Entropy driven incommensurate structures in the frustrated kagome staircase Co₃V₂O₈

Co₃V₂O₈ features spin-3/2 moments arrayed on a kagome staircase lattice. A spin density wave with a continuously evolving propagation vector of k ⃗ = ( 0 , δ , 0 ) , showing both incommensurate states and multiple commensurate lock-ins, is observed at temperatures above the ferromagnetic ground state. Previous work has suggested that this changing propagation vector could be driven by changes in exchange interactions due to Co atom displacements. We present a straightforward model showing that a Hamiltonian with competing (but temperature independent) interactions can semi-quantitatively reproduce this behavior using a mean field approximation. The simulated spin density wave magnetic structures feature buckled kagome planes that are either ferromagnetically or antiferromagnetically ordered. Propagation vectors that differ from δ = 1 / 2 will have multiple different ways of arranging these ferromagnetic layers that have very similar energies. This classical stacking entropy appears to be crucial in stabilizing the temperature-dependent propagation vector.