Hidden polar phase in the quantum paraelectric SrTiO3

Abstract

Hidden phases of quantum materials are collective states that exist outside the equilibrium phase diagram and can host exotic properties with transformative potential. However, because they can often mimic known states, identifying them remains challenging. Strontium titanate (SrTiO3) epitomizes this challenge: upon cooling, it displays signatures of ferroelectricity yet never develops this order. We combined mechanical strain with ultrafast laser pulses and x-ray scattering to discover a new polar state in SrTiO3 that is distinct from ferroelectricity. Its signature are distinctive polar vibrations with nanometer wavelengths. This reveals that strain stabilizes a hidden state characterized by a nanoscale polarization modulation rather than conventional homogeneous ferroelectricity. Our findings may offer an alternative explanation for quantum paraelectricity and demonstrate that probing collective excitations at finite momentum is essential for identifying hidden phases in quantum materials.

Figures (7)

• Figure 1: Ultrafast X-ray scattering from hidden quantum phases. (A) Schematic phase diagram of SrTiO$_3$. The ambient pressure paraelectric phase is shown in purple. The blue and orange denotes a FE phase and a polar acoustic phaseCoak2020. $T_{CW}$ is the FE Curie-Weiss Temperature. Insets: illustrations of expected behavior of the transverse optical (TO) and acoustic (TA) phonon branches in the two phases. Blue (orange) shows the TO (TA) branch freezing at the zone center (finite wavevector) as temperature is lowered. Dashed blue and orange lines represent a new mode that appears when SrTiO$_3$ enters the FE and polar-acoustic phases, respectively. (B) Schematic illustration of the experimental setup at the Bernina station of the Swiss FEL. A THz pulse with a spectrum centered around 0.5 THz (Fig. \ref{['fig:s1']}) is focused onto a 50 $\mu$m-thick SrTiO$_3$ sample mounted on a Razorbill CS130 strain cell. Snapshots of the lattice are measured by diffraction of a 50 fs x-ray pulse with photon energy of 10 keV. The sample temperature was 20 K.
• Figure 2: Structural evolution as a function of tensile strain (A) Rocking curve of the (3,3,3) Bragg peak for representative tensile strains. The change in the effective sample length from the nominal unstrained condition is labeled in the inset of B. The curves are labeled by the measured displacement of the strain-cell relative to that of the green linemethods. Inset: Illustration of THz pump polarization and uniaxial strain directions with respect to crystallographic axes of the sample. (B) The diffraction peak profile on the detector as a function of scattering angle. The solid curves are gaussian fits.
• Figure 3: Coherent polar response under tensile strain. X-ray scattering intensity in reciprocal space around the (3,3,3) Bragg peak in the [$h$,0,$l$] plane, at 300K (A) and 20K (B) respectively. (C) X-ray intensity along [0,0, $l$] direction near the (3,3,3) Bragg peak (logarithmic scale). Inset: electro-optic sampling trace of THz pulse. (D) Relative x-ray intensity $\Delta I(t)/I_0$ for strain at $\Delta L/L = 4.7 \times 10^{-3}$, as a function of the delay between the THz and x-ray pulses, where $\Delta I(t)=I(t)-I_0$ and $I_0$ is the x-ray intensity before the THz excitation. The vertically offset lines correspond to different representative wavevectors along the $[0,0, l]$ direction indicated by the matching color dots in (C).
• Figure 4: Collective polar modes of the hidden phase under strain. (A-C) The color maps represent the magnitude of the Fourier transform (FT) of time-domain data like those in Fig. \ref{['fig3']}D for increasing tensile strain at $20$ K. (D) The magnitude of the FT at $l=0.08$ rlu for the three strain configurations in A-C. Curves are displaced vertically for clarity. The two TA and TO phonon peaks are labeled in orange and blue dots respectively. The illustration in (E) summarizes the observed behavior under strain: two TO branches slightly frequency-split (blue curves) and a large renormalization of a one of two nearly-degenerate TA branches (dashed orange).
• Figure S1: THz pump field spectrum. Fourier transform of the electro-optic sampling trace shown in the inset of Fig. \ref{['fig3']}C.