University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange Doctoral Dissertations Graduate School 8-2019 Study of spin and charge dynamics in one-dimensional cuprates using resonant inelastic x-ray scattering Umesh Kumar Kumar University of Tennessee, [email protected] Follow this and additional works at: https://trace.tennessee.edu/utk_graddiss Recommended Citation Kumar, Umesh Kumar, "Study of spin and charge dynamics in one-dimensional cuprates using resonant inelastic x-ray scattering. " PhD diss., University of Tennessee, 2019. https://trace.tennessee.edu/utk_graddiss/5961 This Dissertation is brought to you for free and open access by the Graduate School at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. To the Graduate Council: I am submitting herewith a dissertation written by Umesh Kumar Kumar entitled "Study of spin and charge dynamics in one-dimensional cuprates using resonant inelastic x-ray scattering." I have examined the final electronic copy of this dissertation for form and content and recommend that it be accepted in partial fulfillment of the equirr ements for the degree of Doctor of Philosophy, with a major in Physics. Steven Johnston Prof., Major Professor We have read this dissertation and recommend its acceptance: Elbio Dagotto Prof., Norman Mannella Prof., David Mandrus Accepted for the Council: Dixie L. Thompson Vice Provost and Dean of the Graduate School (Original signatures are on file with official studentecor r ds.) Study of spin and charge dynamics in one-dimensional cuprates using resonant inelastic x-ray scattering A Dissertation Presented for the Doctor of Philosophy Degree The University of Tennessee, Knoxville Umesh Kumar August 2019 c by Umesh Kumar, 2019 All Rights Reserved. ii Dedicated to my late grandmother - Keshrani Rajput. iii Acknowledgements I would first like to express my deepest gratitude to Prof. Steven Johnston for his constant support and guidance over the past five years. He has been a wonderful and supportive supervisor. Additionally, he provided me opportunities to attend several conference and schools, where I could hone my skills and develop networks. I would also like to thank the members of my committee, Dr. Elbio Dagotto, Dr. Norman Mannella, and Dr. David Mandrus, for their time and helpful suggestions. A major part of this thesis is motivated by resonant inelastic x-ray scattering (RIXS) experiment conducted at ADDRESS Beamline at Paul Scherrer Institut, Villigen, Switzerland. I would like to express my gratitude to Dr. Justine Schlappa and Dr. Thorsten Schmidt for providing us with the high-quality RIXS data. I would also like to express a special thanks to Dr. Alberto Nocera. His experience, innovative ideas, and inputs played an important role in several projects presented in this dissertation. I want to thank my labmates Dr. Shaozhi Li, Dr. Ken Nakatsukasa, Dr. Yan Wang, and Phillip Dee. Additionally, I would like to thank my colleagues Nitin Kaushal, Dr. Niravkumar Patel, Dr. Guangkun Liu, and Dr. Anamitra Mukherjee from Prof. Dagotto's group. I am grateful to all of them for the stimulating discussions on Physics and Philosophy. I have met a number of wonderful people who enriched my stay in Knoxville. I would like to thank Manasa Rath for her constant encouragement during graduate school. I would also like to acknowledge my friend Swarnav, for planning many exciting trips. A special shout out my friends Hasitha, Jeethu, Yadu, Rakesh, Gaurav iv and Vikram for enriching my stay here in the Knoxville. To my friends in cricket and tennis: I am thankful for all the efforts you put in to make all the experiences memorable and enjoyable. Finally, I would like to express eternal thanks to my family, in particular, my brother, Pravesh, who has always been supportive of me pursuing my ambitions. I hope that I do justice to their tremendous belief in me. v Abstract One-dimensional (1D) antiferromagnetic chains and ladders realized in strongly correlated materials have attracted significant interest as a platform for studying quasiparticle fractionalization, quantum criticality, and other emergent phenomena. In this thesis, we examine spin and charge dynamics of 1D antiferromagnets revealed by resonant inelastic x-ray scattering (RIXS) using numerical techniques, including exact diagonalization and density matrix renormalization group. One of the major findings of this thesis is the first direct observation of multi-spinon excitations at the oxygen K-edge of Sr2CuO3, a prototype 1D cuprate, establishing RIXS as a complementary probe to inelastic neutron scattering (INS) in search of quantum spin liquids. In another study on 1D doped antiferromagnets, the RIXS spectra are shown to be rich, containing distinct two- and four-spinon excitations, dispersive antiholon excitations, and combinations thereof, further establishing that RIXS can serve as a probe of spin-charge separation in these materials. Finally, a systematic theoretical investigation of the Cu L-edge RIXS spectra of undoped and doped cuprate two-leg spin-ladders in both the non-spin-conserving and spin-conserving channels is presented. The spectra host many exotic excitations, in particular, singlet two- triplon bound state excitations. Furthermore, direct signatures of charge quasiparticle excitations are revealed by RIXS in the doped ladders. This dissertation helps establish RIXS as an important tool for revealing the signatures of spin and charge fractionalization, and other collective excitations in strongly correlated materials vi Table of Contents 1 Introduction1 1.1 Overview of one-dimensional cuprates..................5 1.2 Ladder cuprates..............................8 1.3 Scope and Organization......................... 10 2 Methods 12 2.1 Light-Matter Interaction and the Kramers-Heisenberg Formalism... 15 2.2 Numerical methods............................ 20 2.2.1 Exact Diagonalization...................... 20 2.2.2 Dynamical Matrix Renormalization Group........... 22 3 Observation of two-spinon and four-spinon excitations in corner- shared Sr2CuO3 using oxygen K-edge resonant inelastic x-ray scat- tering study 27 3.1 Introduction................................ 27 3.2 Methods................................. 31 3.2.1 Experiment............................ 31 3.2.2 Cluster Calculations....................... 31 3.3 Results................................... 32 3.3.1 Experimental results....................... 32 3.3.2 Theoretical results........................ 38 3.4 Discussion................................. 40 vii 3.5 Conclusions................................ 45 4 Multi-spinon and antiholon excitations probed by resonant inelastic x-ray scattering on doped one-dimensional antiferromagnets 46 4.1 Introduction................................ 46 4.2 Model and methods............................ 50 4.3 Results................................... 52 4.3.1 Undoped RIXS spectra...................... 52 4.3.2 Doped RIXS spectra....................... 53 4.4 Discussion................................. 63 4.5 Conclusions................................ 64 5 Systematic study of spin and charge dynamics in two-leg spin ladders probed by resonant inelastic x-ray scattering 65 5.1 Introduction................................ 65 5.2 Methods.................................. 68 5.2.1 Model Hamiltonian........................ 68 5.2.2 RIXS Intensity.......................... 69 5.3 Results and Discussion.......................... 73 5.3.1 Results for the non-spin-conserving channel.......... 76 5.3.2 Results for the spin-conserving channel............. 81 5.3.3 Results for the dynamical correlation functions......... 89 5.3.4 Revisiting Sr14Cu24O41 RIXS data................ 94 5.4 Conclusions................................ 95 6 Summary and Outlook 98 Bibliography 101 Appendices 129 viii A Dipole Matrix Elements for L-edge 130 B Ultrashort Core-hole Lifetime expansion 132 Vita 137 ix List of Tables 5.1 Different values of the exchange parameters (in units of meV) reported 1 in the literature for various spin- 2 ladder systems........... 69 min 5.2 The momentum q and mthres values that define the lower boundaries of the single- and multiparticle excitations that occur in the Majorana 1 fermion description of the spin- 2 ladders................. 76 A.1 Dipole matrix elements for linearly polarized photon transitioning a hole (3d ! 2p) in L-edge RIXS...................... 131 x List of Figures 1.1 Paramagnon and collective mode dispersions in the RIXS spectra...3 1.2 Crystal structure of Sr2CuO3.......................6 1.3 RIXS spectra at oxygen K-edge and Cu L3-edge of Sr2CuO3......7 1.4 Crystal structure of (Sr,Ca)14Cu24O41..................9 2.1 A sketch of scattering process in the RIXS................ 13 2.2 A schematic of the experimental geometry................ 14 2.3 A sketch of the algorithm for computing the real space Kramers- Heisenberg formula using the DMRG method.............. 23 3.1 Summary of the experimental data at the oxygen K-edge....... 33 3.2 Comparison between the experimental and calculated RIXS spectra at the oxygen K-edge............................ 37 3.3 RIXS spectra plotted over the full first Brillouin zone.......... 39 3.4 RIXS spectra dependence on the incidence energy............ 40 3.5 An illustration of various spin excitation processes through creation of spin-flips.................................