Thouless length and valley degeneracy factor of ZnMnO thin films with anisotropic, highly conductive surface layers

Isothermal magnetoresistance (MR) of n-type conducting Zn1–xMnxO thin films on a sapphire substrate with a Mn content of 5 at. % has been studied in in-plane and out-of-plane magnetic fields up to 6 T in the temperature range of 5K to 300 K. During pulsed laser deposition of the ZnMnO thin films, we controlled the thickness and roughness of a highly conductive ZnMnO surface layer. The measured MR has been modeled with constant s-d exchange (0.2 eV in ZnMnO) and electron spin (S=5/2 for Mn2þ) for samples with a single two dimensional (2D) ZnMnO layer, a single three dimensional (3D) ZnMnO layer, or a 2D and 3D (2Dþ3D) ZnMnO layer in parallel. The temperature dependence of modeled Thouless length LTh (LTh ~ T_0.5) is in good agreement with the theory [Andrearczyk et al., Phys. Rev. B 72, 121309(R) (2005)]. The superimposed positive and negative MR model for ZnCoO thin films [Xu et al., Phys. Rev. B 76, 134417 (2007)] has been extended in order to account for the increase in the density of states close to the Fermi level of n-ZnMnO due to substitutional Mn2þ ions and their effect on the negative MR in ZnMnO.