We present a comprehensive theoretical study of the magnetic field dependence of the near-field radiative heat transfer (NFRHT) between two parallel plates. We show that when the plates are made of doped semiconductors, the near-field thermal radiation can be severely affected by the application of a static magnetic field. We find that irrespective of its direction, the presence of a magnetic field reduces the radiative heat conductance, and dramatic reductions up to 700% can be found with fields of about 6 T at room temperature. We show that this striking behavior is due to the fact that the magnetic field radically changes the nature of the NFRHT. The field not only affects the electromagnetic surface waves (both plasmons and phonon polaritons) that normally dominate the near-field radiation in doped semiconductors, but it also induces hyperbolic modes that progressively dominate the heat transfer as the field increases. In particular, we show that when the field is perpendicular to the plates, the semiconductors become ideal hyperbolic near-field emitters. More importantly, by changing the magnetic field, the system can be continuously tuned from a situation where the surface waves dominate the heat transfer to a situation where hyperbolic modes completely govern the near-field thermal radiation. We show that this high tunability can be achieved with accessible magnetic fields and very common materials like $n$-doped InSb or Si. Our study paves the way for an active control of NFRHT and it opens the possibility to study unique hyperbolic thermal emitters without the need to resort to complicated metamaterials.

Radiative corrections to the polarizability tensor of isotropic particles are fundamental to understand the energy balance between absorption and scattering processes. Equivalent radiative corrections for anisotropic particles are not well known. Assuming that the polarization within the particle is uniform, we derived a closed-form expression for the polarizability tensor which includes radiative corrections. In the absence of absorption, this expression of the polarizability tensor is consistent with the optical theorem. An analogous result for infinitely long cylinders was also derived. Magneto optical Kerr effects in non-absorbing nanoparticles with magneto-optical activity arise as a consequence of radiative corrections to the electrostatic polarizability tensor.

We demonstrate magnetic field control of surface plasmon excitations in noble-metal/ferromagnetic/noble metal trilayers, analogous to the effects previously observed in semiconductor structures. We show that the coupling of an external magnetic field to the surface plasmon-polariton wave vector is greatly enhanced in the metallic structure due to the ferromagnetic nature of one of its constituents. The observed coupling could be used to modulate the surface plasmon response in ultrasensitive spectroscopic applications.