Calculation of effective impedance of polycrystals in weak magnetic fields

We present results for the effective surface impedance tensor (EIT) of polycrystals of metals in a weak uniform magnetic field H. The frequency region corresponds to the region in which the local impedance boundary conditions are applicable. We suppose that the resistivity tensor ρik(H) of the single crystal grains out of which the polycrystal is composed, is known up to the terms of O(H2). For polycrystals of metals of arbitrary symmetry, the elements of the EIT can be calculated to the same order in H, even if the tensor ρik(H) is strongly anisotropic. As examples, we write down the EIT of polycrystals of (i) cubic metals, (ii) metals with ellipsoidal Fermi surfaces, and (iii) metals of tetragonal symmetry whose tensor ρik(0) is strongly anisotropic. Although polycrystals are metals that are isotropic on average, in the presence of a uniform magnetic field the structure of the EIT is not the same as the structure of the impedance tensor of an isotropic metal with a spherical Fermi surface. The results cannot be improved either by taking into account higher powers of H, or with respect to the anisotropy of the single crystal grains.