Real-space and reciprocal-space topology in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mrow><mml:msub><mml:mrow><mml:mi>Eu</mml:mi><mml:mo>(</mml:mo><mml:mi>Ga</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>Al</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:math> square net system

Abstract

Magnetotransport measurements of the centrosymmetric square net ${{\mathrm{Eu}(\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x})}_{4}$ compounds reveal evidence of both reciprocal- and real-space topology. For compositions $0.50\ensuremath{\le}x\ensuremath{\le}0.90$, several intermediate field phases are found by magnetization measurements when $H\ensuremath{\parallel}c$, where a maximum in the topological Hall effect is observed, pointing to the existence of topological (real-space topology) or noncoplanar spin textures. For $0.25\ensuremath{\le}x\ensuremath{\le}0.39$, 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 ${{\mathrm{Eu}(\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x})}_{4}$ family is a rare material platform where real- and reciprocal-space topology exist in a single material platform.

Topics & Concepts