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The ordering of the classical Heisenberg model on the pyrochlore lattice withthe antiferromagnetic nearest-neighbor interaction J1 and the ferromagneticnext-nearest-neighbour interaction J2 is investigated by means of a mean-fieldanalysis and a Monte Carlo simulation. For a moderate J2/J1-value, the modelexhibits a first-order transition into an incommensurate multiple-q orderedstate where multiple Bragg peaks coexist in the spin structure factor. We showthat there are two types of metastable multiple-q states, a cubic symmetricsextuple-q state and a non-cubic symmetric quadruple-q state. Based on a MonteCarlo simulation, we find that the cubic sextuple-q state appears just belowthe first-order transition temperature, while another transition from the cubicsextuple-q state to the non-cubic quadruple-q state occurs at a lowertemperature.

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