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K. Lee et al.
racetrack memory, essentially requiring unidirectional motion of all DWs, is very
difficult to implement with a field-driven scheme.
To overcome these obstacles, spin-transfer torque (STT), originally proposed by
Berger and Slonczewski [4, 5], was suggested as an alternative means to drive DW
motion. A simple concept of STT is illustrated in Fig. 2. When conduction electrons
pass through a magnetic metal with a uniform magnetization, they become spinpolarized in the direction of the magnetization of the ferromagnet. As these spinpolarized electrons cross a DW, their spins are flipped as they track the locally varying
magnetization in the DW, resulting in a change in the spin angular momentum of
the electrons. Since the total angular momentum should be conserved in the system,
the change in the spin angular momentum of the conduction electrons results in a
change in the angular momentum of the magnetic moments.
In addition to the adiabatic STT, there exist an additional STT arising from a
deviation from the adiabatic process. When the electron spins are passing through
a DW, for example, with a relatively narrow DW width, the electrons’ spins cannot
adiabatically follow the magnetization profile within the DW anymore. Consequently,
it may lead to the spatial mistracking of spins between the conduction electrons and
the local magnetization. This mistracking of electrons’ spins then introduces another
torque namely the non-adiabatic STT, which has an effect similar to that of a magnetic
field.
The DWs driven by the STTs can be understood by using the Landau-LifshitzGilbert (LLG) equation incorporated with the STTs acting on the local magnetization
(m) within the DWs [7, 8]:
˙
m = −γ 0 m × H + αm × ˙
m − (u · ∇)m + βm × [(u · ∇)m]
(1)
Here, γ is the gyromagnetic ratio, α the Gilbert damping parameter, H the effective
magnetic field, and u the spin drift velocity which is u = gμ B PJ e /2|e|M S , where
g is the g-factor, μ B Bohr magnetron, P spin polarization, e the electron charge, M s
the saturation magnetization, and J e the current density vector with its direction in
the electron flow. The first and second terms on the right side of the equation are the
general torques exerted by the effective magnetic field and damping, respectively. The
third and fourth terms represent the adiabatic and non-adiabatic STTs. For the case
of the DW motion driven by the adiabatic STT, it is known that this always requires
a threshold current density due to the intrinsic energy barrier originating from its
mechanism to drive the DW. Figure 3a. illustrates how the adiabatic STT can drive
the DW motion. For an in-plane magnetized thin film, when the electric current
is applied into +x direction, for example, the adiabatic STT is exerted on the local
magnetic moment oriented in the transverse direction of the wire axis pushing toward
the –x direction. The precession of m driven by the STT initiates a damping torque
perpendicular to the STT (+z), and this leads to the canting of the magnetization into
the out of plane direction. The canting creates magnetic surface charges at the film
surface, generating a demagnetizing field H d against to the creation of the magnetic
surface charges. The demagnetization field provides an additional precession torque
(+x) and a damping torque (−z). In this case, these four torques all cancel out.
K. Lee et al.
racetrack memory, essentially requiring unidirectional motion of all DWs, is very
difficult to implement with a field-driven scheme.
To overcome these obstacles, spin-transfer torque (STT), originally proposed by
Berger and Slonczewski [4, 5], was suggested as an alternative means to drive DW
motion. A simple concept of STT is illustrated in Fig. 2. When conduction electrons
pass through a magnetic metal with a uniform magnetization, they become spinpolarized in the direction of the magnetization of the ferromagnet. As these spinpolarized electrons cross a DW, their spins are flipped as they track the locally varying
magnetization in the DW, resulting in a change in the spin angular momentum of
the electrons. Since the total angular momentum should be conserved in the system,
the change in the spin angular momentum of the conduction electrons results in a
change in the angular momentum of the magnetic moments.
In addition to the adiabatic STT, there exist an additional STT arising from a
deviation from the adiabatic process. When the electron spins are passing through
a DW, for example, with a relatively narrow DW width, the electrons’ spins cannot
adiabatically follow the magnetization profile within the DW anymore. Consequently,
it may lead to the spatial mistracking of spins between the conduction electrons and
the local magnetization. This mistracking of electrons’ spins then introduces another
torque namely the non-adiabatic STT, which has an effect similar to that of a magnetic
field.
The DWs driven by the STTs can be understood by using the Landau-LifshitzGilbert (LLG) equation incorporated with the STTs acting on the local magnetization
(m) within the DWs [7, 8]:
˙
m = −γ 0 m × H + αm × ˙
m − (u · ∇)m + βm × [(u · ∇)m]
(1)
Here, γ is the gyromagnetic ratio, α the Gilbert damping parameter, H the effective
magnetic field, and u the spin drift velocity which is u = gμ B PJ e /2|e|M S , where
g is the g-factor, μ B Bohr magnetron, P spin polarization, e the electron charge, M s
the saturation magnetization, and J e the current density vector with its direction in
the electron flow. The first and second terms on the right side of the equation are the
general torques exerted by the effective magnetic field and damping, respectively. The
third and fourth terms represent the adiabatic and non-adiabatic STTs. For the case
of the DW motion driven by the adiabatic STT, it is known that this always requires
a threshold current density due to the intrinsic energy barrier originating from its
mechanism to drive the DW. Figure 3a. illustrates how the adiabatic STT can drive
the DW motion. For an in-plane magnetized thin film, when the electric current
is applied into +x direction, for example, the adiabatic STT is exerted on the local
magnetic moment oriented in the transverse direction of the wire axis pushing toward
the –x direction. The precession of m driven by the STT initiates a damping torque
perpendicular to the STT (+z), and this leads to the canting of the magnetization into
the out of plane direction. The canting creates magnetic surface charges at the film
surface, generating a demagnetizing field H d against to the creation of the magnetic
surface charges. The demagnetization field provides an additional precession torque
(+x) and a damping torque (−z). In this case, these four torques all cancel out.