Integral Transforms for Conformal Field Theories with a Boundary

A new method is developed for solving the conformally invariant integrals that arise in conformal field theories with a boundary. The presence of a boundary makes previous techniques for theories without a boundary less suitable. The method makes essential use of an invertible integral transform, related to the radon transform, involving integration over planes parallel to the boundary. For successful application of this method several nontrivial hypergeometric function relations are also derived.Comment: 20 pagess, LateX fil

Transition temperature of ferromagnetic semiconductors: a dynamical mean field study

We formulate a theory of doped magnetic semiconductors such as Ga$_{1-x}$Mn$_x$As which have attracted recent attention for their possible use in spintronic applications. We solve the theory in the dynamical mean field approximation to find the magnetic transition temperature $T_c$ as a function of magnetic coupling strength $J$ and carrier density $n$. We find that $T_c$ is determined by a subtle interplay between carrier density and magnetic coupling.Comment: 4 pages, 4 figure

Spin depolarization in the transport of holes across GaMnAs/GaAlAs/p-GaAs

We study the spin polarization of tunneling holes injected from ferromagnetic GaMnAs into a p-doped semiconductor through a tunneling barrier. We obtain an upper limit to the spin injection rate. We find that spin-orbit interaction interaction in the barrier and in the drain limits severely spin injection. Spin depolarization is stronger when the magnetization is parallel to the current than when is perpendicular to it.Comment: Accepted in Phys. Rev. B. 4 pages, 4 figure

Polaron percolation in diluted magnetic semiconductors

We theoretically study the development of spontaneous magnetization in diluted magnetic semiconductors as arising from a percolation of bound magnetic polarons. Within the framework of a generalized percolation theory we derive analytic expressions for the Curie temperature and the magnetization, obtaining excellent quantitative agreement with Monte Carlo simulation results and good qualitative agreement with experimental results.Comment: 5 page

Free energy density for mean field perturbation of states of a one-dimensional spin chain

Motivated by recent developments on large deviations in states of the spin chain, we reconsider the work of Petz, Raggio and Verbeure in 1989 on the variational expression of free energy density in the presence of a mean field type perturbation. We extend their results from the product state case to the Gibbs state case in the setting of translation-invariant interactions of finite range. In the special case of a locally faithful quantum Markov state, we clarify the relation between two different kinds of free energy densities (or pressure functions).Comment: 29 pages, Section 5 added, to appear in Rev. Math. Phy

Spin Coulomb drag in the two-dimensional electron liquid

We calculate the spin-drag transresistivity $\rho_{\uparrow \downarrow}(T)$ in a two-dimensional electron gas at temperature $T$ in the random phase approximation. In the low-temperature regime we show that, at variance with the three-dimensional low-temperature result [$\rho_{\uparrow\downarrow}(T) \sim T^2$], the spin transresistivity of a two-dimensional {\it spin unpolarized} electron gas has the form $\rho_{\uparrow\downarrow}(T) \sim T^2 \ln T$. In the spin-polarized case the familiar form $\rho_{\uparrow\downarrow}(T) =A T^2$ is recovered, but the constant of proportionality $A$ diverges logarithmically as the spin-polarization tends to zero. In the high-temperature regime we obtain $\rho_{\uparrow \downarrow}(T) = -(\hbar / e^2) (\pi^2 Ry^* /k_B T)$ (where $Ry^*$ is the effective Rydberg energy) {\it independent} of the density. Again, this differs from the three-dimensional result, which has a logarithmic dependence on the density. Two important differences between the spin-drag transresistivity and the ordinary Coulomb drag transresistivity are pointed out: (i) The $\ln T$ singularity at low temperature is smaller, in the Coulomb drag case, by a factor $e^{-4 k_Fd}$ where $k_F$ is the Fermi wave vector and $d$ is the separation between the layers. (ii) The collective mode contribution to the spin-drag transresistivity is negligible at all temperatures. Moreover the spin drag effect is, for comparable parameters, larger than the ordinary Coulomb drag effect.Comment: 6 figures; various changes; version accepted for publicatio

Spin-polarized current amplification and spin injection in magnetic bipolar transistors

The magnetic bipolar transistor (MBT) is a bipolar junction transistor with an equilibrium and nonequilibrium spin (magnetization) in the emitter, base, or collector. The low-injection theory of spin-polarized transport through MBTs and of a more general case of an array of magnetic {\it p-n} junctions is developed and illustrated on several important cases. Two main physical phenomena are discussed: electrical spin injection and spin control of current amplification (magnetoamplification). It is shown that a source spin can be injected from the emitter to the collector. If the base of an MBT has an equilibrium magnetization, the spin can be injected from the base to the collector by intrinsic spin injection. The resulting spin accumulation in the collector is proportional to $\exp(qV_{be}/k_BT)$, where $q$ is the proton charge, $V_{be}$ is the bias in the emitter-base junction, and $k_B T$ is the thermal energy. To control the electrical current through MBTs both the equilibrium and the nonequilibrium spin can be employed. The equilibrium spin controls the magnitude of the equilibrium electron and hole densities, thereby controlling the currents. Increasing the equilibrium spin polarization of the base (emitter) increases (decreases) the current amplification. If there is a nonequilibrium spin in the emitter, and the base or the emitter has an equilibrium spin, a spin-valve effect can lead to a giant magnetoamplification effect, where the current amplifications for the parallel and antiparallel orientations of the the equilibrium and nonequilibrium spins differ significantly. The theory is elucidated using qualitative analyses and is illustrated on an MBT example with generic materials parameters.Comment: 14 PRB-style pages, 10 figure

Magnetic properties of the Ag-In-rare-earth 1/1 approximants

We have performed magnetic susceptibility and neutron scattering measurements on polycrystalline Ag-In-RE (RE: rare-earth) 1/1 approximants. In the magnetic susceptibility measurements, for most of the RE elements, inverse susceptibility shows linear behaviour in a wide temperature range, confirming well localized isotropic moments for the RE$^{3+}$ ions. Exceptionally for the light RE elements, such as Ce and Pr, non-linear behaviour was observed, possibly due to significant crystalline field splitting or valence fluctuation. For RE = Tb, the susceptibility measurement clearly shows a bifurcation of the field-cooled and zero-field-cooled susceptibility at $T_{\rm f} = 3.7$~K, suggesting a spin-glass-like freezing. On the other hand, neutron scattering measurements detect significant development of short-range antiferromagnetic spin correlations in elastic channel, which accompanied by a broad peak at $\hbar\omega = 4$~meV in inelastic scattering spectrum. These features have striking similarity to those in the Zn-Mg-Tb quasicrystals, suggesting that the short-range spin freezing behaviour is due to local high symmetry clusters commonly seen in both the systems.Comment: 14 pages, 12 figure