# Nonlinear Optical Microscopy of Interface Layers of Epitaxial Gamet Films
## 1 Introduction  
Magnetic domains are of high interest to researchers due to both the bright underlying physics that governs their organization, and because of an important role played by domains in a lot of applications of magnetic nano- and microstructures [1]. One of the most studied and attractive objects here are the crystalline ferrimagnetic iron garnet films that combine strong magnetooptical (MO) activity with high transparency in the red and infrared spectral ranges, pronounced mechanical properties, and the ability to control the parameters of the MO spectra by modification of their chemical composition [2; 3; 4; 5]. It is generally recognized that garnets are widely used as optical disks [6], resonators [7], and in microwave devices [8]. Moreover, they are known as an efficient platform for spintronic and magnonic devices due to their exciting ability for the transport and processing of spin waves [9; 10; 11]. The most important properties of garnets are determined to a large extent by their domain organization, which is governed by many parameters such as the crystallographic symmetry, type and concentration of dopants, magnetic and crystalline anisotropy, demagnetization fields, etc. [1; 2; 12; 13]. As the properties of the surface and bulk magnetic domains are interconnected, their study is an interesting research task. Furthermore, the development of efficient experimental methods for the visualization of magnetic domains in the surface and bulk areas of garnet films seems also to be quite important. The best-known approaches here are the polarization-sensitive magnetooptical microscopy typically performed in the Faraday or Voigt geometries [14; 15], X-ray diffraction techniques, first of all the surface-sensitive Lorentz microscopy [16; 17], and magnetic force microscopy (MFM) [18; 19]. In the case of yttrium iron garnet films with perpendicular magnetic anisotropy, the Lorentz microscopy allows to study the magnetic domains at the nanoscale. It also revealed an important role played by the demagnetization field in the formation if domains and domain walls dynamics [20]. These studies involved thehigh spatial resolution of the Lorentz microscopy technique (that is below 100 nm), and the temporal resolution of this surface sensitive probe can be made less than 1 ps [21]. This allows the study of spin relaxation dynamics and the domain wall's motion under the application of the external magnetic field. The magnetic force microscopy technique allows the visualization of complicated fractal-like and closure domains at the surface of epitaxial garnet films that are absent in bulky materials; it was recognized that the shape of the surface domains depend on the films' thickness and composition [22]. A special place is occupied by the optical second harmonic generation (SHG) [23], which has been shown to provide giant values of magnetooptical effects in the SHG response predicted prior to their experimental observation [24; 25]. It is also known for its high surface sensitivity if being applied to materials with intrinsic inversion symmetry [26; 27; 28; 29; 30]. In the case of iron garnet films, the application of the SHG technique is beneficial due to (i) symmetry forbidance of the even-order nonlinear optical effects (including SHG) in the bulk of centrosymmetric materials such as yttrium iron garnet crystals (in the electric dipole approximation), which provides high SHG sensitivity to the properties of the interface regions with inevitably broken inversion symmetry [23; 31; 32], (ii) absence of the SHG contribution from the substrates, which is typically centrosymmetric gallium-gadolinium garnet (GGG) of a few hundreds of microns in thickness and which can also reveal weak MO responses, (iii) the large value of the MO effects in the SHG response and (iv) larger (as compared to the linear MO microscopy) SHG spatial resolution originating from the nonlinear nature of the effect, and (v) the ability to use a multiple-color pump and probe experimental schemes.