Origin of intrinsic Gilbert damping

Mitigation of Gilbert Damping in the CoFe/CuOx Orbital Torque System

Charge-spin interconversion processes underpin the generation of spin-orbit torques in magnetic/nonmagnetic bilayers. However, efficient sources of spin currents such as 5d metals are also efficient spin sinks, resulting in a large increase of magnetic damping. Here we show that a partially oxidized 3d metal can generate a strong orbital torque without a significant increase in damping. Measurements of the torque efficiency ξ and Gilbert damping α in CoFe/CuOx and CoFe/Pt indicate that ξ is comparable in the two systems. The increase in damping relative to a single CoFe layer is Δα < 0.002 in CoFe/CuOx and Δα ≈ 0.005-0.02 in CoFe/Pt, depending on CoFe thickness. We ascribe the nonreciprocal relationship between Δα and ξ in CoFe/CuOx to the small orbital-spin current ratio generated by magnetic resonance in CoFe and the lack of an efficient spin sink in CuOx. Our findings provide new perspectives on the efficient excitation of magnetization dynamics via the orbital torque.

Electric and Magnetic Tuning of Gilbert Damping Constant in LSMO/PMN-PT(011) Heterostructure

Electric field control of magnetodynamics in magnetoelectric (ME) heterostructures has&#xD;been the subject of recent interest due to its fundamental complexity and promising applications in&#xD;room temperature devices. The present work focuses on the tuning of magnetodynamic parameters&#xD;of epitaxially grown ferromagnetic (FM) La_0.7Sr_0.3MnO₃(LSMO) on a ferro(piezo)electric (FE)&#xD;Pb(Mg_0.33Nb_0.67)O₃-PbTiO₃(PMN-PT) single crystal substrate. The uniaxial magnetic anisotropy&#xD;of LSMO on PMN-PT confirms the ME coupling at the FM/FE heterointerface. The magnitude of&#xD;the Gilbert damping constant (α) of this uniaxial LSMO film measured along the hard magnetic axis&#xD;is significantly small compared to the easy axis. Furthermore, a marked decrease in the α values of&#xD;LSMO at positive and negative electrical remanence of PMN-PT is observed, which is interpreted&#xD;in the framework of strain induced spin dependent electronic structure. The present results clearly&#xD;encourage the prospects of electric field controlled magnetodynamics, thereby realising the room&#xD;temperature spin-wave based device applications with ultra-low power consumption.

Highly efficient heat-dissipation power driven by ferromagnetic resonance in MFe2O4 (M = Fe, Mn, Ni) ferrite nanoparticles

We experimentally demonstrated that heat-dissipation power driven by ferromagnetic resonance (FMR) in superparamagnetic nanoparticles of ferrimagnetic MFe₂O₄ (M = Fe, Mn, Ni) gives rise to highly localized incrementation of targeted temperatures. The power generated thereby is extremely high: two orders of magnitude higher than that of the conventional Néel-Brownian model. From micromagnetic simulation and analytical derivation, we found robust correlations between the temperature increment and the intrinsic material parameters of the damping constant as well as the saturation magnetizations of the nanoparticles’ constituent materials. Furthermore, the magnetization–dissipation-driven temperature increments were reliably manipulated by extremely low strengths of applied AC magnetic fields under resonance field conditions. Our experimental results and theoretical formulations provide for a better understanding of the effect of FMR on the efficiency of heat generation as well as straightforward guidance for the design of advanced materials for control of highly localized incrementation of targeted temperatures using magnetic particles in, for example, magnetic hyperthermia bio-applications.

Giant magnetoresistance in spin valves realized by substitutingY-site atoms in Heusler lattice

'All-Heusler' spin-valve constructed by two half-metallic Heusler electrodes and a non-magnetic Heusler spacer contains two interfaces that have a crucial influence on the magnetoresistance. In order to reduce the disorder at the interface and protect the half metallicity of the electrode at the same region, we propose a scheme to construct a spin valve by replacing theY-site atoms in the half-metallic Heusler electrode to obtain the corresponding non-magnetic spacer based on the Slater-Pauling rule. In this way, the lattice and band match of the two materials can be ensured naturally. By using Co₂FeAl as electrode and Co₂ScAl as the spacer materials, we construct the Co₂FeAl/Co₂ScAl/Co₂FeAl(001)-spin valve. Based on the first-principles calculation, the most stable FeAl/CoCo-interface is determined both from the phonon spectra and the formation energy when the spacer Co₂ScAl grows on the FeAl-terminated (001) surface of electrode material Co₂FeAl. By comparing the projected density of states of the interfacial atoms with the corresponding density of states of the bulk electrode material, only the value of spin-up state of Al changes from 0.17 states/atom/eV to 0.06 states/atom/eV before and after substitution, the half metallicity at the interface is maintained. As a result, the spin-dependent transport properties show significant theoretical magnetoresistance MR_opwhich can reach up to 10¹⁰% and much larger than 10⁶% reported before.

Influence of a damping parameter on helicity-independent all-optical switching

Ultrafast magnetization switching has aroused much interest in recent years. Due to the complicated physical mechanisms, helicity-independent all-optical switching (HI-AOS) still lacks comprehensive understanding. In this article, we revealed the influence of damping on HI-AOS based on the simulation of the semiclassical atomic spin dynamics model. The results suggested that the smaller damping not only contributes to the increase to the maximum required pulse duration and the pulse fluence threshold for switching but also slows down the rate of magnetization dynamics. Our simulation results could provide some theoretical foundation to explore the optimization parameters of HI-AOS.

Theroy of magnetic inertial dynamics in two-sublattice ferromagnets

The magnetic inertial dynamics have previously been investigated for one sublattice ferromagnets. Here, we develop the magnetization dynamics in two-sublattice ferromagnets including the intra- and inter-sublattice inertial dynamics. First, we derive the magnetic susceptibility of such a ferromagnet. Next, by finding the poles of the susceptibility, we calculate the precession and nutation resonance frequencies. Our results suggest that while the resonance frequencies show decreasing behavior with the increasing intra-sublattice relaxation time, the effect of inter-sublattice inertial dynamics has an opposite effect.

Ultra-high rate of temperature increment from superparamagnetic nanoparticles for highly efficient hyperthermia

The magneto-thermal effect, which represents the conversion of magnetostatic energy to heat from magnetic materials, has been spotlighted for potential therapeutic usage in hyperthermia treatments. However, the realization of its potential has been challenged owing to the limited heating from the magnetic nanoparticles. Here, we explored a new-concept of magneto-thermal modality marked by low-power-driven, fast resonant spin-excitation followed by consequent energy dissipation, which concept has yet to be realized for current hyperthermia applications. We investigated the effect of spin resonance-mediated heat dissipation using superparamagnetic Fe₃O₄ nanoparticles and achieved an extraordinary initial temperature increment rate of more than 150 K/s, which is a significant increase in comparison to that for the conventional magnetic heat induction of nanoparticles. This work would offer highly efficient heat generation and precision wireless controllability for realization of magnetic-hyperthermia-based medical treatment.

Magnetic homogeneity in Fe-Mn co-doped NiO nanoparticles

The effect of Fe and Mn co-doping on the magnetic properties of the antiferromagnetic (AFM) NiO nanoparticles which offer large potential for different magnetic applications have been studied. The Rietveld refinement fitting of powder x-ray diffractometry (XRD) patterns confirmed the phase formation of face-centred cubic crystal structure of NiO and average crystallite size lies in the short range of 32-38 nm. The cavity and broadband ferromagnetic resonance (FMR) measurements taken at room temperature demonstrate the smaller local magnetic inhomogeneity for 4%Mn-4%Fe co-doped NiO nanoparticles as compared to undoped, single doped and co-doped with different concentration NiO nanoparticles. The M-H loops revealed the room temperature ferromagnetism-like behaviour for higher Fe doping concentration and lower Mn doping concentration. This can be attributed to the double exchange interaction. The zero field cooled (ZFC) and field cooled (FC) dc magnetization curves showed a small surface freezing peak (at[Formula: see text] at low temperatures and a blocking peak (at [Formula: see text] at higher temperatures. For samples with 4%Mn-4%Fe and 2%Mn-6%Fe, the blocking peak was found at a relatively high temperature in comparison to other samples. This can be attributed to the presence of magnetic exchange interactions which block the magnetic spins against a thermal increase. The ZFC AC-susceptibility showed three peaks; a surface freezing peak at T_f, a blocking peak at T_B peak and an anomalous peak at T_x in between [Formula: see text] and [Formula: see text], which was found to be most prominent for the 4%Mn-4%Fe co-doped nanoparticles. The neutron diffraction pattern confirmed the AFM order of the core of the 4%Mn-4%Fe co-doped nanoparticles, which indicates an AFM coupling between the Fe²⁺ and Mn²⁺ ions and the Ni²⁺ ions through super-exchange interaction. Therefore, the origin of T_X peak can be attributed to the ferromagnetic coupling between the Fe²⁺ and Mn²⁺ ions which has a maximum strength at equal concentration. Thus, small and equal doping concentration of Fe and Mn in NiO nanoparticles increase the magnetic homogeneity which makes them attractive for magnetic applications.

Study of the magnetic interface and its effect in Fe/NiFe bilayers of alternating order

We present a comprehensive study on the magnetization reversal in the Fe/NiFe bilayer system by alternating the order of the magnetic layers. All the samples show growth-induced uniaxial magnetic anisotropy due to the oblique angle deposition technique. Strong interfacial exchange coupling between the Fe and NiFe layers leads to single-phase hysteresis loops in the bilayer system. The strength of coupling being dependent on the interface changes upon alternating the order of magnetic layers. The magnetic parameters such as coercivity H_C, and anisotropy field H_K become almost doubled when a NiFe layer is grown over the Fe layers. This enhancement in the magnetic parameters is primarily dependent on the increase of the thickness and magnetic moment of the Fe–NiFe interfacial layer as revealed from the polarized neutron reflectivity (PNR) data of the bilayer samples. The difference in the thickness and magnetization of the Fe–NiFe interfacial layer indicates the modification of the microstructure by alternating the order of the magnetic layers of the bilayers. The interfacial magnetic moment increased by almost 18% when the NiFe layer was grown over the Fe layer. In spite of the different values of anisotropy fields and modified interfacial exchange coupling, the Gilbert damping constant values of the ferromagnetic bilayers remain similar to the single NiFe layer.

We deposited Fe/NiFe bilayers using magnetron sputtering and studied their static and dynamic properties. We performed PNR measurements and investigated whether the interfacial exchange coupling is responsible for the tuning of the magnetic properties.

Dynamics of the relativistic electron spin in an electromagnetic field

A relativistic spin operator cannot be uniquely defined within relativistic quantum mechanics. Previously, different proper relativistic spin operators have been proposed, such as spin operators of the Foldy-Wouthuysen and Pryce type, that both commute with the free-particle Dirac Hamiltonian and represent constants of motion. Here we consider the dynamics of a relativistic electron spin in an external electromagnetic field. We use two different Hamiltonians to derive the corresponding spin dynamics. These two are: (a) the Dirac Hamiltonian in the presence of an external field, and (b) the semirelativistic expansion of the same. Considering the Foldy-Wouthuysen and Pryce spin operators we show that these lead to different spin dynamics in an external electromagnetic field, which offers possibilities to distinguish their action. We find that the dynamics of both spin operators involve spin-dependent and spin-independent terms, however, the Foldy-Wouthuysen spin dynamics additionally accounts for the relativistic particle-antiparticle coupling. We conclude that the Pryce spin operator provides a suitable description of the relativistic spin dynamics in a weak-to-intermediate external field, whereas the Foldy-Wouthuysen spin operator is more suitable in the strong field regime.

Spin pumping during the antiferromagnetic-ferromagnetic phase transition of iron-rhodium

FeRh attracts intensive interest in antiferromagnetic (AFM) spintronics due to its first-order phase transition between the AFM and ferromagnetic (FM) phase, which is unique for exploring spin dynamics in coexisting phases. Here, we report lateral spin pumping by which angular momentum is transferred from FM domains into the AFM matrix during the phase transition of ultrathin FeRh films. In addition, FeRh is verified to be both an efficient spin generator and an efficient spin sink, by electrically probing vertical spin pumping from FM-FeRh into Pt and from Py into FeRh, respectively. A dramatic enhancement of damping related to AFM-FeRh is observed during the phase transition, which we prove to be dominated by lateral spin pumping across the FM/AFM interface. The discovery of lateral spin pumping provides insight into the spin dynamics of magnetic thin films with mixed-phases, and the significantly modulated damping advances its potential applications, such as ultrafast spintronics.

Iron–rhodium is a promising material for antiferromagnetic (AFM) spintronics applications. Here, the authors demonstrate a strong enhancement of damping during the ferromagnetic (FM) to AFM phase transition caused by lateral spin pumping from FM domains to the AFM matrix.

Low Gilbert damping and high thermal stability of Ru-seeded L10-phase FePd perpendicular magnetic thin films at elevated temperatures

Bulk perpendicular magnetic anisotropy materials are proposed to be a promising candidate for next-generation ultrahigh density and ultralow energy-consumption spintronic devices. In this work, we experimentally investigate the structure, thermal stability, and magnetic properties of FePd thin films seeded by a Ru layer. An fcc-phase Ru layer induces the highly-ordered L1₀-phase FePd thin films with perpendicular magnetic anisotropy (K _u ~ 10.1 Merg/cm³). The thermal stability of FePd samples is then studied through the annealing process. It is found that a K _u ~ 6.8 Merg/cm³ can be obtained with the annealing temperature of 500 °C. In addition, the damping constant α, an important parameter for switching current density, is determined as a function of the testing temperature. We observe that α increases from 0.006 to 0.009 for as-deposited FePd sample and from 0.006 to 0.012 for 400 °C-annealed FePd sample as the testing temperature changes from 25 °C to 150 °C. These results suggest that Ru-seeded FePd provides great potential in scaling perpendicular magnetic tunnel junctions below 10 nm for applications in ultralow energy-consumption spintronic devices.

Strain-induced perpendicular magnetic anisotropy and Gilbert damping of Tm3Fe5O12 thin films

In the attempt of implementing iron garnets with perpendicular magnetic anisotropy (PMA) in spintronics, the attention turned towards strain-grown iron garnets. One candidate is Tm₃Fe₅O₁₂ (TmIG) which possesses an out-of-plane magnetic easy axis when grown under tensile strain. In this study, the effect of film thickness on the structural and magnetic properties of TmIG films including magnetic anisotropy, saturation magnetization, and Gilbert damping is investigated. TmIG films with thicknesses between 20 and 300 nm are epitaxially grown by pulsed laser deposition on substituted-Gd₃Ga₅O₁₂(111) substrates. Structural characterization shows that films thinner than 200 nm show in-plane tensile strain, thus exhibiting PMA due to strain-induced magnetoelastic anisotropy. However, with increasing film thickness a relaxation of the unit cell is observed resulting in the rotation of the magnetic easy axis towards the sample plane due to the dominant shape anisotropy. Furthermore, the Gilbert damping parameter is found to be in the range of 0.02 ± 0.005.

Comparative study of methodologies to compute the intrinsic Gilbert damping: interrelations, validity and physical consequences

Relaxation effects are of primary importance in the description of magnetic excitations, leading to a myriad of methods addressing the phenomenological damping parameters. In this work, we consider several well-established forms of calculating the intrinsic Gilbert damping within a unified theoretical framework, mapping out their connections and the approximations required to derive each formula. This scheme enables a direct comparison of the different methods on the same footing and a consistent evaluation of their range of validity. Most methods lead to very similar results for the bulk ferromagnets Fe, Co and Ni, due to the low spin-orbit interaction (SOI) strength and the absence of the spin pumping mechanism. The effects of inhomogeneities, temperature and other sources of finite electronic lifetime are often accounted for by an empirical broadening of the electronic energy levels. We show that the contribution to the damping introduced by this broadening is additive, and so can be extracted by comparing the results of the calculations performed with and without SOI. Starting from simulated ferromagnetic resonance spectra based on the underlying electronic structure, we unambiguously demonstrate that the damping parameter obtained within the constant broadening approximation diverges for three-dimensional bulk magnets in the clean limit, while it remains finite for monolayers. Our work puts into perspective the several methods available to describe and compute the Gilbert damping, building a solid foundation for future investigations of magnetic relaxation effects in any kind of material.

Low Magnetic Damping of Ferrimagnetic GdFeCo Alloys

We investigate the Gilbert damping parameter α for rare earth (RE)-transition metal (TM) ferrimagnets over a wide temperature range. Extracted from the field-driven magnetic domain-wall mobility, α was as low as the order of 10^{-3} and was almost constant across the angular momentum compensation temperature T_{A}, starkly contrasting previous predictions that α should diverge at T_{A} due to a vanishing total angular momentum. Thus, magnetic damping of RE-TM ferrimagnets is not related to the total angular momentum but is dominated by electron scattering at the Fermi level where the TM has a dominant damping role. This low value of the Gilbert damping parameter suggests that ferrimagnets can serve as versatile platforms for low-dissipation high-speed magnetic devices.

Another view on Gilbert damping in two-dimensional ferromagnets

A keen interest towards technological implications of spin-orbit driven magnetization dynamics requests a proper theoretical description, especially in the context of a microscopic framework, to be developed. Indeed, magnetization dynamics is so far approached within Landau-Lifshitz-Gilbert equation which characterizes torques on magnetization on purely phenomenological grounds. Particularly, spin-orbit coupling does not respect spin conservation, leading thus to angular momentum transfer to lattice and damping as a result. This mechanism is accounted by the Gilbert damping torque which describes relaxation of the magnetization to equilibrium. In this study we work out a microscopic Kubo-Středa formula for the components of the Gilbert damping tensor and apply the elaborated formalism to a two-dimensional Rashba ferromagnet in the weak disorder limit. We show that an exact analytical expression corresponding to the Gilbert damping parameter manifests linear dependence on the scattering rate and retains the constant value up to room temperature when no vibrational degrees of freedom are present in the system. We argue that the methodology developed in this paper can be safely applied to bilayers made of non- and ferromagnetic metals, e.g., CoPt.

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.

Escape rate for nonequilibrium processes dominated by strong non-detailed balance force

Quantifying the escape rate from a meta-stable state is essential to understand a wide range of dynamical processes. Kramers' classical rate formula is the product of an exponential function of the potential barrier height and a pre-factor related to the friction coefficient. Although many applications of the rate formula focused on the exponential term, the prefactor can have a significant effect on the escape rate in certain parameter regions, such as the overdamped limit and the underdamped limit. There have been continuous interests to understand the effect of non-detailed balance on the escape rate; however, how the prefactor behaves under strong non-detailed balance force remains elusive. In this work, we find that the escape rate formula has a vanishing prefactor with decreasing friction strength under the strong non-detailed balance limit. We both obtain analytical solutions in specific examples and provide a derivation for more general cases. We further verify the result by simulations and propose a testable experimental system of a charged Brownian particle in electromagnetic field. Our study demonstrates that a special care is required to estimate the effect of prefactor on the escape rate when non-detailed balance force dominates.

Signatures of relativistic spin-light coupling in magneto-optical pump-probe experiments

Femtosecond magneto-optical pump-probe measurements of ultrafast demagnetization show an intriguing difference in the first 100 fs of the magneto-optical Kerr response depending on whether the polarization of the pump and probe beams are in parallel or perpendicular configuration (Bigot et al 2009 Nat. Phys. 5 515). Starting from a most general relativistic Hamiltonian we focus on the ultra-relativistic light-spin interaction and show that this coupling term leads to different light-induced opto-magnetic fields when pump and probe polarization are parallel and perpendicular to each other, providing thus an explanation for the measurements. We also analyze other pump-probe configurations where the pump laser is circularly polarized and the employed probe contains only linearly polarized light and show that similar opto-magnetic effects can be anticipated.

Spin relaxation signature of colossal magnetic anisotropy in platinum atomic chains

Recent experimental data demonstrate emerging magnetic order in platinum atomically thin nanowires. Furthermore, an unusual form of magnetic anisotropy - colossal magnetic anisotropy (CMA) - was earlier predicted to exist in atomically thin platinum nanowires. Using spin dynamics simulations based on first-principles calculations, we here explore the spin dynamics of atomically thin platinum wires to reveal the spin relaxation signature of colossal magnetic anisotropy, comparing it with other types of anisotropy such as uniaxial magnetic anisotropy (UMA). We find that the CMA alters the spin relaxation process distinctly and, most importantly, causes a large speed-up of the magnetic relaxation compared to uniaxial magnetic anisotropy. The magnetic behavior of the nanowire exhibiting CMA should be possible to identify experimentally at the nanosecond time scale for temperatures below 5 K. This time-scale is accessible in e.g., soft x-ray free electron laser experiments.

Experimental Investigation of Temperature-Dependent Gilbert Damping in Permalloy Thin Films

The Gilbert damping of ferromagnetic materials is arguably the most important but least understood phenomenological parameter that dictates real-time magnetization dynamics. Understanding the physical origin of the Gilbert damping is highly relevant to developing future fast switching spintronics devices such as magnetic sensors and magnetic random access memory. Here, we report an experimental study of temperature-dependent Gilbert damping in permalloy (Py) thin films of varying thicknesses by ferromagnetic resonance. From the thickness dependence, two independent contributions to the Gilbert damping are identified, namely bulk damping and surface damping. Of particular interest, bulk damping decreases monotonically as the temperature decreases, while surface damping shows an enhancement peak at the temperature of ~50 K. These results provide an important insight to the physical origin of the Gilbert damping in ultrathin magnetic films.

Orbital moment probed spin orbit coupling effects on anisotropy and damping in CoFeB thin films

Spin orbit coupling based direct correlation between magnetic anisotropy and damping is established in CoFeB thin films on compositional and stress variations.

Electric tuning of magnetization dynamics and electric field-induced negative magnetic permeability in nanoscale composite multiferroics

Steering magnetism by electric fields upon interfacing ferromagnetic (FM) and ferroelectric (FE) materials to achieve an emergent multiferroic response bears a great potential for nano-scale devices with novel functionalities. FM/FE heterostructures allow, for instance, the electrical manipulation of magnetic anisotropy via interfacial magnetoelectric (ME) couplings. A charge-mediated ME effect is believed to be generally weak and active in only a few angstroms. Here we present an experimental evidence uncovering a new magnon-driven, strong ME effect acting on the nanometer range. For Co92Zr8 (20 nm) film deposited on ferroelectric PMN-PT we show via ferromagnetic resonance (FMR) that this type of linear ME allows for electrical control of simultaneously the magnetization precession and its damping, both of which are key elements for magnetic switching and spintronics. The experiments unravel further an electric-field-induced negative magnetic permeability effect.

Landauer limit of energy dissipation in a magnetostrictive particle

According to Landauer's principle, a minimum amount of energy proportional to temperature must be dissipated during the erasure of a classical bit of information compensating the entropy loss, thereby linking the information and thermodynamics. Here, we show that the Landauer limit of energy dissipation is achievable in a shape-anisotropic single-domain magnetostrictive nanomagnet having two mutually anti-parallel degenerate magnetization states that store a bit of information. We model the magnetization dynamics using the stochastic Landau-Lifshitz-Gilbert equation in the presence of thermal fluctuations and show that on average the Landauer bound is satisfied, i.e. it is in accordance with the generalized Landauer's principle for small systems with stochastic fluctuations.

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.

Terahertz radiation from magnetic excitations in diluted magnetic semiconductors

We probed, in the time domain, the THz electromagnetic radiation originating from spins in CdMnTe diluted magnetic semiconductor quantum wells containing high-mobility electron gas. Taking advantage of the efficient Raman generation process, the spin precession was induced by low power near-infrared pulses. We provide a full theoretical first-principles description of spin-wave generation, spin precession, and of emission of THz radiation. Our results open new perspectives for improved control of the direct coupling between spin and an electromagnetic field, e.g., by using semiconductor technology to insert the THz sources in cavities or pillars.

Quadratic scaling of intrinsic Gilbert damping with spin-orbital coupling in L10 FePdPt films: experiments and Ab initio calculations

The dependence of the intrinsic Gilbert damping parameter α(0) on the spin-orbital coupling strength ξ is investigated in L1(0) ordered FePd(1-x) Pt(x) films by time-resolved magneto-optical Kerr effect measurements and spin-dependent ab initio calculations. Continuous tuning of α(0) over more than one order of magnitude is realized by changing the Pt/Pd concentration ratio showing that α(0) is proportional to ξ(2) as changes of other leading parameters are found to be negligible. The perpendicular magnetic anisotropy is shown to have a similar variation trend with x. The present results may facilitate the design and fabrication of new magnetic alloys with large perpendicular magnetic anisotropy and tailored damping properties.

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.

Atomistic magnetization dynamics in nanostructures based on first principles calculations: application to Co nanoislands on Cu(111)

The magnetization dynamics of Co nanoislands on Cu(111) is studied on the atomic scale by means of the stochastic Landau-Lifshitz-Gilbert equation. The exchange and anisotropy constants of the spin Hamiltonian are computed from first principles. We focus on hysteresis loops and magnetic switching in dependence on temperature, island size, and strength of an external magnetic field. The magnetic switching of nanoislands whose magnetization is reversed on the sub-nanosecond time scale is found consistent with the Stoner-Wohlfarth theory. We separate the superparamagnetic from the ferromagnetic regime and provide evidence that nanodomains can exist at least on a sub-picosecond time scale.

A microscopic model of current-induced switching of magnetization

The behaviour of the magnetization in a ferromagnetic metal/nonmagnetic insulator/ferromagnetic metal/paramagnetic metal tunnel junction is studied, using the nonequilibrium Keldysh formalism. The two ferromagnets are described using the single-band Hubbard model. The left one is treated in the mean field approximation and the right ferromagnet within a (nonequilibrium) spectral density approach which takes interactions beyond the mean field into account. When a voltage is applied to the junction we observe a change of the relative orientation of the two magnetizations, which can be switched from parallel to antiparallel alignment and vice versa. This switching appears in a self-consistent way, so there is no need to use half-classical methods like the Landau-Lifshitz-Gilbert equation one. The dependence of the critical voltage at which the magnetization changes its sign on the model parameters can be studied in a systematic way.