Magnetoresistance generated from charge-spin conversion by anomalous Hall effect in metallic ferromagnetic/nonmagnetic bilayers

Abstract

A theoretical formulation of magnetoresistance effect in a metallic ferromagnetic/nonmagnetic bilayer originated from the charge-spin conversion by the anomalous Hall effect is presented. Analytical expressions of the longitudinal and transverse resistivities in both nonmagnet and ferromagnet are obtained by solving the spin diffusion equation. The magnetoresistance generated from charge-spin conversion purely caused by the anomalous Hall effect in the ferromagnet is found to be proportional to the square of the spin polarizations in the ferromagnet and has fixed sign. We also find additional magnetoresistances in both nonmagnet and ferromagnet arising from the mixing of the spin Hall and anomalous Hall effects. The sign of this mixing resistance depends on those of the spin Hall angle in the nonmagnet and the spin polarizations of the ferromagnet.

Anomalous Hall magnetoresistance in single-crystal Fe(001) films

“…We found that the ADMR results observed for our Fe films can be well explained by AHMR. Including the conventional AMR effect [2][3][4][5], GSE [17][18][19], and the AHMR effect [14][15][16] gives a general MR form of…”

“…Recently, the discovery of several types of MR effects with different origins has triggered renewed interest in spin-dependent MR. These MR effects include spin Hall magnetoresistance (SMR) in FM/heavy metal bilayers [6][7][8], Rashba-Edelstein magnetoresistance (REMR) in Bi/Ag/CoFeB [9], spin-orbit magnetoresistance (SOT-MR) in a YIG/Pt/Cu system [10], Hanle magnetoresistance (HMR) in HMs [11], anisotropic interfacial magnetoresistance (AIMR) in Pt/Co/Pt [12,13], and anomalous Hall MR (AHMR) in single FM layers [14][15][16]. In a particular magnetic system, several types of MR could coexist.…”

“…Recently, Yang et al [16] reported that the anomalous Hall effect (AHE) in FM films can break the symmetry between y and z directions and generate an additional MR effect with the relation of ρ z > ρ y , which is named as AHMR. AHMR has been explained by the spin accumulation, subsequent spin backflow, and spin-charge conversion inside the magnetic film [14][15][16]. The AHE is a common spin-dependent transport property in FM materials, but it still requires further experimental investigation to confirm whether AHMR is a general phenomenon in metallic FM materials.…”

Coupled Dynamics of Magnetizations in Spin-Hall Oscillators via Spin-Current Injection

“…The pure spin Hall angle in the nonmagnet and the spin polarization of the conductivity in the ferromagnet are ϑ and β, respectively. The quantity g * is related to the F/N interface resistance, whereas g N /S with the F/N cross section area S is defined as g N /S = hσ N /(2e 2 λ N ) [30]. The origin of the z axis locates at the F/N interface.…”

Synchronization of Spin Torque Oscillators through Spin Hall Magnetoresistance

“…where m k = (m kx , m ky , m kz ) is the unit vector pointing in the magnetization direction in the F k layer. The dimensionless coefficients, χ and χ ′ , in metallic ferromagnetic/nonmagnetic bilayers are given by [27,29,30]…”