The paper investigates dynamics of nonsingular vortices in a ferromagnetic spin-1 BEC, where spin and mass superfluidity coexist in the presence of uniaxial anisotropy (linear and quadratic Zeeman effect). The analysis is based on hydrodynamics following from the Gross–Pitaevskii theory. Cores of nonsingular vortices are skyrmions with charge, which is tuned by uniaxial anisotropy and can have any fractal value between 0 and 1. There are circulations of mass and spin currents around these vortices. The results are compared with the equation of vortex motion derived earlier in the Landau–Lifshitz–Gilbert theory for magnetic vortices in easy-plane ferromagnetic insulators. In the both cases the transverse gyrotropic force (analog of the Magnus force in super-fluid and classical hydrodynamics) is proportional to the charge of skyrmions in vortex cores.

1.
Y.
Kawaguchi
and
M.
Ueda
,
Phys. Rep.
520
,
253
(
2012
).
3.
H.
Chen
and
A. H.
MacDonald
, in
Universal Themes of Bose–Einstein Condensation
, edited by
N.
Proukakis
,
D.
Snoke
, and
P.
Littlewood
(
Cambridge University Press
,
2017
), Chap. 27, p.
525
; e-print arXiv:1604.02429.
4.
L. D.
Landau
and
E. M.
Lifshitz
,
Statistical Physics
(
Pergamon Press
,
1980
), Part II.
5.
A.
Lamacraft
,
Phys. Rev. A
77
,
063622
(
2008
).
6.
E. B.
Sonin
, Spin and Mass Superfluidity in Ferromagnetic Spin-1 BEC (
2018
); e-print arXiv:1801.01099.
7.
E. B.
Sonin
,
Phys. Rev. B
95
,
144432
(
2017
).
8.
L.
Onsager
,
Nuovo Cimento Suppl.
6
,
249
(
1949
).
9.
R. P.
Feynman
, in
Progress in Low Temperature Physics
, edited by
C. J.
Gorter
(
North-Holland
,
1955
), Vol.
1
, p.
17
.
10.
A.
Kosevich
,
V.
Voronov
, and
I.
Manzhos
,
Zh. Eksp. Teor. Fiz.
84
,
148
(
1983
)
A.
Kosevich
,
V.
Voronov
, and
I.
Manzhos
, [
Sov. Phys. JETP
57
,
86
(
1983
)].
11.
A. M.
Kosevich
,
B. A.
Ivanov
, and
A. S.
Kovalev
,
Nonlinear Magnetization Waves, Dynamic and Topological Solitons
(
Naukova Dumka
,
Kiev
,
1988
) (in Russian).
12.
A. M.
Kosevich
,
B. A.
Ivanov
, and
A. S.
Kovalev
,
Phys. Rep.
194
,
117
(
1990
).
13.
A.
Thiele
,
Phys. Rev. Lett.
30
,
230
(
1973
).
14.
15.
A. V.
Nikiforov
and
E. B.
Sonin
,
Zh. Eksp. Teor. Fiz.
85
,
642
(
1983
)
A. V.
Nikiforov
and
E. B.
Sonin
, [
Sov. Phys. JETP
58
,
373
(
1983
)].
16.
M. M.
Salomaa
and
G. E.
Volovik
,
Rev. Mod. Phys.
59
,
533
(
1985
);
erratum:
M. M.
Salomaa
and
G. E.
Volovik
,
Rev. Mod. Phys.
60
,
573
(
1988
).
17.
E. B.
Sonin
,
Pis'ma Zh. Eksp. Teor. Fiz.
43
,
601
(
1986
)
E. B.
Sonin
, [
JETP Lett.
43
,
779
(
1986
)].
18.
N. D.
Mermin
and
T. L.
Ho
,
Phys. Rev. Lett.
36
,
594
(
1976
).
19.
E. B.
Sonin
,
Dynamics of Quantised Vortices in Superfluids
(
Cambridge University Press
,
2016
).
20.
E. B.
Sonin
,
Zh. Eksp. Teor. Fiz.
87
,
1670
(
1984
)
E. B.
Sonin
, [
Sov. Phys. JETP
60
,
959
(
1984
)].
21.
S. O.
Demokritov
,
V. E.
Demidov
,
O.
Dzyapko
,
G. A.
Melkov
,
A. A.
Serga
,
B.
Hillebrands
, and
A. N.
Slavin
,
Nature
443
,
430
(
2006
).
22.
F.
Fang
,
R.
Olf
,
S.
Wu
,
H.
Kadau
, and
D. M.
Stamper-Kurn
,
Phys. Rev. Lett.
116
,
095301
(
2016
).
24.
B.
Ivanov
,
V.
Stephanovich
, and
A.
Zhmudskii
,
J. Magn. Magn. Mater.
88
,
116
(
1990
).
25.
A.
Abanov
and
V. L.
Pokrovsky
,
Phys. Rev. B
58
,
R8889
(
1998
).
26.
N.
Nagaosa
and
Y.
Tokura
,
Nat. Nanotechnol.
8
,
899
(
2013
).
You do not currently have access to this content.