208
I. Proskurin and R. L. Stamps
field of antiferromagnetic spintronics [3, 4]. Their abundance in Nature and zero net
magnetization make antiferromagnets potentially useful for applications, while the
existence of two or more magnetic sublattices allows one to explore various topological effects [4]. The focus on optical manipulation of the spin states in magnetic
insulators constitutes the scope of the optospintronics [5]. A prominent direction
in optospintronics is related to the application of microwave cavity resonators [6],
which has already seen a rapid development during the last several years [7].
Being interdisciplinary, spintronics in general, and optomagnonics in particular,
can benefit by looking at the concept of chirality. Chirality or handedness, which
according to the original definition given by Lord Kelvin in his Baltimore Lectures
is related to the lack of symmetry between an object and its mirror image [8]. It is a
universal phenomenon that has proved its significance in various scientific areas from
high-energy physics to life sciences and soft matter [9]. Kelvin’s definition, which is
purely geometric, was generalized later to accommodate dynamical phenomena by
Barron [10]. Thus, according to Barron’s definition, one should distinguish between
true and false chiralities. The former is to be found in the systems that break inversion
symmetry, but at the same time are invariant under a time-reversal transformation
combined with any proper rotation, while the latter is characterized by breaking
time-reversal and inversion symmetries simultaneously [11].
How can the concept of chirality be useful for the development of optospintronics? A general observation is that the goal of the spintronics is manipulation and
transformation of pure spin currents, and spin currents are chiral. Indeed, in agreement with the definition of true chirality, a flow of angular momentum reverses its
sign under spatial inversion, while it remains invariant under the time reversal transformation, which reverses both velocities and spins. Thus, from the symmetry point
of view, pure spin currents are in the same category as, for example, natural optical
activity and circular dichroism in optics. This argument also suggests that materials
with structural chirality may have unique properties for hosting and transferring spin
currents that makes them interesting for applications, which is reflected in the rapid
development of molecular spintronics [12, 13] and related topics such as chiral spin
selectivity [14].
Another observation helpful to establish a link between optics and spintronics
is that not only geometric structures but also physical fields can be characterized
by chirality. Chirality density of the electromagnetic field, for example, has been
known for a long time. Lipkin first noticed that the Maxwell’s equations in vacuum
have a hidden conservation law for a chiral density, which he dubbed zilch due to
the lack of clear physical meaning of this quantity at that time [15]. Later, it was
demonstrated that this conservation law is closely related to electromagnetic duality
[16, 17]. This eventually led to the formulation of the nongeometric symmetries of
the Maxwell’s equations [18], i. e. the symmetries, which are not reduced to spacetime transformations. For several decades, the formal properties of optical chirality,
helicity, and dual symmetries were discussed [19–26] but it was not until Tang and
Cohen showed how electromagnetic chirality density can be used to characterize
dichroism in light interacting with a chiral metamaterial that this was understood for
I. Proskurin and R. L. Stamps
field of antiferromagnetic spintronics [3, 4]. Their abundance in Nature and zero net
magnetization make antiferromagnets potentially useful for applications, while the
existence of two or more magnetic sublattices allows one to explore various topological effects [4]. The focus on optical manipulation of the spin states in magnetic
insulators constitutes the scope of the optospintronics [5]. A prominent direction
in optospintronics is related to the application of microwave cavity resonators [6],
which has already seen a rapid development during the last several years [7].
Being interdisciplinary, spintronics in general, and optomagnonics in particular,
can benefit by looking at the concept of chirality. Chirality or handedness, which
according to the original definition given by Lord Kelvin in his Baltimore Lectures
is related to the lack of symmetry between an object and its mirror image [8]. It is a
universal phenomenon that has proved its significance in various scientific areas from
high-energy physics to life sciences and soft matter [9]. Kelvin’s definition, which is
purely geometric, was generalized later to accommodate dynamical phenomena by
Barron [10]. Thus, according to Barron’s definition, one should distinguish between
true and false chiralities. The former is to be found in the systems that break inversion
symmetry, but at the same time are invariant under a time-reversal transformation
combined with any proper rotation, while the latter is characterized by breaking
time-reversal and inversion symmetries simultaneously [11].
How can the concept of chirality be useful for the development of optospintronics? A general observation is that the goal of the spintronics is manipulation and
transformation of pure spin currents, and spin currents are chiral. Indeed, in agreement with the definition of true chirality, a flow of angular momentum reverses its
sign under spatial inversion, while it remains invariant under the time reversal transformation, which reverses both velocities and spins. Thus, from the symmetry point
of view, pure spin currents are in the same category as, for example, natural optical
activity and circular dichroism in optics. This argument also suggests that materials
with structural chirality may have unique properties for hosting and transferring spin
currents that makes them interesting for applications, which is reflected in the rapid
development of molecular spintronics [12, 13] and related topics such as chiral spin
selectivity [14].
Another observation helpful to establish a link between optics and spintronics
is that not only geometric structures but also physical fields can be characterized
by chirality. Chirality density of the electromagnetic field, for example, has been
known for a long time. Lipkin first noticed that the Maxwell’s equations in vacuum
have a hidden conservation law for a chiral density, which he dubbed zilch due to
the lack of clear physical meaning of this quantity at that time [15]. Later, it was
demonstrated that this conservation law is closely related to electromagnetic duality
[16, 17]. This eventually led to the formulation of the nongeometric symmetries of
the Maxwell’s equations [18], i. e. the symmetries, which are not reduced to spacetime transformations. For several decades, the formal properties of optical chirality,
helicity, and dual symmetries were discussed [19–26] but it was not until Tang and
Cohen showed how electromagnetic chirality density can be used to characterize
dichroism in light interacting with a chiral metamaterial that this was understood for