Magnetization Dynamics In Ferromagnets Research Articles

Accurate Torque Evaluation in Elongated Ultra-Scaled STT-MRAM Devices

Emerging spin-transfer torque magnetoresistive random access memory (STT-MRAM) is attractive for stand-alone and embedded applications. STT-MRAM is nonvolatile, operates fast, and possesses excellent endurance. STT-MRAM is compatible with CMOS technology and can be integrated during the back-end-of-line process. This makes STT-MRAM promising for automotive and IoT applications, microcontrollers, frame buffer memory, and last level cache. The core of modern STT-MRAM cells consists of a magnetic tunnel junction (MTJ), which is a sandwich of two ferromagnetic (FM) layers separated by a tunnel barrier (TB). The FM layers are referred to as reference layer (RL) and free layer (FL). The magnetization of the RL is fixed, while the magnetization of the FL can be reversed. The use of MTJs with perpendicular magnetic anisotropy (PMA) permits to obtain better scalability and lower switching currents. When the magnetization vectors of the FL and RL are parallel (P), the electrical resistance is lower than when the vectors are anti-parallel (AP), which provides a way to store binary information. Importantly, the switching between these two stable configurations is achieved by purely electrical means.To reduce the footprint and benefit from shape-induced anisotropy, an ultra-scaled MRAM cell with a composite FL made of several elongated ferromagnetic pieces, separated by multiple MgO barriers, was proposed and demonstrated [1]. In elongated FLs, shown in Fig.1a, domain walls or magnetization textures can be generated during switching. In this case, additional spin torques created by the presence of magnetization gradients inside the ferromagnetic parts must be considered. This type of torque is typically modeled by the Zhang-Li expression [2]. If the spin dephasing length correctly describes the coupled charge and spin transport through the device, the expression for bulk torque must be generalized [3].In MTJs, however, there exists another torque acting on a FL close to the interface with MgO. This torque, predicted by Slonczewski [4] and Berger [5], was utilized to flip the magnetization in traditional MTJs with a FL fabricated as a flat and thin disk. It is due to the spin-polarized current coming across the TB from the RL. Electrons tunneling from the RL become spin-polarized. When entering the FL, the spin polarized electrons interact with the magnetization via the exchange interaction. When the magnetization vectors in the RL and FL are not aligned, the spin current components normal to the FL magnetization are quickly absorbed. Due to conservation of the angular momentum, the absorption of the normal component of the spin current results in a torque acting on the FL magnetization in the opposite sense. If the current is sufficiently strong, the magnetization of the FL can be switched between the two stable P and AP configurations relative to the RL.As the Slonczewski torque is localized at the interface and Zhang-Li (ZL) torque is acting in the bulk, the two torques are usually assumed to be independent. However, this is not correct [5]. Although the spin component normal to the FL magnetization is indeed quickly absorbed, the interface-polarization induced spin current parallel to the magnetization propagates into the FL at a longer distance determined by the spin-flipping length. This length is about 10nm in typical FL materials. As the interface-polarization induced spin current hits the spin texture, it modifies the ZL torque value determined by the spin polarization in the bulk. The FL in ultra-scaled MRAM cells contains a TB on both interfaces. Here, we compare the ZL torque acting on the domain wall (Fig.1b) for the case, when the interface polarization at the second TB is lower than the spin polarization in the bulk (Fig.1c) or higher (Fig.1d). It is demonstrated that the torque acting on the domain wall can be enhanced compared to the ZL value for the case of larger interface polarization than spin polarization in the bulk. B. Jinnai, J. Igarashi, K. Watanabe et al. High-performance shape-anisotropy magnetic tunnel junctions down to 2.3 nm, in Proc. IEDM Conf., 2020, pp. 24.6.1-24.6.4, doi: 10.1109/IEDM13553.2020.9371972S. Zhang and Z. Li. Roles of nonequilibrium conduction electrons on the magnetization dynamics of ferromagnets. Phys. Rev. Lett., vol. 93, 127204, 2004 doi: 10.1103/PhysRevLett.93.127204J. C. Slonczewski. Current-driven excitation of magnetic multilayers, J. Magn.Magn. Mater., vol. 159, no. 1, pp. L1 - L7, 1996, doi: 10.1016/0304-8853(96)00062-5L. Berger. Emission of spin waves by a magnetic multilayer traversed by a current, Phys. Rev. B, vol. 54, pp. 9353-9358, 1996, doi: 10.1103/PhysRevB.54.9353S. Fiorentini, M. Bendra, J. Ender et al. Spin and charge drift-diffusion in ultra-scaled MRAM cells, Sci. Rep., vol. 12, 20958, pp.1-13, 2022, doi: 10.1038/s41598-022-25586-4 Figure 1

High-temperature magnetization reversal in the inertial regime

Motivated by the remarkable experimental observation of all-optical femtosecond-scale magnetization reversal at relatively high temperatures, a stochastic inertial Landau-Lifshitz-Gilbert-Bloch (iLLGB) equation is written to describe nonequilibrium magnetization dynamics in ferromagnets at elevated temperatures and at short enough timescales that an inertial effect manifests. The effect of thermal agitations is described by a Fokker-Planck equation derived from the iLLGB equation including the longitudinal relaxation effect, which is solved with perturbation theory valid at elevated temperatures. Considering a uniaxially symmetric ferromagnet with uniaxial anisotropy, a thermal diffusion-driven exponential mode and alternating field-driven nutation mode of stable magnetization reversal are identified. Our theory proposes a magnetization reversal mechanism based entirely on transfer of angular momentum to the local magnetization, but which takes into account thermal fluctuations and inertial effect at the same time. The theory explains several key observations in all-optical magnetization reversal experiments; the absence of the need for a static field, the subpicosecond switching timescale, the relative roles of thermal and field effects, and the relevance of circularly polarized light. Our results have direct implications for magnetic recording devices operating close to room temperatures and in the ultrafast regime.

Holographic dual approach to magnetism and magnetization dynamics

We propose a dual gravitational theory corresponding to isotropic ferromagnetic systems based on the holographic duality, and establish the holographic dictionary between physical quantities in ferromagnets and the gravitational theory. Utilizing the holographic dictionary, the holographic calculation in the dual gravitational theory is shown to reproduce thermodynamics of ferromagnets including ferromagnetic phase transitions and low-temperature behaviors originating from magnons and conduction electrons. We further derive the equation for magnetization dynamics in ferromagnets from the equations for scalar fields and non-abelian gauge fields on charged black holes in the dual gravitational theory. From these results, the holographic duality is expected to give a new guiding principle to explore new phenomena in spintronics and magnonics based on the gravitational perspective.

Spin pumping in d -wave superconductor-ferromagnet hybrids

Spin-pumping across ferromagnet/superconductor (F/S) interfaces has attracted much attention lately. Yet the focus has been mainly on s-wave superconductors-based systems whereas (high-temperature) d-wave superconductors such as YBa2Cu3O7-d (YBCO) have received scarce attention despite their fundamental and technological interest. Here we use wideband ferromagnetic resonance to study spin-pumping effects in bilayers that combine a soft metallic Ni80Fe20 (Py) ferromagnet and YBCO. We evaluate the spin conductance in YBCO by analyzing the magnetization dynamics in Py. We find that the Gilbert damping exhibits a drastic drop as the heterostructures are cooled across the normal-superconducting transition and then, depending on the S/F interface morphology, either stays constant or shows a strong upturn. This unique behavior is explained considering quasiparticle density of states at the YBCO surface, and is a direct consequence of zero-gap nodes for particular directions in the momentum space. Besides showing the fingerprint of d-wave superconductivity in spin-pumping, our results demonstrate the potential of high-temperature superconductors for fine tuning of the magnetization dynamics in ferromagnets using k-space degrees of freedom of d-wave/F interfaces.

On the Landau-Lifshitz-Bloch equation with spin torque effects

A mathematical model for current-induced magnetization dynamics in ferromagnets at elevated temperatures is considered. The model is represented by a classical Landau-Lifshitz-Bloch equation containing adiabatic and non-adiabatic torques. In the case of a ferromagnet confined to a bounded domain of R3, we prove existence of a weak solution by using Faedo-Galerkin approach and a compactness method. This paper extends the work done by Le et al. (2016) in the absence of adiabatic and non-adiabatic terms. Furthermore, uniqueness is proved in the case of dimension one and two. Finally, the limiting behaviour in large time is studied for the non-adiabatic case.

Direct observation of spin accumulation in Cu induced by spin pumping

This paper shows how X-ray transmission microscopy can provide spatial mapping of spin accumulations in a thin layer of copper, which are generated without any directly applied charge currents through spin pumping from ferromagnetic magnetization dynamics in adjacent permalloy.

Magnetization dynamics in holographic ferromagnets: Landau-Lifshitz equation from Yang-Mills fields

We introduce a new approach to understand magnetization dynamics in ferromagnets based on the holographic realization of ferromagnets. A Landau-Lifshitz equation describing the magnetization dynamics is derived from a Yang-Mills equation in the dual gravitational theory, and temperature dependences of the spin-wave stiffness and spin transfer torque appearing in the holographic Landau-Lifshitz equation are investigated by the holographic approach. The results are consistent with the known properties of magnetization dynamics in ferromagnets with conduction electrons.

Dynamic coupling of ferromagnets via spin Hall magnetoresistance

The synchronized magnetization dynamics in ferromagnets on a nonmagnetic heavy metal caused by the spin Hall effect is investigated theoretically. The direct and inverse spin Hall effects near the ferromagnetic/nonmagnetic interface generate longitudinal and transverse electric currents. The phenomenon is known as the spin Hall magnetoresistance effect, whose magnitude depends on the magnetization direction in the ferromagnet due to the spin transfer effect. When another ferromagnet is placed onto the same nonmagnet, these currents are again converted to the spin current by the spin Hall effect and excite the spin torque to this additional ferromagnet, resulting in the excitation of the coupled motions of the magnetizations. The in-phase or antiphase synchronization of the magnetization oscillations, depending on the value of the Gilbert damping constant and the field-like torque strength, is found in the transverse geometry by solving the Landau-Lifshitz-Gilbert equation numerically. On the other hand, in addition to these synchronizations, the synchronization having a phase difference of a quarter of a period is also found in the longitudinal geometry. The analytical theory clarifying the relation among the current, frequency, and phase difference is also developed, where it is shown that the phase differences observed in the numerical simulations correspond to that giving the fixed points of the energy supplied by the coupling torque.

Giant magnetoelectric effect in magnetic tunnel junctions coupled to an electromagnetic environment

We study the magnetization dynamics in ferromagnet$\mid$insulator$\mid$ferromagnet and ferromagnet$\mid$insulator$\mid$normal metal ultra-small tunnel junctions, and the associated voltage drop in the presence of an electromagnetic environment assisting the tunneling processes. We show that the environment strongly affects the resulting voltage, which becomes a highly non-linear function of the precession cone angle $\theta$. We find that voltages comparable to the driving frequency $\omega$ can be reached even for small precession cone angles $\theta$, in stark contrast to the case where the environment is absent. Such an effect could be useful for the detection local magnetization precessions in textured ferromagnets or, conversely, for probing the environment via the magnetization dynamics.

Optical spin pumping and magnetization switching in ferromagnets

Motivated by recent experiments on all-optical magnetization switching (AOS), we analyze theoretically optical spin pumping in ferromagnetic metals. It is shown that spin polarizations, induced by linearly and circularly polarized pump pulses, can be comparable in magnitude. We assume that the photoinduced spin polarization influences ultrafast light-induced magnetization dynamics in ferromagnets. In particular, it plays a crucial role in AOS. We analyze the light-induced magnetization dynamics in a system of localized and itinerant spins coupled by s-d exchange interaction, assuming that light heats up the itinerant electrons and, in addition, changes their spin polarization. When the pumped spin polarization has an appropriate sign and magnitude, it triggers magnetization switching. We find that temporal evolution of the magnetization is determined by a complicated interplay between heating, the photoinduced spin polarization, and spin relaxation.

Magnetization dissipation in ferromagnets from scattering theory

The magnetization dynamics of ferromagnets is often formulated in terms of the Landau-Lifshitz-Gilbert (LLG) equation. The reactive part of this equation describes the response of the magnetization in terms of effective fields, whereas the dissipative part is parametrized by the Gilbert damping tensor. We formulate a scattering theory for the magnetization dynamics and map this description on the linearized LLG equation by attaching electric contacts to the ferromagnet. The reactive part can then be expressed in terms of the static scattering matrix. The dissipative contribution to the low-frequency magnetization dynamics can be described as an adiabatic energy pumping process to the electronic subsystem by the time-dependent magnetization. The Gilbert damping tensor depends on the time derivative of the scattering matrix as a function of the magnetization direction. By the fluctuation-dissipation theorem, the fluctuations of the effective fields can also be formulated in terms of the quasistatic scattering matrix. The theory is formulated for general magnetization textures and worked out for monodomain precessions and domain-wall motions. We prove that the Gilbert damping from scattering theory is identical to the result obtained by the Kubo formalism.

Spin pumping and magnetization dynamics in ferromagnet–Luttinger liquid junctions

We study spin transport between a ferromagnet (FM) with time-dependent magnetization and a conducting carbon nanotube or quantum wire, modeled as a Luttinger liquid (LL). The precession of the magnetization vector of the ferromagnet due, for instance, to an outside applied magnetic field causes spin pumping into an adjacent conductor. Conversely, the spin injection causes increased magnetization damping in the ferromagnet. We find that, if the conductor adjacent to the ferromagnet is a Luttinger liquid, spin pumping/damping is suppressed by interactions, and the suppression has clear Luttinger-liquid power-law temperature dependence. We apply our result to a few particular setups. First we study the effective Landau-Lifshitz-Gilbert (LLG) coupled equations for the magnetization vectors of the two ferromagnets in a FM-LL-FM junction. Also, we compute the Gilbert damping for a FM-LL and a FM-LL-metal junction.

Roles of nonequilibrium conduction electrons on the magnetization dynamics of ferromagnets.

The mutual dependence of spin-dependent conduction and magnetization dynamics of ferromagnets provides the key mechanisms in various spin-dependent phenomena. We compute the response of the conduction electron spins in a spatial and time varying magnetization M(r,t) in the time-dependent semiclassical transport theory. We show that the induced nonequilibrium conduction spin density in turn generates four spin torques acting on the magnetization-with each torque playing a different role in magnetization dynamics. By comparing with recent theoretical models, we find that one of these torques which has not been previously identified is crucial to consistently interpreting experimental data on domain wall motion.