Electron theory of fast and ultrafast dissipative magnetization dynamics

Nonreciprocal Phonon Propagation in a Metallic Chiral Magnet

The phonon magnetochiral effect (MChE) is the nonreciprocal acoustic and thermal transports of phonons caused by the simultaneous breaking of the mirror and time-reversal symmetries. So far, the phonon MChE has been observed only in a ferrimagnetic insulator Cu_{2}OSeO_{3}, where the nonreciprocal response disappears above the Curie temperature of 58 K. Here, we study the nonreciprocal acoustic properties of a room-temperature ferromagnet Co_{9}Zn_{9}Mn_{2} for unveiling the phonon MChE close to room temperature. Surprisingly, the nonreciprocity in this metallic compound is enhanced at higher temperatures and observed up to 250 K. This clear contrast between insulating Cu_{2}OSeO_{3} and metallic Co_{9}Zn_{9}Mn_{2} suggests that metallic magnets have a mechanism to enhance the nonreciprocity at higher temperatures. From the ultrasound and microwave-spectroscopy experiments, we conclude that the magnitude of the phonon MChE of Co_{9}Zn_{9}Mn_{2} mostly depends on the Gilbert damping, which increases at low temperatures and hinders the magnon-phonon hybridization. Our results suggest that the phonon nonreciprocity could be further enhanced by engineering the magnon band of materials.

Spin and Orbital Symmetry Breakings Central to the Laser-Induced Ultrafast Demagnetization of Transition Metals

The role of spin and orbital rotational symmetry on the laser-induced magnetization dynamics of itinerant-electron ferromagnets was theoretically investigated. The ultrafast demagnetization of transition metals is shown to be the direct consequence of the fundamental breaking of these conservation laws in the electronic system, an effect that is inherent to the nature of spin-orbit and electron-lattice interactions. A comprehensive symmetry analysis is complemented by exact numerical calculations of the time evolution of optically excited ferromagnetic ground states in the framework of a many-body electronic Hamiltonian. Thus, quantitative relations are established between the strength of the interactions that break the rotational symmetries and the time scales that are relevant for the magnetization dynamics.

Ultrafast signatures of magnetic inhomogeneity in Pd1- x Fe x (x ≤ 0.08) epitaxial thin films

A series of Pd_{1- x} Fe _x alloy epitaxial films (x = 0, 0.038, 0.062, and 0.080), a material promising for superconducting spintronics, was prepared and studied with ultrafast optical and magneto-optical laser spectroscopy in a wide temperature range of 4-300 K. It was found that the transition to the ferromagnetic state causes a qualitative change of both the reflectivity and the magneto-optical Kerr effect transients. A nanoscale magnetic inhomogeneity of the ferromagnet/paramagnet type inherent in the palladium-rich Pd_{1- x} Fe _x alloys reveals itself through the occurrence of a relatively slow, 10-25 ps, photoinduced demagnetization component following a subpicosecond one; the former vanishes at low temperatures only in the x = 0.080 sample. We argue that the 10 ps timescale demagnetization originates most probably from the diffusive transport of d electrons under the condition of nanoscale magnetic inhomogeneities. The low-temperature fraction of the residual paramagnetic phase can be deduced from the magnitude of the slow reflectivity relaxation component. It is estimated as ≈30% for x = 0.038 and ≈15% for x = 0.062 films. The minimal iron content ensuring the magnetic homogeneity of the ferromagnetic state in the Pd_{1- x} Fe _x alloy at low temperatures is about 7-8 atom %.

Speeding up the extended Kalman filter approach for denoising XMCD movies of fast magnetization dynamics

The Kalman filter is a well-established approach to get information on the time-dependent state of a system from noisy observations. In former times it has been used for systems with only a few degrees of freedom (typically about 10). The fast magnetization dynamics is often investigated by x-ray magnetic circular dichroism movies (XMCD movies) where the number of components of the state vector is very large (typically about 10⁵). For such systems the Jacobian matrix which is required in the extended Kalman filter approach cannot be calculated numerically (as it is done in former papers) by use of the Landau-Lifschitz-Gilbert equation of motion in a finite time because of the many degrees of freedom of the state vector. In the present paper it is shown that the calculation of the Jacobian matrix can be much speeded up by using good analytical approximations, which are derived by a tensorial Green's function method to solve the linearized Landau-Lifschitz-Gilbert equation of motion. This makes it possible to investigate the dynamics of magnetic vortices and spin waves in circular discs of Permalloy, which are initiated by time-dependent external magnetic fields.

The indispensable role of the transversal spin fluctuations mechanism in laser-induced demagnetization of Co/Pt multilayers with nanoscale magnetic domains

The switching of magnetic domains induced by an ultrashort laser pulse has been demonstrated in nanostructured ferromagnetic films. This leads to the dawn of a new era in breaking the ultimate physical limit for the speed of magnetic switching and manipulation, which is relevant to current and future information storage. However, our understanding of the interactions between light and spins in magnetic heterostructures with nanoscale domain structures is still lacking. Here, both time-resolved magneto-optical Kerr effect experiments and atomistic simulations are carried out to investigate the dominant mechanism of laser-induced ultrafast demagnetization in [Co/Pt]₂₀ multilayers with nanoscale magnetic domains. It is found that the ultrafast demagnetization time remains constant with various magnetic configurations, indicating that the domain structures play a minor role in laser-induced ultrafast demagnetization. In addition, both in experiment and atomistic simulations, we find a dependence of ultrafast demagnetization time τ _M on the laser fluence, which is in contrast to the observations of spin transport within magnetic domains. The remarkable agreement between experiment and atomistic simulations indicates that the local dissipation of spin angular momentum is the dominant demagnetization mechanism in this system. More interestingly, we made a comparison between the atomistic spin dynamic simulation and the longitudinal spin flip model, highlighting that the transversal spin fluctuations mechanism is responsible for the ultrafast demagnetization in the case of inhomogeneous magnetic structures. This is a significant advance in clarifying the microscopic mechanism underlying the process of ultrafast demagnetization in inhomogeneous magnetic structures.

Generalisation of Gilbert damping and magnetic inertia parameter as a series of higher-order relativistic terms

The phenomenological Landau-Lifshitz-Gilbert (LLG) equation of motion remains as the cornerstone of contemporary magnetisation dynamics studies, wherein the Gilbert damping parameter has been attributed to first-order relativistic effects. To include magnetic inertial effects the LLG equation has previously been extended with a supplemental inertia term; the arising inertial dynamics has been related to second-order relativistic effects. Here we start from the relativistic Dirac equation and, performing a Foldy-Wouthuysen transformation, derive a generalised Pauli spin Hamiltonian that contains relativistic correction terms to any higher order. Using the Heisenberg equation of spin motion we derive general relativistic expressions for the tensorial Gilbert damping and magnetic inertia parameters, and show that these tensors can be expressed as series of higher-order relativistic correction terms. We further show that, in the case of a harmonic external driving field, these series can be summed and we provide closed analytical expressions for the Gilbert and inertial parameters that are functions of the frequency of the driving field.

Ultrafast spin dynamics and switching via spin transfer torque in antiferromagnets with weak ferromagnetism

The spin-torque driven dynamics of antiferromagnets with Dzyaloshinskii-Moriya interaction (DMI) were investigated based on the Landau-Lifshitz-Gilbert-Slonczewski equation with antiferromagnetic and ferromagnetic order parameters (l and m, respectively). We demonstrate that antiferromagnets including DMI can be described by a 2-dimensional pendulum model of l. Because m is coupled with l, together with DMI and exchange energy, close examination of m provides fundamental understanding of its dynamics in linear and nonlinear regimes. Furthermore, we discuss magnetization reversal as a function of DMI and anisotropy energy induced by a spin current pulse.

Relaxation of a Classical Spin Coupled to a Strongly Correlated Electron System

A classical spin which is antiferromagnetically coupled to a system of strongly correlated conduction electrons is shown to exhibit unconventional real-time dynamics which cannot be described by Gilbert damping. Depending on the strength of the local Coulomb interaction U, the two main electronic dissipation channels, namely transport of excitations via correlated hopping and via excitations of correlation-induced magnetic moments, become active on largely different time scales. We demonstrate that correlations can lead to a strongly suppressed relaxation which so far has been observed in purely electronic systems only and which is governed here by proximity to the divergent magnetic time scale in the infinite-U limit.

Temperature dependence of spin pumping and Gilbert damping in thin Co/Pt bilayers

We report on the temperature dependence of the spin-pumping effect and the Gilbert damping in Co/Pt bilayers grown on Silicon oxide by measuring the change of the linewidth in a ferromagnetic resonance (FMR) experiment. By varying the Co thickness d(Co) between 1.5 nm and 50 nm we find that the damping increases inversely proportional to d(Co) at all temperatures between 300 K and 5 K, showing that the spin pumping effect does not depend on temperature. We also find that the linewidth increases with decreasing temperature for all thicknesses down to about 30 K, before leveling off to a constant, or even decreasing again. This behavior is similar to what is found in bulk ferromagnets, leading to the conclusion that in thin films a conductivity-like damping mechanism is present similar to what is known in crystals.

Many-Body Theory of Ultrafast Demagnetization and Angular Momentum Transfer in Ferromagnetic Transition Metals

Exact calculated time evolutions in the framework of a many-electron model of itinerant magnetism provide new insights into the laser-induced ultrafast demagnetization observed in ferromagnetic (FM) transition metal thin films. The interplay between local spin-orbit interactions and interatomic hopping is shown to be at the origin of the observed postexcitation breakdown of FM correlations between highly stable local magnetic moments. The mechanism behind spin- and angular-momentum transfer is revealed from a microscopic perspective by rigorously complying with all fundamental conservation laws. An energy-resolved analysis of the time evolution shows that the efficiency of the demagnetization process reaches almost 100% in the excited states.

Ultrafast reduction in exchange interaction by a laser pulse: alternative path to femtomagnetism

Since the beginning of femtomagnetism, it has been hotly debated how an ultrafast laser pulse can demagnetize a sample and switch its spins within a few hundred femtoseconds, but no consensus has been reached. In this paper, we propose that an ultrafast reduction in the exchange interaction by a femtosecond laser pulse is mainly responsible for demagnetization and spin switching. The key physics is that the dipole selection rule demands two distinctive electron configurations for the ground and excited states and consequently changes the exchange interaction. Although the exchange interaction change is almost instantaneous, its effect on the spin is delayed by the finite spin wave propagation. Consistent with the experimental observation, the delay becomes longer with a stronger exchange interaction pulse. In spin-frustrated systems, the effect of the exchange interaction change is even more dramatic, where the spin can be directly switched from one direction to the other. Therefore, our theory has the potential to explain the essence of major observations in rare-earth transition metal compounds for the last seven years. Our findings are likely to motivate further research in the quest of the origin of femtomagnetism.

Review and prospects of magnonic crystals and devices with reprogrammable band structure

Research efforts addressing spin waves (magnons) in microand nanostructured ferromagnetic materials have increased tremendously in recent years. Corresponding experimental and theoretical work in magnonics faces significant challenges in that spinwave dispersion relations are highly anisotropic and different magnetic states might be realized via, for example, the magnetic field history. At the same time, these features offer novel opportunities for wave control in solids going beyond photonics and plasmonics. In this topical review we address materials with a periodic modulation of magnetic parameters that give rise to artificially tailored band structures and allow unprecedented control of spin waves. In particular, we discuss recent achievements and perspectives of reconfigurable magnonic devices for which band structures can be reprogrammed during operation. Such characteristics might be useful for multifunctional microwave and logic devices operating over a broad frequency regime on either the macroor nanoscale.

Spin excitations in solids from many-body perturbation theory

Collective spin excitations form a fundamental class of excitations in magnetic materials. As their energy reaches down to only a few meV, they are present at all temperatures and substantially influence the properties of magnetic systems. To study the spin excitations in solids from first principles, we have developed a computational scheme based on many-body perturbation theory within the full-potential linearized augmented plane-wave (FLAPW) method. The main quantity of interest is the dynamical transverse spin susceptibility or magnetic response function, from which magnetic excitations, including single-particle spin-flip Stoner excitations and collective spin-wave modes as well as their lifetimes, can be obtained. In order to describe spin waves we include appropriate vertex corrections in the form of a multiple-scattering T matrix, which describes the coupling of electrons and holes with different spins. The electron-hole interaction incorporates the screening of the many-body system within the random-phase approximation. To reduce the numerical cost in evaluating the four-point T matrix, we exploit a transformation to maximally localized Wannier functions that takes advantage of the short spatial range of electronic correlation in the partially filled d or f orbitals of magnetic materials. The theory and the implementation are discussed in detail. In particular, we show how the magnetic response function can be evaluated for arbitrary k points. This enables the calculation of smooth dispersion curves, allowing one to study fine details in the k dependence of the spin-wave spectra. We also demonstrate how spatial and time-reversal symmetry can be exploited to accelerate substantially the computation of the four-point quantities. As an illustration, we present spin-wave spectra and dispersions for the elementary ferromagnet bcc Fe, B2-type tetragonal FeCo, and CrO₂ calculated with our scheme. The results are in good agreement with available experimental data.

Thermal or nonthermal? That is the question for ultrafast spin switching in GdFeCo

GdFeCo is among the most interesting magnets for producing laser-induced femtosecond magnetism, where light can switch its spin moment from one direction to another. This paper aims to set a criterion for the thermal/nonthermal mechanism: we propose to use the Fermi-Dirac distribution function as a reliable criterion. A precise value for the thermalization time is needed, and through a two-level model, we show that since there is no direct connection between the laser helicity and the definition of thermal/nonthermal processes, the helicity is a poor criterion for differentiating a thermal from a nonthermal process. In addition, we propose a four-site model system (Gd2Fe2) for investigating the transient ferromagnetic ordering between Gd and Fe ions. We find that states of two different kinds can allow such an ordering. One state is a pure ferromagnetic state with ferromagnetic ordering among all the ions, and the other is the short-ranged ferromagnetic ordering of a pair of Gd and Fe ions.

Relaxation time of terahertz magnons excited at ferromagnetic surfaces

The temporal and spatial properties of terahertz magnons excited at ferromagnetic fcc Co(100) and bcc Fe(110) surfaces are investigated experimentally. The magnon lifetime is found to be a few tens of femtoseconds at low wave vectors, which reduces significantly as the wave vector approaches the Brillouin zone boundary. Surprisingly, the lifetime is very similar in both systems, in spite of the fact that the excitation energy in the Co(100) film is by a factor of two larger than in the Fe(110) film. The magnon wave packets propagate only a few nanometers within their lifetime. In addition to the fact that our results describe the damping mechanism in ultrafast time scales, they may provide a way to predict the ultimate time scale of magnetic switching in nanostructures.