Cubic and non-cubic 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 J1 and the ferromagnetic next-nearest-neighbour interaction J2 is investigated by means of a mean-field analysis and a Monte Carlo simulation. For a moderate J2/J1-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 non-cubic 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 non-cubic quadruple-q state occurs at a lower temperature. 
Tsuyoshi Okubo, Trung Hai Nguyen, Hikaru Kawamura
cond-mat.stat-mech cond-mat.mtrl-sci cond-mat.str-el