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 (ρ < 50µΩcm) whereas it decreases in proportion to ρ −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 orbitronics device made of transition metals.

In transition metals and their compounds, the orbital degrees of freedom gives rise to an orbital current, in addition to the ordinary spin and charge currents. We reveal that considerably large spin and anomalous Hall effects (SHE and AHE) observed in transition metals originate from an orbital Hall effect (OHE). To elucidate the origin of these novel Hall effects, a simple periodic s-d hybridization model is proposed as a generic model. The giant positive OHE originates from the orbital Aharonov-Bohm phase factor, and induces spin Hall conductivity that is proportional to the spin-orbit polarization at the Fermi level, which is positive (negative) in metals with more than (less than) half-filling.PACS numbers: 72.25. Ba,72.10.Bg,72.80.Ga The Hall effect, first discovered at the end of 19th century, has revealed the profound nature of electron transport in metals and semiconductors via the anomalous Hall effect (AHE) and (fractional) quantum Hall effects. It has recently been recognized that conventional semiconductors and metals exhibit a spin Hall effect (SHE), which is the phenomenon where an electric field induces a spin current (a flow of spin angular momentum s z ) in a transverse direction [1][2][3][4][5]. Recently, a theory of the intrinsic Hall effect proposed by Karplus and Luttinger [6], which occurs in multiband systems and is independent of impurity scattering, has been intensively developed [7,8]. In particular, a quantum SHE has also been predicted and experimentally confirmed [9,10].The spin Hall conductivity (SHC) observed in transition metals has given rise to further issues regarding the origin of the SHE, since the SHC observed in Pt exceeds 200 e −1 · Ω −1 cm −1 , which is approximately 10 4 times larger than that of n-type semiconductors [5], and the SHCs in Nb and Mo are negative [11]. The large SHE and the sign change of the SHC in transition metals has attracted much interest, and many theoretical studies of the SHE have so far been conducted based on realistic multiband models for Ru-oxide [8] and various 4d and 5d metals [12], including Au, W [13], and Pt [14,15]. The calculated results for the SHC semi-quantitatively agree with the observed results. The mechanism for the SHE has been explained in such a way that spin-orbit interactions (SOI) and the phase of hopping integrals of electrons give rise to the Aharonov-Bohm (AB) effect, and therefore the conduction electrons are subject to an effective spin-dependent magnetic field.Since the transition metals have orbital degrees of freedom in addition to the spin and charge degrees of freedom, flow of the atomic orbital angular momentum (l z ), that is, an orbital current, may be realized in a nonequilibrium state. In fact, several authors have predicted the emergence of a large orbital Hall effect (OHE) [8,12,16], which is a phenomenon where an electric field induces a flow of p-and d-orbital angular momentum in a transverse direction. In particular, the predicted orbital Hall conductivity (OHC) in transition metals and oxides [8,12]...

We investigate the intrinsic spin Hall conductivity (SHC) and the d-orbital Hall conductivity (OHC) in metallic d-electron systems, by focusing on the t2g-orbital tight-binding model for Sr2MO4 (M=Ru, Rh, Mo). The conductivities obtained are one or 2 orders of magnitude larger than predicted values for p-type semiconductors with approximately 5% hole doping. The origin of these giant Hall effects is the "effective Aharonov-Bohm phase" that is induced by the d-atomic angular momentum in connection with the spin-orbit interaction and the interorbital hopping integrals. The huge SHC and OHC generated by this mechanism are expected to be ubiquitous in multiorbital transition metal compounds, which opens the possibility of realizing spintronics as well as "orbitronics" devices.

We study the origin of the intrinsic spin Hall conductivity (SHC) and the d-orbital Hall conductivity (OHC) in Pt based on a multiorbital tight-binding model with spin-orbit interaction. We find that the SHC exceeds 1000 e −1 ·Ω −1 cm −1 when the resistivity ρ is smaller than ∼ 10 µΩ cm, whereas it decreases to 300 e −1 · Ω −1 cm −1 when ρ ∼ 100 µΩ cm. In addition, the OHC is still larger than the SHC. The origin of the huge SHE and OHE in Pt is the large "effective magnetic flux" that is induced by the interorbital transition between dxy-and d x 2 −y 2 -orbitals with the aid of the strong spin-orbit interaction. PACS numbers:Recently, the spin Hall effect (SHE) has attracted much attention due to its fundamental interest and its potential application in spintronics. The SHE has a close relation to the anomalous Hall effect (AHE) in ferromagnets: In 1954, Karplus and Luttinger (KL) [1] studied the Hall effect in multiband systems and found that an electric field induces a spin-dependent transverse current in the presence of spin-orbit (SO) interaction. This effect causes the AHE (transverse charge current) in ferromagnetic metals and the SHE (transverse spin current) in paramagnetic metals. These phenomena are fundamental issues in recent condensed matter physics [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. In these years, great progress on the SHE in semiconductors has been made. Murakami et al. [2] and Sinova et al. [3] have studied the intrinsic (impurity-independent) SHE in semiconductors by developing the theory of KL. Now, the SHE in two-dimensional electron gas (2DEG) with a Rashba-type SO interaction is well understood [4][5][6][7]. Although the SHE in semiconductors was recognized by the optical detection of spin accumulation [8,9], it is unfortunately too small for quantitative analysis. Therefore, materials that show a large SHE are highly desirable.

It is shown that a strong impurity potential induces short-range antiferromagnetic (ferrimagnetic) order around itself in a Hubbard model on a half-filled honeycomb lattice. This implies that short-range magnetic order is induced in monolayer graphene by a nonmagnetic defect such as a vacancy with full hydrogen termination or a chemisorption defect.Comment: 5 pages, 8 figure