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Skyrmions in chiral magnets

Skyrmions are nanoscale particlelike magnetic textures discovered in chiral magnets in 2009. Since that time the field has shown tremendous growth, with the identification of more and more skyrmion-supporting materials and the development of additional experimental techniques capable of directly accessing the skyrmion dynamics. Skyrmions represent an example of a collectively interacting system of particles that can exhibit depinning and sliding phenomena, but unlike other such systems, due to the skyrmion topology a Magnus term plays a strong role in the skyrmion dynamics. Numerous recent theoretical and experimental papers have demonstrated that this Magnus term strongly affects the skyrmion motion and the interactions of the skyrmions with quenched disorder or pinning. We explore the rich dynamics that emerge in this novel system.

Preprints:

1. Reversible to irreversible transitions for ac driven skyrmions on periodic substrates
   J.C. Bellizotti Souza, N.P. Vizarim, C.J.O. Reichhardt, C. Reichhardt, and P.A. Venegas
   Using atomistic simulations, we investigate the dynamical behavior of magnetic skyrmions in dimer and trimer molecular crystal arrangements, as well as bipartite lattices at 3/2 and 5/2 fillings, under ac driving over a square array of anisotropy defects. For low ac amplitudes, at all fillings we find reversible motion where the skyrmions return to their original positions at the end of each ac drive cycle and the diffusion is zero. We also identify two distinct irreversible regimes. The first is a translating regime in which the skyrmions form channels of flow in opposing directions and translate by one substrate lattice constant per ac drive cycle. The translating state appears in the dimer and trimer states, and produces pronounced peaks in the diffusivity in the direction perpendicular to the external drive. For larger ac amplitudes, we find chaotic irreversible motion in which the skyrmions can randomly exchange places with each other over time, producing long-time diffusive behavior both parallel and perpendicular to the ac driving direction. arXiv

   
   

2. Skyrmion molecular crystals and superlattices on triangular substrates
   J.C. Bellizotti Souza, N.P. Vizarim, C.J.O. Reichhardt, P.A. Venegas, and C. Reichhardt
   Using atomistic simulations, we show that new types of skyrmion states called skyrmion molecular crystals and skyrmion superlattices can be realized on triangular substrates when there are two or three skyrmions per substrate minimum. We find that as a function of the magnetic field and substrate periodicity, a remarkably wide variety of ordered phases appear similar to those found in colloidal or Wigner molecular crystals, including ferromagnetic and herringbone states. The ability of the skyrmions to annihilate, deform, and change size gives rise to a variety of superlattice states in which a mixture of different skyrmion sizes and shapes produces bipartate or more complex lattice structures. Our results are relevant for skyrmions on structured triangular substrates, in magnetic arrays, or skyrmions in moire materials. arXiv

   
   

3. Shapiro steps and stability of skyrmions interacting with alternating anisotropy under the influence of ac and dc drives
   J.C. Bellizotti Souza, N.P. Vizarim, C.J.O. Reichhardt, C. Reichhardt, and P.A. Venegas
   We use atomistic simulations to examine the sliding dynamics of a skyrmion in a two-dimensional system containing a periodic one-dimensional stripe pattern of variations between low and high values of the perpendicular magnetic anisotropy. The skyrmion changes in size as it crosses the interface between two anisotropy regions. Upon applying combined dc and ac driving in either parallel or perpendicular directions, we observe a wide variety of Shapiro steps, Shapiro spikes, and phase-locking phenomena. The phase-locked orbits have two-dimensional dynamics due to the gyrotropic or Magnus dynamics of the skyrmions, and are distinct from the phase-locked orbits found for strictly overdamped systems. Along a given Shapiro step when the ac drive is perpendicular to the dc drive, the velocity parallel to the ac drive is locked while the velocity in the perpendicular direction increases with increasing drive to form Shapiro spikes. At the transition between adjacent Shapiro steps, the parallel velocity jumps up to the next step value, and the perpendicular velocity drops. The skyrmion Hall angle shows a series of spikes as a function of increasing dc drive, where the jumps correspond to the transition between different phase-locked steps. At high drives, the Shapiro steps and Shapiro spikes are lost. When both the ac and dc drives are parallel to the stripe periodicity direction, Shapiro steps appear, while if the dc drive is parallel to the stripe periodicity direction and the ac drive is perpendicular to the stripe periodicity, there are only two locked phases, and the skyrmion motion consists of a combination of sliding along the interfaces between the two anisotropy values and jumping across the interfaces. arXiv

   
   

Papers:

1. Controlled skyrmion ratchet in linear protrusion defects
   F.S. Rocha, J.C. Bellizotti Souza, N.P. Vizarim, C.J.O. Reichhardt, C. Reichhardt, and P.A. Venegas
   Phys. Rev. B 109, 054407 (2024). arXiv

   
   

2. Skyrmion transport and annihilation in funnel geometries
   F.S. Rocha, J.C. Bellizotti Souza, N.P. Vizarim, C.J.O. Reichhardt, C. Reichhardt, and P.A. Venegas
   J. Phys.: Condens. Matter 36, 115801 (2024). arXiv

   
   

3. Soliton motion induced along ferromagnetic skyrmion chains in chiral thin nanotracks
   J.C. Bellizotti Souza, N.P. Vizarim, C.J.O. Reichhardt, C. Reichhardt, and P.A. Venegas
   J. Mag. Mag. Mater. 587, 171280 (2023). arXiv

   
   

4. Kibble-Zurek scenario and coarsening across nonequilibrium phase transitions in driven vortices and skyrmions
   C. Reichhardt and C.J.O. Reichhardt
   Phys. Rev. Res. 5, 033221 (2023). arXiv

   
   

5. Peak effect, melting, and transport in skyrmion crystals
   C. Reichhardt and C.J.O. Reichhardt
   Phys. Rev. B 108, 014428 (2023). arXiv

   
   

6. Spontaneous skyrmion conformal lattice and transverse motion during dc and ac compression
   J.C. Bellizotti Souza, N.P. Vizarim, C.J.O. Reichhardt, C. Reichhardt, and P.A. Venegas
   New J. Phys. 25, 053020 (2023). arXiv

   
   

7. Magnus induced diode effect for skyrmions in channels with periodic potentials
   J.C. Bellizotti Souza, N.P. Vizarim, C.J.O. Reichhardt, C. Reichhardt, and P.A. Venegas
   J. Phys.: Condens. Matter 51, 015804 (2022). arXiv

   
   

8. Editorial: Generation, detection and manipulation of skyrmions in magnetic nanostructures
   H.Y. Yuan, X. Zhang, and C.J.O. Reichhardt
   Front. Phys. 10, 964975 (2022).

   
   

9. Dynamic phases and reentrant Hall effect for vortices and skyrmions on periodic pinning arrays
   C.J.O. Reichhardt and C. Reichhardt
   Eur. Phys. J. B 95, 135 (2022). arXiv

   
   

10. Clogging, diode and collective effects of skyrmions in funnel geometries
    J.C. Bellizotti Souza, N.P. Vizarim, C.J.O. Reichhardt, C. Reichhardt, and P.A. Venegas
    New J. Phys. 24, 103030 (2022). arXiv

    
    

11. Statics and dynamics of skyrmions interacting with disorder and nanostructures
    C. Reichhardt, C.J.O. Reichhardt, and M.V. Milosevic
    Rev. Mod. Phys. 94, 035005 (2022). arXiv

    
    

12. Commensuration effects on skyrmion Hall angle and drag for manipulation of skyrmions on two-dimensional periodic substrates
    C. Reichhardt and C.J.O. Reichhardt
    Phys. Rev. B 105, 214437 (2022). arXiv

    
    

13. Soliton motion in skyrmion chains: Stabilization and guidance by nanoengineered pinning
    N.P. Vizarim, J.C. Bellizotti Souza, C.J.O. Reichhardt, C. Reichhardt, M.V. Milosevic, and P.A. Venegas
    Phys. Rev. B 105, 224409 (2022). arXiv

    
    

14. Directed motion of liquid crystal skyrmions with oscillating fields
    A. Duzgun, C. Nisoli, C.J.O. Reichhardt, and C. Reichhardt
    New J. Phys. 24, 033033 (2022). arXiv

    
    

15. Fluctuations and pinning for individually manipulated skyrmions
    C.J.O. Reichhardt and C. Reichhardt
    Front. Phys. 9, 767491 (2021). arXiv

    
    

16. Visualizing the strongly reshaped skyrmion Hall effect in multilayer wire devices
    A.K.C. Tan, P. Ho, J. Lourembam, L. Huang, H.K. Tan, C.J.O. Reichhardt, C. Reichhardt, and A. Soumyanarayan
    Nature Commun. 12, 4252 (2021). arXiv

    
    

17. Dynamics and nonmonotonic drag for individually driven skyrmions
    C. Reichhardt and C.J.O. Reichhardt
    Phys. Rev. B 104, 064441 (2021). arXiv

    
    

18. Skyrmion ratchet in funnel geometries
    J.C. Bellizotti Souza, N.P. Vizarim, C.J.O. Reichhardt, C. Reichhardt, and P.A. Venegas
    Phys. Rev. B 104, 054434 (2021). arXiv

    
    

19. Directional locking and the influence of obstacle density on skyrmion dynamics in triangular and honeycomb arrays
    N.P. Vizarim, J.C. Bellizotti Souza, C. Reichhardt, C.J.O. Reichhardt, and P.A. Venegas
    J. Phys.: Condens. Matter 33, 305801 (2021). arXiv

    
    

20. Guided skyrmion motion along pinning array interfaces
    N.P. Vizarim, C. Reichhardt, P.A. Venegas, and C.J.O. Reichhardt
    J. Mag. Mag. Mater. 528, 167710 (2021). arXiv

    
    

21. Skyrmion pinball and directed motion on obstacle arrays
    N.P. Vizarim, C.J.O. Reichhardt, P.A. Venegas, and C. Reichhardt
    J. Phys. Commun. 4, 085001 (2020). arXiv
    

    
    

22. Shapiro steps and nonlinear skyrmion Hall angles for dc and ac driven skyrmions on a two dimensional periodic substrate
    N.P. Vizarim, C. Reichhardt, P.A. Venegas, and C.J.O. Reichhardt
    Phys. Rev. B 102, 104413 (2020). arXiv
    

    
    

23. Skyrmion dynamics and transverse mobility: Skyrmion Hall angle reversal on 2D periodic substrates with dc and biharmonic ac drives
    N.P. Vizarim, C.J.O. Reichhardt, P.A. Venegas, and C. Reichhardt
    Eur. Phys. J. B 93, 112 (2020) arXiv
    

    
    

24. Dynamics of Magnus dominated particle clusters, collisions, pinning and ratchets
    C. Reichhardt and C.J.O. Reichhardt
    Phys. Rev. E 101, 062602 (2020). arXiv
    

    
    

25. Skyrmion dynamics and topological sorting on periodic obstacle arrays
    N.P. Vizarim, C. Reichhardt, C.J.O. Reichhardt, and P.A. Venegas
    New J. Phys. 22, 053025 (2020). arXiv
    

    
    

26. Commensurate states and pattern switching via liquid crystal skyrmions trapped in a square lattice
    A. Duzgun, C. Nisoli, C.J.O. Reichhardt, and C. Reichhardt
    Soft Matter 16, 3338 (2020). arXiv
    

    
    

27. Shear banding, intermittency, jamming and dynamic phases for skyrmions in inhomogeneous pinning arrays
    C. Reichhardt and C.J.O. Reichhardt
    Phys. Rev. B 101, 054423 (2020). arXiv
    

    
    

28. Chiral edge currents for ac driven skyrmions in confined pinning geometries
    C. Reichhardt and C.J.O. Reichhardt
    Phys. Rev. B 100, 174414 (2019). arXiv
    

    
    

29. Reentrant pinning, dynamic row reduction, and skyrmion accumulation for driven skyrmions in inhomogeneous pinning arrays
    C. Reichhardt and C.J.O. Reichhardt
    EPL 129, 21001 (2020). arXiv
    

    
    

30. Nonlinear transport, dynamic ordering, and clustering for driven skyrmions on random pinning
    C. Reichhardt and C.J.O. Reichhardt
    Phys. Rev. B 99, 104418 (2019). arXiv

    
    

31. Skyrmions in anisotropic magnetic fields: Strain and defect dynamics
    R. Brearton, M.W. Olszewski, S. Zhang, M.R. Eskildsen, C. Reichhardt, C.J.O. Reichhardt, G. van der Laan, and T. Hesjedal
    MRS Adv. 4, 643 (2019).

    
    

32. Disordering, clustering, and laning transitions in particle systems with dispersion in the Magnus term
    C.J.O. Reichhardt and C. Reichhardt
    Phys. Rev. E 99, 012606 (2019). arXiv

    
    

33. Reversible to irreversible transitions in periodically driven skyrmion systems
    B.L. Brown, C. Reichhardt, and C.J.O. Reichhardt
    New J. Phys. 21, 013001 (2019). arXiv

    
    

34. Thermal creep and the skyrmion Hall angle in driven skyrmion crystals
    C. Reichhardt and C.J.O. Reichhardt
    J. Phys.: Condens. Matter 31, 07LT01 (2019). arXiv

    
    

35. Nonequilibrium phases and segregation for skyrmions on periodic pinning arrays
    C. Reichhardt, D. Ray, and C.J.O. Reichhardt
    Phys. Rev. B 98, 134418 (2018). arXiv
    

    
    

36. Avalanches and criticality in driven magnetic skyrmions
    S.A. Diaz, C. Reichhardt, D.P. Arovas, A. Saxena, and C.J.O. Reichhardt
    Phys. Rev. Lett. 120, 117203 (2018). arXiv
    

    
    

37. Fluctuations and noise signatures of driven magnetic skyrmions
    S.A. Diaz, C.J.O. Reichhardt, D.P. Arovas, A. Saxena, and C. Reichhardt
    Phys. Rev. B 96, 085106 (2017). arXiv
    

    
    

38. Reversible vector ratchets for skyrmion systems
    X. Ma, C.J. Olson Reichhardt, and C. Reichhardt
    Phys. Rev. B 95, 104401 (2017). arXiv

    
    

39. Shapiro spikes and negative mobility for skyrmion motion on quasi-one-dimensional periodic substrates
    C. Reichhardt and C.J. Olson Reichhardt
    Phys. Rev. B 95, 014412 (2017). arXiv

    
    

40. Noise fluctuations and drive dependence of the skyrmion Hall effect in disordered systems
    C. Reichhardt and C.J. Olson Reichhardt
    New J. Phys. 18, 095005 (2016). arXiv

    
    

41. Emergent geometric frustration of artificial magnetic skyrmion crystals
    F. Ma, C. Reichhardt, W. Gan, C.J. Olson Reichhardt, and W.S. Lew
    Phys. Rev. B 94, 144405 (2016) arXiv

    
    

42. Magnus-induced dynamics of driven skyrmions on a quasi-one-dimensional periodic substrate
    C. Reichhardt and C.J. Olson Reichhardt
    Phys. Rev. B 94, 094413 (2016). arXiv

    
    

43. Shapiro steps for skyrmion motion on a washboard potential with longitudinal and transverse ac drives
    C. Reichhardt and C.J. Olson Reichhardt
    Phys. Rev. B 92, 224432 (2015). arXiv

    
    

44. Magnus-induced ratchet effects for skyrmions interacting with asymmetric substrates
    C. Reichhardt, D. Ray, and C.J. Olson Reichhardt
    New J. Phys. 17, 073034 (2015). arXiv

    
    

45. Quantized transport for a skyrmion moving on a two-dimensional periodic substrate
    C. Reichhardt, D. Ray, and C.J. Olson Reichhardt
    Phys. Rev. B 91, 104426 (2015). arXiv

    
    

46. Collective transport properties of driven skyrmions with random disorder
    C. Reichhardt, D. Ray, and C.J. Olson Reichhardt
    Phys. Rev. Lett. 114, 217202 (2015). arXiv

    
    

47. Comparing the dynamics of skyrmions and superconducting vortices
    C.J. Olson Reichhardt, S.Z. Lin, D. Ray, and C. Reichhardt
    Physica C 503, 52 (2014). arXiv