In this review section, we present a brief background on spintronics, on spin current, on spin-orbit interaction, and on the progress in the research on the measurement of spin current.
Spintronics
Spintronics is an area of intense current scientific interests[1]. It is important for in-formation storage and quantum computing. Fundamental studies of spintronics include investigations of spin transport in materials, as well as measurement of spin accumulation, spin relaxation, and spin current. Especially, spin current plays an important role in an spintronic devices. Our work in this thesis focus on measurenent of spin current. We must understand the definition of spin current before our work.
Spin current
In this paragraph, we explain the definition of spin current. An electron carries both charge and spin which may have two components: up and down. In the semi-classical picture, spin can be described by a unit vector. Traditional charge current is a flow of electron which is the sum of flows of up- and down-spin electrons. The spin information may be neglected in charge current. A spin current differs from a charge current. For a simple description, spin current can be recognized as the difference between the flows of up and down spin electrons. A pure spin current means that equivalent up and down spin flows in the opposite direction. There is no net particle transfer across any cross section of the channel. Measuring spin current in solid state systems provides a new tool to investigate the mesoscopic system, and it also give us hopes that it could be applied in spintronics and quantum information processing in the future. We can say that measurement of spin current is an indispensable part in field of spintronics. It has been found that spin-orbit interaction can be a nice tool to measure spin current all
electrically. In the following two subsections we will introduce spin-orbit interaction in an atom and in semiconductor respectively.
Spin-orbit interaction in an atom
Spin-orbit interaction is a well-known phenomenon which is caused from the interaction of a particle’s spin with its own motion. A particle in an electric field experiences an effective magnetic field in its co-moving frame. For electrons, it brings about lifting of the degeneracy of energy levels of electrons according to their spin states.
In atomic physics, this interaction comes from the electron spin magnetic moment interacting with the magnetic moment due to the orbit motion of the electron. In non-relativistic approximation to Dirac equation, the form of the spin-orbit interaction term in an atom is given by:
HSO,vac = − e~
4m02c2σ · (p × E) , (1.1)
where e is the magnitude of electron charge(e > 0), ~ is the Plank’s constant, m0 is the mass of a free electron, c is the light speed in vacuum, σ = (σx, σy, σz) are the Pauli matrices , p is the momentum of the spin, and E is the electric field that the electron travels through in the atom[2].
When the electron velocity is far less than the speed of light and a small electric field is quite small, the Dirac gap 2m0c2 ≈ 1MeV in the denominator of Eq. (1.1) is too large that the spin-orbit interaction in a single atom is quite week.
We may rewrite equation Eq. (1.1) as HSO,vac= −eΛvac~ σ·(p × E) , where Λvac = 4m~022c2
is the spin-orbit coupling constant in vacuum. Actually, spin-orbit interaction in vacuum or in a single atom has the same coupling constant, but the electric field comes from different sources. In a atom, electric field comes from the atomic nucleus. In vacuum, the electric field comes from the divergence of the potential in space. Even though the spin-orbit coupling in a single atom or in vacuum is very week, it will be magnified in
semiconductor.
Spin-orbit interaction in semiconductor
Spin-orbit interaction in solid state physics have the same form as Eq. (1.1) but difference in the spin-orbit coupling due to the energy gap difference. In semiconductor, spin-orbit coupling may be enhanced with several orders. The coupling strength is mostly derived from the electrons with high velocity under the strong electric field near the core of the atoms, rather than the weak velocity movement. Due to the periodicity of crystal, the electron energy spectrum form energy band structure in the reciprocal vector space. If the crystal system does not have the space inversion symmetry, the band gap will be narrower which result in stronger spin orbit coupling. In GaAs, the spin-orbit coupling constant Λ is about 82.5 ˚A2 which is seven order magnitude greater than Λvac. The perturbing spin-orbit coupling Hamiltonian in GaAs may be written as:
HSO,sc = eΛ
~σ · (p × E) , (1.2)
where Λ is the spin-orbit coupling constant in GaAs. The strength of spin-orbit interaction un semiconductor is manifestly seven order higher in magnitude than that in vacuum such that it becomes a nice tool to detect spin current electrically. Next, we will introduce kinds of principle means of detection of spin current.
Review of measurement of spin current
Generally, there are three kinds of principle means of detection of spin current. Here, we review some of them.
The first method is mechanical measurement[3, 4]. In 2007, E. B. Sonin demonstrates that an equilibrium spin current in two-dimension electron gas (2DEG) with Rashba interaction which is one kind of spin-orbit interaction will lead to a mechanical torque on a substrate near an edge of the Rashba medium[4]. If the substrate is flexible enough
that the torques would distort it, it is a method to detect equilibrium spin currents experimentally that he measure the degree of contortion.
Optical detection is also a general way to measure spin current[5–7]. In 2008, J. Wang, B. F. Zhu, and R. B. Liu described the first non-invasive method of measure pure spin current directly by a polarized light beam [7]. The polarized light beam which act as a
’photon spin current’ will interact with spin current due to the spin-orbit coupling without the Rashba or the Dresselhaus effect. The interaction result in linear and circular optical birefringence. They utilized the birefringence effects to measure to pure spin currents.
The third one is electrical detection[8–12]. In 1985, Mark Johnson and R. H. Silsbee performed the experiment in non-magnetic aluminum strip contacted to two ferromag-netic electrodes[11]. They reported that injecting charge current from one of ferromagferromag-netic electrodes into aluminum strip results in non-equilibrium spin accumulation at the inter-face of aluminum strip and the source ferromagnetic electrode. The spin accumulation defuses away from the interface and forms spin current. If there is a non-equilibrium spin accumulation in the vicinity of the detector, an open-circuit voltage will be developed across the interface. In 2006, S. O. Valenzuela and M. Tinkham demonstrate electrical detection of spin currents in metallic nanostructures. They apply reciprocal spin Hall effect in a diffusive metallic conductor and obtain its spin Hall conductivity. Finally they measure the laterally induced voltage which results from the conversion of the injected spin current into charge imbalance owing to the spin-orbit coupling. There are still Some other means of electrical detection of spin current proposed in resent years including the-oretical and experimental proposition. It is worth to mention that in 2004, Qing-feng Sun et al. propose a journal named ”spin-current induced electric field” [12]. In that article, the authors investigate properties of the induced electric field of a steady-state spin-current without charge current. They regard one electron spin as a magnetic dipole.
Such magnetic dipole current will generate electric field in space. They claim that a spin current with drift velocity 10−2m/s flowing in an infinitely long wire with cross section area of 2 mm×2 mm and the magnetic moment is perpendicular to the current direction.
The spin current causes the potential difference∼ 12 µV at distance -1.1 mm and 1.1 mm on either side of the wire. It is a novel method to measure spin current by measuring the voltage directly induced by spin current. Even though the potential difference their report is measurable, the spin current is up to 640.82 Ampere. That is very giant magnitude of spin current. It is extremely difficult to generate such strong current in the thin wire.