Spintronic devices based on antiferromagnetic (AFM) materials has drawn significant attention due to its potential for information storage with low power consumption and ultrafast switching speeds. Since all the information storage in AFM spintronics devices rely on the switching of AFM domains, there is an urgent requirement to directly measure the AFM domain in real space during the spin switching process. Recently, we developed a novel method to image the AFM domains in single crystal CoO and NiO thin films grown on MgO(001) substrates with the magneto-optical birefringence effect[1,2]. The magneto-optical birefringence effect is found to strongly depend on the photon energy of incident light. Utilizing this optical method, we demonstrated the first real-time imaging of the AFM domain switching process in Fe/CoO system through the spin-flop coupling. While applying a constant field, the domain nucleation dominates the switching process, but while applying an alternative field, the AFM domain switching process is found to be dominated by domain wall motion. Our studies demonstrate that the AFM domain imaging under external fields or current pulse can be achieved in real time, which could be helpful for the understanding of the dynamics of AFM materials and the development of AFM spintronics storage devices.

**References:**

Jia Xu, et. al, New J. Phys. 22, 083030 (2020). Jia Xu, et. al, Phys. Rev. B 100, 134413 (2019).

**Images:**

Imaging the dynamical switch of antiferromagnetic domains by optical microscopy INVITED

The magnetic spin textures with non-trivial topology has been an important topic in the fields of magnetism and spintronics for the last few years [1]. For example, the magnetic skyrmion is a promising topological spin texture, which exists in perpendicularly magnetized systems and can be used as a spintronic information carrier. On the other hand, magnetic bimeron is a topological counterpart of skyrmions in in-plane magnets, which can also be used to carry information. In this talk, we will show the static properties of skyrmions and bimerons with different topological structures in a frustrated ferromagnetic monolayer [2], where the topological spin textures are characterized by the vorticity Qv and helicity η. We will also talk about the dynamics of frustrated skyrmions and bimerons driven by the spin-orbit torques, which depend on the strength of the damping-like and field-like torques. We find that these particle-like topological spin textures with Qv = ±1 can be driven into linear or elliptical motion, which depends on the direction of spin polarization. We numerically reveal the damping dependence of the skyrmion/bimeron Hall angle driven by the damping-like torque. Besides, we will show that the isolated bimeron with Qv = ±1 can be driven into self-rotation by the damping-like torque at certain conditions. The rotation frequency is proportional to the driving current density. In addition, we will computationally demonstrate the possibility of creating a bimeron state with a higher or lower topological charge by the current-driven collision and merging of bimeron states with different Qv. Finally, we will give an outlook on other possible topological spin textures in frustrated magnetic systems, such as the skyrmionium and bimeronium. We believe the results presented in this talk could be useful for understanding the topological spin textures physics in frustrated magnetic systems.

**References:**

[1] Nat. Rev. Phys. 2, 492 (2020); J. Phys. D: Appl. Phys. 53, 363001 (2020); J. Phys.: Condens. Matter 32, 143001 (2020); J. Appl. Phys. 124, 240901 (2018); Nat. Rev. Mats. 2, 17031 (2017); Adv. Mater. 29, 1603227 (2017); Phys. Rep. 704, 1 (2017); J. Phys. D: Appl. Phys. 49, 423001 (2016); Proc. IEEE 104, 2040 (2016); Nat. Rev. Mats. 1, 16044 (2016); J. Phys.: Condens. Matter 27, 503001 (2015); Nat. Nanotech. 8, 899 (2013). [2] Phys. Rev. B 101, 144435 (2020); Appl. Phys. Lett. 117, 012403 (2020); Phys. Rev. Appl. 11, 044046 (2019); Nat. Commun. 8, 1717 (2017).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7f6af7fa51c79a152ccf8514a3846a13.jpg)
Fig. 1. (a) Illustration of a skyrmion with Qv = 1. (b) Illustration of a bimermon with Qv = 1. (c) Top view of simulated static bimeron solutions with different Qv and η. (d) Current-induced collision and merging of an isolated bimeron and a cluster-like bimeron state.

 Static Structures and Dynamics of Frustrated Topological Spin Textures

1. Introduction As quasiparticle-like swirling topological spin textures in nanostructures1, magnetic skyrmions are expected to be widely used in future spintronic applications2. The creation and transmission of an isolated skyrmion in magnetic films are important for skyrmionic applications, which utilize skyrmions as information carriers3. An exemplary application is the racetrack-type storage memory4. Recently, it has been reported that spin-polarized current, spin wave, magnetic field, and temperature gradients, can effectively modulate the dynamics of skyrmions5. As the most widely used method, the magnetic field has been used to manipulate magnetic spin textures in studies6. Slonczewski and Berger first proposed theoretically spin transfer torque (STT)7 can be induced when spin polarized current passes through the magnetic layer/non-magnetic layer. STT is an effect in which the orientation of a magnetic layer in a spin valve can be modified by applying a spin-polarized current. On the other hand, in magnetic multilayered structures, metallic ferromagnets in contact with heavy metals exhibit strong effects due to spin-orbit coupling. Such spin-orbit coupling effects give rise to spin-orbit torque (SOT)8 on the ferromagnetic (FM) materials. In this work, we demonstrate that a skyrmion guide on the nanotrack under both in-plane magnetic field and spin-transfer torque or spin-orbit torques driven. In applying both in-plane magnetic field and STT conditions, we focus on spatially sinusoidal-varying Gilbert damping coefficients and non-adiabatic STT coefficients with in-plane magnetic field. For in-plane magnetic field and SOT conditions, we discuss the effect on damping-like toque, field-like torque with in-plane magnetic field. The results provide a guide for designing and developing the skyrmion transporting nanotrack channel in spintronic devices based on the manipulation of skyrmions. 2. Simulation Methods The skyrmion dynamics guide is based on an ultrathin FM nanotrack structure. All simulations are processed by using the Object Oriented Micromagnetic Framework (OOMMF). The time-dependent magnetization dynamics are governed by the LLG equation including STT (adiabatic and non-adiabatic) and SOT (field-like and damping-like). Note that we consider the effect of both in-plane magnetic field and STT or SOT driven. In the first part, the magnetization dynamics is based on the Landau-Lifshitz-Gilbert (LLG) equation augmented with in-plane magnetic field, adiabatic and non-adiabatic STT: dm/dt=-|γ|m×Heff+α(m×dm/dt)+u(m×dm/dt×m)-βu(m×dm/dt) where m represents the reduced magnetization, M/MS. γ and α are the gyromagnetic ratios and Gilbert damping constant, respectively. β is the strength of the non-adiabatic STT coefficient and u represents the adiabatic STT coefficient. The Gilbert damping coefficient α and the non-adiabatic STT coefficient β are defined as functions of the longitudinal coordinate x as follows: α(x)=αamp{1+sin[2π(x/λα)]} β(x)=βamp{1+sin[2π(x/λβ)-θ]} where αamp is the amplitude of α function and βamp represents the amplitude of β function, respectively. λβ and θ denote the wavelength and phase of β function. In the second part, the magnetization dynamics is based on the Landau-Lifshitz-Gilbert (LLG) equation augmented with in-plane magnetic field, and spin-orbit torque (SOT): dm/dt=-|γ|m×Heff+α(m×dm/dt)+ζDLT m×(mp×m)-ζFLT m×mp where ζSOT, ζDLT, and ζFLT stand for the spin-orbit torque, damping-like torque and field-like torque, respectively. 3. Results and Discussion The effects of varying damping coefficient α and non-adiabatic coefficient β on velocity in both x and y direction, and skyrmion hall angle φ are illustrated in Fig. 1, by fixing external magnetic field as 800 mT. We set αamp and βamp from 0.1 to 0.5 in our simulation to obtain the discipline, by fixing βamp and αamp in Fig. 1(a)-(c) and Fig. 1(d)-(f), respectively. The contour lines in Fig. 1(g)-(i) result from the combinations of αamp and βamp. The results show that the damping coefficient α exhibits declining effect on velocity, while non-adiabatic STT coefficient β exhibits increasing influence. The polarization rate is fixed at 0.4 and the value of field-like torque is modified to change the ratio of K=ζFLT/ζDLT . Applying both magnetic field and SOT to drive skyrmion simultaneously at magnetic field H = 800 mT. The ratio of field-like torque and damping-like torque K and damping-like torque ζDLT both indicates increasing effect on skyrmion velocity, as shown in Fig. 2(a)-(b). However, damping-like torque ζDLT provides more contribution on skyrmion motion.

**References:**

1. X. Zhang, Y. Zhou, K. M. Song, T.-E. Park, J. Xia, M. Ezawa, X. Liu, W. Zhao, G. Zhao and S. Woo, J. Phys. Condens. Matter 32 (14), 143001 (2020). 2. A. Fert, N. Reyren and V. Cros, Nat. Rev. Mater. 2 (7), 1-15 (2017). 3. W. Kang, X. Chen, D. Zhu, S. Li, Y. Huang, Y. Zhang and W. Zhao, presented at the 2018 Design, Automation & Test in Europe Conference & Exhibition (DATE) (unpublished). 4. C. Song, C. Jin, J. Wang, H. Xia, J. Wang and Q. Liu, Appl. Phys. Lett. 111 (19), 192413 (2017). 5. C. Schütte, J. Iwasaki, A. Rosch and N. Nagaosa, Phys. Rev. B 90 (17), 174434 (2014). 6. J. Müller, New J. Phys. 19 (2), 025002 (2017). 7. M. D. Stiles and A. Zangwill, Phys. Rev. B 66 (1), 014407 (2002). 8. Y. Li, K. W. Edmonds, X. Liu, H. Zheng and K. Wang, Adv. Quantum Technol. 2 (1-2), 1800052 (2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/fca6ea5a3e90fff1a8d05d79a4845325.jpg)
Figure 1. Both magnetic field and STT driven skyrmion are applied to study the effect of damping coefficient α on velocity in both x and y direction, and skyrmion hall angle φ: (a) The Vx as a function of α at a fixed β = 0.2-0.5. (b) The Vy as a function of α at a fixed β = 0.2-0.5. (c) The φ as a function of α at a fixed β = 0.2-0.5. The effect of non-adiabatic β on velocity in both x and y direction, and skyrmion hall angle φ. (d) The Vx as a function of β at a fixed α = 0.2-0.5. (e) The Vx as a function of β at a fixed α = 0.2-0.5. (f) The Vx as a function of β at a fixed α = 0.2-0.5. (g) Vx, (h) Vy, and (i) skyrmion hall angle φ at magnetic field H = 800 mT.

![](https://assets.underline.io/uploads/markdown_image/1/image/338c7353053a46418aa778ff47c803f2.jpg)
Figure 2. Applying both magnetic field and SOT to drive skyrmion at magnetic field H = 800 mT: (a) Vx as the function of the ratio of field-like torque and damping-like torque from 0.1 to 10. (b) Vx as the function of damping-like torque , which indicates the polarization.

 Dynamic property of ferromagnetic skyrmion in an in-plane magnetic field

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Imaging the dynamical switch of antiferromagnetic domains by optical microscopy INVITED

Static Structures and Dynamics of Frustrated Topological Spin Textures

Dynamic property of ferromagnetic skyrmion in an in-plane magnetic field

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