Cubic and noncubic multiple-q states in the Heisenberg antiferromagnet on the pyrochlore lattice

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.