Quantifying spin-torque efficiency and magnetoresistance coefficient by microwave photoresistance in spin-torque ferromagnetic resonance

During the spin-torque ferromagnetic resonance (ST-FMR) measurement, the magnetization precession driven by the microwave field yields the radio frequency (rf) oscillating magnetoresistance and its time-averaged change (photoresistance). Here, we find that the strength of photoresistance can be directly determined by using dc bias current Idc modulating the symmetric component VS of the ST-FMR voltage spectrum. By measuring the angular dependence of photoresistance, we can quantify the in-plane and out-of-plane precession angles of ST-FMR, the actual rf current distribution in the magnetic and non-magnetic sublayers, and the magnitude of spin-torque and various magnetoresistance coefficients. These experimentally obtained values and analysis methods can more accurately quantify the spin-torque efficiency of both in-plane and out-of-plane spin polarizations by self-consistent calculation of the precession angle without harsh assumptions. And, we further confirm this universal method in three spintronic systems: the prototypical Pt/Py bilayer with anisotropic magnetoresistance (AMR), Py/Cu/Co20Tb80 spin valve trilayer with AMR and giant magnetoresistance, and [Co/Ni]3/Co/Pt multilayer with AMR and anisotropic interface magnetoresistance. This method eliminates potential deviation in calculating spin-torque efficiency by previously reported line shape analyzation and linewidth modulation methods of the ST-FMR technique and significantly extends its application range in characterizing spintronic materials and nanodevices.