Anisotropic anomalous Hall effect in distorted kagome <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>GdTi</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:msub> <mml:mi>Bi</mml:mi> <mml:mn>4</mml:mn> </mml:msub> <

Topological kagome magnets offer a rich landscape for exploring the intricate interplay of quantum interactions among geometry, topology, spin, and correlation. <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:msub> <a:mi>GdTi</a:mi> <a:mn>3</a:mn> </a:msub> <a:msub> <a:mi>Bi</a:mi> <a:mn>4</a:mn> </a:msub> </a:mrow> </a:math> crystallizes in layered Ti-based kagome nets intertwined with zigzag Gd chains along the <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi>a</b:mi> </b:math> axis and orders antiferromagnetically below <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mo>∼</c:mo> <c:mn>15</c:mn> <c:mspace width="0.16em"/> <c:mi mathvariant="normal">K</c:mi> </c:mrow> </c:math> . Here, we present the temperature- and field-dependent electrical transport of <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:msub> <f:mi>GdTi</f:mi> <f:mn>3</f:mn> </f:msub> <f:msub> <f:mi>Bi</f:mi> <f:mn>4</f:mn> </f:msub> </f:mrow> </f:math> in different directions. The material exhibits anomalous Hall conductivity (AHC) of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mn>410</g:mn> <g:mspace width="0.16em"/> <g:msup> <g:mrow> <g:mi mathvariant="normal">Ω</g:mi> </g:mrow> <g:mrow> <g:mo>−</g:mo> <g:mn>1</g:mn> </g:mrow> </g:msup> <g:mspace width="0.16em"/> <g:mi mathvariant="normal">c</g:mi> <g:msup> <g:mrow> <g:mi mathvariant="normal">m</g:mi> </g:mrow> <g:mrow> <g:mo>−</g:mo> <g:mn>1</g:mn> </g:mrow> </g:msup> </g:mrow> </g:math> at 2 K for <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msub> <m:mi>μ</m:mi> <m:mn>0</m:mn> </m:msub> <m:mi>H</m:mi> <m:mo>∥</m:mo> <m:mi>c</m:mi> </m:mrow> </m:math> , and it is completely absent for <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"> <n:mrow> <n:msub> <n:mi>μ</n:mi> <n:mn>0</n:mn> </n:msub> <n:mi>H</n:mi> <n:mo>∥</n:mo> <n:mi>a</n:mi> </n:mrow> </n:math> , despite the similar magnetizations observed in both orientations. This behavior is quite contradictory, as the anomalous Hall effect (AHE) typically scales with the magnetization. Through first-principles calculations, it is demonstrated that in the presence of time-reversal symmetry broken by the Gd <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"> <o:mrow> <o:mn>4</o:mn> <o:mi>f</o:mi> </o:mrow> </o:math> sublattice and spin-orbit coupling, the magnetization direction controls the orbital mixing in the Ti <p:math xmlns:p="http://www.w3.org/1998/Math/MathML"> <p:msub> <p:mi>t</p:mi> <p:mrow> <p:mn>2</p:mn> <p:mi>g</p:mi> </p:mrow> </p:msub> </p:math> bands, relocating Berry-curvature hot spots and producing the observed orientation-selective AHC. The results establish <q:math xmlns:q="http://www.w3.org/1998/Math/MathML"> <q:mrow> <q:msub> <q:mi>GdTi</q:mi> <q:mn>3</q:mn> </q:msub> <q:msub> <q:mi>Bi</q:mi> <q:mn>4</q:mn> </q:msub> </q:mrow> </q:math> as a platform for investigating new avenues of the AHE, such as directional AHE, and thus shed light on the intricate coupling between magnetic and electronic structures, paving the way for exploring novel quantum phenomena.