Out-of-Plane Torque Influence on Magnetization Switching and Susceptibility in Magnetic Multilayers

Based on both the spin diffusion equation and the Landau-LlTshitz-Gilbert （LLG） equation, we demonstrate the influence of out-of-plane spin torque on magnetization switching and susceptibility in a magnetic multilayer system. The variation of spin accumulation and local magnetization with respect to time are studied in the magnetization reversal induced by spin torque. We also research the susceptibility subject to a microwave magnetic field, which is compared with the results obtained without out-of-plane torque.     

Nanomagnet coupled to quantum spin Hall edge: An adiabatic quantum motor

The precessing magnetization of a magnetic islands coupled to a quantum spin Hall edge pumps charge along the edge. Conversely, a bias voltage applied to the edge makes the magnetization precess. We point out that this device realizes an adiabatic quantum motor and discuss the efficiency of its operation based on a scattering matrix approach akin to Landauer–Büttiker theory. Scattering theory provides a microscopic derivation of the Landau–Lifshitz–Gilbert equation for the magnetization dynamics of the device, including spin-transfer torque, Gilbert damping, and Langevin torque. We find that the device can be viewed as a Thouless motor, attaining unit efficiency when the chemical potential of the edge states falls into the magnetization-induced gap. For more general parameters, we characterize the device by means of a figure of merit analogous to the ZT value in thermoelectrics.     

稀磁半导体(Ga,Mn)As薄膜激光诱导超快磁化动力学过程拟合方法探究

本文对稀磁半导体(Ga, Mn)As薄膜中超快激光诱导磁化动力学响应信号的不同拟合方法进行了对比分析. 通过Landau-Lifshitz-Gilbert(LLG)方程的数值拟合发现, 由于薄膜平面内和平面外磁光响应强度不同, 磁矢量三维进动的叠加可以导致多个频率振动模式的假象. 当使用高于(Ga, Mn)As带边的能量激发时, 磁化进动的磁光响应信号中叠加着来自光极化载流子的响应, 此时单纯利用LLG方程对薄膜整体磁化动力学过程拟合应谨慎使用. 本工作为正确分析和理解脉冲激光对(Ga, Mn)As铁磁性的超快调控提供了拟合方法上的指导.     

Magnetization noise in magnetoelectronic nanostructures

By scattering theory we show that spin current noise in normal electric conductors in contact with nanoscale ferromagnets increases the magnetization noise by means of a fluctuating spin-transfer torque. Johnson-Nyquist noise in the spin current is related to the increased Gilbert damping due to spin pumping, in accordance with the fluctuation-dissipation theorem. Spin current shot noise in the presence of an applied bias is the dominant contribution to the magnetization noise at low temperatures.     

面内形状各向异性能对自旋转矩振荡器零场振荡特性的影响

利用Landau-Lifshitz-Gilbert-Slonczewski方程, 在理论上研究了由磁矩垂直于膜面的自由层和磁矩平行于膜面的极化层组成的自旋转矩振荡器的振荡特性. 数值结果表明面内的形状各向异性能, 可以使自旋转矩振荡器在无磁场情形下产生自激振荡. 此特性可以用能量平衡方程解释, 即面内形状各向异性能可以导致系统中自旋转矩提供的能量与阻尼过程所消耗的能量之间的平衡. 特别是, 面内的形状各向异性能越大, 自旋转矩振荡器的可操控电流范围越大, 并且产生微波信号的频率越大, 但其阈值电流几乎不变.     

Reprint of : Nanomagnet coupled to quantum spin Hall edge: An adiabatic quantum motor

The precessing magnetization of a magnetic islands coupled to a quantum spin Hall edge pumps charge along the edge. Conversely, a bias voltage applied to the edge makes the magnetization precess. We point out that this device realizes an adiabatic quantum motor and discuss the efficiency of its operation based on a scattering matrix approach akin to Landauer–Büttiker theory. Scattering theory provides a microscopic derivation of the Landau–Lifshitz–Gilbert equation for the magnetization dynamics of the device, including spin-transfer torque, Gilbert damping, and Langevin torque. We find that the device can be viewed as a Thouless motor, attaining unit efficiency when the chemical potential of the edge states falls into the magnetization-induced gap. For more general parameters, we characterize the device by means of a figure of merit analogous to the ZT value in thermoelectrics.     

Spin wave dynamics and the determination of intrinsic damping in locally excited Permalloy thin films

Time-resolved scanning Kerr effect microscopy has been used to study magnetization dynamics in Permalloy thin films excited by transient magnetic pulses generated by a micrometer-scale transmission line structure. The results are consistent with magnetostatic spin wave theory and are supported by micromagnetic simulations. Magnetostatic volume and surface spin waves are measured for the same specimen using different bias field orientations and can be accurately calculated by k-space integrations over all excited plane wave components. A single damping constant of Gilbert form is sufficient to describe both scenarios. The nonuniform pulsed field plays a key role in the spin wave dynamics, with its Fourier transform serving as a weighting function for the participating modes. The intrinsic Gilbert damping parameter alpha is most conveniently measured when the spin waves are effectively stationary.     

Dynamics of magnetization in ferromagnet with spin-transfer torque

We review our recent works on dynamics of magnetization in ferromagnet with spin-transfer torque. Driven by constant spin-polarized current, the spin-transfer torque counteracts both the precession driven by the effective field and the Gilbert damping term different from the common understanding. When the spin current exceeds the critical value, the conjunctive action of Gilbert damping and spin-transfer torque leads naturally the novel screw-pitch effect characterized by the temporal oscillation of domain wall velocity and width. Driven by space- and time-dependent spin-polarized current and magnetic field, we expatiate the formation of domain wall velocity in ferromagnetic nanowire. We discuss the properties of dynamic magnetic soliton in uniaxial anisotropic ferromagnetic nanowire driven by spin-transfer torque, and analyze the modulation instability and dark soliton on the spin wave background, which shows the characteristic breather behavior of the soliton as it propagates along the ferromagnetic nanowire. With stronger breather character, we get the novel magnetic rogue wave and clarify its formation mechanism. The generation of magnetic rogue wave mainly arises from the accumulation of energy and magnons toward to its central part. We also observe that the spin-polarized current can control the exchange rate of magnons between the envelope soliton and the background, and the critical current condition is obtained analytically. At last, we have theoretically investigated the current-excited and frequency-adjusted ferromagnetic resonance in magnetic trilayers. A particular case of the perpendicular analyzer reveals that the ferromagnetic resonance curves, including the resonant location and the resonant linewidth, can be adjusted by changing the pinned magnetization direction and the direct current. Under the control of the current and external magnetic field, several magnetic states, such as quasi-parallel and quasi-antiparallel stable states, out-of-plane precession, and bistable states can be realized. Th     

Mapping the Monte Carlo scheme to Langevin dynamics: a Fokker-Planck approach

We propose a general method of using the Fokker-Planck equation (FPE) to link the Monte Carlo (MC) and the Langevin micromagnetic schemes. We derive the drift and diffusion FPE terms corresponding to the MC method and show that it is analytically equivalent to the stochastic Landau-Lifshitz-Gilbert (LLG) equation of Langevin-based micromagnetics. Subsequent results such as the time-quantification factor for the Metropolis MC method can be rigorously derived from this mapping equivalence. The validity of the mapping is shown by the close numerical convergence between the MC method and the LLG equation for the case of a single magnetic particle as well as interacting arrays of particles. We also find that our Metropolis MC method is accurate for a large range of damping factors alpha, unlike previous time-quantified MC methods which break down at low alpha, where precessional motion dominates.     

Spin-torque influence on the high-frequency magnetization fluctuations in magnetic tunnel junctions

Voltage noise measurements were performed in the 3-7 GHz frequency range on magnetic tunnel junctions biased with a dc current. Magnetic noise associated with ferromagnetic resonance excitations is either amplified or reduced depending on the direction of the bias current. This effect is interpreted as the influence of spin transfer torque on the magnetization fluctuations and described using Gilbert dynamics equation including spin transfer torque and effective field terms.     

Electron theory of fast and ultrafast dissipative magnetization dynamics

For metallic magnets we review the experimental and electron-theoretical investigations of fast magnetization dynamics (on a timescale of ns to 100 ps) and of laser-pulse-induced ultrafast dynamics (few hundred fs). It is argued that for both situations the dominant contributions to the dissipative part of the dynamics arise from the excitation of electron-hole pairs and from the subsequent relaxation of these pairs by spin-dependent scattering processes, which transfer angular momentum to the lattice. By effective field theories (generalized breathing and bubbling Fermi-surface models) it is shown that the Gilbert equation of motion, which is often used to describe the fast dissipative magnetization dynamics, must be extended in several aspects. The basic assumptions of the Elliott-Yafet theory, which is often used to describe the ultrafast spin relaxation after laser-pulse irradiation, are discussed very critically. However, it is shown that for Ni this theory probably yields a value for the spin-relaxation time T(1) in good agreement with the experimental value. A relation between the quantity α characterizing the damping of the fast dynamics in simple situations and the time T(1) is derived.     

Spin dynamics in (III,Mn)V ferromagnetic semiconductors: the role of correlations

We address the role of correlations between spin and charge degrees of freedom on the dynamical properties of ferromagnetic systems governed by the magnetic exchange interaction between itinerant and localized spins. For this we introduce a general theory that treats quantum fluctuations beyond the random phase approximation based on a correlation expansion of the Green's function equations of motion. We calculate the spin susceptibility, spin-wave excitation spectrum, and magnetization precession damping. We find that correlations strongly affect the magnitude and carrier concentration dependence of the spin stiffness and magnetization Gilbert damping.     

Current induced domain wall motion in GaMnAs close to the Curie temperature

Domain wall dynamics produced by spin transfer torques is investigated in (Ga, Mn)As ferromagnetic semiconducting tracks with perpendicular anisotropy, close to the Curie temperature. The domain wall velocities are found to follow a linear flow regime which only slightly varies with temperature. Using the D?ring inequality, boundaries of the spin polarization of the current are deduced. A comparison with the predictions of the mean field k·p theory leads to an estimation of the carrier density whose value is compatible with results published in the literature. The spin polarization of the current and the magnetization of the magnetic atoms present similar temperature variations. This leads to a weak temperature dependence of the spin drift velocity and thus of the domain wall velocity. A combined study of field- and current-driven motion and deformation of magnetic domains reveals a motion of domain walls in the steady state regime without transition to the precessional regime. The ratio between the non-adiabatic torque β and the Gilbert damping factor α is shown to remain close to unity.     

Impact of magnetic surface anisotropy on the precessional switching of magnetization in Pt-alloy nanofilms

Precessional switching of magnetization in CoPt and FePt nanofilms is investigated by solving the Landau–Lifshitz–Gilbert (LLG) equation analytically and numerically. Switching in these films occurs only above a critical value of the magnetic field, and it further depends on the magnetocrystalline anisotropy and saturation magnetization of the film. The presence of magnetic surface anisotropy in these films reduces the switching time significantly. Also, the switching time in the case of Pt-alloys of Co and Fe is low compared to that in the case of pure Co and Fe films.     

Spin orbit torques in Pt-based heterostructures with van der Waals interface

Spin orbit torques(SOTs) in ferromagnet/heavy-metal heterostructures have provided great opportunities for efficient manipulation of spintronic devices. However, deterministically field-free switching of perpendicular magnetization with SOTs is forbidden because of the global two-fold rotational symmetry in conventional heavy-metal such as Pt. Here,we engineer the interface of Pt/Ni heterostructures by inserting a monolayer MoTe_2 with low crystal symmetry. It is demonstrated that the spin orbit efficiency, as well as the out-of-plane magnetic anisotropy and the Gilbert damping of Ni are enhanced, due to the effect of orbital hybridization and the increased spin scatting at the interface induced by MoTe_2.Particularly, an out-of-plane damping-like torque is observed when the current is applied perpendicular to the mirror plane of the MoTe_2 crystal, which is attributed to the interfacial inversion symmetry breaking of the system. Our work provides an effective route for engineering the SOT in Pt-based heterostructures, and offers potential opportunities for van der Waals interfaces in spintronic devices.     

Critical current density for spin transfer torque switching with composite free layer structure

Critical current density of composite free layer (CFL) in magnetic tunneling junction is investigated. CFL consists of two exchange coupled ferromagnetic layers, where the coupling is parallel or anti-parallel. Instability condition of the CFL under the spin transfer torque, which is related with critical current density, is obtained by analytic spin wave excitation model and confirmed by macro-spin Landau–Lifshitz–Gilbert equation. The critical current densities for the coupled two identical layers are investigated with various coupling strengths, and spin transfer torque efficiencies.     

Broad-Band FMR Linewidth of Co_2MnSi Thin Films with Low Damping Factor:The Role of Two-Magnon Scattering

The low Gilbert damping factor,which is usually measured by ferromagnetic resonance,is crucial in spintronic applications.Two-magnon scattering occurs when the orthogonality of the ferromagnetic resonance mode and other degenerate spin wave modes was broken by magnetic anisotropy,voids,second phase,surface defects,etc.,which is important in analysis of ferromagnetic resonance linewidth.Direct fitting to linewidth with Gilbert damping is advisable only when the measured linewidth is a linear function of measuring frequency in a broad band measurement.We observe the nonlinear ferromagnetic resonance linewidth of Co_2MnSi thin films with respect to measuring frequency in broad band measurement.Experimental data could be well fitted with the model including two-magnon scattering with no fixed parameters.The fitting results show that two-magnon scattering results in the nonlinear linewidth behavior,and the Gilbert damping factor is much smaller than reported ones,indicating that our Co_2 MnSi films are more suitable for the applications of spin transfer torque.     

垂直磁各向异性自旋阀结构中的铁磁共振

本文在理论上研究了垂直磁各向异性自旋阀结构中磁场激发和调节的铁磁共振. 通过线性展开包含自旋转移矩项的Landau-Lifshitz-Gilbert方程,获得了磁场激发和调节的铁磁共振谱. 给出了共振线宽、共振频率和共振磁场随直流电流密度大小和方向以及直流磁场的变化关系. 通过调节直流电流密度的大小和方向,系统的有效阻尼可以达到最小. 关键词： 自旋阀 自旋转移矩 垂直磁各向异性 铁磁共振     

Zero-Magnetic-Field Oscillation of Spin Transfer Nano-Oscillator with a Second-Order-Perpendicular-Anisotropy Free Layer

Tie zero-magnetic-field oscillation behavior of spin torque nano-oscillator(STNO) with a perpendicularly magnetized free layer with second-order uniaxial anisotropy is studied theoretically based on the Landau-LifshitzGilbert-Slonczewski equation.It is demonstrated numerically that the second-order uniaxial anisotropy plays a significant role in the occurrence of a zero-magnetic-field steady-state precession,which can be understood in terms of the energy balance between the energy accumulation due to the spin torque and the energy dissipation due to the Gilbert damping.In particular,a relatively large zero-magnetic-field-oscillation current region,in which the corresponding microwave frequency is increased while the threshold current still maintains an almost constant value,can be obtained by modulating the second-order uniaxial anisotropy of the free layer.These results suggest a tunable zero-magnetic-Reld STNO,and it may be a promising configuration for STNO's applications in future wireless communications.