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

TL;DR

This study explores how biquadratic exchange influences phase transitions in a planar classical Heisenberg ferromagnet, revealing complex behaviors including multiple phase transition types and a detailed phase diagram with critical points.

Contribution

It provides the first detailed phase diagram showing the effects of biquadratic exchange on phase transition orders and critical behavior in a stacked triangular lattice Heisenberg model.

Findings

Biquadratic exchange induces separate second-order phase transitions.

Presence of first-order transitions at intermediate exchange ratios.

Identification of triple and tricritical points in the phase diagram.

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 $J_{1}/J_{2} \leq 1$. 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.