Static susceptibilities of dipolar ferromagnets belowTc

Abstract

We study the static susceptibility tensor for the isotropic Heisenberg model with short-range nearest-neighbor exchange and long-range dipolar interactions. We derive analytic expressions for the eigenvalues and eigenvectors of the susceptibility. To this end one has to take proper account of the Goldstone modes, which lead to ``critical'' fluctuations at all temperatures below ${T}_{c}.$ We discuss how the dipolar interaction modifies these effects. Instead of one longitudinal and two transverse susceptibilities in the isotropic limit, we get one longitudinal, one transverse---Goldstone-mode associated---and one intermediate susceptibility in the general dipolar case. We present a ``phase diagram'' exhibiting six distinct regions in the temperature--wave-vector plane. For each region we give the characteristic leading dependencies of all three susceptibilities.