Dipolar Induced Nuclear Spin-Lattice Relaxation in Ferromagnetic Insulators

Abstract

We consider the nuclear spin-lattice relaxation rate (T1−1) in a cubic ferromagnetic insulator with an isotropichyperfine interaction. In the absence of dipolar fields, angular momentum conservation forbids the two-magnon process. The electronic dipole-dipole interaction breaks down this symmetry requirement, thus inducing a Raman process. The mechanism we have calculated is as follows: (1) a nuclear spin flips and creates a virtual spin wave via the hyperfine interaction; (2) this virtual magnon is absorbed, via the dipolar field, by a thermal magnon, creating a third final-state spin wave. The relaxation rate is found to be given by T1−1=(A2/ℏ2ωex) (gβM/ℏωex)2F(kBT/gβH), for H≫M and ℏωex≫kBT. Here H is the sum of the applied dc magnetic field and the anisotropy field, Mis the saturation magnetization, ℏωex is the exchange energy, and A is the strength of the isotropic hyperfine interaction. The function F(kBT/gβH), which is evaluated numerically is nearly proportional to (T/H)2 for kBT≫gβH. Using parameters typical of 57Fe in YIG, with H = 5×103 Oe, this process is faster than the three-magnon process, up to about 30°K. At this temperature, T1∼50 sec. At higher temperatures, the three-magnon process, which is proportional to T7/2, dominates.