Weak localization of magnons in a disordered two-dimensional antiferromagnet

We propose the weak localization of magnons in a disordered two-dimensional antiferromagnet. We derive the longitudinal thermal conductivity ${\kappa }_{xx}$ for magnons of a disordered Heisenberg antiferromagnet in the linear-response theory with the linear-spin-wave approximation. We show that the back scattering of magnons is enhanced critically by the particle-particle-type multiple impurity scattering. This back scattering causes a logarithmic suppression of ${\kappa }_{xx}$ with the length scale in two dimensions. We also argue a possible effect of inelastic scattering on the temperature dependence of ${\kappa }_{xx}$. This weak localization is useful to control turning the magnon thermal current on and off.