Effect of biquadratic exchange on the axial Heisenberg model: Application to the magnetic phase transitions in UNi2Si2.

Abstract

The influence of biquadratic exchange on the Heisenberg model with strong axial anisotropy is examined for the case of spins on a body-centered tetragonal lattice with competing bilinear exchange interactions along the c axis. Contrary to the usual axial next-nearest-neighbor Ising model with third-neighbor exchange also included, a low-temperature spin-wave calculation reveals that biquadratic exchange can stabilize the sequence of phases period 3\ensuremath{\rightarrow}period 2. Mean-field analysis, with support from Monte Carlo simulations, suggests a higher-temperature transition to an incommensurate state. This sequence of phase transitions has recently been observed in ${\mathrm{UNi}}_{2}$${\mathrm{Si}}_{2}$. The importance of fluctuations is emphasized.