Temperature dependence of spin-lattice relaxation in rare-earth iron garnets

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Abstract
The spin-lattice relaxation rate in iron garnets containing ions of the rare-earth series features a peak in the temperature range from 30 to 100 K that is consistent throughout the group. This effect is important in microwave applications at liquid nitrogen temperatures because magnetic losses increase directly with the intrinsic ferrimagnetic resonance linewidth ΔH, which in turn is proportional to the relaxation rate τ−1. The decrease in X-band linewidth with lowering temperatures is accounted for by the Orbach exponential relation for τ−1 of individual paramagnetic rare-earth ions. To explain the decrease in ΔH above the peak, the Orbach function is multiplied by the magnetic exchange energy between the iron and rare-earth spins. Computations of the linewidth as a function of temperature for Dy3+, Ho3+, Er3+, and Yb3+ are made by utilizing the multiple sublattice molecular-field theory. By fitting theory to data, values are extracted for excited state energy splitting D that enters the exponent (−D/kT) of the Orbach function. Measurement data from high purity yttrium iron garnet also confirm that iron relaxation rates decrease monotonically with reducing temperatures, indicating that microwave magnetic loss at cryogenic temperatures can be reduced below room temperature values if offending rare-earth impurities are removed.

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