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Spin-Orbit Excitons in CoO

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 Added by Chris Stock
 Publication date 2019
  fields Physics
and research's language is English




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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 $sim$ 300 K, make the magnetic excitation spectrum highly structured in both energy and momentum. We extend previous theoretical work on PrTl$_{3}$ [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.



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Motivated by the presence of an unquenched orbital angular momentum in CoO, a team at Chalk River, including a recently hired research officer Roger Cowley, performed the first inelastic neutron scattering experiments on the classic Mott insulator [Sakurai $textit{et al.}$ 1968 Phys. Rev. $mathbf{167}$ 510]. Despite identifying magnon modes at the zone boundary, the team was unable to parameterise the low energy magnetic excitation spectrum below $Trm{_{N}}$ using conventional pseudo-bosonic approaches. It would not be for another 40 years that Roger, now at Oxford and motivated by the discovery of the high-$T_{c}$ cuprate superconductors [Bednorz & Muller 1986 Z. Phys. B $mathbf{64}$ 189], would make another attempt at the parameterisation of the magnetic excitation spectrum that had previously alluded him. Upon his return to CoO, Roger found a system embroiled in controversy, with some of its most fundamental parameters still remaining undetermined. Faced with such a formidable task, Roger performed a series of inelastic neutron scattering experiments in the early 2010s on both CoO and a magnetically dilute structural analogue MgO. These experiments would prove instrumental in the determination of both single-ion [Cowley $textit{et al.}$ 2013 Phys. Rev. B $mathbf{88}$ 205117] and cooperative magnetic parameters [Sarte $textit{et al.}$ 2018 Phys. Rev. B $mathbf{98}$ 024415] for CoO. Both these sets of parameters would eventually be used in a spin-orbit exciton model [Sarte $textit{et al.}$ 2019 Phys. Rev. B $mathbf{100}$ 075143], developed by his longtime friend and collaborator Bill Buyers, to successfully parameterise the complex spectrum that both measured at Chalk River almost 50 years prior. The story of CoO is of one that has come full circle, one filled with both spectacular failures and intermittent, yet profound, little victories.
137 - Devendra Kumar 2016
We report the magnetization study of the compound La$_{0.75}$Ba$_{0.25}$CoO$_3$ where Ba$^{2+}$ doping is just above the critical limit for percolation of ferromagnetic clusters. The field cooled (FC) and zero field cooled (ZFC) magnetization exhibit a thermomagnetic irreversibility and the ac susceptibility show a frequency dependent peak at the ferromagnetic ordering temperature (T$_C$$approx$203~K) of the clusters. These features indicate about the presence of a non-equilibrium state below T$_C$. In the non-equilibrium state, the dynamic scaling of the imaginary part of ac susceptibility and the static scaling of the nonlinear susceptibility clearly establish a spin-glass like cooperative freezing of ferromagnetic clusters at 200.9(2)~K. The existence of spin-glass like freezing of ferromagnetic clusters is further substantiated by the ZFC aging and memory experiments. We also observe certain dynamical features which are not present in a typical spin-glass, such as, initial magnetization after ZFC aging first increases and then decreases with the wait time and an imperfect recovery of relaxation in negative temperature cycling experiments. This imperfect recovery transforms to perfect recovery on concurrent field cycling. Our analysis suggests that these additional dynamical features have their origin in inter-cluster exchange interaction and cluster size distribution. The inter-cluster exchange interaction above the magnetic percolation gives a superferromagnetic state in some granular thin films but our results show the absence of typical superferromagnetic like state in La$_{0.75}$Ba$_{0.25}$CoO$_3$.
Magnetism of a misfit layered cobaltite [Ca$_2$Co$_{4/3}$Cu$_{2/3}$O$_4$]$_x^{rm RS}$[CoO$_2$] ($x sim$ 0.62, RS denotes a rocksalt-type block) was investigated by a positive muon spin rotation and relaxation ($mu^+$SR) experiment. A transition to an incommensurate ({sf IC}) spin density wave ({sf SDW}) state was found below 180 K (= $T_{rm C}^{rm on}$); and a clear oscillation due to a static internal magnetic field was observed below 140 K (= $T_{rm C}$). Furthermore, an anisotropic behavior of the zero-field $mu^+$SR experiment indicated that the {sf IC-SDW} propagates in the $a$-$b$ plane, with oscillating moments directed along the c axis. These results were quite similar to those for the related compound [Ca$_2$CoO$_3$]$_{0.62}^{rm RS}$[CoO$_2$], {sl i.e.}, Ca$_3$Co$_4$O$_9$. Since the {sf IC-SDW} field in [Ca$_2$Co$_{4/3}$Cu$_{2/3}$O$_4$]$_{0.62}^{rm RS}$[CoO$_2$] was approximately same to those in pure and doped [Ca$_2$CoO$_3$]$_{0.62}^{rm RS}$[CoO$_2$], it was concluded that the {sf IC-SDW} exist in the [CoO$_2$] planes.
In systems where electrons form both dispersive bands and small local spins, we show that changes of the spin configuration can tune the bands through a Lifshitz transition, resulting in a continuous metal-insulator transition associated with a progressive change of the Fermi surface topology. In contrast to a Mott-Hubbard and Slater pictures, this spin-driven Lifshitz transition appears in systems with small electron-electron correlation and large hybridization. We show that this situation is realized in 5$d$ distorted perovskites with an half-filled $t_{2g}$ bands such as NaOsO$_3$, where the strong $p-d$ hybridization reduces the local moment, and spin-orbit coupling causes a large renormalization of the electronic mobility. This weakens the role of electronic correlations and drives the system towards an itinerant magnetic regime which enables spin-fluctuations.
By means of muon spin spectroscopy, we have found that K$_{0.49}$CoO$_2$ crystals undergo successive magnetic transitions from a high-T paramagnetic state to a magnetic ordered state below 60 K and then to a second ordered state below 16 K, even though K_{0.49}CoO_2 is metallic at least down to 4 K. An isotropic magnetic behavior and wide internal-field distributions suggest the formation of a commensurate helical spin density wave (SDW) state below 16 K, while a linear SDW state is likely to exist above 16 K. It was also found that K_{0.49}CoO_2 exhibits a further transition at 150 K presumably due to a change in the spin state of the Co ions. Since the T dependence of the internal-field below 60 K was similar to that for Na_{0.5}CoO_2, this suggests that magnetic order is more strongly affected by the Co valence than by the interlayer distance/interaction and/or the charge-ordering.
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