1 Chiral Coupling to Magnetodipolar Radiation
9
x ˆ
y ˆ
z ˆ
n
o
r
t
c
e
l
e
s
a
g
2D
YIG
M
YIG
w
s
Co
YIG
Co
M
d
microwave
Fig. 1.3 A magnetic (Co) nanowire transducer separated by a non-magnetic spacer (optional) from
a YIG film. The dipolar coupling is maximized for the antiparallel magnetization. The direction of
the magnon spin currents pumped into the ±ˆ y-directions is indicated by the green arrows, whose
size indicates the magnitude of the magnon currents. The black arrows indicate the (nearly uniform)
microwave input to the magnetic nanowire
cated much finer than this wave length. A small stripline cross section also increases
Joule heating and thereby limits the maximum applicable currents. A new strategy is
to use magnetic nanowires with high coercivity and resonance frequencies that can
be fabricated with the same feature sizes as normal metal ones. Rather than applying
an AC current directly, magnetic nanowires can be used as “antennas” that are excited
by proximity coplanar wave guides [5, 25–29]. A direct contact between film and
nanowires can suppress chirality by the interface exchange interaction and associated
spin transfer [6], but an insulating spacer of a few atomic monolayers strongly suppresses exchange without much affecting the dipolar interaction. Figure 1.3 shows a
typical configuration with a Co nanowire on top of the YIG film.
1.3.1 Chiral Magnetodipolar Field
The dipolar field from the magnetic nanowire fundamentally differs from the Oersted
field of the AC current-biased normal metal wire discussed above. The precessing
magnetization is a magnetic dipole and generates a rotating dipolar field rather than
the oscillating axially symmetric field of the normal metal wire sketched in Fig. 1.1.
The amplitudes of dipolar waves decay faster than that of (monopolar) currentinduced ones, but are still long-ranged compared to e.g. the exchange interaction. The
nanowire and its equilibrium magnetization are parallel to the z-direction as shown
in Fig. 1.3. When driven with a frequency ω, the macrospin (Kittel) magnetization
dynamics of a wire with thickness d and width w is the real part of
˜
M x,y (r, t) = ˜
m x,y + d))(y + w/2))(−y + w/2)e
−iωt
,
(1.22)
where is the Heaviside step function and ˜
m x,y are constant amplitudes that
depend on the geometry and the excitation power. The corresponding dipolar magnetic field [47]
9
x ˆ
y ˆ
z ˆ
n
o
r
t
c
e
l
e
s
a
g
2D
YIG
M
YIG
w
s
Co
YIG
Co
M
d
microwave
Fig. 1.3 A magnetic (Co) nanowire transducer separated by a non-magnetic spacer (optional) from
a YIG film. The dipolar coupling is maximized for the antiparallel magnetization. The direction of
the magnon spin currents pumped into the ±ˆ y-directions is indicated by the green arrows, whose
size indicates the magnitude of the magnon currents. The black arrows indicate the (nearly uniform)
microwave input to the magnetic nanowire
cated much finer than this wave length. A small stripline cross section also increases
Joule heating and thereby limits the maximum applicable currents. A new strategy is
to use magnetic nanowires with high coercivity and resonance frequencies that can
be fabricated with the same feature sizes as normal metal ones. Rather than applying
an AC current directly, magnetic nanowires can be used as “antennas” that are excited
by proximity coplanar wave guides [5, 25–29]. A direct contact between film and
nanowires can suppress chirality by the interface exchange interaction and associated
spin transfer [6], but an insulating spacer of a few atomic monolayers strongly suppresses exchange without much affecting the dipolar interaction. Figure 1.3 shows a
typical configuration with a Co nanowire on top of the YIG film.
1.3.1 Chiral Magnetodipolar Field
The dipolar field from the magnetic nanowire fundamentally differs from the Oersted
field of the AC current-biased normal metal wire discussed above. The precessing
magnetization is a magnetic dipole and generates a rotating dipolar field rather than
the oscillating axially symmetric field of the normal metal wire sketched in Fig. 1.1.
The amplitudes of dipolar waves decay faster than that of (monopolar) currentinduced ones, but are still long-ranged compared to e.g. the exchange interaction. The
nanowire and its equilibrium magnetization are parallel to the z-direction as shown
in Fig. 1.3. When driven with a frequency ω, the macrospin (Kittel) magnetization
dynamics of a wire with thickness d and width w is the real part of
˜
M x,y (r, t) = ˜
m x,y + d))(y + w/2))(−y + w/2)e
−iωt
,
(1.22)
where is the Heaviside step function and ˜
m x,y are constant amplitudes that
depend on the geometry and the excitation power. The corresponding dipolar magnetic field [47]