An Explicit Function Expression for dc Bias and Temperature Dependence of Magnetoresistances in Magnetic Tunnel Junctions

An explicit function expression for the bias voltage or/and temperature dependences of tunnel magnetoresistance ratio and resistances were obtained with a unique set of intrinsic parameters. Two of these intrinsic parameters are the Curie temperature TC and the density of state (DOS) for itinerant majority and minority electrons ξ(ρM/ρm),which are the eigen parameters of ferromagnetic electrodes. Others are the spin-dependent matrix-element ratio (i.e.,|Td|2/|TJ|2 ) and the anisotropic-wavelength-cutoff energy EγC of spin-wave spectrum in magnetic tunnel junction (MT J), which are the structure parameters of an MTJ. These intrinsic parameters can be predetermined using the experimental measurement or, in principle, using the first-principle calculation method for an MTJ with the three key layers of FM/I/FM. Furthermore, a series of experimental data for an MTJ, for example, a spin-valve-type MTJ of Ta (5 nm)/Ni79Fe21(25 nm)/Ir22Mn78(12 nm)/Co75Fe25(4 nm)/Al(0.8 nm)-oxide/Co75Fe25(4 nm)/Ni79Fe21(20 nm)/Ta (5 nm) in this work, can be self-consistently evaluated and explained using such concise explicit function formulations.