Carrier States and Ferromagnetism in Diluted Magnetic Semiconductors

Applying the dynamical coherent potential approximation to a simple model, we have systematically studied the carrier states in $A_{1-x}$Mn$_xB$-type diluted magnetic semiconductors (DMS's). The model calculation was performed for three typical cases of DMS's: The cases with strong and moderate exchange interactions in the absence of nonmagnetic potentials, and the case with strong attractive nonmagnetic potentials in addition to moderate exchange interaction. When the exchange interaction is sufficiently strong, magnetic impurity bands split from the host band. Carriers in the magnetic impurity band mainly stay at magnetic sites, and coupling between the carrier spin and the localized spin is very strong. The hopping of the carriers among the magnetic sites causes ferromagnetism through a {\it double-exchange (DE)-like} mechanism. We have investigated the condition for the DE-like mechanism to operate in DMS's. The result reveals that the nonmagnetic attractive potential at the magnetic site assists the formation of the magnetic impurity band and makes the DE-like mechanism operative by substantially enhancing the effect of the exchange interaction. Using conventional parameters we have studied the carrier states in Ga$_{1-x}$Mn$_x$As. The result shows that the ferromagnetism is caused through the DE-like mechanism by the carriers in the bandtail originating from the impurity states.Comment: 20 pages, 14 figure

The Free Energy and the Scaling Function of the Ferromagnetic Heisenberg Chain in a Magnetic Field

A nonlinear susceptibilities (the third derivative of a magnetization $m_S$ by a magnetic field $h$ ) of the $S$=1/2 ferromagnetic Heisenberg chain and the classical Heisenberg chain are calculated at low temperatures $T.$ In both chains the nonlinear susceptibilities diverge as $T^{-6}$ and a linear susceptibilities diverge as $T^{-2}.$ The arbitrary spin $S$ Heisenberg ferromagnet $[$ ${\cal H} = \sum_{i=1}^{N} \{ - J{\bf S}_{i} {\bf S}_{i+1} - (h/S) S_{i}^{z} \}$ $(J>0),$ $]$ has a scaling relation between $m_S,$ $h$ and $T:$ $m_S(T,h) = F( S^2 Jh/T^2).$ The scaling function $F(x)$=(2$x$/3)-(44$x^{3}$/135) + O($x^{5}$) is common to all values of spin $S.$Comment: 16 pages (revtex 2.0) + 6 PS figures upon reques

On the location of two blow up points on an annulus for the mean field equation

We consider the mean field equation on two-dimensional annular domains, and prove that if $P$ and $Q$ are two blow up points of a blowing-up solution sequence of the equation, then we must have $P=-Q$.Comment: To appear in CRA

Universal low-temperature properties of quantum and classical ferromagnetic chains

We identify the critical theory controlling the universal, low temperature, macroscopic properties of both quantum and classical ferromagnetic chains. The theory is the quantum mechanics of a single rotor. The mapping leads to an efficient method for computing scaling functions to high accuracy.Comment: 4 pages, 2 tables and 3 Postscript figure

Nuclear Astrophysics

Nuclear astrophysics is that branch of astrophysics which helps understanding some of the many facets of the Universe through the knowledge of the microcosm of the atomic nucleus. In the last decades much advance has been made in nuclear astrophysics thanks to the sometimes spectacular progress in the modelling of the structure and evolution of the stars, in the quality and diversity of the astronomical observations, as well as in the experimental and theoretical understanding of the atomic nucleus and of its spontaneous or induced transformations. Developments in other sub-fields of physics and chemistry have also contributed to that advance. Many long-standing problems remain to be solved, however, and the theoretical understanding of a large variety of observational facts needs to be put on safer grounds. In addition, new questions are continuously emerging, and new facts endanger old ideas. This review shows that astrophysics has been, and still is, highly demanding to nuclear physics in both its experimental and theoretical components. On top of the fact that large varieties of nuclei have to be dealt with, these nuclei are immersed in highly unusual environments which may have a significant impact on their static properties, the diversity of their transmutation modes, and on the probabilities of these modes. In order to have a chance of solving some of the problems nuclear astrophysics is facing, the astrophysicists and nuclear physicists are obviously bound to put their competence in common, and have sometimes to benefit from the help of other fields of physics, like particle physics, plasma physics or solid-state physics.Comment: LaTeX2e with iopart.cls, 84 pages, 19 figures (graphicx package), 374 updated references. Published in Reports on Progress in Physics, vol.62, pp. 395-464 (1999

Trans-Magnetosonic Accretion in a Black Hole Magnetosphere

We present the critical conditions for hot trans-fast magnetohydrodynamical (MHD) flows in a stationary and axisymmetric black-hole magnetosphere. To accrete onto the black hole, the MHD flow injected from a plasma source with low velocity must pass through the fast magnetosonic point after passing through the ``inner'' or ``outer'' Alfven point. We find that a trans-fast MHD accretion solution related to the inner Alfven point is invalid when the hydrodynamical effects on the MHD flow dominate at the magnetosonic point, while the other accretion solution related to the outer Alfven point is invalid when the total angular momentum of the MHD flow is seriously large. When both regimes of the accretion solutions are valid in the black hole magnetosphere, we can expect the transition between the two regimes. The variety of these solutions would be important in many highly energetic astrophysical situations.Comment: 27 pages, 12 figures, accepted to Ap