204
M. Mochizuki
1
2
0
Time (×10 3 /J)
0.5
1.5
1
2
0
Time (×10 3 /J)
0.5
1.5
0
5
-5
V
x (
V)
2
(a)
(b)
(c)
(d)
H ||x
0
5
-5
0
2
-2
0
-2
Hex
x
y
z
2
Hz
x
y
z
Hx
30°
CCW Rotation mode
Breathing mode
V
x ( V)
V
x ( V)
V
x ( V)
=0°
=30°
Hex
V x =4.24 V
V x =0 V
AC
DC
H =3×10 -3
H ||z
=0.05452
V x =0 V
V x =0 V
AC
DC
H =2×10 -3
=0.06182
V x =2.65 V
V x = 1.19 V
AC
DC
H =3×10 -3
=0.04938
V x =1.81 V
V x =0.56 V
AC
DC
H =2×10 -3
=0.06664
-0.05
0
V
x ( V)
DC
-0.025
Vx
DC
Vx
DC
H ||x
H ||y
0.02
0.04
0.06
0.08
0.1
-0.025
0
0.025
Vy
DC
Vy
DC
H ||x
H ||y
(e)
(f)
-0.025
0.05
0
0
0.02
0.02
0.04
0.06
0.08
0.1
0.12
Vx
DC H ||z
Vy
DC H ||z
(g)
(h)
Frequency
Frequency
Rotation
(CW)
=0.08721
V
y (
V)
DC
Rotation
(CCW)
=0.04938
Breathing
=0.08721
V
x ( V)
DC
V
y ( V)
DC
Rotation
(CCW)
=0.04938
Breathing
=0.08721
Rotation(CW)
=0.08721
Fig. 8.9 a, b Calculated time profiles of spin voltages induced by a the counterclockwise (CCW)
rotation mode activated by a microwave field H ω and b the breathing mode activated by a
microwave field H ω of a skyrmion crystal confined in a quasi-two-dimensional magnet under a
perpendicular H ex field with θ = 0 ◦ . c, d Those under a tilted H ex field with θ = 30 ◦ . The amplitude
H ω and frequency ω of microwave are presented where ω(=2π f ) is fixed at the eigenfrequency
of the spin-wave mode. The DC component V DC
x
evaluated by fitting the simulated time profiles
are shown as well. e–h Calculated microwave-frequency dependence of the DC component V DC
μ
(μ = x, y) of the spin voltage under a tilted H ex field with θ = 30 ◦ , i.e., e V DC
x
for H ω y,
(f) V DC
y
for H ω y, (g) V DC
x
for H ω (h) V DC
y
for H ω The microwave amplitude is fixed
at H ω = 0.6 × 10 −3 for e–h. The parameters are fixed at J = 1, D = 0.27, H z = 0.036, and
α = 0.04, whereas the system of N = 96 × 111 sites with a skyrmion crystal composed of twelve
magnetic skyrmions is used for all the simulations (Reproduced from [31].)
M. Mochizuki
1
2
0
Time (×10 3 /J)
0.5
1.5
1
2
0
Time (×10 3 /J)
0.5
1.5
0
5
-5
V
x (
V)
2
(a)
(b)
(c)
(d)
H ||x
0
5
-5
0
2
-2
0
-2
Hex
x
y
z
2
Hz
x
y
z
Hx
30°
CCW Rotation mode
Breathing mode
V
x ( V)
V
x ( V)
V
x ( V)
=0°
=30°
Hex
V x =4.24 V
V x =0 V
AC
DC
H =3×10 -3
H ||z
=0.05452
V x =0 V
V x =0 V
AC
DC
H =2×10 -3
=0.06182
V x =2.65 V
V x = 1.19 V
AC
DC
H =3×10 -3
=0.04938
V x =1.81 V
V x =0.56 V
AC
DC
H =2×10 -3
=0.06664
-0.05
0
V
x ( V)
DC
-0.025
Vx
DC
Vx
DC
H ||x
H ||y
0.02
0.04
0.06
0.08
0.1
-0.025
0
0.025
Vy
DC
Vy
DC
H ||x
H ||y
(e)
(f)
-0.025
0.05
0
0
0.02
0.02
0.04
0.06
0.08
0.1
0.12
Vx
DC H ||z
Vy
DC H ||z
(g)
(h)
Frequency
Frequency
Rotation
(CW)
=0.08721
V
y (
V)
DC
Rotation
(CCW)
=0.04938
Breathing
=0.08721
V
x ( V)
DC
V
y ( V)
DC
Rotation
(CCW)
=0.04938
Breathing
=0.08721
Rotation(CW)
=0.08721
Fig. 8.9 a, b Calculated time profiles of spin voltages induced by a the counterclockwise (CCW)
rotation mode activated by a microwave field H ω and b the breathing mode activated by a
microwave field H ω of a skyrmion crystal confined in a quasi-two-dimensional magnet under a
perpendicular H ex field with θ = 0 ◦ . c, d Those under a tilted H ex field with θ = 30 ◦ . The amplitude
H ω and frequency ω of microwave are presented where ω(=2π f ) is fixed at the eigenfrequency
of the spin-wave mode. The DC component V DC
x
evaluated by fitting the simulated time profiles
are shown as well. e–h Calculated microwave-frequency dependence of the DC component V DC
μ
(μ = x, y) of the spin voltage under a tilted H ex field with θ = 30 ◦ , i.e., e V DC
x
for H ω y,
(f) V DC
y
for H ω y, (g) V DC
x
for H ω (h) V DC
y
for H ω The microwave amplitude is fixed
at H ω = 0.6 × 10 −3 for e–h. The parameters are fixed at J = 1, D = 0.27, H z = 0.036, and
α = 0.04, whereas the system of N = 96 × 111 sites with a skyrmion crystal composed of twelve
magnetic skyrmions is used for all the simulations (Reproduced from [31].)