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Efficient manipulation of magnetic order with electric current pulses is desirable for achieving fast spintronic devices. The Rashba-Edelstein effect, wherein spin polarization is electrically induced in noncentrosymmetric systems, provides a mean to achieve staggered spin-orbit torques. Initially predicted for spin, its orbital counterpart has been disregarded up to now. Here we report a generalized Rashba-Edelstein effect, which generates not only spin polarization but also orbital polarization, which we find to be far from being negligible. We show that the orbital Rashba-Edelstein effect does not require spin-orbit coupling to exist. We present first-principles calculations of the frequency-dependent spin and orbital Rashba-Edelstein tensors for the noncentrosymmetric antiferromagnets CuMnAs and Mn 2 Au. We show that the electrically induced local magnetization can exhibit Rashba-like or Dresselhaus-like symmetries, depending on the magnetic configuration. We compute sizable induced magnetizations at optical frequencies, which suggest that electric-field driven switching could be achieved at much higher frequencies. Efficient manipulation of magnetic order with electric current pulses is desirable for achieving fast spintronic devices and the Rashba-Edelstein effect provides a mean to achieve staggered spin-orbit torques. Here the authors show a generalized Rashba-Edelstein effect generating not only spin polarization but also orbital polarization.

Unraveling the origin of ultrafast demagnetization in multisublattice ferromagnetic materials requires femtosecond x-ray techniques to trace the magnetic moment dynamics on individual elements, but this could not yet be achieved in the hard x-ray regime. We demonstrate here the first ultrafast demagnetization dynamics in the ferromagnetic heavy 5d-transition metal Pt using circularly-polarized hard x-rays at an x-ray free electron laser (XFEL). The decay time of laser-induced demagnetization of L10-FePt is determined to be τ Pt = 0.61 0.04 ps using time-resolved x-ray magnetic circular dichroism at the Pt L3 edge, whereas magneto-optical Kerr measurements indicate the decay time for the total magnetization as τ total < 0.1 ps . A transient magnetic state with a photo-modulated ratio of the 3d and 5d magnetic moments is demonstrated for pump-probe delays larger than 1 ps. We explain this distinct photo-modulated transient magnetic state by the induced-moment behavior of the Pt atom and the x-ray probing depth. Our findings pave the way for the future use of XFELs to disentangle atomic spin dynamics contributions.

Manipulation of magnetisation with ultrashort laser pulses is promising for information storage device applications. The dynamics of the magnetisation response depends on the energy transfer from the photons to the spins during the initial laser excitation. A material of special interest for magnetic storage are FePt nanoparticles, for which switching of the magnetisation with optical angular momentum was demonstrated recently. The mechanism remained unclear. Here we investigate experimentally and theoretically the all-optical switching of FePt nanoparticles. We show that the magnetisation switching is a stochastic process. We develop a complete multiscale model which allows us to optimize the number of laser shots needed to switch the magnetisation of high anisotropy FePt nanoparticles in our experiments. We conclude that only angular momentum induced optically by the inverse Faraday effect will provide switching with one single femtosecond laser pulse.

Unraveling the origin of ultrafast demagnetization in multisublattice ferromagnetic materials requires femtosecond x-ray techniques to trace the magnetic moment dynamics on individual elements, but this could not yet be achieved in the hard x-ray regime. We demonstrate here the first ultrafast demagnetization dynamics in the ferromagnetic heavy 5d-transition metal Pt using circularly-polarized hard x-rays at an x-ray free electron laser (XFEL). The decay time of laser-induced demagnetization of L1 0 -FePt is determined to be τ Pt = 0.61 ± 0.04 ps using time-resolved x-ray magnetic circular dichroism at the Pt L 3 edge, whereas magneto-optical Kerr measurements indicate the decay time for the total magnetization as τ total < 0.1 ps . A transient magnetic state with a photo-modulated ratio of the 3d and 5d magnetic moments is demonstrated for pump–probe delays larger than 1 ps. We explain this distinct photo-modulated transient magnetic state by the induced-moment behavior of the Pt atom and the x-ray probing depth. Our findings pave the way for the future use of XFELs to disentangle atomic spin dynamics contributions.

Unraveling the origin of ultrafast demagnetization in multisublattice ferromagnetic materials requires femtosecond x-ray techniques to trace the magnetic moment dynamics on individual elements, but this could not yet be achieved in the hard x-ray regime. We demonstrate here the first ultrafast demagnetization dynamics in the ferromagnetic heavy 5d-transition metal Pt using circularly-polarized hard x-rays at an x-ray free electron laser (XFEL). The decay time of laser-induced demagnetization of L1(0)-FePt is determined to be tau(Pt) = 0.61 +/- 0.04 ps using time-resolved x-ray magnetic circular dichroism at the Pt L-3 edge, whereas magneto-optical Kerr measurements indicate the decay time for the total magnetization as tau(total) < 0.1 ps. A transient magnetic state with a photomodulated ratio of the 3d and 5d magnetic moments is demonstrated for pump-probe delays larger than 1 ps. We explain this distinct photo-modulated transient magnetic state by the induced-moment behavior of the Pt atom and the x-ray probing depth. Our findings pave the way for the future use of XFELs to disentangle atomic spin dynamics contributions.

Atomistic spin dynamics (ASD) is a standard tool to model the magnetization dynamics of a variety of materials. The fundamental dynamical model underlying ASD is entirely classical. In this paper, we present two approaches to effectively incorporate quantum effects into ASD simulations, thus enhancing their low temperature predictions. The first allows to simulate the magnetic behavior of a quantum spin system by solving the equations of motion of a classical spin system at an effective temperature relative to the critical temperature. This effective temperature is determined a priori from the microscopic properties of the system. The second approach is based on a \\semi model where classical spins interact with an environment with a quantum-like power spectrum. The parameters that characterize this model can be calculated ab initio or extracted from experiments. This semi-classical model quantitatively reproduces the absolute temperature behavior of a magnetic system, thus accounting for the quantum mechanical aspects of its dynamics, even at low temperature. The methods presented here can be readily implemented in current ASD simulations with no additional complexity cost.

In optimal covariance cleaning theory, minimizing the Frobenius norm between the true population covariance matrix and a rotational invariant estimator is a key step. This estimator can be obtained asymptotically for large covariance matrices, without knowledge of the true covariance matrix. In this study, we demonstrate that this minimization problem is equivalent to minimizing the loss of information between the true population covariance and the rotational invariant estimator for normal multivariate variables. However, for Student's t distributions, the minimal Frobenius norm does not necessarily minimize the information loss in finite-sized matrices. Nevertheless, such deviations vanish in the asymptotic regime of large matrices, which might extend the applicability of random matrix theory results to Student's t distributions. These distributions are characterized by heavy tails and are frequently encountered in real-world applications such as finance, turbulence, or nuclear physics. Therefore, our work establishes a connection between statistical random matrix theory and estimation theory in physics, which is predominantly based on information theory.

Electrical control of magnetization is of crucial importance for integrated spintronics devices. Spin-orbit torques (SOT) in heavy-metal/ferromagnetic heterostructures have emerged as promising tool to achieve efficiently current-induced magnetization reversal. However, the microscopic origin of the SOT is being debated,with the spin Hall effect (SHE) due to nonlocal spin currents and the spin Rashba-Edelstein effect (SREE) due to local spin polarization at the interface being the primary candidates. We investigate the electrically induced out-of-equilibrium spin and orbital polarizations in pure Pt films and in Pt/3d-metal (Co, Ni, Cu) bilayer films using ab initio electronic structure methods and linear-response theory. We compute atom-resolved response quantities that allow us to identify the induced spin-polarization contributions that lead to fieldlike SOTs, mostly associated with the SREE, and dampinglike (DL) SOTs, mostly associated with the SHE, and compare their relative magnitude, dependence on the magnetization direction, as well as their Pt-layer thickness dependence. We find that both the FL and DL components contribute to the resulting SOT at the Pt/Co and Pt/Ni interfaces, with the former contributions being larger at the Pt interface layer and the latter larger in the Co or Ni layers. Our calculations show that the electrically-induced transverse orbital polarization is exceedingly larger than the induced spin polarization and present even without spin-orbit coupling, in contrast to the spin polarization.

The orbital Hall effect has been theoretically predicted but its direct observation is a challenge. Here, we report the magneto-optical detection of current-induced orbital accumulation at the surface of a light 3\\(d\\) transition metal, Cr. The orbital polarization is in-plane, transverse to the current direction, and scales linearly with current density, consistent with the orbital Hall effect. Comparing the thickness-dependent magneto-optical measurements with \\(\\textit{ab initio}\\) calculations, we estimate an orbital diffusion length in Cr of \\(6.6\\pm 0.6\\) nm.

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 and 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.