Neutron scattering investigation of thed−dexcitations below the Mott gap of CoO

Abstract

Neutron scattering is used to investigate the single-ion spin and orbital excitations below the Mott-Hubbard gap in CoO. Three excitations are reported at 0.870±0.009 eV, 1.84±0.03, and 2.30±0.15 eV. These were parameterized within a weak crystal field scheme with an intra-orbital exchange of J(dd)=1.3 ± 0.2 eV and a crystal field splitting 10Dq=0.94 ± 0.10 eV. A reduced spinorbit coupling of λ=-0.016± 0.003 eV is derived from dilute samples of Mg0.97Co0.03O, measured to remove complications due to spin exchange and structural distortion parameters which split the cubic phase degeneracy of the orbital excitations complicating the inelastic spectrum. The 1.84 eV, while reported using resonant x-ray and optical techniques, was absent or weak for non resonant x-ray experiments and overlaps with the expected position of a 4 A2 level. This transition is absent in the dipolar approximation but expected to have a finite quadrupolar matrix element that can be observed with neutron scattering techniques at larger momentum transfers. Our results agree with a crystal field analysis (in terms of Racah parameters and Tanabe-Sugano diagrams) and with previous calculations performed using local-density band theory for Mott insulating transition metal oxides. The results also demonstrate the use of neutron scattering for measuring dipole forbidden transitions in transition metal oxide systems.

Ordered magnetism in the intrinsically decorated jeff=12α−CoV3O8

“…These Co 2+ moments are coupled via a 3D network of competing ferromagnetic and stronger antiferromagnetic superexchange interactions within the ab plane and along c, respectively, resulting in long range antiferromagnetic order of the Co 2+ moments at T N ∼19 K, despite a Weiss temperature near 0 K. A comparison of our results to the random 3D Ising magnets and other compounds where spin-orbit coupling is present indicate that both the presence of an orbital degree of freedom, in combination with strong crystal field effects and wellseparated j eff manifolds may be key in making the dynamics robust against disorder. As outlined in the main text, a comparison between the current study and previous studies on other Co 2+ -based magnets 60,75,81,91,94,166,185 suggests that the low temperature magnetism of α-CoV 3 O 8 may be solely attributed to the ground state doublet spin-orbit manifold, and thus can be simplified to a j = 1 2 model. To utilize such a model in the current study, the Landé g-factor g J was required to be projected onto individual j ≡ j eff manifolds.…”

“…A key difference between MnF 2 and both α-CoV 3 O 8 and FeF 2 is the presence of strong crystal field effects and spin-orbit coupling in the latter two compounds 133,175 . It is also worth noting that unlike the case of pure CoO 81,91,94,[181][182][183][184] where the large and far reaching exchange constants result in a significant and ultimately problematic entanglement of spin-orbit levels 94 , in the case of α-CoV 3 O 8 , the exchange constants are weak and the Weiss temperature is near 0 K. Both observations suggest that the presence of both strong crystal field effects and spin-orbit coupling with well-separated j eff manifolds, as is the case for α-CoV 3 O 8 , may be central to making the dynamics robust against strong disorder.…”

“…Operator Projection Factor α Before proceeding with the projection of the Landé gfactor onto the j eff = 1 2 ground state spin-orbit manifold, it is important to note that such a doublet manifold is a consequence of an approach commonly used 60,75,81,91,94 to address the orbital triplet ground state in Co 2+ . Such an approach first defines an effective total angular momentumĵ eff =l +Ŝ, wherel is a fictitious orbital angular momentum operator, with eigenvalue l =1 to reflect an triplet orbital degeneracy 104 .…”

“…The determination of the projection factor α begins by first defining the crystal field HamiltonianĤ CEF describing the effects of the crystalline electric field on the free ion states of the d 7 Co 2+ resulting from the symmetry imposed by the crystal lattice 75,81,91,186 . Assuming both negligible distortions away from purely octahedral coordination and negligible admixture between the 4 F ground and first excited 4 P free ion states, a weak crystal field approach can be employed 187 Utilizing the diagonalized crystal field Hamiltonian above, a transformation matrix C can be defined as…”

Soft striped magnetic fluctuations competing with superconductivity inFe1+xTe

“…[78] We have searched for high energy orbital transitions without success and this is discussed in the supplementary information (see also Ref. [79][80][81][82][83].…”