Spin-orbit excitons in CoO

Abstract

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

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“…Considering the local octahedral field and spin-orbit coupling, the ground state of Co 2+ can be projected onto a j eff = 1 2 [46,47] with the 3 2 spin-orbit levels well separated in energy [45]. α-CoV 2 O 6 differs from rocksalt CoO where a large exchange constant induces strong mixing between the j eff spin-orbit levels [48][49][50]. The local crystalline distortion further supports an Ising anisotropy in the spin orientation [51,52], evidenced by a gap in the magnetic dynamics and also the critical scattering discussed below.…”

hv 2-concept breaks the photon-count limit of RIXS instrumentation

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Van Vleck excitons in Ca2RuO4

“…Previously utilized to address the temperature dependence of the low energy magnetic fluctuations in PrTl 3 by Buyers et al 36 and more recently to understand the complex excitation spectra in CoO, 37 the spin-orbit exciton model employs the direct proportionality of the magnetic neutron cross section and the magnetic dynamic structural factor S(Q, ω) given by…”

“…Using these definitions, it can be shown 36,37 thatĤ can be divided into a sum of a single-ion (Ĥ 1 ) and an inter-ion (Ĥ 2 ) term given bŷ…”

“…As shown by Buyers et al 36 in the context of PrTl 3 , and further applied to CoO by Sarte et al, 37,42 the evaluation of the equation-of-motion begins by first defining an inter-level susceptibilityG…”