The magnetocaloric effect of ferromagnetic manganites: modeling and interpretation of properties with Landau and mean field theory . J.S. Amaral , M.S. Reis, V.S. Amaral Departamento de Física da Universidade de Aveiro and CICECO J.P. Araújo, T.M. Mendonça - PowerPoint PPT Presentation
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The magnetocaloric effect of ferromagnetic manganites: modeling and interpretation of properties with Landau and mean field theory
J.S. Amaral, M.S. Reis, V.S. Amaral
Departamento de Física da Universidade de Aveiro and CICECO
J.P. Araújo, T.M. Mendonça
Departamento de Física da Universidade do Porto and IFIMUP
Departamento de Química and CQ-VR
Departamento de Cerâmica e Vidro da Universidade de Aveiro
13th Workshop on magnetism and Intermetallics – Porto 2007
E. Brück et al.
Toshiba Corp. 2003
Astronautics corp 2001, USA
T is a trivalent rare-earth ion
D is a divalent dopant)
Asamitsu et al.
Secondary ErMnO3 phase
Gibbs free energy expansion:
Minimizing the free energy, we obtain the magnetic equation of state:
By representing isothermal magnetization data in an Arrott plot (H/M versus M2), polynomial fits give the values of A, B and C coefficients.
With A,B and C coefficients determined, magnetic entropy change can be estimated by
And can be compared with results obtained by numerical integration of the Maxwell relation.
In the case of manganites, the B coefficient represents magnetoelastic couplings and electron spin condensation energy.
By changing the dependence of B with T it is possible to calculate and estimate the dependence of the magnetocaloric effect with such couplings (REF)
We begin by considering the general mean-field law:
If the f function is monotonous (like the Brillouin function), then for corresponding values of M:
We can then plot plot a graph of H/T versus 1/T for regular M intervals
And linear fits for each M value will show the dependence of the exchange field with magnetization
The magnetic entropy change with applied magnetic field can be estimated by
Therefore the magnetic entropy variation between an applied field H1 and H2 is given by:
Which can be easily calculated numerically by using