Theory of hyperfine- and exchange-field distributions in amorphous speromagnets with application to amorphous yttrium iron garnet

The hyperfine-field distribution in amorphous speromagnetic ${\mathrm{Y}}_3$ ${\mathrm{Fe}}_5$ ${\mathrm{O}}_{12}$ (yttrium iron garnet, YIG) is shown to result dominantly from local spin disorder via its supertransferred component $H_{\mathrm{ST}}$. Since this same spin disorder determines local exchange fields $H_{\mathrm{ex}}$, the hyperfine-field distribution indirectly contains much information concerning the distribution of $H_{\mathrm{ex}}$ in the "spin-glass" environment. A theory is presented which relates $H_{\mathrm{ST}}$ and $H_{\mathrm{ex}}$ through local spin disorder and in terms of which both the distributions of hyperfine and exchange fields can be represented in terms of a few common parameters. The theory, which should be directly applicable to a whole range of ferric amorphous insulators, is applied here to amorphous YIG and provides an excellent interpretation of the details of the observed hyperfine spectrum. From this fit we derive, via the theory, the predicted distribution of exchange fields in amorphous YIG. We find, in particular, that the mean exchange field $〈H_{\mathrm{ex}}〉$ is only some 6% of its equivalent in crystalline YIG in accord with the ~ 15-fold difference in spin-ordering temperatures between the crystalline amorphous phases.