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UNIVERSIT´ E CATHOLIQUE DE LOUVAIN Facult´ e des Sciences Appliqu´ ees Unit´ e

UNIVERSIT´ E CATHOLIQUE DE LOUVAIN Facult´ e des Sciences Appliqu´ ees Unit´ e de Physico-Chimie et de Physique des Mat´ eriaux QUANTUM HALL EFFECT SKYRMIONS: NUCLEAR MAGNETIC RESONANCE AND HEAT CAPACITY EXPERIMENTS Dissertation pr´ esent´ ee en vue de l’obtention du grade de ‘Docteur en Sciences Appliqu´ ees’ par Sorin MELINTE Promoteur: Prof. Vincent BAYOT Septembre 2001 UNIVERSIT´ E CATHOLIQUE DE LOUVAIN Facult´ e des Sciences Appliqu´ ees Unit´ e de Physico-Chimie et de Physique des Mat´ eriaux QUANTUM HALL EFFECT SKYRMIONS: NUCLEAR MAGNETIC RESONANCE AND HEAT CAPACITY EXPERIMENTS Dissertation pr´ esent´ ee en vue de l’obtention du grade de ‘Docteur en Sciences Appliqu´ ees’ par Sorin Melinte Membres du jury: Jury: Prof. Vincent Bayot, promoteur Dr. Mladen Horvati´ c Prof. Jean-Paul Issi Prof. Jean-Pierre Michenaud Prof. Mansour Shayegan Prof. Piotr Sobieski, pr´ esident Septembre 2001 Închinare mamei mele, Ilinca în memoria lui Nistor, tat˘ al meu, surghiunit prin Siberia comunist˘ a lui Carmen ¸ si Eusebiu p˘ arintelui meu duhovnicesc, Nicodim Oration Il n‘y a en v´ erit´ e qu’une seule g´ ehenne pour ceux qui ont mal v´ ecu: l’anonymat, l’obscurit´ e et l’eﬀacement d´ eﬁnitif, qui du L´ eth´ e, la rivi` ere d’Oubli, les conduit au ﬂeuve sans sourires, puis les emporte au large, ` a l’oc´ ean sans limite et sans fond qui char- rie tout ce qui n’a servi ` a rien, tout ce qui n’a rien fait, tout ce qui est rest´ e sans gloire et inconnu. Plutarque V. Bayot C. Berthier J.-M. Beuken J.-P. Colinge S.M. Girvin E. Grivei M. Horvati´ c J.-P. Issi L.-P. L´ evy J.-P. Michenaud I. Pop M. Shayegan Abstract Of all the new physics generated by the highly perfect two-dimensional (2D) electron systems, the quantum Hall eﬀects (QHEs), integer and fractional, with their richness and complexity are perhaps the most active and excit- ing. The fractional QHE is the manifestation of a new state of electron matter - a peculiar, uniform density incompressible liquid phase, observed at low temperature (T) and in the presence of a strong magnetic ﬁeld (B) perpendicular to the 2D electron layers. Part of the intellectual fascination with the QHE phases stems from the challenge of ﬁnding new concepts to describe their properties. The energy levels available to an electron conﬁned to a 2D layer in a perpendicular magnetic ﬁeld are known as Landau levels. Each Landau level can accommodate many electrons; dividing the number of electrons per unit sample area by the degeneracy of a Landau level deﬁnes the ﬁlling factor ν. At a precise value of the magnetic ﬁeld (ν = 1), the 2D electrons condense into a ferromagnetic QHE ground state: the electronic system is an itinerant ferromagnet with a quantized Hall resistivity. The low-energy electron-spin dynamics of this QHE ferromagnet is extremely unusual be- cause of the subtle interplay between Coulomb interaction among electrons and Zeeman coupling of electronic spins to the external B. The elemen- tary excitations are spin-textured objects, called Skyrmions, which display complex equilibrium behavior reﬂecting liquid, crystalline and glassy phases. Qualitatively novel physics arises, moreover, because these topological exci- tations carry electrical charge and possess an eﬀective spin larger than that of a single electron. Thermodynamic measurements on 2D electron systems in the fractional QHE regime were long considered futile because the eﬀects were thought to be too small to observe. This thesis aims to revise this pessimistic outlook by reporting measurements of heat capacity and standard nuclear magnetic resonance down to very low T. Nuclear magnetic resonance (NMR) and calorimetric measurements in the mK temperature range are a tour de force v of experimental technique and conﬁrm the existence of QHE Skyrmions. In multiple-quantum-well GaAs/AlxGa1−xAs heterostructures, we found a dra- matic enhancement of the nuclear spin-lattice relaxation rate around ν = 1, that cannot be explained at present without express consideration of Skyrmi- ons being accommodated in the ferromagnetic QHE ground state. The elec- tron spin polarization peak (detected in NMR Knight shift measurements) and the observation of nuclear heat capacity of GaAs quantum wells are con- sequences of the strong, Skyrmion-mediated hyperﬁne coupling between the nuclear spin system and 2D electrons in the vicinity of ν = 1. The B- and T-dependencies of the nuclear-spin lattice relaxation rate around ν = 1 seem to be inﬂuenced by the inhomogeneity of the 2D electron system. The quan- titative analysis of the nuclear spin-lattice relaxation rate measurements is more diﬃcult as the interplay between the electron-electron interaction and disorder is not well understood. Compelling evidence for QHE Skyrmions comes from tilted magnetic ﬁeld studies. Introducing an in-plane magnetic ﬁeld causes a spin phase transition in the electronic system: Skyrmion-like excitations transform to single spin-ﬂip excitations above a critical Zeeman energy. We report on tilted magnetic ﬁeld heat capacity and nuclear magnetic resonance measure- ments that may elucidate the discrepancies in the literature concerning the range of Zeeman energies over which Skyrmions are the stable excitations of the ν = 1 ground state. We found a critical Zeeman energy of ∼0.04 (in units of Coulomb energy), consistent with Hartree-Fock calculations which take into account the ﬁnite thickness of the electron layers. Remarkably, the heat capacity (measured as a function of temperature near ν = 1) displays a sharp peak at very low T, suggestive of a Skyrmion solid-to-liquid phase transition. We performed quasi-adiabatic thermal ex- periments revealing that the mechanism responsible for the peak in heat capacity vs temperature is a dramatic enhancement of nuclear spin diﬀusion across the quantum well-barrier interface. Finally, QHE excitation gap measurements allow microscopic properties of Skyrmions (such as the number of encompassed reversed spins) to be established and explored. Our results reveal that the spin of a thermally activated Skyrmion–anti-Skyrmion pair at ν = 1 is ∼9, which corroborates with both Skyrmion spin measured in conventional single-layer 2D electron systems and theoretical predictions. vi Preface În sudoarea fet ¸ii tale ît ¸i vei mˆ anca pˆ ainea ta, pˆ an˘ a te vei întoarce în p˘ amˆ antul din care e¸ sti luat: c˘ aci p˘ amˆ ant e¸ sti ¸ si în p˘ amˆ ant te vei întoarce. Întˆ aia carte a lui Moise To promise at the beginning a nice story is most courtly and fashion- able. This thesis explores the physics of two-dimensional electron systems exhibiting the quantum Hall eﬀects (integer and fractional) - an extremely rich set of phenomena with truly fundamental implications. The quantum Hall eﬀect (QHE) is a large subject with undeﬁned frontiers. This book introduces the readers to basic experimental and theoretical aspects of the quantum Hall eﬀect. It cannot and do not survey all important and exciting topics in this ﬁeld. This thesis is intended to cover the subject of QHE Skyrmions. It does so by providing a close examination of two experiments of vital importance as, I believe, they prevented Skyrmions to fade away and furnished ample evidence for their intriguing behavior. It also attempts to show that the growth of high-quality, multiple two-dimensional electron systems is one of the main factors that have made possible the rise of novel low-temperature spectroscopy methods, which have tried, and still try, to oﬀer deep insights into the QHE physics. The data included in this thesis has been collected on two GaAs/AlxGa1−xAs multiple-quantum-well het- erostructures containing two-dimensional electron layers; the stages in the experimental procedure and data analysis were largely the same for both samples studied. Chapter 1 sets the scene. Here I present the samples and basic magneto- transport experiments. The treatment that I have given to the integral QHE is necessarily perfunctory; for neither the oscillating density of states nor the presence of disorder can be detached from the explanation of the vii phenomenon. I hope that I have not entirely omitted anything that is es- sential to its comprehension. Traditionally, the discussion of the fractional QHE follows after the discussion of the integer QHE. The perspectives on the fractional QHE are various. Many of them were inspired by the art- ful Laughlin’s argument. An overview of the fractional QHE is given from this point of view. The book is cursory in the treatment of few key topics: (1) QHE excitation gaps, (2) ﬁnite thickness corrections and Landau level mixing, (3) mixed-spin QHE ground states and spin-reversed quasiparticles, and (4) QHEs in tilted magnetic ﬁelds. I’m asking in Chapter 2 what is meant by QHE ferromagnets and what QHE Skyrmions are. Although much of the detail of the physics has been stripped away to get to the essentials, I tried hard to make the answer to these questions clear and the presentation responsible. This chapter repre- sents my attempt to understand the seminal ideas and ﬁrst steps in building up the theory of QHE ferromagnets. It does not try to replace the existing books and review articles on this subject, ﬁlled with worthy cogitations and wisdom. It rather tries to present a thorough account of the theoretical formalism necessary for understanding the following Experimental Work. Chapter 3 focuses on heat capacity experiments. uploads/Finance/ sorin-melinte-quantum-hall-effect-skyrmions-nuclear-magnetic-resonance-and-heat-capacity-experiments.pdf