Electron-Spin-Resonance Study of Manganese-Substituted Spinel

An ESR study was made of ${\mathrm{Mn}}_x{\mathrm{Mg}}_{1-x}{\mathrm{Al}}_2{\mathrm{O}}_4$ for ${10}^{-4\mathrm{}}\le x\le 1.0$ at 300 K using powder samples. An analysis was made within the framework of the spin Hamiltonian $\mathcal{H}={\mu }_B\overrightarrow{\mathrm{S}}·\overrightarrow{\mathrm{g}}·\overrightarrow{\mathrm{H}}+\overrightarrow{\mathrm{S}}·\overleftrightarrow{D}·\overrightarrow{\mathrm{S}}+\overrightarrow{\mathrm{S}}·\overleftrightarrow{A}·\overrightarrow{\mathrm{I}}$. The parameters were determined to be $g=2.00\mathrm{}$, $A=84\mathrm{}$ G, and $D=4\mathrm{}$ G. At low concentrations the 12-line spectrum exhibited each fine-structure pentad of the hyperfine hexad resolved into a singlet and unresolved quartet. A perturbation-theory analysis based on the above Hamiltonian revealed the powder spectrum to be sensitive to an additional Hamiltonian term or perhaps some anisotropy in $A$. With increasing concentration, it is found that exchange has a magnitude of 1 kG by the time $x={10}^{-2\mathrm{}}$. At intermediate and high concentrations when the spectrum collapsed into a single line, the analysis employed the Anderson theory of exchange to give exchange rates $\frac{{\omega }_E}{\gamma }$ between 2 and 15 kG.