2
T. Yu and G. E. W. Bauer
high-momentum Fourier components these must be small in size and placed close to
the magnetic medium. Not only the amplitude, but also the direction of the excited
spin waves depend on the excitation conditions that obey right-hand rules and are
therefore chiral.
In this chapter, we focus on the chirality of the dipolar coupling between the
magnetization dynamics in ferromagnetic heterostructures [5–10], while those in
optics [11–17], plasmonics [18, 19], and magnetic structures with Dzyaloshinskii–
Moriya interaction are treated in other chapters. We focus on the favorite material
of magnonics, viz. the ferrimagnetic insulator yttrium iron garnet (YIG) with high
Curie temperature and outstanding magnetic and acoustic quality [20]. Its magnons
can be excited electrically by heavy metal contacts [21], acoustically [22], as well
as by a large spectrum of electromagnetic waves from gigahertz (microwaves) to
petahertz (light). Magnonic transducers with spatially separated contact that excite
and detect magnons [5, 21, 23–29] are sensitive probes to study magnon transport.
We illustrate the chiral physics for thin YIG films with in-plane magnetizations, but
other materials and configurations can be treated by changing the model parameters.
The spin waves of in-plane magnetized films can be classified by the interaction that governs their dispersion as a function of wave vector, into the dipolar,
dipolar-exchange and exchange type with energies ranging from a few gigahertz to
many terahertz [1–4, 23]. The long-wavelength modes are dipolar, whereas the shortwavelength ones are exchange. Bulk volume modes and surface (Damon–Eshbach)
modes propagate along or perpendicular to the magnetization direction with different
dispersion relations [30–33]. Moreover, the surface modes are chiral: their propagation direction (linear momentum) is fixed by the outer product of surface normal and
magnetization direction, allowing unidirectional spin current generation by dominantly exciting one surface of a magnetic film [34–37]. However, Damon–Eshbach
spin waves are not well suited for applications—their group velocity tends to be
zero when the linear momentum is larger than the inverse of film thickness, leading
to a small spin conductivity. They are also very sensitive to dephasing by surface
roughness [38], and do not exist in sufficiently thin films.
An alternative to intrinsically chiral spin waves is the chiral excitation of nonchiral ones. Micromagnetic simulations [5] revealed that the AC dipolar field emitted
by a magnetic nanowire on top of an in-plane magnetized film with magnetization
normal to the wire can excite unidirectional spin waves. We have been motivated by
experiments on an array of magnetic nanowires on top of an ultrathin YIG film that
generated unidirectional spin waves parallel to the surface and perpendicular to the
nanowires [7] to develop a general theory of coherent and incoherent chiral excitation
of magnons [6, 8] by the dipolar interaction between the dynamics of a magnetic film
and a magnetic transducer. The chirality can be traced to the different stray fields
generated by spin waves with opposite polarization and propagation. By angular
momentum conservation electromagnetic waves with particular polarization emitted
by a magnetic transducer couple only the circularly polarized component of a spin
wave with a certain propagation direction [11]. When dipolar or crystal anisotropy
mixes the right and left circularly polarized components, magnons are still excited
preferentially, but not exclusively, in one direction. Finally, a (short-range) exchange
T. Yu and G. E. W. Bauer
high-momentum Fourier components these must be small in size and placed close to
the magnetic medium. Not only the amplitude, but also the direction of the excited
spin waves depend on the excitation conditions that obey right-hand rules and are
therefore chiral.
In this chapter, we focus on the chirality of the dipolar coupling between the
magnetization dynamics in ferromagnetic heterostructures [5–10], while those in
optics [11–17], plasmonics [18, 19], and magnetic structures with Dzyaloshinskii–
Moriya interaction are treated in other chapters. We focus on the favorite material
of magnonics, viz. the ferrimagnetic insulator yttrium iron garnet (YIG) with high
Curie temperature and outstanding magnetic and acoustic quality [20]. Its magnons
can be excited electrically by heavy metal contacts [21], acoustically [22], as well
as by a large spectrum of electromagnetic waves from gigahertz (microwaves) to
petahertz (light). Magnonic transducers with spatially separated contact that excite
and detect magnons [5, 21, 23–29] are sensitive probes to study magnon transport.
We illustrate the chiral physics for thin YIG films with in-plane magnetizations, but
other materials and configurations can be treated by changing the model parameters.
The spin waves of in-plane magnetized films can be classified by the interaction that governs their dispersion as a function of wave vector, into the dipolar,
dipolar-exchange and exchange type with energies ranging from a few gigahertz to
many terahertz [1–4, 23]. The long-wavelength modes are dipolar, whereas the shortwavelength ones are exchange. Bulk volume modes and surface (Damon–Eshbach)
modes propagate along or perpendicular to the magnetization direction with different
dispersion relations [30–33]. Moreover, the surface modes are chiral: their propagation direction (linear momentum) is fixed by the outer product of surface normal and
magnetization direction, allowing unidirectional spin current generation by dominantly exciting one surface of a magnetic film [34–37]. However, Damon–Eshbach
spin waves are not well suited for applications—their group velocity tends to be
zero when the linear momentum is larger than the inverse of film thickness, leading
to a small spin conductivity. They are also very sensitive to dephasing by surface
roughness [38], and do not exist in sufficiently thin films.
An alternative to intrinsically chiral spin waves is the chiral excitation of nonchiral ones. Micromagnetic simulations [5] revealed that the AC dipolar field emitted
by a magnetic nanowire on top of an in-plane magnetized film with magnetization
normal to the wire can excite unidirectional spin waves. We have been motivated by
experiments on an array of magnetic nanowires on top of an ultrathin YIG film that
generated unidirectional spin waves parallel to the surface and perpendicular to the
nanowires [7] to develop a general theory of coherent and incoherent chiral excitation
of magnons [6, 8] by the dipolar interaction between the dynamics of a magnetic film
and a magnetic transducer. The chirality can be traced to the different stray fields
generated by spin waves with opposite polarization and propagation. By angular
momentum conservation electromagnetic waves with particular polarization emitted
by a magnetic transducer couple only the circularly polarized component of a spin
wave with a certain propagation direction [11]. When dipolar or crystal anisotropy
mixes the right and left circularly polarized components, magnons are still excited
preferentially, but not exclusively, in one direction. Finally, a (short-range) exchange