Renormalization of the EffectivegFactor of Magnons

Within the framework of the Heisenberg model we have calculated the renormalization of the effective $g$ factor of magnons in cubic ferromagnets and antiferromagnets. We find a $f\left(k\right)\mathrm{}{T}^{\frac{3}{2}}$ enhancement of $g$ in ferromagnets, where $f\left(k\right)\mathrm{}\sim k^2$ for small $k$, and a $-\frac{1}{2}\frac{{\chi }_{\parallel }}{{\chi }_{\perp }}$ depression of $g$ for all antiferromagnetic magnons. We estimate that this effect will have experimental consequences of 10% or more at reasonable temperatures.