Secondary and Higher-Order Ferroics Multiferroics

The value of coefficient B is defined by crystalline fields originated from equilibrium positions of lattice ions. Magnetic spins are coupled with these fields via weak relativistic spin-orbit interaction (giving rise to above magnetic anisotropy energy), while electric dipoles are coupled with electric crystalline field electrostatically. In ferroelastics, the elastic dipoles constituting order parameter interact with elastic strain or gradients of crystalline field. 

that the description of first order phase transitions can be carried out within the above formalism but after adding the term C T,p)v (where the coefficient C(T,p) = C(Tc,p) must be positive) to Eq. (1.5). Contribution of this term is important for the system stability because for the phase transition of the first order the coefficient B 0 in Eq. (1.5). In general case, if it is necessary to consider the higher order terms in thermodynamic potential expansion, the last term in it must be positive for the system stability. 

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