Spiral order from orientationally correlated random bonds in classical XY models

Abstract

We discuss the stability of ferromagnetic long-range order in three-dimensional classical XY ferromagnets upon substitution of a small subset of equally oriented bonds by impurity bonds, on which the ferromagnetic exchange J_{⊥}>0 is replaced by a strong antiferromagnetic coupling J_{imp}<0. In the impurity-free limit, the effective low-energy Hamiltonian is that of spin waves. In the presence of a single, sufficiently strongly frustrating impurity bond, the ground state is twofold degenerate, corresponding to either clockwise or counterclockwise canting of the spins in the vicinity of the impurity bond. For a small but finite concentration of impurity bonds, the effective low-energy Hamiltonian is that of Ising variables encoding the sense of rotation of the local canting around the impurities. Those degrees of freedom interact pairwise through a dipolar interaction mediated by spin waves. A spatially random distribution of impurities leads to a ferromagnetic Ising ground state, which indicates the instability of the XY ferromagnet towards a spiral state, with wave vector and transition temperature both proportional to the concentration of impurity bonds. This mechanism of spiral order by disorder is relevant for magnetic materials such as YBaCuFeO_{5}, for which our theory predicts a ratio between the spiral ordering temperature and the modulus of the spiral wave vector close to the measured ones.