Cubic and noncubic multiple-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>q</mml:mi></mml:math>states in the Heisenberg antiferromagnet on the pyrochlore lattice

Abstract

The ordering of the classical Heisenberg model on the pyrochlore lattice with the antiferromagnetic nearest-neighbor interaction ${J}_{1}$ and the ferromagnetic next-nearest-neighbor interaction ${J}_{2}$ is investigated by means of a mean-field analysis and a Monte Carlo simulation. For a moderate ${J}_{2}/{J}_{1}$ value, the model exhibits a first-order transition into an incommensurate multiple-$q$ ordered state where multiple Bragg peaks coexist in the spin structure factor. We show that there are two types of metastable multiple-$q$ states: a cubic symmetric sextuple-$q$ state and a noncubic symmetric quadruple-$q$ state. Based on a Monte Carlo simulation, we find that the cubic sextuple-$q$ state appears just below the first-order transition temperature, while another transition from the cubic sextuple-$q$ state to the noncubic quadruple-$q$ state occurs at a lower temperature.