Anomalous Hall Effect in $t_{2g}$ Orbital Kagome Lattice due to
  Non-collinearity:Significance of Orbital Aharonov-Bohm Effect

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Abstract

A new mechanism of spin structure-driven anomalous Hall effect (AHE) in tilted ferromagnetic metals is proposed by taking account of the d-orbital degree of freedom. We find that a conduction electron acquires a Berry phase due to the complex d-orbital wavefunction, in the presence of non-collinear spin structure and the spin orbit interaction. The AHE driven by this orbital-derived Berry phase is much larger than the AHE induced by spin chirality, and it naturally explains the salient features of spin structure-driven AHE in pyrochlore Nd$_2$Mo$_2$O$_7$. Since the proposed AHE can occur even for coplanar spin orders ($M_z=0$), it is expected to emerge in other interesting geometrically frustrated systems.

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Berry Phase Theory of Anomalous Hall Effect: Application to Colossal Magnetoresistance Manganites

A. Millis, Yong Baek Kim, P Majumdar … (1999)

We show that the Anomalous Hall Effect (AHE) observed in Colossal Magnetoresistance Manganites is a manifestation of Berry phase effects caused by carrier hopping in a non-trivial spin background. We determine the magnitude and temperature dependence of the Berry phase contribution to the AHE, finding that it increases rapidly in magnitude as the temperature is raised from zero through the magnetic transition temperature T_c, peaks at a temperature $T_{max} > T_c$ and decays as a power of T, in agreement with experimental data. We suggest that our theory may be relevant to the anomalous hall effect in conventional ferromagnets as well.

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Orbital analogue of the quantum anomalous Hall effect in p-band systems.

Congjun Wu (2008)

We investigate the topological insulating states of the p-band systems in optical lattices induced by the on site orbital angular momentum polarization, which exhibit gapless edge modes in the absence of Landau levels. This effect arises from the energy-level splitting between the on site p_{x}+ip_{y} and p_{x}-ip_{y} orbitals by rotating each optical lattice site around its own center. At large rotation angular velocities, this model naturally reduces to two copies of Haldane's quantum Hall model. The distribution of the Berry curvature in momentum space and the quantized Chern numbers are calculated. The experimental realization of this state is feasible.

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Study of Intrinsic Spin Hall Effect and Orbital Hall Effect in 4d- and 5d- Transition Metals

H. Kontani, T. Tanaka, M Naito … (2007)

We study the intrinsic spin Hall conductivity (SHC) in various $5d$-transition metals (Ta, W, Re, Os, Ir, Pt, and Au) and 4d-transition metals (Nb, Mo, Tc, Ru, Rh, Pd, and Ag) based on the Naval Research Laboratory tight-binding model, which enables us to perform quantitatively reliable analysis. In each metal, the obtained intrinsic SHC is independent of resistivity in the low resistive regime ($\rho < 50 \mu\Omega\text{cm}$) whereas it decreases in proportion to $\rho^{-2}$ in the high resistive regime. In the low resistive regime, the SHC takes a large positive value in Pt and Pd, both of which have approximately nine $d$-electrons per ion ($n_d=9$). On the other hand, the SHC takes a large negative value in Ta, Nb, W, and Mo where $n_d<5$. In transition metals, a conduction electron acquires the trajectory-dependent phase factor that originates from the atomic wavefunction. This phase factor, which is reminiscent of the Aharonov-Bohm phase, is the origin of the SHC in paramagnetic metals and that of the anomalous Hall conductivity in ferromagnetic metals. Furthermore, each transition metal shows huge and positive $d$-orbital Hall conductivity (OHC), independently of the strength of the spin-orbit interaction (SOI). Since the OHC is much larger than the SHC, it will be possible to realize a {\it orbitronics device} made of transition metals.