1. University of Wisconsin-Madison Department of Materials Science and Engineering Opportunities for Coherent Scattering in Ferroelectrics and Multiferroics Paul G. Evans Department of Materials Science and Engineering University of Wisconsin, Madison evans@engr.wisc.edu

2. University of Wisconsin-Madison Department of Materials Science and Engineering Outline Ferroelectrics and multiferroics –Manipulate electrical polarization and magnetism using applied fields –Time resolution is crucial –Knowing where the atoms are in steady state is helpful, but there are many other opportunities. Our work: Dynamics in complex oxides (extreme conditions, short times, coupling of ferroelectricity with magnetism) Goals: What can be uniquely probed by coherent techniques?

3. University of Wisconsin-Madison Department of Materials Science and Engineering 100s MV/cm or more: Bond breaking? Several MV/cm to tens of MV/cm: High-field regimes of interatomic interactions. Up to 1 MV/cm: Polarization domain dynamics controls electromechanical and switching properties. Two motivations: 1. Electric field scales for ferroelectric phenomena

4. University of Wisconsin-Madison Department of Materials Science and Engineering More Generally: Electrostatically Driven Materials Ahn et al., Rev. Mod. Phys. 78, 1185 (2006)

5. University of Wisconsin-Madison Department of Materials Science and Engineering Applicable to a Wide Range of Systems Ahn et al., Rev. Mod. Phys. 78, 1185 (2006)

6. University of Wisconsin-Madison Department of Materials Science and Engineering What Can be Learned? How fast can these transitions be? How homogeneous are they in space? What other structural transitions can be driven? Fundamental physics of these phase transitions have been previously available only by changing T (or doping, or H, etc.). Nothing fast! Short pulses go along with high E fields.

7. University of Wisconsin-Madison Department of Materials Science and Engineering New Potential to Understand the High-Field Regime Souza et al., Phys. Rev. Lett. 89, 117602 (2002).

8. University of Wisconsin-Madison Department of Materials Science and Engineering Ti-O 3 and Ba-O 1 pairs move rigidly at high fields  Phonon modes becomes stiffer and dielectric constant becomes smaller.  Piezoelectric response should get weaker at high electric fields E > 16 MV/cm for BaTiO 3 or E > 2.5 MV/cm for PbTiO 3 Changes in Atomic Interactions at High Fields N. Sai, K. M. Rabe, and D. Vanderbilt, Phys. Rev. B 66, 104108 (2002). BaTiO 3

9. University of Wisconsin-Madison Department of Materials Science and Engineering Two motivations: 2. Timescales of Dynamic Phenomena NSLS II: 15 ps Other sources ~100 ps FELs?

10. University of Wisconsin-Madison Department of Materials Science and Engineering Epitaxial PZT Thin Film Capacitors Tunability 1)Composition: throughout tetragonal range, x > 0.5. 2)Thickness: few unit cells to hundreds of nm. 3)Device configuration.

11. University of Wisconsin-Madison Department of Materials Science and Engineering Avalanche photodiode monochromator sample Advanced Photon Source Synchrotron X-ray Microscopy Fresnel zone plate e-e-

12. University of Wisconsin-Madison Department of Materials Science and Engineering Synchronization With B. Adams and S. Ross (APS).

13. University of Wisconsin-Madison Department of Materials Science and Engineering Knife edge scan Microdiffraction and time-resolved x-ray scattering Spatial Resolution Piezoelectric lattice distortion in Pb(Zr x Ti 1-x )O 3, Grigoryev et al., Phys. Rev. Lett. 96, 187601 (2006) Time Resolution ~110 nm Cr fluorescence intensity Cr knife edge position (nm) 2  (deg.) time (ps) strain (%)

14. University of Wisconsin-Madison Department of Materials Science and Engineering Local piezoelectric response switching Each point is a result of 21000 switching cycles Switching is reproducible Measure domain wall velocities Structural signatures of polarization switching What is the structure during switching?

15. University of Wisconsin-Madison Department of Materials Science and Engineering E 2.19 MV/cm Voltage pulse turned on Voltage pulse turned off O Pb Ti a c E Piezoelectricity in large electric fields

16. University of Wisconsin-Madison Department of Materials Science and Engineering Three regimes: 1) E < 1.8 MV/cm Linear piezoelectricity similar to low fields. 2) E ~ 2 MV/cm Meets predicted bond elongation induced by high tetragonality. 3) E > 2.5 MV/cm Indicates the system might be approaching the regime of strong repulsive interaction. Piezoelectric strain at high electric fields tetragonality c/a = 1.1  3 = d 33  E 3, d 33  45 pm/V

17. University of Wisconsin-Madison Department of Materials Science and Engineering Ultrahigh piezoelectric strain 2.69% Elastic piezoelectric strain of 2.69%. intensity 35 nm PZT, ~24.4 V pulse, 8 ns duration

18. University of Wisconsin-Madison Department of Materials Science and Engineering Can we see polarization switching at the intrinsic coercive electric field? Mechanical hysteresis with 50 ns pulses. E c (low frequency) E c (intrinsic, prediction) This would involve using pulses so fast that the domains cannot respond. What is the structure during intrinsic switching?

19. University of Wisconsin-Madison Department of Materials Science and Engineering Questions Interfaces are important. What is the structure of the entire device? How does it change in applied fields? So far we’ve discussed the film independently of its electrodes, and as a homogeneous structure. But this is clearly not the case.

20. University of Wisconsin-Madison Department of Materials Science and Engineering Potential first step: Coherent probes for domain dynamics Partially switched: large disorder More completely switched: less disorder Hypothetical domain configuration Resulting coherent scattering pattern Results give domain dynamics, structure, nucleation physics.

21. University of Wisconsin-Madison Department of Materials Science and Engineering Where do we stand? N. A. Spaldin and M. Fiebig, Science 309, 391 (2005).

22. University of Wisconsin-Madison Department of Materials Science and Engineering Nanomagnetism and Spintronics Krivorotov et al., Science 307, 228 (2005). Coherent Magnetic Oscillations due to Spin Transfer Torque Perspective by Covington, Science 307, 215 (2005). Dynamics are relatively slow now, but only beginning to be explored.

23. University of Wisconsin-Madison Department of Materials Science and Engineering Spintronics with Complex Materials H. Bea et al., Appl. Phys. Lett. 89, 242114 (2006). Exchange Bias in Complex Oxide Systems BiFeO 3 is ferroelectric, so now expect dynamics in the structure and the magnetism – and coupling between them.

24. University of Wisconsin-Madison Department of Materials Science and Engineering e.g. Wang et al. Science 299, 1719 (2003). Pt electrode (150 nm) BiFeO 3 (400 nm) SrTiO 3 (001) substrate BiFeO 3 Thin Films SrRuO 3 (15 nm)

25. University of Wisconsin-Madison Department of Materials Science and Engineering Polarization Switching in BiFeO 3 poled with +10 V Integrated intensity: 1 5  m poled with -10 V Integrated intensity: 0.76 5  m poled with +10 V Integrated intensity: 1.1 5  m

26. University of Wisconsin-Madison Department of Materials Science and Engineering Nonresonant Magnetic X-ray Scattering Non-resonant magnetic x-ray scattering, after DeBergevin and Brunel, (1980)

27. University of Wisconsin-Madison Department of Materials Science and Engineering Antiferromagnetic Domains in Cr Evans and Isaacs J. Phys. D (2006). Evans, et al. Science (2002).

28. University of Wisconsin-Madison Department of Materials Science and Engineering Magnetism in BiFeO 3 Fe (Is this the spin polarization?)

29. University of Wisconsin-Madison Department of Materials Science and Engineering {111} Family Structural {½ ½ ½} Family Magnetic Reflections with unmixed indices Reflections with indices having mixed signs

30. University of Wisconsin-Madison Department of Materials Science and Engineering Dynamics of the “Other” Multiferroic Relationships How does antiferromagnetism respond to applied electric fields? 1.Rearrangement of spin polarization domains? 2.Canted (slightly) ferromagnetic spin arrangement? Can we reach a tetragonal phase? What happens to domains? Canted structure? Ederer and Spaldin, Phys. Rev. B (2005).

31. University of Wisconsin-Madison Department of Materials Science and Engineering Conclusion Ferroelectrics in extreme electric fields: non-linear piezoelectricity. Can we exploit high strains (2.7% so far) and high bandwidths (few GHz so far)? Other phenomena in extreme electric fields? What is the structure under high electric fields? Multiferroics: piezoelectricity, switching. Dynamics of relationship between magnetism and polarization? What is the magnetic structure? Can we probe magnetism coherently? This work was supported by DOE through the BES X-ray and Neutron Scattering Program and by NSF through the Ceramics program of the Division of Materials Research.