Ferrites with the structural formula $Ln$FeO₃ ($Ln$ = lanthanide) usually crystallize in the orthorhombic phase, forming canted antiferromagnetic crystals with a small residual magnetic moment. These well-known ferrites can also form metastable layered hexagonal structures that can be stabilized in the form of nanoparticles or epitaxial thin films. We have explored the formation of these ferrite phases by growing thin films on a hexagonal YSZ(111) substrate surface, which provides a stabilizing template for the formation of the hexagonal ferrite phase. Unfortunately, even on a hexagonal substrate, the ferrites may form orthorhombic crystallites or films with a mixed phase composition. The structures of the metastable film phases are not well known. The formation of the orthorhombic or the hexagonal phases depends on both thermodynamic (temperature, pressure) and kinetic (growth rate) process parameters, giving a very multidimensional parameter space for either mapping the phase boundaries or finding the optimal crystal growth conditions in the accessible parameter space.

We have utilized a combination of several machine learning techniques [1,2] to simplify the process-phase-space optimization task by utilizing in-situ reflection high-energy electron diffraction (RHEED) images. The workflow is illustrated in Fig. 1.

The surface structure of a growing film is analyzed by real-time RHEED, which provides information on the surface crystallinity, lattice parameters, and phase purity. The image processing relies on a convolutional neural network (ML1) that is used to segment the image data and isolate diffraction features. [2] Clustering is then used to determine the phase purity of the film surface. Real-time imaging means that it is possible to combine structural quality metrics (crystallinity, phase purity) with temporal metrics (growth rate, phase stability). Examples of calculated quality metrics are shown in Fig. 2(a). At the start of an experiment, a Gaussian process (ML2) optimizer [1] is bootstrapped with quality factors determined from a small number of test films grown at process conditions selected by the operator. After that, the autonomous process starts by allowing the Gaussian process to automatically select process conditions for subsequent growth experiments.

An example of the effectiveness of the autonomous synthesis workflow is illustrated for pulsed laser deposition of EuFeO₃ films in Fig. 2. A shadow mask is used in the film growth chamber to fabricate up to 12 thin films on a single substrate (Fig. 1). Experiments needed for both model bootstrapping and condition optimization can thus be done quickly on a single substrate without the need for sample transfers. The operator initially guesses deposition process parameters in a four-dimensional space (temperature, oxygen pressure, ablation pulse energy, deposition rate) and the quality factors are determined for each film, as shown in Fig. 2(a). In this case, the operator did not find the conditions where a flat, high-crystallinity surface is obtained.

The Gaussian process, however, found the optimal process conditions in just four tries, as shown in Fig. 2(b), obtaining phase-pure films with a clear streak pattern, corresponding to a nanometer-scale flat surface without three-dimensional structures.

The main advantage of the autonomous process is to rapidly probe different regions in a multidimensional parameter space. For a human operator, it is difficult to perform optimization experiments effectively when the parameter space dimensionality is larger than two or three. The autonomous workflow greatly reduces the number of required experiments.

References

• [1] I. Ohkubo et al., Mater. Today Phys. 16, 100296 (2021).
• [2] H. Liang et al., Phys. Rev. Materials 6, 063805 (2022).

Authors

• I. Ohkubo^a, Z. Hou^a, T. Aizawa^a, T. Chikyow^a, T. Mori^a, K. Tsuda^a, H. Liang^b, V. Stanev^b, A. G. Kusne^b, I. Takeuchi^b, Y. Tsukahara^c, K. Ito^c, R. Takahashi^c, J. N. Lee, and  M. Lippmaa
• ^aNIMS
• ^bUniversity of Maryland
• ^cNihon University