Fig. 1: Crystal lattice of ferroelectric ammonium sulfate [(NH₄)₂SO₄] with tilted ammonium (NH₄⁺) tetrahedra (nitrogen: blue, hydrogen: white) and sulfate (SO₄^2-) tetrahedra (sulfur: yellow, oxygen: red). The green arrow shows the direction of macroscopic polarization P. Blue arrows: local dipoles between sulphur and oxygen atoms. The electron density maps shown in the bottom left panel, in Fig. 2, and the movie are taken in the plane shown in grey. Bottom left: Stationary electron density of sulfur and oxygen atoms, displaying high values on the sulfur (red) and smaller values on the oxygens (yellow). Bottom right: Change of local dipoles at a delay time of 2.8 picoseconds (ps) after excitation of the ammonium sulfate crystallites. An anisotropic shift of charge reduces the dipole pointing to the right and increases the other 3 dipoles.

Researchers from the Max-Born-Institute in Berlin have now demonstrated how atomic vibrations modulate the macroscopic electric polarization of the prototype ferroelectric ammonium sulphate [Fig. 1] on a time scale of a few picoseconds (1 picosecond (ps) = 1 millionth of a millionth of a second). In the current issue of the journal Structural Dynamics [5, 024501 (2018)], they report an ultrafast x-ray experiment which allows for mapping the motion of charges over distances on the order of the diameter of an atom (10^-10m = 100 picometers) in a quantitative way. In the measurements, an ultrashort excitation pulse sets the atoms of the material, a powder of small crystallites, into vibration. A time-delayed hard x-ray pulse is diffracted from the excited sample and measures the momentary atomic arrangement in form of an x-ray powder diffraction pattern. The sequence of such snapshots represents a movie of the so-called electron-density map from which the spatial distribution of electrons and atomic vibrations are derived for each instant in time ([Fig. 2], [Movie]).

Fig 3: Upper panel: Change of the S-O bond length as a function of the delay time. The maximum change of 0.1 pm is 1000 times smaller than the bond length itself, i.e., the atomic motions cannot be observed in Fig. 2. Middle panel: Charge transfer from one oxygen atom to the SO₃ group of the sulfate ion (left black arrows in Fig. 2) as a function of delay time. Lower panel: Change of the macroscopic polarization P along the c axis which is the sum of all microscopic dipole changes of the local S-O dipoles within the sulfhate ions (red and blue arrows in Fig. 1 bottom right).