Composite Materials in High Magnetic Fields


PERIODIC COMPOSITE MATERIALS...........................


Poster:








THEORY

A method is developed for calculating the magnetotransport properties of a composite conducting medium which has a periodic microstructure. The method is based on a Fourier series expansion of the local electric potential. Because a large number of expansion coefficients need to be used in order to get reliable results for the bulk effective behavior, a special approach is developed which does not require solving a large set of coupled linear algebraic equations for them. Results are obtaned for a number of models where periodic arrays of insulating inclusions of various shapes are embedded in a uniform host material. These samples include cases where the inclusions are well separated as well as cases where they touch and where they overlap.
see: Y. M. Strelniker and D. J. Bergman Phys. Rev. B 50, 14001-14015 (1994).
( Abstract+Paper) .

PREDICTION
OF NEW EFFECT IN 3D

The above calculational method is applied to a study of the strong-field magneto-transport of a uniform free-electron metal, inside which is embedded a simple cubic array of identical spheres or cylinders, which have a different resistivity tensor. When the magnetic field is strong enough, the magnetoresistance exhibits very strong variations with the direction of the field. The strong dependence on the field direction is qualitatively, and sometimes even quantitatively, similar to what is observed in some metallic crystals which have a non-compact Fermi surface.

see: D. J. Bergman and Y. M. Strelniker, Phys. Rev. B 49, 16256-16267 (1994). ( Abstract+Paper). ( Figs. 2, 3, 3, 3, 9, 11, 13, )

PREDICTION
FOR FILMS

We consider a geometry in which the magnetic field and the volume averaged current density are mutually perpendicular and both lie in the plane of the film and we study how the resistivity changes when they are rotated in this plane. We show that magnetotransport anisotropy, similar to what has recently been predicted to occur for infinite 3D periodic composites, should appear even in the case of a thin film.

see: D. J. Bergman and Y. M. Strelniker, Phys. Rev. B 51, 13845-13848 (1995).
( Abstract). (Figs. 1, 2, , and 3 )

EXPLANATION

A detailed theoretical and numerical study is presented of the anisotropic magnetotransport which was recently predicted to occur in composite conductors with a periodic microstructure. Contour plots and three dimensional graphs of the local dissipation rate around an isolated obstacle and around a periodic array of obstacles, as well as vector plots of the distorted current pattern, are produced and used to discuss the details of the anisotropic magnetoresistance. The problem of an isolated spherical or cylindrical inclusion in a homogeneous host has a closed form solution. This is exploited in order to give a perturbation treatment of the problem of multiple inclusions. A good qualitative understanding of many features of the anisotropy can be achieved by considering the interference between the current distortion patterns produced by just two obstacles of either spherical or cylindrical shape. As a result of these discussions, we have now achieved a more complete understanding of how the anisotropic magnetotransport arises in a periodic composite conductor.



see: Interference of Current Distortion Patterns and Magnetoresistance Anisotropy in a Composite with Periodic Microstructure,
by Y. M. Strelniker and D. J. Bergman, Phys. Rev. B 53, 11051-11059 (1996) ( Abstract+paper) ( Figs. 3, 4, 5, 6, 7, 8, 9, 12, 5, ) ( The color vertion of Fig. a ). ( and Fig. b.. ).

Other color figures.

EXPERIMENTAL VERIFICATION and COOPERATIONS




















Anisotropic Magnetoresistance of a Classical Antidot Array

see below


EXPERIMENT


Was done in

Max-Planck-Institut
fur Festkorperforschung
,
Stuttgart, Germany

A periodic array of cylindrical voids, embedded in a thin film of n-doped GaAs, displays a pronounced anisotropy of the classical magnetoresistance. For a geometry, where the magnetic field lies in the plane of the film, we observe a characteristic dependence on the angle between current and magnetic field. This experimental finding


provides a first verification of a recently predicted effect and agrees well with theoretical calculations. The observed anisotropy is due to interactions among current distortions by neighboring voids.

see: M. Tornow, D. Weiss, K. v. Klitzing,
K. Eberl, D. J. Bergman, and Y. M. Strelniker

Anisotropic Magnetoresistance of a Classical Antidot Array,

Phys. Rev. Lett., 77 , 147 (1996).




see: M. Tornow, D. Weiss, K. v. Klitzing,
K. Eberl, D. J. Bergman, and Y. M. Strelniker

Anisotropic Magnetoresistance of a Classical Antidot Array,

Phys. Rev. Lett., 77 , 147 (1996).


PERCOLATING COMPOSITE MATERIALS




The critical behavior of magneto-transport in a percolating medium in the presence of a magnetic field H of arbitrary strength is discussed. A discrete network model is used to solve the problem exactly for a three-dimensional Sierpinski gasket fractal, and to perform direct Monte Carlo simulation of a percolating medium. A new and very efficient algorithm is used to calculate transport properties in the vicinity of the percolation threshold. We find that there is strong magneto-resistance near the percolation threshold. We also find a new scaling behavior of the effective ohmic resistivity and Hall coefficient as functions of the concentration p and magnetic field H. This scaling is due to the appearance a new, field dependent length---the magnetic correlation length. In a percolating metal-insulator mixture, the resistivity ratio with and without a field is predicted to saturate (as the concentration tends to percolation threshold) at a value that is proportional to H in power 3.1.

see: Theory of High Field Magneto-Transport in a Percolating Medium,
A. K. Sarychev, D. J. Bergman and Y. M. Strelniker,
Phys. Rev. B 48, 3145, 851 (1993). ( Abstract+paper). ( Figs. 2, 4, 12,)




see also: High Field Magneto-Transport in a Percolating Medium,
A. K. Sarychev, D. J. Bergman and Y. M. Strelniker

Europhys Lett. 21, 851 (1993). ( Abstract+paper).







Comments should be sent to Yakov M. Strelniker
strelnik@ory.ph.biu.ac.il Back to Home