The nature of the Verwey transition occurring at T V ≈ 125 K in magnetite (Fe 3 O 4 ) has been an outstanding problem over many decades. A complex low temperature electronic order was recently discovered and associated structural fluctuations persisting above T V are widely reported, but the origin of the underlying correlations and hence of the Verwey transition remains unclear. Here we show that local structural fluctuations in magnetite emerge below the Curie transition at T C ≈ 850 K, through X-ray pair distribution function analysis. Around 80% of the low temperature correlations emerge in proportion to magnetization below T C . This confirms that fluctuations in Fe-Fe bonding arising from magnetic order are the primary electronic instability and hence the origin of the Verwey transition. Such hidden instabilities may be important to other spin-polarised conductors and orbitally degenerate materials.

Co 2+ ions in an octahedral crystal field stabilize a j eff = 1/2 ground state with an orbital degree of freedom and have been recently put forward for realizing Kitaev interactions, a prediction we have tested by investigating spin dynamics in two cobalt honeycomb lattice compounds, Na 2 Co 2 TeO 6 and Na 3 Co 2 SbO 6 , using inelastic neutron scattering. We used linear spin wave theory to show that the magnetic spectra can be reproduced with a spin Hamiltonian including a dominant Kitaev nearest-neighbor interaction, weaker Heisenberg interactions up to the third neighbor, and bond-dependent off-diagonal exchange interactions. Beyond the Kitaev interaction that alone would induce a quantum spin liquid state, the presence of these additional couplings is responsible for the zigzag-type long-range magnetic ordering observed at low temperature in both compounds. These results provide evidence for the realization of Kitaev-type coupling in cobalt-based materials, despite hosting a weaker spin-orbit coupling than their 4d and 5d counterparts.

CoO has an odd number of electrons in its unit cell, and therefore is expected to be metallic. Yet, CoO is strongly insulating owing to significant electronic correlations, thus classifying it as a Mott insulator. We investigate the magnetic fluctuations in CoO using neutron spectroscopy. The strong and spatially far-reaching exchange constants reported in [Sarte et al. Phys. Rev. B 98 024415 (2018)], combined with the single-ion spin-orbit coupling of similar magnitude [Cowley et al. Phys. Rev. B 88, 205117 (2013)] results in significant mixing between j eff spin-orbit levels in the low temperature magnetically ordered phase. The high degree of entanglement, combined with the structural domains originating from the Jahn-Teller structural distortion at ∼ 300 K, make the magnetic excitation spectrum highly structured in both energy and momentum. We extend previous theoretical work on PrTl3 [Buyers et al. Phys. Rev. B 11, 266 (1975)] to construct a mean-field and multi-level spin exciton model employing the aforementioned spin exchange and spin-orbit coupling parameters for coupled Co 2+ ions on a rocksalt lattice. This parameterization, based on a tetragonally distorted type-II antiferromagnetic unit cell, captures both the sharp low energy excitations at the magnetic zone center, and the energy broadened peaks at the zone boundary. However, the model fails to describe the momentum dependence of the excitations at high energy transfers, where the neutron response decays faster with momentum than the Co 2+ form factor. We discuss such a failure in terms of a possible breakdown of localized spin-orbit excitons at high energy transfers. arXiv:1908.00459v2 [cond-mat.str-el] 2 Aug 2019Motivated by previous work on PrTl 3 27,58 , the theoretical portion of this paper begins by first writing down the equations-of-motion for the response function in terms of commutators involving the magnetic HamiltonianĤ. We