Temperature-Dependent Crystal Field and Hyperfine Interactions

Abstract

The effects of temperature variation on the spin-Hamiltonian parameters of several paramagnetic ions bound in simple crystals have been measured by magnetic-resonance techniques. Whenever possible the data have been analyzed for implicit (thermal-expansion) and explicit (lattice-vibration) temperature dependences using isothermal volume dependences determined in earlier hydrostatic-pressure experiments. In MgO the $g$ shifts of two $F$-state ions, ${\mathrm{V}}^{2+}$ and ${\mathrm{Cr}}^{3+}$, increase and the cubic-field splittings of two $S$-state ions, ${\mathrm{Mn}}^{2+}$ and ${\mathrm{Fe}}^{3+}$, decrease with increasing temperature almost exactly as would be expected from thermal expansion alone. The axial crystalline-field splitting of locally compensated ${\mathrm{Cr}}^{3+}$ ions also increases with temperature at a rate attributable primarily to thermal expansion. The absence of appreciable explicit temperature dependence of crystalline-field parameters in MgO is consistent with an effective point-charge model for the source of the lattice potential and cubically symmetric lattice vibrations. In zinc blende, however, the cubic-field splitting of ${\mathrm{Mn}}^{2+}$ decreases more rapidly with rising temperature than may be accounted for by thermal expansion alone, presumably because of failure of the point-charge approximation. The hyperfine couplings of ${({\mathrm{V}}^{51})}^{2+}$ and ${({\mathrm{Mn}}^{55})}^{2+}$ in MgO decrease with increasing temperature, whereas a much smaller increase would be expected due to thermal expansion. Similar explicit variations of the ${({\mathrm{Mn}}^{55})}^{2+}$ hyperfine interaction are found in ZnS, ZnO, CdTe, and KMg${\mathrm{F}}_{3}$. The effect may be approximately represented by a power law of the form $A(T)=A(0)(1\ensuremath{-}C{T}^{n})$ where $n\ensuremath{\sim}\frac{3}{2}$. The significance of this result for nuclear-magnetic-resonance studies of concentrated magnetic materials is indicated. The general nature of the explicit temperature dependence is discussed but no detailed theoretical analysis is possible at this time.