Dear Dinesh,

Generally, MCE is calculated using Maxwell’s relation (Pecharsky V K and Gschneidner K A 1999 J. Appl. Phys. 86, 565 ).

Maxwell's relations are a set of equations in thermodynamics which are derivable from the symmetry of second derivatives and from the definitions of the thermodynamic potentials. These relations are named for the nineteenth-century physicist James Clerk Maxwell.

To study magnetocaloric effect using isotherm M(H) curves, please read the following publications:

1-Giant magnetocaloric effect in Gd2NiMnO6 and Gd2CoMnO6 ferromagnetic

insulators

J. Krishna Murthy1 , K. Devi Chandrasekhar2 , Sudipta Mahana3 , D. Topwal3

, and A. Venimadhav1

Abstract

We have investigated magnetocaloric effect in double perovskite Gd2NiMnO6 (GNMO) and Gd2CoMnO6 (GCMO) samples by magnetic and heat capacity measurements. Ferromagnetic ordering is observed at ~130 K (~112 K) in GNMO (GCMO), while the Gd exchange interactions seem to dominate for T < 20 K. In GCMO, below 50 K, an antiferromagnetic behaviour due to 3d-4f exchnage interaction is observed. A maximum entropy (-∆SM) and adiabatic temperature change of ~35.5 J Kg-1 K -1 (~24 J Kg-1 K -1) and 10.5 K (6.5 K) is

observed in GNMO (GCMO) for a magnetic field change of 7 T at low temperatures.

Absence of magnetic and thermal hysteresis and their insulating nature make them promising for low temperature magnetic refrigeration.

For full paper, see attached file.

2-Role of coexisting ferromagnetic and antiferromagnetic phases

on the magnetocaloric effect in metamagnetic Tb2Ni2Sn

Pramod Kumar, Niraj K. Singh, K. G. Suresha)

Abstract

We report the anomalous magnetocaloric behavior in the polycrystalline compound

Tb2Ni2Sn. The magnetization measurements show that this compound shows multiple magnetic transitions, which are attributed to the coexistence of ferromagnetic and antiferromagnetic phases at low temperatures. With increase in field and temperature, the compound undergoes a metamagnetic transition to a ferromagnetic state. In the temperature range where the antiferromagnetic phase is dominant, it exhibits inverse (negative) magnetocaloric effect. At temperatures close to the Neel temperature, the compound shows positive magnetocaloric effect. Below the critical field needed for the metamagnetic transition, the temperature variation of the magnetocaloric effect is seen to be correlated with the ferromagnetic fraction.

For full paper, see attached file.

3-The magnetocaloric effect and critical behaviour of

the Mn0.94Ti0.06CoGe alloy

Abstract

Structural, magnetic and magnetocaloric properties of the Mn0.94Ti0.06CoGe alloy have been investigated using x-ray diffraction, DC magnetization and neutron diffraction measurements. Two phase transitions have been detected, at T-str = 235 K and T-C = 270 K. A giant magnetocaloric effect has been obtained at around

Tstr associated with a structural phase transition from the low temperature orthorhombic TiNiSi-type structure to the high temperature hexagonal Ni2In-type structure, which is confirmed by neutron study. In the vicinity of the structural transition, at T-str, the magnetic entropy change, -Delta S-M reached a maximum

value of 14.8 J kg(-1) K-1 under a magnetic field of 5 T, which is much higher than that previously reported for the parent compound MnCoGe. To investigate the nature of the magnetic phase transition around T-C = 270 K from the ferromagnetic to the paramagnetic state, we performed a detailed critical exponent study. The

critical components gamma, beta and delta determined using the Kouvel-Fisher method, the modified Arrott plot and the critical isotherm analysis agree well. The values deduced for the critical exponents are close to the theoretical prediction from the mean-field model, indicating that the magnetic interactions are long range. On

the basis of these critical exponents, the magnetization, field and temperature data around T-C collapse onto two curves obeying the single scaling equation M(H, epsilon) = epsilon(beta)f +/- (H/ epsilon(beta+gamma)).

For full paper, see attached paper.

4-https://orbi.ulg.ac.be/bitstream/2268/1744/1/JApplPhys_101_103904.pdf

5-https://www.google.ps/url?sa=t&rct=j&q=&esrc=s&source=web&cd=5&cad=rja&uact=8&ved=0ahUKEwi6_KzfrrnKAhUFHJAKHckHAl0QIAhCMAQ&url=http%3A%2F%2Fwebcache.googleusercontent.com%2Fsearch%3Fq%3Dcache%3A31YbAi5EGAwJ%3Awww.nve.com%2FDownloads%2FGC-07.pdf%2B%26cd%3D5%26hl%3Den%26ct%3Dclnk%26gl%3Dps&usg=AFQjCNGTNwTvJ0DEE1SwEsswSUKG07PPAA&sig2=NAF59NlZ95L0F1HCyyZm6g

6-https://www.google.ps/search?biw=1366&bih=667&q=related:www.sciencedirect.com/science/article/pii/S092583881003080X+calculate+magnetocaloric+effect+(MCE)+using+isotherm+M(H)+curves&tbo=1&sa=X&ved=0ahUKEwi6_KzfrrnKAhUFHJAKHckHAl0QHwhQMAc

7-http://www.nature.com/articles/srep11929

Hoping this will be helpful,

Rafik

You have to be careful about the first-order transitions. For many cases, to obtain the isothermal entropy change from the experimental M vs. H curves is a poor approach (for instance, see http://www.sciencedirect.com/science/article/pii/S092583881003080X).