Session W54: Transport and Dynamics of Skyrmions

Few-nm tracking of magnetic vortex core trajectories near and inside defects

Nanoscale magnetic textures such as vortices and skyrmions have attracted attention for applications in memory, logic, or microwave sources. For these applications, the effect of defects on the magnetization dynamics is critical, which can cause pinning or deviations of the trajectory as predicted by the Thiele equation. We report on the experimental observation of magnetic vortex core motion inside and near defects. We use a 3D time-resolved Kerr microscope to track the trajectory of a magnetic vortex core with spatial resolution of several nanometers and nanosecond time resolution [1]. We position the vortex core within a thin permalloy disk using a static magnetic field and excite the vortex core dynamics using a fast magnetic pulse. In a region relatively free of defects, the trajectory of the vortex core is a circular spiral path, decaying to the equilibrium position. When the moving vortex core approaches a defect that causes significant vortex pinning, however, we observe that the vortex core continues moving but deviates from its circular path in response to the defect. Sufficiently close to a large defect, we also observe enhanced damping to a new pinned equilibrium within the defect. This technique provides a method for probing the motion of nanoscale spin textures as they interact with defects in the material either leading to pinning or altered dynamics.

[1] M. Mehrnia, J. Trimble, and J. Berezovsky, Three dimensional frequency-and phase-multiplexed magnetooptical microscopy, Opt. Express 27, 33942 (2019).   

Relaxation of magnetic skyrmions driven in a channel

Understanding the behavior of magnetic skyrmions on tracks is an important step in the pursuit of skyrmion-based devices. Many proposed devices confine magnetic skyrmions to narrow magnetic strips that are thin enough to be considered two-dimensional. We investigated how driven magnetic skyrmions would relax when subjected to a drive after starting in an initially disordered state due to the strength of the Magnus force. We used a coarse grain particle model for magnetic skyrmions, to determine the relaxation behavior of skyrmions in a 2d channel with a constant and periodic drive. To do this, we looked at a covering factor to qualitatively understand the positioning of skyrmions in respect to their position along the height of the channel. We also looked at how the average distance between skyrmions is affected as a function of time. We show that even in this constrained geometry, the skyrmions order faster with increasing strength of the Magnus force. Conversely, when the skyrmions are subjected to a periodic drive after reaching the steady state, they relax faster with a decrease in the strength of the Magnus force.   

Local Ferromagnetic Resonance of Mesoscopic Structures Using Deterministically Placed Nanodiamonds

Nitrogen-vacancy (NV) centers in diamond offer a powerful method of measuring local magnetization dynamics in ferromagnetic materials. To date, measurements of ferromagnetic resonance (FMR) using NV centers have relied on a stochastic distribution of NV centers or their rough placement on a micron scale. Here, we demonstrate sub-100 nm placement accuracy of NV-containing nanodiamonds using an atomic force microscope and use this capability to perform optically detected FMR measurements on mesoscopically-patterned permalloy structures. By probing FMR using nanodiamonds deterministically placed at different sites on individual nanoscale ferromagnetic structures, we detect localized differences in the FMR signal and compare these with results from micromagnetic simulations. The technique has potential application in the study of localized spin dynamics of individual magnetic nanostructures as well for probing the dynamics of individual domain walls.   

Topological Spin Textures in Three Dimensions

Chiral magnets are a series of magnets with broken inversion symmetry. A new type of spin interaction therein, the Dzyaloshinskii-Moriya interaction, stimulates the formation of many novel topological spin textures. One important example is the emergence of magnetic skyrmion, whose nontrivial topology enables unique dynamical property and thermal stability, and gives rise to promising applications in future spintronic devices. However, skyrmion is just a two-dimensional texture. Its three-dimensional (3D) counterparts are widely unexplored. In this talk, I will discuss realization of 3D skyrmionic textures, including target skyrmion¹, skyrmion bundle², and skyrmionic vortices³. I will also discuss the magnetic hopfion, a rigorously defined 3D topological texture. We propose the presence of zero-field hopfion in synthetic chiral magnetic multilayers⁴. All these 3D textures exhibit novel dynamical properties that can be formulated in terms of collective coordinates⁵. These works could stimulate the development of 3D spintronics.

References: 

¹F. Zheng, H. Li, S. Wang, D. Song, C. Jin, W. Wei, A. Kovacs, J. Zang, M. Tian, Y. Zhang, H. Du, and R. E. Dunin-Borkowski, Physical Review Letters 119, 197205 (2017). 

²J. Tang, Y. Wu, W. Wang, L. Kong, B. Lv, W. Wei, J. Zang, M. Tian, and H. Du, Nature Nanotechnology (2021) in press.

³K. Niitsu, Y. Liu, A. C. Booth, X. Z. Yu, N. Mathur, M. J. Stolt, D. Shindo, S. Jin, J. Zang, N. Nagaosa, and Y. Tokura, Nature Materials (2021) in press.

⁴Y. Liu, R. K. Lake, J. Zang, Physical Review B 98, 174437 (2018).

⁵Y. Liu, W. T. Hou, X. F. Han, and J. Zang, Physical Review Letters 124, 127204 (2020).   

Magnetization switching and spin oscillation dynamics in non-collinear antiferromagnets

Antiferromagnets (AFs) are promising candidates for next-generation spintronic devices, because of distinct benefits, such as fast magnetization dynamics and reduced crosstalk from magnetostatic interactions [1]. Towards this end, non-collinear AFs are particularly interesting for AF spintronics, since they exhibit a large anomalous Hall effect which can be used for detecting the magnetic order [2], which furthermore can be modulated electrically by the spin-orbit torques [3]. However, the detailed spin dynamics in the non-collinear AFs have not been satisfactorily explored. Here, we theoretically investigate spin dynamics in the non-collinear AFs, Mn3Sn. We prepare a minimal atomistic-spin model on a two-dimensional kagome lattice. From the model, we numerically calculate the switching dynamics among six degenerate stable configurations and compute AF resonance oscillations and the frequency. From the result, we find that different responses can be expected from in-plane and out-of-plane measurements, because of phase differences among the spin precessions. This work provides further insights required for non-collinear AF spintronics.

[1] T. Jungwirth, et al., Nat. Nanotech. 11, 231 (2016).

[2] S. Nakatsuji et al., Nature 527, 212 (2015).

[3] H. Tsai et al., Nature 580, 608 (2020).   

Imaging Neel Vector Switching Using Nitrogen Vacancy Centers in Diamond

Control of the orientation of the antiferromagnetic order parameter in systems with multiple easy-axes is provides a promising route to high frequency information processing.  NV relaxometry arising from the resulting terahertz magnetic dynamics could provide diagnostic imaging. Nitrogen vacancy (NV) centers are sensitive, local and non-invasive probes of magnetic dynamics but have until recently been limited to detection of dynamics at or below the NV resonant frequency (~3 GHz). It has recently been shown that two magnons in ferromagnetic and antiferromagnetic systems may scatter emitting electromagnetic noise at their difference frequency. Thus THz frequency dynamics associated antiferromagnetic magnons, which would otherwise be undetectable using an NV, can be detected when this difference frequency is resonant with the NV precession. Switching the Neel vector from one easy-axis to another can be achieved by means of current-induced spin-orbit torque.   

Field-driven resonances of magnetic Hopfions

Here, we report on micromagnetic simulations of fast dynamics in three dimensional spin textures. We focus on the resonant spin wave modes of magnetic Hopfions up to 15 GHz driven by external magnetic fields. A sharp transition is found around 66 mT coinciding with a transition from Hopfions to torons. The modes exhibit characteristic amplitudes in frequency space accompanied by unique localization patterns in real space, and are found to be robust to damping around topological features, particularly vortex lines in Hopfions and Bloch points in torons. Most remarkably, we have identified pronounced differences in spin wave spectra between Hopfions, torons and target skyrmions that can serve as fingerprints in future experimental validation studies of these novel 3d topological spin textures.   

Electrical generation and deletion of magnetic skyrmions via vertical current injection

Due to its distinct topological features, magnetic skyrmions have recently been considered to be a novel information carrier in spintronics[1, 2]. The electrical creation/deletion of a magnetic skyrmion is ecessential in realizing skyrmion-based spintronics devices. Therefore, various experimental demonstrations of skyrmion creation/deletion have been reported using diverse methods [3, 4]. However, most of them have been created near a randomly created defect site, disturbing the skyrmion motion after the creation. Here, we introduce a new method for electrical creating, deleting, and shifting magnetic skyrmions by adopting a vertical current injection. We will show proof-of-concept demonstration of skyrmion reacetrack memory.   

Orbital angular momentum of a domain wall and geometrically twisted magnons

We theoretically study the dynamics of a domain wall in a ferromagnetic nanotube driven by electrons and magnons by investigating the electron-domain-wall and magnon-domain wall interactions. Due to the geometry of the sample, domain walls are classified by the Skyrmion charge which counts the winding number of magnetic textures on the domain wall [1]. The domain wall with a non-zero Skyrmion charge generates an emergent magnetic field for interacting particles, which exerts the Lorentz force on moving electrons and magnons and thereby deflects their trajectories. This deflection is manifested as the generation of the finite orbital angular momenta of the electrons and magnons that traverse the domain wall [2,3]. For the case of electrons, we can interpret the exchange of orbital angular momenta between electrons and the domain wall as a current-induced torque. From this peculiar torque, the domain wall with the non-zero Skyrmion charge can be driven by an arbitrary small current without the Walker breakdown. For the case of magnons, we obtain the exact solution for the magnon on the Skyrmion-textured domain wall and also their scattering properties with the domain wall with the aid of supersymmetric quantum mechanics (SUSY QM) [4]. We also show that there is a critical wavenumber for the total reflection and it is discretized by the Skyrmion charge of the domain wall. Our results show that the orbital angular momenta of magnetic systems and quasi-particles can be intertwined in a curved geometry.   

Triplon Spin Current

Spin current is a central concept of modern spintronics. Spin Seebeck effect (SSE), i.e., the spin current generation driven by a thermal gradient is one of the representative methods of creating DC spin current. SSE has been investigated from the viewpoint of its potential applications such as temperature sensor. Therefore, so far famous functional magnets such as ferro or ferrimagnets have been the main targets in SSE experiments. However, in recent years, it is gradually revealed that SSE can be an excellent tool to observe fundamental magnetic natures of attractive magnets. Namely, SSE is very powerful to detect dynamical features of various magnets including spin liquids and frustrated magnets. In fact, using SSE, we have uncovered several new features of different magnetic states such as a 1D spin liquid and a spin-nematic liquid. In this meeting, I will report our recent work about the SSE in the dimerized spin-Peierls phase of a quantum spin chain magnet CuGeO₃, whose elementary excitations are given by spin-1 triplons. We observed a new spin current carried by triplon excitations for the first time and developed the microscopic theory of the triplon spin current. I will explain the essential aspects of the triplon spin current.   

Emergence of spin-orbit coupled ferromagnetic surface state derived from Zak phase in a nonmagnetic insulator FeSi

A chiral compound FeSi is a prototypical example of the strongly-correlated d-electron insulators. Its peculiar charge and spin dynamics have provoked many important physical concepts such as d-electron Kondo insulator and insulator-to-metal transition due to on-site strong Coulomb interaction. Triggered by recent new insights into topological aspects of correlated insulators, FeSi is attracting renewed attention. However, it remains highly nontrivial that compounds made of light (and usually common) elements, like FeSi, can bear topological characteristics.

In this study, we demonstrate a novel surface state hosting metallic conduction and ferromagnetic order in FeSi with insulating and nonmagnetic bulk state. We identify that the surface state is not categorized into the class of topological insulators but can be described by the central concept in modern theory of polarization, i.e., Zak phase. Owing to the unique dipolar charge distribution of Zak-phase origin, the surface state produces the strong SOC properties despite the absence of heavy-metal elements. By taking advantage of the emergent SOC, we also realize spintronic functionalities related to current-induced spin-dynamics. (e.g., magnetization switching). Our results shed light on compounds made of common elements and demonstrate another route for SOC-based spin manipulation [1].

[1] Y. Ohtsuka, N. Kanazawa et al., Science Advances in press.