Session H41: Skyrmion Crystals

Various topological spin textures and their dynamics in helimagnets

The ability to manipulate topological spin textures such as skyrmions is a key to the development of electronic devices that are very low in power consumption¹. Recently, hexagonal skyrmion lattice (hex-SkL) have been discovered in several systems, such as chiral/polar^2-3 magnets and ferromagnets with uniaxial anisotropy⁴. In addition to the hex-SkL, we have observed the first for a square lattice of merons and antimerons (sq-ML)—topologically distinguish with skyrmions in a thin plate of the helimagnet Co₈Zn₉Mn₃⁵. By finely varying the magnetic field applied perpendicularly to the plate, the transformation between the sq-ML and hex-SkL has been obtained. We found that the skyrmions were very robust, lasting even as we lowered the temperature of the plate, but the merons and antimerons were much more sensitive, and relaxed into spin helices as the temperature fell.
The transition between a hex-SkL and non-topological spin textures, helical or conical structure, have been also demonstrated by the in-situ Lorentz transformation electron microscopy observations with current excitation or field cooling in a helimagnet FeGe⁶. The skyrmion dynamics, such as the collective transformation of sparsely-populated skyrmions to microcrystals of skyrmions, and the current-driven skyrmion motion have been observed.
This work has been done in collaboration with Profs. Yoshinori Tokura, Naoto Nagaosa, Taka-hisa Arima, Yusuke Tokunaga and Fumitaka Kagawa, and with Drs. Wataru Koshibae, Yasujiro Taguchi, Daisuke Morikawa, Naoya Kanazawa, Tomoyuki Yokouchi and Kiyou Shibata.
[1] N. Nagaosa and Y. Tokura, Nat. Nanotechnol. 8, 899 (2013).
[2] X.Z. Yu, et al., Nature 465, 901 (2010).
[3] I. Kézsmárki, et al., Nat. Mater. 14, 1116 (2015).
[4] X.Z. Yu, et al., PNAS 109, 8856 (2012).
[5] X.Z. Yu, et al., Nature 564, 95 (2018).
[6] X.Z. Yu, et al., Nat. Phys. 14, 832 (2018).   

Field-tuned skyrmion crystals: anomalous quantum oscillations induced by Zeeman fields

Recent experiments on chiral magnets have observed skyrmion crystal phases which are stable in the presence of Dzyaloshinsky-Moriya interactions and Zeeman fields. Skyrmion crystal coupled to itinerant electrons manifests itself in electronic transport as the anomalous “topological Hall effect” caused by a real-space Berry-phase mechanism. This also leads a formation of Chern bands which depend on the properties of the skyrmion crystal unit cell. Our study has shown that incorporating quartic spin interactions into a system which hosts a skyrmion crystal results in a field-tunable skyrmion lattice constant. Itinerant electrons coupled to such skyrmion crystals can then be described by a Hofstadter-type model whose Chern bands depend strongly on the Zeeman field coupled to the local moments. Such metallic magnets serve as candidates for observing Zeeman-field-induced anomalous quantum oscillations.   

Unpinning the skyrmion lattice in MnSi

Materials hosting magnetic skyrmion lattices are promising materials for future spintronic applications. Given their potential technological use, it is important to understand the response of these magnetic textures under different physical and chemical environments. We have investigated the behavior of the skyrmion lattice in MnSi_1-xGa_x single crystals with variations in the temperature and the magnitude and direction of a magnetic field using small angle neutron scattering and magnetization measurements. Our results indicate that the disorder caused by the inclusion of even of small amount of a heavier element such as Ga can substantially change the pinning of the skyrmion lattice when compared to pure MnSi.   

Magnetic Hysteresis of the Skyrmion Lattice in MnSi

Understanding the complex dynamics of skyrmion formation and destruction is key to developing new technologies which make use of them. Here we report the observation of a hysteresis effect associated with forming and destroying the SkL in the chiral magnet MnSi using small angle neutron scattering (SANS). This effect is very small when compared to the applied field of the cryomagnet (~ 1 mT vs 200 mT), but is observable and reproducable by the added precision of a custom built solenoid supplementing the cryomagnet. This hysteresis effect is due to an intrinsic energy barrier associated with forming and destroying the SkL. We have explored the time dependence and magnetic history dependence of the phenomenon to better understand its origin, which we believe to be related to the intrinsic topological energy barrier associated with forming the skyrmions.   

Transitions between skyrmion- and hedgehog-lattice states in cubic chiral magnets MnSi1-xGex

Topological spin textures such as magnetic skyrmions and spin hedgehogs show novel emergent phenomena, which can be exploited for spintronic functionalities. Whereas the formation or deletion of them has been intensively studied so far, switching of spin textures among different topologically-nontrivial classes remains largely unexplored.
We report on transitions between skyrmion- and hedgehog-lattice states in cubic chiral magnets MnSi_1-xGe_x with variation of lattice constant controlled by Si/Ge substitution. By combining neutron scattering, Lorentz transmission electron microscopy and high-field transport measurements, we observe three different topological spin textures: skyrmion lattice in x = 0-0.25 as well as two distinct hedgehog lattices in x = 0.3-0.7 and x = 0.8-1, as respectively characterized by large topological Hall effects.
The emergence of various topological spin states in the chemical-pressure-controlled materials suggests a new route for direct manipulation of the spin-texture topology by a simple mechanical method such as pressure.
  

First-principles study of oxide skyrmion crystal Chern insulator

The magnetic skyrmion crystal (SkX), formed by a topological vortex-like spin in condensed matter, has attracted considerable attention in last decade. We performed density functional calculations for SkX in electron-doped EuO monolayer and found Chern insulating ground state where Chern number C=2[1]. Calculated large anomalous Nernst effect [1,2] and electric-field effect will be discussed.
[1] Y. P. Mizuta, H. Sawahata, and F. Ishii, "Large anomalous Nernst coefficient in an oxide skyrmion crystal Chern insulator", Phys. Rev. B, in press. arXiv:1803.08148.
[2] Y. P. Mizuta, and F. Ishii, "Large anomalous Nernst effect in a skyrmion crystal", Sci. Rep. 6, 28076 (2016).   

Collective antiskyrmion-mediated phase transition and defect-induced melting in chiral magnetic films

The topological stability of skyrmions goes beyond the energetics of materials and strongly depends on the dynamics of magnetization textures, and the combined effects of energetics, topology, and magnetization dynamics, lead to wildly rich phenomena. Based on detailed high-resolution micromagnetic simulations, we have found a new first-order field-induced phase transition in which a skyrmion lattice inverts its polarity through a metastable creation and annihilation of an antiskyrmion lattice. Importantly, we have observed that in the presence of even a single defect in the material, the phase transition becomes second-order and progresses through a gradual melting of the skyrmion lattice. Our analysis suggests that in a perfect skyrmion lattice the response to an external magnetic field is an abrupt collective phenomenon due to topological constraints, whereas a single defect disrupts the constraint and facilitates topological charge melting, consequently leading to the gradual response of the material to an external field. This provides a basis for a much wider scope of experiments on skyrmion lattices, with emphasis on the interplay between topological constraints and material defects.   

Skyrmion Crystals in Decorated Transition Metal Dichalcogenides.

We investigate the existence of skyrmion crystal phases in decorated transition metal dichalcogenides (TMDs) such as X/MoS₂, for {X=Co,Ni,Fe}. We model the system using a frustrated triangular lattice, in the presence of in-plane and out-of-plane Dzyaloshinskii-Moriya interaction. We study the phase diagram by varying the strength of the Heisenberg exchange, Dzyaloshinskii-Moriya interaction, and anisotropy. We also perform Monte Carlo simulations to study the H-T (magnetic field - temperature) phase diagram. We study the appearance of the antiferromagnetic skyrmion crystals residing on the three sublattices of the decorated TMDs. The phase transitions and characteristics of the phases are obtained by computing the specific heat C and the spin structure factor S_k.   

Chiral domain topology, Moiré patterns, and magnetism in M1/3Nb(Ta)S(Se)2 (M=transition metals)

Transition metal dichalcogenides (TMDs) have been extensively investigated as 2D materials last decade. A large amount of transition metals can be intercalated into the van der Waals gaps of a wider range of TMD materials, but a limited studies have been recently reported in intercalated TMDs. The limited examples include Fe_xTaS₂ crystals with x=1/4 and 1/3, which exhibit intriguing configurations of antiphase and/or chiral domains related to ordering of intercalated M ions with 2a×2a and √3a×√3a superstructures, respectively. In addition, Cr_1/3NbS₂ undergoes helical spin order below 133 K, and shows an interesting solitonic behavior when in-plane magnetic fields are applied in the helical spin state. We have explored a series of chiral M_1/3Ta(Nb)S(Se)₂ (M=transition metals) to investigate the correlation among crystallographic and magnetic domain topologies and their physical properties. These results as well as Moiré patterns with self-twisted TMDs induced by intercalation will be discussed.
  

Monte Carlo studies of the phases and phase diagram of quasi 2D Skyrmion systems

We present results for large-scale Monte Carlo simulations of the field-temperature phase diagram of thin-film chiral magnets with ferromagnetic exchange and Dzyaloshinskii-Moriya interaction. Using spin structure factors, skyrmion density structure factors, magnetization and specific heat, we show that there are five interesting regions of the phase diagram: (1) a skyrmion solid phase, (2) a skyrmion liquid regime, (3) a helical phase, (4) a fluctuating helical regime, and (5) a field-polarized regime. Using orientational order parameters we identify the phase boundaries for the skyrmion melting transition and the helical melting transition. We also investigate the phase diagram as a function of film thickness L, showing how that the interlayer correlations and the maximum transition temperature for the skyrmion solid evolves as a function of L/L_D, where L_D is the helical pitch length.   

Computational-Guided Search for Ultrasmall Skyrmions in Ferrimagnets

Magnetic skyrmions are topologically protected spin textures. They can potentially improve density and energy efficiency in memory and logic devices. With the immense material's space, it could take years to experimentally explore all the possible materials for skyrmions' device application. To guide experiments, we employ computational models to identify several materials for stabilizing ultrasmall skyrmions at room temperature. One of the more promising candidates is amorphous rare-earth-transition-metal ferrimagnet. Our atomistic stochastic Landau-Liftshitz-Gilbert (LLG) model has revealed that Néel skyrmions, with a diameter of 10 nm or less, are stable in 5 nm thick GdFe and GdCo at room temperature. Following this guidance, we have fabricated GdCo samples and controlled the Dzyaloshinskii-Moriya interaction (DMI) through tuning the interfacial layers. Results from these samples are used as feedbacks to refine our computational models. Using this computational-guided approach, the time needed to explore promising materials for skyrmions-based devices will be vastly reduced.   

Imaging Skyrmion Magnetization Dynamics in Time-Resolved Lorentz Electron Microscopy

The creation, annihilation, movement, and control of magnetic skyrmions with different tools has been the subject of intensive research in recent years. So far, little attention has been given to the use of light as (yet another) external knob to trigger magnetic changes in skyrmion-hosting materials.
With a combination of camera-rate and ultrafast pump-probe Lorentz Transmission Electron Microscopy we directly resolve the spatio-temporal evolution of the skyrmion magnetization ensuing (fs and ns) optical excitation. The laser-induced creation and annihilation of skyrmions in bulk (Bloch) and interfacial (Néel) systems is reported, and the ultimate speed of such writing and erasing is discussed. In a 60-nm thick slab of the prototypical chiral magnet FeGe, we study how the extreme cooling rates of the crystal ( > 10⁷ K/s) following the photoexcitation can quench the magnetization into a disordered metastable skyrmion lattice.   

Dynamics in Multiferroic Skyrmion GaV4S8

GaV₄S₈ is a rare example of a material hosting a multiferroic Neel-type Skyrmion [1]. We have grown 91 mg single crystals of this material and explored the field/temperature phase diagram using Small Angle Neutron Scattering (SANS) as a probe. We have also investigated the dynamics of the skyrmion phase. In this study, we apply a static field along the [111] crystallographic direction. We also apply a modulated magnetic field along this direction and observe time tagged events on our detector to observe the time dependence. In this talk, we will discuss our results in the context of recent AC susceptibility measurements [2].

References: [1] I. Kézsmárki et al., Nature Materials 14, 1116 (2015)
[2] Ádám Butykai et al., Phys. Rev. B 96, 104430 (2017)