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.

A highly excited atom having an electron that has moved into a level with large principal quantum number is a hydrogen-like object, termed a Rydberg atom. The giant size of Rydberg atoms leads to huge interaction effects. Monitoring these interactions has provided insights into atomic and molecular physics on the single-quantum level. Excitons--the fundamental optical excitations in semiconductors, consisting of an electron and a positively charged hole--are the condensed-matter analogues of hydrogen. Highly excited excitons with extensions similar to those of Rydberg atoms are of interest because they can be placed and moved in a crystal with high precision using microscopic energy potential landscapes. The interaction of such Rydberg excitons may allow the formation of ordered exciton phases or the sensing of elementary excitations in their surroundings on a quantum level. Here we demonstrate the existence of Rydberg excitons in the copper oxide Cu2O, with principal quantum numbers as large as n = 25. These states have giant wavefunction extensions (that is, the average distance between the electron and the hole) of more than two micrometres, compared to about a nanometre for the ground state. The strong dipole-dipole interaction between such excitons is indicated by a blockade effect in which the presence of one exciton prevents the excitation of another in its vicinity.

Optical second harmonic spectroscopy is introduced as a powerful supplement for the determination of complex magnetic structures. Experimental efforts are simplified and new degrees of freedom are opened. Thereby, some principal or technical restrictions of neutron or magnetic x-ray diffraction experiments are overcome. High spatial resolution leads to additional information about magnetically ordered matter. As an example, the noncollinear magnetic structure of the hexagonal manganites RMnO3 ( R = Sc, Y, Ho, Er, Tm, Yb, Lu) is analyzed. The results show that some earlier conclusions on their magnetic symmetry and properties should be revised.

The recent observation of dipole-allowed P -excitons up to principal quantum numbers of n = 25 in cuprous oxide has given insight into exciton states with unprecedented spectral resolution. While so far the exciton description as a hydrogen-like complex has been sufficient for cubic crystals, we demonstrate here distinct deviations: The breaking of rotational symmetry leads to mixing of high angular momentum F -and H-excitons with the P -excitons so that they can be observed in absorption. The F -excitons show a three-fold splitting that depends systematically on n, in agreement with theoretical considerations. From detailed comparison of experiment and theory we determine the cubic anisotropy parameter of the Cu2O valence band. PACS numbers:Introduction. Excitonic effects are decisive for the optical properties of semiconductors and insulators [1]. Not only leads the Coulomb interaction between an electron and a hole to a series of bound states, the excitons, with energies below the band gap, but also above the gap the Coulomb effects lead to a massive redistribution of oscillator strength towards the low-energy states compared to a free particle description. Due to this importance it has been a major goal to develop a detailed understanding of excitons on a quantitative level [1]. The description of the bound exciton states by the hydrogenic model has turned out to be extremely successful in this respect, in particular, for bulk semiconductors of cubic symmetry.For excitons with wavefunction extensions much larger than the crystal unit cell (the Mott-Wannier excitons) the hydrogen formula for their binding energy, R/n 2 with the Rydberg energy R in a state of principal quantum number n, can be simply adapted to the solid state case by (i) changing the reduced mass of electron and proton m to that of electron and hole m * , and (ii) screening the carrier interaction by the dielectric constant ε:The influence of the many-body crystal environment is thus comprised in material properties that for cubic semiconductors are, as a rule, isotropic such as the scalar dielectric constant ε, leading to a formula for excitonic energies that is identical to the one in a system with rotational symmetry. The material environment typically causes a reduction of the atomic Rydberg energy by 2 − 3 orders of magnitude into the meV range.For the hydrogen problem the spatial symmetry is determined by the continuous rotation group SO(3), where the square of the orbital momentum L 2 = l(l + 1)

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Two of the most striking experimental findings when investigating exciton spectra in cuprous oxide using high-resolution spectroscopy are the observability and the fine structure splitting of F excitons reported by J. Thewes et al. [Phys. Rev. Lett. 115, 027402 (2015)]. These findings show that it is indispensable to account for the complex valence band structure and the cubic symmetry of the solid in the theory of excitons. This is all the more important for magnetoexcitons, where the external magnetic field reduces the symmetry of the system even further. We present the theory of excitons in Cu2O in an external magnetic field and especially discuss the dependence of the spectra on the direction of the external magnetic field, which cannot be understood from a simple hydrogen-like model. Using high-resolution spectroscopy, we also present the corresponding experimental spectra for cuprous oxide in Faraday configuration. The theoretical results and experimental spectra are in excellent agreement as regards not only the energies but also the relative oscillator strengths. Furthermore, this comparison allows for the determination of the fourth Luttinger parameter κ of this semiconductor.

In spite of the fact that inversion is a symmetry operation of both the crystalline and the magnetic lattice of NiO, second harmonic generation (SHG) has been observed below the Néel temperature. A spectroscopic study shows that the signal is due to combined magnetic-dipole and electric-dipole transitions between the (3d)(8) levels of the Ni(2+) ion in the crystal field. The SHG is resonant in both the incoming and the outgoing light waves and thus greatly enhanced. A quadratic coupling of the nonlinear polarization to the order parameter was found. This allows the investigation of individual domains.