1The emergence of the spontaneous polarization in the hexagonal RMnO 3 system (R = Sc, Y, In, Dy -Lu) is one of the singular properties and, at the same time, one of the greatest mysteries of this class of compounds. Taking YMnO 3 as reference compound for the series (see Methods), Curie temperatures inexplicably spreading from 910 K to 1250 K have been reported 10-16, 18, 19 . In some of these cases ferroelectricity has been claimed to emerge together with a trimerizing lattice distortion in a single-step transition 16,18,19 . In other cases these two features have been proposed to occur separately [10][11][12][13][14][15] . On the theoretical side, the two-transition scenario has initially been supported by density-functional-theory calculations 20 . A more detailed analysis, however, suggests improper ferroelectricity triggered by the lattice trimerization in a single-step transition 21,22 , in which secondary anomalies are yet possible due to the breaking of residual symmetries 23 . Direct measurement of the spontaneous polarization as function of temperature would clarify this puzzling situation. This was done once in a pyrocurrent measurement which pointed to an onset of ferroelectricity at 933 K 16 . All attempts to reproduce this experiment failed, however. Thus, in spite of 50 years of research, the emergence of the polar order in the hexagonal RMnO 3 multiferroics is surrounded by contradictions. This uncertainty extends to the universality class of this ferroelectric transition, as this basic question depends on the precise nature of the state undergoing the polar instability. The universality class and the corresponding critical behavior determines important physical properties from the macro-to the nanoscale. Understanding such functionalities is infinitely more difficult if the emergence of the ferroelectric order itself is unclear. Thus, for putting the intense research on the unusual properties of ferroelectric order in the hexagonal RMnO 3 system 2, 3, 5,8,9 onto a solid basis, this situation must be resolved. 2Here we present nonlinear optical experiments in which the electromagnetic field of a frequency-doubled light wave couples directly and linearly to the spontaneous polarization of YMnO 3 .They reveal a polarization emerging at T C 1259 K with a subdued increase in amplitude showing no anomalies or discontinuities. Piezoresponse force microscopy (PFM) confirms that the ferroelectric domain pattern is seeded right below T C . Monte-Carlo simulations reveal how topologically created vortex-like defects in the MnO 5 tilt pattern determine the ferroelectric state and many of its unusual properties. In particular, we show that the "second transition" below T C is not associated to a phase transition, but caused by a finite-size scaling effect.At room temperature, the spontaneous polarization P s = 5.6 µC/cm 2 of YMnO 3 is observed together with unit-cell-trimerizing tilts of the MnO 5 bipyramids and Y displacements along the c axis. The tilt is parameterized 22, 23 by the observable amplitude ...

The success of oxide electronics depends on the ability to design functional properties such as ferroelectricity with atomic accuracy. However, despite tremendous advances in ferroelectric heterostructures, the development towards multilevel architectures with precise layer-by-layer command over the polarization is impeded by the lack of continuous control over the balance of electrostatics, strain, chemistry and film thickness during growth. Moreover, the polarization in the deeper layers becomes inaccessible when these are buried by the ongoing deposition. Taking ferroelectric BaTiO3 and multiferroic BiFeO3 as model systems, we observe and engineer the emergence, orientation and interaction of ferroelectric polarization in ultrathin heterostructures with monolayer accuracy. We achieve this by optical second harmonic generation which tracks the evolution of spontaneous polarization in real time throughout the deposition process. Such direct and in situ access to the polarization during growth leads us to heterostructures with user-defined polarization sequences—towards a new class of functional ferroic materials.

An optical probe of the ferroelectric domain distribution and manipulation in BiFeO3 thin films is reported using optical second harmonic generation. A unique relation between the domain distribution and its integral symmetry is established. The ferroelectric signature is even resolved when the film is covered by a top electrode. The effect of voltage-induced ferroelectric switching is imaged.

The manipulation of domains by external fields in ferroic materials is of major interest for applications. In multiferroics with strongly coupled magnetic and electric order, however, the magnetoelectric coupling on the level of the domains is largely unexplored. We investigated the field-induced domain dynamics of TbMnO3 in the multiferroic ground state and across a first-order spin-flop transition. In spite of the discontinuous nature of this transition, the reorientation of the order parameters is deterministic and preserves the multiferroic domain pattern. Landau-Lifshitz-Gilbert simulations reveal that this behavior is intrinsic. Such magnetoelectric correlations in spin-driven ferroelectrics may lead to domain wall-based nanoelectronics devices.

No abstract