Spin-orbit coupling controlled two-dimensional magnetism in chromium trihalides

<a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>Cr</a:mi> <a:msub> <a:mi>X</a:mi> <a:mn>3</a:mn> </a:msub> </a:mrow> </a:math> ( <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mi>X</b:mi> </b:mrow> </b:math> = Cl, Br, I) have the same crystal structure and Hamiltonian but different ligand spin-orbit coupling (SOC) constant <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:msub> <c:mi>λ</c:mi> <c:mi>X</c:mi> </c:msub> </c:math> , providing an excellent material platform exploring for exotic two-dimensional (2D) spin orders. Their microscopic mechanism underlying 2D spin physics remain unestablished, along with experimental corroboration of Kitaev exchange interaction, central to realizing topological quantum spin liquids. Finding direct evidence for Kitaev interaction and determining its value has been an essential but formidable challenge in Kitaev physics. Here we report the direct Kitaev interaction signature in magnetic anisotropy measured by ferromagnetic resonance (FMR) spectroscopy. We present measured values of Heisenberg <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mi>J</d:mi> </d:math> , Kitaev <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mi>K</e:mi> </e:math> , and off-diagonal symmetric <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mi mathvariant="normal">Γ</f:mi> </f:math> exchange interactions in <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:mi>Cr</h:mi> <h:msub> <h:mi>X</h:mi> <h:mn>3</h:mn> </h:msub> </h:mrow> </h:math> determined using FMR and exact diagonalization. <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mi>K</i:mi> </i:math> and <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:mi mathvariant="normal">Γ</j:mi> </j:math> exhibit dominant dependencies on <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"> <l:msub> <l:mi>λ</l:mi> <l:mi>X</l:mi> </l:msub> </l:math> , indicating its central role in 2D magnetism. Our study provides a foundation for designing 2D magnetic materials exhibiting novel behaviors by tuning intrinsic material parameters such as SOC.