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Johannes Wasmer authoredJohannes Wasmer authored
jij-prediction.tex 8.55 KiB
\section{Machine learning exchange interactions}
\label{sec:ml-exc-inter}
% Slide PhD project flowchart % Section phd-project
\begin{frame}
\frametitle{Vision: Electronic structure learning}
% frametitle notes: PhD project flowchart
\framesubtitle{as integrated, high-level multiscale workflows}
\vspace*{0em}
\includegraphics[width=1.0\textwidth]{../resources/fig/presentation-2023-02/atomistic-ml/classification-of-atomistic-ml_presentation-2023-02_02-emph-both_ktikz.pdf}
\vspace*{2em}
\begin{columns}[t]
\hspace{1em}
\begin{column}{0.6\linewidth}
\begin{center}
Better \enquote{initial guess}
for fast SCF convergence
\end{center}
\end{column}
\vrule{}
\hspace{1em}
\begin{column}{0.39\linewidth}
\begin{center}
Magnetic property prediction
(ML-Exc) for spin dynamics
\end{center}
\end{column}
\end{columns}
\end{frame}
% Slide MTIs (magnetic topological insulators) % Section co-doping
{
\setbeamercolor{background canvas}{bg=}
\includepdf[pages=1]{../resources/fig/presentation-2023-03/ruess/ruess-TIs.pdf}
}
% Slide study design % Section co-doping
\begin{frame}[plain,c]
\frametitle{Project \enquote{ML-Exc}}
\framesubtitle{Magnetic co-doping of topological insulators}
\hspace*{1em} \ce{Bi2Te3} \hspace*{3em} Dimer clusters of \(3d\), \(4d\) transition
metal defects\vspace*{-1em}
\begin{columns}[c]
\hspace*{1em}
\begin{column}{0.6\textwidth}
\begin{center}
\includegraphics[width=0.35\textheight]{../resources/fig/external/papers/mozumderHighthroughputMagneticCodoping2024/processed/Fig1-a.pdf}%
\hspace*{-0.5em}
\includegraphics[width=0.80\textwidth]{../resources/fig/external/papers/mozumderHighthroughputMagneticCodoping2024/processed/FigA3-extract-6.pdf}%
\end{center}
\end{column}
\hspace*{3em}
\begin{column}{0.4\textwidth}
{\small
Single-impurity dabase, N=2'000.
\href{https://go.fzj.de/judit}{go.fzj.de/judit}\vspace*{1em}
Dimer database, N=2'000\footcite{mozumderHighthroughputMagneticCodoping2024}.\vspace*{3em}
Co-doping can help to control
\begin{itemize}
\item critical \(T_c\) of QAHE \item exchange splitting \(\Delta_{xc}\)
\item long-range magnetic ordering
\end{itemize}\vspace*{1em}
for applications in spintronics and
fault-tolerant quantum computing.
}
\end{column}
\end{columns}
\end{frame}
% Slide AiiDA-KKR workflows % Section co-doping
\begin{frame}[plain,c]
\frametitle{Project \enquote{ML-Exc}}
\framesubtitle{\logoAiida{}-KKR workflows\footcite{russmannAiiDAKKRPluginIts2021}}
\vspace*{-1em}
\begin{columns}[t]
\hspace*{-2em}
\begin{column}{0.3\linewidth}
% {\footnotesize Single impurity}
\begin{center}
\includegraphics[width=0.8\linewidth]{../resources/fig/presentation-2023-03/ruess/ruess-aiida-kkr-paper-workflow-c.pdf}
\end{center}
\end{column}
\begin{column}{0.5\linewidth}
\hspace*{-3em}
\begin{center}
% {\footnotesize \(N+1\) impurities}
\includegraphics[width=0.8\linewidth]{../resources/fig/external/papers/mozumderHighthroughputMagneticCodoping2024/processed/FigA2-no-subfigure-labels.pdf}%
\end{center}
\end{column}
\end{columns}
\vspace*{-0em}
\begin{flushright}
Extended Heisenberg Hamiltonian.
\(H = -\frac{1}{2}\sum_{i,j}J_{ij} \, \vec{S}_i \cdot \vec{S}_j
-\frac{1}{2}\sum_{i,j}\vec{D}_{ij} \cdot \left( \vec{S}_i \times \vec{S}_j \right)
\)
Exchange constants from method of infinitesimal rotations\footcite{liechtensteinLocalSpinDensity1987}.
\( % Liechtenstein infinitesimal roation Jij from KKR-GF
\mathcal{J}_{ij} = -\frac{1}{\pi} \operatorname{Im} \int_{-\infty}^{E_F}
\mathrm{d} E \operatorname{Tr}[\delta t_i G_{ij} \delta t_j G_{ji}]
\)
\end{flushright}
\end{frame}
% Slide results Jijs 1 % Section co-doping
{
\setbeamercolor{background canvas}{bg=}
\includepdf[pages=1]{../resources/fig/external/papers/mozumderHighthroughputMagneticCodoping2024/originals/Fig4.pdf}
}
% Slide AiiDA-Spirit workflows % Section jij-prediction
\begin{frame}[plain,c]
\frametitle{Spin dynamics with \logoAiida{}-\raisebox{-0.4em}{\logoSpiritWithText{}}\footcite{russmannAiiDASpiritPluginAutomated2022}}
\vspace*{-2em}
\begin{columns}[t]
\begin{column}{0.4\linewidth}
\begin{center}
\includegraphics[width=1.0\linewidth]{../resources/fig/external/papers/mozumderHighthroughputMagneticCodoping2024/processed/FigA2-no-subfigure-labels.pdf}%
% \includegraphics[width=1.0\linewidth]{../resources/fig/presentation-2023-03/ruess/ruess-aiida-kkr-paper-workflow-c.pdf}\footcite{russmannAiiDAKKRPluginIts2021}
\vspace*{1em}
Liechtenstein formula
\[
\mathcal{J}_{ij} = -\frac{1}{\pi} \operatorname{Im} \int_{-\infty}^{E_F}
\mathrm{d} E \operatorname{Tr}[\delta t_i G_{ij} \delta t_j G_{ji}]
\]
ML-IAP approach. \(E_k = \sum_k E_k \longrightarrow J_{ij} =
\sum_k \left( J_{ij} \right)_k\)
\end{center}
\end{column}
\begin{column}{0.55\linewidth}
\begin{center}
\includegraphics[width=1.0\linewidth]{../resources/fig/presentation-2023-03/ruess/ruess-aiida-spirit-paper-workflow.pdf}%
Landau-Lifshitz-Gilbert equation
\[
\frac{\partial \vec{S}_i}{\partial t}=-\gamma^{\prime} \vec{S}_i \times \vec{B}_i^{\text {eff }}-\lambda \vec{S}_i \times\left(\vec{S}_i \times \vec{B}_i^{\text {eff }}\right)
\]
% \vspace*{2em}
\normalsize{\href{https://juspin.de}{juspin.de}}
\end{center}
\end{column}
\end{columns}
\end{frame}
% Slide project design % Section jij-prediction
\begin{frame}[plain,c]
\frametitle{Project \enquote{ML-Exc}}
\framesubtitle{Model selection}
\begin{table}[H]
\resizebox{\columnwidth}{!}{%
\centering
\input{../resources/table/jij-prediction-model-selection}%
% \caption[short caption]{Long caption.}
% \label{tab:model-selection}
}
\end{table}
\end{frame}
% Slide exc-int tensor prediction % Section jij-prediction
\begin{frame}
\frametitle{Project \enquote{ML-Exc}}
\framesubtitle{Tensorial interaction}
Heisenberg Hamiltonian in tensor form.
\[\mathcal{H}_H=-\sum_{j>i} \vec{m}_i \cdot \mathcal{J}_{i j} \vec{m}_j\]
Tensor components: isotropic, anti-symmetric (DMI) and anisotropic or
traceless symmetric part (neglected so far).
\[\mathcal{J}_{i j}=J_{i j} \mathbb{1} + \mathcal{J}_{i j}^A+\mathcal{J}_{i
j}^S\]
with \(J_{i j}^{x x}=J_{i j}^{y y}=J_{i j}^{z z}=\frac{1}{3} J_{i j}\) and
\[\mathcal{J}_{i j}^A=\left[\begin{array}{ccc}
0 & J_{i j}^{x y} & J_{i j}^{x z} \\
J_{i j}^{y x} & 0 & J_{i j}^{y z} \\
J_{i j}^{z x} & J_{i j}^{z y} & 0
\end{array}\right]=\left[\begin{array}{ccc}
0 & J_{i j}^{x y} & -J_{i j}^{z x} \\
-J_{i j}^{x y} & 0 & J_{i j}^{y z} \\
J_{i j}^{z x} & -J_{i j}^{y z} & 0
\end{array}\right]=\left[\begin{array}{ccc}
0 & -D_{i j}^z & D_{i j}^y \\ D_{i j}^z & 0 & -D_{i j}^x \\
-D_{i j}^y & D_{i j}^x & 0
\end{array}\right]\]
\end{frame}
% Slide higher-order exchange interactions
{
\setbeamercolor{background canvas}{bg=}
\includepdf[pages=1]{../resources/fig/external/presentations/spinqx23/hkatsumoto/spinqx23-hkatsumoto-page24.pdf}
}
% Slide relativistic exchange interactions
{
\setbeamercolor{background canvas}{bg=}
\includepdf[pages=1]{../resources/fig/external/presentations/spinqx23/hkatsumoto/spinqx23-hkatsumoto-page25.pdf}
}
% Slide best-of-aml % Section odds-and-ends
\begin{frame}[plain,c]
\frametitle{Community resources}
\framesubtitle{Best of atomistic machine learning}
\vspace*{-4em}
\begin{columns}[c]
\begin{column}{0.5\linewidth}
\vspace*{3em}
\begin{center}
% \includegraphics[width=0.7\textwidth]{../resources/fig/github/best-of-aml-thumbnail-2023-09-05.png}%
\includegraphics[width=0.9\textwidth]{../resources/fig/github/best-of-aml-thumbnail-2024-07-08.png}%
Largest list of atomistic ML tools on the web (400+), auto-ranked,
regular updates\footcite{wasmerBestAtomisticMachine2023}
\vspace*{2em}
\Large{\href{https://go.fzj.de/best-of-aml}{go.fzj.de/baml}}
\end{center}
\end{column}
\begin{column}{0.4\linewidth}
\includegraphics[width=0.85\textwidth]{../resources/fig/github/best-of-aml-contents-2024-07-08.png}%
\end{column}
\end{columns}
\end{frame}
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