A low temperature nonlinear optical rotational anisotropy spectrometer for the determination of crystallographic and electronic symmetries

A compact and stable incidence-plane-rotating second harmonics detector

We describe a compact and stable setup for detecting the optical second harmonics, in which the incident plane rotates with respect to the sample. The setup is composed of rotating Fresnel rhomb optics and a femtosecond ytterbium-doped fiber laser source operating at the repetition frequency of 10 MHz. The setup including the laser source occupies an area of 1 m² and is stable so that the intensity fluctuation of the laser harmonics can be less than 0.2% for 4 h. We present the isotropic harmonic signal of a gold mirror of 0.5 pW and demonstrate the integrity and sensitivity of the setup. We also show the polarization-dependent six-fold pattern of the harmonics of a few-layer WSe₂, from which we infer the degree of local-field effects. Finally, we describe the extensibility of the setup to investigate the samples in various conditions such as cryogenic, strained, ultrafast non-equilibrium, and high magnetic fields.

Fast reflective optic-based rotational anisotropy nonlinear harmonic generation spectrometer

We present a novel Rotational Anisotropy Nonlinear Harmonic Generation (RA-NHG) apparatus based primarily upon reflective optics. The data acquisition scheme used here allow for fast accumulation of RA-NHG traces, mitigating low frequency noise from laser drift, while permitting real-time adjustment of acquired signals with significantly more data points per unit angle rotation of the optics than other RA-NHG setups. We discuss the design and construction of the optical and electronic components of the device and present example data taken on a GaAs test sample at a variety of wavelengths. The RA-second harmonic generation data for this sample show the expected four-fold rotational symmetry across a broad range of wavelengths, while those for RA-third harmonic generation exhibit evidence of cascaded nonlinear processes possible in acentric crystal structures.

Fourier domain rotational anisotropy-second harmonic generation

We describe a novel scheme of detecting rotational anisotropy-second harmonic generation (RA-SHG) signals using a lock-in amplifier referenced to a fast scanning RASHG apparatus. The method directly measures the nth harmonics of the scanning frequency corresponding to SHG signal components of Cn symmetry that appear in a Fourier series expansion of a general RA-SHG signal. GaAs was used as a test sample allowing comparison of point-by-point averaging with the lock-in based method. When divided by the C_∞ signal component, the lock-in detected data allowed for both self-referenced determination of ratios of Cn components of up to 1 part in 10⁴ and significantly more sensitive measurement of the relative amount of different Cn components when compared with conventional methods.

Direct measurement of proximity-induced magnetism at the interface between a topological insulator and a ferromagnet

When a topological insulator (TI) is in contact with a ferromagnet, both time-reversal and inversion symmetries are broken at the interface. An energy gap is formed at the TI surface, and its electrons gain a net magnetic moment through short-range exchange interactions. Magnetic TIs can host various exotic quantum phenomena, such as massive Dirac fermions, Majorana fermions, the quantum anomalous Hall effect and chiral edge currents along the domain boundaries. However, selective measurement of induced magnetism at the buried interface has remained a challenge. Using magnetic second-harmonic generation, we directly probe both the in-plane and out-of-plane magnetizations induced at the interface between the ferromagnetic insulator (FMI) EuS and the three-dimensional TI Bi2Se3. Our findings not only allow characterizing magnetism at the TI-FMI interface but also lay the groundwork for imaging magnetic domains and domain boundaries at the magnetic TI surfaces.

On the use of structured light in nonlinear optics studies of the symmetry group of a crystal

We put forward a technique that allows to extract information about the symmetry group to which certain nonlinear crystals belong using a single illuminating beam. It provides such information by considering the outcome of a nonlinear optics process characterized by the electric nonlinear susceptibility tensor, whose structure is dictated by such symmetry group. As an example, we consider the process of spontaneous parametric down-conversion, when it is pumped with a special type of Bessel beam. The observation of the spatial angular dependence of the lower-frequency generated light provides direct information about the symmetry group of the crystal. We should stress that the choice of the appropriate illumination is of paramount importance for unveiling the sought-after information.

High-speed measurement of rotational anisotropy nonlinear optical harmonic generation using position-sensitive detection

We present a method of performing high-speed rotational anisotropy nonlinear optical harmonic generation experiments at rotational frequencies of several hertz by projecting the harmonic light reflected at different angles from a sample onto a stationary position-sensitive detector. The high rotational speed of the technique, 10(3) to 10(4) times larger than existing methods, permits precise measurements of the crystallographic and electronic symmetries of samples by averaging over low frequency laser-power, beam-pointing, and pulse-width fluctuations. We demonstrate the sensitivity of our technique by resolving the bulk fourfold rotational symmetry of GaAs about its [001] axis using second-harmonic generation.

Grain Structures and Boundaries on Microcrystalline Copper Covered with an Octadecanethiol Monolayer Revealed by Sum Frequency Generation Microscopy

An octadecanethiol (ODT) self-assembled monolayer on microcrystalline copper was investigated by sum frequency generation (SFG) imaging microscopy. The crystal grain and grain boundaries of the copper surface were mapped in the SFG image based on the strong brightness contrast of the SFG signal across the boundary. Local SFG spectra reveal significant difference with each other as well as the average SFG spectra, indicating the heterogeneity of the copper surface resulting from copper grains with distinct crystallographic facets and orientations. It is demonstrated that the SFG signal of crystalline domain areas contains azimuthal anisotropy with respect to the plane of incidence. In addition, the statistical orientation analyses of amplitude ratio of CH3-sym/CH3-asym and corresponding contour maps imply that the orientation of ODT molecules is affected by the underlying copper.

Structural distortion-induced magnetoelastic locking in Sr(2)IrO(4) revealed through nonlinear optical harmonic generation

We report a global structural distortion in Sr_{2}IrO_{4} using spatially resolved optical second and third harmonic generation rotational anisotropy measurements. A symmetry lowering from an I4_{1}/acd to I4_{1}/a space group is observed both above and below the Néel temperature that arises from a staggered tetragonal distortion of the oxygen octahedra. By studying an effective superexchange Hamiltonian that accounts for this lowered symmetry, we find that perfect locking between the octahedral rotation and magnetic moment canting angles can persist even in the presence of large noncubic local distortions. Our results explain the origin of the forbidden Bragg peaks recently observed in neutron diffraction experiments and reconcile the observations of strong tetragonal distortion and perfect magnetoelastic locking in Sr_{2}IrO_{4}.