Dynamic magnetic susceptibility and electrical detection of ferromagnetic resonance

Abstract

The dynamic magnetic susceptibility of magnetic materials near ferromagnetic resonance (FMR) is very important in interpreting dc-voltage obtained in an electrical detection of FMR. Based on the causality principle and the assumption that the usual microwave absorption lineshape around FMR is Lorentzian, general forms of dynamic magnetic susceptibility of an arbitrary sample and the corresponding dc-voltage lineshapes of the electrical detection of FMR are obtained. Our main findings are: 1) The dynamic magnetic susceptibility is not a Polder tensor for a material with an arbitrary magnetic anisotropy. Two off-diagonal matrix elements of the tensor near FMR are not in general opposite to each other. However, the linear response coefficient of the magnetization to the total radio frequency (rf) field (sum of the applied external rf field and the internal rf field due to the precessing magnetization, a quantity cannot be measured directly) is a Polder tensor. This may explain why two off-diagonal susceptibility matrix elements are always assumed to be opposite to each other in analyses.2) The frequency dependence of dynamic magnetic susceptibility near FMR is fully characterized by six real numbers while its field dependence is fully characterized by seven real numbers. 3) A recipe of how to determine these numbers by standard microwave absorption measurements for a sample with an arbitrary magnetic anisotropy is proposed. Our results allow one to unambiguously separate the contribution of the anisotropic magnetoresistance to dc-voltage signals from that of the anomalous Hall effect. With these results, one can reliably extract the information of spin pumping and the inverse spin Hall effect, and determine the spin-Hall angle. 4) The field-dependence of the susceptibility matrix elements at a fixed microwave frequency may have several peaks when the effective magnetic field is not a monotonic function of the applied magnetic field. In contrast, the frequency-dependence of the susceptibility matrix elements at a fixed applied magnetic field has only one FMR peak. Furthermore, in the case that resonance frequency is not sensitive to the externally applied static magnetic field, the field dependence of matrix elements of the dynamic magnetic susceptibility, as well as dc-voltage, may have another non-resonance broad peak. Thus, one should be careful in interpreting observed peaks.

The origin of spin current in YIG/nonmagnetic metal multilayers at ferromagnetic resonance

“…However, as plotted in Fig. 2a, it is clear that most spectra consist of a superposition of a Lorentz-and a dispersive-type resonance lineshape 26,27 For a given θ, the DC-voltage curve was fitted to Eq. Thus it shows that substantial amount of the DC-voltage came from the AMR and AHE of a ferromagnetic metal that resulted in an asymmetric lineshape, and the only possibility is that the Pt surface in contact with YIG was magnetized and generated a spin rectification voltage 28 .…”

“…Angular dependence:The DC-voltage from ISHE, AMR and/or AHE of a ferromagnetic metal near the FMR has a symmetric Lorentz-lineshape and an asymmetric dispersive-lineshape26,27,0 and Γ are respectively the resonance field and resonant peak width. U sym and U asy are the voltages of the symmetry and asymmetry components of DC-voltage that depend on angle θ as 39 sin(2 ) sin( ) U cos( ) are the voltages due to the spin rectification.…”

A theory for anisotropic magnetoresistance in materials with two vector order parameters

“…In the case of polycrystalline sample, n is absent, and Eq. ( 2) reduce to the well known generalized Ohm's law of polycrystalline materials [16,27] with only ρ 1 , R 1 and A 1 terms. R 1 -term and A 1 -term are the usual anomalous Hall effect and AMR and PHR, respectively.…”

“…Thus, a proper linear combination of Ricci tensor and Ricci curvature (scaler) multiplying metric tensor is equal to the energy-momentum tensor. The method was also used in condensed matter physics for Ohm's laws in ferromagnet [27] and for the anomalous spin-Hall effects (ASHEs) and anomalous inverse spin-Hall effects (AISHEs) [29,30], which is also called magnetization dependent spin-Hall and inverse spin-Hall effects. Interestingly, our analysis predicts that ρ xx (θ = 180 0 ) = ρ xx (θ = 0 0 ) in general.…”

Universal field dependence of magnetic resonance near zero frequency

“…This usually happens when the magnetization reorients itself to find new equilibrium states. 7,8 For example, the antiferromagnetic spin flops from an easy-axis to a hard-plane when the applied field is strong enough and this gives rise to the zero resonance frequency at the transition point. 9 According to the modern theory of phase transitions, 10 the change of the ground state of a system in the thermodynamic limit may be accompanied by critical phenomena and there exists a set of critical exponents characterizing the scaling behavior of the physical quantities near the transition point.…”