Role of entropy in domain wall motion in thermal gradients

A theory of skyrmion crystal formation

A generic theory about skyrmion crystal (SkX) formation in chiral magnetic thin films and its fascinating thermodynamic behaviours is presented. A chiral magnetic film can have many metastable states with an arbitrary skyrmion density up to a maximal value when the parameter κ, which measures the relative Dzyaloshinskii-Moriya interaction (DMI) strength, is large enough. The lowest energy state of an infinite film is a long zig-zag ramified stripe skyrmion occupying the whole film in the absence of a magnetic field. Under an intermediate field perpendicular to the film, the lowest energy state has a finite skyrmion density. This is why a chiral magnetic film is often in a stripy state at a low field and a SkX only around an optimal field when κ is above a critical value. The lowest energy state is still a stripy helical state no matter with or without a field when κ is below the critical value. The multi-metastable states explain the thermodynamic path dependences of the various metastable states of a film. The decrease of the κ value with the temperature explains why SkXs become metastable at low temperatures in many skyrmion systems. These findings open a new avenue for SkX manipulation and skyrmion-based applications.

Switching Crystallographic Chirality in Ba(TiO)Cu4(PO4)4 by Laser Irradiation

Switching crystallographic chirality is nontrivial because there is no simple conjugate field to chirality. Here we demonstrate chirality switching in an inorganic crystalline material by manipulating the boundaries of chiral domains with laser irradiation. Our study material is Ba(TiO)Cu₄(PO₄)₄, exhibiting a chiral structure at room temperature and a chiral-achiral phase transition at 710 °C. By irradiation of a laser beam with a wavelength at which Ba(TiO)Cu₄(PO₄)₄ exhibits strong optical absorption, local heating is induced. This leads to reconstructions of chiral domain boundaries, revealed by optical rotation measurements. In the reconstruction process, energetically unstable domain boundaries tend to be minimized, affecting resultant domain patterns. On the basis of this feature, we successfully manipulate chiral domain patterns by scanning the laser beam on the sample surface. Our findings provide a unique approach to controlling chirality in inorganic crystalline materials.

Topology dependence of skyrmion Seebeck and skyrmion Nernst effect

We explore the dynamics of skyrmions with various topological charges induced by a temperature gradient in an ultra-thin insulating magnetic film. Combining atomistic spin simulations and analytical calculations we find a topology-dependent skyrmion Seebeck effect: while skyrmions and antiskyrmions move to the hot regime, a topologically trivial localized spin structure moves to the cold regime. We further reveal the emergence of a skyrmion Nernst effect, i.e. finite, topology-dependent velocities transverse to the direction of the temperature gradient. These findings are in agreement with accompanying simulations of skyrmionic motion induced by monochromatic magnon currents, allowing us to demonstrate that the magnonic spin Seebeck effect is responsible for both, skyrmion Seebeck and Nernst effect. Furthermore we employ scattering theory together with Thiele's equation to identify linear momentum transfer from the magnons to the skyrmion as the dominant contribution and to demonstrate that the direction of motion depends on the topological magnon Hall effect and the topological charge of the skyrmion.

Influence of magnetic domain walls on all-optical magnetic toggle switching in a ferrimagnetic GdFe film

We present a microscopic magnetic domain imaging study of single-shot all-optical magnetic toggle switching of a ferrimagnetic Gd26Fe74 film with out-of-plane easy axis of magnetization by X-ray magnetic circular dichroism photoelectron emission microscopy. Individual linearly polarized laser pulses of 800 nm wavelength and 100 fs duration above a certain threshold fluence reverse the sample magnetization, independent of the magnetization direction, the so-called toggle switching. Local deviations from this deterministic behavior close to magnetic domain walls are studied in detail. Reasons for nondeterministic toggle switching are related to extrinsic effects, caused by pulse-to-pulse variations of the exciting laser system, and to intrinsic effects related to the magnetic domain structure of the sample. The latter are, on the one hand, caused by magnetic domain wall elasticity, which leads to a reduction of the domain-wall length at features with sharp tips. These features appear after the optical switching at positions where the line of constant threshold fluence in the Gaussian footprint of the laser pulse comes close to an already existing domain wall. On the other hand, we identify the presence of laser-induced domain-wall motion in the toggle-switching event as a further cause for local deviations from purely deterministic toggle switching.

Universality classes of the domain-wall creep motion driven by spin-transfer torques

With the stochastic Landau-Lifshitz-Gilbert equation, we numerically simulate the creep motion of a magnetic domain wall driven by the adiabatic and nonadiabatic spin-transfer torques induced by the electric current. The creep exponent μ and the roughness exponent ζ are accurately determined from the scaling behaviors. The creep motions driven by the adiabatic and nonadiabatic spin-transfer torques belong to different universality classes. The scaling relation between μ and ζ based on certain simplified assumptions is valid for the nonadiabatic spin-transfer torque, while invalid for the adiabatic one. Our results are compatible with the experimental ones, but go beyond the existing theoretical prediction. Our investigation reveals that the disorder-induced pinning effect on the domain-wall rotation alters the universality class of the creep motion.

The origin of spin wave pulse-induced domain wall inertia

The fundamental problem of domain wall (DW) inertia-the property that gives to inertial behaviors remains unclear in the physics of magnetic solitons. To understand its nature as well as to achieve accurate DW positioning and efficient manipulation of domain wall motion (DWM), spin wave (SW) pulse-induced DW transient effect is studied both numerically and theoretically in a magnetic nanostrip. It is shown for the first time that there occurs inevitable deceleration/automotion after SW pulse, which indicates nonzero DW inertia. The induced DWM is revealed to relate to two factors: energy storing within DW and out-of-plane tilting of DW. To explain the DWM dynamics, a one-dimensional collective model is developed to account for the excitation of spin wave pulse. The model successfully bridges DW energy, DW tilting and DW displacement and provides descriptions in accordance with numerical findings. It is made clear that the DW automotion hence DW inertia originate from the process of DW relaxation toward equilibrium. The DW inertia is expressed in terms of effective mass and turns out to be a time-dependent function with damping constantαas the governing parameter, which opposes the nature of intrinsic mass. For case containing multiple DWs, the total effective mass is shown to concern the reached velocity and stored energy of DWs instead of the number of DWs, which is against common intuition.

Reconfiguration of magnetic domain structures of ErFeO3 by intense terahertz free electron laser pulses

Understanding the interaction between intense terahertz (THz) electromagnetic fields and spin systems has been gaining importance in modern spintronics research as a unique pathway to realize ultrafast macroscopic magnetization control. In this work, we used intense THz pulses with pulse energies in the order of 10 mJ/pulse generated from the terahertz free electron laser (THz-FEL) to irradiate the ferromagnetic domains of ErFeO₃ single crystal. It was found that the domain shape can be locally reconfigured by irradiating the THz − FEL pulses near the domain boundary. Observed domain reconfiguration mechanism can be phenomenologically understood by the combination of depinning effect and the entropic force due to local thermal gradient exerted by terahertz irradiation. Our finding opens up a new possibility of realizing thermal-spin effects at THz frequency ranges by using THz-FEL pulses.

Thermal gradient driven domain wall dynamics

The issue of whether a thermal gradient acts like a magnetic field or an electric current in the domain wall (DW) dynamics is investigated. Broadly speaking, magnetization control knobs can be classified as energy-driving or angular-momentum driving forces. DW propagation driven by a static magnetic field is the best known example of the former in which the DW speed is proportional to the energy dissipation rate, and the current-driven DW motion is an example of the latter. Here we show that DW propagation speed driven by a thermal gradient can be fully explained as the angular momentum transfer between thermally generated spin current and DW. We found DW-plane rotation speed increases as DW width decreases. Both DW propagation speed along the wire and DW-plane rotation speed around the wire decrease with the Gilbert damping. These facts are consistent with the angular momentum transfer mechanism, but are distinct from the energy dissipation mechanism. We further show that magnonic spin-transfer torque (STT) generated by a thermal gradient has both damping-like and field-like components. By analyzing DW propagation speed and DW-plane rotational speed, the coefficient ([Formula: see text]) of the field-like STT arising from the non-adiabatic process, is obtained. It is found that [Formula: see text] does not depend on the thermal gradient; increases with uniaxial anisotropy [Formula: see text] (thinner DW); and decreases with the damping, in agreement with the physical picture that a larger damping or a thicker DW leads to a better alignment between the spin-current polarization and the local magnetization, or a better adiabaticity.

Diffusion of interface and heat conduction in the three-dimensional Ising model

We investigate the relationship between a diffusive motion of an interface, heat conduction, and the roughening transition in the three-dimensional Ising model. We numerically compute the thermal conductivity and the diffusion constant and find that the diffusion constant shows a crossover in its temperature dependence. The crossover temperature is equal to the roughening transition temperature in equilibrium and deviates from it when heat flows in the system. From these results, we discuss the possibility that heat conduction causes a shift of the roughening transition temperature.

Thermal gradients for the stabilization of a single domain wall in magnetic nanowires

By means of Monte Carlo simulations we studied field driven nucleation and propagation of transverse domain walls (DWs) in magnetic nanowires subjected to temperature gradients. Simulations identified the existence of critical thermal gradients that allow the existence of reversal processes driven by a single DW. Critical thermal gradients depend on external parameters such as temperature, magnetic field and wire length, and can be experimentally obtained through the measurement of the mean velocity of the magnetization reversal as a function of the temperature gradient. Our results show that temperature gradients provide a high degree of control over DW propagation, which is of great importance for technological applications.

Numerical simulations of critical dynamics in anisotropic magnetic films with the stochastic Landau-Lifshitz-Gilbert equation

With the stochastic Landau-Lifshitz-Gilbert (sLLG) equation, critical dynamic behaviors far from equilibrium or stationary around the order-disorder and pinning-depinning phase transitions in anisotropic magnetic films are investigated. From the dynamic relaxation with and without an external field, the Curie temperature and critical exponents of the order-disorder phase transition are accurately determined. For the pinning-depinning phase transition induced by quenched disorder, the nonstationary creep motion of domain wall activated by finite temperatures is simulated, and the thermal rounding exponent is extracted. The results show that the dynamic universality class of the sLLG equation is different from those of the Monte Carlo dynamics and quenched Edwards-Wilkinson equation, and it may lead to alternative understanding of experiments. The dynamic approach shows its great efficiency for the sLLG equation.

Light-Induced Metastable Magnetic Texture Uncovered by in situ Lorentz Microscopy

Magnetic topological defects, such as vortices and Skyrmions, can be stabilized as equilibrium structures in nanoscale geometries and by tailored intrinsic magnetic interactions. Here, employing rapid quench conditions, we report the observation of a light-induced metastable magnetic texture, which consists of a dense nanoscale network of vortices and antivortices. Our results demonstrate the emergence of ordering mechanisms in quenched optically driven systems, which may give a general access to novel magnetic structures on nanometer length scales.

Inertia-Free Thermally Driven Domain-Wall Motion in Antiferromagnets

Domain-wall motion in antiferromagnets triggered by thermally induced magnonic spin currents is studied theoretically. It is shown by numerical calculations based on a classical spin model that the wall moves towards the hotter regions, as in ferromagnets. However, for larger driving forces the so-called Walker breakdown-which usually speeds down the wall-is missing. This is due to the fact that the wall is not tilted during its motion. For the same reason antiferromagnetic walls have no inertia and, hence, no acceleration phase leading to higher effective mobility.

The inverse thermal spin-orbit torque and the relation of the Dzyaloshinskii-Moriya interaction to ground-state energy currents

Using the Kubo linear-response formalism we derive expressions to calculate the electronic contribution to the heat current generated by magnetization dynamics in ferromagnetic metals with broken inversion symmetry and spin-orbit interaction (SOI). The effect of producing heat currents by magnetization dynamics constitutes the Onsager reciprocal of the thermal spin-orbit torque (TSOT), i.e. the generation of torques on the magnetization due to temperature gradients. We find that the energy current driven by magnetization dynamics contains a contribution from the Dzyaloshinskii-Moriya interaction (DMI), which needs to be subtracted from the Kubo linear response of the energy current in order to extract the heat current. We show that the expressions of the DMI coefficient can be derived elegantly from the DMI energy current. Guided by formal analogies between the Berry phase theory of DMI on the one hand and the modern theory of orbital magnetization on the other hand we are led to an interpretation of the latter in terms of energy currents as well. Based on ab initio calculations we investigate the electronic contribution to the heat current driven by magnetization dynamics in Mn/W(0 0 1) magnetic bilayers. We predict that fast domain walls drive strong heat currents.

Swift thermal steering of domain walls in ferromagnetic MnBi stripes

We predict a fast domain wall (DW) motion induced by a thermal gradient across a nanoscopic ferromagnetic stripe of MnBi. The driving mechanism is an exchange torque fueled by magnon accumulation at the DWs. Depending on the thickness of the sample, both hot-to-cold and cold-to-hot DW motion directions are possible. The finding unveils an energy efficient way to manipulate DWs as an essential element in magnetic information processing such as racetrack memory.

Controlling the magnetic structure of Co/Pd thin films by direct laser interference patterning

Nanosecond pulsed two-beam laser interference is used to generate two-dimensional temperature patterns on a magnetic thin film sample. We show that the original domain structure of a [Co/Pd] multilayer thin film changes drastically upon exceeding the Curie temperature by thermal demagnetization. At even higher temperatures the multilayer system is irreversibly changed. In this area no out-of-plane magnetization can be found before and after a subsequent ac-demagnetization. These findings are supported by numerical simulations using the Landau-Lifshitz-Bloch formalism which shows the importance of defect sites and anisotropy changes to model the experiments. Thus, a one-dimensional temperature pattern can be transferred into a magnetic stripe pattern. In this way one can produce magnetic nanowire arrays with lateral dimensions of the order of 100 nm. Typical patterned areas are in the range of several square millimeters. Hence, the parallel direct laser interference patterning method of magnetic thin films is an attractive alternative to the conventional serial electron beam writing of magnetic nanostructures.