Emergent Phenomena in Spin Crossover Systems
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Emergent Phenomena in Spin Crossover Systems Jace Alex Cruddas B.Sc. (Hons) Candidate’s ORCID A thesis submitted for the degree of Doctor of Philosophy at The University of Queensland in Year School of Mathematics and Physics Abstract In general, a spin crossover (SCO) system is any complex, material or framework containing two thermodynamically accessible spin-states: one high-spin (HS) and one low-spin (LS). The transition between spin-states is addressable by temperature, pressure, light irradiation, electric and magnetic fields, and chemical environment. The transition itself can be first-order, exhibiting hysteresis, continuous or a crossover. Typically, accompanied by the ferroelastic ordering of spin-states. It can also be part of an incomplete or multi-step transition accompanied by the antiferroelastic ordering of spin-states. In general, any alterations to the structural characteristics of SCO systems can have an effect on their bulk properties and behaviours. Consequently, constructing structure-property relations has traditionally been an extremely challenging task, and one of both great theoretical and experimental interest. Understanding the mechanisms behind these bulk properties and behaviours could lead to the rational design of SCO systems with enhanced applications and the synthesis of novel properties and behaviours. In this thesis we show that a simple, elastic model of SCO systems hosts almost all experimentally reported SCO properties and behaviours. We demonstrate clear structure-property relations that explain these results, derive the mechanisms of multi-step transitions and explain why and how intermolecular interactions play a role. We also propose that a new exotic state of matter could exist in elastically frustrated SCO materials and frameworks. In this phase “spin-state ice”, so-called in analogy to water- and spin- ice, the metal ions lack any kind of long-range order. Instead, local clusters of metal ions follow a local ‘ice rule’. For example on the kagome lattice, each triangle is constrained to have two metal ions in one spin-state and one in the other. The excitations are deconfined quasi-particles, with a fractionalised spin midway between that of the HS and LS states. We show that distinctive signatures of spin-state ice can be measured by neutron scattering, electron paramagnetic resonance, and thermodynamic experiments. Unlike other examples of ices that have been theorized to exist, the unique nature of SCO systems allows for multiple spin-state ice phases to exist on the same lattice with unique properties that can be tuned with external parameters, like temperature and pressure. Declaration by author This thesis is composed of my original work, and contains no material previously published or written by another person except where due reference has been made in the text. I have clearly stated the contribution by others to jointly-authored works that I have included in my thesis. I have clearly stated the contribution of others to my thesis as a whole, including statistical assistance, survey design, data analysis, significant technical procedures, professional editorial advice, financial support and any other original research work used or reported in my thesis. The content of my thesis is the result of work I have carried out since the commencement of my higher degree by research candidature and does not include a substantial part of work that has been submitted to qualify for the award of any other degree or diploma in any university or other tertiary institution. I have clearly stated which parts of my thesis, if any, have been submitted to qualify for another award. I acknowledge that an electronic copy of my thesis must be lodged with the University Library and, subject to the policy and procedures of The University of Queensland, the thesis be made available for research and study in accordance with the Copyright Act 1968 unless a period of embargo has been approved by the Dean of the Graduate School. I acknowledge that copyright of all material contained in my thesis resides with the copyright holder(s) of that material. Where appropriate I have obtained copyright permission from the copyright holder to reproduce material in this thesis and have sought permission from co-authors for any jointly authored works included in the thesis. Publications included in this thesis • [1] Jace Cruddas, and Ben J. Powell, Structure–property relationships and the mechanisms of multistep transitions in spin crossover materials and frameworks, Inorg. Chem. Frount., Advance Article, 10.1039/D0QI00799D (2020). • [2] Jace Cruddas, and Ben J. Powell, Spin-State Ice in Elastically Frustrated Spin-Crossover Materials, J. Am. Chem. Soc. 141, 19790 (2019). Submitted manuscripts included in this thesis • [3] Jace Cruddas, and Ben J. Powell, Multiple Coulomb phases with temperature tunable ice rules in pyrochlore spin crossover materials, arXiv:2007.13983 (2020). Other publications during candidature • [176] Gian Ruzzi, Jace Cruddas, Rozz H. McKenzie and Ben J. Powell, Equivalence of elastic and Ising models for spin crossover materials, arXiv:2008.08738 (2020). Contributions by others to the thesis Elise P. Kenny and Ben J. Powell helped with the proof-reading of this thesis. Ross H. McKenzie provided the argument summarized in Fig. 3.3. All the others contributions made to this thesis are clearly documented on the page preceding the relevant chapter. Statement of parts of the thesis submitted to qualify for the award of another degree No works submitted towards another degree have been included in this thesis. Research involving human or animal subjects No animal or human subjects were involved in this research. Acknowledgments I would like to thank Elise Kenny for proof reading my thesis, and Ben Powell, Ross McKenzie, Xiuwen Zhou, Alejandro Mezio, Cameron Kepert, Suzanne Neville, Stephan Rachel, Nic Shannon, Yaroslav Kharkov, Grace Morgan, Timo Nieminen, Gian Ruzzi, Nadeem Muhammad, Nena Batenberg and Blake Peterson for their helpful conversations. In addition, I would like to extend my thanks to my family, my friends, the bartenders who served me, the bartenders who refused to serve me, and the current and former personnel of the School of Mathematics and Physics for their immeasurable support. Financial support This work was funded by the Australian Research Council through grant number DP200100305 and an Australian Government Research Training Program Scholarship. Keywords spin crossover, spin transitions, ice, spin ice, exotic states of matter, fractionalization, quasi-particles, structure-property relations, phase transitions, frustration Australian and New Zealand Standard Research Classifications (ANZSRC) 020499 Condensed Matter Physics not elsewhere classified, 60% 030206 Solid State Chemistry, 20% 030207 Transition Metal Chemistry, 20% Fields of Research (FoR) Classification 0204 Condensed Matter Physics, 60% 0302 Inorganic Chemistry, 40% Contents Abstract . ii Contents vii List of Figures ix List of Tables xii 1 Introduction 1 1.1 Frustration . 3 1.1.1 Importance of Frustration . 3 1.1.2 Landau theory and phase transitions . 4 1.1.3 Unfrustrated systems . 7 1.1.4 Frustrated Systems . 11 1.2 Microscopic Origin of Spin Crossover Systems . 19 1.2.1 A Brief Introduction to Coordination Chemistry . 19 1.2.2 Crystal field theory . 21 1.2.3 Molecular orbital theory . 23 1.2.4 Ligand Field Theory . 26 1.3 Spin crossover . 30 1.3.1 Importance of Spin Crossover . 30 1.3.2 Spin Crossover in the Solid state . 30 1.3.3 Models of Spin Crossover . 32 1.4 Thesis Outline . 37 2 Structure–property relationships 41 2.1 Introduction . 41 2.2 Model . 45 2.2.1 Elastic interactions in materials . 48 2.3 Methods . 49 2.4 Results and Discussion . 50 2.4.1 Nearest- and Next Nearest-Neighbour Interactions . 50 vii viii CONTENTS 2.4.2 Third Nearest-Neighbour Interactions . 53 2.4.3 Longer Range Interactions . 56 2.5 Conclusions . 59 2.6 Supplementary Information . 60 2.6.1 Expansion of the potential . 60 2.6.2 Additional results . 61 3 Spin-State Ice 73 3.1 Introduction . 73 3.2 Model . 78 3.3 Monte Carlo calculations . 81 3.4 Results and discussion . 81 3.5 Conclusions . 86 3.6 Supplementary Information . 88 3.6.1 Mapping between spin ice rules and spin-state ice rules . 88 3.6.2 Snapshots of Monte Carlo simulations . 88 4 Multiple Coulomb phases 95 4.1 Introduction . 95 4.2 Model . 96 4.3 Results and Discussion . 98 4.4 Conclusion . 102 4.5 Supplementary Information . 104 4.5.1 Monte Carlo simulations . 104 5 Conclusion 109 Bibliography 111 List of Figures 1.1 Illustration of spontaneous symmetry breaking transition. 3 1.2 Cartoon of frustration. 4 1.3 Cartoon phase diagram of H2O................................ 5 1.4 First-order transition. 6 1.5 Magnetic phases of the Ising model. 8 1.6 Ising Mean-field phase diagrams. 10 1.7 Illustration the 1h phase and the ice rules. 12 1.8 Examples of frustrated Lattices. 13 1.9 Ice rules for equivalent systems. 14 1.10 Illustration of pinch point singularities in the structure factor. 17 1.11 Propagation of defects in vertex ice. 18 1.12 Example of a coordination complex. 20 1.13 Molecular geometries of coordination complexes. 20 1.14 Illustration of crystal field splitting. 22 1.15 Illustration of bonding and antibonding orbitals. 24 1.16 Molecular orbitals for a ML6 complex. 25 1.17 Possible spin-states for a ML6 complex. 27 6 1.18 Tanabe-Sugano diagram for a ML6 complex with d . ................... 29 1.19 Vibronic levels for a spin crossover complex. 29 1.20 Examples of spin crossovers and transitions. 31 1.21 Thermodynamic properties of a non-interacting Ising-like model. 35 1.22 Thermodynamic properties of an Ising-like model. 35 1.23 Diagram of the elastic model. 36 2.1 Antiferroelastic spin-state orderings for the elastic model with non-zero k1, k2, k3 and k5.