A method for detecting ferroelectric domains in ferroelectrics

Abstract

The present application relates to the terahertz field and specifically provides a method for detecting ferroelectric domains in ferroelectrics. The method comprises the following steps: S1, irradiating a ferroelectric to be tested with a laser, causing the ferroelectric to generate terahertz waves; S2, changing the polarization state of the laser to obtain corresponding terahertz wave time-domain spectra under different polarization states; and S3, obtaining ferroelectric domain information of the ferroelectric based on the terahertz wave time-domain spectra. The laser in step S1 is a femtosecond pulse laser, and the ferroelectric to be tested is a terahertz wave radiation source in a terahertz emission spectroscopy system in which the femtosecond pulse laser is used. The present application does not require external electrodes and wires to the ferroelectric, and can achieve all-optical detection of ferroelectric domains on a picosecond time scale or shorter. Furthermore, the present method does not require converting nonlinear current into ohmic current, which does not result in the loss of physical information contained in the nonlinear current. Therefore, the present method has a high accuracy in detecting ferroelectric domains.

Description

Technical Field

[0001] The present application relates to the terahertz field, and in particular to a method for detecting ferroelectric domains in a ferroelectric. Background Art

[0002] A crystalline medium that exhibits spontaneous polarization, whose direction can change with the direction of an external electric field, is referred to as a ferroelectric. Typically, the directions of spontaneous polarization in ferroelectrics vary, but within a small region, the spontaneous polarization of each unit cell has the same direction. This small region is called a ferroelectric domain. Ferroelectric domains are regions of the ferroelectric where the spontaneous polarization has the same direction. Under the influence of an electric field, domain walls can move, changing the orientation of the domains. This domain orientation can alter the optical properties of the ferroelectric. Therefore, detecting ferroelectric domains in ferroelectrics is crucial for their application in optical devices.

[0003] A paper titled "Optically induced ferroelectric polarization switching in amolecular ferroelectric with reversible photoisomerization" discloses a method for detecting ferroelectric domains using optical means, which requires connecting electrodes and wires to the ferroelectric body to apply voltage. However, on the one hand, this results in a long response time for the experimental system, typically on the order of nanoseconds or longer, making it impossible to detect the ferroelectric domain information contained in the ultrafast optical process, resulting in inaccurate ferroelectric domain detection results. On the other hand, the nonlinear current in the ferroelectric body needs to be converted into an ohmic current through the electrode contact portion for detection. However, the conversion efficiency between nonlinear current and ohmic current is low, and only the relevant characteristics of the ohmic current can be detected, resulting in the loss of physical information contained in the nonlinear current, resulting in low accuracy of ferroelectric domain detection results.

[0004] In summary, due to the loss of a lot of nonlinear information, the accuracy of existing ferroelectric domain detection methods is low. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for detecting ferroelectric domains in ferroelectrics in response to the above-mentioned deficiencies in the prior art, so as to solve the problem that the accuracy of the existing ferroelectric domain detection method is low due to the loss of a large amount of nonlinear information.

[0006] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] The present application provides a method for detecting ferroelectric domains in a ferroelectric, the method comprising the following steps: S1, irradiating a ferroelectric to be tested with a laser, so that the ferroelectric to be tested generates a terahertz wave; S2, changing the polarization state of the laser, and obtaining a terahertz wave time-domain spectrum under different polarization states; S3, obtaining ferroelectric domain information of the ferroelectric based on the terahertz wave time-domain spectrum; wherein the laser in step S1 is a femtosecond pulse laser, and the ferroelectric to be tested is a terahertz wave radiation source in a terahertz emission spectrum system of the femtosecond pulse laser.

[0008] Furthermore, the terahertz emission spectroscopy system includes a laser, a half-wave plate, and a photodetector. The laser emitted by the laser transmits through the half-wave plate and irradiates the surface of the ferroelectric. The ferroelectric radiates terahertz waves under the irradiation of the laser, and the terahertz waves enter the photodetector.

[0009] Furthermore, the terahertz emission spectrum system also includes a quarter wave plate, which is arranged on the side of the half wave plate away from the laser, so that the laser light emitted by the laser first passes through the half wave plate and then passes through the quarter wave plate.

[0010] Furthermore, the heights of the laser, the half-wave plate, the quarter-wave plate, and the photodetector are equal, and the incident angle of the laser on the surface of the ferroelectric is 45°.

[0011] Furthermore, the laser is a titanium sapphire femtosecond laser, and the ferroelectric is one of transition metal disulfide, group V sulfide, layered perovskite, SnTe, SnS, SnSe, indium selenide, and CuInP2S6.

[0012] Furthermore, in step S2 , the polarization state of the pump light is changed by the polarization angles of the half-wave plate and the quarter-wave plate.

[0013] Furthermore, step S2 includes changing the polarization state of the linearly polarized laser by changing the polarization angle of the half-wave plate; and also includes fixing the polarization direction of the half-wave plate and changing the rotation angle of the quarter-wave plate to change the polarization state of the circularly polarized laser.

[0014] Furthermore, step S3 includes acquiring amplitude information and phase information of the time domain spectrum of the terahertz wave.

[0015] Furthermore, the amplitude information is obtained by the difference of the vertical coordinates at the peak and valley positions in the terahertz wave time domain spectrum; the phase information is obtained by Fourier transforming, bandpass filtering and fitting the terahertz wave time domain spectrum.

[0016] Furthermore, the fitting process uses the expression y=y0+A*sin(pi*(xx c) / w), where y0 is a constant term representing the overall upward or downward shift of the electromagnetic wave, A represents the amplitude, and -pi*x c / w represents the phase change of the electromagnetic wave, y is the dependent variable representing the intensity, x is the independent variable representing time, pi is the pi of the circumference ratio, and x c represents the fitting constant, with the range -w < x c < w, and the independent variable changes x c ; w represents the time taken for the electromagnetic wave to advance half a cycle.

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows: In this application, a terahertz emission spectroscopy system based on femtosecond pulsed laser is used to detect ferroelectric domains in ferroelectrics. In this application, precise detection of ferroelectric domains can be achieved without externally connecting electrodes and wires to the ferroelectric, and the preparation process is simple. All-optical detection of ferroelectric domains can be achieved on a picosecond time scale or shorter, so that ultrafast processes in ferroelectrics can be detected, and thus ferroelectric domains in ferroelectrics can be detected. Under the action of an ultrafast optical field, there are spontaneous polarization effects and bulk photovoltaic effects (BPVE) in ferroelectrics; the bulk photovoltaic effect is a second-order nonlinear effect. In this application, the hysteresis response of the ferroelectric to the optical field and the accompanying bulk photovoltaic effect caused by ferroelectric polarization are used for ultrafast detection. The coexistence and coupling of ferroelectric polarization and nonlinear optical effects provide a basis for all-optical detection of ferroelectric domains. The non-volatile bulk photovoltaic effect in ferroelectrics has switchable in-plane and out-of-plane bulk photovoltaic effects; the reversal of ferroelectric polarization is accompanied by the switching of the bulk photovoltaic effect in all directions because they are all reversed under inversion symmetry. The movement speed of ferroelectric domains is generally on the picosecond scale, and it is difficult for existing detection methods to achieve real-time observation. Since all-optical detection of ferroelectric domains can be achieved on a picosecond time scale or shorter, and due to the high detection accuracy, the method of this application can detect the reversal of ferroelectric domains in real time. And this ultrafast optical method is non-contact and non-destructive.

[0018] The method of the present application does not require the conversion of nonlinear current into ohmic current, and will not result in the loss of physical information contained in the nonlinear current. Specifically, the mutual coupling of photogenerated carriers and ferroelectric polarizations exhibits a nonvolatile nonlinear photocurrent based on the ferroelectric photovoltaic effect. The method of the present invention does not result in the loss of physical information such as the phase, polarization, and amplitude of the nonlinear current; thus, the accuracy of ferroelectric domain detection is high. In the present application, the hysteresis loop of the ferroelectric is regulated by a pump laser on a femtosecond time scale, and the present application obtains the hysteresis loop by changing the polarization state of the pump light. Specifically, the coexistence and coupling of the in-plane and out-of-plane spontaneous ferroelectric polarizations in the ferroelectric with the nonlinear optical responses of the electron cloud in real space offset (shift current) and Rashba spin splitting are utilized to achieve all-optically regulated nonvolatile nonlinear optical responses. The delayed response of the ferroelectric domain to the ultrafast light field strongly depends on the magnitude of the ferroelectric photovoltaic effect caused by the real-space offset of the electron cloud and the Rashba spin splitting. The magnitude of the ferroelectric photovoltaic effect, caused by the real-space offset and Rashba spin splitting of the controlled electron cloud, can be modified by adjusting the polarization state of the pump light. Therefore, the detection method of this application has high accuracy and sensitivity. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 Schematic diagram of step S1 in a method for detecting ferroelectric domains in a ferroelectric provided in this application (the pump light is linearly polarized light);

[0020] Figure 2 Schematic diagram of step S1 in another method for detecting ferroelectric domains in a ferroelectric provided by the present application (the pump light is circularly polarized light);

[0021] Figure 3 The horizontal component (E) of the terahertz wave generated when the 90° and 270° vertically polarized pump lights excite the ferroelectric in step S1 of the method for detecting ferroelectric domains in the present application is xz (t)) and the vertical component (E y (t)) time domain spectrum;

[0022] Figure 4 The horizontal component (E) of the terahertz wave generated when the 90° and 270° vertically polarized pump lights excite the non-ferroelectric in step S1 of the method for detecting ferroelectric domains in ferroelectrics provided by the present application is xz (t)) and the vertical component (E y (t)) Time domain spectrum;

[0023] Figure 5 The present invention provides a method for detecting ferroelectric domains in ferroelectrics, which includes terahertz wave time-domain spectroscopy of ferroelectrics radiated by pump light excited by left-handed circularly polarized light (-45°, LCP) and right-handed circularly polarized light (45°, RCP);

[0024] Figure 6 The hysteresis loop result obtained in step S3 of the method for detecting ferroelectric domains in a ferroelectric provided in this application under the radiation of a linearly polarized ultrafast light field;

[0025] Figure 7 The dependence of the terahertz wave amplitude obtained in step S3 under the linear polarization ultrafast light field radiation on the linear polarization angle in the method for detecting ferroelectric domains in a ferroelectric provided by the present application;

[0026] Figure 8 A simplified schematic diagram of the spatial distribution of ferroelectric domains at 71°, 180°, and 109° in the ferroelectric;

[0027] Figure 9 This invention provides a method for detecting ferroelectric domains in ferroelectrics, and obtains a hysteresis loop result under circularly polarized pump light radiation. DETAILED DESCRIPTION

[0028] In order to make the implementation process of the present invention clearer, it will be described in detail below with reference to the accompanying drawings.

[0029] The present invention provides a method for detecting ferroelectric domains in a ferroelectric body, the method comprising the following steps:

[0030] S1, laser irradiates the ferroelectric to be tested, and the ferroelectric to be tested generates terahertz waves;

[0031] Due to the broken inversion symmetry, relatively low band gap, and reversible spontaneous polarization in and out of plane of ferroelectrics, pump light generated by a laser shines on the ferroelectric, causing it to radiate terahertz waves. To facilitate the control of the polarization state of the pump light, a polarization control device is placed between the laser and the ferroelectric. Specifically, the laser can be a titanium sapphire femtosecond laser, capable of generating ultrafast femtosecond pulsed light fields with pulse widths ranging from 10 fs to 200 fs, repetition rates ranging from 1 kHz to 82 MHz, and central wavelengths ranging from 400 nm to 800 nm. Ferroelectrics are any ferroelectric crystal or thin film capable of radiating terahertz waves. Specifically, ferroelectric materials can include transition metal dichalcogenides (MX2, M = W / Mo, X = S / Se / Te), group V sulfides, layered perovskites, SnTe, SnS, SnSe, indium selenide (InSe, In2Se3), copper indium phosphosulfide (CuInP2S6), and others. The thickness of the ferroelectric can be 10 nm to 5 mm to ensure that strong terahertz waves can be generated and radiated to the ferroelectric surface. Preferably, the thickness of the ferroelectric semiconductor is 100 nm to 1 mm. Terahertz signals generated by thinner films are difficult to detect, while those generated by thicker films are absorbed by the surface material. The ferroelectric is in the form of a thin film, with a circular or rectangular surface. Specifically, the linear dimension or diameter of the ferroelectric is 500 μm to 1 cm, allowing the pump light spot size to be easily illuminated on the ferroelectric. More specifically, the linear dimension or diameter of the ferroelectric is 1-5 times the diameter of the focused spot. In the embodiment of the present invention, the minimum focusable spot size is 1 mm, and the linear dimension or diameter of the ferroelectric is 1 mm to 5 mm. Generally speaking, smaller spots increase light intensity, while larger spots decrease light intensity. This can meet the light intensity requirements of most samples. The ferroelectric generates terahertz waves when irradiated by ultrafast femtosecond pulsed light fields.

[0032] The pump light can be incident on the ferroelectric surface either perpendicularly or obliquely. Specifically, the pump light incident angle (ferroelectric) is between -90° and 90°. Preferably, the pump light incident angle (ferroelectric) is between -45° and 45°. An angle of 45° maximizes system radiation efficiency and terahertz wave generation efficiency, facilitating system optimization. The generated terahertz wave can be on the same side of the ferroelectric as the pump light, or on opposite sides. This means that terahertz waves can be generated by either reflection or transmission. Figure 1 and Figure 2 Both are schematic diagrams of the process of generating terahertz waves by reflection.

[0033] The polarization control device can be a half-wave plate (HWP) or a combination of a half-wave plate and a quarter-wave plate (QWP). The polarization control device does not change the propagation direction of the pump light, but only changes the polarization state of the pump light, and can achieve continuous control of the polarization state of the pump light between linear polarization light, elliptically polarized light and circularly polarized light. In the experiment of this application, the corresponding incident angle is 45°, and the spot diameter of the pump light is about 4mm. The pump light becomes linearly polarized light after passing through the half-wave plate, and the polarization plane of the linearly polarized light can be adjusted by rotating the half-wave plate to change the linear polarization direction of the pump light. After passing through the half-wave plate, the pump light is irradiated on the surface of the ferroelectric, and the ferroelectric radiates terahertz waves outward.

[0034] The ellipticity, chirality, polarization azimuth, etc. of the radiated terahertz wave are closely related to the helicity of the femtosecond pulse light field. Figure 2 As shown, by fixing the half-wave plate and rotating the quarter-wave plate, the polarization state of the pump light can be controlled, achieving continuous regulation from linear polarization to elliptical polarization and then circular polarization. The pump light passes through the half-wave plate and then the quarter-wave plate, and then strikes the surface of the ferroelectric, which radiates outward, generating terahertz waves. The helicity of the spin-polarized photocurrent that generates the terahertz wave can be controlled and switched by the helicity of the pump light.

[0035] The experiment used a combination of terahertz wire-grid polarizers (WGPs) to measure the terahertz electric field in both horizontal and vertical polarization directions. Specifically, a terahertz wire-grid polarizer was placed on the path of the terahertz wave entering the photodetector. Its characteristic direction was the direction of the metal wires. The terahertz wave along this characteristic direction was absorbed, while the terahertz wave component perpendicular to the characteristic direction was transmitted. More specifically, the characteristic direction of the terahertz wire-grid polarizer was aligned vertically, typically with the horizontal plane corresponding to the laser beam. This way, the terahertz component in the vertical direction was absorbed, while the horizontal component parallel to the horizontal plane was transmitted, resulting in the horizontal component of the terahertz wave. The characteristic direction of the terahertz wire grid polarizer can be along the horizontal direction, so that the terahertz wave component in the horizontal direction is absorbed and the terahertz wave component in the vertical direction is transmitted, and the vertical component is obtained by the light detector; or detection can be performed by combining two parallel terahertz wire grid polarizers with their characteristic directions along the vertical direction and a terahertz wire grid polarizer with its characteristic direction at 45° to the horizontal direction. The generated terahertz wave is transmitted through the two terahertz wire grid polarizers to obtain the vertical component of the terahertz wave, thereby obtaining the time domain spectrum of the terahertz wave.

[0036] Figure 3 The horizontal component of the terahertz wave (E) generated when the ferroelectric is excited by the 90° and 270° vertically polarized pump light xz (t)) and the vertical component (E y(t)) time-domain spectrum. Specifically, 90° and 270° have the same polarization direction. Due to the hysteresis effect, the terahertz waves generated under the same excitation conditions have different amplitudes, phases, and even polarities, resulting in a dual-valued characteristic caused by the hysteresis response. The ferroelectric in the embodiment of this application is indium tin trioxide. Figure 3 The left half of the figure shows the horizontal component E generated by 90° and 270° vertical linear polarization light excitation. xz (t) Comparison of the time-domain electric field signal of the terahertz wave. Other conditions are the same, and the horizontal component E generated by the same linearly polarized pump light excitation xz (t) The terahertz wave amplitude and waveform are significantly different, indicating that two intensities of nonlinear photocurrent appear under the excitation of the same linearly polarized femtosecond light field. Figure 3 The right half of the figure shows the vertical component E generated by 90° and 270° vertical linear polarization light excitation. y (t) Comparison of the time-domain electric field signal of the terahertz wave and the horizontal component E of the terahertz wave xz (t), vertical component E y (t) Not only are the amplitudes unequal, but the polarities of the terahertz waveforms are opposite, proving that the nonlinear photocurrent behaves as a non-artifactual dual-valued function of the ultrafast femtosecond light field. This indicates that there is a phase delay in the ferroelectric, which can change the polarity of the time-domain signal and achieve polarization reversal. The directions of the ultrafast electric fields corresponding to the two vertical polarizations are opposite, causing the directions of the ferroelectric domains in the ferroelectric to be opposite, that is, achieving the reversal of the ferroelectric domains, thus forming a nonlinear photocurrent reversal of the terahertz wave. Finally, in the time-domain spectrum, the horizontal component of the terahertz wave, E xz (t) and the vertical component E y The polarity of (t) is opposite, so the terahertz wave radiated by the ferroelectric can detect the ferroelectric domain in the ferroelectric.

[0037] As a comparison, Figure 4 The horizontal component E of the terahertz wave generated when the pump light with 90° and 270° vertical polarization excites the non-ferroelectric xz (t) and the vertical component E y (t) Time domain spectrum. Specifically, the non-ferroelectric material is indium arsenide (p-InAs(100)). Figure 4 a shows the horizontal component E generated by 90° and 270° vertical linear polarization light excitation xz (t) Comparison of terahertz wave time-domain electric field signals. Figure 4 b shows the vertical component E generated by 90° and 270° vertical linear polarization light excitation y(t) Comparison of terahertz wave time-domain electric field signals. The amplitude, waveform, and polarity of the terahertz waves generated by 90° and 270° vertical linear polarization light excitation are basically the same. This is because there is no spontaneous electric polarization process in non-ferroelectric materials, and the photocurrents generated by the ultrafast electric fields in opposite directions are almost the same, so the horizontal component E of the terahertz wave is xz (t) and the vertical component E y The time domain spectra corresponding to (t) almost overlap. By comparing the terahertz waves generated by InAs under the same conditions, it is shown that non-ferroelectrics do not exhibit a double-valued function with respect to the ultrafast femtosecond light field. This non-volatile characteristic only occurs in ferroelectric semiconductors. Figure 3 and Figure 4 A comparison shows that ferroelectrics and non-ferroelectrics can radiate different terahertz waves under the same conditions, and the radiated terahertz waves are closely related to the electric domains in the ferroelectrics. The detection method of the present application does not require external electrodes and wires to the ferroelectrics, and there is no corresponding nonlinear signal loss. Therefore, the ferroelectric domains in the ferroelectrics can be accurately detected by terahertz waves.

[0038] S2, changing the polarization state of the laser to obtain the terahertz wave time domain spectrum under different polarization states;

[0039] The electric field of the pump light provides an external electric field for the ferroelectric. The ferroelectric is polarized in this ultrafast external electric field. As the polarization state of the pump light changes, the electric polarization process in the ferroelectric also changes, thereby changing the photocurrent in the ferroelectric. Ultimately, the terahertz wave generated by the ferroelectric changes; that is, the corresponding terahertz time-domain spectra under different polarization states are obtained.

[0040] Specifically, by changing the polarization state of the laser through the control device, that is, changing the polarization state of the pump light, the terahertz time domain spectra under different polarization states are obtained. Figure 1 The linear polarization system shown and Figure 2 More specifically, Figure 1 The figure is a schematic diagram of the case where the polarization control device is a half-wave plate, where the coordinate system XYZ is the laboratory coordinate system, the XY axis is parallel to the direction in the ferroelectric plane, and the Z axis is perpendicular to the XY plane. The electric field plane of the pump light can be continuously controlled by the half-wave plate to control the direction of the electric field vector of the linearly polarized femtosecond pulse light field. That is, by changing the rotation angle of the half-wave plate, the linear polarization direction of the pump light can be changed, thereby obtaining linearly polarized pump light with different polarization directions. Figure 2As shown, a half-wave plate is used to fix the pump light in a vertical polarization direction, that is, the polarization direction is along the Z axis. Then, it passes through a quarter-wave plate. By rotating the quarter-wave plate, the conversion between linear polarization, elliptical polarization, and circular polarization is achieved. Specifically, the light field is first fixed in horizontal polarization by rotating the half-wave plate. When the electric field plane of the horizontally polarized light forms a 45° angle with the fast axis of the quarter-wave plate, the light field changes from a linear polarization state to a left-handed circular polarization state (LCP) after passing through the quarter-wave plate. When the electric field plane of the horizontally polarized light forms a -45° angle with the fast axis of the quarter-wave plate, the light field changes from a linear polarization state to a right-handed circular polarization state (RCP) after passing through the quarter-wave plate. The control device can be used to change the polarization state of the pump light, enabling a continuous change from linear polarization to elliptical polarization and then to circular polarization.

[0041] For Figure 1 The linear polarization system shown in the figure obtains two sets of terahertz time-domain spectra, namely the first set of terahertz time-domain spectra and the second set of terahertz time-domain spectra; the polarization angle of the half-wave plate is first changed from horizontal polarization (0°) to vertical polarization (90°), then to horizontal polarization (180°), then from horizontal polarization (180°) to vertical polarization (90°), and finally back to horizontal polarization (0°). The rotation step angle can be set by itself, generally 10-20°, to obtain the first set of terahertz time-domain spectra; the polarization angle of the half-wave plate is first changed from horizontal polarization (0°) to vertical polarization (90°), then to horizontal polarization (180°), and then from horizontal polarization (180°) to horizontal polarization (360°); to obtain the second set of terahertz time-domain spectra.

[0042] For Figure 2 The circular polarization system shown in the figure obtains a set of terahertz time-domain spectra; the half-wave plate is fixed, and the rotation angle of the quarter-wave plate is rotated. The polarization state of the pump light is transformed from linearly polarized light (LP, 0°) to right-handed circularly polarized light (RCP, 45°), then to left-handed circularly polarized light (LCP, 135°), and finally back to linearly polarized light (LP, 0°). The specific step angle can be determined by yourself, and the third set of terahertz time-domain spectra is obtained; the polarization angle of the quarter-wave plate is changed from horizontal polarization (0°) to vertical polarization (90°), then to horizontal polarization (180°), and then from horizontal polarization (180°) to horizontal polarization (360°); the fourth set of terahertz time-domain spectra is obtained.

[0043] The first, second, third and fourth groups of terahertz time-domain spectra can be detected multiple times to take the average value, or they can be detected once. Each group contains the horizontal component E of the terahertz wave. xz (t) and the vertical component Ey (t) Time domain spectrum.

[0044] Specifically, the relationship between the electric field plane orientation (i.e., polarization state) of the pump light and the photocurrent density is: Among them, J shift is the shift photocurrent density, e is the unit charge, is Planck's constant, ω is the frequency of the pump light, E α is the ultrafast light field, σ (1) is the linear conductivity, R is the shift vector. It indicates the shift photocurrent J shift With ultrafast light field E α The polarization state of the pump light changes, which will cause the change of the photocurrent and thus the change of the terahertz wave time domain spectrum. (1) Does not follow a linear progressive relationship (ie J = σ (1) E dc ), the second-order nonlinear response corresponding to the first-order nonlinear polarization characteristic The hysteresis loop shows the intrinsic hysteresis characteristics of ferroelectricity.

[0045] More specifically, the reasoning process of the above relationship is as follows: In the ultrafast light field E α In the real space displacement of the electron (displacement vector R) causes eE α The energy displacement of R, this energy shift eE α R should not exceed the bandwidth W of the valence and conduction bands ( τ is the relaxation time), therefore, the maximum electric field strength E max =W / eR. The absorption intensity of ferroelectric can be described as: P in =σ (1) |E α | 2 , where σ (1) is the linear conductivity; according to the energy flux density vector relationship, the light intensity is proportional to the square of the electric field intensity modulus, specifically expressed as: I=|E α | 2 Energy conversion efficiency r = P out / P in r=1 / ωτ,P out Photovoltaic energy. out It can be expressed as: out =J shift E max Therefore, J shift Can be described as

[0046] Figure 5This is the time-domain spectrum of terahertz radiation emitted by a ferroelectric excited by left-handed circularly polarized light (-45°, LCP) and right-handed circularly polarized light (45°, RCP). The terahertz pulse width is approximately 2.7 ps. Figure 5 a is the horizontal component E of the terahertz wave generated by the excitation of right-handed circularly polarized light and left-handed circularly polarized light xz (t) Time domain electric field signal. Figure 5 b is the vertical component E of the terahertz wave generated by the excitation of right-handed circularly polarized light and left-handed circularly polarized light. y (t) Time domain electric field signal. The unequal amplitude or reverse (positive and negative polarity) waveform of the terahertz wave is the residual polarization effect caused by the displacement of electrons during the excitation process. Specifically, when other experimental conditions remain unchanged, the time domain waveform of the horizontal component of the terahertz wave generated by the circularly polarized pump light of different helicities is significantly different, and the horizontal component of the terahertz wave radiated by the ferroelectric shows obvious circular dichroism, which indicates that the external light field of left-handed circular polarization and right-handed circular polarization makes the internal electric polarization process different, thereby generating different photocurrent signals, resulting in different box signals. Since the shift current and the injected current simultaneously dominate the nonlinear physical process along the xz plane, the polarity of the horizontal component spectrum of the terahertz wave is not reversed. However, under the excitation of circularly polarized pump light with opposite optical rotation, the vertical component E of the terahertz wave y The amplitude of (t) is basically the same, and the polarity of the waveform is completely reversed, indicating that the generation of terahertz waves along the y-axis is almost completely dominated by the injection current effect. The simpler the physical mechanism of terahertz generation, the easier it is to correspond the polarization state of the pump light to the photocurrent. Therefore, it is more accurate to detect ferroelectric domains by terahertz waves generated by photocurrent, that is, by E yThe accuracy of component detection is high. The electric polarization process corresponding to the vertical component of the terahertz wave of circularly polarized light of different chirality shows obvious polarization helicity dependence. Under the excitation of left-handed circularly polarized light (-45°, LCP) and right-handed circularly polarized light (45°, RCP), the vertical component of the terahertz wave generated by the ferroelectric achieves waveform reversal, and the terahertz wave radiation intensity is stronger, indicating that its response to circularly polarized light excitation is more obvious than the horizontal component, the dominant mechanism is more unique, and it is easier to observe the non-volatile ferroelectric effect. The ferroelectric is reversed in the light field to form efficient spin-polarized charges; the reversal of the terahertz signal under left-handed and right-handed excitation means that the injection current caused by the photovoltaic effect of the circular polarizer dominates the physical process of terahertz generation, forming an efficient spin-polarized charge, which makes the electric polarization process inside the ferroelectric faster, and makes the correspondence between the terahertz wave signal generated by the photocurrent and the ferroelectric domain more accurate. Therefore, the detection sensitivity of the method of the present application is higher. Furthermore, the inversion phenomenon indicates that the ferroelectric domain is in a bistability state, which can be exploited to distinguish whether the memory cell is in the "1" or "0" state, thereby creating a ferroelectric memory. Therefore, the ferroelectric domains within the ferroelectric can be detected using both left-handed and right-handed circularly polarized light. When characterized using the vertical component of the terahertz wave, polarity reversal can be achieved, resulting in highly accurate detection.

[0047] S3, obtaining the ferroelectric domain information of the ferroelectric according to the terahertz wave time-domain spectrum.

[0048] The generation of terahertz waves is related to the nonlinear photocurrent in ferroelectric materials. The nonlinear photocurrent is related to the ferroelectric domains in the ferroelectric, that is, the electric polarization process in the ferroelectric. Therefore, the terahertz waves generated by the radiation contain information about the ferroelectric domains. Existing detection methods require external electrodes and wires to detect the ferroelectric domains in the ferroelectric, so the time scale is limited to the nanosecond time scale or longer. On the other hand, the nonlinear current generated by the ferroelectric itself needs to be converted into an ohmic current through electrodes, which will also cause the disappearance of its own physical properties, and the coupling characteristics cannot be observed, thus making it impossible to detect. The present application uses the terahertz waves radiated by the ferroelectric to detect the ferroelectric domains in the ferroelectric. The detection process is an all-optical detection process, does not require external electrodes and wires, and does not cause nonlinear information loss caused by low current conversion efficiency. In addition, the method of the present application can detect the coexistence and coupling between the nonlinear optical response and ferroelectric polarization in the ferroelectric on the picosecond time scale, which contains more nonlinear information. Therefore, the accuracy of the present application in detecting ferroelectric domains is higher. In addition, the vibration frequency of the ferroelectric domain is in the terahertz frequency range, so compared with detection in other bands, the accuracy of this application is higher.

[0049] This application uses a femtosecond pulsed optical field to achieve all-optical arbitrary regulation of ferroelectrics, and obtains physical information related to ferroelectric domains by processing and analyzing information such as the amplitude, phase, and polarization of the radiated terahertz wave. Specifically, the amplitude information of the terahertz wave is obtained by using the difference in the ordinates at the peak and valley positions in the terahertz wave time-domain spectrum obtained in step S2. Perform Fourier transform on the terahertz wave time-domain spectrum obtained in step S2, judge the central frequency position, perform band-pass filtering on the terahertz wave time-domain spectrum, obtain the terahertz wave signal at the central frequency, and use the formula y = y0 + A * sin(pi * (x - x c ) / w) to fit the terahertz wave signal at the central frequency to obtain the phase information of the terahertz wave at the central frequency. Here, y0 is a constant term, representing the overall upward or downward shift of the electromagnetic wave; A represents the amplitude size, -pi * x c / w represents the phase change of the electromagnetic wave, y is the dependent variable representing the intensity size, x is the independent variable representing time, pi is the pi of the circumference ratio, x c represents the fitting constant, and the range is -w < x c < w, the independent variable changes x c ; w represents the time taken for the electromagnetic wave to advance half a cycle. Represent the amplitude information and phase information of the terahertz wave in the Cartesian coordinate system. When drawing, note that the abscissa is in the order of 0° - 90° - 180° - 90° - 0° (for linear polarization), and draw the hysteresis loop diagram of the phase / amplitude - polarized optical field.

[0050] Taking the amplitude of the terahertz wave in the first group of terahertz time-domain spectra and the third group of terahertz time-domain spectra as the ordinate, and the polarization angle of the half-wave plate or the rotation angle of the quarter-wave plate as the abscissa, obtain as Figure 6 (linear polarization) and Figure 9 (circular polarization) shown hysteresis loops. Obtaining the hysteresis loop diagram means obtaining the ferroelectric domains of the ferroelectric. The curves do not completely coincide, indicating the double-valued function characteristics of the ferroelectric, with a hysteresis response, thus enabling the hysteresis loop to be obtained. Specifically, the width of the hysteresis loop can reflect the ferroelectric properties of the ferroelectric. The wider the width of the hysteresis loop, the better the ferroelectric properties of the ferroelectric and the stronger the ability to store information. Taking the amplitude of the second group of terahertz time-domain spectra and the fourth group of terahertz time-domain spectra as the dependent variable, and the polarization angle of the half-wave plate or the rotation angle of the quarter-wave plate as the polar coordinate variable, obtain the dependence trend relationship of the terahertz wave amplitude on different pump light polarization states in the polar coordinate system, as Figure 7 shown (the second group of terahertz time-domain spectra). The spatial distribution orientation of the ferroelectric domains is shown in the polar coordinate system. The angle corresponding to the extreme value position, that is, the planned orientation, is the polarization direction existing in the ferroelectric. That is, the direction from the center position of the polar coordinate to the extreme value of the petal is the polarization orientation, and the included angle between the polarization orientations is the included angle between the polarization directions.

[0051] This application uses an all-optical detection process, without the need for external electrodes and wires, and also realizes the detection of hysteresis loops, avoiding the loss of nonlinear information and achieving higher accuracy of detection results. This application obtains the curve of the horizontal component of the terahertz wave changing with the polarization angle by changing the polarization angle of the half-wave plate ( Figure 6 a) and the curve of the vertical component of the terahertz wave changing with the polarization angle ( Figure 6 b) It is possible to start from vertical polarization and finally return to vertical polarization; the resulting curves do not overlap, that is, the ferroelectric exhibits a dual-valued function characteristic, with a hysteresis response, resulting in a hysteresis loop. The pattern of the hysteresis loop represents different ferroelectric domain distributions. More specifically, when the pump light polarization state changes, J λ Instead of returning along its original path (ab→bc), it decreases along a curve slightly higher than the initial trajectory (cd→da). Therefore, the ferroelectric domain can be α The unequal amplitude or reverse waveform of the terahertz wave is due to the residual polarization effect caused by the displacement of electrons during the excitation process. Figure 6 As shown in the figure, the second-order nonlinear photocurrent changes with the polarization direction of linearly polarized light under zero bias voltage, that is, the typical The hysteresis loop can simultaneously observe the coupling of ferroelectric physics and nonlinear physics, that is, non-volatile nonlinear current. The pattern of the hysteresis loop represents the distribution of a ferroelectric domain. Specifically, the width of the hysteresis loop can reflect the ferroelectric properties of the ferroelectric. The wider the width of the hysteresis loop, the better the ferroelectric properties of the ferroelectric and the stronger the ability to store information. The method of the present application obtains hysteresis loops corresponding to the horizontal and vertical components, indicating that the ferroelectric properties within and between the surfaces of the ferroelectric can be detected, and therefore the detection results are more accurate.

[0052] More specifically, Figure 6 A butterfly The existence of clearly reveals the non-zero memory characteristics of the photocurrent generating terahertz waves that varies with the polarization of the pump light. Figure 6 b shows the special amplitude of terahertz waves The hysteresis loop confirms that the On-Off switching spectrum hysteresis has no artifacts, and the bistable switching photocurrent can be rewritten in a non-volatile manner. The second-order nonlinear characteristics of ferroelectrics are obviously irreversible. When the polarization state of the pump light changes, the photocurrent intensity will not return along the original path (ab→bc), but will change along a curve slightly higher than the original path (cd→da). The change in the nonlinear response of the ferroelectric always lags behind the change in the ultrafast femtosecond light field, that is, the ferroelectric has memory characteristics. In other words, the intensity of the photocurrent in the ferroelectric is not only related to the polarization of the current pump light, but also to the state at the previous moment. In this way, the method of the present application can detect this memory characteristic, and the detection method of the present application has a high accuracy. Preferably, since the memory characteristics of the terahertz vertical component are stronger, that is, the difference when the polarization changes back and forth is larger, therefore, using Figure 6 As shown in b The ferroelectric domains can be detected with higher accuracy.

[0053] Figure 7 is the dependence of the terahertz wave amplitude on the linear polarization angle of the linearly polarized pump light, specifically the horizontal component E of the terahertz wave in polar coordinates xz (t) and the vertical component E y Dependence of the amplitude of (t) on the linear polarization angle. Figure 7 a indicates E xz The amplitude of (t) shows double rotational symmetry with the linear polarization angle, indicating that a second-order nonlinear effect based on the crystal tensor element is generated, and a slight deviation occurs in the polar axis direction from 0° to 180°, which is mainly due to the photocurrent offset caused by the polarization enhancement along the x-axis. The domain wall direction can be obtained from the angle between the petals. The angle between the polar directions of the two petals is about 180°, and the domain wall is 180°. Figure 7 As shown in b, the polar coordinate center position to the extreme value direction of the petal is the polarization orientation. It can be seen from the figure that E xz There are two petals; E y There are four petals; the angle between the polarization orientations is the domain wall orientation. Specifically, E xz There is 1; E y There are three; specifically, the vertical component E of the terahertz wave yThe change in the amplitude of (t) reveals four extreme positions, indicating the presence of four polarization orientations within the ferroelectric plane, aligned along angles of ~60°, ~130°, ~240°, and ~310°, respectively. More specifically, representing the orientation of the domain walls, the angles between the four polarization orientations are approximately ~71° and ~109°, indicating that the spontaneous ferroelectric polarization within the ferroelectric plane exhibits a relatively complex multi-domain state to maintain a low energy state. In other words, the angle corresponding to the extreme position, or the planned orientation, is the polarization direction within the ferroelectric, and the angle between the polarization orientations is the angle between the polarization directions. Therefore, the specific orientation of the ferroelectric domain can be determined based on the dependence of the terahertz wave amplitude on the linear polarization angle of the linearly polarized pump light.

[0054] Specifically, the amplitude is obtained after experimental data processing, and then expressed in polar coordinates. The angle between the polarization directions of the petals in the polar coordinate system is used to obtain the domain wall orientation. Specifically, the fitting line in the figure has a calculated fitting formula, which is based on nonlinear tensor calculation and can be used to fit the polarization angle dependence of terahertz waves. The fitting formula is as follows:

[0055]

[0056]

[0057] Among them, θ THz is the refraction angle of the terahertz emission inside the ferroelectric, d 15 d 22 d 31 d 33 is a non-zero tensor element obtained based on the second-order nonlinear tensor analysis method, α represents the polarization angle of the pump light, S1 and S2 are constant terms that are independent of the polarization angle, and are related to d 15 d 31 d 33 , t is the independent variable.

[0058] Figure 6 The information of ferroelectric hysteresis loop is displayed in Cartesian coordinate system, highlighting the physical characteristics of ferroelectric dual-valued function. Figure 7 The dependence of the terahertz wave amplitude on the linear polarization angle of the linearly polarized pump light is shown, and the spatial orientation of the ferroelectric domain is shown based on the direction and angle of the extreme values; Figure 6 and Figure 7 The ferroelectric domains represented by the horizontal component and the vertical component affect each other and are distributed or projected both in-plane and out-of-plane. In the present invention, the in-plane and out-of-plane refer to the inner and interlayer regions of the layered ferroelectric material.

[0059] Figure 8A simplified schematic diagram of the spatial distribution of ferroelectric domains at 71°, 180°, and 109° is shown. The angles of the four polarization directions are 71°, 180°, and 109° domain walls, respectively. Specifically, the boundary between domains is called a domain wall, and a domain refers to a small area with the same spontaneous polarization direction. These ultrafast ferroelectric spontaneous polarization domains can be detected under the excitation of ultrafast femtosecond pulsed light fields, providing a new method for measuring ferroelectric domains and polarization arrangement directions. The method of this application uses an all-optical detection method, eliminating the need for electrodes and wires on the ferroelectric, avoiding the loss of nonlinear information and thus achieving higher detection accuracy.

[0060] The relationship between the spin-polarized photocurrent and the applied ultrafast femtosecond light field constitutes a typical hysteresis loop. Figure 9 For circularly polarized pump light (such as Figure 2 The results under the stimulation of Figure 6 The results are different under excitation with linearly polarized pump light. This is because ferroelectric domains tend to extend in the same direction as the polarized light field and contract in the opposite direction. In other words, the electric polarization process is related to the polarization state of the pump light. Changes in the polarization state of the pump light will cause changes in the ultrafast electric field, thereby changing the movement of the domain wall and ultimately causing the ferroelectric domain to change. Therefore, the shapes of the hysteresis loops obtained under excitation with linearly polarized pump light and circularly polarized pump light are different. Figure 9 a is the curve of the horizontal component of the terahertz wave changing with the rotation angle of the quarter-wave plate, that is, the butterfly curve Figure 9 b is the curve of the vertical component of the terahertz wave changing with the rotation angle of the quarter-wave plate, and the hysteresis loop is obtained. Similar photocurrent intensities do not return along the original path (PO / OQ), but decrease along a curve slightly higher than the original path (RP / QR). Changes in the ferroelectric's nonlinear response lag behind changes in the applied light field, indicating that the ferroelectric domains of the ferroelectric are closely related to the applied ultrafast electric field. Therefore, the method of the present invention can obtain hysteresis loops and detect ferroelectric domains in an ultrafast all-optical manner.

[0061] By using theoretical analysis, we can derive the mechanism of terahertz wave generation, and based on the fitting results, we can specifically determine which physical mechanism plays a dominant role. Specifically, under the excitation of linearly polarized light, it is mainly the shift current generated by the LBPV effect (linear body photovoltaic effect) that causes the strong terahertz radiation process in the ferroelectric; under the excitation of elliptically polarized light, although the injection current caused by the CBPV effect (circular body photovoltaic effect) dominates the second-order nonlinear physical process of terahertz wave radiation, the shift current caused by the LBPV effect also contributes to the generation process. Taking indium selenide as an example for analysis, the ferroelectric semiconductor indium selenide satisfies the C3V crystal symmetry. Based on this symmetry, the terahertz radiation generated by the LBPV and CBPV effects can be described as: E λ (t,ψ)∝C λ (t)sin2ψ+L 1λ (t)cos4ψ+L 2λ (t)sin4ψ+D λ (t), where λ = y or xz, C λ (t) describes the CBPV response or helicity-dependent photocurrent, which exhibits 2ψ rotational symmetry with the polarization state; L 1λ and L 2λ Both represent the LBPV effect or shift current, which shows a 4ψ rotation dependence on the polarization state. 1λ and L 2λ The term and the non-zero second-order nonlinear susceptibility d 15 d 31 and d 33 Related. D λ Theoretical analysis shows that under the excitation of circularly polarized light, the LBPV effect and CBPV effect have a great influence on E xz The contribution of the component terahertz radiation process is 1:1; while for E y The injection current caused by the CBPV effect dominates the nonlinear process along the y-axis. The process dominated by a single factor has fewer influencing factors, is easier to detect, and has higher sensitivity; thus, the terahertz wave E under circularly polarized light excitation is used. y Components can be detected more easily and with greater accuracy.

[0062] Specifically, by rotating the angle of the quarter-wave plate, the polarization state of the pump light can be transformed from linearly polarized light (LP, 0°) to right-handed circularly polarized light (RCP, 45°) and then to left-handed circularly polarized light (LCP, 135°), and the dependence trend of the terahertz wave amplitude on different pump light polarization states can be measured. Figure 6 Similar to the case of circular polarization, the round-trip paths do not overlap, and the ferroelectric memory characteristics, that is, the light-induced hysteresis phenomenon, also exist under circular polarization, and the memory characteristics corresponding to the vertical component of the terahertz wave are stronger, and the accuracy and sensitivity of detection are higher. Specifically, the second-order nonlinearity of the ferroelectric is obviously irreversible. When switching the polarization of light (LP→RCP→LP→LCP→LP), the photocurrent intensity will not return along the original path (PO / OQ), but will decrease along a curve slightly higher than the original path (RP / QR). The change in the nonlinear response of the ferroelectric always lags behind the change in the external light field, indicating that the hysteresis response curve is closely related to the polarization state of the pump light. Similar to the shifted current response, the injected current is also related to the quantum phase of the Bloch wave function. The hysteresis loop is the ultrafast modulation of the second-order nonlinearity by the ultrafast light field, allowing the external light field to couple to the polarization while maintaining the Bloch form of the wave function. Therefore, the accuracy of the detection of ferroelectric domains in this application is relatively high. Changes in the polarization state of the pump light cause changes in the spin-related nonlinear response. Due to the existence of spin-ferroelectric coupling, the change in the nonlinear response will affect the hysteresis response of the ferroelectric, making the corresponding relationship more accurate, thereby achieving precise detection of ferroelectric domains; that is, the spin-polarized photocurrent and ferroelectric polarization coupling play an important role in the detection of ferroelectric domains. The spin-polarized photocurrent and ferroelectric polarization coupling are closely related to the polarization state of the pump light. Therefore, the accuracy of detecting ferroelectric domains is relatively high.

[0063] Spin-polarized photocurrent can be controlled and switched by the helicity of the ultrafast femtosecond light field, while recording the nonlinear characteristics and ferroelectric bistability in ferroelectrics. Under the excitation of the ultrafast light field, spin-polarized charge is generated. The induced spin-polarized charge oscillates under the high-speed electric field and collides with the lattice ions to produce atomic displacement, thereby affecting the internal structure of the ferroelectric, and then changing the ferroelectric domain and realizing the polarization process. The process is an ultrafast process, which makes the detection sensitivity higher. More specifically, the coexistence and coupling between Rashba physics and spontaneous ferroelectric polarization in ferroelectric semiconductors are realized on the picosecond time scale. Due to the coexistence and coupling between Rashba spin splitting and ferroelectric polarization, the spin structure or Rashba parameter reversal can be controlled and switched by the reversal of ferroelectric polarization, manipulating the electron spin degree of freedom, and manipulating the non-volatile Rashba effect in current spin electronics. Therefore, the sensitivity of the present application in detecting ferroelectric domains is high.

[0064] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A method for detecting ferroelectric domains in a ferroelectric, characterized in that: The method comprises the following steps: S1, laser irradiation of a ferroelectric to be tested, whereby the ferroelectric to be tested generates a terahertz wave; S2, changing the polarization state of the laser to obtain the terahertz wave time domain spectrum under different polarization states; S3, obtaining ferroelectric domain information of the ferroelectric according to the terahertz wave time-domain spectrum; The laser in step S1 is a femtosecond pulse laser, and the ferroelectric to be measured is a terahertz wave radiation source in a terahertz emission spectroscopy system of a femtosecond pulse laser.

2. The method for detecting ferroelectric domains in a ferroelectric according to claim 1, wherein: The terahertz emission spectroscopy system includes a laser, a half-wave plate, and a light detector. The laser emitted by the laser transmits through the half-wave plate and irradiates the surface of the ferroelectric. Under the irradiation of the laser, the ferroelectric radiates terahertz waves, which enter the light detector.

3. The method for detecting ferroelectric domains in a ferroelectric according to claim 2, wherein: The terahertz emission spectroscopy system further includes a quarter wave plate, which is disposed on a side of the half wave plate away from the laser, so that laser light emitted by the laser first passes through the half wave plate and then passes through the quarter wave plate.

4. The method for detecting ferroelectric domains in a ferroelectric according to claim 3, wherein: The laser, the half-wave plate, the quarter-wave plate, and the light detector have the same height, and the incident angle of the laser on the surface of the ferroelectric is 45°.

5. The method for detecting ferroelectric domains in a ferroelectric according to claim 4, wherein: The laser is a titanium sapphire femtosecond laser, and the ferroelectric is one of transition metal disulfide, group V sulfide, layered perovskite, SnTe, SnS, SnSe, indium selenide, and CuInP2S6.

6. The method for detecting ferroelectric domains in a ferroelectric according to claim 5, wherein: In the step S2, the polarization state of the laser light is changed by the polarization angles of the half-wave plate and the quarter-wave plate.

7. The method for detecting ferroelectric domains in a ferroelectric according to claim 6, wherein: The step S2 includes changing the polarization state of the linearly polarized laser by changing the polarization angle of the half-wave plate; and also includes fixing the polarization direction of the half-wave plate and changing the rotation angle of the quarter-wave plate to change the polarization state of the circularly polarized laser.

8. The method for detecting ferroelectric domains in a ferroelectric according to claim 1 or 7, characterized in that: The step S3 includes acquiring amplitude information and phase information of the time domain spectrum of the terahertz wave.

9. The method for detecting ferroelectric domains in a ferroelectric according to claim 8, wherein: The amplitude information is obtained by the difference of the vertical coordinates at the peak and valley positions in the terahertz wave time domain spectrum; the phase information is obtained by performing Fourier transform, bandpass filtering and fitting processing on the terahertz wave time domain spectrum.

10. The method for detecting ferroelectric domains in a ferroelectric according to claim 9, wherein: The fitting process uses the expression y = y 0+ A *sin(pi*( x - x c ) / w ),in y 0 is a constant term, representing the overall upward or downward movement of the electromagnetic wave, A Indicates the amplitude, -pi* x c / w represents the phase change of electromagnetic waves, y is the dependent variable representing the intensity, x The independent variable represents time, pi is the circumference ratio π, x c Represents the fitting constant, ranging from - w < x c < w ; w Indicates the time it takes for an electromagnetic wave to advance 1 / 2 cycle.

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