Materials with large spin–orbit interactions generate pure spin currents with spin polarizations parallel to the interfacial surfaces that give rise to conventional spin–orbit torques. These spin–orbit torques can only efficiently and deterministically switch magnets with in-plane magnetization. Additional symmetry breaking, such as in non-collinear antiferromagnets, can generate exotic, unconventional spin–orbit torques that are associated with spin polarizations perpendicular to the interfacial planes. Here, we use micromagnetic simulations to investigate whether such exotic spin–orbit torques can generate magnetic droplet solitions in out-of-plane magnetized geometries. We show that a short, high current pulse followed by a lower constant current can nucleate and stabilize magnetic droplets. Through specific current pulse lengths, it is possible to control the number of droplets in such a system, since torques are generated over a large area. Additionally, the nucleation current scales with the out-of-plane component of the spin polarization and is linear as a function of magnetic field strength.

1.
A.
Hoffmann
,
S.
Ramanathan
,
J.
Grollier
,
A. D.
Kent
,
M.
Rozenberg
,
I. K.
Schuller
,
O.
Shpyrko
,
R.
Dynes
,
Y.
Fainman
,
A.
Frano
,
F. E. E. G.
Galli
,
V.
Lomakin
,
S. P.
Ong
,
A. K.
Petford-Long
,
J. A.
Schuller
,
M. D.
Stiles
,
Y.
Takamura
, and
Y.
Zhu
, “
Quantum materials for energy-efficient neuromorphic computing
,” arXiv:2204.01832 (
2022
).
2.
J.
Torrejon
,
M.
Riou
,
F. A.
Araujo
,
S.
Tsunegi
,
G.
Khalsa
,
D.
Querlioz
,
P.
Bortolotti
,
V.
Cros
,
K.
Yakushiji
,
A.
Fukushima
 et al., “
Neuromorphic computing with nanoscale spintronic oscillators
,”
Nature
547
,
428
431
(
2017
).
3.
J.
Grollier
,
D.
Querlioz
,
K.
Camsari
,
K.
Everschor-Sitte
,
S.
Fukami
, and
M. D.
Stiles
, “
Neuromorphic spintronics
,”
Nat. Electron.
3
,
360
370
(
2020
).
4.
S.
Kaka
,
M. R.
Pufall
,
W. H.
Ripphard
,
T. J.
Silva
,
S. E.
Russek
, and
J. A.
Katine
, “
Mutual phase-locking of microwave spin torque nano-oscillators
,”
Nature
437
,
389
392
(
2005
).
5.
F.
Mancoff
,
N.
Rizzo
,
B.
Engel
, and
S.
Tehrani
, “
Phase-locking in double-point-contact spin-transfer devices
,”
Nature
437
,
393
395
(
2005
).
6.
T.
Kendziorczyk
and
T.
Kuhn
, “
Mutual synchronization of nanoconstriction-based spin Hall nano-oscillators through evanescent and propagating spin waves
,”
Phys. Rev. B
93
,
134413
(
2016
).
7.
R.
Lebrun
,
S. S.
Tsunegi
,
P.
Bortolotti
,
H.
Kubota
,
A. S.
Jenkins
,
M.
Romera
,
K.
Yakushiji
,
A.
Fukushima
,
J.
Grollier
,
S.
Yuasa
, and
V.
Cros
, “
Mutual synchronization of spin torque nano-oscillators through a long-range and tunable electrical coupling scheme
,”
Nat. Commun.
8
,
15825
(
2017
).
8.
M.
Romera
,
P.
Talatchian
,
S.
Tsunegi
,
F. A.
Araujo
,
V.
Cros
,
P.
Bortolotti
,
J.
Trastoy
,
K.
Yakushiji
,
A.
Fukushima
,
H.
Kubota
 et al., “
Vowel recognition with four coupled spin-torque nano-oscillators
,”
Nature
563
,
230
234
(
2018
).
9.
M.
Riou
,
J.
Torrejon
,
B.
Garitaine
,
F. A.
Araujo
,
P.
Bortolotti
,
V.
Cros
,
S.
Tsunegi
,
K.
Yakushiji
,
A.
Fukushima
,
H.
Kubota
 et al., “
Temporal pattern recognition with delayed-feedback spin-torque nano-oscillators
,”
Phys. Rev. Appl.
12
,
024049
(
2019
).
10.
A.
Awad
,
P.
Dürrenfeld
,
A.
Houshang
,
M.
Dvornik
,
E.
Iacocca
,
R. K.
Dumas
, and
J.
Åkerman
, “
Long-range mutual synchronization of spin Hall nano-oscillators
,”
Nat. Phys.
13
,
292
299
(
2017
).
11.
M.
Zahedinejad
,
A.
Awad
,
S.
Muralidhar
,
R.
Khymyn
,
H.
Fulara
,
H.
Mazraati
,
M.
Dvornik
, and
J.
Åkerman
, “
Two-dimensional mutually synchronized spin Hall nano-oscillator arrays for neuromorphic computing
,”
Nat. Nanotechnol.
15
,
47
52
(
2020
).
12.
A.
Houshang
,
M.
Zahedinejad
,
S.
Muralidhar
,
R.
Khymyn
,
M.
Rajabali
,
H.
Fulara
,
A. A.
Awad
,
J.
Åkerman
,
J.
Chȩciński
, and
M.
Dvornik
, “
Phase-binarized spin Hall nano-oscillator arrays: Towards spin Hall Ising machines
,”
Phys. Rev. Appl.
17
,
014003
(
2022
).
13.
A.
Kosevich
,
B.
Ivanov
, and
A.
Kovalev
, “
Magnetic solitons
,”
Phys. Rep.
194
,
117
238
(
1990
).
14.
B.
Ivanov
and
A.
Kosevich
, “
Bound-states of a large number of magnons in a ferromagnet with one-ion anisotropy
,”
Sov. Phys. JETP
45
,
2000
2015
(
1977
).
15.
M.
Hoefer
,
T. J.
Silva
, and
M. W.
Keller
, “
Theory for a dissipative droplet soliton excited by a spin torque nanocontact
,”
Phys. Rev. B
82
,
054432
(
2010
).
16.
S. M.
Mohseni
,
S.
Sani
,
J.
Persson
,
T. A.
Nguyen
,
S.
Chung
,
Y.
Pogoryelov
,
P.
Muduli
,
E.
Iacocca
,
A.
Eklund
,
R.
Dumas
 et al., “
Spin torque–generated magnetic droplet solitons
,”
Science
339
,
1295
1298
(
2013
).
17.
F.
Macià
,
D.
Backes
, and
A.
Kent
, “
Stable magnetic droplet solitons in spin-transfer nanocontacts
,”
Nat. Nanotechnol.
9
,
992
(
2014
).
18.
E.
Iacocca
,
R. K.
Dumas
,
L.
Bookman
,
M.
Mohseni
,
S.
Chung
,
M. A.
Hoefer
, and
J.
Åkerman
, “
Confined dissipative droplet solitons in spin-valve nanowires with perpendicular magnetic anisotropy
,”
Phys. Rev. Lett.
112
,
047201
(
2014
).
19.
D.
Backes
,
F.
Macià
,
S.
Bonetti
,
R.
Kukreja
,
H.
Ohldag
, and
A. D.
Kent
, “
Direct observation of a localized magnetic soliton in a spin-transfer nanocontact
,”
Phys. Rev. Lett.
115
,
127205
(
2015
).
20.
S.
Lendínez
,
N.
Statuto
,
D.
Backes
,
A. D.
Kent
, and
F.
Macià
, “
Observation of droplet soliton drift resonances in a spin-transfer-torque nanocontact to a ferromagnetic thin film
,”
Phys. Rev. B
92
,
174426
(
2015
).
21.
S.
Chung
,
A.
Eklund
,
E.
Iacocca
,
S. M.
Mohseni
,
S. R.
Sani
,
L.
Bookman
,
M. A.
Mark
,
A.
Hoefer
,
R. K.
Dumas
, and
J.
Åkerman
, “
Magnetic droplet nucleation boundary in orthogonal spin-torque nano-oscillators
,”
Nat. Commun.
7
,
11209
(
2016
).
22.
S.
Chung
,
Q. T.
Le
,
M.
Ahlberg
,
A. A.
Awad
,
M.
Weigand
,
I.
Bykova
,
R.
Khymyn
,
M.
Dvornik
,
H.
Mazraati
,
A.
Houshang
,
S.
Jiang
,
T. N. A.
Nguyen
,
E.
Goering
,
G.
Schütz
,
J.
Gräfe
, and
J.
Åkerman
, “
Direct observation of Zhang-Li torque expansion of magnetic droplet solitons
,”
Phys. Rev. Lett.
120
,
217204
(
2018
).
23.
F.
Macià
and
A. D.
Kent
, “
Magnetic droplet solitons
,”
J. Appl. Phys.
128
,
100901
(
2020
).
24.
B.
Divinskiy
,
S.
Urazhdin
,
V.
Demidov
,
A.
Kozhanov
,
A.
Nosov
,
A.
Rinkevich
, and
S.
Demokritov
, “
Magnetic droplet solitons generated by pure spin currents
,”
Phys. Rev. B
96
,
224419
(
2017
).
25.
A.
Manchon
,
J.
Železný
,
I. M.
Miron
,
T.
Jungwirth
,
J.
Sinova
,
A.
Thiaville
,
K.
Garello
, and
P.
Gambardella
, “
Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems
,”
Rev. Mod. Phys.
91
,
035004
(
2019
).
26.
D.
MacNeill
,
G.
Stiehl
,
M.
Guimaraes
,
R.
Buhrman
,
J.
Park
, and
D.
Ralph
, “
Control of spin–orbit torques through crystal symmetry in WTe2/ferromagnet bilayers
,”
Nat. Phys.
13
,
300
305
(
2017
).
27.
T.
Nan
,
C. X.
Quintela
,
J.
Irwin
,
G.
Gurung
,
D.-F.
Shao
,
J.
Gibbons
,
N.
Campbell
,
K.
Song
,
S.-Y.
Choi
,
L.
Guo
 et al., “
Controlling spin current polarization through non-collinear antiferromagnetism
,”
Nat. Commun.
11
,
1
7
(
2020
).
28.
Y.
Liu
,
Y.
Liu
,
M.
Chen
,
S.
Srivastava
,
P.
He
,
K. L.
Teo
,
T.
Phung
,
S.-H.
Yang
, and
H.
Yang
, “
Current-induced out-of-plane spin accumulation on the (001) surface of the IrMn3 antiferromagnet
,”
Phys. Rev. Appl.
12
,
064046
(
2019
).
29.
J.
Holanda
,
H.
Saglam
,
V.
Karakas
,
Z.
Zang
,
Y.
Li
,
R.
Divan
,
Y.
Liu
,
O.
Ozatay
,
V.
Novosad
,
J. E.
Pearson
 et al., “
Magnetic damping modulation in IrMn3/Ni80Fe20 via the magnetic spin Hall effect
,”
Phys. Rev. Lett.
124
,
087204
(
2020
).
30.
A.
Vansteenkiste
,
J.
Leliaert
,
M.
Dvornik
,
M.
Helsen
,
F.
Garcia-Sanchez
, and
B.
Van Waeyenberge
, “
The design and verification of MuMax3
,”
AIP Adv.
4
,
107133
(
2014
).
31.
D.
Xiao
,
V.
Tiberkevich
,
Y. H.
Liu
,
Y. W.
Liu
,
S. M.
Mohseni
,
S.
Chung
,
M.
Ahlberg
,
A. N.
Slavin
,
J.
Åkerman
, and
Y.
Zhou
, “
Parametric autoexcitation of magnetic droplet soliton perimeter modes
,”
Phys. Rev. B
95
,
024106
(
2017
).
32.
X. F.
Han
,
M.
Grimsditch
,
J.
Meersschaut
,
A.
Hoffmann
,
Y.
Ji
,
J.
Sort
,
J.
Nogués
,
R.
Divan
,
J. E.
Pearson
, and
D. J.
Keavney
, “
Magnetic instability regions in patterned structures: Influence of element shape on magnetization reversal dynamics
,”
Phys. Rev. Lett.
98
,
147202
(
2007
).
33.
C.
Song
,
C.
Jin
,
S.
Zhang
,
S.
Chen
,
J.
Wang
, and
Q.
Liu
, “
Effect of perpendicular magnetic field on bubble-like magnetic solitons driven by spin-polarized current with Dzyaloshinskii–Moriya interaction
,”
J. Appl. Phys.
120
,
183901
(
2016
).
You do not currently have access to this content.