Topological Hall effect driven by short-range magnetic order in ${\mathrm{EuZn}}_2{\mathrm{As}}_2$

Short-range (SR) magnetic orders such as magnetic glass orders or fluctuations in a quantum system usually host exotic states or critical behaviors. Like the long-range (LR) magnetic orders, SR magnetic orders can also break time-reversal symmetry and drive the nonzero Berry curvature leading to novel transport properties. In this work, we report that in $\mathrm{Eu}{\mathrm{Zn}}_2{\mathrm{As}}_2$ compound, besides the LR $A$-type antiferromagnetic (AF) order, the SR magnetic order is observed in a wide temperature region. Magnetization measurements and electron spin resonance (ESR) measurements reveal the ferromagnetic (FM) correlations for this SR magnetic order which results in an obvious anomalous Hall effect above the AF transition. Moreover the ESR results reveal that this FM SR order coexists with LR AF order exhibiting anisotropic magnetic correlations below the AF transition. The interactions of LR and SR magnetism evolving with temperature and field can host nonzero spin chirality and berry curvature leading to additional topological Hall contribution even in a centrosymmetric simple AF system. Our results indicate that $\mathrm{Eu}{\mathrm{Zn}}_2{\mathrm{As}}_2$ is a fertile platform to investigate exotic magnetic and electronic states.

Figure 1

(a) Temperature dependent longitudinal resistivity ${\rho }_{xx}\left(T\right)$. (b) Temperature dependence of magnetic susceptibilities [$\chi \left(T\right)$] with the applied field of 0.1 T perpendicular (${\mu }_{0}H\parallel ab$) and parallel (${\mu }_{0}H\parallel c$) to the $c$ axis of the crystal respectively. The inset: the inverses of magnetic susceptibilities for ${\mu }_{0}H\parallel ab$ and ${\mu }_{0}H\parallel c$ fitted by the Curie-Weiss law. (c) Neutron diffraction scans along the ($00L$) reciprocal-lattice direction for 3.6 and 60 K. (d) The neutron intensity of magnetic peak (0 0 2.5) as a function of temperature. (e) The schematic crystal and magnetic structure of $\mathrm{Eu}{\mathrm{Zn}}_2{\mathrm{As}}_2$ below $T_{AF}$.

Figure 2

The field dependent longitudinal resistivity ${\rho }_{xx}\left({\mu }_{0}H\right)$ (a), and Hall resistivity ${\rho }_{xy}\left({\mu }_{0}H\right)$ (b) at 2, 5, 8, 12, 16, 20, 25, 30, 35, and 50 K. According to the formula ${\rho }_{xy}={\rho }_{xy}^N+{\rho }_{xy}^A+{\rho }_{xy}^T=R_0{\mu }_{0}H+AM+{\rho }_{xy}^T$, the AHE component ${\rho }_{xy}^A$ and THE component ${\rho }_{xy}^T$ are extracted from the total Hall resistivity ${\rho }_{xy}$. The field dependent magnetization $M\left({\mu }_{0}H\right)$ (c), anomalous Hall resistivity ${\rho }_{xy}^A\left({\mu }_{0}H\right)$ (d), and topological Hall resistivity ${\rho }_{xy}^T\left({\mu }_{0}H\right)$ (e) at 2, 5, 8, 12, 16, 20, 25, 30, 35, and 50 K. The absolute values of $M\left({\mu }_{0}H\right), {\rho }_{xy}^A\left({\mu }_{0}H\right)$, and ${\rho }_{xy}^T\left({\mu }_{0}H\right)$ shift at various temperatures. In ${\rho }_{xy}^T\left({\mu }_{0}H\right)$ curves, the second-shoulder features are marked by arrows.

Figure 3

(a) ESR spectra of $\mathrm{Eu}{\mathrm{Zn}}_2{\mathrm{As}}_2$ at 4.5, 6, 8, 9, 14, 16, 20, 35, 75, and 300 K with the applied field along the $c$ axis. (b) ESR spectra of $\mathrm{Eu}{\mathrm{Zn}}_2{\mathrm{As}}_2$ with $\theta$ from $0^{\circ }$ to ${90}^{\circ }$, where $\theta$ is the angle between the applied field and the $ab$ plane of the crystal. (c) Temperature dependence of resonance field $H_{\mathrm{res}}(\theta$) (left) and line width $\mathrm{\Delta }H$ (right). (d) Angular dependence of $H_{\mathrm{res}}$ ($\theta$) (upper) and $\mathrm{\Delta }H(\theta$) (lower) at 4.5 K. Red lines represent the fitting curves for $H_{\mathrm{res}}(\theta$) and $\mathrm{\Delta }H(\theta$) by formulas as $H_{\mathrm{res}}=a_1\{1+{\sin }^2\left(\theta \right)+a_2{[3{\cos }^2\left(\theta \right)-1]}^2\}$ and $\mathrm{\Delta }H=a_1\{1+{\sin }^2\left(\theta \right)+a_2{[3{\sin }^2\left(\theta \right)-1]}^2\}$ respectively, where $a_1$ and $a_2$ are fitting coefficients. The blue line can be expressed as $H_{\mathrm{res}}=a_1[1+{\sin }^2\left(\theta \right)]$ and $\mathrm{\Delta }H=a_1[1+{\sin }^2\left(\theta \right)]$ [27].

Figure 4

The phase diagram for $\mathrm{Eu}{\mathrm{Zn}}_2{\mathrm{As}}_2$. Top: The schematic of various magnetic states in different temperature regions. The canted AF state can host local nonzero spin chirality. FM fluctuations can host local FM domains. For paramagnetic (PM) state the spins are random and isotropic. Bottom: The color plot for topological Hall resistivity. The black broken lines divide the diagram into three regions. The arrow around 12 K indicates the vanishing of the second shoulder for THE.