Possible absence of trimeron correlations above the Verwey temperature in Fe3O4

The origin of the metal to insulator transition in ${\mathrm{Fe}}₃{\mathrm{O}}₄$ remains a challenge due to the complexity of the system: it is a mixed valent, strongly correlated system where many interactions such as Jahn-Teller distortion, exchange, and phonons are very close in energetics. A recent interpretation of the Verwey transition as an ordering of a three-site magnetic polaron, the trimeron, has been put forward. Here we investigate the existence of the trimeron correlations in the high-temperature phase of ${\mathrm{Fe}}₃{\mathrm{O}}₄$ using high-resolution iron $2p3d$ resonant inelastic scattering magnetic linear dichroism. Guided by theoretical simulations, we reveal that the polarization dependence of the low-energy spin-orbital excitations is incompatible with tetragonal Jahn-Teller trimeron-type distortion. We conclude that the lowest-energy state of the high-temperature phase of ${\mathrm{Fe}}₃{\mathrm{O}}₄$ arises from an intricate interplay between trigonal crystal-field, exchange, and spin-orbit interactions.