Magnetic structure of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>EuZn</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi>Sb</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math> single-crystal thin film

Magnetic topological materials are a class of compounds which can host massless electrons controlled by the magnetic order. One such compound is EuZn$_2$Sb$_2$, which has recently garnered interest due to its strong interplay between the Eu magnetism and charge carriers. However the topology of the electronic band structure, which depends on the ground state magnetic configuration of the europium sublattice, has not been determined. Based on our \textit{ab-initio} calculations, we find that an in-plane and out-of-plane \textit{A}-type antiferromagnetic (AFM) order generates a topological crystalline insulator and Dirac semimetal respectively, whereas a ferromagnetic (FM) order stabilizes a Weyl semimetal. Our resonant x-ray elastic scattering measurements of single-crystal thin film EuZn$_2$Sb$_2$ reveal both a sharp magnetic peak at $\textit{\textbf{Q}}$=$(0,0,\frac{1}{2})$ and broad $\textit{\textbf{Q}}$=$(0,0,1)$ below $T_{\mathrm{N}}=12.9$\,K, which is associated with an \textit{A}-type AFM and FM order, respectively. Our measurements indicate that the FM and AFM layers are spatially separated along the crystal $c$ axis, with the former limited to the top three atomic layers. We propose that EuZn$_2$Sb$_2$ behaves as a Weyl semimetal in the surface FM layers, and as a topological crystalline insulator in the lower AFM layers.