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.

/pdf/second-harmonic-generation-as-a-tool-for-studying-electronic-2jobylwfik.pdf

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

The structure of our material world is characterized by a large hierarchy of length scales that determines material properties and functions. Increasing spatial resolution in optical imaging and spectroscopy has been a long standing desire, to provide access, in particular, to mesoscopic phenomena associated with phase separation, order, and intrinsic and extrinsic structural inhomogeneities. A general concept for the combination of optical spectroscopy with scanning probe microscopy emerged recently, extending the spatial resolution of optical imaging far beyond the diffraction limit. The optical antenna properties of a scanning probe tip and the local near-field coupling between its apex and a sample provide few-nanometer optical spatial resolution. With imaging mechanisms largely independent of wavelength, this concept is compatible with essentially any form of optical spectroscopy, including nonlinear and ultrafast techniques, over a wide frequency range from the terahertz to the extreme ultraviolet. ...

Nano-optical imaging and spectroscopy of order, phases, and domains in complex solids

In this review I discuss the application of scanning magnetic imaging to fundamental studies of superconductors, concentrating on three scanning magnetic microscopies—scanning SQUID microscopy (SSM), scanning Hall bar microscopy (SHM) and magnetic force microscopy (MFM). I briefly discuss the history, sensitivity, spatial resolution, invasiveness and potential future developments of each technique. I then discuss a selection of applications of these microscopies. I start with static imaging of magnetic flux: an SSM study provides deeper understanding of vortex trapping in narrow strips, which are used to reduce noise in superconducting circuitry. Studies of vortex trapping in wire lattices, clusters and arrays of rings and nanoholes show fascinating ordering effects. The cuprate high-Tc superconductors are shown to have predominantly d-wave pairing symmetry by magnetic imaging of the half-integer flux quantum effect. Arrays of superconducting rings act as a physical analog for the Ising spin model, with the half-integer flux quantum effect helping to eliminate one source of disorder in antiferromagnetic arrangements of the ring moments. Tests of the interlayer tunneling model show that the condensation energy available from this mechanism cannot account for the high critical temperatures observed in the cuprates. The strong divergence in the magnetic fields of Pearl vortices allows them to be imaged using SSM, even for penetration depths of a millimeter. Unusual vortex arrangements occur in samples comparable in size to the coherence length. Spontaneous magnetization is not observed in Sr2RuO4, which is believed to have px ± ipy pairing symmetry, although effects hundreds of times bigger than the sensitivity limits had been predicted. However, unusual flux trapping is observed in this superconductor. Finally, unusual flux arrangements are also observed in magnetic superconductors. I then turn to vortex dynamics: imaging of vortices in rings of highly underdoped cuprates places limits on spin-charge separation in these materials. Studies of spontaneous generation of fluxoids upon cooling rings through the superconducting transition provide clues to dynamical processes relevant to the early development of the universe, while studies of vortex motion in cuprate grain boundaries allow the measurement of current–voltage characteristics at the femtovolt scale for these technologically important defects. Scanning SQUID susceptometry allows the measurement of superconducting fluctuations on samples comparable in size to the coherence length, revealing stripes in susceptibility believed to be associated with enhanced superfluid density on the twin boundaries in the pnictide superconductor Co doped Ba-122, and indicating the presence of spin-like excitations, which may be a source of noise in superconducting devices, in a wide variety of materials. Scanning magnetic microscopies allow the absolute value of penetration depths to be measured locally over a wide temperature range, providing clues to the symmetry of the order parameter in unconventional superconductors. Finally, MFM tips can be used to manipulate vortices, providing information on flux trapping in superconductors.

https://iopscience.iop.org/article/10.1088/0034-4885/73/12/126501/pdf

Fundamental studies of superconductors using scanning magnetic imaging

We describe an improved two-dimensional optical scanning technique combined with an ultrafast Sagnac interferometer for delayed-probe imaging of surface wave propagation. We demonstrate the operation of this system, which involves the use of a single focusing objective, by monitoring surface acoustic wave propagation on opaque substrates with picosecond temporal and micron lateral resolutions. An improvement in the lateral resolution by a factor of 3 is achieved in comparison with previous setups for similar samples.

/pdf/scanning-ultrafast-sagnac-interferometry-for-imaging-two-3waamme43z.pdf

Scanning ultrafast Sagnac interferometry for imaging two-dimensional surface wave propagation

Magnetic stripe domains in the spin reorientation transition region are investigated in (Fe/Ni)/Cu(001) and Co/Cu/(Fe/Ni)/Cu(001) using photoemission electron microscopy. For (Fe/Ni)/Cu(001), the stripe domain width decreases exponentially as the Fe/Ni film approaches the spin reorientation transition point. For Co/Cu/(Fe/Ni)/Cu(001), the Fe/Ni stripe orientation is aligned with the Co in-plane magnetization, and the stripe domain width decreases exponentially with increasing the interlayer coupling between the Fe/Ni and Co films. By considering magnetic stripes within an in-plane magnetic field, we reveal a universal dependence of the stripe domain width on the magnetic anisotropy and on the interlayer coupling.

Magnetic stripe domains in coupled magnetic sandwiches.

A scanning near-field optical microscope is combined with a modified Sagnac interferometer to generate high-resolution magnetic contrast images of a magneto-optical disk (MOD) in reflection. The interferometer acts as a magnetic sensor to determine the Kerr rotation of reflected circularly polarized light. A separate shear-force sample topography is obtained simultaneously with the optical. This technique allows successful magnetic imaging of samples with complicated surface topographies, as demonstrated with the MOD. For these initial measurements, the resolution with nonmetal-coated fiber tips is 300 nm, and the magnetic phase sensitivity is 1 mrad.

Kerr-rotation imaging in scanning near-field optical microscopy using a modified Sagnac interferometer

We report on a scanning near-field optical microscope which operates in ultrahigh vacuum and allows magneto-optical Kerr-effect measurements at variable temperatures and in external magnetic fields with subwavelength lateral resolution. High magneto-optical contrast is achieved by combination with a Sagnac interferometer. In this way, magnetic domain patterns of ultrathin films of Fe/Cu(100), grown at 80 K, were studied in situ. A domain phase consisting of perpendicularly magnetized submicron wide stripes with directional order was observed.

In situ near-field imaging of magnetic domain patterns in ultrathin iron films

Cu(100)上,Fe超薄膜のストライプ磁区形成を介した磁化反転

We report on a study of the magnetic-field induced magnetization-reversal process in ultrathin films of Fe/Cu(100) in the vicinity of the spin-reorientation transition. Magnetic domain patterns were visualized by scanning near-field magneto-optical microscopy in situ in ultrahigh vacuum and in presence of external magnetic fields. We find that for films with perpendicular anisotropy, magnetization reversal happens via formation of stripe domains with sub-$\ensuremath{\mu}\mathrm{m}$ stripe widths. Observed hysteresis effects are explained by pinning of stripes.

Magnetization reversal via the formation of stripe domains in ultrathin Fe films on Cu(100)

We report on the combination of a scanning near-field optical microscope and a modified Sagnac interferometer for magnetic-domain imaging in the reflection mode The Sagnac interferometer is used for detection of the magneto-optical Kerr effect Since the interferometer is inherently insensitive to polarization changes caused by topography effects, magnetic-domain imaging is not limited to samples with flat surfaces In this way, it is possible to image magnetic bits written on the tracks of a magneto-optical disc that has a rather pronounced surface profile

Magnetic domain imaging with a scanning near-field optical microscope using a modified Sagnac interferometer.

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