SKYRMION CRYSTAL FROM RKKY INTERACTION MEDIATED
BY 2D ELECTRON GAS
Cristian D. Batista1,2, Zhentao Wang1, Ying Su3 and Shizeng Lin3
1

2Department of Physics and Astronomy, The University of Tennessee, Knoxville,Tennessee 37996, USA

Neutron Scattering Division and Shull-Wollan Center,Oak Ridge National Laboratory,
Oak Ridge, Tennessee 37831, USA
3

Theoretical Division, T-4 and CNLS, Los Alamos National Laboratory, Los Alamos,
New Mexico 87545, USA
E-Mail: cbatist2@utk.edu

We consider a C6 invariant lattice of magnetic moments coupled via a Kondo
exchange 𝐽 with a 2D electron gas (2DEG) [1]. The effective Ruderman-Kittel-KasuyaYosida (RKKY) interaction between the moments stabilizes a magnetic skyrmion crystal
in the presence of magnetic field and easy-axis anisotropy (see Fig. 1). An attractive
aspect of this mechanism is that the magnitude of the magnetic ordering wave
vectors, 𝑸𝝂 ( 𝜈 = 1,2,3 ), is dictated by the Fermi wave number 𝑘𝐹 : |𝑸| = 2𝑘𝐹 .
Consequently, the topological contribution to the Hall conductivity of the 2DEG becomesof the order of the quantized value, 𝑒 2 /ℎ, when 𝐽 is comparable to the Fermi energy 𝜀𝐹 .

Fig. 1: Phase diagrams ofthe TL single RKKY
model with easy-axis
single ion anisotropy in amagnetic field.

[1] https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.124.207201

NOVEL MATERIALS WITH MAGNETIC SKYRMIONS AND
THEIR THREE-DIMENSIONAL DYNAMICS
S. Seki1
1

Department of Applied Physics and Institute of Engineering Innovation, University ofTokyo, Bunkyo-ku, Tokyo 113-8656, Japan
E-Mail: seki@ap.t.u-tokyo.ac.jp

Magnetic skyrmion, i.e., a topologically stable swirling spin configuration, has recently
attracted attention as a particle-like object potentially suitable for the design of highdensity information bits. Previous observations of skyrmions have mostly focused on
noncentrosymmetric systems, where Dzyaloshinskii-Moriya interaction plays animportant role [1,2]. On the other hand, recent theoretical studies suggest that skyrmionscan be stabilized even in centrosymmetric systems by considering different microscopic
mechanisms. For example, geometrical frustration of short-range exchange interactions
on triangular lattice is predicted to stabilize a hexagonal lattice of skyrmions [3]. Anotherpotential mechanism is the RKKY and four-spin interactions mediated by itinerant
electrons, which is expected to favor a skyrmion lattice state for highly-symmetric (suchas hexagonal or tetragonal) crystal lattice systems [4].
In this talk, I overview the recent experimental discovery of skyrmions incentrosymmetric systems [5-9]. In particular, we focus on the case of centrosymmetrictetragonal magnet GdRu2Si2, where the square lattice of skyrmions with extremely small
diameter (1.9 nm, i.e. the smallest value ever reported for single-component bulkmaterials) has been observed [8,9]. Our results demonstrate that skyrmions can bestabilized even without geometrically frustrated lattice nor inversion symmetry breaking,and suggest that rare-earth intermetallics with highly-symmetric crystal lattice may
ubiquitously host nanometric skyrmions of exotic origins.
[1] S. Muehlbauer et al., Science 323, 915 (2009)[2] S. Seki et al., Science 336, 198 (2012)[3] A. O. Leonov et al., Nat. Commun. 6, 8275 (2015)[4] S. Hayami et al., Phys. Rev. B 95, 224424 (2017)[5] R. Takagi, S. Seki et al., Sci. Adv. 4, 3402 (2018)[6] T. Kurumaji et al., Science 365, 6456 (2019)[7] M. Hirschberger et al., Nat. Commun. 10, 5831 (2019)[8] N. D. Khanh, S. Seki et al., Nat. Nanotechnol. 15, 444 (2020)[9] Y. Yasui, S. Seki et al., Nat. Commun. (in press)

EMERGENT ELECTROMAGNETISM IN SPIRAL MAGNETS
Naoto Nagaosa1,21

RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
Dept. of Applied Physics, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan
Email: nagaosa@riken.jp

2Emergent electromagnetism in non-collinear magnets has attracted recent intensive
interest. Skyrmion is a representative example, where the non-coplanar spin structure
gives the emergent magnetic field associated with the scalar spin chirality, i.e., the solid
angle subtended by the spins. Spiral magnet with non-collinear but co-planar spin
configuration, is characterized by the vector spin chirality, which is time-reversal even,and is not directly related to the Hall effect.
Here I discuss the emergent electromagnetic phenomena, i.e., Berry phase effects, ofthe conduction electrons coupled to the spiral spin structure. It includes the emergent
inductance [1], [2], and transverse conductivity due to the combined effect of spin orbit
interaction and exchange field.
These works have been done in collaboration with Daichi Kurebayashi, Tomoyuki
Yokouchi, Fumitaka Kagawa, Max Hirschberger, Yoshichika Otani, and Yoshinori Tokura.
[1] N. Nagaosa, Jpn. J. Appl. Phys. 58, 120909 (2019)[2] T. Yokouchi et al., Nature 586, 232–236 (2020)

STABILIZATION OF ZERO-FIELD SKYRMIONS IN
FERROMAGNETIC AND SYNTHETIC ANTIFERROMAGNETICSYSTEMS
V. Cros1, W. Legrand1, Y. Sassi1, F. Ajejas1, A. Finco2, E. Burgos Parra1, C.
Leveillé3, A. Haykal2, R. Tanos2, F. Fabre2, I. Robert-Philipp2, K.
Bouzehouane1, J. V. Kim4, T. Devolder4, N. Jaouen3, V. Jacques2, N.
Reyren1, A. Fert1
1

Unité Mixte de Physique CNRS, Thales, Université Paris-Saclay, Palaiseau, France
2
Laboratoire Charles Coulomb L2C, Montpellier, France
3
Synchrotron SOLEIL, Saint-Aubin, Gif-sur-Yvette Cedex, France
4

Laboratoire C2N, CNRS, Univ. Paris-Saclay, Palaiseau, France
E-Mail: vincent.cros@cnrs-thales.fr

In this study, we show that inserting a bias layer in the ferromagnetic multilayer stack,and utilizing interlayer electronic coupling between this bias layer and the ferromagnetic
skyrmion multilayer, we successfully demonstrate the stabilization of sub 100 nm
skyrmions at room temperature. We then show that room-temperature antiferromagnetic
skyrmions can be stabilized in synthetic antiferromagnet (SAF) systems. To this aim, weelaborate a material system in which perpendicular magnetic anisotropy,
antiferromagnetic coupling and chiral order can be adjusted concurrently. Utilizing thesame bias layer, we demonstrate by Magnetic Force Microscopy [1] and by spin NV
relaxometry [2] that the spin-spiral state obtained in a SAF system with vanishing
perpendicular anisotropy can be turned into isolated antiferromagnetic skyrmions stableat zero field. These experimental results are completed with model-based estimations of
their size and stability, showing that room-temperature stable antiferromagneticskyrmions below 10 nm in radius can be anticipated in further optimized SAF systems[6]. Antiferromagnetic skyrmions in SAF systems may thus solve major issues associatedto ferromagnetic skyrmions for low-power spintronic devices.
[1] W. Legrand et al., Nature Materials 19, 34 (2020)[2] A. Finco et al., arXiv:2006.13130
French ANR grant TOPSKY (ANR-17-CE24-0025), DARPA TEE program grant(MIPR#HR0011831554), FLAG-ERA SOgraphMEM, and EU grant SKYTOP (H2020
FET Proactive 824123) are acknowledged for their financial support.

BEYOND HEISENBERG SOLIDS:FROM MULTI-SPIN INTERACTIONS TO NOVEL CHIRALPARTICLES
Stefan Blügel1
1

Peter Grünberg Institute and Institute for Advanced Simulation,
Forschungszentrum Jülich, 52425 Jülich, Germany
E-Mail: s.bluegel@fz-juelich.de

It became customary to study the stability, lifetime, dynamics, thermodynamics andtransport properties of localized nanoscale magnetization particles such as skyrmionics
by classical spin-lattice models with pairwise Heisenberg-type exchange interactions.
The mapping of fermionic many-body systems onto a classical Heisenberg model is a
nontrivial thing and by far not unique. In this presentation I motivate beyond
Heisenberg multi-spin interactions [1]. I give examples, where these interactions play adecisive role [2]. I focus on MnGe in the B20-phase, which exhibits a three-dimensional
spin-texture. We introduce a novel class of magnetic exchange interactions [3] – thetopological-chiral interactions (TCI) rooted in the so-called topological orbital moment,
which manifests as a result of finite scalar spin chirality in non-coplanar magnets. The
long-wave length limit of the interactions relates to the highly acclaimed Faddeev
model demonstrating that the interaction is an origin of 3D magnetization textures all
the way down to hopfions.
[1] M. Hoffmann, S. Blügel, PRB 10, 024418 (2019)[2] A. Krönlein, M. Schmitt, M. Hoffmann, J. Kemmer, N. Seubert, M. Vogt, J.
Küspert, M. Böhme, B. Alonazi, J. Kügel, H. A. Albrithen, M. Bode, G. Bihlmayer, andS. Blügel, PRL 120, 207202 (2018)[3] S. Grytsiuk, J.-P. Hanke, M. Hoffmann, J. Bouaziz, O. Gomonay, G. Bihlmayer, S.
Lounis, Y. Mokrousov, S. Blügel, Nat. Commun. 11, 511 (2020)

FRACTIONAL ANTIFERROMAGNETIC SKYRMION LATTICE
IN MnSc2S4
Oksana Zaharko1, Shang Gao1,2,3, Guratinder Kaur1,2, Christian Rüegg 1,2,
H. Diego Rosales4, Flavia A. Gomez Albarracin4, Daniel C. Cabra4,
Vladimir Tsurkan3
1

Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institut, Villigen,
Switzerland
2
Department of Quantum Matter Physics, University of Geneva, Geneva, Switzerland
34

RIKEN Center for Emergent Matter Science, Wako, Japan
Instituto de Física de Líquidos y Sistemas Biológicos, UNLP-CONICET, Facultad deCiencias Exactas, La Plata, Argentina
5Experimental Physics V, University of Augsburg, Augsburg, Germany,
Institute of Applied Physics, Chisinau, Republic of Moldova
E-Mail: oksana.zaharko@psi.ch

By combining neutron scattering neutron experiments with extensive Monto Carlosimulations we identify a fractional antiferromagnetic skyrmion lattice stabilized in theMnSc2S4 spinel [1]. The triple-q phase is stabilized by perturbing the J1-J2-J3 Hamiltonianby anisotropic couplings and single-ion anisotropy. This scenario is realised in MnSc2S4
owing to its enormous ground-state degeneracy [2].

Figure. Left: The Mn2+ triangular lattice layers along the [111] direction can bedivided into three sublattices which form cylinders of fractional skyrmions. Right: Spintexture of one triangular sublattice. The fractional skyrmions with opposite winding
directions are described in the two spheres shown on the right.
Our work demonstrates that the theoretically proposed antiferromagnetic skyrmionscan be stabilized in real materials.
[1] https://doi.org/10.1038/s41586-020-2716-8[2] DOI: 10.1038/NPHYS391

TOPOLOGICAL MAGNETIC PHASE IN THE CANDIDATE WEYL
SEMIMETAL CeAlGe
P. Puphal1, V. Pomjakushin1, N. Kanazawa2, V. Ukleev1, D.J. Gawryluk1,J.-Z. Ma1, M. Naamneh1, N.C. Plumb1, L. Keller1, R. Cubitt3,E. Pomjakushina1, and J.S. White1
1Paul Scherrer Institute (PSI), CH-5232 Villigen, Switzerland
Department of Applied Physics, University of Tokyo, Tokyo 113-8656, Japan3
Institut Laue-Langevin (ILL), 71 avenue des Martyrs, 38042 Grenoble, France2E-Mail: jonathan.white@psi.ch

In topological materials science, the aim is to find pronounced phenomena rooted in
the concepts of topology in new materials, and harness them for novel and robustfunctions. Promising materials classes include magnetic materials hosting nanoscale
magnetic skyrmions, or Dirac and Weyl semimetals, which are hallmarked by topologicalinvariants in real- or reciprocal spaces, respectively. With recent attention focused onmagnetic topological materials, here we consider the question if novel functionalities may
be found in systems with electronic and magnetic structures that are both topologically
nontrivial, and where they coexist and may be coupled. In this context, I will present ourrecent experimental work on the polar tetragonal magnet CeAlGe [1]. This system waspredicted recently to be an easy-plane ferromagnetic type-II Weyl semimetal, yet themagnetic and electrical properties were little-explored. From magnetometry, neutron
scatteringandelectricaltransport
measurements, we find CeAlGe to be a hostof nanoscale and incommensuratelymodulated multi-k magnetic phases. For anintermediate field along the polar c-axis, oneof the incommensurate phases generates a
topological Hall effect, and we propose it tobe generated by a novel magnetic structure
containing anti-meron pairs [Fig. 1]. We
discuss the implication for the existence ofsuch magnetic phases in Weyl semimetals
and the possibilities for new functionalities.
[1] P. Puphal et al., PRL 124, 017202 (2020)

Fig. 1: View along the polar c-axisof the proposed topological magnetic
structure in CeAlGe. Blue squares
indicate merons of opposite helicity.

MAGNETIC SKYRMIONS FOR UNCONVENTIONALCOMPUTING AND REVEALING LATENT INFORMATION
Karin Everschor-Sitte1
1

Institute of Physics, Johannes Gutenberg-Universität, 55128 Mainz, Germany
E-Mail: kaeversc@uni-mainz.de

Novel computational paradigms in combination with proper hardware solutions are
required to overcome the limitations of our state-of-the-art computer technology [1-3]. In
this talk, I will address the potential of topologically stabilized magnetic whirls – socalled skyrmions – for two unconventional computing schemes – reservoir computing
and stochastic computing. Reservoir computing is a computational scheme that allows todrastically simplify spatial-temporal recognition tasks. We have shown that random
skyrmion fabrics provide a suitable physical implementation of the reservoir [4,5] andallow to classify patterns via their complex resistance responses either by tracing thesignal over time or by a single spatially resolved measurement [6]. Stochastic computing
allows to speed up a calculation while trading for numerical precision. Information isencoded in terms of bit-streams as a probability. A key requirement and simultaneously achallenge are that the incoming bitstreams are uncorrelated. The Brownian motion ofmagnetic skyrmions allows creating a device that reshuffles the bit-streams [7,8]. In any
type of hardware-based computation, some sort of readout of the system is needed. Whileoften a significant effort is made in enhancing the resolution of an experimental technique
to obtain further insight into the sample and its physical properties, an advantageous data
analysis has the potential to provide a deeper insight into given data set [9].
[1] J. Grollier, D. Querlioz, K.Y. Camsari, KES, S. Fukami, M.D. Stiles, Nat. Electron.
(2020)[2] E. Vedmedenko, R. Kawakami, D. Sheka, ..., KES, et al., J. Phys. D (2020)[3] G. Finocchio, M. Di Ventra, K.Y. Camsari, KES, et al., arXiv:1907.07176[4] D. Prychynenko, M. Sitte, et al., KES, Phys. Rev. Appl. 9, 014034 (2018)[5] G. Bourianoff, D. Pinna, M. Sitte and KES, AIP Adv. 8, 055602 (2018)[6] D. Pinna, G. Bourianoff and KES, arXiv:1811.12623[7] D. Pinna, F. Abreu Araujo, J.-V. Kim, et al., Phys. Rev. Appl. 9, 064018 (2018)[8] J. Zazvorka, F. Jakobs, D. Heinze, ..., KES, et al., Nat. Nanotech. 14, 658 (2019)[9] I. Horenko, D. Rodrigues, T. O’Kane and KES, arXiv:1907.04601