18
1 Introduction
quasi-1D collinear Heisenberg antiferromagnet in the low temperature (AF1) phase
[59, 60], consisting of two interpenetrating Cu
2+ sublattices with spins aligned along
the b-axis.
At 213 K the spins on one sublattice flop into the ac-plane [61] and form
an incommensurate spin-cycloid phase (AF2) with magnetic ordering vector q =
(0.506, 0, −0.483) [55, 56], depicted in Fig. 1.6b, c. The first-order nature of the
AF1 - AF2 phase transition has been observed in specific heat measurements [62–64].
A magnetically-induced ferroelectric polarisation P b ∼ 100 μC m
−2 in this phase
occurs in the b-direction, which also exhibits ferroelectric hysteresis loops [46].
Between 229.3 and 230 K an intermediate commensurate, collinear magnetic phase
(AF3) forms [57], and above 230 K is the paramagnetic phase (PM).
1.3.3.1 Electromagnon in CuO
An electromagnon has been observed in the multiferroic AF2 phase of CuO using
THz-TDS by Jones et al. [8]. The change in absorption coefficient α relative to the
absorption at 200 K in the AF1 phase are shown in Figs 1.7a, b, for various orientations
of the electric and magnetic fields of the THz pulse relative to the crystal axes.
Representative temperatures chosen were 212 K (AF1 phase), 216 K (AF2 phase),
and 246 K (PM phase). The electromagnon is evident as a strong absorption feature
at 0.7 THz in the AF2 phase and is active only for THz electric fields parallel to the
[101] direction, regardless of the orientation of the THz magnetic field, confirming
the excitation’s electric dipole-active nature. The change in absorption coefficient α
was presented, rather than the absolute absorption coefficient α, in order to avoid the
influence of the broad A
3
u phonon mode at 12.4 THz, which dominates the absorption
in the THz region due its significant linewidth [8, 65], as shown in Fig. 1.7c.
The authors of Ref. [8] also investigated the temperature dependence of the electromagnon, which is shown in Fig. 1.8. The electromagnon spectrum consists of the
main electromagnon mode at ∼ 0.7 THz with a weaker shoulder feature at higher frequencies. The electromagnon emerges rapidly at the AF1-AF2 phase transition, and a
decrease in absorption strength and a redshift of the mode frequency occurs as temperature increases. No electromagnon is observed for temperatures above the AF2-AF3
and AF3-PM phase transitions. Both the absorption strength and frequency of the
electromagnon were observed to closely track the size of the ferroelectric polarisation
along [010] in the AF2 phase, which both confirms the identification of this mode as
an electromagnon, and intruigingly suggests an intimate link between the strength of
the electromagnon and the spin-cycloidal ordering in the AF2 phase. Drude-Lorentz
oscillator fits to the electromagnon spectra in CuO produced an oscillator strength of
∼ 0.07; this is comparable to the strength of the lower-frequency electromagnon
observed in TbMnO 3 ( ∼ 0.05) which has been assigned to an eigenmode of the
spin-cycloid [66], as opposed to the strength of the higher frequency electromagnons
( ∼ 2.0) attributed to the exchange-striction mechanism [48].
A theoretical investigation of electromagnons in CuO was undertaken by Cao
et al. [67]. Using symmetry analysis they showed that the electromagnon observed
1 Introduction
quasi-1D collinear Heisenberg antiferromagnet in the low temperature (AF1) phase
[59, 60], consisting of two interpenetrating Cu
2+ sublattices with spins aligned along
the b-axis.
At 213 K the spins on one sublattice flop into the ac-plane [61] and form
an incommensurate spin-cycloid phase (AF2) with magnetic ordering vector q =
(0.506, 0, −0.483) [55, 56], depicted in Fig. 1.6b, c. The first-order nature of the
AF1 - AF2 phase transition has been observed in specific heat measurements [62–64].
A magnetically-induced ferroelectric polarisation P b ∼ 100 μC m
−2 in this phase
occurs in the b-direction, which also exhibits ferroelectric hysteresis loops [46].
Between 229.3 and 230 K an intermediate commensurate, collinear magnetic phase
(AF3) forms [57], and above 230 K is the paramagnetic phase (PM).
1.3.3.1 Electromagnon in CuO
An electromagnon has been observed in the multiferroic AF2 phase of CuO using
THz-TDS by Jones et al. [8]. The change in absorption coefficient α relative to the
absorption at 200 K in the AF1 phase are shown in Figs 1.7a, b, for various orientations
of the electric and magnetic fields of the THz pulse relative to the crystal axes.
Representative temperatures chosen were 212 K (AF1 phase), 216 K (AF2 phase),
and 246 K (PM phase). The electromagnon is evident as a strong absorption feature
at 0.7 THz in the AF2 phase and is active only for THz electric fields parallel to the
[101] direction, regardless of the orientation of the THz magnetic field, confirming
the excitation’s electric dipole-active nature. The change in absorption coefficient α
was presented, rather than the absolute absorption coefficient α, in order to avoid the
influence of the broad A
3
u phonon mode at 12.4 THz, which dominates the absorption
in the THz region due its significant linewidth [8, 65], as shown in Fig. 1.7c.
The authors of Ref. [8] also investigated the temperature dependence of the electromagnon, which is shown in Fig. 1.8. The electromagnon spectrum consists of the
main electromagnon mode at ∼ 0.7 THz with a weaker shoulder feature at higher frequencies. The electromagnon emerges rapidly at the AF1-AF2 phase transition, and a
decrease in absorption strength and a redshift of the mode frequency occurs as temperature increases. No electromagnon is observed for temperatures above the AF2-AF3
and AF3-PM phase transitions. Both the absorption strength and frequency of the
electromagnon were observed to closely track the size of the ferroelectric polarisation
along [010] in the AF2 phase, which both confirms the identification of this mode as
an electromagnon, and intruigingly suggests an intimate link between the strength of
the electromagnon and the spin-cycloidal ordering in the AF2 phase. Drude-Lorentz
oscillator fits to the electromagnon spectra in CuO produced an oscillator strength of
∼ 0.07; this is comparable to the strength of the lower-frequency electromagnon
observed in TbMnO 3 ( ∼ 0.05) which has been assigned to an eigenmode of the
spin-cycloid [66], as opposed to the strength of the higher frequency electromagnons
( ∼ 2.0) attributed to the exchange-striction mechanism [48].
A theoretical investigation of electromagnons in CuO was undertaken by Cao
et al. [67]. Using symmetry analysis they showed that the electromagnon observed