Analytical expressions for the magnetization curves of a magnetic-tunnel-junction-like system

Abstract

Magnetization curves are predicted for a magnetic-tunnel-junction-like system in some special cases of interest: (i) weak interlayer magnetic coupling/high exchange anisotropy field HE and (ii) strong coupling/low HE. Analytical expressions for different switching fields are derived in these situations. These fields depend on the magnetizations (MA,MB) and thicknesses (tA,tB) of the two ferromagnetic layers, on the bilinear (J1) and biquadratic (J2) coupling parameters, and on the exchange (HE) and uniaxial (HA) anisotropy fields of the pinned layer. In the first case, the whole system is found to behave as two uncoupled layers with equivalent exchange and planar anisotropy fields. The effect of the biquadratic coupling J2 on the hysteresis curves is discussed for both ferromagnetic and antiferromagnetic coupling cases. In the second case, the system behaves as a single (ferromagnetic/antiferromagnetic) bilayer with effective exchange and magnetocrystalline anisotropy fields. These findings confirm some of the results inferred from a ferromagnetic resonance analysis and previously reported.