Spin Waves Near a Magnetic-Reorientation Phase Transition

The behavior of spin‐waves near a magnetic‐reorientation transition which should occur at $\mathrm{Tc}\text{=8}\mathrm{K}$ in Yb iron garnet is examined theoretically. We derive a spin wave dispersion relation of the form $\mathrm{\hslash \omega =}\sqrt{[{\mathrm{Dk}}^2\text{\hspace{0.17em}+\hspace{0.17em}4}\mathrm{a}(\mathrm{Tc}-\mathrm{T}\mathrm{)]\hspace{0.17em}[}{\mathrm{Dk}}^2\text{\hspace{0.17em}+\hspace{0.17em}2}\mathrm{c}]}$ , for $\mathrm{T}$ approaching $\mathrm{Tc}$ from below with H⇒ varied so that the locus of H⇒ and $\mathrm{T}$ corresponds to the coexistance curve for the transition. At $\mathrm{T}=\mathrm{Tc}$ the $\mathrm{k}\text{⇒=0}$ spin wave becomes “soft” as one of the principal curvatures of the free energy vanishes. For $\mathrm{T}$ below $\mathrm{Tc}$ a reorientation of the sublattices occurs. The exact time‐dependent spin‐spin correlation for a simplified model of the $\mathrm{YbIG}$ transition is found to exhibit divergent static fluctuations at the transition but no softening of the spin‐wave mode. This result indicates the importance of relaxation for soft mode behavior. Lastly we consider the effect of spin fluctuations on the mean field critical behavior for the model and for the 8K transition in $\mathrm{YbIG}$ . The results indicate that for the 8K transition mean field behavior should persist at least to within ${\text{2×10}}^{\text{−3}}\mathrm{K}$ of $\mathrm{Tc}$ .