Antiferromagnets with anisotropic spin-spin interactions: Stability of the zero-field structure in an external field

The transition from the polarized paramagnetic state to the antiferromagnetic phase in an applied external magnetic field has been investigated theoretically by linear spin-wave theory at T=0. Our analysis applies to spins arranged in a lattice of cubic symmetry. In addition to the Zeeman term, the Hamiltonian consists of bilinear interactions. Antiferromagnetic transition to a state described by an ordering vector Q is discussed in terms of softening of the corresponding spin-wave excitation in the paramagnetic phase. It is shown that the onset of antiferromagnetic order can be calculated by solving an eigenvalue problem. The smallest eigenvalue of the Fourier transformed 2×{}2 interaction matrix, which describes the spin-spin interactions in the plane perpendicular to B, determines Bc, Q, and the direction of the antiferromagnetic component. For sufficiently anisotropic spin-spin interactions, these quantities can depend on the direction of B with respect to the crystalline axes.However, when the spin structure shows an easy-plane anisotropy, which is possible for ordering vectors of the type Q=(h,0,0) and Q=(h,h,h), and for some vectors at the Brillouin-zone boundary, the direction of B has no such effect. The general results were first applied to investigate the stability of the easy-axis type-III antiferromagnetism of the fcc lattice, characterized by Q={π}/a(1,1/2,0). It was shown that, if the spin-spin interactions are sufficiently anisotropic, type-III order becomes unstable against type-I order [Q={π}/a(1,0,0)] when a strong enough field B is applied along a [111] crystalline axis. If the anisotropy is comparable to the isotropic next-nearest-neighbor coupling, like in K₂{IrCl}₆$, a high-field ordering vector, between the type-I and -III vectors, is predicted. As another application, the magnetic phase diagram of nuclear spins in copper was investigated. Antiferromagnetic type-I ordering has been found in this fcc metal below TN=60 nK.We studied the puzzle presented by the neutron-diffraction measurements of Annila et al., which show that type-I order is absent in the high-field reigon below Bc=0.25 mT when B{∥}[111], although this kind of ordering was observed in the same fields when B{∥}[100] or [110]. Soft-mode analysis shows that the high-field ordering vector for B{∥}[111] is of the general type, Q=(h,k,l), where {}h{}, {}k{}, and {}l{} are all unequal and nonzero, in agreement with our previous suggestion based on the mean-field theory. We predict various (h,k,l) structures in fields B{}Bc for several field alignments other than [111]. The magnetic phase diagram of nuclear spins in copper can be explained on the basis of the previously calculated spin-spin interactions at least in fields B{}Bc if the calculated parameters are changed only slightly.