Atomistic Spin Dynamics Simulations Research Articles

Ultrafast cooling and heating scenarios for the laser-induced phase transition in CuO

The multiferroic compound CuO exhibits low-temperature magnetic properties similar to antiferromagnetic iron oxides, while the electronic properties have much more in common with the high-${T}_{c}$ cuprate superconductors. This suggests novel possibilities for the ultrafast optical excitation of magnetism. On the basis of atomistic spin dynamics simulations, we study the effect of phonon-assisted multimagnon absorption and photodoping on the spin dynamics in the vicinity of the first-order phase transition from collinear to spin-spiral magnetic order. Similar as in recent experiments, we find that for both excitations the phase transition can proceed on the picosecond timescale. Interestingly, however, these excitation mechanisms display very distinct dynamics. Following photodoping, the spin system first cools down on subpicosecond time scales, which we explain as an ultrafast magnetocaloric effect. Opposed to this, following phonon-assisted multimagnon excitation, the spin systems rapidly heats up and subsequently evolves to the noncollinear phase even under the influence of isotropic exchange interactions alone.

Robust picosecond writing of a layered antiferromagnet by staggered spin-orbit fields

Ultrafast electrical switching by current-induced staggered spin-orbit fields, with minimal risk of overshoot, is shown in layered easy-plane antiferromagnets with basal-plane biaxial anisotropy. The reliable switching is due to the field-like torque, relaxing stringent requirements with respect to precision in the time-duration of the excitation pulse. We investigate the switching characteristics as a function of the spin-orbit field strength, pulse duration, pulse rise and fall time and damping by atomistic spin dynamics simulations and an effective equation of motion for the antiferromagnetic order-parameter. The condition, determining the critical spin-orbit field strength for switching is determined and we go on to show that robust picosecond writing is possible at feasible current magnitudes.

Switching of antiferromagnetic chains with magnetic pulses

Recent experimental studies have demonstrated the possibility of information storage in short antiferromagnetic chains on an insulator substrate [S. Loth et al., Science 335, 196 (2012)]. Here, using the density functional theory and atomistic spin dynamics simulations, we show that a local magnetic control of such chains with a magnetic tip and magnetic pulses can be used for fast switching of their magnetization. Furthermore, by changing the position of the tip one can engineer the magnetization dynamics of the chains.

Magnetic phase diagram of an Fe monolayer on W(110) and Ta(110) surfaces based onab initiocalculations

We present detailed investigations of the magnetic properties of an Fe monolayer on W and Ta (110) surfaces based on the ab initio screened Korringa-Kohn-Rostoker method. By calculating tensorial exchange coupling coefficients, the ground states of the systems are determined using atomistic spin dynamics simulations. Different types of ground states are found in the systems as a function of relaxation of the Fe layer. In case of W(110) substrate this is reflected in a reorientation of the easy axis from in-plane to out-of-plane. For Ta(110) a switching appears from the ferromagnetic state to a cycloidal spin spiral state, then to another spin spiral state with a larger wave vector and, for large relaxations, a rotation of the normal vector of the spin spiral is found. Classical Monte Carlo simulations indicate temperature-induced transitions between the different magnetic phases observed in the Fe/Ta(110) system. These phase transitions are analyzed both quantitatively and qualitatively by finite-temperature spin wave theory.

Non-Collinear Magnetic Configurations at Finite Temperature in Thin Films

The finite-temperature magnetism of a monolayer on a bcc (110) surface was examined using a model Hamiltonian containing ferromagnetic or antiferromagnetic exchange interactions, Dzyaloshinsky-Moriya (DM) interactions, and easy-axis on-site anisotropy. We examined the competition between the collinear ground state parallel to the easy axis and the spin spiral state in the plane perpendicular to this axis preferred by the DM interaction. Using approximative methods to calculate the magnon spectrum at finite temperatures, it was found that even if the ground state is collinear, increasing the DM interaction strongly decreases the critical temperature where this collinear order disappears. Using atomistic spin dynamics simulations, it was found that at this critical temperature the system transforms into the non-collinear state. Including external magnetic field helps stabilizing the ferromagnetic state. An effect due to the finite size of the magnetic monolayer was included in the model considering a different value for the anisotropy at the edges of the monolayer. This effect was shown to stabilize the spin spiral state by fixing the phase at the ends of the stripe.

Temperature-dependent ferromagnetic resonance via the Landau-Lifshitz-Bloch equation: Application to FePt

Using the Landau-Lifshitz-Bloch (LLB) equation for ferromagnetic materials, we derive analytic expressions for temperature-dependent absorption spectra as probed by ferromagnetic resonance. By analyzing the resulting expressions, we can predict the variation of the resonance frequency and damping with temperature and coupling to the thermal bath. We base our calculations on the technologically relevant ${\mathrm{L}1}_{0}\phantom{\rule{0.16em}{0ex}}\mathrm{FePt}$, parametrized from atomistic spin dynamics simulations, with the Hamiltonian mapped from ab initio parameters. By constructing a multimacrospin model based on the LLB equation and exploiting GPU acceleration, we extend the study to investigate the effects on the damping and resonance frequency in $\ensuremath{\mu}\mathrm{m}$-sized structures.

Thermally driven domain-wall motion in Fe on W(110)

It has recently been shown that domain walls (DWs) in ferromagnets can be moved in the presence of thermal gradients. In this work we study the motion of narrow domain walls in low-dimensional systems when subjected to thermal gradients. The system chosen is a monolayer of Fe on W(110) which is known to exhibit a large anisotropy while having a soft exchange, resulting in a very narrow domain wall. The study is performed by means of atomistic spin dynamics simulations coupled to first-principles calculations. By subjecting this system to thermal gradients we observe a temperature-dependent movement of the domain wall. The thermal gradient always makes the domain wall move towards the hotter region of the sample with a velocity proportional to the gradient. Our material specific study is complemented by model simulations to discern the interplay between the thermal gradient, magnetic anisotropy, and the exchange interaction and shows that the larger DW velocities are found for materials with broader domain-wall width. The relatively slow DW motion of the Fe/W(110) system is hence primarily caused by its narrow domain-wall width, which results from its large magnetic anisotropy and soft exchange.

Relativistic and thermal effects on the magnon spectrum of a ferromagnetic monolayer

A spin model including magnetic anisotropy terms and Dzyaloshinsky–Moriya interactions is studied for the case of a ferromagnetic monolayer with C2v symmetry like Fe/W(110). Using the quasiclassical stochastic Landau–Lifshitz–Gilbert equations, the magnon spectrum of the system is derived using linear response theory. The Dzyaloshinsky–Moriya interaction leads to asymmetry in the spectrum, while the anisotropy terms induce a gap. It is shown that, in the presence of lattice defects, both the Dzyaloshinsky–Moriya interactions and the two-site anisotropy lead to a softening of the magnon energies. Two methods are developed to investigate the magnon spectrum at finite temperatures. The theoretical results are compared to atomistic spin dynamics simulations and good agreement is found between them.

Atomistic spin dynamics of low-dimensional magnets

We investigate the magnetic properties of a range of low-dimensional ferromagnets using a combination of first-principles calculations and atomistic spin dynamics simulations. This approach allows us to evaluate the ground state and finite temperature properties of experimentally well characterized systems such as Co/Cu(111), Co/Cu(001), Fe/Cu(001) and Fe/W(110), for different thicknesses of the magnetic layer. We compare our calculated spin wave spectra with experimental data available in the literature, and find a good quantitative agreement. We also predict magnon spectra for systems for which no experimental data exist at the moment, and estimate the role of temperature effects.

Accelerating the switching of magnetic nanoclusters by anisotropy-driven magnetization dynamics

In this work the magnetization dynamics of clusters supported on non-magnetic substrates is shown to exhibit an unprecedented complex response when subjected to external magnetic fields. The field-driven magnetization reversal of small Co clusters deposited on a Cu(111) surface has been studied by means of first-principles calculations and atomistic spin dynamics simulations. For applied fields ranging from 1 Tesla to 10 Tesla, we observe a coherent magnetization reversal with switching times in the range of several tenths of picoseconds to several nanoseconds, depending on the field strength. We find a non-monotonous dependence of the switching times with respect to the strength of the applied field, which we prove to have its origin in the complex magnetic anisotropy landscape of these low dimensional systems. This effect is shown to be stable for temperatures around 10 K, and is possible to realize over a range of exchange interactions and anisotropy landscapes. Possible experimental routes to achieve this unique switching behaviour are discussed.

Theoretical Analysis of Inertia-like Switching in Magnets: Applications to a Synthetic Antiferromagnet

The magnetization dynamics of a synthetic antiferromagnet subjected to a short-magnetic-field pulse has been studied by using a combination of first principles calculations and atomistic spin-dynamics simulations. We observe switching phenomena on the time scale of tens of picoseconds, and inertia-like behavior in the magnetization dynamics. We explain the latter in terms of a dynamic redistribution of magnetic energy from the applied-field pulse to other possible energy terms, such as the exchange interaction and the magnetic anisotropy, without invoking concepts such as the inertia of an antiferro-magnetic vector. We also demonstrate that such dynamics can also be observed in a ferromagnetic material where the incident-field pulse pumps energy to the magnetic anisotropy.

Thickness-dependent magnetic structure of ultrathin Fe/Ir(001) films: From spin-spiral states toward ferromagnetic order

We present a detailed study of the ground-state magnetic structure of ultrathin Fe films on the surface of fcc Ir(001). We use the spin-cluster expansion technique in combination with the relativistic disordered local moment scheme to obtain parameters of spin models and then determine the favored magnetic structure of the system by means of a mean-field approach and atomistic spin dynamics simulations. For the case of a single monolayer of Fe, we find that layer relaxations very strongly influence the ground-state spin configurations, whereas Dzyaloshinskii-Moriya (DM) interactions and biquadratic couplings also have remarkable effects. To characterize the latter effect, we introduce and analyze spin collinearity maps of the system. While for two monolayers of Fe we find a single-$q$ spin spiral as ground state due to DM interactions, for the case of four monolayers, the system shows a noncollinear spin structure with nonzero net magnetization. These findings are consistent with experimental measurements indicating ferromagnetic order in films of four monolayers and thicker.

Thermally activated magnetization reversal in monatomic magnetic chains on surfacesstudied by classical atomistic spin-dynamics simulations

We analyse the spontaneous magnetization reversal of supported monatomic chains of finitelength due to thermal fluctuations via atomistic spin-dynamics simulations. Our approachis based on the integration of the Landau–Lifshitz equation of motion of a classical spinHamiltonian in the presence of stochastic forces. The associated magnetizationlifetime is found to obey an Arrhenius law with an activation barrier equal to thedomain wall energy in the chain. For chains longer than one domain wall width, thereversal is initiated by nucleation of a reversed magnetization domain primarilyat the chain edge followed by a subsequent propagation of the domain wall tothe other edge in a random-walk fashion. This results in a linear dependence ofthe lifetime on the chain length, if the magnetization correlation length is notexceeded. We studied chains of uniaxial and triaxial anisotropy and found that atriaxial anisotropy leads to a reduction of the magnetization lifetime due to ahigher reversal attempt rate, even though the activation barrier is not changed.

Suppression of Standing Spin Waves in Low-Dimensional Ferromagnets

We examine the experimental absence of standing spin wave modes in thin magnetic films, by means of atomistic spin dynamics simulations. Using Co on Cu(001) as a model system, we demonstrate that by increasing the number of layers, the optical branches predicted from adiabatic first-principles calculations are strongly suppressed, in agreement with spin-polarized electron energy loss spectroscopy measurements reported in the literature. Our results suggest that a dynamical analysis of the Heisenberg model is sufficient in order to capture the strong damping of the standing modes.

Ultrafast switching in a synthetic antiferromagnetic magnetic random-access memory device

The dynamics of a synthetic antiferromagnet (a metallic trilayer) have been explored and are shown to exhibit ultrafast switching on a time scale of tens of ps. This conclusion is based on first-principles, atomistic spin dynamics simulations. The simulations are performed at finite temperature, as well as at $T=0$ K (the macrospin limit), and we observe a marked temperature dependence of the switching phenomenon. It is shown that, to reach very high switching speeds, it is important that the two ferromagnetic components of the synthetic antiferromagnet have oppositely directed external fields to one another. Then a complex collaboration between precession switching of an internal exchange field and the damping switching of the external field occurs, which considerably accelerates the magnetization dynamics. We discuss a possible application of this fast switching as a magnetic random access memory device, which has as a key component intrinsic antiferromagnetic couplings and an applied Oersted field.

Magnon softening in a ferromagnetic monolayer: A first-principles spin dynamics study

We study the Fe/W(110) monolayer system through a combination of first principles calculations and atomistic spin dynamics simulations. We focus on the dispersion of the spin waves parallel to the [001] direction. Our results compare favorably with the experimental data of Prokop et al. [Phys. Rev. Lett. 102, 177206], and correctly capture a drastic softening of the magnon spectrum, with respect to bulk bcc Fe. The suggested shortcoming of the itinerant electron model, in particular that given by density functional theory, is refuted. We also demonstrate that finite temperature effects are significant, and that atomistic spin dynamics simulations represent a powerful tool with which to include these.

Atomistic spin dynamics simulations on Mn-doped GaAs and CuMn

The magnetic dynamical behavior of two random alloys have been investigated in atomistic spin dynamics (ASD) simulations. For both materials, magnetic exchange parameters calculated with first principles electronic structure methods were used. From experiments it is well known that CuMn is a highly frustrated magnetic system and a good manifestation of a Heisenberg spin glass. In our ASD simulations the behavior of the autocorrelation function indicate spin glass behavior. The diluted magnetic semiconductor (DMS) Mn-doped GaAs is engineered with hopes of high enough Curie temperatures to operate in spintronic devices. Impurities such as As antisites and Mn interstitials change the exhange couplings from being mainly ferromagnetic to also have antiferromagnetic components. We explore how the resulting frustration affects the magnetization dynamics for a varying rate of As antisites.

Simulation of a spin-wave instability from atomistic spin dynamics

We study the spin dynamics of a Heisenberg model at finite temperature in the presence of an external field or a uniaxial anisotropy. For the case of the uniaxial anisotropy our simulations show that the macro moment picture breaks down. An effect which we refer to as a spin-wave instability (SWI) results in a non-dissipative Bloch-Bloembergen type relaxation of the macro moment where the size of the macro moment changes, and can even be made to disappear. This relaxation mechanism is studied in detail by means of atomistic spin dynamics simulations.

Dynamics of diluted magnetic semiconductors from atomistic spin-dynamics simulations: Mn-doped GaAs

The dynamical behavior of the magnetism of diluted magnetic semiconductors (DMSs) has been investigated by means of atomistic spin-dynamics simulations. The conclusions drawn from the study are argued to be general for DMS systems in the low-concentration limit, although all simulations are done for 5% Mn-doped GaAs with various concentrations of As antisite defects. The magnetization curve $M(T)$ and the Curie temperature ${T}_{C}$ have been calculated and are found to be in good correspondence to the results from Monte Carlo simulations and experiments. Furthermore, equilibrium and nonequilibrium behaviors of the magnetic pair-correlation function have been extracted. The dynamics of DMS systems reveals a substantial short-ranged magnetic order even at temperatures at or above the ordering temperature, with a nonvanishing pair-correlation function extending up to several atomic shells. For the high As antisite concentrations the simulations show a short-ranged antiferromagnetic coupling and a weakened long-ranged ferromagnetic coupling. For sufficiently large concentrations we do not observe any long-ranged ferromagnetic correlation. A typical dynamical response shows that starting from a random orientation of moments, the spin correlation develops very fast $(\ensuremath{\sim}1\text{ }\text{ps})$ extending up to 15 atomic shells. Above $\ensuremath{\sim}10\text{ }\text{ps}$ in the simulations, the pair correlation is observed to extend over some 40 atomic shells. The autocorrelation function has been calculated and compared with ferromagnets such as bcc Fe and spin-glass materials. We find no evidence in our simulations for a spin-glass behavior for any concentration of As antisites. Instead the magnetic response is better described as slow dynamics, at least when compared to that of a regular ferromagnet such as bcc Fe.

A method for atomistic spin dynamics simulations: implementation and examples

We present a method for performing atomistic spin dynamic simulations. A comprehensivesummary of all pertinent details for performing the simulations such as equations ofmotions, models for including temperature, methods of extracting data and numericalschemes for performing the simulations is given. The method can be applied in afirst-principles mode, where all interatomic exchange is calculated self-consistently, or it canbe applied with frozen parameters estimated from experiments or calculated fora fixed spin-configuration. Areas of potential application to different magneticquestions are also discussed. The method is finally applied to one situation wherethe macrospin model breaks down; magnetic switching in ultra strong magneticfields.