Electronic structure of charge-orderedFe3O4from calculated optical, magneto-optical Kerr effect, and OK-edge x-ray absorption spectra

Abstract

The electronic structure of the low-temperature (LT) monoclinic magnetite, Fe 3 O 4 , is investigated using the local spin density approximation (LSDA) and the LSDA+U method. The selfconsistent charge ordered LSDA+U solution has a pronounced [001] charge density wave character.In addition, a minor [00 1 2 ] modulation in the phase of the charge order (CO) also occurs. While the existence of CO is evidenced by the large difference between the occupancies of the minority spin t 2g states of "2+" and "3+" Fe B cations, the total 3d charge disproportion is small, in accord with the valence-bond-sum analysis of structural data. Weak Fe orbital moments of ∼0.07µ B are obtained from relativistic calculations for the CO phase which is in good agreement with recent x-ray magnetic circular dichroism measurements. Optical, magneto-optical Kerr effect, and O Kedge x-ray absorption spectra calculated for the charge ordered LSDA+U solution are compared to corresponding LSDA spectra and to available experimental data. The reasonably good agreement between the theoretical and experimental spectra supports the relevance of the CO solution obtained for the monoclinic LT phase. The results of calculations of effective exchange coupling constants between Fe spin magnetic moments are also presented.

Spin and orbital moments inFe3O4

“…Furthermore, it is clear that our results are consistent with the values obtained using XMCD by Goering et al, 17 and with recent theoretical predictions. 6,7 In conclusion, our experiments have found that there is a spin moment of approximately 4 B for all temperatures and for the three principal crystallographic directions. Consequentially, the orbital moment, determined by comparison with bulk magnetometry, is therefore nearly fully quenched, in agreement with Goering et al 17,19 We do not observe the significant orbital moments reported by Huang et al 15 or Li et al 20 No evidence of any anomalies in the spin or orbital moments at the Verwey transition is observed.…”

“…1,2 This is accompanied by a transition to a low symmetry structure, the precise nature of which is still being discussed. [3][4][5] Above this transition, band-structure calculations predict that Fe 3 O 4 should be a half metal, with conduction only associated with the minority spin electrons 6,7 and thus possess 100% spin polarization. Experimentally somewhat lower values have been reported ͓for example, 40% ͑Ref.…”

“…Although the O 2p states play an important role in the electronic structure, with evidence of their orbital ordering observed below T V , 13 the magnetic moment associated with these states is generally calculated to be less than 0.1 B . 6 There have been two recent reports of spin-polarized Compton scattering studies of magnetite, one of which addressed the issue of the spin and orbital moments. 20 The technique provides a measurement of the spin moment only and it is unambiguously sensitive to the bulk rather than the surface.…”

Complex-Orbital Order in Fe3O4and Mechanism of the Verwey Transition

“…The electronic state in the low-temperature phase has been investigated using LDA+U calculations [16][17][18][19] based on the monoclinic lattice structure shown by Wright et al 4) From the LDA+U calculations, a state with simultaneous charge and antiferro-orbital ordering is obtained. In the state, the B2a, B2b, and B3 sites are vacant, and the xy orbitals are occupied at the B4 sites.…”

“…15) Based on the three-band model, Seo et al have proposed a mechanism of the Verwey transition with a bond dimerisation caused by the Peierls instability, where charge ordering is irrelevant to the transition. 15) Recently, the electronic state in the lowtemperature phase has been investigated using local density approximation+Hubbard U (LDA+U) calculations [16][17][18][19] based on the monoclinic lattice structure shown by Wright et al 4) In the LDA+U calculations, a state with simultaneous charge and antiferro-orbital ordering is obtained.…”