 to 320 K (Fig. 5) . The magnetic entropy change, (- ∆ S

), of materials with second order transitions can be estimated reliably using the Maxwell relation [17]:

T dH T H H M

T S

H H

µ H

M ^{∆ =}

∫

∆ _∆

0 max

0

) , ) (

,

( . (3)

Where µ

H

is the maximum external field.

Figure 6 shows the variation of (- ∆ S

) with temperature for the Fe

Ru

B

alloy. The maxima in the (- ∆ S

) versus T curves are found to be in the vicinity of T

and it is about 1.5 J kg

K

for a magnetic field change of 5T.

On the other hand, magnetic refrigerants are desired to have not only a large (- ∆ S

) but also a large refrigerant relative cooling power (RCP) defined by [18-19]:

RCP =−∆S_M^max ×δT^FWHM. (4)

Where

and δ T

are the maximum of the entropy variation and the full-width at half maximum in the temperature dependence of the magnetic entropy change (- ∆ S

). We list in Table 1 the T

, the (- ∆ S

max

) and the RCP values for our alloy in different magnetic applied field in comparison with other results reported in the literature. The lower values of (- ∆ S

max

) compared with those of the Fe–B based amorphous alloys are explained by the small value of the iron magnetic moment which is associated to a noncollinear magnetic structure at low temperature.

3.3. Theoretical considerations

According to phenomenological model in Ref. [28], the dependence of magnetization on variation of temperature and Curie temperature T

may be expressed by:

( )

( )

[

]

M

M(T) M^{i f}  − _C + +









 −

= 2

. (5)

Where M

is an initial value of magnetization at ferromagnetic transition and M

is a final value of magnetization at paramagnetic transition, where ( )

f i

C

M M

S A B

−

=2 −

,

B is magnetization sensitivity

dT

dM

at ferromagnetic state before transition, S

is

magnetization sensitivity

dT

dM

at Curie temperature T

and

C −









 +

= 2

.

We must evaluate the magnetic entropy ( ∆ S

). Firstly, we not that:

T dH T H M

T S

H µ H

M ^{∆ =}

∫

∆ _∆

0 max

0

) ) (

,

( .

(6) Substituting this equation, Eq. (5), into Eq. (6), we obtain:

( )

2( ( ))

2 sec )

,

( M M h AT T B µ H

A H

T

S_{M H} ^{i f} _C 









  − +







 −

−

=

∆

∆ _∆

(7)

We note that, the magnetic entropy ( ∆ S

) has a maximum at T=T

and we may write ( ∆ S

max

) as:

max

2M B µ0H A M

S_Max ^{i f} 









 +







 −

−

=

∆ .

(8)

Eq. (8) is an important equation for taking into consideration of value of the magnetic entropy change to evaluate magnetic cooling efficiency with its full-width at half-maximum.

A determination of full-width at half-maximum δ T

can be carried out as follows [28-33]:

( )

( )









+

−

= ⁻ −

B M

M A

M M A T A

f i

f FWHM i

2 cosh 2

2 ₁

δ

(9)

This equation gives a full-width at half-maximum magnetic entropy change contributing for estimation of magnetic cooling efficiency as follows

A magnetic cooling efficiency is estimated by considering magnitude of magnetic entropy change, ∆ S

and its full-width at half maximum δ T

[29].

A product of (− ∆ S

) and δ T

is called relative cooling power (RCP) based on magnetic entropy change.

FWHM

M T

S RCP=−∆ ×δ

( )

( )









+

−

× −



 



 − −

= ⁻

B M

M A

M M H A

A µ M B

M

f i

f i f

i 2

cosh 2

2 _{0 max} ¹ .

(10)

From this phenomenological model, we can then obtain the values of

| ∆ S

|, δ T

and RCP for the Fe

Ru

B

alloy under magnetic field variation

Theoretical investigation was made with parameters as displayed in Table 2. These parameters were determined from experimental data. Fig. 7 shows magnetization versus temperature in different magnetic applied field of amorphous Fe

Ru

B

alloy. It is seen that the results of calculation are in a good agreement with the experimental results. Figs. 7 shows also predicted values for change of magnetic entropy versus temperature. The values of maximum magnetic entropy change, full-width at half-maximum, and relative cooling power in 2T and 5T magnetic field variation, were calculated by using Eqs. (8)-(10), respectively, and tabulated in Table 2. These results suggest that this phenomenological model is useful to predict magnetocaloric properties such as magnetic entropy change

and relative cooling power RCP.

4. Conclusion

In conclusion, the magnetic and magnetocaloric properties of Fe

Ru

B

alloy were investigated in details. Our alloy exhibits a ferromagnetic behavior below T

=254 K. Based on the Landau theory and Banerjee's criterion, we have found that the sample undergoes a second-order magnetic phase transition. For a magnetic field change of 0 - 2 T, a maximum magnetic entropy value of 0.8 J/kg K is determined around T

. The order of this value is lower than those reported in Fe-B based amorphous alloys, which can be attributed to the presence of a minor AFM contribution at low temperature in this system.

Dependence of the magnetization on temperature variation for Fe

Ru

B

in

different magnetic applied fields was simulated. Comparisons between our

theoretical investigation and experimental results are presented, and they are in good agreement.

Acknowledgements

This work is mainly supported by the PHC Maghreb 15MAG07.

References

[1] P. L. Paulose, V. Nagarajan, S. M. Bhagat and R. Vijayaraghavan, Sol. St.

Comm. 61 (1988) 151.

[2] F. L. Kong , C. T. Chang , A. Inoue , E. Shalaan , F. Al-Marzouki. J. Alloys.

Comp 615 (2014) 163.

[3] M. Nabiałek, P. Pietrusiewicz , K. Bloch. J. Alloys. Comp 628 (2015) 424.

[4] J. Lee, S. Lee, W. Han, H. An, C.Yoon. J. Alloys. Comp 509 (2011) 7764.

[5] A. Boutahar, A. Ettayfi, G. Elouhmi, H. Lassri, E. K. Hlil, D. Fruchart, J.

Supr. Novel Mag. 27 (2014) 2401.

[6] P. L. Paulose, V. Nagarajan, R. Nagarajan, R. Vijayaraghavan, Sol. St. Comm. 67 (1987) 685.

[7] S. Lofland and S.M. Bhagat, P.L. Paulose and V. Nagarajan,Sol. St Comm, 89 (1994) 497.

[8] A. Boutahar, M. Phejar, V. Paul Boncour. L. Bessais, H. Lassri, J. Supercond and Nov Magne. 27 (2014) 1795.

[9] V. K. Pecharsky, K. A. Gschneidner Jr, Phys. Rev. Lett. 78 (1997) 4494.

[10] K. A. Gschneidner, V. K. Pecharsky, Annu. Rev. Mater. Sci. 30 (2000) 387.

[11] V. Provenzano, A. J. Shapiro, R. D. Shull, Nature (London) 429 (2004) 853.

[12] V. Franco, J. S. Blázquez, C. F. Conde, A. Conde, Appl. Phys. Lett. 88 (2006) 042505.

[13] R. Caballero-Flores, V. Franco, A. Conde, K. E. Knipling, M. A. Willard,

Appl. Phys. Lett. 96 (2010) 182506.

[14] J. Inoue, M. Shimizu, J. Phys. F 12 (1982) 1811.

[15] P. E. Brommer, Physica B. 154 (1989) 197.

[16] S. K. Banerjee, Phys. Lett. 12 (1964) 16.

[17] V. K. Pecharsky, K. Gschneidner, J. Appl. Phys, 86 (1999) 565.

[18] A. Boutahar, H. Lassri, E. K. Hlil. J. Supr. Novel Mag. 27 (2014) 2865.

[19] A. Boutahar, H. Lassri, K. Zehani, L. Bessais, E. K. Hlil, J. Magn. Magn.

Mater. 369 (2014) 92.

[20] S. Min, K. Kim, S.Yu, K. Lee, J. Magn. Magn. Mater 449 (2007) 423.

[21] V. Franco, A. Conde, L. F. Kiss, J. Appl. Phys, 104 (2008) 033903.

[22] R. Caballero, V. Franco, A. Conde, K. E. Knipling, M. A. Willard, Appl. Phys. Lett, 96 (2010) 182506.

[23] H. Zhang, R. Li , T. Xu, F. Liu, T. Zhang, J. Magn. Magn. Mater 347(2013)131.

[24] A. Kolano, M. Kowalczyk, R. Kolano, R. Szymczak, H. Szymczak, M. Polak, J. Alloy and Comp 479 (2009) 71.

[25] J. Lee, S. Jae Lee, W. Han, H. Hwan, C. Seung Yoon, J. Alloy and Comp 509 (2011) 7764.

[26] J. Du, Q. Zheng, Y. B. Li, Q. Zhang, D. Li, Z.D. Zhang, J. Appl. Phys. 103 (2008) 023918.

[27] L. Liang, X. Hui, G. L. Chen, Mater. Sci. Eng. B 147 (2008) 13.

[28] M. A. Hamad, Phase. Transitions. 85 (2012) 106.

[29] M. A. Hamad, Mater. Lett. 82 (2012)181.

[30] M. A. Hamad, Phase. Trans. 85(2012) 106.

[31] Ah. Dhahri, M. Jemmali , E. Dhahri , M. A. Valente, J. Alloy and Comp 638 (2015) 221.

[32] N. PavanKumar , G. Lalitha , E. Sagar , P. Venugopal Reddy, Physica B 457 (2015) 275.

[33] R. Tlili , R. Hammouda, M. Bejar, E. Dhahri, J. Magn. Magn. Mater 386 (2015) 81.

Figures and tables captions

Fig. 1 Variation of magnetization and dM/dT as a function of temperature in an applied magnetic field of 0.05 T for the amorphous Fe

Ru

B

alloy.

Fig. 2 Hysteresis loops of the amorphous Fe

Ru

B

alloy.

Fig. 3 Temperature dependence of Landau coefficients for the amorphous

Fe

Ru

B

alloy. The units for a(T), b(T) and c(T) are T

kg/J, T

kg

/J

, T

kg

/J

, respectively.

Fig. 4 Arrott plots of the amorphous Fe

Ru

B

alloy at different temperatures close to T

.

Fig. 5 Magnetization versus applied magnetic field µ

H, measured at different temperatures, for the amorphous Fe

Ru

B

alloy.

Fig. 6 Temperature dependence of magnetic entropy change (- ∆ S

) under different magnetic fields for the amorphous Fe

Ru

B

alloy.

Fig. 7: Magnetization and magnetic entropy change in different magnetic applied field for the amorphous Fe

Ru

B

alloy versus temperature.

Table 1: Summary of magnetocaloric properties of the amorphous Fe

Ru

B

alloy compared with other magnetic materials.

Table 2: Model parameters for the amorphous Fe

Ru

B

alloy in different magnetic applied field and the predicted values of magnetocaloric properties.

Table 1

Table 2

Sample

µ

Sample µ0H

(T)

TC(K) -∆SMmax

(J/kg K)

RCP (J/kg)

Ref.

Fe

Ru

B

Fe

Ru

B

Gd 2 294 5 196 [18]

Fe

Nb

B

Fe

Cr

B

Fe

Zr

B

Cu

Fe

Mn

P

B

C

Fe

Cr

Cu

Nb

Si

B

Fe

V

B

Si

Fe

Mn

Si

B

Gd

Ni

Al

Gd

Dy

Al

Co

(T) (emu/g) (emu/g) (K) (emu/g K) (emu/g K) (J/kg K) (J/kg)

Fe60Ru20B20 2 83.476 26.737 255 -0.049 -0.395 0.79 142

Fe60Ru20B20 5 91.5 30.18 255 -0.029 -0.302 1.51 394

0 10 20 30 40 50

0 50 100 150 200 250 300 350

-0,5 -0,4 -0,3 -0,2 -0,1 0,0 0,1 0,2

dM/dT(emu/g K)

T (K)

M(emu/g)

T_C=254K

Fe60Ru20B20

M(T)

µ0H=0.05 T dM/dT(T)

Fig. 1

-7 0 7

-1 0

1 Fe₆₀Ru₂₀B₂₀

µ0H (kOe)

µFe(µB)

5 K 80 K

Fig. 2

0 100 200 300

-6 0 6

0 100 200 300

0,00 0,05 0,10

0 100 200 300

0 4 8 12

(10-6 )

T (K) T (K)

b(T) a(T)

TC=255 K

Tc Tc

T (K) (10-8 )

c(T)

Fig. 3

0 1000 2000 3000

0 5000 10000

320K

H/M (Oe g /emu)

M ² (e m u ² / g ²)

5K Fe₆₀Ru₂₀B₂₀

Fig. 4

0 2 4 6 8 10 12 14 16 0

50 100

Fe60Ru20B20

M(emu/g)

µ0H(T)

5K 10K 20K 40K 60K 80K 100K 120K 150K 180K 210K 240K 270K 300K 310K 320K

Fig. 5

0 100 200 300

0,0 0,7

1,4 Fe60Ru20B20

-∆∆∆∆S m(J/Kg K)

T(K)

5T 4T 3T 2T 1T

Fig. 6

Fig. 7

Highlights

-The amorphous alloy has been synthesized using melt spinning method.

-Magnetic, magnetocaloric properties and phenomenological model of amorphous Fe

Ru

B

alloy are investigated in detail

-Theoretical investigation of the magnetocaloric effect using a

phenomenological model is reported.