Hamiltonian learning for spin-spiral moiré magnets from electronic magnetotransport

Abstract

Two-dimensional noncollinear magnetic states, such as spin-spiral magnets, offer an excellent platform for investigating fundamental phenomena, with potential for advancing stray-field-free spintronics. However, detection and characterization of noncollinear magnetic states in two-dimensional systems remain challenging, motivating the development of alternative probing methods. Here, we present a methodology for extracting the spin-spiral $\mathbf{q}$ vector from lateral electronic transport measurements. Our approach leverages the magnetic field and bias dependence of the conductance to train a supervised machine learning algorithm, which enables us to extract the $\mathbf{q}$ vectors of arbitrary spin-spiral magnets. We demonstrate that this methodology is robust to the presence of impurities in the system and noise in the conductance data. Our findings show that the conductance pattern reveals a complex dependence on the $\mathbf{q}$ vector of the spin spiral, providing a new strategy to learn magnetic structures directly from transport experiments.

Figures (6)

• Figure 1: (a) Schematic of an electrical gated device to probe noncollinear magnetic order in a twisted vdW structure (see the inset). Red arrows show local magnetic moments localized on the sites of the triangular moiré superlattice. $\mathbf{b}_{1,2}$ are reciprocal lattice basis vectors and $\vec{B} = B \mathbf{e}_z$ is a perpendicular external magnetic field. (b) Schematic representation of the Hamiltonian learning approach employed for the extraction of the $\mathbf{q} = (q_1, q_2)$ of the SSM by leveraging the conductance $G(\mu, \phi, q_{1,2})$.
• Figure 2: (a) Density of states of the Hofstadter butterfly for a triangular-lattice nanoribbon as a function of the chemical potential $\mu$ and normalised magnetic flux $\phi/\phi_0$. (b) Conductance without a magnetic exchange proximity. (c)-(f) Exchange proximity-induced conductance change $\Delta G$ for different special values of $\mathbf{q}$ calculated using \ref{['Landauer_conductance']} for $J = t$ and $W = 0.2t$.
• Figure 3: Prediction results for $|\mathbf{q}|$ (a) and $\theta$ (b) for previously unseen inputs with the number of PCs $N_{PCA} = 500$, $J = t$, and $W = 0.2t$.
• Figure 4: (a)-(d) The dependence of the fidelity as a function of the noise strength $\eta_{test}$ in the conductance for different noise strengths used in the training $\eta_{train}=0.01,\, 0.05,\, 0.1$. (e) The dependence of the fidelity vs exchange coupling $J_{test}$ in testing data for different exchange couplings used in the training $J_{train}=0.2t$ and $t$. (f) The fidelity vs noise dependence for different exchange couplings $J_{train}= J_{test} = 0.2t$ and $t$. Solid and dashed lines in (e)-(f) show the $|\mathbf{q}|$-fidelity $\cal F_{|\bf{q}|}$ and angular fidelity $\cal F_{\theta}$, respectively.
• Figure 5: Prediction results for $|\mathbf{q}|$ (a) and $\theta$ (b) obtained with the NN trained and tested with the noisy data with $\eta_{train} = 0.05$ and $\eta_{test} = 0.05$; $N_{PCA} = 500$, $J = t$, and $W = 0.2t$.