Induced staggered magnetic fields in antiferromagnets: Microscopic mechanisms

The induced staggered magnetic field effects recently proposed by Blume et al. on the basis of general symmetry considerations are discussed in terms of detailed microscopic mechanisms, with special reference to the experimental situation in dysprosium aluminum garnet (DAG). It is shown that all of the low-field effects observed in DAG can be accounted for quantitatively by a mechanism based on the way in which the completing interactions affect the spin-spin correlations. Approximate calculations of the high-field effects are also discussed, and it is found that the same mechanism is probably responsible for these as well. A second mechanism, which is based upon the inequivalence of the $g$ tensors of different spins is also considered, and although this mechanism does not appear to be important in any of the experiments performed to date, we find that it will be the dominant mechanism at both low and high temperatures. It is possible for the two mechanisms to compete, and if this should be the case, it would lead to a new phase transition in a hitherto uninvestigated region of the phase diagram below about 1.1 K. Two additional mechanisms involving higher-order Zeeman effects and anisotropic non-Ising spin-spin interactions are also considered, but their effects are found to be negligible in DAG. In other antiferromagnets for which symmetry also allows induced staggered field effects, any or all of these microscopic mechanisms may be important, and a correspondingly wide range of behavior may be expected. Semiquantitative estimates predict relatively small effects in Co${\mathrm{F}}_2$ and Fe${\mathrm{F}}_2$, but large and readily observable effects in several rare-earth gallium and aluminum garnets.