Orbital Dimer Model for Spin-Glass State in Y₂Mo₂O₇

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The formation of a spin glass usually requires both structural disorder and frustrated magnetic interactions. Consequently, the origin of spin-glass behaviour in Y₂Mo₂O₇ - in which magnetic Mo⁴⁺ ions occupy a frustrated pyrochlore lattice with minimal compositional disorder - has been a longstanding question. Here, we use neutron and X-ray pair-distribution function (PDF) analysis to develop a disorder model that resolves apparent incompatibilities between previously-reported PDF, EXAFS and NMR studies and provides a new and physical mechanism for spin-glass formation. We show that Mo⁴⁺ ions displace according to a local "2-in/2-out" rule on each Mo₄ tetrahedron, driven by orbital dimerisation of Jahn-Teller active Mo⁴⁺ ions. Long-range orbital order is prevented by the macroscopic degeneracy of dimer coverings permitted by the pyrochlore lattice. Cooperative O²⁻ displacements yield a distribution of Mo-O-Mo angles, which in turn introduces disorder into magnetic interactions. Our study demonstrates experimentally how frustration of atomic displacements can assume the role of compositional disorder in driving a spin-glass transition.