Real-space and reciprocal-space topology in the Eu(Ga$_{1-x}$Al$_x$)$_4$ square net system

TL;DR

This study uncovers evidence of both real-space and reciprocal-space topologies in Eu(Ga$_{1-x}$Al$_x$)$_4$ compounds through magnetotransport measurements and theoretical calculations, highlighting their potential as a unique platform for topological phenomena.

Contribution

It demonstrates the coexistence of real-space and reciprocal-space topologies in a single material system, supported by experimental magnetotransport data and density functional theory calculations.

Findings

Intermediate field phases indicate real-space topological spin textures.

Large anomalous Hall effect linked to reciprocal-space topology.

Dirac point near Fermi energy splits into Weyl nodes in the spin-polarized state.

Abstract

Magnetotransport measurements on the centrosymetric square-net Eu(Ga$_{1-x}$Al$_x$)$_4$ compounds reveal evidence for both reciprocal- and real-space topology. For compositions $0.50 \leq x \leq 0.90$, several intermediate field phases are found by magnetization measurements when $H \parallel c$, where a maximum in the topological Hall effect (THE) is observed, pointing to the existence of topological (real-space topology) or non-coplanar spin textures. For $0.25 \leq x \leq 0.39$, magnetization measurements reveal an intermediate field state, but no transition is visible in the Hall measurements. For $x = 0.15$, only one magnetic transition occurs below the N\'eel temperature $T_N$, and no intermediate field spin reorientations are observed. The Hall effect varies smoothly before the spin-polarized (SP) state. However, in the SP state, Hall measurements reveal a large anomalous Hall effect (AHE) for all compositions, a consequence of reciprocal-space topology. Density functional theory calculations in the paramagnetic state indeed reveal a Dirac point that lies very near the Fermi energy, which is expected to split into Weyl nodes in the SP state, thereby explaining the observed AHE. These results suggest the Eu(Ga$_{1-x}$Al$_x$)$_4$ family is a rare material platform where real- and reciprocal-space topology exist in a single material platform.