Ab initio calculation of the perpendicular giant magnetoresistance of finite Co/Cu(001) and Fe/Cr(001) superlattices with fluctuating layer thicknesses

Abstract

The results of rigorous quantum calculations of the current-perpendicular-to-plane giant magnetoresistance (CPP GMR) of finite Co/Cu(001) and Fe/Cr(001) superlattices with perfectly flat interfaces but with growth-induced fluctuations in layer thicknesses are reported. They are based on an exact numerical evaluation of the Kubo formula using tight-binding parametrization with s, p, d bands and hopping to first and second neighbors of an ab initio band structure. These calculations show that three distinct regimes of CPP transport occur. When there are no fluctuations, CPP transport is in the ballistic regime. The CPP GMR ratio ${\mathrm{R}}_{\mathrm{CPP}}$ of finite Co/Cu and Fe/Cr superlattices in the ballistic regime reach saturation values equal to ${\mathrm{R}}_{\mathrm{CPP}}$ of an infinite superlattice after only ≈3–5 repeats of a superlattice unit cell and the maximum values of ${\mathrm{R}}_{\mathrm{CPP}}$ are of the order of 100%. When small fluctuations in layer thickness corresponding to only one atomic plane at the interface being displaced are introduced, transport changes from ballistic to Ohmic. The calculated GMR ratio ${\mathrm{R}}_{\mathrm{CPP}}$ increases initially linearly with the number N of ferromagnet/spacer bilayers and then saturates for N≈40–50. The theoretical maximum values of ${\mathrm{R}}_{\mathrm{CPP}}$ for Co/Cu and Fe/Cr superlattices in the Ohmic regime are in the region 800–1000 %. The zero-field and saturation-field resistances increase linearly with N (good Ohm's law) and the calculated zero-field resistance of the Co/Cu superlattice is within 10% of the resistance observed in a Co/Cu sample of the same composition and thickness. Small spontaneous (growth-induced) fluctuations in layer thickness can thus account well for the observed CPP GMR. When superlattices with large fluctuations in layer thickness are grown deliberately (pseudorandom spin valves), the Ohmic regime changes into, experimentally as yet unexplored, Anderson localization regime. The results for Co/Cu and Fe/Cr superlattices in which layer thicknesses are made to fluctuate typically between 2 and 10 atomic planes show that strong disorder of the sequence of ferromagnet/spacer interfaces has virtually no effect on the saturation-field resistance ${\mathrm{R}}_{\mathrm{FM}}$, which remains as low as in the Ohmic regime. The zero-field resistance, on the other hand, increases approximately exponentially with the number of bilayers N due to Anderson localization with a localization length ≈30–40 nm. The CPP GMR ratio ${\mathrm{R}}_{\mathrm{CPP}}$, therefore, also increases approximately exponentially with N and values as high as ${\mathrm{R}}_{\mathrm{CPP}}$≈3×${10}^4$ are predicted for Fe/Cr valves with N≈50 bilayers. Somewhat smaller (${\mathrm{R}}_{\mathrm{CPP}}$≈${10}^4$) enhancement of the CPP GMR is obtained for Co/Cu pseudorandom spin valves. The conditions under which such enhancement should be observable are discussed.