Novel ordering of the pyrochlore Heisenberg antiferromagnet with the ferromagnetic next-nearest-neighbour interaction

The ordering property of the classical pyrochlore Heisenberg antiferromagnet with the ferromagnetic next-nearest-neighbour interaction is investigated by means of a Monte Carlo simulation. The model is found to exhibit a first-order transition at a finite temperature into a peculiar ordered state. While the spin structure factor, i.e. the thermal average of the squared Fourier amplitude of the spin, exhibits a finite long-range order characterized by the commensurate spin order of period four, the thermal average of the spin itself almost vanishes. This means that although the amplitude of the spin Fourier component is long-range ordered the associated phase degree of freedom remains fluctuating.