# Magnetic Field Effect of Near-Field Radiative Heat Transfer for SiC Nanowires/Plates
## 1 Introduction  
When the distance between two materials is less than the thermal characteristic wavelength, also known as the characteristic wavelength of thermal radiation, evanescent waves play a dominant role in radiative heat transfer. The energy transfer can be further enhanced and [PERSON]'s theory of thermal radiation is no longer valid, which is called near-field radiative heat transfer [1; 2; 3; 4]. At nanometer distances, near-field radiative heat transfer can be several orders of magnitude greater than that between two far field blackbodies, especially when surface plasmon polaritons (SPPs) or surface phonon polaritons (SPhPs) are excited [5; 6; 7; 8; 9]. Due to the advent of near field radiative heat transfer and its wide potential applications in micro- and nano-scale thermophotovoltaic (TPV) cells, thermal imaging and local thermal management, near-field radiative heat transfer had attracted significant attention [10; 11; 12; 13; 14; 15; 16; 17]. Some researchers have found that applying an external magnetic field to a semiconductor causes some changes in its optical properties. Under the action of a magnetic field, the atoms, or ions within the intrinsic magnetic moment material, produce magnetic induction phenomenon, resulting in the orderly arrangement of the magnetic moment, which affects the transmission of light in its internal features, called the magneto-optical effect. This effect can break the time reversal invariance of the quantum mechanics of materials, and the Kirchhoff's law is no longer valid [18; 19; 20]. [PERSON] et al. [21] discovered the near-field radiative characteristics of magneto dielectric uniaxial anisotropic media (MDUAM)that have both magnetic and electric anisotropy. However, the above works all focused on near-field radiative heat transfer (NFRHT) for homogeneous isotropic media. Then, [PERSON] et al. [22] studied the NFRHT between graphene and anisotropic magneto-dielectric hyperbolic metamaterials (AMDHMs) according to the fluctuational dissipation theorem. They found that extraordinary propagating modes enable the total NFRHT flux to exceed that between graphene and SiC nanowires by several fold. Although the above research considered the impact of magnetic permeability, the effect of the magnetic field was lacking the MDUAM and AMDHMs were all ideal models, and the magnetic field strength was not quantified. SiC is a widely used semiconductor that can be manufactured as optical control elements, such as wavelength-selective photodetectors, photovoltaic cells, and absorbers. Few studies of NFRHT for SiC have been conducted, and most studies investigated the SPhP coupling of SiC. [PERSON] et al. [23] theoretically investigated the improvement of near-field radiative transfer between SiC plates due to strong SPhPs coupling. [PERSON] et al. [24] studied the effect of magnetic polaritons (MPs) inside the SiC grating microstructures on near-field radiative transfer. The presented MPs greatly affected the spectral heat flux beside the SPhPs. However, the above works all focused on near-field radiative transfer for reciprocal materials, lacking studies on effect of non-reciprocal materials as magneto-optical materials. Hence, we investigated the non-reciprocal effect between magneto-optical materials under near-field in order to explore new phenomena. In a previous study, the optical characteristics of the magneto-optical materials, such as SiC, InSb, and HgCdTe, was examined as an external magnetic field was applied, and a detailed description of the dielectric constant was verified and provided [25; 26]. In this work, we theoretically calculate the near field radiative transfer based on SiC nanowires with different filling ratios and gap distances under an external magnetic field by using fluctuation-dissipation theorem and local effective medium theory (EMT), in which Lorentz-Drude equations of dielectric constant tensor are proposed to describe the dielectric constant as a magnetic field is applied toon the SiC.