Selection of the ground state in type-I fcc antiferromagnets in an external magnetic field.

Abstract

Selection of the ground-state spin structure through quantum fluctuations is investigated in type-I fcc antiferromagnets. Second-order real-space perturbation theory is used to account for the quantum effects in the most strongly coupled spin-spin pairs. We find that the ground state for isotropic Heisenberg spin-spin interactions is a single-k state in fields below B=0.407${\mathit{B}}_{\mathit{c}}$, where a discontinuous transition takes place to a triple-k structure, stable up to the transition at B=${\mathit{B}}_{\mathit{c}}$ to the fully polarized state. The triple-k structure assumes a particularly simple, up-up-up-down configuration at B=0.5${\mathit{B}}_{\mathit{c}}$. We also study type-I fcc antiferromagnets with easy-plane anisotropy. The results are relevant for understanding the nuclear magnetic ordering in copper and silver at nanokelvin temperatures. Our work and the earlier spin-wave analysis are in accord with the observed type-I order in copper when the external magnetic field is aligned along the [001] and [110] crystalline directions, but in partial disagreement with the previous perturbation analyses. We investigate also an up-up-down spin configuration, which is consistent with the antiferromagnetic (2/3 2) / 3 0) Bragg reflection observed in copper. It has been proposed that the (2/3 2) / 3 0) order is stabilized by quantum fluctuations as theoretically calculated spin-spin interactions favor type-I modulation in the mean-field theory. We find, however, that quantum fluctuations favor type-I order rather than the (2/3 2) / 3 0) modulation. This result urges refined calculations of indirect nuclear-spin interactions in copper.