Landau diamagnetism
and
de Hass van Alphen effect
by Enas Hamasha
Stastical mechanics ph 761
Dr. Abdulla Obeidat
Landau diamagnetism its
quantized charged particles
orbits which affected by magnetic
field
Landau, 1930 observed its
electronic orbits to be quantized
and don’t on the classical form and
also conclude that the magnetic
susceptibility for this materials is
negative
Diamagnetism do not depend on
the temperature but produced from
external magnetic field effect on
internal electron motion for atoms
The diamagnetism materials have a
negative magnetic susceptibility and
 <<1 smaller than one such
materials appear this property clearly:
.Cu, Au, Hg, and H2O
And landau arrives to quantized the
electrons orbits using by the
mathematical calculation The semi
classical approximation by onsagar
and Walfshter and assumptions
(Bohr-sommerfeld) relation
landau concluded that the orbital
electron quantized where the
magnetic flux equal
Φn =(n+γ)(2ΠЋc/q)
de Hass van Alphen effect
It’s the oscillation of the magnetic
moment of Fermi gas in a metal
where change magnetic field and at
low temperature
When apply the magnetic field on
the surface metal the orbits of
electron is closed and magnetic
parallel to Z-axis and have
periodicity and cyclotron frequency
ωc
When applying the B on the metal
surface the temperature must be
low such zero or around it, and the
metal must to be Fermi surface
and electrons move in the Fermi
surface produce magnetic moment
we can studying the orbits energy
when we applying variable
magnetic field in zero Kelvin and
seeing what happens for orbit
energy when increasing field in the
figure below
the presence of B lead to occurs
the degeneracy in the levels
means that increases the number of
electrons orbits in one level and
results from apply the magnetic
field in low temperature to become
new levels called “ landau levels”
At low temperature and when
increases the field so landau levels
start becomes increases and go on
increases to leave the Fermi
surface and this lead to oscillation
effects in metals and called the
result frequency from oscillation “de
“ Hass van Alphen frequency
ρB=D
. ρ :constant
We conclude from this relation the
degeneracy proportional to
magnetic field means when
increases the applying magnetic
field the levels increases
degeneracy
when apply B on the surface and
increases the degeneracy increases
for every level and then translate
electron from higher level to lower
such that there from S+1 level to S
level and when be S +1 level vacated
because have electron moved to
lower one S so Fermi level translate
. an abrupt form to S level
we can calculate the total number
of electron in this case
by :
N = SρBs
Where, N: the # of electron in the
levels
S : the completely filled
levels
constant : ρ
Bs : the magnetic field where every
level filled
And we can conclude the curve
which the total electronic energy
versus 1/B
the changing total energy with
magnetic field changed and
observe the oscillation in the energy
U may be detected by
measurement of the magnetic
,moment
the thermal and transport ,
properties of the metals also
oscillate as successive orbital levels
cut through the Fermi levels when
the field is increased And this is the
oscillation for magnetic moment in
the figure the de Hass van Alphen
effect for Fermi gas in low
,temperature
the oscillation occurs in equal
intervals from 1/B such that
∆ (1/B) = 2πq/ЋcS
where S: extremal area on the
Fermi surface
S predict the shape and the volume
of the surface
Extremal area: for the Fermi
surface of general shape the
section at different values of radius
with different periods the response
will be the sum of contributions from
,all sections or all orbits
But the dominant response of the
system comes from orbits whose
periods stationary with respect to
small change in the radius of free
electron Fermi sphere this orbits
called extremal orbits seeing in
:figure below
Thank you