1.3 Electromagnons in Improper Ferroelectrics
13
roelectricity and magnetism in BiFeO 3 : ferroelectricity arises due to the 6s
2 lone pair
in the Bi
3+ ions, while the magnetism has its origins in the spins on the Fe
3+ ions.
Since the discovery of magnetoelectricity in BiFeO 3 , a variety of other mechanisms giving rise to magnetoelectric multiferroicity in materials have been discovered, including charge ordering [32], magnetic exchange striction [33], and
the type of magnetoelectricity typified by TbMnO 3 , spin-spiral magnetic ordering
[34, 35]. Compared to BiFeO 3 , the ferroelectric polarisation in TbMnO 3 is small
(∼ 0.08 μC cm
−2 ) and multiferroicity only occurs at low temperatures (∼ 28 K),
making it a far less practical material for applications. However, the interest in
TbMnO 3 stems from the magnetic origin of the ferroelectricity; the ferroelectricity
in such materials is induced by competing magnetic interactions forming a magnetic
state that breaks inversion symmetry, for instance an incommensurate spin-cycloid
[36, 37]. This so-called “improper” ferroelectricity can result in strong magnetoelectric coupling [38, 39].
Improper ferroelectrics also exhibit dynamic magnetoelectric coupling, whereby
an oscillating electric field couples to a spin wave, or magnon. This results in a
novel quasiparticle excitation at terahertz frequencies - the electromagnon [8, 40–
44]. This opens up possibilities for a new paradigm in the control of magnetic order,
using the electric fields of THz frequency optical pulses [45]. However, the improper
ferroelectric phase generally occurs only at low temperatures, typically below ∼ 70 K
[38]; for many desired technological applications to be realised, room-temperature
improper ferroelectrics are strongly desired. A promising material system in the
search for room temperature improper ferroelectrics is cupric oxide (CuO), which
exhibits a magnetically-induced ferroelectric phase with spin-cycloidal ordering and
electromagnons up to ∼230 K [8, 46].
This section will provide background to the second topic of study presented in this
thesis—the behaviour of electromagnons in the improper ferroelectric multiferroic
material cupric oxide (CuO). A brief description and theoretical background to spin
wave excitations in magnetically ordered materials, magnons, will be provided in
Sect. 1.3.1, before discussing the unique quasiparticle excitation that can occur in
improper ferroelectric materials, electromagnons, in Sect. 1.3.2. Lastly Sect. 1.3.3
will discuss multiferroicity and electromagnons in the principal multiferroic material
system under study in this thesis, CuO.
1.3.1 Magnons
Having discussed the effect that the properties of a particular material have on the
polarisation state of light propagating through it in Sect. 1.1, we may also consider
the converse - what effect do the electric and magnetic fields of light have on the
material? Here we consider the effects of optical electric and magnetic fields in the
linear regime only, where the field strengths are small. The effects of large field
strength optical pulses on materials will be discussed in further detail in Sect. 5.1.
13
roelectricity and magnetism in BiFeO 3 : ferroelectricity arises due to the 6s
2 lone pair
in the Bi
3+ ions, while the magnetism has its origins in the spins on the Fe
3+ ions.
Since the discovery of magnetoelectricity in BiFeO 3 , a variety of other mechanisms giving rise to magnetoelectric multiferroicity in materials have been discovered, including charge ordering [32], magnetic exchange striction [33], and
the type of magnetoelectricity typified by TbMnO 3 , spin-spiral magnetic ordering
[34, 35]. Compared to BiFeO 3 , the ferroelectric polarisation in TbMnO 3 is small
(∼ 0.08 μC cm
−2 ) and multiferroicity only occurs at low temperatures (∼ 28 K),
making it a far less practical material for applications. However, the interest in
TbMnO 3 stems from the magnetic origin of the ferroelectricity; the ferroelectricity
in such materials is induced by competing magnetic interactions forming a magnetic
state that breaks inversion symmetry, for instance an incommensurate spin-cycloid
[36, 37]. This so-called “improper” ferroelectricity can result in strong magnetoelectric coupling [38, 39].
Improper ferroelectrics also exhibit dynamic magnetoelectric coupling, whereby
an oscillating electric field couples to a spin wave, or magnon. This results in a
novel quasiparticle excitation at terahertz frequencies - the electromagnon [8, 40–
44]. This opens up possibilities for a new paradigm in the control of magnetic order,
using the electric fields of THz frequency optical pulses [45]. However, the improper
ferroelectric phase generally occurs only at low temperatures, typically below ∼ 70 K
[38]; for many desired technological applications to be realised, room-temperature
improper ferroelectrics are strongly desired. A promising material system in the
search for room temperature improper ferroelectrics is cupric oxide (CuO), which
exhibits a magnetically-induced ferroelectric phase with spin-cycloidal ordering and
electromagnons up to ∼230 K [8, 46].
This section will provide background to the second topic of study presented in this
thesis—the behaviour of electromagnons in the improper ferroelectric multiferroic
material cupric oxide (CuO). A brief description and theoretical background to spin
wave excitations in magnetically ordered materials, magnons, will be provided in
Sect. 1.3.1, before discussing the unique quasiparticle excitation that can occur in
improper ferroelectric materials, electromagnons, in Sect. 1.3.2. Lastly Sect. 1.3.3
will discuss multiferroicity and electromagnons in the principal multiferroic material
system under study in this thesis, CuO.
1.3.1 Magnons
Having discussed the effect that the properties of a particular material have on the
polarisation state of light propagating through it in Sect. 1.1, we may also consider
the converse - what effect do the electric and magnetic fields of light have on the
material? Here we consider the effects of optical electric and magnetic fields in the
linear regime only, where the field strengths are small. The effects of large field
strength optical pulses on materials will be discussed in further detail in Sect. 5.1.