118
S. Krishnia and W. S. Lew
Fig. 12 a–c Magnetic contrast of a PMA wire measured using differential Kerr microscopy. d–
f Schematic showing the directions of the field like torque (T NA ) due to Rashba field. g High
speed DW velocity in PMA wire with current density. The current-induced DW motion exhibits
creep and flow regimes similar to the field-driven DW motion. The solid line is the liner fit to the
DW flow regime. Inset shows the field-driven DW velocity to compare the field-like nature of the
current-induced Rashba field [56]
the spin–orbit coupling due to broken inversion asymmetry [64]. The asymmetric
exchange interaction is often called Dzyaloshinskii-Moriya interaction (DMI). The
proposed mechanism explains the direction and large velocities of the DWs without
any signature of Walker breakdown. The mechanism of DMI is explained in next
section.
3.2.2 Dzyaloshinskii-Moriya Interaction
The Dzyaloshinskii-Moriya interaction (DMI) is a three-site antisymmetric exchange
interaction and known to originate when magnetic thin films are interfaced with a
strong spin–orbit coupling materials [65–67]. It is an indirect interaction between
two atomic spins S i and S j through an atom of high spin–orbit coupling, located in
the adjacent heavy metal layer. The energy associated with the DM interaction, the
DMI energy (E DM ) is often given byE DM = D i j ·
S i × S j
,
(7)
here, D ij is the DM interaction vector and its direction depends on the studied
system. For a ferromagnetic thin film that is grown on heavy metal of high spin–orbit
coupling, the DMI constant is given byD i j = d u i j × z,
(8)
where, u ij is the unit distance vector between the two spins S i and S j , z is the unit
vector perpendicular to the thin film plane from heavy metal to ferromagnetic thin
film and d is a coefficient proportional to the spin–orbit coupling [68]. The DM
S. Krishnia and W. S. Lew
Fig. 12 a–c Magnetic contrast of a PMA wire measured using differential Kerr microscopy. d–
f Schematic showing the directions of the field like torque (T NA ) due to Rashba field. g High
speed DW velocity in PMA wire with current density. The current-induced DW motion exhibits
creep and flow regimes similar to the field-driven DW motion. The solid line is the liner fit to the
DW flow regime. Inset shows the field-driven DW velocity to compare the field-like nature of the
current-induced Rashba field [56]
the spin–orbit coupling due to broken inversion asymmetry [64]. The asymmetric
exchange interaction is often called Dzyaloshinskii-Moriya interaction (DMI). The
proposed mechanism explains the direction and large velocities of the DWs without
any signature of Walker breakdown. The mechanism of DMI is explained in next
section.
3.2.2 Dzyaloshinskii-Moriya Interaction
The Dzyaloshinskii-Moriya interaction (DMI) is a three-site antisymmetric exchange
interaction and known to originate when magnetic thin films are interfaced with a
strong spin–orbit coupling materials [65–67]. It is an indirect interaction between
two atomic spins S i and S j through an atom of high spin–orbit coupling, located in
the adjacent heavy metal layer. The energy associated with the DM interaction, the
DMI energy (E DM ) is often given byE DM = D i j ·
S i × S j
,
(7)
here, D ij is the DM interaction vector and its direction depends on the studied
system. For a ferromagnetic thin film that is grown on heavy metal of high spin–orbit
coupling, the DMI constant is given byD i j = d u i j × z,
(8)
where, u ij is the unit distance vector between the two spins S i and S j , z is the unit
vector perpendicular to the thin film plane from heavy metal to ferromagnetic thin
film and d is a coefficient proportional to the spin–orbit coupling [68]. The DM