Spin current

The quality of the SOC calculation in O2 can be checked by estimation of the fc Sj" — A3E transition probability. The transition is forbidden by selection rules for electric dipole radiation with account of SOC, and occurs as magnetic dipole spin-current borrowing intensity from microwave transitions between spin-sublevels of the ground state [41]. 

Magetoresistivity-based sensors, which are based on a resistivity change induced by a magnetic field, have found wide application in industry. However, such sensors are usually fabricated of metals and hence it is difficult to integrate them with conventional semiconductor devices. To develop magetoresistive sensors in semiconductors, one of the key problems is how to effectively inject spin-polarized electrons into paramagnetic semiconductors. The spin Hall effect (SHE), which involves a spin-current transverse to an applied electric field, " potentially provides a new way to resolve this issue. 

Given by Fukutome." and SA are the projections parallel and perpendicular to S. Abbreviations TICS, time-reversal-invariant closed shell CCW, charge-current wave ASCW, axial spin-current wave ASDW, axial spin density wave ASW, axial spin wave TSCW, torsional spin-current wave TSDW, torsional spin density wave TSW, torsional spin wave. The numbers in parentheses refer to the numbering of the subgroups in Table I. 

If N(r, r ) or S(r, f ) has a nonvanishing imaginary part there is a corresponding current density. The charge-current wave (CCW) class, for example, has a complex number density matrix, whereas the axial spin-current wave (ASCW) class has a purely imaginary spin density matrix. 

In one method, the sensor is calibrated after installation. The offset is subtracted and the amplification is adjusted to the altered sensitivity. In addition, the temperature drift of the sensor and the drift of the permanent magnet used in the specific application can be programmed into the ASIC [35]. In a second method, the offset is actively compensated for by chopping [36]. Here, the applied current and the taps of the Hall voltage are continuously commutated. An advanced version of this technique is the spinning-current method, in which 8 or even 12 different current directions are used [37, 38]. The current direction is spun... 

To study the magnetic properties of matter one would often like to be able to obtain information on the currents in the system and their coupling to possible external magnetic fields. Important classes of experiments for which this information is relevant are nuclear magnetic resonance and the quantum Hall effects. SDFT does not provide explicit information on the currents. RDFT in principle does, but standard implementations of it are formulated in a spin-only version, which prohibits extraction of information on the currents. Furthermore, the formalism of RDFT is considerably more complicated than that of SDFT. In this situation the formulation of nonrelativistic current-DFT (CDFT), accomplished by Vignale and Rasolt [140, 141], was a major step forward. CDFT is formulated explicitly in terms of the (spin) density and the nonrelativistic paramagnetic current density vector jp(r). Some recent applications of CDFT are Refs. [142, 143, 144, 145]. E. K. U. Gross and the author have shown that the existence of spin currents implies the existence of a link between the xc functionals of SDFT and those of CDFT [146], Conceptually, this link is similar to the one of Eq. (99) between functionals of DFT and SDFT, but the details are quite different. Some approximations for xc functionals of CDFT are discussed in Refs. [146, 147, 148]. 

Many of the CC theoretical predictions, such as control of atomic and molecular processes via N versus M photon transitions [137], have been tested and demonstrated experimentally [138-146]. CC methods have also proved to be valid in the context of solid-state systems. In particular, it was shown that excitation by N and M multiphoton processes, having opposite parities, leads to symmetry breaking and the generation of DC electric currents [147-151]. These predictions have been confirmed experimentally in a number of semiconductors [152-155]. Similar techniques were shown to lead to the control of phonon emission [156] or injection of spin currents [157]. 

R. Bhat, J. Sipe, Optically injected spin currents in semiconductors, Phys. Rev. Lett. 85... 

Algebraic Theory of Particle Physics Hadron Dynamics In Terms of Unitary Spin Current, 1967 Current Algebras and Applications to Particle Physics, 1968... 

Fig. 14. Left Illustration of staggered charge or spin current pattern in the square lattice for d-CDW or d-SDW. Right Magnetoresistance (j T ac-plane) oscillations in the low temperature d-CDW state of the organic quasi-ID conductor Q -(BEDT-TTF)2KHg(SCN)4. The oscillations result from the Landau quantisation of energy levels eq. (55) around the nodal Dirac points in fig. 7. The circles are from experiment (T = IAK, B = 157 , = 45°), and the full line...

The order parameter is purely imaginary because it is connected with persistent commensurate spin currents around lattice plaquettes. This state breaks spin rotational symmetry but not time reversal symmetry because the latter inverses both current and spin direction leaving the order... 

Now, using (16.8.12), we can express A, as a sum of various currents. Amongst them the axial-vector isotopic spin current... 

Spin-dynamics cannot be treated with LDA and GGA functionals because the local torque on spins vanishes this is not the case for EXX methods, recently extended to treat non-collinear magnetism and spin currents " ... 

We note, in closing, that current densities may be defined for the individual up-spin and down-spin components of P, and consequently for the spin density, the spin current, obtained by replacing P r r ) in (5.10.4) by the various components of spin density, will clearly be a 9-component tensor density. Such densities occur in the discussion of properties that depend jointly on spin and electron velocity. 

This is similar to a quantity encountered (p. 395) in discussing magnetic shielding, and it reduces in a similar way. The only difference is that it contains an extra operator S and the analogous result will therefore contain a spin-current density instead of the usual (electron-) current density. 

In terms of the spin current, the factor Yjf in (11.8.28) is easily reduced to give... 

The indirect electron spin-spin coupling may also be analysed in terms of spin currents (Problem 11.17). Briefly, one spin dipole produces, via the spin-orbit interaction, small circulating currents around the various nuclei, the currents being different for up-spin and down-spin components the resulting spin polarization is picked up by a second spin and leads to the tensor interaction already derived. 

Express the g-tensor components in (11.8.22) in the alternative form (see (11.8.31) et seq.) that involves the field-induced spin current density near the nucleus. 

Show how the coupling-tensor elements in (11.8.25) may be rewritten in terms of spin currents. 

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