Analytical expression for the harmonic Hall voltages in evaluating spin orbit torques

Solid understanding of current induced torques is key to the development of current and voltage controlled magnetization dynamics in ultrathin magnetic heterostructures. A versatile technique is needed to evaluate such torques in various systems. Here we examine the adiabatic (low frequency) harmonic Hall voltage measurement that has been recently developed to study current induced effective field that originate from the spin orbit effects. We analytically derive a form that can be used to evaluate the harmonic Hall voltages and extract relevant parameters in two representative systems, i.e. out of plane and in-plane magnetized systems. Contributions from the anomalous Hall and planar Hall effects are considered

Current-Induced Instability of a Perpendicular Ferromagnet in Spin Hall Geometry

We develop a theoretical formula of spin Hall torque in the presence of two ferromagnets. While the direction of the conventional spin Hall torque always points to the in-plane direction, the present system enables to manipulate the torque direction acting on one magnetization by changing the direction of another magnetization. Based on the diffusion equation of the spin accumulation and the Landauer formula, we derive analytical formula of the spin Hall torque. The present model provides a solution to switch a perpendicular ferromagnet deterministically at zero field using the spin Hall effect.Comment: 5 pages, 2 figures, conference proceeding of Joing MMM/Intermag conference 201

Unidirectional planar Hall voltages induced by surface acoustic waves in ferromagnetic thin films

The electromotive forces induced by surface acoustic waves (SAWs) are investigated in ferromagnetic thin films. CoFeB thin films deposited on LiNbO$_3$ substrates are patterned into Hall-bars to study the acoustoelectric transport properties of the device. The longitudinal and transverse dc voltages that develop in the Hall bars, which are parallel and orthogonal to the flow of the SAW, respectively, are measured under application of an in-plane magnetic field. The longitudinal voltage scales linearly with the SAW power and reverses its polarity upon changing the direction to which the SAW propagates, suggesting generation of a dc acoustic current via the SAW excitation. The magnetic field has little influence on the acoustic current. In contrast, the SAW induced transverse voltage shows significant dependence on the relative angle between the magnetic field and the SAW propagation direction. Such field angle dependent voltage resembles that of the planar Hall voltage induced by electric current. Interestingly, the angle dependent acoustic transverse voltage does not depend on the SAW propagation direction. Moreover, the magnitude of the equivalent angle dependent acoustic transverse resistance is more than one order of magnitude larger than that of the planar Hall resistance. These results show the unique acoustoelectric transport properties of ferromagnetic thin films

Critical current destabilizing perpendicular magnetization by the spin Hall effect

The critical current needed to destabilize the magnetization of a perpendicular ferromagnet via the spin Hall effect is studied. Both the dampinglike and fieldlike torques associated with the spin current generated by the spin Hall effect is included in the Landau-Lifshitz-Gilbert equation to model the system. In the absence of the fieldlike torque, the critical current is independent of the damping constant and is much larger than that of conventional spin torque switching of collinear magnetic systems, as in magnetic tunnel junctions. With the fieldlike torque included, we find that the critical current scales with the damping constant as $\alpha^{0}$ (i.e., damping independent),$\alpha$, and $\alpha^{1/2}$ depending on the sign of the fieldlike torque and other parameters such as the external field. Numerical and analytical results show that the critical current can be significantly reduced when the fieldlike torque possesses the appropriate sign, i.e. when the effective field associated with the fieldlike torque is pointing opposite to the spin direction of the incoming electrons. These results provide a pathway to reducing the current needed to switch magnetization using the spin Hall effect.Comment: 12 pages, 8 figure

Tunable inertia of chiral magnetic domain walls

The time it takes to accelerate an object from zero to a given velocity depends on the applied force and the environment. If the force ceases, it takes exactly the same time to completely decelerate. A magnetic domain wall (DW) is a topological object that has been observed to follow this behavior. Here we show that acceleration and deceleration times of chiral Neel walls driven by current are different in a system with low damping and moderate Dzyaloshinskii-Moriya (DM) exchange constant. The time needed to accelerate a DW with current via the spin Hall torque is much faster than the time it needs to decelerate once the current is turned off. The deceleration time is defined by the DM exchange constant whereas the acceleration time depends on the spin Hall torque, enabling tunable inertia of chiral DWs. Such unique feature of chiral DWs can be utilized to move and position DWs with lower current, key to the development of storage class memory devices

Interference induced enhancement of magneto-optical Kerr effect in ultrathin magnetic films

We have studied the magneto-optical spectra of ultrathin magnetic films deposited on Si substrates coated with an oxide layer (SiOx). We find that the Kerr rotation angle and the ellipticity of ~1 nm thick CoFeB thin films, almost transparent to visible light, show a strong dependence on the thickness of the SiOx layer. The Kerr signal from the 1 nm CoFeB thin film can be larger than that of ~100 nm thick CoFeB films for a given SiOx thickness and light wavelength. The enhancement of the Kerr signal occurs when optical interference takes place within the SiOx layer. Interestingly, under such resonance condition, the measured Kerr signal is in some cases larger than the estimation despite the good agreement of the measured and calculated reflection amplitude. We infer the discrepancy originates from interface states that are distinct from the bulk characteristics. These results show that optical interference effect can be utilized to study the magneto-optical properties of ultrathin films

Microwave assisted resonant domain wall nucleation in permalloy nanowires

We have designed a system to study microwave assisted domain wall nucleation in permalloy nanowires. We find a substantial decrease in the nucleation field when microwave fields are applied, in comparison to pulse fields. A clear resonance peak is observed in the frequency dependence of the nucleation field, which coincides with the uniform mode ferromagnetic resonance frequency. Owing to the well-defined nucleation process, the switching field distribution is small in contrast to previous reports. Our results show that localized microwave field provides an efficient tool for injecting domain walls into magnetic nanowires

Spin Hall magnetoresistance in metallic bilayers

Spin Hall magnetoresistance (SMR) is studied in metallic bilayers that consist of heavy metal (HM) layer and a ferromagnetic metal (FM) layer. We find nearly a ten-fold increase of SMR in W/CoFeB compared to previously studied HM/ferromagnetic insulator (FI) systems. The SMR increases with decreasing temperature despite the negligible change in the W layer resistivity with temperature. A model is developed to account for the absorption of the longitudinal spin current to the FM layer, one of the key characteristics of a metallic ferromagnet. We find that the model not only quantitatively describes the HM layer thickness dependence of SMR, allowing accurate estimation of the spin Hall angle and the spin diffusion length of the HM layer, but also can account for the temperature dependence of SMR by assuming a temperature dependent spin polarization of the FM layer. These results illustrate the unique role a metallic ferromagnetic layer plays in defining spin transmission across the HM/FM interface

Domain wall resistance in CoFeB-based heterostructures with interface Dzyaloshinskii-Moriya interaction

We have studied the domain wall resistance in W/Ta/CoFeB/MgO heterostructures. The Ta layer thickness is varied to control the type of domain walls via changes in the interfacial Dzyaloshinskii Moriya interaction. We find a nearly constant domain wall resistance against the Ta layer thickness. Adding contributions from the anisotropic magnetoresistance, spin Hall magnetoresistance and anomalous Hall effect describe well the domain wall resistance of the thick Ta layer films. However, a discrepancy remains for the thin Ta layer films wherein chiral N\'eel-like domain walls are found. These results show the difficulty of studying the domain wall type from resistance measurements

Optical detection of spin orbit torque and current induced heating

We have studied spin orbit torque in heavy metal (HM)/ferromagnetic metal (FM) bilayers using magneto-optical Kerr effect. A double modulation technique is developed to separate signals from spin orbit torque and Joule heating. At a current density of ~1x10$^{10}$ A/m$^2$, we observe optical signals that scale linearly and quadratically with the current density, both in similar magnitude. The spin orbit torque estimated using this technique is consistent with that evaluated using spin transport measurements. We find that changes in the refractive index of the film with temperature is the main source of the heating induced signal