At short time scales, the inertia term becomes relevant for the magnetization dynamics of ferromagnets and leads to nutation for the magnetization vector. For the case of spatially extended magnetic systems, for instance, Heisenberg spin chains with the isotropic spin-exchange interaction, this leads to the appearance of a collective excitation, the “nutation wave,” whose properties are elucidated by analytical arguments and numerical studies. The one-particle excitations can be identified as relativistic massive particles. These particles, the “nutatons,” acquire their mass via the Brout–Englert–Higgs mechanism, through the interaction of the wave with an emergent topological gauge field. This spin excitation would appear as a peak in the spectrum of the scattering structure factor in inelastic neutron scattering experiments. The high frequency and speed of the nutation wave can open paths for realizing ultrafast spin dynamics.

1.
2.
E.
Beaurepaire
,
J.-C.
Merle
,
A.
Daunois
, and
J.-Y.
Bigot
,
Phys. Rev. Lett.
76
,
4250
(
1996
).
3.
T.
Gerrits
,
H. A. M.
van den Berg
,
J.
Hohlfeld
,
L.
Bär
, and
Th.
Rasing
,
Nature
418
,
509
(
2002
).
4.
A.
Kirilyuk
,
A. V.
Kimel
, and
T.
Rasing
,
Rev. Mod. Phys.
82
,
2731
(
2010
).
5.
I.
Tudosa
,
C.
Stamm
,
A. B.
Kashuba
,
F.
King
,
H. C.
Siegmann
,
J.
Stöhr
,
G.
Ju
,
B.
Lu
, and
D.
Weller
,
Nature
428
,
831
(
2004
).
6.
L.
Landau
and
E.
Lifshitz
,
Phys. Z. Sowjetunion
8
,
153
(
1935
).
7.
T. L.
Gilbert
,
IEEE Trans. Mag.
40
,
3443
(
2004
).
8.
M.-C.
Ciornei
,
J. M.
Rubi
, and
J.-E.
Wegrowe
,
Phys. Rev. B
83
,
020410(R)
(
2011
).
9.
J.-E.
Wegrowe
and
C.
Ciornei
,
Am. J. Phys.
80
,
607
(
2012
).
10.
E.
Olive
,
Y.
Lansac
, and
J.-E.
Wegrowe
,
Appl. Phys. Lett.
100
,
192407
(
2012
).
11.
E.
Olive
,
Y.
Lansac
,
M.
Meyer
,
M.
Hayoun
, and
J.-E.
Wegrowe
,
J. Appl. Phys.
117
,
213904
(
2015
).
12.
M.
Fähnle
,
D.
Steiauf
, and
C.
Illg
,
Phys. Rev. B
84
,
172403
(
2011
).
13.
S.
Bhattacharjee
,
L.
Nordström
, and
J.
Fransson
,
Phys. Rev. Lett.
108
,
057204
(
2012
).
14.
R.
Mondal
,
M.
Berritta
,
A. K.
Nandy
, and
P. M.
Oppeneer
,
Phys. Rev. B
96
,
024425
(
2017
).
15.
I.
Makhfudz
,
B.
Krüger
, and
O.
Tchernyshyov
,
Phys. Rev. Lett.
109
,
217201
(
2012
).
16.
K.
Neeraj
,
N.
Awari
,
S.
Kovalev
,
D.
Polley
,
N. Z.
Hagstrm
,
S. S. P. K.
Arekapudi
,
A.
Semisalova
,
K.
Lenz
,
B.
Green
,
J.-C.
Deinert
 et al., arXiv:1910.11284 (
2019
).
17.
R.
Bastardis
,
F.
Vernay
, and
H.
Kachkachi
,
Phys. Rev. B
98
,
165444
(
2018
).
18.
L. D.
Landau
and
E. M.
Lifshitz
,
Statistical Physics Part 2
(
Pergamon Press
,
New York
,
1980
).
19.
See https://en.wikipedia.org/wiki/Wave_equation for an introduction to wave equation, especially on wave equation in one space dimension.
20.
A.
Auerbach
,
Interacting Electrons and Quantum Magnetism
(
Springer-Verlag New York
,
1994
).
21.
R. D.
Willett
,
C. P.
Landee
, and
D. D.
Swank
,
J. Appl. Phys.
49
,
1329
(
1978
).
22.
D. D.
Swank
,
C. P.
Landee
, and
R. D.
Willett
,
Phys. Rev. B
20
,
2154
(
1979
).
23.
R. D.
Willett
,
C. P.
Landee
,
R. M.
Gaura
,
D. D.
Swank
,
H. A.
Groenendijk
, and
A. J.
van Duynevelt
,
J. Magn. Magn. Mater
15–18
,
1055
(
1980
).
24.
M.
Madami
,
S.
Bonetti
,
G.
Consolo
,
S.
Tacchi
,
G.
Carlotti
,
G.
Gubbiotti
,
F. B.
Mancoff
,
M. A.
Yar
, and
J.
erman
,
Nat. Nanotechnol.
6
,
635
(
2011
).
25.
C.
Liu
,
J.
Chen
,
T.
Liu
,
F.
Heimbach
,
H.
Yu
,
Y.
Xiao
,
J.
Hu
,
M.
Liu
,
H.
Chang
,
T.
Stueckler
 et al.,
Nat. Commun.
9
,
738
(
2018
).
26.
P. W.
Higgs
,
Phys. Rev. Lett.
13
,
508
(
1964
).
27.
F.
Englert
and
R.
Brout
,
Phys. Rev. Lett.
13
,
321
(
1964
).
28.
D.
Sherman
,
U. S.
Pracht
,
B.
Gorshunov
,
S.
Poran
,
J.
Jesudasan
,
M.
Chand
,
P.
Raychaudhuri
,
M.
Swanson
,
N.
Trivedi
,
A.
Auerbach
 et al.,
Nat. Phys.
11
,
188
(
2015
).
29.
M.
Lohöfer
and
S.
Wessel
,
Phys. Rev. Lett.
118
,
147206
(
2017
).
30.
S.
Sachdev
,
Quantum Phase Transitions
(
Cambridge University Press
,
Cambridge, UK
,
2011
).
31.
D.
Pekker
and
C. M.
Varma
,
Annu. Rev. Condens. Matter Phys.
6
(
1
),
269
297
(
2015
).
32.
M.
Peskin
and
D.
Schroeder
,
Introduction to Quantum Field Theory
(
Perseus
,
Cambridge
,
MA
,
1995
).
33.
I.
Makhfudz
,
Phys. Rev. B
89
,
024401
(
2014
).
34.
I.
Makhfudz
,
J. Phys.: Condens. Matter
30
,
225801
(
2018
).
35.
P. D.
Mannheim
, arXiv:1506.04120v2 (
2015
).
36.
T.
Nussle
,
P.
Thibaudeau
, and
S.
Nicolis
,
Phys. Rev. B
100
,
214428
(
2019
).

Supplementary Material

You do not currently have access to this content.