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Magnetic domain walls in antiferromagnets have been proposed as key components for faster conventional information processing, thanks to their enhanced stability and ultrafast propagation. However, how non-conventional computing methods like reservoir computing might take advantage of these properties remains an open question. In this work, we show how complex domain wall patterns can form through the proliferation of multiple domain walls from the energy stored in a single seed domain wall driven to move at a high speed close to the relativistic limit. We demonstrate that the resulting magnetic texture, consisting of up to hundreds of domain walls with an overall conserved topological charge as the initial seed domain wall, can possess chaotic spatiotemporal dynamics depending on the strength of staggered spin-orbit field induced via applied current. These findings allow us to design a multiple-domain-wall reservoir with high short-term memory and nonlinearity with respect to spin-orbit field inputs, that is suitable for ultrafast, energy-efficient, non-conventional reservoir computing., Comment: 30 pages, 5 figures

We utilize ultrafast photoexcitation to drive coherent lattice oscillations in the layered ferrimagnetic crystal Mn3Si2Te6, which significantly stiffen below the magnetic ordering temperature. We suggest that this is due to an exchange-mediated contraction of the lattice, stemming from strong magneto-structural coupling in this material. Additionally, simulations of the transient incoherent dynamics reveal the importance of spin relaxation channels mediated by optical and acoustic phonon scattering. Our findings highlight the importance of spin-lattice coupling in van der Waals magnets and a promising route for their dynamic optical control through their intertwined electronic, lattice, and spin degrees of freedom.

The experimental discovery of single-pulse ultrafast magnetization switching in ferrimagnetic alloys, such as GdFeCo and MnRuGa, opened the door to a promising route toward faster and more energy efficient data storage. A recent semi-phenomenological theory has proposed that a fast, laser-induced demagnetization below a threshold value puts the system into a dynamical regime where angular momentum transfer between sublattices dominates. Notably, this threshold scales inversely proportional to the number of exchange-coupled nearest neighbours considered in the model, which in the simplest case is directly linked to the underlying lattice structure. In this work, we study the role of the lattice structure on the laser-induced ultrafast magnetization switching in ferrimagnets by complementing the phenomenological theory with atomistic spin dynamics computer simulations. We consider a spin model of the ferrimagnetic GdFeCo alloy with increasing number of exchange-coupled neighbours. Within this model, we demonstrate that the laser-induced magnetization dynamics and switching depends on the lattice structure. Further, we determine that the critical laser energy for switching reduces for decreasing number of exchange-coupled neighbours.

The discovery of current-induced spin-orbit torque (SOT) orthogonal reorientation, also known as orthogonal switching, of metallic Mn$_2$Au and CuMnAs has opened the door for ultrafast writing of an antiferromagnet (AFM). Phenomenological theory predicts that the minimum field necessary for SOT switching -- critical field -- for ultrashort pulses increases inversely proportional to the pulse duration, thereby limiting the use of ultrafast stimulus as driving force for switching. We explore the possibility that by varying the working temperature the critical field reduces enabling orthogonal switching in response to ultrashort pulses. To do so, we extend previous theory to finite temperature and show that the critical field for an orthogonal switching strongly depends on temperature. We determine how the temperature dependence of the critical field varies as a function of the pulse duration. While for long pulses, the temperature dependence of the critical field is determined by the anisotropy field, for ultrashort pulses, it is determined by the characteristic frequency of the AFM. We show that the short and long pulse duration limits for the critical field can be connected by an analytical expression.

Both helicity-independent and helicity-dependent all-optical switching processes driven by single ultrashort laser pulse have been experimentally demonstrated in ferrimagnetic alloys as GdFeCo. Although the switching has been previously reproduced by atomistic simulations, the lack of a robust micromagnetic framework for ferrimagnets limits the predictions to small nano-systems, whereas the experiments are usually performed with lasers and samples of tens of micrometers. Here we develop a micromagnetic model based on the extended Landau-Lifshitz-Bloch equation, which is firstly validated by directly reproducing atomistic results for small samples and uniform laser heating. After that, the model is used to study ultrafast single shot all-optical switching in ferrimagnetic alloys under realistic conditions. We find that the helicity-independent switching under a linearly polarized laser pulse is a pure thermal phenomenon, in which the size of inverted area directly correlates with the maximum electron temperature in the sample. On the other hand, the analysis of the helicity-dependent processes under circular polarized pulses in ferrimagnetic alloys with different composition indicates qualitative differences between the results predicted by the magnetic circular dichroism and the ones from inverse Faraday effect. Based on these predictions, we propose experiments that would allow to resolve the controversy over the physical phenomenon that underlies these helicity-dependent all optical processes., Comment: manuscript and supplementary material, 25+19 pages, 6+10 figures

A change of orbital state alters the coupling between ions and their surroundings drastically. Orbital excitations are hence key to understand and control interaction of ions. Rare-earth (RE) elements with strong magneto-crystalline anisotropy (MCA) are important ingredients for magnetic devices. Thus, control of their localized 4f magnetic moments and anisotropy is one major challenge in ultrafast spin physics. With time-resolved X-ray absorption and resonant inelastic scattering experiments, we show for Tb metal that 4f-electronic excitations out of the ground state multiplet occur after optical pumping. These excitations are driven by inelastic 5d-4f-electron scattering, alter the 4f-orbital state and consequently the MCA with important implications for magnetization dynamics in 4f-metals, and more general for the excitation of localized electronic states in correlated materials., Comment: Manuscript (23 pages, 5 figures) and Supplementary Information (32 pages, 10 figures)

Single femtosecond pulse toggle switching of ferrimagnetic alloys is an essential building block for ultrafast spintronics. Very different element-specific demagnetization dynamics is believed to be a hard limit for switching in ferrimagnets. This suggests that ferrimagnets composed of two ions of different nature, such as rare earth transition metal alloys, are necessary for switching. However, experimental observation of toggle switching in Mn$_2$Ru$_x$Ga Heusler alloys, has contested this limit since Mn ions are of the same nature. To shed some light into this question, we present an atomistic spin model for the simulation of single pulse toggle switching of Mn$_2$Ru$_x$Ga. The magnetic parameters entering in our model are extracted from previous experimental observations. We show that our model is able to quantitatively reproduce measured magnetization dynamics of single pulse toggle switching. We demonstrate that differently to previous understanding toggle switching in Mn$_2$Ru$_x$Ga is possible even when both Mn sublattices demagnetization at very similar rate., Comment: Submitted to Appl. Phys. Lett. Special Topic: 'Ultrafast and THz spintronics'

Magnetic solitons offer functionalities as information carriers in multiple spintronic and magnonic applications. However, their potential for nanoscale energy transport has not been revealed. Here we demonstrate that antiferromagnetic solitons, e.g. domain walls, can uptake, transport and release energy. The key for this functionality resides in their relativistic kinematics; their self-energy increases with velocity due to Lorentz contraction of the soliton and their dynamics can be accelerated up to the effective speed of light of the magnetic medium. Furthermore, their classification in robust topological classes allows to selectively release this energy back into the medium by colliding solitons with opposite topology. Our work uncovers important energy-related aspects of the physics of antiferromagnetic solitons and opens up the attractive possibility for spin-based nanoscale and ultra-fast energy transport devices.

The Landau-Lifshitz (LL) equation, originally proposed at the macrospin level, is increasingly used in Atomistic Spin Dynamic (ASD) models. The models are based on a spin Hamiltonian featuring atomic spins of fixed length, with the exchange introduced using the Heisenberg formalism. ASD models are proving a powerful approach to the fundamental understanding of ultrafast magnetisation dynamics, including the prediction of the thermally induced magnetisation switching phenomenon in which the magnetisation is reversed using an ultrafast laser pulse in the absence of an externally applied field. The paper outlines the ASD model approach and considers the role and limitations of the LL equation in this context., Comment: 9 pages, 1 figure

A hierarchical multiscale approach to model the magnetization dynamics of ferromagnetic ran- dom alloys is presented. First-principles calculations of the Heisenberg exchange integrals are linked to atomistic spin models based upon the stochastic Landau-Lifshitz-Gilbert (LLG) equation to calculate temperature-dependent parameters (e.g., effective exchange interactions, damping param- eters). These parameters are subsequently used in the Landau-Lifshitz-Bloch (LLB) model for multi-sublattice magnets to calculate numerically and analytically the ultrafast demagnetization times. The developed multiscale method is applied here to FeNi (permalloy) as well as to copper- doped FeNi alloys. We find that after an ultrafast heat pulse the Ni sublattice demagnetizes faster than the Fe sublattice for the here-studied FeNi-based alloys.

Atomistic spin model simulations are immensely useful in determining temperature dependent magnetic prop- erties, but are known to give the incorrect dependence of the magnetization on temperature compared to exper- iment owing to their classical origin. We find a single parameter rescaling of thermal fluctuations which gives quantitative agreement of the temperature dependent magnetization between atomistic simulations and experi- ment for the elemental ferromagnets Ni, Fe, Co and Gd. Simulating the sub-picosecond magnetization dynam- ics of Ni under the action of a laser pulse we also find quantitative agreement with experiment in the ultrafast regime. This enables the quantitative determination of temperature dependent magnetic properties allowing for accurate simulations of magnetic materials at all temperatures.

The detailed derivation of the quantum Landau-Lifshitz-Bloch (qLLB) equation for simple spin-flip scattering mechanisms based on spin-phonon and spin-electron interactions is presented and the approximations are discussed. The qLLB equation is written in the form, suitable for comparison with its classical counterpart. The temperature dependence of the macroscopic relaxation rates is discussed for both mechanisms. It is demonstrated that the magnetization dynamics is slower in the quantum case than in the classical one., Comment: 11 pages, 7 figures

There has been much interest recently in the discovery of thermally induced magnetisation switching, where a ferrimagnetic system can be switched deterministically without and applied magnetic field. Experimental results suggest that the reversal occurs due to intrinsic material properties, but so far the microscopic mechanism responsible for reversal has not been identified. Using computational and analytic methods we show that the switching is caused by the excitation of two magnon bound states, the properties of which are dependent on material factors. This discovery allows us to accurately predict the switching behaviour and the identification of this mechanism will allow new classes of materials to be identified or designed to use this switching in memory devices in the THz regime.

After the application of an ultrashort laser pulse, the antiferromagnetic alignment in rare earth-transition metal alloys can temporarily become ferromagnetic with the rare-earth polarity. Proposed models merely describe this effect, without showing the route for its manipulation. Here we use extensive atomistic spin model simulations and micromagnetic theory for ferrimagnets at elevated temperatures to predict that the polarity of this transient ferromagnetic-like state can be controlled by initial temperature. We show that this arises because the magnetic response of each lattice has a different temperature dependence, at low temperatures the transition metal responds faster than the rare earth, while at high temperatures this role is interchanged. Our findings contribute to the physical understanding and control of this state and thus open new perspectives for its use in ultrafast magnetic devices.

Ultrafast laser-induced magnetic switching in rare earth, transition metal ferrimagnetic alloys has recently been reported to occur by ultrafast heating alone. Using atomistic simulations and a ferrimagnetic Landau-Lifshitz-Bloch formalism, we demonstrate that for switching to occur it is necessary that angular momentum is transferred from the longitudinal to transverse magnetization components. This dynamical path leads to magnetization switching and subsequent ultrafast precession caused by the inter-sublattice exchange field on the nanoscale.

We derive the Landau-Lifshitz-Bloch (LLB) equation for a two-component magnetic system valid up to the Curie temperature. As an example, we consider disordered GdFeCo ferrimagnet where the ultrafast optically induced magnetization switching under the action of heat alone has been recently reported. The two-component LLB equation contains the longitudinal relaxation terms responding to the exchange fields from the proper and the neighboring sublattices. We show that the sign of the longitudinal relaxation rate at high temperatures can change depending on the dynamical magnetization value and a dynamical polarisation of one material by another can occur. We discuss the differences between the LLB and the Baryakhtar equation, recently used to explain the ultrafast switching in ferrimagnets. The two-component LLB equation forms basis for the largescale micromagnetic modeling of nanostructures at high temperatures and ultrashort timescales.

We compute the temperature-dependent spin-wave spectrum and the magnetization for a spin system using the unified decoupling procedure for the high-order Green's functions for the exchange coupling and anisotropy, both in the classical and quantum case. Our approach allows us to establish a clear crossover between quantum-mechanical and classical methods by developing the classical analog of the quantum Green's function technique. The results are compared with the classical spectral density method and numerical modeling based on the stochastic Landau-Lifshitz equation and the Monte Carlo technique. As far as the critical temperature is concerned, there is a full agreement between the classical Green's functions technique and the classical spectral density method. However, the former method turns out to be more straightforward and more convenient than the latter because it avoids any \emph{a priori} assumptions about the system's spectral density. The temperature-dependent exchange stiffness as a function of magnetization is investigated within different approaches.

The ultra-fast magnetisation relaxation rates during the laser-induced magnetisation process are analyzed in terms of the Landau-Lifshitz-Bloch (LLB) equation for different values of spin $S$. The LLB equation is equivalent in the limit $S \rightarrow \infty$ to the atomistic Landau-Lifshitz-Gilbert (LLG) Langevin dynamics and for $S=1/2$ to the M3TM model [B. Koopmans, {\em et al.} Nature Mat. \textbf{9} (2010) 259]. Within the LLB model the ultra-fast demagnetisation time ($\tau_{M}$) and the transverse damping ($\alpha_{\perp}$) are parameterized by the intrinsic coupling-to-the-bath parameter $\lambda$, defined by microscopic spin-flip rate. We show that for the phonon-mediated Elliott-Yafet mechanism, $\lambda$ is proportional to the ratio between the non-equilibrium phonon and electron temperatures. We investigate the influence of the finite spin number and the scattering rate parameter $\lambda$ on the magnetisation relaxation rates. The relation between the fs demagnetisation rate and the LLG damping, provided by the LLB theory, is checked basing on the available experimental data. A good agreement is obtained for Ni, Co and Gd favoring the idea that the same intrinsic scattering process is acting on the femtosecond and nanosecond timescale., Comment: 9 pages, 7 figures

We compare femtosecond pump-probe experiments in Ni and micromagnetic modelling based on the Landau-Lifshitz-Bloch equation coupled to a two-temperature model, revealing a predominant thermal ultrafast demagnetization mechanism. We show that both spin (femtosecond demagnetization) and electron-phonon (magnetization recovery) rates in Ni increase as a function of the laser pump fluence. The slowing down for high fluences arises from the increased longitudinal relaxation time.

Recent experimental results have pushed the limits of magnetization dynamics to pico- and femtosecond timescales. This ultra-fast spin dynamics occurs in extreme conditions of strong and rapidly varying fields and high temperatures. This situation requires new description of magnetization dynamics, even on a phenomenological level of the atomistic Landau-Lifshitz-Gilbert equation, taking into account that the correlation time for electron system could be of the order of the inverse characteristic spin frequency. For this case we introduce the thermodynamically correct phenomenological approach for spin dynamics based on the Landau-Lifshitz-Miyasaki-Seki equation. The influence of the noise correlation time on longitudinal and transverse magnetization relaxation is investigated. We also demonstrate the effect of the noise correlation time on demagnetisation rate of different materials during laser-induced dynamics.