Size effects on the phase transitions in a thin multiferroic film

ABSTRACT

The phenomenological Landau theory was applied for treating the phase transitions in a thin multiferroic film. The multiferroic phase in the relevant bulk was assumed to emerge following two successive phase transitions of the second order. The coupling between the order parameters was implied to be biquadratic as for a multiferroic-magnetoelectric. The variation of the free energy density functional yielded a system of two nonlinear differential Euler-Lagrange equations with four boundary conditions. The boundary value problem was analyzed numerically. It was shown that the phase diagram in the film can differ radically from that in bulk for particular sets of the phenomenological parameters.

KEYWORDS:

• Multiferroic thin film
• phase transition
• size effect
• Landau theory
• numerical analysis

Funding

The authors acknowledge the financial support from RFBR (Russia), grant 13-07-12416.