Scientific RePoRts | (2018) 8:3433 | DOI:10.1038/s41598-018-21623-3
Lifetime of racetrack skyrmions
Pavel F. Bessarab
, Gideon P. Müller
, Igor S. Lobanov
, Filipp N. Rybakov
Nikolai S. Kiselev
, Hannes Jónsson
, Valery M. Uzdin
, Stefan Blügel
& Anna Delin
The skyrmion racetrack is a promising concept for future information technology. There, binary bits are
carried by nanoscale spin swirls–skyrmions–driven along magnetic strips. Stability of the skyrmions is
a critical issue for realising this technology. Here we demonstrate that the racetrack skyrmion lifetime
can be calculated from rst principles as a function of temperature, magnetic eld and track width.
Our method combines harmonic transition state theory extended to include Goldstone modes, with an
atomistic spin Hamiltonian parametrized from density functional theory calculations. We demonstrate
that two annihilation mechanisms contribute to the skyrmion stability: At low external magnetic eld,
escape through the track boundary prevails, but a crossover eld exists, above which the collapse in the
interior becomes dominant. Considering a Pd/Fe bilayer on an Ir(111) substrate as a well-established
model system, the calculated skyrmion lifetime is found to be consistent with reported experimental
measurements. Our simulations also show that the Arrhenius pre-exponential factor of escape depends
only weakly on the external magnetic eld, whereas the pre-exponential factor for collapse is strongly
eld dependent. Our results open the door for predictive simulations, free from empirical parameters,
to aid the design of skyrmion-based information technology.
Spin textures with topological charge, also called skyrmions
, hold great promise as a basis for a new type of
. In particular, information ow can be associated with metastable skyrmions driven
along a magnetic strip, as suggested in skyrmion racetrack schemes
. It has been demonstrated that skyrmions
are sensitive to controlled external stimuli such as electric current
, which is benecial for ecient, low power
data processing. For such a technology to be viable, however, the skyrmion lifetime, τ, is an essential quantity. It
is a quantitative measure of stability and needs to be long enough to enable information storage with negligible
loss. Prediction of the lifetime of skyrmions in arbitrary materials and materials combinations as a function of
temperature and various external parameters such as applied magnetic eld is thus of central importance for
developing an optimized skyrmion-based technology. Although skyrmions owe their stability to topology, the
lifetime cannot be derived from topological considerations per se. e celebrated notion of topological protection
of a single skyrmion localized in a ferromagnetic ground state of innite spatial dimensions described in the
language of continuum eld theory with xed magnetization length translates to energy barriers, whose heights
become nite for physical systems and described in practice by the escape of the skyrmion to the ferromagnetic
state by radial collapse, or through the system boundary.
Here, we show that it is indeed possible to calculate–from rst principles–the lifetime of skyrmions. To
demonstrate our method, we present results for an fcc-stacked lm of one monolayer of Pd and Fe on an Ir(111)
substrate, one of the best investigated systems hosting single Néel-type skyrmions stabilized by interface gen-
erated Dzyaloshinskii-Moriya (DM) interaction
. We compare the results to an hcp-stacked Pd lm on Fe/
Ir(111), which emerges experimentally as a structurally metastable state
. e spin textures appearing in PdFe/
Ir(111) system as a function of applied magnetic eld have been characterized using spin-polarized scanning tun-
neling microscopy at low temperature
. At zero and low applied magnetic eld, this system exhibits a spin-spiral
state with a period of 6–7 nm, see Fig.1, panels A and D in ref.
. As the magnetic eld is increased to about 1 T,
skyrmions start to form (Fig.1, panel E in ref.
). e observed skyrmions are quite small, with a diameter of just
Science Institute of the University of Iceland, 107, Reykjavik, Iceland.
ITMO University, 197101, St. Petersburg,
Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA,
D-52425, Jülich, Germany.
Department of Physics, KTH Royal Institute of Technology, Stockholm, SE-10691,
Aalto University, FI-00076, Espoo, Finland.
Department of Physics, St. Petersburg State University, St.
Petersburg, 198504, Russia ITMO University, 197101, St. Petersburg, Russia.
Department of Applied Physics, School
of Engineering Sciences, KTH Royal Institute of Technology, Electrum 229, SE-16440, Kista, Sweden.
e-Science Research Center), KTH Royal Institute of Technology, SE-10044, Stockholm, Sweden.
Physics and Astronomy, Uppsala University, Box 516, SE-75120, Uppsala, Sweden. Correspondence and requests for
materials should be addressed to P.F.B. (email: email@example.com) or A.D. (email: firstname.lastname@example.org)
Received: 6 October 2017
Accepted: 7 February 2018
Published: xx xx xxxx