1 Chiral Coupling to Magnetodipolar Radiation
3
coupling between film and transducer is not sensitive to the propagation direction,
and reduces the chirality.
Recently, two remarkable experiments confirmed our predictions. By NV magnetometry Bertelli et al. [39] observed chiral pumping of spin waves by a stripline
antenna. Wang et al. [40] measured unidirectional microwave transmission mediated
by two magnetic wires on top of a thin magnetic film, i.e. chiral magnon-magnon
coupling.
The chiral coupling to spin waves enables the generation and control of spin
currents [6–8] or spin accumulations [9, 10] in ferromagnetic insulators, which is
beneficial for spintronic devices. In this short review, we comprehensively illustrate
two kinds of chiral coupling to the magneto-dipolar radiation, including the evanescent field of a thin stripline that carries an AC current (Sect. 1.2) and that of a magnetic
wire under resonant excitation (Sect. 1.3).
1.2 Chiral Excitation of Spin Waves by Metallic Stripline
We call a wave “chiral” when it propagates with handedness, i.e. in a certain direction
that is determined by two other control vectors, such as surface normal and magnetic
field. A rotating electrical dipole [41, 42] excites surface plasmon polaritons in
one direction only [18, 19, 41], while a precessing magnetic dipole excite magnons
unidirectionally [43, 44]. Here we analyze solutions of the combined Maxwell and
Landau–Lifshitz–Gilbert equations that explain the available experimental evidence.
We analyze the near microwave field from a normal metal strip line in Sect. 1.2.1 and
its effect on a thin magnetic film in Sect. 1.2.2 (see Fig. 1.1). We focus for simplicity
on a configuration in which the film normal is along the x-direction, ˆ
z is parallel to
a stripline that is assumed to be very long, and the excited spin waves propagate in
the y-direction.
1.2.1 Oersted Magnetic Fields
We first demonstrate that even though the magnetic field of a stripline is linearlypolarized in real space (see Fig. 1.1), it is chiral in momentum space. Ampere’s Law
states that the current density J(r) generates the vector potential [42]
A(r, t) =
μ 0
4π
dr
dt
J(r
, t
)
|r − r |
δ
t
+
|r − r
|
c
− t
,
(1.1)
where μ 0 is the vacuum permeability and the delta-function represents (nonrelativistic) retardation. For a harmonic source J (t) ∼ J(ω)e
−iωt ,
3
coupling between film and transducer is not sensitive to the propagation direction,
and reduces the chirality.
Recently, two remarkable experiments confirmed our predictions. By NV magnetometry Bertelli et al. [39] observed chiral pumping of spin waves by a stripline
antenna. Wang et al. [40] measured unidirectional microwave transmission mediated
by two magnetic wires on top of a thin magnetic film, i.e. chiral magnon-magnon
coupling.
The chiral coupling to spin waves enables the generation and control of spin
currents [6–8] or spin accumulations [9, 10] in ferromagnetic insulators, which is
beneficial for spintronic devices. In this short review, we comprehensively illustrate
two kinds of chiral coupling to the magneto-dipolar radiation, including the evanescent field of a thin stripline that carries an AC current (Sect. 1.2) and that of a magnetic
wire under resonant excitation (Sect. 1.3).
1.2 Chiral Excitation of Spin Waves by Metallic Stripline
We call a wave “chiral” when it propagates with handedness, i.e. in a certain direction
that is determined by two other control vectors, such as surface normal and magnetic
field. A rotating electrical dipole [41, 42] excites surface plasmon polaritons in
one direction only [18, 19, 41], while a precessing magnetic dipole excite magnons
unidirectionally [43, 44]. Here we analyze solutions of the combined Maxwell and
Landau–Lifshitz–Gilbert equations that explain the available experimental evidence.
We analyze the near microwave field from a normal metal strip line in Sect. 1.2.1 and
its effect on a thin magnetic film in Sect. 1.2.2 (see Fig. 1.1). We focus for simplicity
on a configuration in which the film normal is along the x-direction, ˆ
z is parallel to
a stripline that is assumed to be very long, and the excited spin waves propagate in
the y-direction.
1.2.1 Oersted Magnetic Fields
We first demonstrate that even though the magnetic field of a stripline is linearlypolarized in real space (see Fig. 1.1), it is chiral in momentum space. Ampere’s Law
states that the current density J(r) generates the vector potential [42]
A(r, t) =
μ 0
4π
dr
dt
J(r
, t
)
|r − r |
δ
t
+
|r − r
|
c
− t
,
(1.1)
where μ 0 is the vacuum permeability and the delta-function represents (nonrelativistic) retardation. For a harmonic source J (t) ∼ J(ω)e
−iωt ,