Manfred Fiebig

Observation of coupled magnetic and electric domains

Ferroelectromagnets are an interesting group of compounds that complement purely (anti-)ferroelectric or (anti-)ferromagnetic materials—they display simultaneous electric and magnetic order. With this coexistence they supplement materials in which magnetization can be induced by an electric field and electrical polarization by a magnetic field, a property which is termed the magnetoelectric effect. Aside from its fundamental importance, the mutual control of electric and magnetic properties is of significant interest for applications in magnetic storage media and ‘spintronics’. The coupled electric and magnetic ordering in ferroelectromagnets is accompanied by the formation of domains and domain walls. However, such a cross-correlation between magnetic and electric domains has so far not been observed. Here we report spatial maps of coupled antiferromagnetic and ferroelectric domains in YMnO3, obtained by imaging with optical second harmonic generation. The coupling originates from an interaction between magnetic and electric domain walls, which leads to a configuration that is dominated by the ferroelectromagnetic product of the order parameters.

Magnetic phase control by an electric field.

The quest for higher data density in information storage is motivating investigations into approaches for manipulating magnetization by means other than magnetic fields. This is evidenced by the recent boom in magnetoelectronics and ‘spintronics’, where phenomena such as carrier effects in magnetic semiconductors and high-correlation effects in colossal magnetoresistive compounds are studied for their device potential. The linear magnetoelectric effect—the induction of polarization by a magnetic field and of magnetization by an electric field—provides another route for linking magnetic and electric properties. It was recently discovered that composite materials and magnetic ferroelectrics exhibit magnetoelectric effects that exceed previously known effects by orders of magnitude, with the potential to trigger magnetic or electric phase transitions. Here we report a system whose magnetic phase can be controlled by an external electric field: ferromagnetic ordering in hexagonal HoMnO3 is reversibly switched on and off by the applied field via magnetoelectric interactions. We monitor this process using magneto-optical techniques and reveal its microscopic origin by neutron and X-ray diffraction. From our results, we identify basic requirements for other candidate materials to exhibit magnetoelectric phase control.

Low-threshold amplified spontaneous emission and lasing from colloidal nanocrystals of caesium lead halide perovskites

Metal halide semiconductors with perovskite crystal structures have recently emerged as highly promising optoelectronic materials. Despite the recent surge of reports on microcrystalline, thin-film and bulk single-crystalline metal halides, very little is known about the photophysics of metal halides in the form of uniform, size-tunable nanocrystals. Here we report low-threshold amplified spontaneous emission and lasing from ∼10 nm monodisperse colloidal nanocrystals of caesium lead halide perovskites CsPbX3 (X=Cl, Br or I, or mixed Cl/Br and Br/I systems). We find that room-temperature optical amplification can be obtained in the entire visible spectral range (440–700 nm) with low pump thresholds down to 5±1 μJ cm−2 and high values of modal net gain of at least 450±30 cm−1. Two kinds of lasing modes are successfully observed: whispering-gallery-mode lasing using silica microspheres as high-finesse resonators, conformally coated with CsPbX3 nanocrystals and random lasing in films of CsPbX3 nanocrystals.

Anisotropic conductance at improper ferroelectric domain walls

Transition metal oxides hold great potential for the development of new device paradigms because of the field-tunable functionalities driven by their strong electronic correlations, combined with their earth abundance and environmental friendliness. Recently, the interfaces between transition-metal oxides have revealed striking phenomena, such as insulator-metal transitions, magnetism, magnetoresistance and superconductivity. Such oxide interfaces are usually produced by sophisticated layer-by-layer growth techniques, which can yield high-quality, epitaxial interfaces with almost monolayer control of atomic positions. The resulting interfaces, however, are fixed in space by the arrangement of the atoms. Here we demonstrate a route to overcoming this geometric limitation. We show that the electrical conductance at the interfacial ferroelectric domain walls in hexagonal ErMnO(3) is a continuous function of the domain wall orientation, with a range of an order of magnitude. We explain the observed behaviour using first-principles density functional and phenomenological theories, and relate it to the unexpected stability of head-to-head and tail-to-tail domain walls in ErMnO(3) and related hexagonal manganites. As the domain wall orientation in ferroelectrics is tunable using modest external electric fields, our finding opens a degree of freedom that is not accessible to spatially fixed interfaces.

Observation of ferrotoroidic domains

Domains are of unparalleled technological importance as they are used for information storage and for electronic, magnetic and optical switches. They are an essential property of any ferroic material. Three forms of ferroic order are widely known: ferromagnetism, a spontaneous magnetization; ferroelectricity, a spontaneous polarization; and ferroelasticity, a spontaneous strain. It is currently debated whether to include an ordered arrangement of magnetic vortices as a fourth form of ferroic order, termed ferrotoroidicity. Although there are reasons to expect this form of order from the point of view of thermodynamics, a crucial hallmark of the ferroic state—that is, ferrotoroidic domains—has not hitherto been observed. Here ferrotoroidic domains are spatially resolved by optical second harmonic generation in LiCoPO4, where they coexist with independent antiferromagnetic domains. Their space- and time-asymmetric nature relates ferrotoroidics to multiferroics with magnetoelectric phase control and to other systems in which space and time asymmetry leads to possibilities for future applications.

Second-harmonic generation as a tool for studying electronic and magnetic structures of crystals: review

Second-harmonic generation (SHG) in magnetically ordered crystals is reviewed. The symmetry of such crystals is determined by the arrangement of both the charges and the spins, so their contributions to the crystallographic and the magnetic structures, respectively, must be distinguished. Magnetic SHG is introduced as a probe for magnetic structures and sublattice interactions. The specific degrees of optical experiments - including spectral, spatial, and temporal resolution - lead to the observation of novel physical effects that cannot be revealed by other techniques of probing magnetism. These include local or hidden phase transitions, interacting magnetized and polarized sublattices and domain walls, and magnetic interfaces. SHG in various centrosymmetric and noncentrosymmetric crystal classes of antiferromagnetic oxides such as Cr2O3, hexagonal RMnO3(R=Sc,Y,In,Ho-Lu), magnetic garnet films, CuB2O4, CoO, and NiO, is discussed.

The toroidal moment in condensed-matter physics and its relation to the magnetoelectric effect

The concept of toroidal moments in condensed-matter physics and their long-range ordering in a so-called ferrotoroidic state is reviewed. We show that ferrotoroidicity as a form of primary ferroic order can be understood both from microscopic (multipole expansion) and macroscopic (symmetry-based expansion of the free energy) points of view. The definition of the local toroidal moment and its transformation properties under the space-inversion and time reversal operations are highlighted and the extension to periodic bulk systems is discussed. Particular attention is paid to the relationship between the toroidal moment and the antisymmetric magnetoelectric effect and to limitations of the magnetoelectric response in ferrotoroidic systems and ferroic materials in general. Experimental access to the ferrotoroidic state by magnetoelectric susceptibility measurements, x-ray diffraction and optical techniques or direct measurement of the bulk toroidization is discussed. We outline the pertinent questions that should be clarified for continued advancement of the field and mention some potential applications of ferrotoroidic materials.

Spin-rotation phenomena and magnetic phase diagrams of hexagonal RMnO3

Magnetic phase diagrams of the hexagonal RMnO3 (with R=Sc, Y, Ho, In, Er, Tm, Yb, Lu) compounds in the magnetic-field/temperature plane are established by linear and nonlinear magneto-optical techniques. Eight different magnetic phases of the Mn3+ sublattice and at least three different phases of the R3+ sublattices are distinguished. Phase coexistence and photoinduced modification of the magnetic structure are observed. Magnetic reorientations of the Mn3+ lattice can occur via in-phase or antiphase rotation of the triangularly frustrated spins in the adjacent crystallographic planes.

Electrostatic topology of ferroelectric domains in YMnO3

Trimerization-polarization domains in ferroelectric hexagonal YMnO3 were resolved in all three spatial dimensions by piezoresponse force microscopy. Their topology is dominated by electrostatic effects with a range of 100 unit cells and reflects the unusual electrostatic origin of the spontaneous polarization. The response of the domains to locally applied electric fields explains difficulties in transferring YMnO3 into a single-domain state. Our results demonstrate that the wealth of nondisplacive mechanisms driving ferroelectricity that emerged from the research on multiferroics are a rich source of alternative types of domains and domain-switching phenomena.

Domain topography of antiferromagnetic Cr2O3 by second‐harmonic generation

The interference of the time‐invariant magnetic‐dipole contribution with the time‐noninvariant electric‐dipole contribution to the second harmonic (SH) provides a mechanism which is sensitive to the reduction of symmetry of Cr2O3 by antiferromagnetic ordering of spins. A pronounced polarization dependence of the SH on the sign of the order parameter is observed in the 1.7–3.1 eV spectral range. The effect is used to study the domain structure of Cr2O3 by use of a CCD camera. Exposure times in the order of minutes are sufficient to yield a high‐resolution image of domains in samples of 10 mm2.