Excitation Spectra of Square Lattice Antiferromagnets: Theoretical Explanation of Experimental Observations

189 Pages·2016·7.672 MB·English

by  Bastien Dalla Piazza (auth.)

Springer Theses
Recognizing Outstanding Ph.D. Research
Bastien Dalla Piazza

Excitation Spectra
of Square Lattice
Antiferromagnets
Theoretical Explanation of
Experimental Observations
Springer Theses
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Bastien Dalla Piazza
Excitation Spectra of Square
Lattice Antiferromagnets
Theoretical Explanation of Experimental
Observations
Doctoral Thesis accepted by
EPFL, Institute of Condensed Matter Physics,
Switzerland
123
Author Supervisor
Dr. Bastien DallaPiazza Prof. HenrikM. Ronnow
Institute of Condensed Matter Physics, Institute of Condensed Matter Physics,
Laboratoryfor Quantum Magnetism Laboratoryfor Quantum Magnetism
EPFL EPFL
Lausanne Lausanne
Switzerland Switzerland
ISSN 2190-5053 ISSN 2190-5061 (electronic)
SpringerTheses
ISBN978-3-319-26418-9 ISBN978-3-319-26419-6 (eBook)
DOI 10.1007/978-3-319-26419-6
LibraryofCongressControlNumber:2015958537
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’
Supervisor s Foreword
It is a great pleasure for me to write this foreword to the Ph.D. thesis of Bastien
DallaPiazza.TomymindhesolvedapuzzleIhadbeenponderingformorethana
decade,andtherebyprovidedthecurrentstateoftheartinourunderstandingofthe
Heisenberg model in two dimensions, and more widely concerning the duality
between semiclassical and purely quantum states of matter.
Named after one of the fathers of the theory of quantum mechanics, the
Heisenbergmodelretainsaspecialpositionasoneofthesimplestarenastofurther
our understanding of many-body quantum physics. It spans the range of possible
behavior from ordered states with semiclassical spin-wave excitations in three
dimensions to purely quantum disordered states with no classical analogue and
fractionalizedso-calledspinonexcitationsinonedimension.Intwodimensions,the
Heisenbergmodelresidesveryclosetotheboundarybetweentheseregimes.Ithad
for decades been established that at (but only at) zero temperature even in two
dimensionstheHeisenbergmodeldoesformlong-rangestaticorderwithdynamics
that, at first glance, seems well described as semiclassical spin waves—just like in
three dimensions, or as in a classical version of the model.
However, 15 years ago we discovered experimentally that this spin-wave
description fails for a special region of momenta or periodicity—the ðπ;0Þ
zone-boundaryanomaly.Since thenIhavechallengedleadingtheoristsinthefield
for an explanation. But it was Bastien, with invaluable theoretical guidance from
DmitriIvanov,who—inmyopinion—crackedthenut.Havingalreadysuccessfully
tackled other theoretical challenges, including the systematic derivation of
spin-wave excitations from a so-called Hubbard model in insulating cuprates—
presented as Part 2 of this thesis, the zone-boundary anomaly project was born
during a discussion between Bastien, Dmitri, and myself. I explained the phe-
nomenological problem. Dmitri suggested a possible theoretical avenue (warning
thattheavenuewouldbelong,winding,andsteep).And,Bastiensetoffinpursuit.
Needless to say, the guidance from Dmitri was invaluable—my own naïve ques-
tionsperhapslessso—butitwouldbefairtostatethatthefinalachievementisfully
Bastien’s.
v
vi Supervisor’sForeword
For me it was a privilege to see the evolution from idea through pages of
handwritten algebra and millions of CPU hours and definition of new quantities—
such as “the average spinon separation”—to a remarkable conclusion:
The zone boundary anomaly reflects break-down of spin-waves into fractional
spinon-like excitations.
With this, Bastien has shown us that what at first glance behaves like a semi-
classicalsystemleadsadoublelifefullofquantumentanglement,whichisactually
morechallengingtounderstandthan,e.g.,theone-dimensionalcasewhichispurely
quantum with no classical Façade. As such I hope Bastien’s work will inspire
further efforts and lead to a better understanding of this dual nature.
I remain deeply grateful to Bastien for his work and the many enlightening
discussionswehadonthisandothertopics.AndItrustthatyou—thereader—will
enjoy this thesis and what it uncovers.
Lausanne, Switzerland Prof. Henrik M. Ronnow
November 2015
Preface
This thesis is divided into two main chapters which correspond to originally
separated projects. The two topics broadly relate to the square lattice antiferro-
magnet, and more precisely to its excitation spectrum as measured by different
techniques. I nonetheless felt it would be artificial to shape the two topics into a
single one. I thus chose to present the two topics separately in their dedicated
chapters.
Itthenfallsuponthisintroductiontoprovidesomelinkbetweenthesechapters.
A strong link is contained first into the scientific approach that gave birth to these
works. Both topics were motivated by prior experimental results on specific
materials that raised questions about their theoretical interpretation. It just so
happened that the materials considered were all realizations of the square lattice
antiferromagnet.Ofcoursecallingthisacoincidenceisanexaggeration.Indeed,the
magneticpropertiesofthesquarelatticeantiferromagnetareoneofthefundamental
problems of the quantum magnetism research domain and, in a broader context,
a possible key ingredient of the still controversial high temperature superconduc-
tivity problem. The mentioned experimental results allowed to characterize with
unprecedented accuracy the magnetic excitation spectrum, which then required
detailed theoretical modeling.
While the two topics share many aspects, they also represent different comple-
mentary pieces of work of scientific research. The first topic in Chap. 1 studies
theoretically the fundamental Heisenberg model for which a variety of physical
realizations exist. The emphasis is on developing original theoretical methods and
using those to extract some fundamental properties of this model, hopefully
improving its understanding. On the other hand the second topic in Chap. 2 is
geared towards using established theoretical tools in order to give a detailed the-
oreticalcharacterizationofmaterials.Theemphasisthereisonreachingahighlevel
of detail in existing theories in order to allow a quantitative interpretation of
experimentally measured quantities. This quantitative analysis then allows com-
parison across different experimental techniques helping to build an overall
consistent experimental picture.
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viii Preface
The occurrence of these two approaches in a single thesis is reminiscent of the
position which was mine in the Laboratory for Quantum Magnetism. As a theo-
reticallyorientedstudentinanotherwiseexperimentallaboratory,itoftenfellonme
to provide some simple “first order” theoretical description, using conventional
theoretical tools such as the mean-field approximation, or spin-wave theory. Upon
thesuccessorfailureofsuchsimpleapproach,moresophisticatedapproachescould
be undertaken. In the case of the first project in Chap. 1, the established failure of
spin-wave theory to capture some striking aspects of measurements lead to
undertaking a completely different theoretical approach. On the other hand the
relativesuccessofspin-wavetheoryinthecontextofthesecondprojectinChap.2
leadstorefiningitaccountingforfinedetailsofspecificmaterials.Overall,Ibelieve
the two projects make for an equilibrated picture of what has been my work as a
theorist in the Laboratory for Quantum Magnetism.
Abstract
Thefirstpartofthisthesispresentsthetheoreticalstudyofananomalyofunknown
originintheexcitationspectrumofthequantumspin-1=2Heisenbergsquarelattice
antiferromagnet. The anomaly manifests itself in inelastic neutron scattering data
for short wavelength/high energy excitations. Instead of the expected sharp semi-
classicalharmonicmodes,abroadcontinuumemergessuggestingthepossibilityof
fractionalized excitations. A theoretical framework based on the Gutzwiller
projection is developed and allows to link the observed continuum to unbound
fractional quasiparticle pairs, while the sharp harmonic excitations may be descri-
bed by bound ones.
The second part of this thesis presents the detailed theoretical modeling of the
spin-wave dispersion relation measured in insulating cuprate materials. Starting
fromtheone-bandHubbard modelwithextendedhoppingamplitudes,aneffective
low-energy theory is derived allowing to describe on the same footing different
insulatingcupratemagneticexcitationspectra. Theeffectivetheoryisfittedagainst
experimental data and microscopic model parameters are extracted. The high level
ofdetailsincludedinoureffectivetheoryallowsaconsistentcharacterizationofthe
studied materials as measured by various magnetic or electronic experimental
techniques.
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