Suppression of the Walker breakdown in confined wires is key to improving the operation and reliability of magnetic domain-wall-based devices, including logic, memory, and sensor applications. Here, via micromagnetic simulations, we demonstrate that periodical wire-width modulation with suitable geometric parameters can fully suppress the Walker breakdown of a field-driven domain wall, conserving its spin structure in the whole operating field range of a device. Key differences in the efficacy of the wire-width modulation are observed for wires with different widths and thicknesses such that different domain wall states are energetically stable. In particular, the approach is found to be effective in expanding the field-operating window of a device in the case of smaller wire widths and thicknesses (below 150 nm wide and 15 nm thick), whereas in larger wires, the advantages from the suppression in the Walker breakdown are counteracted by the increase in domain wall pinning and the reduction in the nucleation field for new domain walls. Simulations on intersecting magnetic wires prove the importance of suppression of the Walker breakdown. Since the domain wall behavior is chirality dependent, introducing periodical wire-width modulation conserves the spin structure, thus reducing stochasticity of the domain wall propagation.
REFERENCES
1.
O.
Boulle
, G.
Malinowski
, and M.
Kläui
, “Current-induced domain wall motion in nanoscale ferromagnetic elements
,” Mater. Sci. Eng. R Rep.
72
(9
), 159
–187
(2011
). 2.
D. A.
Allwood
, G.
Xiong
, C. C.
Faulkner
, D.
Atkinson
, D.
Petit
, and R. P.
Cowburn
, “Magnetic domain-wall logic
,” Science
309
(5741
), 1688
–1692
(2005
). 3.
S. S. P.
Parkin
, M.
Hayashi
, and L.
Thomas
, “Magnetic domain-wall racetrack memory
,” Science
320
, 190
–194
(2008
).4.
M.
Diegel
, R.
Mattheis
, and E.
Halder
, “Multiturn counter using movement and storage of 180 magnetic domain walls
,” Sens. Lett.
5
(1
), 118
–122
(2007
). 5.
M.
Diegel
, S.
Glathe
, R.
Mattheis
, M.
Scherzinger
, and E.
Halder
, “A new four bit magnetic domain wall based multiturn counter
,” IEEE Trans. Magn.
45
(10
), 3792
–3795
(2009
). 6.
B.
Borie
, M.
Voto
, L.
Lopez-Diaz
, H.
Grimm
, M.
Diegel
, M.
Kläui
, and R.
Mattheis
, “Reliable propagation of magnetic domain walls in cross structures for advanced multiturn sensors
,” Phys. Rev. Appl.
8
(4
), 044004
(2017
). 7.
C.
Cui
, O. G.
Akinola
, N.
Hassan
, C. H.
Bennett
, M. J.
Marinella
, J. S.
Friedman
, and J. A. C.
Incorvia
, “Maximized lateral inhibition in paired magnetic domain wall racetracks for neuromorphic computing
,” Nanotechnology
31
(29
), 294001
(2020
). 8.
Y.
Wang
, H.
Yu
, L.
Ni
, G. B.
Huang
, M.
Yan
, C.
Weng
, and J.
Zhao
, “An energy-efficient nonvolatile in-memory computing architecture for extreme learning machine by domain-wall nanowire devices
,” IEEE Trans. Nanotechnol.
14
(6
), 998
–1012
(2015
). 9.
R.
Sbiaa
, “Multistate magnetic domain wall devices for neuromorphic computing
,” Phys. Status Solidi RRL
15
(7
), 2100125
(2021
). 10.
B.
Borie
, A.
Kehlberger
, J.
Wahrhusen
, H.
Grimm
, and M.
Kläui
, “Geometrical dependence of domain-wall propagation and nucleation fields in magnetic-domain-wall sensors
,” Phys. Rev. Appl.
8
(2
), 024017
(2017
). 11.
B.
Borie
, J.
Wahrhusen
, H.
Grimm
, and M.
Kläui
, “Geometrically enhanced closed-loop multi-turn sensor devices that enable reliable magnetic domain wall motion
,” Appl. Phys. Lett.
111
(24
), 242402
(2017
). 12.
T. J.
Hayward
, “Intrinsic nature of stochastic domain wall pinning phenomena in magnetic nanowire devices
,” Sci. Rep.
5
(1
), 13279
(2015
). 13.
T. J.
Hayward
and K. A.
Omari
, “Beyond the quasi-particle: Stochastic domain wall dynamics in soft ferromagnetic nanowires
,” J. Phys. Appl. Phys.
50
(8
), 084006
(2017
). 14.
E.
Lage
, R.
Mattheis
, and J.
McCord
, “Stochasticity of domain wall pinning in curved ferromagnetic nanowires investigated by high-resolution Kerr microscopy
,” J. Magn. Magn. Mater.
487
, 165273
(2019
). 15.
M.
Kläui
, “Head-to-head domain walls in magnetic nanostructures
,” J. Phys. Condens. Matter
20
(31
), 313001
(2008
). 16.
G. S. D.
Beach
, C.
Nistor
, C.
Knutson
, M.
Tsoi
, and J. L.
Erskine
, “Dynamics of field-driven domain-wall propagation in ferromagnetic nanowires
,” Nat. Mater.
4
(10
), 741
–744
(2005
). 17.
A.
Mougin
, M.
Cormier
, J. P.
Adam
, P. J.
Metaxas
, and J.
Ferré
, “Domain wall mobility, stability and Walker breakdown in magnetic nanowires
,” Europhys. Lett.
78
(5
), 57007
(2007
). 18.
N. L.
Schryer
and L. R.
Walker
, “The motion of 180° domain walls in uniform dc magnetic fields
,” J. Appl. Phys.
45
(12
), 5406
–5421
(1974
). 19.
J.-Y.
Lee
, K.-S.
Lee
, S.
Choi
, K. Y.
Guslienko
, and S.-K.
Kim
, “Dynamic transformations of the internal structure of a moving domain wall in magnetic nanostripes
,” Phys. Rev. B
76
(18
), 184408
(2007
). 20.
T. A.
Moore
, P.
Möhrke
, L.
Heyne
, A.
Kaldun
, M.
Kläui
, D.
Backes
, J.
Rhensius
, L. J.
Heyderman
, J.-U.
Thiele
, G.
Woltersdorf
, A.
Fraile Rodríguez
, F.
Nolting
, T. O.
Menteş
, MÁ
Niño
, A.
Locatelli
, A.
Potenza
, H.
Marchetto
, S.
Cavill
, and S. S.
Dhesi
, “Magnetic-field-induced domain-wall motion in permalloy nanowires with modified Gilbert damping
,” Phys. Rev. B
82
(9
), 094445
(2010
). 21.
J.-Y.
Lee
, K.-S.
Lee
, and S.-K.
Kim
, “Remarkable enhancement of domain-wall velocity in magnetic nanostripes
,” Appl. Phys. Lett.
91
(12
), 122513
(2007
). 22.
J.
Brandão
, S.
Azzawi
, A. T.
Hindmarch
, and D.
Atkinson
, “Understanding the role of damping and Dzyaloshinskii-Moriya interaction on dynamic domain wall behaviour in platinum-ferromagnet nanowires
,” Sci. Rep.
7
(1
), 4569
(2017
). 23.
M. T.
Bryan
, T.
Schrefl
, and D. A.
Allwood
, “Dependence of transverse domain wall dynamics on permalloy nanowire dimensions
,” IEEE Trans. Magn.
46
(5
), 1135
–1138
(2010
). 24.
K.
Weerts
, W.
Van Roy
, G.
Borghs
, and L.
Lagae
, “Suppression of complex domain wall behavior in Ni80Fe20 nanowires by oscillating magnetic fields
,” Appl. Phys. Lett.
96
(6
), 062502
(2010
). 25.
Y.
Nakatani
, A.
Thiaville
, and J.
Miltat
, “Faster magnetic walls in rough wires
,” Nat. Mater.
2
(8
), 521
–523
(2003
). 26.
E. R.
Lewis
, D.
Petit
, L.
O’Brien
, A.
Fernandez-Pacheco
, J.
Sampaio
, A.-V.
Jausovec
, H. T.
Zeng
, D. E.
Read
, and R. P.
Cowburn
, “Fast domain wall motion in magnetic comb structures
,” Nat. Mater.
9
(12
), 980
–983
(2010
). 27.
X.-P.
Ma
, S.-D.
Kim
, S.-Y.
Park
, Y. S.
Choi
, H.-G.
Piao
, and D.-H.
Kim
, “Suppression of Walker breakdown in gapped magnetic nanowires
,” J. Appl. Phys.
124
(8
), 083905
(2018
). 28.
J.
Brandão
and D.
Atkinson
, “Controlling the stability of both the structure and velocity of domain walls in magnetic nanowires
,” Appl. Phys. Lett.
109
(6
), 062405
(2016
). 29.
H.-G.
Piao
, J.-H.
Shim
, S.-H.
Lee
, D.
Djuhana
, S.-K.
Oh
, S.-C.
Yu
, and D.-H.
Kim
, “Domain wall propagation in wavy ferromagnetic nanowire
,” IEEE Trans. Magn.
45
(10
), 3926
–3929
(2009
). 30.
D. M.
Burn
and D.
Atkinson
, “Suppression of Walker breakdown in magnetic domain wall propagation through structural control of spin wave emission
,” Appl. Phys. Lett.
102
(24
), 242414
(2013
). 31.
D. M.
Burn
, E.
Arac
, and D.
Atkinson
, “Magnetization switching and domain-wall propagation behavior in edge-modulated ferromagnetic nanowire structures
,” Phys. Rev. B
88
(10
), 104422
(2013
). 32.
S.-H.
Lee
, J.-H.
Shim
, H.-G.
Piao
, S.-C.
Yu
, S. K.
Oh
, and D.-H.
Kim
, “Micromagnetic study of forced oscillation of magnetic domain wall in ferromagnetic nanowires with variation of damping constant
,” J. Supercond. Nov. Magn.
25
(8
), 2795
–2798
(2012
). 33.
E.
Semenova
, D.
Berkov
, N.
Gorn
, and R.
Mattheis
, “Field operating window of nanodevices employing the domain wall propagation through the stripes intersection: Numerical optimization
,” J. Appl. Phys.
124
(15
), 153901
(2018
). 34.
Z.
Luo
, A.
Hrabec
, T. P.
Dao
et al, “Current-driven magnetic domain-wall logic
,” Nature
579
, 214
–218
(2020
). 35.
T.
Shibata
, T.
Shinohara
, T.
Ashida
, M.
Ohta
, K.
Ito
, S.
Yamada
, Y.
Terasaki
, and T.
Sasaki
, “Linear and symmetric conductance response of magnetic domain wall type spin-memristor for analog neuromorphic computing
,” Appl. Phys. Express
13
(4
), 043004
(2020
). 36.
Novotechnik Messwertaufnehmer OHG
, GMR multiturn; see https://www.novotechnik.de/produkte/sensortechnologien/gmr-multiturn/; accessed 24 November 2021.37.
A.
Vansteenkiste
, J.
Leliaert
, M.
Dvornik
, M.
Helsen
, F.
Garcia-Sanchez
, and B.
Van Waeyenberge
, “The design and verification of MuMax3
,” AIP Adv.
4
(10
), 107133
(2014
). 38.
S.
Ingvarsson
, L.
Ritchie
, X. Y.
Liu
, G.
Xiao
, J. C.
Slonczewski
, P. L.
Trouilloud
, and R. H.
Koch
, “Role of electron scattering in the magnetization relaxation of thin Ni81Fe19 films
,” Phys. Rev. B
66
(21
), 214416
(2002
). 39.
V.
Estévez
and L.
Laurson
, “Head-to-head domain wall structures in wide permalloy strips
,” Phys. Rev. B
91
(5
), 054407
(2015
). 40.
Y.
Nakatani
, A.
Thiaville
, and J.
Miltat
, “Head-to-head domain walls in soft nano-strips: A refined phase diagram
,” J. Magn. Magn. Mater.
290–291
, 750
–753
(2005
). 41.
R. D.
McMichael
and M. J.
Donahue
, “Head to head domain wall structures in thin magnetic strips
,” IEEE Trans. Magn.
33
(5
), 4167
–4169
(1997
). 42.
E. R.
Lewis
, D.
Petit
, L.
Thevenard
, A. V.
Jausovec
, L.
O’Brien
, D. E.
Read
, and R. P.
Cowburn
, “Magnetic domain wall pinning by a curved conduit
,” Appl. Phys. Lett.
95
(15
), 152505
(2009
). © 2022 Author(s). Published under an exclusive license by AIP Publishing.
2022
Author(s)
You do not currently have access to this content.
