456
L. Shen et al.
34. H. Velkov, O. Gomonay, M. Beens, G. Schwiete, A. Brataas, J. Sinova, R.A. Duine,
Phenomenology of current-induced skyrmion motion in antiferromagnets. New J. Phys. 18,
075016 (2016)
35. L. Shen, J. Xia, G. Zhao, X. Zhang, M. Ezawa, O.A. Tretiakov, X. Liu, Y. Zhou, Dynamics of
the antiferromagnetic skyrmion induced by a magnetic anisotropy gradient. Phys. Rev. B 98,
134448 (2018)
36. K.M.D. Hals, Y. Tserkovnyak, A. Brataas, Phenomenology of current-induced dynamics in
antiferromagnets. Phys. Rev. Lett. 106, 107206 (2011)
37. A. Salimath, F. Zhuo, R. Tomasello, G. Finocchio, A. Manchon, Controlling the deformation
of antiferromagnetic skyrmions in the high-velocity regime. Phys. Rev. B 101, 024429 (2020)
38. C. Jin, C. Song, J. Wang, Q. Liu, Dynamics of antiferromagnetic skyrmion driven by the spin
Hall effect. Appl. Phys. Lett. 109, 182404 (2016)
39. Z. Yang, S. Zhang, Y.C. Li, Chaotic dynamics of spin-valve oscillators. Phys. Rev. Lett. 99,
134101 (2007)
40. G. Wang, D. Chen, J. Lin, X. Chen, The application of chaotic oscillators to weak signal
detection. IEEE Trans. Industr. Electron. 46, 440 (1999)
41. A. Fukushima, T. Seki, K. Yakushiji, H. Kubota, H. Imamura, S. Yuasa, K. Ando, Spin dice: A
scalable truly random number generator based on spintronics. Appl. Phys. Express 7, 083001
(2014)
42. W.L. Ditto, A. Miliotis, K. Murali, S. Sinha, M.L. Spano, Chaogates: morphing logic gates that
exploit dynamical patterns. Chaos 20, 037107 (2010)
43. C. Jin, J. Wang, W. Wang, C. Song, J. Wang, H. Xia, Q. Liu, Array of synchronized nanooscillators based on repulsion between domain wall and skyrmion. Phys. Rev. Appl. 9, 044007
(2018)
44. F. Garcia-Sanchez, J. Sampaio, N. Reyren, V. Cros, J.V. Kim, A skyrmion-based spin-torque
nano-oscillator. New J. Phys. 18, 075011 (2016)
45. S. Zhang, J. Wang, Q. Zheng, Q. Zhu, X. Liu, S. Chen, C. Jin, Q. Liu, C. Jia, D. Xue, Currentinduced magnetic skyrmions oscillator. New J. Phys. 17, 023061 (2015)
46. Y. Zhou, E. Iacocca, A.A. Awad, R.K. Dumas, F.C. Zhang, H.B. Braun, J. Akerman,
Dynamically stabilized magnetic skyrmions. Nat. Commun. 6, 8193 (2015)
47. M. Zahedinejad, A.A. Awad, S. Muralidhar, R. Khymyn, H. Fulara, H. Mazraati, M. Dvornik,
J. Akerman, Two-dimensional mutually synchronized spin Hall nano-oscillator arrays for
neuromorphic computing. Nat. Nanotechnol. 15, 47 (2020)
48. Y. Feng, J. Xia, L. Qiu, X. Cai, L. Shen, F.J. Morvan, X. Zhang, Y. Zhou, G. Zhao, A skyrmionbased spin-torque nano-oscillator with enhanced edge. J. Magn. Magn. Mater. 491, 165610
(2019)
49. J.H. Guo, J. Xia, X.C. Zhang, P.W.T. Pong, Y.M. Wu, H. Chen, W.S. Zhao, Y. Zhou, A
ferromagnetic skyrmion-based nano-oscillator with modified profile of Dzyaloshinskii-Moriya
interaction. J. Magn. Magn. Mater. 496, 165912 (2020)
50. C. Jin, Y. Ma, C. Song, H. Xia, J. Wang, C. Zhang, Z. Zeng, J. Wang, Q. Liu, High-frequency
spin transfer nano-oscillator based on the motion of skyrmions in an annular groove. New J.
Phys. 22, 033001 (2020)
51. L. Shen, J. Xia, G. Zhao, X. Zhang, M. Ezawa, O.A. Tretiakov, X. Liu, Y. Zhou, Spin torque
nano-oscillators based on antiferromagnetic skyrmions. Appl. Phys. Lett. 114, 042402 (2019)
52. X. Zhang, Y. Zhou, M. Ezawa, Magnetic bilayer-skyrmions without skyrmion Hall effect. Nat.
Commun. 7, 10293 (2016)
53. J. Xia, X. Zhang, M. Ezawa, Z. Hou, W. Wang, X. Liu, Y. Zhou, Current-driven dynamics
of frustrated skyrmions in a synthetic antiferromagnetic bilayer. Phys. Rev. Appl. 11, 044046
(2019)
54. S.S. Parkin, R. Bhadra, K.P. Roche, Oscillatory magnetic exchange coupling through thin
copper layers. Phys. Rev. Lett. 66, 2152 (1991)
55. J. Zang, M. Mostovoy, J.H. Han, N. Nagaosa, Dynamics of Skyrmion crystals in metallic thin
films. Phys. Rev. Lett. 107, 136804 (2011)
L. Shen et al.
34. H. Velkov, O. Gomonay, M. Beens, G. Schwiete, A. Brataas, J. Sinova, R.A. Duine,
Phenomenology of current-induced skyrmion motion in antiferromagnets. New J. Phys. 18,
075016 (2016)
35. L. Shen, J. Xia, G. Zhao, X. Zhang, M. Ezawa, O.A. Tretiakov, X. Liu, Y. Zhou, Dynamics of
the antiferromagnetic skyrmion induced by a magnetic anisotropy gradient. Phys. Rev. B 98,
134448 (2018)
36. K.M.D. Hals, Y. Tserkovnyak, A. Brataas, Phenomenology of current-induced dynamics in
antiferromagnets. Phys. Rev. Lett. 106, 107206 (2011)
37. A. Salimath, F. Zhuo, R. Tomasello, G. Finocchio, A. Manchon, Controlling the deformation
of antiferromagnetic skyrmions in the high-velocity regime. Phys. Rev. B 101, 024429 (2020)
38. C. Jin, C. Song, J. Wang, Q. Liu, Dynamics of antiferromagnetic skyrmion driven by the spin
Hall effect. Appl. Phys. Lett. 109, 182404 (2016)
39. Z. Yang, S. Zhang, Y.C. Li, Chaotic dynamics of spin-valve oscillators. Phys. Rev. Lett. 99,
134101 (2007)
40. G. Wang, D. Chen, J. Lin, X. Chen, The application of chaotic oscillators to weak signal
detection. IEEE Trans. Industr. Electron. 46, 440 (1999)
41. A. Fukushima, T. Seki, K. Yakushiji, H. Kubota, H. Imamura, S. Yuasa, K. Ando, Spin dice: A
scalable truly random number generator based on spintronics. Appl. Phys. Express 7, 083001
(2014)
42. W.L. Ditto, A. Miliotis, K. Murali, S. Sinha, M.L. Spano, Chaogates: morphing logic gates that
exploit dynamical patterns. Chaos 20, 037107 (2010)
43. C. Jin, J. Wang, W. Wang, C. Song, J. Wang, H. Xia, Q. Liu, Array of synchronized nanooscillators based on repulsion between domain wall and skyrmion. Phys. Rev. Appl. 9, 044007
(2018)
44. F. Garcia-Sanchez, J. Sampaio, N. Reyren, V. Cros, J.V. Kim, A skyrmion-based spin-torque
nano-oscillator. New J. Phys. 18, 075011 (2016)
45. S. Zhang, J. Wang, Q. Zheng, Q. Zhu, X. Liu, S. Chen, C. Jin, Q. Liu, C. Jia, D. Xue, Currentinduced magnetic skyrmions oscillator. New J. Phys. 17, 023061 (2015)
46. Y. Zhou, E. Iacocca, A.A. Awad, R.K. Dumas, F.C. Zhang, H.B. Braun, J. Akerman,
Dynamically stabilized magnetic skyrmions. Nat. Commun. 6, 8193 (2015)
47. M. Zahedinejad, A.A. Awad, S. Muralidhar, R. Khymyn, H. Fulara, H. Mazraati, M. Dvornik,
J. Akerman, Two-dimensional mutually synchronized spin Hall nano-oscillator arrays for
neuromorphic computing. Nat. Nanotechnol. 15, 47 (2020)
48. Y. Feng, J. Xia, L. Qiu, X. Cai, L. Shen, F.J. Morvan, X. Zhang, Y. Zhou, G. Zhao, A skyrmionbased spin-torque nano-oscillator with enhanced edge. J. Magn. Magn. Mater. 491, 165610
(2019)
49. J.H. Guo, J. Xia, X.C. Zhang, P.W.T. Pong, Y.M. Wu, H. Chen, W.S. Zhao, Y. Zhou, A
ferromagnetic skyrmion-based nano-oscillator with modified profile of Dzyaloshinskii-Moriya
interaction. J. Magn. Magn. Mater. 496, 165912 (2020)
50. C. Jin, Y. Ma, C. Song, H. Xia, J. Wang, C. Zhang, Z. Zeng, J. Wang, Q. Liu, High-frequency
spin transfer nano-oscillator based on the motion of skyrmions in an annular groove. New J.
Phys. 22, 033001 (2020)
51. L. Shen, J. Xia, G. Zhao, X. Zhang, M. Ezawa, O.A. Tretiakov, X. Liu, Y. Zhou, Spin torque
nano-oscillators based on antiferromagnetic skyrmions. Appl. Phys. Lett. 114, 042402 (2019)
52. X. Zhang, Y. Zhou, M. Ezawa, Magnetic bilayer-skyrmions without skyrmion Hall effect. Nat.
Commun. 7, 10293 (2016)
53. J. Xia, X. Zhang, M. Ezawa, Z. Hou, W. Wang, X. Liu, Y. Zhou, Current-driven dynamics
of frustrated skyrmions in a synthetic antiferromagnetic bilayer. Phys. Rev. Appl. 11, 044046
(2019)
54. S.S. Parkin, R. Bhadra, K.P. Roche, Oscillatory magnetic exchange coupling through thin
copper layers. Phys. Rev. Lett. 66, 2152 (1991)
55. J. Zang, M. Mostovoy, J.H. Han, N. Nagaosa, Dynamics of Skyrmion crystals in metallic thin
films. Phys. Rev. Lett. 107, 136804 (2011)