  We demonstrate that a weak external magnetic field can induce negative
magneto-thermal-resistance for magnons in a disordered two-dimensional
antiferromagnet. We study the main effect of a weak external magnetic field on
the longitudinal thermal conductivity, $\kappa_{xx}$, for a disordered
antiferromagnet using the weak-localization theory for magnons. We show that
the weak-localization correction term of $\kappa_{xx}$ positively increases
with increasing the magnetic field parallel to the ordered spins. Since this
increase corresponds to a decrease of the thermal resistivity, this phenomenon
is negative magneto-thermal-resistance for magnons. This negative
magneto-thermal-resistance and the weak localization of magnons will be used to
control the magnon thermal current in antiferromagnetic spintronics devices. We
also discuss several implications for further experimental and theoretical
studies for disordered magnets.
