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.

PREDICTION
OF NEW EFFECT IN 3D 
The above calculational method
is
applied to a study of the strongfield magnetotransport
of a uniform freeelectron 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 noncompact
Fermi surface.

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.

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. 


EXPERIMENTAL VERIFICATION and COOPERATIONS 



EXPERIMENT




PERCOLATING COMPOSITE MATERIALS 


The critical behavior of magnetotransport 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
threedimensional 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 magnetoresistance 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
lengththe magnetic correlation length. In a percolating
metalinsulator 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.


