A phenomenological theory of possible sequences of ferrotoroidal phase transitions in boracites

A phenomenological theory of the sequence of two second-order phase transit ions with close temperatures is considered; such transitions occur in the N i-Br boracite. The thermodynamic potential is written as a function of pola rization P-i, magnetization M-i, and toroidal moment T-i vectors and fields E-i and H-i; T-i is treated as an order parameter. It is assumed that only one coefficient of T-i(2) passes through zero as T decreases. The possibil ity of a sequence of two proper ferrotoroidal phase transitions alone, the T-1 and T-2 components is demonstrated. Spontaneous Ti, Pi, and Mj vector v alues and equations for susceptibility tensors (dielectric chi (ij) = dP(i) /dE(j), magnetic k(ij) = dM(i)/dH(j), and magnetoelectric alpha (ij) = dP(i )/dH(j) = dM(j)/dE(i)) were obtained for three phases. Some of these values have well-defined anomalies in the vicinity of transitions. All possible s equences of ferrotoroidal phase transitions in boracites are considered. De pending on two potential coefficient values, these sequences may consist of one, two, or three such transitions. (C) 2001 MAIK "Nauka/Interperiodica".