The discovery that the near-field radiative heat transfer enables to overcome the limit set by Planck's law holds the promise to have an impact in different nanotechnologies that make use of thermal radiation, and the challenge now is to find strategies to actively control and manipulate this near-field thermal radiation. Here, we predict a huge anisotropic thermal magnetoresistance (ATMR) in the near-field radiative heat transfer between magneto-optical particles when the direction of an external magnetic field is changed with respect to the heat current direction. We illustrate this effect with the case of two InSb particles where we find that the ATMR amplitude can reach values of up to 800% for a magnetic field of 5 T, which is many orders of magnitude larger than its spintronic analogue. This thermomagnetic effect could find broad applications in the field of ultrafast thermal management as well as magnetic and thermal remote sensing.

We present here a generalization of the thermal discrete dipole approximation (TDDA) that allows us to describe the near-field radiative heat transfer between finite objects of arbitrary shape that exhibit magneto-optical (MO) activity. We also extend the TDDA approach to describe the thermal emission of a finite object with and without MO activity. Our method is also valid for optically anisotropic materials described by an arbitrary permittivity tensor and we provide simple closed formulas for the basic thermal quantities that considerably simplify the implementation of the TDDA method. Moreover, we show that by employing our TDDA approach one can rigorously demonstrate Kirchhoff's radiation law relating the emissivity and absorptivity of an arbitrary MO object. Our work paves the way for the theoretical study of the active control of emission and radiative heat transfer between MO systems of arbitrary size and shape.