8
1 An Overview of Spintronics
atom, whose L = 0, was done by T. E. Phipps, and J. B. Taylor reproduced the two
spots effect (Phipps and Taylor 1927). This posed a problem to Bohr–Sommerfeld
hypothesis. The interpretation of Stern–Gerlach’s results, nowadays, is referred to the
electrons having a magnetic moment called spin. However, the concept of electron
spin was first proposed in 1925 by Ralph De LaerKronig, Goudsmit and Uhlenbeck
in order to explain the fine structures in the atomic spectra in the presence of external
magnetic field known as Zeeman effect. While the quantum mechanics with three
quantum numbers n, l and m could not explain the fine structures, a fourth quantum
number was needed. Goudsmit and Uhlenbeck suggested the idea of spinning electron, which gives rise to an angular momentum in addition to the orbital angular
momentum (Goudsmit and Uhlenbeck 1926). The idea of spinning electron did not
convince Wolfgang Pauli, who argued that the electron is so small that it needs to
rotate around itself with the speed of light in order to give rise to the measured angular
momentum.
1.5 Quantum Mechanics of Spin
Theory of quantum mechanics, consisting of Heisenberg’s matrix mechanics and
Schrödinger’s wave mechanics, predicts energy quantization and suggests a way
to find out the energy difference between the levels. Moreover, it also allows one
to calculate the probability of transition between the energy states having different
quantization level. In wave mechanics, the wavefunction evolution with time and
space for a single particle can be written by Schrödinger’s equation as follows:
i
dψ( r )
dt
= H 0 · ψ( r ).
(1.1)
Neglecting spin, we may write
H 0 =
|
p|
2
2m
+ V ( r )
p = p x ˆ
x + p y ˆ
y + p z ˆ
z = −i
d
dx
ˆ
x − i
d
dy
ˆ
y − i
d
dz
ˆ
z
r =
x ˆ
x + y ˆ
y + z ˆ
z
, t
(1.2)
where ‘hats’ indicates unit vectors along the axes of coordinates. It is noteworthy that
Eq. (1.1) does not include the spin part. Hence the question raises, how to include
the ‘spin’ part?
1 An Overview of Spintronics
atom, whose L = 0, was done by T. E. Phipps, and J. B. Taylor reproduced the two
spots effect (Phipps and Taylor 1927). This posed a problem to Bohr–Sommerfeld
hypothesis. The interpretation of Stern–Gerlach’s results, nowadays, is referred to the
electrons having a magnetic moment called spin. However, the concept of electron
spin was first proposed in 1925 by Ralph De LaerKronig, Goudsmit and Uhlenbeck
in order to explain the fine structures in the atomic spectra in the presence of external
magnetic field known as Zeeman effect. While the quantum mechanics with three
quantum numbers n, l and m could not explain the fine structures, a fourth quantum
number was needed. Goudsmit and Uhlenbeck suggested the idea of spinning electron, which gives rise to an angular momentum in addition to the orbital angular
momentum (Goudsmit and Uhlenbeck 1926). The idea of spinning electron did not
convince Wolfgang Pauli, who argued that the electron is so small that it needs to
rotate around itself with the speed of light in order to give rise to the measured angular
momentum.
1.5 Quantum Mechanics of Spin
Theory of quantum mechanics, consisting of Heisenberg’s matrix mechanics and
Schrödinger’s wave mechanics, predicts energy quantization and suggests a way
to find out the energy difference between the levels. Moreover, it also allows one
to calculate the probability of transition between the energy states having different
quantization level. In wave mechanics, the wavefunction evolution with time and
space for a single particle can be written by Schrödinger’s equation as follows:
i
dψ( r )
dt
= H 0 · ψ( r ).
(1.1)
Neglecting spin, we may write
H 0 =
|
p|
2
2m
+ V ( r )
p = p x ˆ
x + p y ˆ
y + p z ˆ
z = −i
d
dx
ˆ
x − i
d
dy
ˆ
y − i
d
dz
ˆ
z
r =
x ˆ
x + y ˆ
y + z ˆ
z
, t
(1.2)
where ‘hats’ indicates unit vectors along the axes of coordinates. It is noteworthy that
Eq. (1.1) does not include the spin part. Hence the question raises, how to include
the ‘spin’ part?