# Probing Ferroic States in Oxide Thin Films Using Optical Second Harmonic Generation
## 3 Probing Ferroic States in Thin Films Using SHG
### Domain Wall Architecture  
During the last decade, a wide variety of novel phenomena has been discovered at domain walls in ferroic systems ranging from unusual electronic conductance to inseparably entangled spin and charge degrees of freedom [114]. Ferroic domain walls are two-dimensional functional objects that can be created and erased on demand, introducing new opportunities for the next generation of rewritable nanoelectronics [115; 116; 117].  
To investigate these nanosized objects, a combination of multiple techniques is required. For instance, a conducting scanning probe tip can be used to write a desired domain pattern and create 180\({}^{\circ}\) domain walls, but it cannot provide information on their internal architecture, i.e., polarization orientation, symmetry, etc. STEM is commonly used to investigate the atomic configuration across a domain wall section [97; 118] but the information is limited to a single projection perpendicular to the domain wall propagation. SHG can provide complementary information on the polar structure of the domain walls. By directly relating the nonlinear susceptibility tensor elements with the symmetry linked to ferroic order in the system, SHG can selectively pick up the signal from different types of domain-wall configurations, determining their internal polarization orientation [119]. The domain wall architecture can therefore be investigated in three dimensions using a combination of STEM and SHG for cross-section and top view structure analysis, respectively.  
The SHG image of a ferroelectric PZT thin film exhibiting a mixed _a-/c_-domain state is shown in Figure 15a. The image, acquired with an in-plane polarization sensitivity [97], displays stripes along the [001]\({}_{\text{DSO}}\) orientation corresponding to [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]\({}_{\text{DSO}}\)-polarized _a_-domains together with an artificially poled region.  
Strikingly, a non-zero SHG intensity is observed at the edges of the tip-poled region which cannot be explained by the assumed Ising-like 180\({}^{\circ}\) domain walls architecture in strained thin films [97; 120]. At 180\({}^{\circ}\) Ising-like domain walls, the contributions of SHG response from the neighboring opposite domains interfere destructively due to a 180\({}^{\circ}\) phase difference [79; 88]. In addition, in the present optical configuration, i.e., normal incidence, the sensitivity is not set to an out-of-plane oriented polarization. The likely explanation for a non-zero SHG signal at the domain wall is therefore the existence of an in-plane polarization component within the ferroelectric domain wall itself. This corresponds to the presence of a Neel or Bloch component of the polarization, usually observed at domain walls in ferromagnetic systems [121]. It is also interesting to note that, although the PFM line profile in the switched region in Figure 15b shows a single _c_-domain state, the SHG signal profile, which probes the total film thickness, reveals the presence of persisting buried _a_-domains in the same region [97].  
The combination of STEM and SHG allows the investigation of 180\({}^{\circ}\) domain walls in cross-section and top view, respectively. The Ising component observed when mapping atomic displacement across the wall (Figure 15c) combined with a polarization component perpendicular to the domain wall plane identified by SHG imaging (Figure 15a), led to the demonstration of mixed Ising-Neel behavior of the PZT thin film ferroelectric wall [97; 122].