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Jean-Francois Mercure Phd Thesis THE DE HAAS VAN ALPHEN EFFECT NEAR A QUANTUM CRITICAL END POINT IN SR3RU2O7 Jean-François Mercure A Thesis Submitted for the Degree of PhD at the University of St. Andrews 2008 Full metadata for this item is available in the St Andrews Digital Research Repository at: https://research-repository.st-andrews.ac.uk/ Please use this identifier to cite or link to this item: http://hdl.handle.net/10023/683 This item is protected by original copyright This item is licensed under a Creative Commons License The de Haas van Alphen effect near a quantum critical end point in Sr3Ru2O7 A thesis presented by Jean-Fran¸cois Mercure to the University of St Andrews in application for the degree of Doctor of Philosophy September 2008 Declarations I, Jean-Fran¸cois Mercure, hereby certify that this thesis, which is approximately 42000 words in length, has been written by me, that it is the record of work carried out by me, and that it has not been submitted in any previous application for a higher degree. date signature of candidate I was admitted as a research student in October 2004 and as a candidate for the degree of Doctor of Philosophy in October 2004; the higher study for which this is a record was carried out in the University of St Andrews between 2004 and 2008. date signature of candidate I hereby certify that the candidate has fulfilled the conditions of the Resolution and Regulations appropriate for the degree of Doctor of Philosophy in the University of St Andrews and that the candidate is qualified to submit this thesis in application for that degree. date signature of supervisor In submitting this thesis to the University of St Andrews we understand that we are giving permission for it to be made available for use in accordance with the regulations of the University Library for the time being in force, subject to any copyright vested in the work not being affected thereby. We also understand that the title and abstract will be published, and that a copy of the work may be made and supplied to any bona fide library or research worker, that my thesis will be electronically accessible for personal or research use, and that the library has the right to migrate my thesis into new electronic forms as required to insure continued access to the thesis. We have obtained any third-party copyright permissions that may be required in order to allow such access and migration. The following is an agreed request by candidate and supervisor regarding the elec- tronic publication of this thesis: Access to Printed copy and electronic publication of thesis through the University of St Andrews. date signature of candidate date signature of supervisor i Abstract Highly correlated electron materials are systems in which many new states of matter can emerge. A particular situation which favours the formation of exotic phases of the electron liquid in complex materials is that where a quantum critical point (QCP) is present the phase diagram. Neighbouring regions in parameter space reveal unusual physical properties, described as non-Fermi liquid behaviour. One of the important problems in quantum criticality is to find out how the Fermi surface (FS) of a material evolves near a QCP. The traditional method for studying the FS of materials is the de Haas van Alphen effect (dHvA). A quantum critical end point (QCEP) has been reported in the highly correlated metal Sr3Ru2O7, which is tuned using a magnetic field high enough to perform the dHvA experiment. It moreover features a new emergent phase in the vicinity of the QCEP, a nematic type of electron ordering. The subject of this thesis is the study of the FS of Sr3Ru2O7 using the dHvA effect. Three aspects were explored. The first was the determination of the FS at fields both above and below that where the QCEP arises. The second was the search for quantum oscillations inside the nematic phase. The third was a reinvestigation of the behaviour of the quasiparticle effective masses near the FS. In collaboration with angle resolved photoemission spectroscopy experimental- ists, a complete robust model for the FS of Sr3Ru2O7 at zero fields was determined. Moreover, the new measurements of the quasiparticle masses revealed that no mass enhancements exist anywhere around the QCEP, in contradiction with previous spe- cific heat data and measurements of the A coefficient of the power law of the resistivity. Finally, we report dHvA oscillations inside the nematic phase, and the temperature dependence of their amplitude suggests strongly that the carriers consist of Landau quasiparticles. ii Acknowledgements I would like first to thank my supervisor, Prof. Andrew Mackenzie, for guiding me through this undertaking. He let me carry out this project in my own way, putting up with my stubbornness and pushed me to lay my work onto firm scientific grounds. He enabled me to travel throughout this Ph. D. , and to perform experiments in one of the most famous and historic laboratories, the Cavendish Laboratory in Cambridge. I also wish to thank the ones who taught me the secrets of cryogenics and the dHvA experiments themselves, Dr. Rodolfo Borzi, Dr. Robin Perry and Dr. Philipp Gegenwart. I thank Dr. Chris Hooley for all the encouragement he gave me, and for all the theoretical insights over sometimes very basic physics. I am grateful to Dr. Santiago Grigera and Dr. Andrew Green for helpful discussions and the stimula- tion interactions between theorists and experimentalists, and making life within our research group very dynamic. I thank my everyday partner in the lab, Andreas Rost for putting up with my temperament and at times take charge of most of the lab with me. Thanks to Andrew Berridge for putting theory at my level of understanding. I am grateful to Reg Gavine, without whom cryogenics would not be possible. Thanks to Andreas, Andrew, Jason, Naoki, Alexandra, Jan, Demian, Patrick and Anne-Christine for making life in the lab so much fun. I wish to thank Dr. Michael Sutherland for providing me the opportunity to work in the Cavendish Laboratory, guiding me through my experiments with the Big Fridge. I am grateful to him for allowing me to spend so much time in Cambridge. I thank particularly Swee Goh and Eoin O’Farrell for all the time that they spent with me on my experiments. I thank Mike, Swee, Eoin and Dr. Sibel Ozcan¨ for making my stay there very enjoyable. Finally, I would like to thank my partner in life Dr. V´eronique Pag´e, for all the encouragement and for supporting me in everything I do. This new life in Scotland and England would not have been the same without her at my side. I also thank our friends that were here or still are, James, Joachim, Elisabeth, Dimali and Paul. The Overseas Research Students Awards Scheme (ORS), le Fonds Qu´eb´ecois de la Recherche sur la Nature et les Technologies (FQRNT), the Engineering and Physical Sciences Research Council (EPSRC) the University of St Andrews have funded my research and stay in St Andrews. iii Contents Introduction 1 1 Scientific Background 4 1.1 Stronglycorrelatedmetals . 4 1.1.1 TheFermiLiquid ........................ 4 1.1.2 Non-Fermi liquids and quantum criticality . .. 6 1.2 The strontium ruthenate oxide Sr3Ru2O7 ................ 8 1.2.1 Generalphysicalproperties . 8 1.2.2 Crystallinestructure . 10 1.2.3 Electronicstructure . 12 1.2.4 Metamagnetism and quantum criticality . 15 1.2.5 Disorder sensitive phase formation . 18 1.3 ThedeHaasvanAlphenEffect . 19 1.3.1 Oscillationsatzerotemperature . 20 1.3.2 Oscillationsatfinitetemperature . 24 1.3.3 The role of disorder and impurities . 26 1.3.4 2D systems and the angular dependence of dHvA . 27 1.3.5 Spinsplitting ........................... 33 1.3.6 First dHvA measurements in Sr3Ru2O7 ............. 34 2 Experimental methods and analysis procedures 36 2.1 AC susceptibility in a 3He/4Hedilutionrefrigerator . 37 2.1.1 Basics of AC susceptibility with equations . .. 37 2.1.2 Oscillatory signal in the field modulation method . ... 38 2.1.3 ThedHvAapparatus ...................... 41 2.2 DeHaasvanAlphendataanalysis . 45 2.2.1 Analytical expression for the oscillations . .... 45 2.2.2 Fourier transforms and windowing . 48 2.2.3 Appropriate normalisation of Fourier transforms . ..... 50 2.2.4 Massanalysis ........................... 52 2.2.5 Fourier transforms using large field windows . .. 53 2.2.6 Theenvelopeextractionmethod . 55 2.2.7 TheDingleanalysis ....................... 57 2.3 AC susceptibility in an adiabatic demagnetisation refrigerator . 58 2.3.1 The adiabatic demagnetisation refrigerator . .... 58 2.3.2 AC susceptibility apparatus for large crystals . .... 60 2.3.3 Thermal equilibrium tests and calibration . .. 62 iv Contents v 2.4 Systematic procedure for the search for high purity samples ..... 65 2.4.1 PowderX-raydiffraction . 67 2.4.2 Residualresistivity . 68 2.4.3 Zero field AC susceptibility . 70 2.4.4 The de Haas van Alphen effect as a measure of disorder . 72 2.4.5 Magnetisation .......................... 73 2.4.6 Complete quantitative results of the search . .. 77 2.5 Laueorientationofthesamples . 81 2.6 Avoiding eddy current heating in dHvA experiments . .... 83 3 The de Haas van Alphen experiment on Sr3Ru2O7 86 3.1 Determination of experimental parameters . .... 87 3.1.1 Comparison of detection harmonics . 88 3.1.2 Modulation field dependence of dHvA . 89 3.1.3 Analysis of eddy current heating . 91 3.2 dHvAoscillationsandspectra . 93 3.2.1 dHvAoscillations . .. .. 93 3.2.2 dHvA spectra and quasiparticle masses at c-axis ....... 94 3.2.3 Dingle analysis of c-axisdHvA ................. 100 3.3 AngulardependenceofdHvA . 101 3.3.1 Mapping of the metamagnetic transition . 102 3.3.2 Angular dependence of dHvA spectra .
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