Ideal Weyl semimetal induced by magnetic exchange

We report theoretical and experimental evidence that ${\mathrm{EuCd}}_2{\mathrm{As}}_2$ in magnetic fields greater than 1.6 T applied along the $c$ axis is a Weyl semimetal with a single pair of Weyl nodes. Ab initio electronic structure calculations, verified at zero field by angle-resolved photoemission spectra, predict Weyl nodes with wave vectors $\mathbf{k}=(0,0,\pm 0.03)\times 2\pi /c$ at the Fermi level when the Eu spins are fully aligned along the $c$ axis. Shubnikov–de Haas oscillations measured in fields parallel to $c$ reveal a cyclotron effective mass of $m_c^{*}=0.08m_e$ and a Fermi surface of extremal area $A_{\mathrm{ext}}=0.24{\mathrm{nm}}^{-2}$, corresponding to 0.1% of the area of the Brillouin zone. The small values of $m_c^{*}$ and $A_{\mathrm{ext}}$ are consistent with quasiparticles near a Weyl node. The identification of ${\mathrm{EuCd}}_2{\mathrm{As}}_2$ as a model Weyl semimetal opens the door to fundamental tests of Weyl physics.

Figure 1

Crystal structure of ${\mathrm{EuCd}}_2{\mathrm{As}}_2$ and location of Weyl nodes in the Brillouin zone. (a) The trigonal unit cell for the space group $P\overline{3}m1$ (No. 164). The Weyl fermions predominantly occupy orbitals in the double-corrugated ${\mathrm{Cd}}_2{\mathrm{As}}_2$ layers, which are sandwiched between the Eu layers [15]. (b) The Weyl nodes lie along the $A\text{−}\mathrm{\Gamma }\text{−}A$ high-symmetry line and are separated by $\mathrm{\Delta }{k}_z$ (not shown to scale). (c) In the fully polarized state, singly degenerate conduction and valence bands meet at a pair of Weyl nodes (shown here schematically). The nodes act as a source and sink of Berry curvature (indicated by arrows).

Figure 2

Exchange-induced Weyl nodes in ${\mathrm{EuCd}}_2{\mathrm{As}}_2$. (a), (c) In zero field, the Eu spins order in an $A$-type antiferromagnetic structure at $T<T_N$, with the spins lying in the $ab$ plane. The corresponding band structure is gapped at $\mathrm{\Gamma }$, and every band is doubly degenerate due to the combination of inversion and time-reversal symmetries. (b), (d) The Eu moments can be fully polarized along the $c$ axis in a small coercive field ($B>B_c$), lifting the double degeneracy of the bands and creating a pair of Weyl nodes along $\mathrm{\Gamma }\text{−}A$, at $k_z=0.03$ r.l.u.

Figure 3

ARPES and high-field magnetotransport of ${\mathrm{EuCd}}_2{\mathrm{As}}_2$. (a), (c) ARPES spectrum as a function of wave vector along the $M\text{−}\mathrm{\Gamma }\text{−}M$ high-symmetry line measured at $T\simeq 5\mathrm{K}$ with incident photon energy of 130 eV. The data shown here are a sum of two measurements taken with linear-vertical and linear-horizontal polarization, respectively, to compensate the effect of selection rules. Nonlinear scaling was applied to the intensity to enhance the visibility of bands with a small photoemission cross section. (b), (d) Electronic bands calculated by DFT (in red). (e) The second derivative of the longitudinal resistivity ${\rho }_{xx}^{″}\left(B\right)$ as a function of field applied along the $c$ axis. (f) Plot of $1/B_{\mathrm{int}}$ at the minima and maxima in ${\rho }_{xx}$ against Landau level index, with integers assigned to the minima, where $B_{\mathrm{int}}=B+{\mu }_{0}M$ is the internal field. The Shubnikov–de Haas (SdH) frequency $F$ is obtained from the gradient of the linear fit shown. (g) Temperature dependence of the amplitude in the SdH oscillation, measured at $B=10\mathrm{T}$. The line is a fit to the Lifshitz-Kosevich formula, from which the cyclotron effective mass $m_c^{*}$ of the charge carriers is estimated. The quoted error in $m_c^{*}$ derives from the least-squares fit, but the uncertainty in the measurement is expected to be larger because of the long period of the oscillations and the relatively narrow field range.

Figure 4

Magnetotransport of ${\mathrm{EuCd}}_2{\mathrm{As}}_2$. (a) ${\rho }_{xx}$ and ${\sigma }_{yx}$ as a function of field. (b) Definition of the $xyz$ axes relative to the crystal orientation and directions of the current and applied field used in the measurement.