# Probing Ferroic States in Oxide Thin Films Using Optical Second Harmonic Generation
## 3 Probing Ferroic States in Thin Films Using SHG
### Imaging of Ferroic Switching Events  
Optical SHG polarizer and anisotropy measurements probe the net polarization state of thin films in various domain configuration and phases. To visualize domains, domain walls and electric field induced switching events, the symmetry investigation can be combined with spatial resolution when performing SHG imaging. Understanding the dynamics and switching mechanisms of ferroic switching events is the first step towards a deterministic control over the targeted functionality. While ferroelectric switching events can be probed at the nanoscale using a combination of STEM and PFM [95; 96; 97], complex switching events in magnetoelectric multiferroic compounds require the ability to map several coexisting order parameters at the single domain scale. In BFO thin films, the electric-field-induced change in the antiferromagnetic domain configuration has been demonstrated [108; 109] at the scale of the ferroelectric domains. In Figure 12a,b, the local change of magnetic order after voltage application is shown using a combination of PFM and photoemission electron microscopy (PEEM) [108]. This seminal work established the one-to-one coupling between the ferroelectric domain architecture and the corresponding antiferromagnetic domains. The electric field control over this domain correlation led to the deterministic observation of electric field induced magnetization reversal in BFO-based heterostructure at room temperature [11; 12; 13; 14; 110]. Using spatially-resolved SHG, the respective domain structure of each ferroic order and their mutual coupling can be non-invasively probed. As mentioned previously, the as-grown domain architecture in ferroic thin films is typically well below the optical resolution limit (see Figure 12). On the other hand, using scanning probe techniques, it is possible to electrically write macroscopic single domains that are large enough for SHG imaging. Taking advantage of interference effects between oppositely polarized domains and surface contributions [88], one can selectively resolve either the voltage induced domain walls or domains; see Figure 12c-e. Starting from an as-grown ordered ferroelectric domain pattern, SHG imaging together with symmetry component analysis can distinguish between different types of scanning tip-induced switching events [88]. Therefore, specific switching events induced by the trailing field (originating from the lateral movement of the tip during the scan) [111; 112] can be optically probed, as shown in Figure 12f,g. Figure 11: SHG to probe strain relaxation. (**a–c**) Polarizer measurements for different BFO film thicknesses can quantify the amount of T- and R-phases associated with a certain thickness. Reprinted from [107]. Furthermore, the simultaneous evolution of several ferroic orders upon application of external fields can also be visualized using spatially resolved SHG [113]. By symmetry component analysis of the local SHG response, contributions from both ferroelectric domains and antiferromagnetic domain variants were deconvoluted in BFO thin films (Figure 13). The individual symmetry components were isolated using spatially resolved polarizer measurements. The anisotropy of the light polarimetry distribution was identified and correlated to the presence of different antiferromagnetic domain variants, superimposed on the ferroelectric response; see Figure 13b. Comparing the spatially resolved SHG response of the domain structure before and after application of a scanning probe-tip induced external electric field, it could be observed that the switching of the ferroelectric polarization was accompanied by a change in the antiferromagnetic domain state [113]. This optical ferroic domain-mapping capacity demonstrated in the case of BFO thin films opens new avenues toward the determination of magnetoelectric switching dynamics in multiferroic-based heterostructures. Figure 12: Switching events in BFO thin films.