Weak Antilocalization Effect up to ~ 120 K in the van der Waals Crystal Fe5-xGeTe2 with Near Room Temperature Ferromagnetism

The weak antilocalization (WAL) effect is known as a quantum correction to the classical conductivity, which never appeared in two-dimensional magnets. In this work, we reported the observation of a WAL effect in the van der Waals ferromagnet Fe5-xGeTe2 with a Curie temperature Tc ~ 270 K, which can even reach as high as ~ 120 K. The WAL effect could be well described by the Hikami-Larkin-Nagaoka and Maekawa-Fukuyama theories in the presence of strong spin-orbit coupling (SOC). Moreover, A crossover from a peak to dip behavior around 60 K in both the magnetoresistance and magnetoconductance was observed, which could be ascribed to a rare example of temperature driven Lifshitz transition as indicated by the angle-resolved photoemission spectroscopy measurements and first principles calculations. The reflective magnetic circular dichroism measurements indicate a possible spin reorientation that kills the WAL effect above 120 K. Our findings present a rare example of WAL effect in two-dimensional ferromagnet and also a magnetotransport fingerprint of the strong SOC in Fe5-xGeTe2. The results would be instructive for understanding the interaction Hamiltonian for such high Tc itinerant ferromagnetism as well as be helpful for the design of next-generation room temperature spintronic or twistronic devices.

A novel augmented Lagrangian method of multipliers for optimization with general inequality constraints

We introduce a twice differentiable augmented Lagrangian for nonlinear optimization with general inequality constraints and show that a strict local minimizer of the original problem is an approximate strict local solution of the augmented Lagrangian. A novel augmented Lagrangian method of multipliers (ALM) is then presented. Our method is originated from a generalization of the Hetenes-Powell augmented Lagrangian, and is a combination of the augmented Lagrangian and the interior-point technique. It shares a similar algorithmic framework with existing ALMs for optimization with inequality constraints, but it can use the second derivatives and does not depend on projections on the set of inequality constraints. In each iteration, our method solves a twice continuously differentiable unconstrained optimization subproblem on primal variables. The dual iterates, penalty and smoothing parameters are updated adaptively. The global and local convergence are analyzed. Without assuming any constraint qualification, it is proved that the proposed method has strong global convergence. The method may converge to either a Kurash-Kuhn-Tucker (KKT) point or a singular stationary point when the converging point is a minimizer. It may also converge to an infeasible stationary point of nonlinear program when the problem is infeasible. Furthermore, our method is capable of rapidly detecting the possible infeasibility of the solved problem. Under suitable conditions, it is locally linearly convergent to the KKT point, which is consistent with ALMs for optimization with equality constraints. The preliminary numerical experiments on some small benchmark test problems demonstrate our theoretical results.