Spin Transfer Torque Magnetoresistive Random Access Memory
55
are not collinear with the free layer magnetization, each itinerant electron will align
itself with the localized moment due to exchange interaction. As a consequence, the
component of the moment s normal to the free layer magnetization M will be lost.
However, the loss in s will be absorbed by the free layer in the form of a torque due to
the conservation of angular momentum. With an adequate amount of spin polarized
current, either steady state precession or magnetization reversal may be induced.
To switch from parallel to anti-parallel configuration, the electron current would
have to be sent from the free layer downwards, as depicted in Fig. 6b. The up-spins,
being aligned in the same direction as the reference layer, will transmit through the
MTJ with ease, while the down-spins will get reflected by the reference layer. These
reflected spins will then exert the torque in the same manner as previously described.
STT is a localized effect occurring at the interface between the tunnel barrier and
the free layer. Therefore, by summing up the torque exerted by each spin polarized
electron s onto the free layer with magnetization M and volume V, the rate of change
of free layer magnetization due to the torque τ || exerted along the same plane as M,
can be expressed as:
d M
dt
τ ||
=
1
V
P
d N
dt
gμ B
2M s
(M × (M × s)) = τ || (M × (M × s)),
(10)
where P is the spin polarization efficiency,
d N
dt
=
I
e
is the rate of unpolarized electron
flow per unit time, g is the Landé g-factor, μ B is the Bohr magneton, and M s is the
saturation magnetization of the free layer for normalization. Equation (10) is also
known as the in-plane torque term, which will be useful in describe the magnetization
dynamics (see Sect. 3.4). The amount of torque induced on the free layer magnetization is also dependent on the relative alignment between the spin polarized current
and the free layer moment (assuming a macrospin approximation).
In addition, an additional torque τ ⊥ perpendicular to the M may be induced in the
case of a 3D model if the spin moment s has an out-of-plane component. The origin
of τ ⊥ remains under hot debate, but its effect is similar to an external magnetic field
and can be described as:
d M
dt
τ ⊥
= τ ⊥ (M × s).
(11)
3.3 Magnetization Energies
The origin of magnetism arises from quantum mechanism; wherein an electron, in
addition to its intrinsic spin angular momentum, has an orbital angular momentum
which gives rise to a magnetic moment. These electrons, each generating its own
dipole moment (expressed in Bohr magnetons), fill in the lowest possible energy
55
are not collinear with the free layer magnetization, each itinerant electron will align
itself with the localized moment due to exchange interaction. As a consequence, the
component of the moment s normal to the free layer magnetization M will be lost.
However, the loss in s will be absorbed by the free layer in the form of a torque due to
the conservation of angular momentum. With an adequate amount of spin polarized
current, either steady state precession or magnetization reversal may be induced.
To switch from parallel to anti-parallel configuration, the electron current would
have to be sent from the free layer downwards, as depicted in Fig. 6b. The up-spins,
being aligned in the same direction as the reference layer, will transmit through the
MTJ with ease, while the down-spins will get reflected by the reference layer. These
reflected spins will then exert the torque in the same manner as previously described.
STT is a localized effect occurring at the interface between the tunnel barrier and
the free layer. Therefore, by summing up the torque exerted by each spin polarized
electron s onto the free layer with magnetization M and volume V, the rate of change
of free layer magnetization due to the torque τ || exerted along the same plane as M,
can be expressed as:
d M
dt
τ ||
=
1
V
P
d N
dt
gμ B
2M s
(M × (M × s)) = τ || (M × (M × s)),
(10)
where P is the spin polarization efficiency,
d N
dt
=
I
e
is the rate of unpolarized electron
flow per unit time, g is the Landé g-factor, μ B is the Bohr magneton, and M s is the
saturation magnetization of the free layer for normalization. Equation (10) is also
known as the in-plane torque term, which will be useful in describe the magnetization
dynamics (see Sect. 3.4). The amount of torque induced on the free layer magnetization is also dependent on the relative alignment between the spin polarized current
and the free layer moment (assuming a macrospin approximation).
In addition, an additional torque τ ⊥ perpendicular to the M may be induced in the
case of a 3D model if the spin moment s has an out-of-plane component. The origin
of τ ⊥ remains under hot debate, but its effect is similar to an external magnetic field
and can be described as:
d M
dt
τ ⊥
= τ ⊥ (M × s).
(11)
3.3 Magnetization Energies
The origin of magnetism arises from quantum mechanism; wherein an electron, in
addition to its intrinsic spin angular momentum, has an orbital angular momentum
which gives rise to a magnetic moment. These electrons, each generating its own
dipole moment (expressed in Bohr magnetons), fill in the lowest possible energy