Successive Orthorhombic Distortions in Kagome Metals by Molecular Orbital Formation

The kagome lattice, with its inherent frustration, hosts a plethora of exotic phenomena, including the emergence of 3q charge-density-wave order. The high rotational symmetry required to realize such an unconventional charge order is broken in many kagome materials by orthorhombic distortions at high temperature, the origin of which remains much less examined despite their ubiquity. In this study, synchrotron X-ray diffraction reveals a structural phase transition from a parent hexagonal structure to an orthorhombic ground state, mediated by a critical regime with diffuse scattering in the prototypical kagome metals RRu₃Si₂ (R = Nd, Pr). Structural analysis uncovers partially ordered bonds between kagome layers in the orthorhombic phases. Accordingly, a short-range correlated dimer model on the kagome layers reproduces the diffuse scattering, with the short-range order arising from competing structures induced by the geometrical frustration of the kagome lattice. The observations point to molecular orbital formation between Ru <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mn>4</mml:mn> <mml:msub><mml:mi>d</mml:mi> <mml:msup><mml:mi>z</mml:mi> <mml:mn>2</mml:mn></mml:msup> </mml:msub> </mml:mrow> <mml:annotation>$4d_{z^2}$</mml:annotation></mml:semantics> </mml:math> orbitals as the driving force behind the transition, consistent with ab initio calculations. A framework based on electronegativity and a tolerance factor is proposed to evaluate the stability of the hexagonal phase in various kagome metals, guiding the design of highly symmetric materials.