Introduction

The modern micro- and nanoelectronics development is expressed in the ever-growing demand for increasing of the information storage density and its recording and reading speed. The implementation of ultrafast ferroelectric switching by short electromagnetic pulses of the optical or THz range can be a solution to the problem of ultrafast information recording. Application of this technique will allow to build new effective and non-volatile memory devices. However, the problem of ultrafast but permanent ferroelectric order parameter switching is not solved yet.

One of the main signs of the possibility of ferroelectric polarization switching is the soft phonon mode excitation, which means a direct effect on the order parameter. The soft mode excitation has already been experimentally demonstrated in ferroelectrics by exciting them with ultrashort optical or THz pulses [1,2,3,4]. Today, there are several works that show the possibility of direct or indirect transient ferroelectrics polarization switching by strong THz pulses [5,6,7]. However, the permanent polarization switching in these works was not reported.

Another way to achieve ultrafast polarization control is to select materials that are more suitable for this. In this regard, materials with hidden properties and so-called “hidden phases” are of great interest. “Hidden phases” are metastable states of matter that are usually not available on equilibrium phase diagrams. These phases can exhibit exotic properties and provide novel functionality and applications.

One of these materials is strontium titanate (SrTiO3). SrTiO3 is a potential ferroelectric with the ABO3 perovskite structure and the point group \(m\overline{3 }m\) at room temperature. The phase transition from the paraelectric to the ferroelectric phase does not occur at SrTiO3 up to the temperature of absolute zero, since it is suppressed by quantum fluctuations [8].

Due to the high value of static permittivity and low dielectric losses in the microwave range at room temperature [9, 10] SrTiO3 is widely used in the production of capacitor structures with a high density of information recording [11, 12] and DRAM [13]. It has also been shown [14,15,16,17] that the SrTiO3 characteristics in the THz range make it a suitable material for use in control and tuning devices for terahertz radiation, as well as in tunable microwave components.

The presence of the soft ferroelectric mode in SrTiO3 makes it possible to develop new possibilities for its application. In [18], THz-induced soft mode excitation in SrTiO3 was demonstrated at low temperatures by second harmonic generation technique. In our work we have shown that an ultrafast phase transition to a polar state can be induced by the terahertz excitation in quantum paraelectric SrTiO3 even at room temperature. This significantly expands the possibility of its application in electronic devices in the THz range, as well as memory devices.

Materials and methods

The SrTiO3 crystal is centrosymmetric at room temperature in the absence of external field. According to the electric dipole approximation, the optical second harmonic generation (SHG) due to the second-order nonlinear optical susceptibility in such a crystal is forbidden by the symmetry rules. Then, the anisotropy of the signal of the second optical harmonic upon excitation of SrTiO3 by terahertz pulses may indicate that a polar phase that does not have inversion symmetry is initiated in the crystal.

A Cr:forsterite laser with 100 fs pulse duration at 1240 nm central wavelength and 10 Hz repetition rate was used in the experiment. Optical pulses pumped an OH1 nonlinear organic crystal for generation of THz pulses via optical rectification. The THz beam was focused onto the SrTiO3 surface using off-axis parabolic mirror onto a spot with 300 um diameter which guarantee electric field up to 300kV/cm at 0.15 uJ THz pulse energy. THz-induced second harmonic generation at wavelength of 620 nm was measured at normal incidence transmission geometry at room temperature and dry air conditions. The fundamental wavelength of 1240 nm was cut using interference filter to ensure the only SHG signal hits photomultiplier tube.

Results and discussions

In order to determine whether the phase in SrTiO3 induced by the action of the electric field of a terahertz pulse is polar, the form χ(3) is studied, the various elements of which can be obtained by rotating the polarization of the incident electric field and analyzing the polarization of the SHG wave. Static polarization dependences were taken at the moment of exposure to the peak electric field of the THz pulse.

In the experimental geometry (Fig. 1) the THz and probe electromagnetic waves were directed along the normal to the (110) surface of the SrTiO3 crystal and, accordingly, propagated along the direction z||[110]. The polarization of one of the electromagnetic waves, whether optical or THz, was fixed while the polarization of the second wave rotated in direction perpendicular to the plane of propagation. The SHG probe was analyzed when the sample passed through the polarizer, the axis of which was oriented to one of two perpendicular directions x||[001] (\({I}_{p}^{(2\omega )}\)) or y|| [1-10] (\({I}_{s}^{(2\omega )}\)).

Fig. 1
figure 1

Sketch of the experimental setup for the polarization rotation of a THz pulse and b optical probe pulse

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Figure 2 shows the experimental results, indicated by dots, of the dependences of the SHG intensity in SrTiO3 on the polarization rotation of the incoming terahertz (Fig. 1a) and optical (Fig. 1b) waves.

Fig. 2
figure 2

SHG intensity polar plot upon polarization rotation of a THz pulse and b optical probe pulse

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In centrosymmetric medium with \(m\overline{3 }m\) point group symmetry, the main contribution providing second harmonic generation has quadrupole nature [19, 20]. If electric field, of either low or high frequency, is applied then the total nonlinear polarization is determined by two terms, quadrupole\({P}_{Q}^{(2\omega )}\), which is field independent, and electric-dipole\({P}_{ED}^{(2\omega )}\left({E}_{THz}\right)\), which is field dependent (the latter is called “electric-field induced SHG”, EFISH [21], or “THz field induced SHG” [3], TFISH):

$${P}^{(2\omega )}={P}_{Q}^{(2\omega )}+{P}_{ED}^{(2\omega )}\left({E}_{THz}\right)$$

The interplay between these two terms determines the dependence of SHG intensity on THz field. It has already been shown that SHG intensity has quadratic dependence on the THz electric field [3], then the field-independent term \({P}_{Q}^{2\omega }\) can be neglected.

Nonlinear polarization in an SrTiO3 crystal with a point symmetry group \(m\overline{3 }m\) is described by nonzero components of the third-order nonlinear susceptibility tensor \({\chi }_{ijkl}^{(3)}\):\({\chi }_{xxxx}={\chi }_{yyyy}={\chi }_{zzzz}={\chi }_{1}\),\({\chi }_{xxyy}={\chi }_{xxzz}={\chi }_{yyxx}={\chi }_{yyzz}={\chi }_{zzyy}={\chi }_{2}\),\({\chi }_{xyxy}={\chi }_{xyyx}={\chi }_{xzzx}={\chi }_{yxxy}={\chi }_{yxyx}={\chi }_{yzyz}={\chi }_{yzzy}={\chi }_{zxxz}={\chi }_{zxzx}={\chi }_{zyyz}={\chi }_{zyzy}={\chi }_{3}\). The experimental dependences of the SHG intensity were approximated as a function of the rotation of the polarization plane of the incident radiation (terahertz or optical) for the analyzed orthogonal polarizations of the SHG wave (\({I}_{p}^{(2\omega )}\) or \({I}_{s}^{(2\omega )}\)):

$$ I_{p, THz}^{{\left( {2\omega } \right)}} \propto E_{p,THz}^{2} I_{\omega }^{2} \left( {0.0032 \times \left( {\chi_{2} + \chi_{3} } \right) \times \cos (\phi_{THz} )^{2} + \left( {0.0217\chi_{1} + 0.02813\chi_{2} + 0.0916\chi_{3} } \right) \times \cos (\phi_{THz} )^{2} + 0.1667\left( {\chi_{1} - \chi_{2} } \right) \times \sin (\phi_{THz} )^{2} } \right)^{2} $$
$$ I_{s, THz}^{{\left( {2\omega } \right)}} \propto E_{s,THz}^{2} I_{\omega }^{2} (0.0094\left( {\chi_{1} - \chi_{3} )^{2} \times \cos (\phi_{THz} )^{2} \times \sin (\phi_{THz} )^{2} } \right) $$
$$ I_{p,opt}^{{\left( {2\omega } \right)}} \propto kE_{THz}^{2} (I_{p}^{\left( \omega \right)} )^{2} \left( {0.0032 \times \left( {\chi_{2} + \chi_{3} } \right) \times \cos (\phi_{opt} } \right) + \left( {0.0217\chi_{1} + 0.02813\chi_{2} + 0.0916\chi_{3} } \right) \times \cos (\phi_{opt} ))^{2} $$
$$ I_{s,opt}^{{\left( {2\omega } \right)}} \propto lE_{THz}^{2} I_{s,\omega }^{2} (\left( {0.0192\chi_{1} - 0.0192\chi_{2} - 0.0425\chi_{3} )^{2} \times \sin (\phi_{opt} )^{2} } \right) $$

where the variable parameters were the \({\chi }_{1},{\chi }_{2},{\chi }_{3}\) components, \({E}_{THz}\) is an electric fields of terahertz wave, \({I}_{\omega }^{2}\) is an optical beam intensity and k and l are coefficients of proportionality. The numerical coefficients in the expressions arise as a result of the transition from the laboratory coordinate system to the crystallographic one.

The joint approximation of the experimental results the relative values of the components of the third-order nonlinear susceptibility tensor were found: \({\chi }_{1}=0\), \({\chi }_{2}/{ \chi }_{3}=0.604\).

Conclusion

In conclusion we have shown that the action of THz pulses on the SrTiO3 crystal leads to the breaking of the inversion symmetry and the initiation of the polar state on ultrafast (during the duration of the terahertz pulse) time scale. The relative values of the third-order nonlinear susceptibility tensor components were found by joint approximation of the experimentally obtained polarization dependences of the SHG intensity.