Magnetotransport and electronic structure of EuAuSb: A candidate antiferromagnetic Dirac semimetal

We have investigated the magnetic, thermodynamic, and electrical transport properties of EuAuSb single crystals as well as carrying out band structure calculations. The powder x-ray diffraction data confirm that EuAuSb crystallizes in ZrBeSi-type hexagonal structure with space group $P{6}_3/mmc$. The magnetic measurements reveal an antiferromagnetic (AFM) ordering in EuAuSb at ${\mathit{T}}_N=3.3$ K. This transition is further confirmed by heat capacity and electrical resistivity data. The isothermal magnetization data saturate at low magnetic field of ${\mu }_0{H}_s^c=2.9$ and ${\mu }_0{H}_s^{ab}=3.8$ T for $\mathit{H}\perp \mathit{c}$ and $\mathit{H}\parallel \mathit{c}$, respectively, while the magnetization along $\mathit{H}\perp \mathit{c}$ displays a metamagnetic transition around ${\mu }_0{H}_m^{ab}=0.95$ T. The electrical resistivity exhibits a metallic behavior down to 35 K; after that it shows an upturn until $T_N$ due to the influence of short-range interactions. The longitudinal and transverse magnetoresistances of EuAuSb are negative ($\sim -45\%$ and $-42\%$ in 10 T at 2 K, respectively); in the high field at $\mathit{T}\le 40$ K, they switch to a positive value above 40 K. Further, we observe a humplike anomaly in the Hall resistivity [${\rho }_{xy}\left(\mathit{H}\right)$] data below $T_N$, which is most likely a manifestation of the topological Hall effect. Our two-band model analysis of ${\rho }_{xy}\left(\mathit{H}\right)$ data indicates both hole and electron charge carriers contribute to the electrical transport of the compound. The electronic band structure calculations reveal a $\mathrm{\Gamma }$-centered nodal line in the absence of spin-orbit coupling (SOC). In the presence of SOC, the compound hosts the Dirac point. The $Z_2$ invariants, in the presence of effective time-reversal and inversion symmetries, categorize this system as a nontrivial topological material. Our combined experimental and theoretical studies suggest EuAuSb to be a potential AFM topological semimetal.

Figure 1

(a) The powder XRD pattern of crushed single crystals of EuAuSb was recorded at room temperature. The observed and calculated intensities are represented by red circles and solid black line, respectively. A solid blue line presents the difference between observed and calculated intensities. Olive tick marks are Bragg peak positions. (b) The single-crystal XRD pattern of EuAuSb. The inset shows an optical image of single crystals.

Figure 2

The temperature-dependent magnetic susceptibility ($M/H$) measured under various magnetic fields for (a) $H\parallel c$ and (b) $H\perp c$. Insets of (a) and (b) show the inverse magnetic susceptibility as a function of temperature for $H\parallel c$ and $H\perp c$, respectively. The solid brown line represents the Curie-Weiss fit above 100 K. (c) The isothermal magnetization as a function of magnetic field at 2 K for $H\parallel c$ and $H\perp c$. The inset of (c) displays the derivative of magnetization data for $H\perp c$.

Figure 3

Temperature-dependent heat capacity ($C_p$) of EuAuSb single crystal. Top inset shows a plotting of $C_p/T$ vs $T^2$. The red line fits the expression $C{}_{ph}/\mathit{T}=\gamma +\beta T^2$. Bottom inset displays the magnetic entropy $S{}_m$ as a function of temperature.

Figure 4

(a) The temperature-dependent electrical resistivity of EuAuSb single crystal. The inset shows electrical resistivity with various fields up to 10 T. Panels (b) and (c) represent the field-dependent transverse and longitudinal magnetoresistance at selective temperatures, respectively.

Figure 5

Panels (a) and (c) present the Hall resistivity as a function of magnetic field at various temperatures from 2 to 300 K. (b) The field dependence of $\mathrm{\Delta }{\rho }_{xy}$ at various temperatures, obtained after subtracting the Hall resistivity at 20 K from the total Hall resistivity at low temperatures (see the text). The red solid line in (c) is the fitting of the two-band model [Eq. (1)]. The temperature variation of (d) carrier densities $({\mathit{n}}_h,{\mathit{n}}_e)$ and (e) mobilities $({\mu }_h,{\mu }_e)$.

Figure 6

The red and blue solid lines present field-dependent observed ${\rho }_{xy}$ and calculated ${\rho }_{xy}^O+S_H{\rho }_{xx}^{2}M$, respectively. The ordinary term is assumed to ${\rho }_{xy}^O\left(2\text{K}\right)\approx {\rho }_{xy}\left(20\text{K}\right)$ (dotted orange line) after rescaling. The solid green and dotted cyan line display ${\rho }_{xx}^{2}M$ and ${\rho }_{xx}M$ as a function of field, respectively. The inset shows field dependence of topological Hall component. All these results are based on the data of 2 K.

Figure 7

(a) The crystal structure of EuAuSb. (b) The irreducible Brillouin zone of the bulk along with the (001) projected surface.

Figure 8

(a)–(c) AFM configurations for $2\times 1\times 1$ supercell with Eu spins. Here, AFM1, AFM2, and AFM3 are $A$-, $C$-, and $G$-type AFM, respectively. Blue and green arrows denote the spin-up and spin-down, respectively.

Figure 9

Electronic band structure along high-symmetry points without SOC for (a) AFM1 and (c) AFM2 case. Electronic band structure with SOC along [110] direction for (b) AFM1 and (d) AFM2 case.

Figure 10

(a) Total and projected density of states of EuAuSb. (b) Electronic band structure along high-symmetry points without SOC. (c) Electronic band structure along $M\text{−}\mathrm{\Gamma }\text{−}K$ path without SOC. (d) Electronic band structure with SOC along [110] direction. Here, inset shows the band structure along $H\text{−}A\text{−}L$ path with a Dirac point at $A$. (e) The Fermi surfaces, i.e., hole and electron pockets with SOC.

Figure 11

(a) The surface states with Au termination and (b) the corresponding energy gap plane in the $k_z=0$ plane.