Chiral and Topological Nature of Magnetic Skyrmions

134 Pages·2018·6.24 MB·English

by  Shilei Zhang

Springer Theses
Recognizing Outstanding Ph.D. Research
Shilei Zhang

Chiral and
Topological Nature
of Magnetic
Skyrmions
Springer Theses
Recognizing Outstanding Ph.D. Research
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Shilei Zhang
Chiral and Topological
Nature of Magnetic
Skyrmions
Doctoral Thesis accepted by
the University of Oxford, Oxford, UK
123
Author Supervisor
Dr. Shilei Zhang Prof. ThorstenHesjedal
Clarendon Laboratory, University of Oxford
Departmentof Physics Oxford,UK
University of Oxford
Oxford,UK
ISSN 2190-5053 ISSN 2190-5061 (electronic)
SpringerTheses
ISBN978-3-319-98251-9 ISBN978-3-319-98252-6 (eBook)
https://doi.org/10.1007/978-3-319-98252-6
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To Valen:
The resonance with you scatters through
every corner of my phase space.
’
Supervisor s Foreword
Magnetic skyrmions are swirls in a magnetic spin system, analogous to the
skyrmionparticleoriginallydescribedinthecontextofpionfields.Intheirinternal
structure, constituent spins point in all the directions wrapping a sphere, which is
mathematically described by a distinct topological index and can be a source of
emergentphenomenasuchasthetopologicalHalleffect.Skyrmionsareobservedin
non-centrosymmetric B20 compounds in which Dzyaloshinskii–Moriya (DM)
interaction plays a role. The competition between symmetric and antisymmetric
exchange interactions gives rise to long-range ordered modulations, which are
manifested by the hexagonal skyrmion lattice at specific temperatures and fields.
Magnetic skyrmion materials hold the promise of rich novel physics and have the
great advantage of a robust topological magnetic structure, which makes them
stableagainstthesuperparamagneticeffectandarethereforeacandidateforthenext
generation of spintronic memory devices.
Dr. Shilei Zhang’s thesis aims for a comprehensive introduction to this fasci-
nating field of skyrmions, building up the theory of magnetic skyrmions step by
step from the atomic level (Chap. 1). An important focus of this book is on the
experimental x-ray scattering techniques, in particular resonant elastic x-ray scat-
tering (REXS), which have been used to study skyrmions across all length scales.
Chapter 2 introduces the scattering theory, starting from single electrons and
extending toall relevant ordered phases, as well asthe main scattering techniques,
i.e.thereflectionandthegrazingincidencegeometry.Usingtheuniquecapabilities
of REXS, such as element selectivity and sensitivity to both charge and spin
ordering,itispossibletounambiguouslyresolveallmagneticphases.Thisincludes
the clear discrimination of the conical, ferrimagnetic and paramagnetic phases,
which are indistinguishable in both small angle neutron scattering and Lorentz
transmission electron microscopy.
Cu OSeO is a highly unique magnetoelectric material displaying a diverse
2 3
rangeofinterestingmagnetictexturesandproperties.UntilShilei’sgroundbreaking
work,onlysingle-domain,long-rangeorderedskyrmionlatticeshadbeenknownto
exist in a small pocket in the temperature-magnetic field phase diagram, and their
occurrence is believed to be a universal feature of all B20-type skyrmion-carrying
vii
viii Supervisor’sForeword
materials. In Chap. 3, the discovery of a new skyrmion state that consists of
multiple, in-plane rotated hexagonal skyrmion lattices is presented. This multido-
mainskyrmionstateisobtainedformagneticfieldstiltedawayfromthecrystalline
[001] axis, or in general, for fields not aligned along major crystallographic axes.
The origin of the multidomain state can be understood in the framework of com-
peting anisotropies and magnetoelectric effects.
Thekeyquantity that definesthetopologicalpropertiesofamagnetic skyrmion
is the winding number in real-space. The common, indirect approach to determine
the winding number is to experimentally obtain an image of the magnetisation
distribution, and compare it with simulations of the contrast of various, possible
magnetisation patterns. However, it is of crucial importance that the topological
quantity can be unambiguously determined experimentally, as this enables the
profound understanding of the physical systems. In Chap. 4, Shilei presents a new
general physical principle that allows direct access to the topological property of
materialsthroughlight-matterinteraction.Itisnaturallyencodedinthepolarisation
dependence of the resonant x-ray scattering process, which is a universal process
applicable to many different materials and systems. In particular, the circular
dichroism and the linear polarisation dependence, the so-called polarisation-
azimuthal maps, turn REXS into a powerful probe of topology. He introduces the
topology determination principle and presents analytical solutions, numerical
calculations, as well as experimental data, which show that this novel technique is
exclusively sensitive to the winding number.
One of the major challenges in skyrmion science is the determination of the
three-dimensionalmagnetisationdistribution.Ithasbeenpredictedalreadyin2013
thatatwistedskyrmionsurfacestateshouldexistinthin-filmhelimagnets,however,
such a surface state has never been directly observed. The key parameter that
identifies such a twisted state is the helicity angle of the surface skyrmions, which
remained elusive for all magnetic characterisation techniques so far. Only the two
extreme types of so-called Néel- and Bloch-type skyrmions have been recognised
and experimentally confirmed to exist. Their helicity angle v is 0° and 90°,
respectively.InChap.5,directexperimentalevidenceandasystematicstudyofthe
twisted skyrmion surface state with a non-trivial helicity angle is presented. Using
circular dichroism in resonant elastic x-ray scattering, the helicity angle of sky-
rmions can be unambiguously determined. A rigorous theoretical treatment
demonstrates the suitability for studying all types of skyrmion-hosting materials,
and other topological structures.
ThecrowningChap.6introducestheDichroismExtinctionRule(DER),relating
the circular dichroism in resonant magnetic scattering with the structure of the
motif. The method, as a dichroic effect, is sensitive to all types of modulated spin
spirals in magnetic materials. These spirals are ubiquitous in almost all areas of
condensedmatterphysics,reachingfromhelimagnets,multiferroics,andmolecular
magnets to frustrated systems, and indeed also comprise skyrmions, which can be
thoughtofasbeingcomposedofchiralbases.Magneticmicroscopymethods,such
as Lorentz transmission electron microscopy, scanning probe microscopy, Kerr
microscopy, photoemission electron microscopy, and x-ray microscopy failed to
Supervisor’sForeword ix
retrieve the full information of such structures, mostly due to their limited spatial
resolution, the accessibility to all three components of the magnetisation vector
and/orthesmallprobingarea,unsuitedforthelengthscalesofinterest.Ontheother
hand, neutron and x-ray diffraction techniques, which are commonly used, cannot
directlyrevealtheunderlyingtypeofspinspiral,asdatarefinement,computational
modelling, as well as theoretical comparisons have to be performed, yielding no
unique answer. In stark contrast to these disadvantages, Shilei’s novel light-matter
interaction-based DER principle offers a one-to-one correspondence between spin
structure and measured signal, thus allowing for the real-space spin structure to be
unambiguously determined.
An important focus of this book is on experimental x-ray scattering techniques
thathavebeenusedtostudyskyrmionsacrossalllengthscales.Theintroductionof
linear and circular polarisation give rise to new REXS-based techniques that ele-
gantly relate the geometrical properties of circular dichroism to the underlying
microscopic spin structure of a material. Shilei’s discoveries will have a profound
impact on skyrmion science and beyond, as the widely applicable experimental
techniquespavethewayforthein-depthstudyoftopologicalmagneticstructuresin
general.
Oxford, UK Prof. Thorsten Hesjedal
April 2018
Abstract
This work focuses on characterising the chiral and topological nature of magnetic
skyrmions in non-centrosymmetric helimagnets. In these materials, the skyrmion
lattice phase appears as a long-range-ordered, close-packed lattice of nearly
millimetre-levelcorrelationlength,whilethesizeofasingleskyrmionis3–100nm.
This is a very challenging range of length scales (spanning 5 orders of magnitude
fromtensofnmtomm)formagneticcharacterisationtechniques.Asaresult,only
three methods have been proven to be applicable for characterising certain aspects
ofthemagneticinformation:neutrondiffraction,electronmicroscopy,andmagnetic
force microscopy. Nevertheless, none of them reveals the complete information
about this fascinating magnetically ordered state. On the largest scale, the sky-
rmions form a three-dimensional lattice. The lateral structure and the depth profile
areofimportanceforunderstandingthesystem.Onthemesoscopicscale,therigid
skyrmion lattice can break up into domains, with the domain size about tens to
hundreds of micrometres. The information of the domain shape, distribution, and
thedomainboundaryisofgreatimportanceforamagneticsystem.Onthesmallest
scale, a single skyrmion has an extremely fine structure that is described by the
topological winding number, helicity angle, and polarity. These pieces of infor-
mation reveal the underlying physics of the system, and are currently the focus of
spintronics applications. However, so far, there is no experimental technique that
allowsonetoquantitativelystudythesefinestructures.Ithastobeemphasisedthat
the word ‘quantitative’ here means that no speculations have to be made and no
theoretical modelling is required to assist the data interpretation—what has been
measured must be straightforward, and give a unique and unambiguous answer.
Motivated by these questions, we developed soft x-ray scattering techniques
that allow us to acquire much deeper microscopic information of the magnetic sky-
rmions—reaching far beyond what has been possible so far. We will show that by
usingonlyonetechnique,alltheinformationaboutthemagneticstructure(spanning5
ordersofmagnitudeinlength)canbeaccuratelymeasured.Thekeydevelopmentofthe
thesis is the Dichroism Extinction Rule, which is summarised in Chap. 6, and
quintessentially summarises this work.
xi