Symmetry, Orbital Order and Long Range Order in Quantum Materials from Their Crystal Structure Building Blocks

Correlated electron quantum materials’ wide array of controllable properties (magnetism, superconductivity, metal-insulator transitions), arise from an interplay of local degrees of freedom (charge, orbital and spin) and emerging long-range order. In materials where the open d-shell of transition metal ions forms the building blocks of the emergent states, the local ionic environment of the transition metal site plays a key role in determining the local orbital states, possible exchange interactions and resulting quantum states. In this work, I will focus on symmetry-informed computational tools and the insights they provide to understand magnetic and multiferroic quantum materials, including the role of trigonal symmetry breaking in van der Waals 2D magnets with composition MX₂ and MX₃ (M a transition metal, X={Cl,Br,I}) halides, the role of trimer orbitals and correlations in ferroelectric and spin-liquid candidates Kagome Halides (M₃X₈) - which were recently used in field-free Josephson diodes [2] - , and in multiferroic materials containing stereochemically active lone pairs on Bi²⁺ and Pb³⁺ ions used to break inversion symmetry. We find that this interplay is key to understanding the materials' magnetic properties, metallic or insulating behavior, and even to the materials' stability.<br/><br/>[1] 'Trigonal symmetry breaking and its electronic effects in the two-dimensional dihalides MX₂ and trihalides MX₃' , Alexandru B. Georgescu, Andrew J. Millis, James M. Rondinelli, PRB, <b>105</b>, 245153 (2022)<br/>[2] 'The field-free Josephson diode in a van der Waals heterostructure' , Heng Wu, Yaojia Wang, Yuanfeng Xu, Pranava K Sivakumar, Chris Pasco, Ulderico Filippozzi, Stuart S P Parkin, Yu-Jia Zeng, Tyrel McQueen, Mazhar N Ali, <i>Nature,</i><b> 604</b>, 653–656 (2022)