Absence of long-range order in a three-dimensional geometrically frustrated antiferromagnet

Classical Heisenberg spins on a lattice of corner-sharing tetrahedra with nearest-neighbor antiferromagnetic interactions are investigated with Monte Carlo (MC) techniques. The system is highly frustrated with an infinitely degenerate ground state. Mean-field theory predicts no long-range order (LRO) at any temperature. The MC calculations are consistent with this result, thus providing evidence that thermal fluctuations beyond the mean-field approximation do not stabilize LRO. The possibility of incommensurate and spin nematic order is considered. The temperature dependence of some spin-glass order parameters, such as the Edwards-Anderson order parameter and the single-spin autocorrelation function, are also investigated. The results show that no spin freezing occurs at nonzero temperatures.