Session A42: Chiral and Topological Spin Textures

Manipulation of topological spin structures at ultrathin magnetic interfaces by oxygen adsorption and interlayer exchange coupling

Magnetic skyrmions have been investigated from fundamental physics to applications for next generation high-density information encoding. Such non-collinear magnetic structures at interfaces are usually attributed to the Dzyaloshinskii-Moriya interaction (DMI) when the inversion symmetry is broken.
Here we report two ultrathin ferromagnetic systems, where the first one demonstrates a microscopic insight on how the oxygen adsorption modulates the spin reorientation transition (SRT) of a Fe/Ni bilayer on Cu(100) and consequently impacts on the DMI of the interface. The second case shows that even in a negligible DMI interface, such as Co/Au(111), magnetic skyrmion bubbles can be stabilized at room temperature in the metastable phase of spin canting configuration within the SRT by interlayer exchange coupling across a non-magnetic spacer layer. The magnetic images are measured by X-ray magnetic circular dichroism (XMCD) based photoemission electron microscopy (PEEM), and the experimental results are discussed with the help of micromagnetic simulations.   

Equilibrium thermodynamic properties of chiral skyrmions in ferromagnetic materials

The equilibrium statistical thermodynamics of chiral magnetic skyrmions developing in a ferromagnetic material having the shape of an ultrathin cylindrical dot is investigated. This is accomplished by determining via analytical calculations for both hedgehog and vortex-like skyrmions: 1) the internal energy of a single chiral skyrmion; 2) the skymion radius depending on magnetic and geometric parameters; 3) the skyrmion configurational entropy; 4) the partition function; 5) the free energy; 6) the pressure and 7) the equation of state of a skyrmion diameters population. For the calculation of the thermodynamic functions we nake the analogy between the skyrmion diameters population and the three-dimensional Maxwell-Boltzmann distribution of particles of an ideal gas [1]. It is shown that, in correspondence of the average skyrmion volumes, the pressure curves of the skyrmion diameters population intersect the pressure curves of the ideal gas at different temperatures. These results could advance the field of materials science with special regard to skyrmionics.
[1] R. Zivieri et al., Phys. Rev. B 99, 174440 (2019).   

Theory of the Lifetime of Metastable Skyrmions in Chiral Magnets

Understanding the lifetime of metastable skyrmions in chiral magnetic materials is both of fundamental interest and of practical importance. We use the Landau-Lifshitz-Gilbert equation with thermal noise to derive the activated rate for an isolated metastable skyrmion to decay into the stable ferromagnetic state. Our formalism includes damping as well as the effects of entropic corrections to the energy barrier within a Gaussian approximation. We show that the nature of the saddle point that needs to be crossed for the decay of a skyrmion changes from a Bloch point singularity in 2D systems to a chiral bobber in films with thickness L > L_D=2π J/D. We will present numerical and variational results as a function of ferromagnetic exchange J, Dzyaloshinskii-Moriya interaction D, effective anisotropy K, and the external field B, and discuss the relation between the size and lifetime of metastable skyrmions.   

Melting the skyrmion lattice - from solid to liquid via a hexatic phase

The most commonly seen phase transition is possibly "melting", a transition from ordered crystalline solids to disordered isotropic liquids. While melting in three-dimensions is always a single, fist-order phase transition, in two-dimensional systems a scenario of two continuous phase transitions separated by an intermediate "oriented liquid" state, the so-called hexatic phase, has been proposed theoretically and evidenced experimentally in colloidal systems, Wigner solids and liquid crystals. Fundamentally different from these real-matter particles, skyrmions are countable soliton configurations localized in continuous filds with non-trivial topology, and these emergent quasi-particles can form two-dimensional lattices, whose melting dynamics remains unexplored. Here we show, by direct imaging with cryo-Lorentz transmission
electron microscopy, that the phase of the skyrmion ensembles in the material Cu2OSeO3 can be tuned by magnetic fild from two-dimensional skyrmion solids, through the long-speculated skyrmion hexatic phase, to skyrmion liquids, with the local spin order preserved throughout the whole process. Remarkably, our quantitative analysis demonstrates that this mesoscopic phase transition can be well described as topological-defect-induced crystal melting in two dimensions. By uncovering the novel phase behaviors of skyrmionic quasi-particles, we demonstrate skyrmion ensembles as an ideal platform for exploring novel properties in two-dimensions.   

Quantifying Order in Magnetic Systems with Convolutional Neural Networks

Quantifying the order parameters in simulations of disordered magnetic systems to reliably represent magnetic states requires efficient interpretation of the often irregular magnetic patterns contained in large data sets. In helimagnetic materials with impurities, or at non-zero temperatures, the helical and skyrmion textures become distorted and embedded in noisy backgrounds with varying topological properties. Standard approaches based on quantifying the order parameters by averaging the spin states over a lattice, or computing pair correlation functions often become inconclusive. In this presentation, we discuss an approach based on applying convolutional neural networks (CNNs) to extract representative features of skyrmionic textures from simulated snapshots of complex magnetic backgrounds. Using large-scale micromagnetic simulations of a broad class of helimagnetic materials we show that CNNs are capable of not only accurately resolving the underlying magnetic textures, but also allow for regression to accurately predict classes of micromagnetic models representative of the observable magnetic textures. We then draw general conclusions about the uniqueness and invertibility of micromagnetic models of helimagnetic materials.   

Creation of magnetic skyrmions by surface acoustic waves in Pt/Co/Ir trilayer films

A magnetic skyrmion, a particle-like noncoplanar topological spin structure characterized by a nonzero topological integer called the skyrmion number, has great potential for various spintronic applications. In particular, efficient and practical means to create skyrmions is an important technological issue. However, creation of skyrmions has been achieved by only using currents so far, and moreover, in these methods, the skyrmions are only created at a specific position in the films.
In this presentation, we demonstrate a novel approach for skyrmion creation by employing surface acoustic waves (SAWs); in asymmetric multilayers of Pt/Co/Ir, we experimentally observed at room temperature that skyrmions can be created by propagating SAWs in a wide area of the magnetic film due to the long propagation length of SAWs. Micromagnetic simulation reveals inhomogeneous torque arising from both SAWs and thermal fluctuations creates a pair of Néel and antiskyrmion-like structure, which subsequently transforms to Néel skyrmion due to the instability of antiskyrmion-like structure in systems with interfacial Dzyaloshinskii-Moriya interaction. Our finding provides a novel guiding principle for efficient manipulation of topological spin objects without Joule heating dissipation.   

Thermal Collapse of a Skyrmion

Thermal collapse of an isolated skyrmion on a two-dimensional spin lattice has been investigated. The method is based upon solution of the system of stochastic Landau-Lifshitz equations for up to 104 spins. The recently developed pulse- noise algorithm has been used for the stochastic component of the equations. The collapse rate follows the Arrhenius law. Analytical formulas derived within a continuous spin-field model support numerically-obtained values of the energy barrier. The pre-exponential factor is independent of the phenomenological damping constant that implies that the skyrmion is overcoming the energy barrier due to the energy exchange with the rest of the spin system. Our findings agree with experiments, as well as with recent numerical results obtained by other methods.   

Operando study of chiral magnetic textures under electrical bias using Lorentz scanning transmission electron microscopy

We develop a device fabrication process that is compatible with operando Lorentz Scanning Transmission Electron Microscopy (LSTEM) for studying chiral magnetic textures and their electric current dependent behavior with nanometer-scale spatial resolution. Chiral magnetic spin textures appear in our samples as a result of the interplay between magnetic energy terms including interfacial Dzyaloshinskii-Moriya Interaction and perpendicular magnetic anisotropy (PMA) at heavy metal/ferromagnet interfaces. High-resolution LSTEM can resolve the internal structure of spin textures including details as small as a few nm. As a first step, we examine stripe domain and field nucleated Néel Skyrmions in devices as we vary the stack repetition and ferromagnet thicknesses. We find rich magnetic textures with a strong history dependence as the magnitude of PMA approaches zero.   

Robust magnetization dynamics and magnetocaloric anomalies across the phase diagrams of noncollinear magnets

Incommensurate magnetic structures stabilized by the Dzyaloshinskii-Moriya interaction exhibit long-range phase coherence over macroscopic length scales. Depending on the crystal symmetry, the magnetocrystalline anisotropy controls the orientation of the propagation vector and may also enhance the robustness of the magnetic texture. We present recent studies on the magnetic phase evolution of noncollinear spin textures analyzing the nonlinear ac magnetic response and magnetocaloric effect for selected crystalline magnetic materials with broken inversion symmetry: Cr_1/3NbS₂, GaV4S8, and MnSi. Each realize solitonic spin textures of varying dimension and helicity due to distinct differences in magnetocrystalline anisotropy. By analyzing the anomalous nonlinear response and dynamic magnetic loss, we characterize the rigidity of the various spin textures against an ac magnetic field. Additionally, our magnetocaloric measurements uncover phase regimes characterized by field-induced spin fluctuations, where entropy increases across the metamagnetic transition. The combined analysis reveals details about the complex ordering and magnetization processes that may be useful for identifying new magnetic phases emerging from long-period spin textures.   

Surface acoustic waves (SAW) and pinning of magnetic domain walls in a ferromagnetic multilayer.

The pinning of magnetic domain walls (DW) results in reduced velocities and non-deterministic motion of domain walls. Perpendicular anisotropy (PMA) materials display narrow, stable DWs but the pinning barriers have a significant effect due to the small width. We investigate the effects of SAW on pinning and motion of domain walls in films of Cr(2nm)/Pt(2nm)/[Co(0.3nm)/Pt(0.6nm)]₅ that are patterned into micron wide stripes between a pair of inter-digital transducers (IDTs), all on a 128 -Y cut LiNbO₃ substrate. Measurements were made using a magneto-optical Kerr effect microscope. Preliminary measurements of DW motion using magnetic field pulses, varying both the width and the height of the pulse identified the location, pinning potential and critical field of highly reproducible strong pinning sites. The effect of SAW on these well characterized pinning sites indicate that SAW are able to depin DW even from deep pinning potentials. The standing wave generated by the IDT pair allows for measurements at both the and antinodes of the SAW. Between these deep pinning sites, DW motion is consistent with creep behavior, with increasing SAW amplitude increasing the DW velocity.   

Skyrmions and antiskyrmions from current-induced boundary instabilities

We study generation and dynamics of skyrmions and antiskyrmions using current-induced torques at interfaces between adjacent regions with differing properties such as DMI (Dzyaloshinskii-Moriya interaction), anisotropy, exchange, etc.. The generation of skyrmions and antiskyrmions can be interpreted as a current-induced Doppler shift acting on the magnons localized at the interface. These localized modes are analyzed by using the Bogoliubov-de-Gennes Hamiltonian written for magnons. We confirm our theoretical predictions using micromagnetics simulations, where we observe that a current pulse closes the magnon band gap, leading to instabilities in the magnetic texture at the interface between different regions. From micromagnetic simulations, we observe that the closure of the magnon band gap effectively causes the system to form skyrmions and/or antiskyrmions, depending on the type of DMI present.   

Stability of biskyrmions in centrosymmetric magnetic films

In [1], we investigate analytically and numerically the stability of biskyrmions in films of finite thickness, taking into account the nearest-neighbor exchange interaction, perpendicular magnetic anisotropy (PMA), dipole-dipole interaction (DDI), and the discreteness of the atomic lattice. The biskyrmion is characterized by the topological charge Q=2, the spatial scale λ, and another independent length d that can be interpreted as a separation of two Q=1 skyrmions inside a Q=2 topological defect in the background of uniform magnetization. We find that biskyrmions with d of order λ can be stabilized by the magnetic field within a certain range of the ratio of PMA to DDI in a film having a sufficient number of atomic layers Nz. The shape of biskyrmions has been obtained by the numerical minimization of the energy of interacting spins in a 1000×1000×Nz atomic lattice. It is close to the exact solution of the Belavin-Polyakov model when d is below the width of the ferromagnetic domain wall. We compute the magnetic moment of a biskyrmion and discuss ways of creating biskyrmions in experiment.

[1]D. Capic, D. Garanin and E.M. Chudnovsky, Stability of biskyrmions in centrosymmetric magnetic films, Phys. Rev. B 100, 014432 (2019).   

Magnetic domain dynamics in an insulating quantum ferromagnet

The structure of free-energy manifolds with many local minima are of great interest in the context of quantum computation and optimization. In the disordered ferromagnet, LiHo_xY_1-xF_4, quenched disorder and frustration, driven by the combination of chemical substitution and the anisotropic magnetic dipolar coupling, give rise to one such example of a complex, traversable free-energy landscape. We probe the structure of this landscape and the dynamics of the driven system by measuring the statistics and form of magnetic avalanches due to domain-wall motion. For large avalanches at temperatures approaching the Curie point, we find a response free of the signatures of drag effects. By contrast, in the low temperature limit, drag effects contribute to the dynamics, which we attribute to enhanced pinning from local random fields due to the disorder. Furthermore, as an applied transverse magnetic field is increased, the dynamics of the system can be tuned by progressively strengthening the random-field pinning and then increasing the quantum tunneling rate. Tuning from a classical regime to a quantum regime dominated by tunneling reveals the structure of the free-energy surface and barriers to domain reorientation, with applications to quantum annealing.