An exciton is a quasiparticle composed of an electron and a hole bound by Coulomb interactions. These hydrogenic quasiparticles emit very narrow-spectrum light. The properties of the emitted light, such as polarization, photon energy, and intensity, can be utilized to achieve sensitive measurements of the space surrounding an exciton. Combination of exciton spectroscopy with microscopy enables the real-space imaging of such properties achieving spin-resolved high-energy-resolution spectroscopy. In this review paper, we unveil the versatile spatial patterns created by genuine fractional quantum Hall (FQH) effects. This technique can shed new light on a diverse range of systems beyond those exhibiting FQH effects. Thus, this technique is a powerful tool for probing the microscopic nature of many systems that are not well understood.

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  After a brief introduction of the spin-polarized scanning tunneling microscopy (SP-STM), its measurement techniques are described based on our recent experimental results. We have observed anomalously high spin contrast for epitaxially grown Mn(001)/Fe(001) samples. This phenomenon can be attributed to a single atom or a cluster of Mn attached to the apex of the thin film Fe tip. This interpretation is supported by a recent first-principle calculation of model magnetic tips. These results stress the importance of the identification of the magnetic tip and its precise control at an atomic level for the purpose of SP-STM measurement.

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  Photoelectron emission microscope (PEEM) is used to analyze ferromagnetic materials by using circularly polarized x-ray and utilizing x-ray magnetic circular dichroism (XMCD) effect. At first, the principles of PEEM and XMCD are explained, and the features of PEEM are mentioned. Then, as examples of PEEM application to ferromagnetic material analysis, recent two results are introduced: the observation of magnetic domain structure and elemental distribution on FeNi alloys processed by high-pressure torsion; the magnetic domain observation of FeCo thin films fabricated by alternate monoatomic layer deposition.

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  A magnetic domain imaging method using linearly polarized light is introduced. Combination of linearly polarized synchrotron radiation and photoemission electron microscope (PEEM) allows us to image domains not only for ferromagnetic (FM) but also for antiferromagnetic (AFM) materials. Since element specific observation is possible, magnetic properties of specified atoms in interfaces are easily investigated. This method is utilized for the study of the magnetic coupling at interfaces between FM surface and AFM substrates. Examples of imaging for AFM domains on NiO(001), and Fe/NiO(001) interface systems are introduced. The spin orientation in domain walls of AFM NiO is also observed.

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  A novel Lorentz electron microscopy —twin-Foucault imaging (TFI) method— is introduced. The twin-Foucault imaging method enables observation of two Foucault images simultaneously by using an electron biprism instead of an objective aperture. The electron biprism is installed between two electron beams deflected by magnetic domains. Potential applied to the biprism deflects the two electron beams further, and two Foucault images are then obtained in one visual field. The twin-Foucault images are able to extract the magnetic domain structures and to reconstruct an ordinary electron micrograph. The Foucault method was demonstrated with 180° domain and 90°/180° domain structures of manganite La_1−αSr_αMnO₃.

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