  Recently, the application of an external magnetic field to actively control
the near-field heat transfer has emerged as an appealing and promising
technique. Existing studies have shown that an external static magnetic field
tends to reduce the subwavelength radiative flux exchanged between two planar
structures containing magneto-optical (MO) materials, but so far the nearfield
thermomagnetic effects in systems with more such structures at different
temperatures have not been reported. Here, we are focused on examining how the
presence of an external magnetic field modifies the radiative energy transfer
in a many-body configuration consisting of three MO n-doped semiconductors
slabs, separated by subwavelength vacuum gaps. To exactly calculate the
radiative flux transferred in such an anisotropic planar system, a general
Green-function-based approach is offered, which allows one to investigate the
radiative heat transfer in arbitrary manybody systems with planar geometry. We
demonstrate that, under specific choices of the geometrical and thermal
parameters, the applied magnetic field is able to either reduce or enhance the
near-field energy transfer in three-element MO planar systems, depending on the
interplay between the damped evanescent fields of the zero-field surface waves
and the propagating hyperbolic modes induced by magnetic fields. Our study
broadens the understanding concerning to the use of external fields to actively
control the heat transfer in subwavelength regimes, and may be leveraged for
potential applications in the realm of nanoscale thermal management.
