196
M. Mochizuki
the microwave magnetic field cannot avoid activating the intense ferromagnetic resonance mode, which inevitably results in large loss of energy and significant rise of
temperature.
To drive isolated skyrmions in the ferromagnetic phase efficiently, it is necessary to activate the skyrmions selectively avoiding the situation that the weak
skyrmion resonance modes are masked by the intense ferromagnetic resonance
mode. This seemingly impossible operation can be achieved by taking advantage
of the microwave electric field. More concretely, when a microwave electric field is
applied to a magnetic bilayer system or a thin-film specimen of chiral-lattice magnet
fabricated on insulating substrate, the isolated skyrmions can be selectively activated
through temporal variation of the extent of spatial inversion asymmetry and resulting temporal oscillation of the Dzyaloshinskii-Moriya interaction. The calculated
microwave absorption spectra (the imaginary parts of the electromagnetic susceptibilities Imχ
em ) in this case are displayed in Fig. 8.6b, which clearly show selective
activations of the resonance modes of the skyrmion defect.
When the spin-wave modes of isolated skyrmions are activated in a system shown
in Fig. 8.6c with a microwave electric field, their translational motion can be driven
as shown in Fig. 8.6d. Figure 8.6e displays trajectories of the skyrmion translational
motion when a microwave electric field with each resonance frequency is applied
for a certain duration (Note that the length scale is different between the horizontal
and vertical axes). Interestingly, the breathing mode turns out to drive the skyrmion
most quickly although the intensity of this mode is not so large.
Another interesting aspect to be mentioned is the trajectory is straight and exactly
parallel to the x axis (direction toward which the H ex field is tilted) when the counterclockwise rotation mode is excited. It is recognized that one of the most promising
forms of the skyrmion-based magnetic memories is the skyrmion race track memory
based on the skyrmion motion in magnetic nanowires driven by a spin-polarized
electric current, which can be regarded as the race track memory with its ferromagnetic domains being replaced with magnetic skyrmions. However, one of the critical
problems that hinders its realization is the skyrmion Hall effect. The current-driven
skyrmions have not only a velocity component parallel to the electric current but
also that perpendicular to it. Due to this effect, the skyrmion cannot avoid colliding
to the horizontal edges of devices, which results in absorption and pinning of the
skyrmions. In contrast to the current-driven case, we can achieve the translational
motion of skyrmions exactly parallel to the nanowire and thus can avoid this kind
of problem when we drive them by microwave irradiation under a tilted H ext field.
For the breathing mode and the clockwise rotation mode, the skyrmion moves in a
direction slanted from the tilting direction of the H ex field. Even in these cases, we
can achieve the skyrmion motion exactly parallel to the nanowire by tuning the tilting
direction of H ex . It is always possible to realize the straight and parallel skyrmion
motion in a nanowire without collision to the edges in this way because the H ex field
can be oriented in an arbitrary direction in contrast to an electric current flowing
always along the nanowire.
M. Mochizuki
the microwave magnetic field cannot avoid activating the intense ferromagnetic resonance mode, which inevitably results in large loss of energy and significant rise of
temperature.
To drive isolated skyrmions in the ferromagnetic phase efficiently, it is necessary to activate the skyrmions selectively avoiding the situation that the weak
skyrmion resonance modes are masked by the intense ferromagnetic resonance
mode. This seemingly impossible operation can be achieved by taking advantage
of the microwave electric field. More concretely, when a microwave electric field is
applied to a magnetic bilayer system or a thin-film specimen of chiral-lattice magnet
fabricated on insulating substrate, the isolated skyrmions can be selectively activated
through temporal variation of the extent of spatial inversion asymmetry and resulting temporal oscillation of the Dzyaloshinskii-Moriya interaction. The calculated
microwave absorption spectra (the imaginary parts of the electromagnetic susceptibilities Imχ
em ) in this case are displayed in Fig. 8.6b, which clearly show selective
activations of the resonance modes of the skyrmion defect.
When the spin-wave modes of isolated skyrmions are activated in a system shown
in Fig. 8.6c with a microwave electric field, their translational motion can be driven
as shown in Fig. 8.6d. Figure 8.6e displays trajectories of the skyrmion translational
motion when a microwave electric field with each resonance frequency is applied
for a certain duration (Note that the length scale is different between the horizontal
and vertical axes). Interestingly, the breathing mode turns out to drive the skyrmion
most quickly although the intensity of this mode is not so large.
Another interesting aspect to be mentioned is the trajectory is straight and exactly
parallel to the x axis (direction toward which the H ex field is tilted) when the counterclockwise rotation mode is excited. It is recognized that one of the most promising
forms of the skyrmion-based magnetic memories is the skyrmion race track memory
based on the skyrmion motion in magnetic nanowires driven by a spin-polarized
electric current, which can be regarded as the race track memory with its ferromagnetic domains being replaced with magnetic skyrmions. However, one of the critical
problems that hinders its realization is the skyrmion Hall effect. The current-driven
skyrmions have not only a velocity component parallel to the electric current but
also that perpendicular to it. Due to this effect, the skyrmion cannot avoid colliding
to the horizontal edges of devices, which results in absorption and pinning of the
skyrmions. In contrast to the current-driven case, we can achieve the translational
motion of skyrmions exactly parallel to the nanowire and thus can avoid this kind
of problem when we drive them by microwave irradiation under a tilted H ext field.
For the breathing mode and the clockwise rotation mode, the skyrmion moves in a
direction slanted from the tilting direction of the H ex field. Even in these cases, we
can achieve the skyrmion motion exactly parallel to the nanowire by tuning the tilting
direction of H ex . It is always possible to realize the straight and parallel skyrmion
motion in a nanowire without collision to the edges in this way because the H ex field
can be oriented in an arbitrary direction in contrast to an electric current flowing
always along the nanowire.