Wiggling atoms switch the electric polarization of crystals

Ferroelectric crystals display a macroscopic electric polarization, a superposition of many dipoles at the atomic scale which originate from spatially separated electrons and atomic nuclei. The macroscopic polarization is expected to change when the atoms are set in motion but the connection between polarization and atomic motions has remained unknown. A time-resolved x-ray experiment now elucidates that tiny atomic vibrations shift negative charges over a 1000 times larger distance between atoms and switch the macroscopic polarization on a time scale of a millionth of a millionth of a second.

Ferroelectric materials have received strong interest for applications in electronic sensors, memories, and switching devices. In this context, fast and controlled changes of their electric properties are essential for implementing specific functions efficiently. This calls for understanding the connection between atomic structure and macroscopic electric properties, including the physical mechanisms governing the fastest possible dynamics of macrosopic electric polarizations.

Fig. 1: Crystal lattice of ferroelectric ammonium sulfate [(NH4)2SO4] with tilted ammonium (NH4+) tetrahedra (nitrogen: blue, hydrogen: white) and sulfate (SO42-) 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 2: (a) Stationary electron density in the grey plane shown in Fig. 1. (b) Change of electron density at a delay time of 2.8 picoseconds (ps) after excitation of the ammonium sulfate crystallites. The circles mark the atomic positions, the black arrows indicate the transfer of electronic charge between one of the oxygen atom and the SO3 group of a single sulfate ion. The vibrational displacements of the atoms are smaller than the line thickness of the circles and, thus, invisible on this length scale. (c) The reverse charge transfer occurs at a delay time of 3.9 ps.

The electron density maps show that electrons move over distances of 10-10m between atoms which are more than a thousand times larger than their displacements during the vibrations [Fig. 3]. This behavior is due to the complex interplay of local electric fields with the polarizable electron clouds around the atoms and determines the momentary electric dipole at the atomic scale. Applying a novel theoretical concept, the time-dependent charge distribution in the atomic world is linked to the macroscopic electric polarization [Fig. 3]. The latter is strongly modulated by the tiny atomic vibrations and fully reverses its sign in time with the atomic motions. The modulation frequency of 300 GHz is set by the frequency of the atomic vibrations and corresponds to a full reversal of the microscopic polarization within 1.5 ps, much faster than any existing ferroelectric switching device. At the surface of a crystallite, the maximum electric polarization generates an electric field of approximately 700 million volts per meter.

Movie: The movie shows the entire temporal evolution of the electron density map.

The results establish time-resolved ultrafast x-ray diffraction as a method for linking atomic-scale charge dynamics to macroscopic electric properties. This novel strategy allows for testing quantum-mechanical calculations of electric properties and for characterizing a large class of polar and/or ionic materials in view of their potential for high-speed electronics.

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).

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A1-P-2025.01
Melting, bubblelike expansion, and explosion of superheated plasmonic nanoparticles

S. Dold, T. Reichenbach, A. Colombo, J. Jordan, I. Barke, P. Behrens, N. Bernhardt, J. Correa, S. Düsterer, B. Erk, T. Fennel, L. Hecht, A. Heilrath, R. Irsig, N. Iwe, P. Kolb, B. Kruse, B. Langbehn, B. Manschwetus, P. Marienhagen, F. Martinez, K.-H. Meiwes-Broer, K. Oldenburg, C. Passow, C. Peltz, M. Sauppe, F. Seel, R. M. P. Tanyag, R. Treusch, A. Ulmer, S. Walz, M. Moseler, T. Möller, D. Rupp, B. v. Issendorff

Physical review letters 134 (2025) 136101/1-7

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A3-P-2025.01
Second-harmonic generation in OP-GaAs0.75P0.25 heteroepitaxially grown from the vapor phase

L. Wang, S. R. Vangala, S. Popien, M. Beutler, J. M. Mann, V. L. Tassev, E. Büttner, V. Petrov

CrystEngComm 27 (2025) 1373-1376

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A3-P-2025.02
Diode-pumped Kerr-lens mode-locked Yb:MgWO4 laser

H.-Y. Nie, Z.-L. Lin, P. Loiko, H.-J. Zeng, L. Zhang, Z. Lin, G. Z. Elabedine, X. Mateos, V. Petrov, G. Zhang, W. Chen

Optics Letters 50 (2025) 1049-1052

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A3-P-2025.03
Growth, anisotropy, and spectroscopy of Tm3+ and Yb3+ doped MgWO4 crystals

G. Z. Elabedine, R. M. Solé, S. Slimi, M. Aguiló, F. Díaz, W. Chen, V. Petrov, X. Mateos

CrystEngComm 27 (2025) 1619-1631

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A3-P-2025.04
Growth, structure, spectroscopic, and laser properties of Ho-doped yttrium gallium garnet crystal

S. Slimi, H. Yu, H. Zhang, C. Kränkel, P. Loiko, R. M. Solé, M. Aguiló, F. Díaz, W. Chen, U. Griebner, V. Petrov, X. Mateos

Optics Express 33 (2025) 2529-2541

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A3-P-2025.05
Growth, spectroscopy and laser operation of disordered Tm,Ho:NaGd (MoO4)2 crystal

G. Z. Elabedine, Z. Pan, P. Loiko, H. Chu, D. Li, K. Eremeev, K. Subbotin, S. Pavlov, P. Camy, A. Braud, S. Slimi, R. M. Solé, M. Aguiló, F. Díaz, W. Chen, U. Griebner, V. Petrov, X. Mateos

Journal of Alloys and Compounds 1020 (2025) 179211/1-12

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A3-P-2025.06
Kerr-lens mode-locked, diode-pumped Yb,Gd:YAP laser generating 23 fs pulses

H.-Y. Nie, P. Zhang, P. Loiko, Z.-L. Lin, H.-J. Zeng, G. Zhang, Z. Li, X. Mateos, H.-C. Liang, V. Petrov, Z. Chen, W. Chen

Optics Express 33 (2025) 11793-11799

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A3-P-2025.07
Nanoindentation and laser-induced optical damage tests of CdSe nonlinear crystals

G. Exner, A. Carpenter, K. Cissner, A. Hildenbrand-Dhollande, S. Schmitt, A. Grigorov, M. Piotrowski, S. Guha, V. Petrov

Journal of the Optical Society of America B 42 (2025) A10-A14

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A3-P-2025.08
Phase-matching properties of AgGa(Se1-xTex)2 for SHG of a CO2 laser

K. Kato, V. Petrov, K. Miyata

Proceedings of SPIE 13347 (2025) 133470S/1-4

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A3-P-2025.09
Phase-matching properties of ZnSiAs2 in the mid-IR

T. Okamoto, N. Umemura, K. Kato, V. Petrov

Proceedings of SPIE 13347 (2025) 133470C/1-5

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A3-P-2025.10
Direct generation of 3.5 optical-cycle pulses from a rare-earth laser

N. Zhang, Y. Wang, H. Ding, F. Liang, Y. Zhao, J. Xu, H. Yu, H. Zhang, V. Petrov

Optics Letters 50 (2025) 3150-3153

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A3-P-2025.11
Power scaling of a non-resonant optical parametric oscillator based on periodically poled LiNbO3 with spectral narrowing

S. Das, T. Temel, G. Spindler, A. Schirrmacher, I. B. Divliansky, R. T. Murray, M. Piotrowski, L. Wang, W. Chen, O. Mhibik, V. Petrov

Optics Express 33 (2025) 5662-5669

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A3-P-2025.12
Sub-40-fs diode-pumped ytterbium-doped mixed rare-earth calcium oxoborate laser

H.-J. Zeng, Z.-L. Lin, H. Lin, P. Loiko, L. Zhang, Z. Lin, H.-C. Liang, X. Mateos, V. Petrov, G. Zhang, W. Chen

Optics Express 33 (2025) 17965-17975

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A3-P-2025.13
Spectroscopy and SESAM mode-locking of a disordered Yb:Gd2SrAl2O7 crystal

H.-J. Zeng, Z.-L. Lin, P. Loiko, F. Yuan, G. Zhang, Z. Lin, X. Mateos, V. Petrov, W. Chen

Optics Express 33 (2025) 15057-15066

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A3-P-2025.14
Watt-level, 1.6 ps χ(2)-lens mode-locking of an in-band pumped Nd:LuVO4 laser

H. Iliev, V. Aleksandrov, V. Petrov, L. S. Petrov, H. Zhang, H. Yu, I. Buchvarov

Optics Express 33 (2025) 17773-17781

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A3-P-2025.15
Refined phase-matching predictions for AgGa1-xInxS2 mixed chalcopyrite crystals

K. Kato, K. Miyata, V. Petrov

Journal of the Optical Society of America B 42 (2025) A6-A9

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A3-P-2025.16
35-fs diode-pumped mode-locked ytterbium-doped multi-component alkaline-earth fluoride laser

Z. Zhang, Z.-Q. Li, P. Loiko, H.-J. Zeng, G. Zhang, Z.-L. Lin, S. Normani, A. Braud, F. Ma, X. Mateos, H.-C. Liang, V. Petrov, D. Jiang, L. Su, W. Chen

Optics Letters 50 (2025) 1835-1838

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A3-P-2025.17
Diode-pumped few-optical-cycle laser based on an ytterbium-doped disordered strontium yttrium borate crystal

H. Zeng, Z. Lin, S. Sun, P. Loiko, H. Lin, G. Zhang, Z. Lin, C. Mou, X. Mateos, V. Petrov, W. Chen

Optics Letters 50 (2025) 2203-2206

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A3-P-2025.18
Refined Sellmeier and thermo-optic dispersion formulas for CdGeAs2

K. Kato, K. Miyata, V. Petrov

Journal of the Optical Society of America B 42 (2025) A24-A28

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A3-P-2025.19
Diode-pumped mode-locked Yb:Ca3La2(BO3)4 laser generating 35 fs pulses

H.-J. Zeng, Z.-L. Lin, G. Zhang, Z. Pan, P. Loiko, X. Mateos, V. Petrov, H. Lin, W. Chen

Optics Express 33 (2025) 22988-22996

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