Frustrated Diamond Antiferromagnets:
We tend to conflate the general notion of frustration with geometrical frustration, a property of a lattice. However, even simple geometries can exhibit frustration if interactions beyond nearest-neighbor are considered. In many magnetic materials, these are common. In this project, we are interested in a class of spinel oxides which can be viewed as antiferromagnets on the diamond lattice. Despite the fact that the diamond lattice is bipartite - and hence allows a simple collinear Néel state - these materials show classic experimental signs of frustration. This includes a low ordering temperature relative to the Curie-Weiss temperature and significant short-range correlations seen in neutron scattering above the Néel temperature.
^ TOPOur work:
We considered a classical model with competing first and second neighbor antiferromagnetic exchange interactions, motivated by quantum chemistry. When the second neighbor exchange constant is larger than 1/8 of the nearest neighbor exchange, the ground states are highly degenerate, consisting of co-planar spirals. What is unusual is that the set of ground state wavevectors (characterizing the spiral axis and pitch) forms a "spiral" surface in momentum space. This type of (large) degeneracy had not been considered previously to our knowledge.
In our paper, we showed that the energetic degeneracy is split by entropic corrections to the free energy at non-zero temperature, a process known as order by disorder . Specifically, entropy selects some specific directions on the spiral surface, which depends upon the ratio of exchange constants. In this counter-intuitive situation, the system is actually more ordered with increasing temperature, at least for low temperatures.
In reality, there must be some weak additional perturbations to the Hamiltonian that spoil the degeneracy of the ground state. The most likely candidate is a third-neighbor exchange, which favors some particular directions on the spiral surface. Interestingly, these are different directions than are favored by entropy. What ensues from this competition is a multi-stage ordering: at very low temperatures, the energetic splitting controls the ground state, while at higher temperatures, the entropic splitting is more important.
Read the paper.
