3.2 Different Kinds of MR
77
3.2 Different Kinds of MR
As a prelude, let us first discuss briefly about different kinds of MR.
3.2.1 Ordinary Magnetoresistance
For a normal metal, when there is a flow of current, motion of electrons at various
parts of the Fermi surface takes place in such a way so that the scattering becomes
minimum. In such case, the electrons should follow the path that offers minimum
scattering while traversing the sample. Now, the externally applied magnetic field
forces the electrons to follow a different path instead of the least scattering one.
As a result, electrons will suffer more scattering, which means that the change in
resistivity is positive, hence leading to positive MR (ρ). In both cases, when the
magnetic field is parallel (where, ,ρ II = corresponding positiveMR) and transverse
(where, ,ρ T = correspondingpositiveMR) to the current direction, both ρ II and
ρ T are positive with ρ T > ρ I I . Such ordinary MR can be classified into three
distinct cases as discussed below, based on the structure of electron orbitals at Fermi
surface:
1. In case of closed Fermi surfaces in metallic systems, the motion of electrons is
confined to their orbit in k-space. In this case, the effect of magnetic field occurs
as an enhancement in the cyclotron frequency of the electron in its closed orbit.
Thus, in general, a positive MR is expected.
2. For metals with equal numbers of electrons and holes, MR increases with H up
to the highest field measured and independent of crystallographic orientation.
Bismuth falls in this class.
3. Metals containing Fermi surfaces having open orbits, oriented along some crystallographic directions, exhibit large MR when the magnetic fields are applied
in those same directions. However, the resistance founds to saturate when the
magnetic fields are applied in a direction, where those orbits are closed.
3.2.2 Magnetoresistance of Ferromagnetic Transition Metals
Observation of negative MR in ferromagnetic metal is quite interesting (Fert and
Campbell 1976) and can be explained as follows: A very significant perception of
this problem was introduced by Mott. He described the transport properties of Ni,
which requires only a few electron volts to alter the configuration from (3d
8 4s
2 ) to
(3d
9 4s
1 ) or (3d
10 ). In general, Ni is considered to be (3d
9.4 4s
0.6 ). It is well known that
the d-band is very narrow, hence m
∗
d m e , where m
∗
d /m e = mass of the electrons
at d-band/free state. Since the s-band is nearly free, m
∗
s ∼ m e , where m
∗
s = mass of
the electrons at s-band.
77
3.2 Different Kinds of MR
As a prelude, let us first discuss briefly about different kinds of MR.
3.2.1 Ordinary Magnetoresistance
For a normal metal, when there is a flow of current, motion of electrons at various
parts of the Fermi surface takes place in such a way so that the scattering becomes
minimum. In such case, the electrons should follow the path that offers minimum
scattering while traversing the sample. Now, the externally applied magnetic field
forces the electrons to follow a different path instead of the least scattering one.
As a result, electrons will suffer more scattering, which means that the change in
resistivity is positive, hence leading to positive MR (ρ). In both cases, when the
magnetic field is parallel (where, ,ρ II = corresponding positiveMR) and transverse
(where, ,ρ T = correspondingpositiveMR) to the current direction, both ρ II and
ρ T are positive with ρ T > ρ I I . Such ordinary MR can be classified into three
distinct cases as discussed below, based on the structure of electron orbitals at Fermi
surface:
1. In case of closed Fermi surfaces in metallic systems, the motion of electrons is
confined to their orbit in k-space. In this case, the effect of magnetic field occurs
as an enhancement in the cyclotron frequency of the electron in its closed orbit.
Thus, in general, a positive MR is expected.
2. For metals with equal numbers of electrons and holes, MR increases with H up
to the highest field measured and independent of crystallographic orientation.
Bismuth falls in this class.
3. Metals containing Fermi surfaces having open orbits, oriented along some crystallographic directions, exhibit large MR when the magnetic fields are applied
in those same directions. However, the resistance founds to saturate when the
magnetic fields are applied in a direction, where those orbits are closed.
3.2.2 Magnetoresistance of Ferromagnetic Transition Metals
Observation of negative MR in ferromagnetic metal is quite interesting (Fert and
Campbell 1976) and can be explained as follows: A very significant perception of
this problem was introduced by Mott. He described the transport properties of Ni,
which requires only a few electron volts to alter the configuration from (3d
8 4s
2 ) to
(3d
9 4s
1 ) or (3d
10 ). In general, Ni is considered to be (3d
9.4 4s
0.6 ). It is well known that
the d-band is very narrow, hence m
∗
d m e , where m
∗
d /m e = mass of the electrons
at d-band/free state. Since the s-band is nearly free, m
∗
s ∼ m e , where m
∗
s = mass of
the electrons at s-band.