5 Spintronics and Synchrotron Radiation
143
following form, taking magnetizations normalized to the saturation magnetization,
m i=1,2 for the two FM layers
d − →
m 2
dt
= −γ 0 ( − →
m 2 ×
− →
H e f f ) +
α
γ 0 M S2
( − →
m 2 ×
d − →
m 2
dt
) − P spin
J
e
h
2
gμ B
M 2
S2 t
[ − →
m 2 × ( − →
m 2 × − →
m 1 )]
(5.6)
The first term corresponds to the tangential force describing the magnetization
precession around effective field
− →
H e f f [green arrow in Fig. 5.7c], which takes into
account the external applied magnetic field, magnetic anisotropy fields, coupling
fields, etc. The second term gives a phenomenological description of magnetization
dissipation of the system. The coefficient α, named Gilbert damping, (about 10
−2
for standard FM materials), describes the damping rate of the motion of − →
m 2 towards
the equilibrium position oriented along
− →
H e f f [blue arrow in Fig. 5.7c]. The magnetization relaxation is induced by a damping force tangential to the magnetization
trajectory. The third term is the so-called Slonczewski torque (or in-plane torque)
where μ B is the Bohr magneton, t the layer thickness, J the injected current density,
and P spin the amplitude of spin polarization at the interface NM/F 2 and M S2 the magnetization of the ferromagnet F 2 . This simplified description allows making clear the
nature of the main contribution of the spin-transfer force that can be described as
a non-conservative force acting in the same direction than the natural damping, i.e.
perpendicularly to the magnetization trajectory. Depending on the sign of the injected
current, the spin-transfer torque decreases or increases the effective damping [purple
and red arrows in Fig. 5.7c]; it favours the stability of the parallel or the antiparallel
magnetic configuration.
For large current density (∼10
7 A cm
−2 for a typical material system), the STT
fully compensates the damping torque, steady magnetization precession occurring at
the ferromagnetic frequency (typical in the GHz range for the ferromagnetic materials
and in the THz range for antiferromagnetic ones) can be established. The spin transfer
induced magnetization dynamics can convert into oscillations of resistance through
the magnetoresistive effect described previously, and in turn into a radiofrequency
voltage signal. Spin-torque effect thus makes it possible to convert a dc current into
a rf voltage and so to build microwave oscillators at the nanoscale.
For larger current density, the torque can become sufficient to commute the
magnetization between the two stable configurations. A negative current will, for
instance, destabilize the parallel magnetization configuration, while stabilizing the
anti-parallel configuration, allowing to commute from P to AP configuration. Identically, a positive current allows to commute from AP to P configuration.
First experimental results allowing to confirm the theoretical predictions of the
existence of STTs have been obtained by M. Tsoi et al., using point contact geometry for injection of a large current into a magnetic layer [24]. Then after, it has been
demonstrated that magnetization commutation can be achieved back and forth by the
STT effect in Co/Cu/Co spin valves [25]. Figure 5.8a represents magnetization rever-
143
following form, taking magnetizations normalized to the saturation magnetization,
m i=1,2 for the two FM layers
d − →
m 2
dt
= −γ 0 ( − →
m 2 ×
− →
H e f f ) +
α
γ 0 M S2
( − →
m 2 ×
d − →
m 2
dt
) − P spin
J
e
h
2
gμ B
M 2
S2 t
[ − →
m 2 × ( − →
m 2 × − →
m 1 )]
(5.6)
The first term corresponds to the tangential force describing the magnetization
precession around effective field
− →
H e f f [green arrow in Fig. 5.7c], which takes into
account the external applied magnetic field, magnetic anisotropy fields, coupling
fields, etc. The second term gives a phenomenological description of magnetization
dissipation of the system. The coefficient α, named Gilbert damping, (about 10
−2
for standard FM materials), describes the damping rate of the motion of − →
m 2 towards
the equilibrium position oriented along
− →
H e f f [blue arrow in Fig. 5.7c]. The magnetization relaxation is induced by a damping force tangential to the magnetization
trajectory. The third term is the so-called Slonczewski torque (or in-plane torque)
where μ B is the Bohr magneton, t the layer thickness, J the injected current density,
and P spin the amplitude of spin polarization at the interface NM/F 2 and M S2 the magnetization of the ferromagnet F 2 . This simplified description allows making clear the
nature of the main contribution of the spin-transfer force that can be described as
a non-conservative force acting in the same direction than the natural damping, i.e.
perpendicularly to the magnetization trajectory. Depending on the sign of the injected
current, the spin-transfer torque decreases or increases the effective damping [purple
and red arrows in Fig. 5.7c]; it favours the stability of the parallel or the antiparallel
magnetic configuration.
For large current density (∼10
7 A cm
−2 for a typical material system), the STT
fully compensates the damping torque, steady magnetization precession occurring at
the ferromagnetic frequency (typical in the GHz range for the ferromagnetic materials
and in the THz range for antiferromagnetic ones) can be established. The spin transfer
induced magnetization dynamics can convert into oscillations of resistance through
the magnetoresistive effect described previously, and in turn into a radiofrequency
voltage signal. Spin-torque effect thus makes it possible to convert a dc current into
a rf voltage and so to build microwave oscillators at the nanoscale.
For larger current density, the torque can become sufficient to commute the
magnetization between the two stable configurations. A negative current will, for
instance, destabilize the parallel magnetization configuration, while stabilizing the
anti-parallel configuration, allowing to commute from P to AP configuration. Identically, a positive current allows to commute from AP to P configuration.
First experimental results allowing to confirm the theoretical predictions of the
existence of STTs have been obtained by M. Tsoi et al., using point contact geometry for injection of a large current into a magnetic layer [24]. Then after, it has been
demonstrated that magnetization commutation can be achieved back and forth by the
STT effect in Co/Cu/Co spin valves [25]. Figure 5.8a represents magnetization rever-