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.     

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.     

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.     

Radiation-spin interaction, Gilbert damping, and spin torque

Magnetization relaxation processes, which are represented by the Gilbert damping term and the spin torque term in the Landau-Lifshitz-Gilbert (LLG) equation, are described by the radiation-spin interaction (RSI), where the radiation field is produced by magnetization precessional motion itself. It is shown that the LLG equation including the Gilbert damping term and the spin torque term is derived from the spin Hamiltonian containing the RSI. The derivation of the LLG equation is given in a self-consistent method. It is also shown that, according to RSI, the magnitude of the magnetization vector deviates from the magnetization saturation with the order of O(alpha(2)), where alpha is the Gilbert damping parameter.     

Time resolved magnetization dynamics of ultrathin Fe(001) films: spin-pumping and two-magnon scattering

The time-resolved magnetic response of ultrathin epitaxial Fe(001) films grown on GaAs(001) and covered by Au, Pd, and Cr capping layers was investigated by time and spatially resolved Kerr effect measurements. The magnetization was excited by an in-plane magnetic field pulse using the transient internal field generated at a Schottky barrier while the wavelength of the excitation (resonant mode) was roughly 4 microm. Each of the three cap layers affected the spin relaxation in a unique way. Au cap layers resulted in the bulk Gilbert damping of the Fe film. Pd cap layers caused an additional Gilbert damping due to spin-pump or spin-sink effects. Cr cap layers lead to a strong extrinsic damping which can be described by two-magnon scattering. In this case the strength of the extrinsic damping can be controlled by a field induced shift of the spin wave manifold with respect to the excited k vector.     

Enhanced gilbert damping in thin ferromagnetic films

The precession of the magnetization of a ferromagnet is shown to transfer spins into adjacent normal metal layers. This "pumping" of spins slows down the precession corresponding to an enhanced Gilbert damping constant in the Landau-Lifshitz equation. The damping is expressed in terms of the scattering matrix of the ferromagnetic layer, which is accessible to model and first-principles calculations. Our estimates for permalloy thin films explain the trends observed in recent experiments.     

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.     

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.     

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.     

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.     

Brownian motion of massive skyrmions in magnetic thin films

We report on the thermal effects on the motion of current-driven massive magnetic skyrmions. The reduced equation for the motion of skyrmion has the form of a stochastic generalized Thiele’s equation. We propose an ansatz for the magnetization texture of a non-rigid single skyrmion that depends linearly with the velocity. By using this ansatz it is found that the skyrmion mass tensor is closely related to intrinsic skyrmion parameters, such as Gilbert damping, skyrmion-charge and dissipative force. We have found an exact expression for the average drift velocity as well as the mean-square velocity of the skyrmion. The longitudinal and transverse mobility of skyrmions for small spin-velocity of electrons is also determined and found to be independent of the skyrmion mass.     

Unifying ultrafast magnetization dynamics

We present a microscopic model that successfully explains the ultrafast equilibration of magnetic order in ferromagnetic metals at a time scale tau(M) of only a few hundred femtoseconds after pulsed laser excitation. It is found that tau(M) can be directly related to the so-called Gilbert damping factor sigma that describes damping of GHz precessional motion of the magnetization vector. Independent of the spin-scattering mechanism, an appealingly simple equation relating the two key parameters via the Curie temperature T(C) is derived, tau(M) approximately c(0)h/k(B)T(C)sigma, with h and k(B) the Planck and Boltzmann constants, respectively, and the prefactor c(0) approximately 1/4). We argue that phonon-mediated spin-flip scattering may contribute significantly to the sub-ps response.     

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.     

Study on the Gilbert damping of polycrystalline YIG films with different capping layers

This paper describes the effect of 5-nm thick platinum (Pt), aluminum (Al) and silicon oxide (SiO_x) capping layers on the static and dynamic magnetic properties of 400-nm thick polycrystalline YIG films deposited on a Pt buffer layer. Both static and dynamic magnetic properties of Pt capped YIG film are totally different among all YIG films. Namely, the squareness of the magnetization curve for Pt capped YIG film increases, indicating that Pt capped YIG film is magnetically softer than other YIG films. Interestingly, the effective Gilbert damping parameter of Pt capped YIG films is about four times as large as those of other YIG films, and its value is approximately 9.52 × 10⁻⁴. However, the value of Gilbert damping is 2.55 × 10⁻⁴, 3.46 × 10⁻⁴ and 3.85 × 10⁻⁴ respectively for no capping, SiOx capping and Al capping samples respectively. This huge change in Gilbert damping parameter is mainly originating from the spin pumping effect, which arises at the interface of a material having strong spin orbit interaction such as Pt. Moreover, the enourmous increase in the value of effective anisotropic field and decrese in effective saturation magnetization indicates interface anisotropy is induced in Pt capped sample. These results suggest that the static and dynamic magnetic properties of YIG film can be controlled by selecting an appropriate capping layer.     

Thickness dependent magnetization dynamics of perpendicular anisotropy Co/Pd multilayer films

We present the measurements of the picosecond magnetization dynamics of Co/Pd multilayer films. The dynamic magnetization properties of sputtered multilayer films were analyzed as a function of Co layer thicknesses and applied bias field. Both the eigenfrequencies of the magnetization precession in the multilayers and the associated Gilbert damping exhibit extreme sensitivity to the magnetic layer thickness on an atomic monolayer scale. The eigenfrequency increases more than threefold when the Co thickness decreases from 7.5 to 2.8 Å, mainly due to the changes in effective saturation magnetization and perpendicular anisotropy constant. A concomitant 2.6-fold increase in the damping of the oscillations is observed and attributed to stronger interface dissipation in thinner Co layers. In addition, we introduce a quasi-1D micromagnetic model in which the multilayer stack is described as a one-dimensional chain of macrospins that represent each Co layer. This model yields excellent agreement with the observed resonance frequencies without any free parameters, while being much simpler and faster than full 3D micromagnetic modeling.     

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     

Ab initio calculation of the Gilbert damping parameter via the linear response formalism

A Kubo-Greenwood-like equation for the Gilbert damping parameter α is presented that is based on the linear response formalism. Its implementation using the fully relativistic Korringa-Kohn-Rostoker band structure method in combination with coherent potential approximation alloy theory allows it to be applied to a wide range of situations. This is demonstrated with results obtained for the bcc alloy system Fe(1-x)Co(x) as well as for a series of alloys of Permalloy with 5d transition metals. To account for the thermal displacements of atoms as a scattering mechanism, an alloy-analogy model is introduced. The corresponding calculations for Ni correctly describe the rapid change of α when small amounts of substitutional Cu are introduced.     

Dynamics of vortexlike domain walls in triaxial magnetic films with the Goss orientation of the surface

The stationary dynamics of vortexlike domain walls in films with three magnetic axes and Goss orientation of the surface is studied for the first time with a micromagnetic method that exactly takes into account all basic types of interaction (including dipole-dipole interaction). Consideration is carried out using a 2D model of magnetization distribution by numerically solving Landau and Lifshitz’s nonlinear equations with attenuation in the Gilbert form. Dynamic configurations of domain walls are established, and the dependences of the domain wall velocity on an applied magnetic field, damping parameter, and magnetic film thickness are found.     

磁环中非晶丝的阻抗效应分析

依据Landau-Lifshitz阻尼项和Gilbert阻尼项的磁矩转动方程,提出统一形式的磁化率张量表达式.基于等效磁导率将非晶丝中各向异性的电磁场求解问题转化为等效的各向同性问题,进而分析了套在绝缘磁环或导电磁环中非晶丝的阻抗.采用基于有限元的数值方法仿真磁环中非晶丝的阻抗,仿真结果验证了理论分析结论.理论分析和仿真实验均表明,外磁体的附加阻抗将严重降低阻抗变化率,破坏巨磁阻抗特性.为此,提出采用回路形式降低附加阻抗的方法,并基于仿真实验验证了该方法的有效性. 关键词： 巨磁阻抗效应 非晶材料 Maxwell方程 有限元     

Ferromagnetic resonance linewidth in exchange-biased ferromagnet/antiferromagnet bilayers with ac field-cooling procedure

Out-of-plane ferromagnetic resonance spectra of Co₂₀Ni₈₀/FeMn bilayers with a ground state consisting of stripe ferromagnetic domains as accommodated by ac field-cooling process were measured and analyzed by the Landau–Lifshitz–Gilbert equation. One weak resonance peak that might be the surface spin-wave was observed beside the main resonance peak when the applied field was perpendicular to the film plane. In order to explain the linewidth, the extrinsic magnetic relaxation must be considered, in addition to the intrinsic Gilbert damping effect and the broadening induced by magnetic inhomogeneity. The characteristic of the extrinsic magnetic relaxation is consistent with the two-magnon scattering model. PACS 75.70.-i; 75.70.Cn; 76.50.+g; 75.30.Gw