Chapter 3
Giant Magnetoresistance (GMR)
3.1 Introduction to Magnetoresistance
Magnetoresistance (MR) property of a material/system refers to the change in its
electrical resistance, when the magnetic field is turned on. MR
ρ
ρ
is usually
defined by
ρ
ρ
=
R(H) − R(0)
R(0)
(3.1)
The effect was first discovered by William Thomson, more commonly known
as Lord Kelvin, in 1856. He demonstrated a change in the electrical resistance of
ferromagnetic materials, e.g., iron sample by applying an external magnetic field.
He showed that the resistance increases by 0.2% when the current and the applied
magnetic field are in the same direction, while it decreases by 0.4% when they are
perpendicular to each other. In this case, MR occurs because the drift velocity (v) of
all the charge carriers is not supposed to be identical. Now, application of magnetic
field
H
to a crystal of thickness t gives rise to Hall voltage given by, V = E y
t =
v ×
H
, where
v denotes the drift velocity and
E is the applied transport
driving electric field. The details of Hall effect and the voltage created by this effect
are not within the scope of this book. Such Hall voltage compensates exactly the
Lorentz force for carriers with average velocity. This means that charge carriers,
which are comparatively slow moving, will be compensated to a large extent and can
be considered as overcompensated. On the other hand, charge carriers that are pretty
fast-moving carriers will not be compensated to a reasonable extent, i.e., they can
be considered as undercompensated. This in turn results in trajectories and those are
not lying along the applied magnetic field. Consequently, there is a rise in resistivity
caused by an effective fall in the mean free path. This leads to positive MR. Thus, in
general, a positive MR is expected which is referred to as ordinary MR. Interestingly,
© Springer Nature Singapore Pte Ltd. 2021
P. Dey and J. N. Roy, Spintronics,
https://doi.org/10.1007/978-981-16-0069-2_3
75
Giant Magnetoresistance (GMR)
3.1 Introduction to Magnetoresistance
Magnetoresistance (MR) property of a material/system refers to the change in its
electrical resistance, when the magnetic field is turned on. MR
ρ
ρ
is usually
defined by
ρ
ρ
=
R(H) − R(0)
R(0)
(3.1)
The effect was first discovered by William Thomson, more commonly known
as Lord Kelvin, in 1856. He demonstrated a change in the electrical resistance of
ferromagnetic materials, e.g., iron sample by applying an external magnetic field.
He showed that the resistance increases by 0.2% when the current and the applied
magnetic field are in the same direction, while it decreases by 0.4% when they are
perpendicular to each other. In this case, MR occurs because the drift velocity (v) of
all the charge carriers is not supposed to be identical. Now, application of magnetic
field
H
to a crystal of thickness t gives rise to Hall voltage given by, V = E y
t =
v ×
H
, where
v denotes the drift velocity and
E is the applied transport
driving electric field. The details of Hall effect and the voltage created by this effect
are not within the scope of this book. Such Hall voltage compensates exactly the
Lorentz force for carriers with average velocity. This means that charge carriers,
which are comparatively slow moving, will be compensated to a large extent and can
be considered as overcompensated. On the other hand, charge carriers that are pretty
fast-moving carriers will not be compensated to a reasonable extent, i.e., they can
be considered as undercompensated. This in turn results in trajectories and those are
not lying along the applied magnetic field. Consequently, there is a rise in resistivity
caused by an effective fall in the mean free path. This leads to positive MR. Thus, in
general, a positive MR is expected which is referred to as ordinary MR. Interestingly,
© Springer Nature Singapore Pte Ltd. 2021
P. Dey and J. N. Roy, Spintronics,
https://doi.org/10.1007/978-981-16-0069-2_3
75