Effect of biquadratic exchange on phase transitions of a planar classical Heisenberg ferromagnet

Abstract

Effect of biquadratic exchange on phase transitions of a planar classical Heisenberg (or XY) ferromagnet on a stacked triangular lattice is investigated by standard Monte Carlo and histogram Monte Carlo simulations in the region of a bilinear to biquadratic exchange interaction ratio J 1/ J 2⩽1. The biquadratic exchange is found to cause separate second-order phase transitions in a strong biquadratic exchange limit, followed by simultaneous dipole and quadrupole ordering, which is of first order for an intermediate range of the exchange ratio and changes to a second-order one again as J 1/ J 2 is further increased. Thus, a phase diagram featuring both triple and tricritical points is obtained. Furthermore, a finite-size scaling analysis is used to calculate the critical indices for both dipole and quadrupole kinds of ordering.