Anisotropic magnetic systems

Papers

The criterion for the existence of weak ferromagnetism in the low-temperature distorted phases of La₂CuO₄-type compounds is derived on the basis of a general superexchange Hamiltonian. It is found that a ferromagnetic canting out of the CuO₂ planes is excluded in the pure low-temperature tetragonal phase. The anisotropic superexchange interactions between the copper spins are obtained from a Hubbard model which includes all copper 3d and oxygen 2p orbitals, and all on-site Coulomb matrix elements. The results apply when the oxygen octahedra surrounding each copper have tetragonal symmetry. Explicit expressions for the net ferromagnetic moment and the in-plane and the out-of-plane gaps in the spin-wave spectrum are derived and estimated in terms of the microscopic parameters of the cuprates.

We have extended and generalized earlier studies of the magnetic anisotropies of the Cu spins in the copper-oxide planes generated by the spin-orbit coupling on the coppers and by the nonlocal Coulomb interactions between neighboring ions. Our derivation of the anisotropic magnetic Hamiltonian includes the contributions from general matrix elements of the Coulomb interaction both between the copper ions of a single bond and between the adjacent copper and oxygen sites. The results apply for a general rotation axis of the oxygen octahedra, with the assumption of tetragonal site symmetry of the copper. This mechanism leads to a form of the anisotropic spin interaction between the Cu ions which is identical to the one generated by kinetic superexchange in the presence of purely local Coulomb interactions. Together with the numerical estimates for the resulting spin couplings, this indicates that the Coulomb direct exchange leads to significant contributions to the isotropic spin interaction and the out-of-plane anisotropy, but does not affect qualitatively the magnetic order in the ground state.

We study the classical n-vector spin glass with anisotropic quenched random Dzyaloshinskii-Moriya (DM) interaction. A random DM interaction with m independent and separated couplings defines a generalized gauge glass model with a rotational symmetry and a broken global reflection invariance. It is shown that this model is in the same universality class as the random gauge XY ("gauge glass") model. With an additional uniaxial anisotropy, a crossover from Ising-like to gauge glass critical behaviour is found for a sufficiently large variance of the DM interaction. A new situation arises when there is correlation between the separated random DM couplings. We show that the critical behaviour of a spin glass with two correlated couplings of the anisotropic DM interaction is in a new universality class. The critical exponents eta and nu of this model are calculated at two-loop order near six dimensions. We also present a simplified and more rigorous field theoretic analysis of the gauge glass model.

The critical exponents of the classical spin glasses with symmetry are obtained to order of the -expansion around six dimensions, where . This new unitary symmetry is realized in the m-vector () spin glasses with anisotropic quenched random Dzyaloshinskii-Moriya (DM) interaction. Such a random DM interaction with n correlated couplings leads to critical exponents which are different from those of any isotropic m-vector spin glass and thus belong to new universality classes.