Current-Driven Domain Wall Dynamics in Magnetic …
111
would be more dominant if K u V ≤ 60k B T [24]s, where K U V is the product of
perpendicular anisotropy constant and the magnetic volume. For our device, K U =
1.88 × 10
5 J/m
3 , V = 1.5 × 10
–6 (width) × 2.8 × 10
–9 (thickness) × 8 × 10
–9 (DW
width), where DW width is estimated using =
√
A/K U and A = 1 × 10
–11 J/m
[25]. This gives the product K U V = 40 eV, which is 1400k B T. Thus temperature
alone cannot account for compensating the anisotropy.
3 Current-Induced Domain Wall Driving
In the previous section, we have discussed various methods of the DW injection
in nanowires. These DWs are then shifted to the read sensor for the operation of a
memory device. There are two main methods to drive the DWs: by magnetic fields and
by electric currents. The magnetic field induces bi-directional motion of DWs i.e. the
magnetic domain that are oriented parallel to the external magnetic field expand while
the magnetic domains oriented antiparallel to the external magnetic field shrinks.
3
In the case of electric current, all the DWs move in the same direction that makes
current-driven DW dynamics important to be studied for device application. Here, we
describe the mechanisms of DW dynamics induced by current. Two torque transfer
mechanisms have been proposed in literature namely, spin-transfer torque (STT) in
conventional ferromagnets [26–28]. and spin–orbit torques (SOTs) in systems with
heavy-metal and ferromagnetic interface[29–31]. The magnetization dynamics is
governed by the Landau-Lifshitz-Gilbert (LLG) equation which is discussed in the
following sections.
3.1 Spin-Transfer Torque Driven Domain Wall Dynamics
In this section, we will discuss how a DW is driven in order to transfer the data from
the strip-line to the read sensor. The first method is through direct application of electrical current to the ferromagnetic nanowire [18, 32–34]. By doing so, the injected
current will be spin polarized as it travels through the ferromagnetic nanowire due to
the spin polarization effect. When the conduction electrons or unpolarized spins are
injected into a ferromagnetic wire of a specific magnetization direction, the unpolarized spins are scattered by local magnetic moments through s-d [35] or s-f [36]
exchange interactions. The spins which are parallel to the local magnetic moments
are less scattered while the others are more scattered. The spin dependent scattering
generates spin current in which majority of the spins of conduction electrons become
aligned along the direction of the local magnetic moments. A schematic illustrating
3 Spin Dynamics in Confined Magnetic Structures III. Edited by Burkard Hillebrands and Andre
Thiaville. Series: Topics in Applied Physics. 2006, Springer, ISBN: 9,783,540,398,424.
111
would be more dominant if K u V ≤ 60k B T [24]s, where K U V is the product of
perpendicular anisotropy constant and the magnetic volume. For our device, K U =
1.88 × 10
5 J/m
3 , V = 1.5 × 10
–6 (width) × 2.8 × 10
–9 (thickness) × 8 × 10
–9 (DW
width), where DW width is estimated using =
√
A/K U and A = 1 × 10
–11 J/m
[25]. This gives the product K U V = 40 eV, which is 1400k B T. Thus temperature
alone cannot account for compensating the anisotropy.
3 Current-Induced Domain Wall Driving
In the previous section, we have discussed various methods of the DW injection
in nanowires. These DWs are then shifted to the read sensor for the operation of a
memory device. There are two main methods to drive the DWs: by magnetic fields and
by electric currents. The magnetic field induces bi-directional motion of DWs i.e. the
magnetic domain that are oriented parallel to the external magnetic field expand while
the magnetic domains oriented antiparallel to the external magnetic field shrinks.
3
In the case of electric current, all the DWs move in the same direction that makes
current-driven DW dynamics important to be studied for device application. Here, we
describe the mechanisms of DW dynamics induced by current. Two torque transfer
mechanisms have been proposed in literature namely, spin-transfer torque (STT) in
conventional ferromagnets [26–28]. and spin–orbit torques (SOTs) in systems with
heavy-metal and ferromagnetic interface[29–31]. The magnetization dynamics is
governed by the Landau-Lifshitz-Gilbert (LLG) equation which is discussed in the
following sections.
3.1 Spin-Transfer Torque Driven Domain Wall Dynamics
In this section, we will discuss how a DW is driven in order to transfer the data from
the strip-line to the read sensor. The first method is through direct application of electrical current to the ferromagnetic nanowire [18, 32–34]. By doing so, the injected
current will be spin polarized as it travels through the ferromagnetic nanowire due to
the spin polarization effect. When the conduction electrons or unpolarized spins are
injected into a ferromagnetic wire of a specific magnetization direction, the unpolarized spins are scattered by local magnetic moments through s-d [35] or s-f [36]
exchange interactions. The spins which are parallel to the local magnetic moments
are less scattered while the others are more scattered. The spin dependent scattering
generates spin current in which majority of the spins of conduction electrons become
aligned along the direction of the local magnetic moments. A schematic illustrating
3 Spin Dynamics in Confined Magnetic Structures III. Edited by Burkard Hillebrands and Andre
Thiaville. Series: Topics in Applied Physics. 2006, Springer, ISBN: 9,783,540,398,424.