Temperature-Dependent Crystal Field and Hyperfine Interactions

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, V²⁺ and Cr³⁺, increase and the cubic-field splittings of two S-state ions, Mn²⁺ and Fe³⁺, decrease with increasing temperature almost exactly as would be expected from thermal expansion alone. The axial crystalline-field splitting of locally compensated Cr³⁺ 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 Mn²⁺ 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 (V⁵¹)²⁺ and (Mn⁵⁵)²⁺ in MgO decrease with increasing temperature, whereas a much smaller increase would be expected due to thermal expansion. Similar explicit variations of the (Mn⁵⁵)²⁺ hyperfine interaction are found in ZnS, ZnO, CdTe, and KMgF₃. The effect may be approximately represented by a power law of the form A(T)=A(0)(1-CTⁿ) where n~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.