64
3 Rotatable-Polarisation Terahertz Time-Domain Spectroscopy of Anisotropic Media
3.4.4.1 Anisotropy of the Electromagnon Absorption in CuO
To examine the absorption of the electromagnon and to precisely determine its selection rule, we examined the temperature-dependent change in absorption coefficient
between the AF1 and AF2 phase, expressed as
α(ω, ψ in ) = −
2
d
ln |
T (ω, ψ in )|,
(3.8)
where d is the sample thickness and |
T (ω, ψ in )| is the absolute part of the complex
transmission function. The transmission function at each value of ψ in was found from
the ratio of the total transmitted THz intensity, using
|
T (ω)| =
|
E s
x (ω)| 2 + |
E s
y (ω)| 2
|
E r
x (ω)| 2 + |
E r
y (ω)| 2
,
(3.9)
where the superscripts s and r denote the sample (at 215 K) and reference (at 210 K)
spectra, and the subscripts x and y denote the horizontally and vertically polarized
components, respectively.
The change in absorption induced by multiferroicity, α(ω), as ψ in is varied
is reported in Fig. 3.12a. The electromagnon is evident as a peak in α around
0.7 THz with a weaker tail at higher frequencies, and a strength that decreases as ψ in
moves away from [101] (close to ψ in = 0
◦ ) towards [010] (close to ψ in = ±90
◦ ).
This verifies that the electromagnon is only excited when applying a THz electric
field along the [101] direction, as reported by Jones et al. [35] using measurements
at only a few fixed angles. A cut through the peak of the absorption at 0.72 THz is
shown in Fig. 3.12b, represented by the dashed line in Fig. 3.12a. The maximum
change in absorption occurs when ψ in = 6
◦ , with a precision of 5
◦ defined by half
the angular step size of the scan. To more precisely determine the orientation of
maximum absorption, an angular range of 40
◦ containing the peak of the absorption
was scanned with a smaller angular step size, shown in Fig. 3.12c. The experimental
data (dots) were fit (solid line) to a cosine model, A cos(2(ψ in + φ)) + C, where A
and C are constants and φ is a phase offset. From this fit the angle of maximum
absorption occurs at ψ in = 5
◦ .
An additional feature that can be observed in Fig. 3.12a is that as ψ in approaches
±90
◦ , where it is close to the [010] direction, α is observed to become negative,
corresponding to a larger transmission in the AF2 phase than in the AF1 phase. This
can be attributed to the static polarization along [010] that arises in the multiferroic
phase altering the absorption of the higher-lying phonon modes [37].
3 Rotatable-Polarisation Terahertz Time-Domain Spectroscopy of Anisotropic Media
3.4.4.1 Anisotropy of the Electromagnon Absorption in CuO
To examine the absorption of the electromagnon and to precisely determine its selection rule, we examined the temperature-dependent change in absorption coefficient
between the AF1 and AF2 phase, expressed as
α(ω, ψ in ) = −
2
d
ln |
T (ω, ψ in )|,
(3.8)
where d is the sample thickness and |
T (ω, ψ in )| is the absolute part of the complex
transmission function. The transmission function at each value of ψ in was found from
the ratio of the total transmitted THz intensity, using
|
T (ω)| =
|
E s
x (ω)| 2 + |
E s
y (ω)| 2
|
E r
x (ω)| 2 + |
E r
y (ω)| 2
,
(3.9)
where the superscripts s and r denote the sample (at 215 K) and reference (at 210 K)
spectra, and the subscripts x and y denote the horizontally and vertically polarized
components, respectively.
The change in absorption induced by multiferroicity, α(ω), as ψ in is varied
is reported in Fig. 3.12a. The electromagnon is evident as a peak in α around
0.7 THz with a weaker tail at higher frequencies, and a strength that decreases as ψ in
moves away from [101] (close to ψ in = 0
◦ ) towards [010] (close to ψ in = ±90
◦ ).
This verifies that the electromagnon is only excited when applying a THz electric
field along the [101] direction, as reported by Jones et al. [35] using measurements
at only a few fixed angles. A cut through the peak of the absorption at 0.72 THz is
shown in Fig. 3.12b, represented by the dashed line in Fig. 3.12a. The maximum
change in absorption occurs when ψ in = 6
◦ , with a precision of 5
◦ defined by half
the angular step size of the scan. To more precisely determine the orientation of
maximum absorption, an angular range of 40
◦ containing the peak of the absorption
was scanned with a smaller angular step size, shown in Fig. 3.12c. The experimental
data (dots) were fit (solid line) to a cosine model, A cos(2(ψ in + φ)) + C, where A
and C are constants and φ is a phase offset. From this fit the angle of maximum
absorption occurs at ψ in = 5
◦ .
An additional feature that can be observed in Fig. 3.12a is that as ψ in approaches
±90
◦ , where it is close to the [010] direction, α is observed to become negative,
corresponding to a larger transmission in the AF2 phase than in the AF1 phase. This
can be attributed to the static polarization along [010] that arises in the multiferroic
phase altering the absorption of the higher-lying phonon modes [37].