Use of Abrikosov-Gorkov Density of State to Extract Spin Polarization at the Metal-Insulator Transition

We have discovered and applied an analytical solution of the Abrikosov-Gorkov $^{1}$ density of states (DOS), describing superconductors with impurities, to extract the spin-polarization of 3-dimensional amorphous (a-) Gd$_{x}$Si$_{1-x}$ in the quantum critical regime (QCR) of a magnetic field tunable metal-insulator transition (MIT). The analysis of the experimental spin-polarized (SP) tunneling conductance of an Al/Al$_{2}$O$_{3}$/a-Gd$_{x}$Si$_{1-x}$ planar tunnel junction at T=25mK in parallel magnetic field H$\le $3.0T indicates a larger polarization near the MIT of a-Gd$_{x}$Si$_{1-x}$ (x=0.14) as compared to previous work $^{2}$, where a SP Bardeen-Cooper-Schrieffer DOS $^{3}$ was used. We will present polarization values at different applied magnetic fields in the QCR. \newline $^{1 }$A. A. Abrikosov and L. P. Gor'kov, Zh. Eksperim. I Teor. Fiz. 39, 1781 (1960). A.A. Abrikosov and L.P. Gorkov, Zh. Eksp. Teor. Fiz. 39, 866 (1961). Soviet Phys.---JETP 12, 1243 (1961). \newline $^{2}$ W. Teizer, F. Hellman, and R. C. Dynes. Phys. Rev. B 67, 121102 (2003). \newline $^{3}$ J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Phys. Rev. 108, 1175 (1957).