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Supplemental Material

Visualization of ferroelectric domains in a hydrogen-bonded molecular

crystal using emission of terahertz radiation

M. Sotome1, N. Kida1, S. Horiuchi2,3 , and H. Okamoto1

1Department of Advanced Materials Science, The University of Tokyo, 5-1-5 Kashiwa-

no-ha, Chiba 277-8561, Japan.

2National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba

305-8562, Japan.

3CREST, Japan Science and Technology Agency (JST), Tokyo 102-0075, Japan.

Content

S1. Sample preparations

S2. Terahertz-radiation experiments

S3. Mechanism of terahertz radiation

S4. Coherence length for terahertz radiation

S5. Terahertz-radiation imaging experiments

S6. Terahertz-radiation vector images

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S1. Sample preparations

Single crystals of croconic acid were grown by slow evaporation of the solution of

raw materials in 1 N hydrochloric acid and purified in repeated crystallization

procedures, as followed by the recipe in Ref. 5 (In Ref. 5, it was reported that the

obtained single crystal is of single phase, which was confirmed by four-circle X-ray

diffractometer). Yellowish crystals with a typical size of 0.6 mm 1 mm 0.4 mm

were obtained. The crystal orientation was checked by a back Laue photograph.

S2. Terahertz-radiation experiments

In the terahertz radiation experiments, we used single crystals with large ac

surfaces, which were obtained by cleaving as-grown crystals. The thickness of the

crystal along the perpendicular direction to the ac plane is 80800 m. We detected

radiated terahertz waves in the time domain using the photoconducting sampling

technique with a photoswitching device made on low-temperature-grown GaAs (LT-

GaAs) coupled with a dipole antenna. The experimental setup is schematically shown in

Fig. S1. The femtosecond laser pulses delivered from a mode-locked Ti:sapphire laser

(the central wavelength of 800 nm, the repetition rate of 80 MHz, the pulse width of 100

fs) were divided into two beams; one beam is used for pump pulses and the other beam

is used for trigger pulses for the detection of terahertz radiations. The pump pulses were

irradiated on ac plane of the sample in the normal incidence [Fig. S1(a)].

The polarization direction of the incident light was set parallel to the horizontal (X)

axis. The radiated terahertz electromagnetic wave was collimated by a pair of off-axis

paraboloic mirrors and was focused on the LT-GaAs detector. In order to enhance the

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collection efficiency of the terahertz waves, we attached a Si lens on the backside of the

LT-GaAs detector. The gap of the antenna was also set parallel to X axis, so that the X-

components of the terahertz electric fields were detected. The induced photocurrents

were measured by a lock-in method. By changing the arrival time of the trigger pulse at

the detector, we recorded the terahertz electric fields in the time domain.

S3. Mechanism of terahertz radiation

When a non-centrosymmetric medium is irradiated by a femtosecond laser pulse

with a finite width of frequency, the electric polarization P is modulated via the

difference frequency mixing within the pulse. This process is expressed as P()=0(2)(-

; 1, -2)E1E2 (=1-2), where E is the electric field of the incident light at

frequency and (2) is the second-order nonlinear optical susceptibility. The frequency

width of the femtosecond laser pulse is 10 THz, resulting in a radiation of

electromagnetic wave in the terahertz frequency region. In Fig. S2, we show electric-

field-amplitude spectra obtained from the time evolutions of the radiated electric fields

shown in Fig. 1(c) by Fourier transformations. The spectra range from 0.2 THz to 3.5

THz.

According to the X-ray diffraction data, the space group of croconic acid is Pca21

[5]. Within the electric dipole approximation, non-zero tensor components of (2) are

aac, aca, bbc, bcb, caa, cbb, and ccc. In our experimental geometry [Fig. 2(b)], only ccc,

caa , and acc survive. We confirmed that caa and acc are negligibly small, as compared

to ccc . Then, the terahertz eclectic field ETHz can be expressed as

ETHz∝❑ccc cos3 θ EX EX . ( S 1 )

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S4. Coherence length for terahertz radiation

The coherence length lc for the terahertz radiation was defined as

lc=λTHz

2|ng−nTHz|, (S 2 )

where THz is the wavelength of the radiated terahertz wave, nTHz is the refractive index

in the terahertz frequency region, and ng is the optical group refractive index of the

incident light. In order to estimate the nTHz spectrum along the c-axis, we performed the

standard terahertz time-domain spectroscopy in transmission geometry. We used ac

surface crystal with the thickness of 980 m. Figure S3(a) shows the nTHz spectrum; we

only obtained the nTHz spectrum below 1.5 THz due to the presence of the strong

absorption above 1.5 THz. In croconic acid, ng at 800 nm used for the excitation was

evaluated to be 2.4 by visible optical spectroscopy [15]. Using these values, we

obtained lc in the terahertz frequency region, as shown in Fig. S3(b). lc at 1 THz was

416 m, which is about 1/10 of lc of ZnTe (3 mm at 1 THz) [10].

S5. Terahertz-radiation imaging experiments

The setup of the terahertz-radiation imaging experiments is schematically shown in

Fig. S1. The sample was attached to a holder placed on a two dimensional stepping

stage, which can independently move in X- and Z-directions [Fig. S1(a)]. The pump

pulses were focused on a sample by a lens (focal length f = 70 mm) or an object lens

(N.A. = 0.3, f = 5 mm). The corresponding spatial resolution was 16 m or 6 m,

respectively, which was evaluated by a conventional knife edge method. We fixed the

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delay time, at which the amplitude of the radiated terahertz wave reaches a maximum,

and monitored its magnitude. Using a raster scan over the entire crystal area, we

obtained a terahertz radiation image. In the raster scan, data were accumulated for 200

msec in each 6 m 6 m area. For the measurements under external electric fields

(Eex), two gold wires were attached on both sides (ab planes) of a crystal with carbon

paste and a bias voltage of up to 1 kV was applied along c.

S6. Terahertz-radiation vector images

Full vector images of the polarization of the crystal shown in Fig. 3(a) are presented

in Fig. S4. The main panel of Fig. S4 is the image of the entire crystal, which

corresponds to the visible image of Fig. 3(a) and the terahertz radiation image in Fig.

(b). Right three panels show the magnified vector images of the boxed areas in the main

panel. Each arrow indicates the direction of the polarization at each position. These

results indicate that the red and blue regions shown in Fig. 3(b) have polarizations

directed right and left, respectively; the polarizations are directed along c axis not only

inside domains but also near DWs.

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Figure S1 A schematic of the experimental setup to directly detect radiated terahertz

electromagnetic waves in the time domain. (a) Magnified view near the sample. is

defined as the angle between the crystallographic c and X axis. The electric field of the

incident light was set parallel to the X axis. The sample is placed in a X-Z stage in order

to measure the spatial image of the terahertz radiation. (b) Overview of the experimental

setup with the photoconducting sampling technique with a low- temperature-grown

GaAs (LT-GaAs) antenna detector. A wire grid polarizer (WG1) is set between off-axis

parabolic mirrors in all the measurements to detect horizontal (X) components of the

radiated terahertz electric fields. For the vector imaging of electric polarization P,

another wire grid polarizer (WG2) is inserted in front of WG1.

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Figure S2 Fourier spectra of electric-field amplitudes of the terahertz radiations with the

external electric field of ± 33.3 kV/cm shown in Fig. 1(c).

Figure S3 (a) Refractive index and (b) coherence length for the terahertz radiation with

800 nm excitations in the terahertz frequency region.

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Figure S4 Terahertz vector image of the polarization in the same area shown in Fig.

3(b). Right three panels show the expanded views of boxed areas in the main panel.