Magnetic structure and excitations of the topological semimetal ${\mathrm{YbMnBi}}_2$

We investigated the magnetic structure and dynamics of ${\mathrm{YbMnBi}}_2$, with elastic and inelastic neutron scattering, to shed light on the topological nature of the charge carriers in the antiferromagnetic phase. We confirm $C$-type antiferromagnetic ordering of the Mn spins below $T_{\mathrm{N}}=290\mathrm{K}$ and determine that the spins point along the $c$ axis to within about $3^{\circ }$. The observed magnon spectrum can be described very well by the same effective spin Hamiltonian that was used previously to model the magnon spectrum of ${\mathrm{CaMnBi}}_2$. Our results show conclusively that the creation of Weyl nodes in ${\mathrm{YbMnBi}}_2$ by the time-reversal symmetry-breaking mechanism can be excluded in the bulk.

Figure 1

(a) The unit cell of ${\mathrm{YbMnBi}}_2$ for space group $P4/nmm$ (No. 129). The proposed Weyl fermions are contained in the Bi square net in the center of the unit cell. The magnetic exchange between the $ab$-plane nearest-neighbor ($J_1$), $ab$-plane next-nearest-neighbor ($J_2$), and $c$-axis nearest-neighbor ($J_c$) Mn ions was used in the linear spin-wave model to describe the magnon spectrum. (b) The definition of high-symmetry lines and planes in the first Brillouin zone of the tetragonal lattice. The spin-wave spectrum in the $\left(h0l\right)$ and $\left(hk0\right)$ reciprocal lattice planes was mapped in this work. Here, the reciprocal lattice vector is defined as $\mathbf{G}=h{\mathbf{b}}_1+k{\mathbf{b}}_2+l{\mathbf{b}}_3$, where $|{\mathbf{b}}_1|=|{\mathbf{b}}_2|=2\pi /a$ and $|{\mathbf{b}}_3|=2\pi /c$.

Figure 2

(a) Temperature dependence of the magnetic susceptibility of ${\mathrm{YbMnBi}}_2$ measured with the field applied along the $a$ and $c$ axes (${\chi }_a$ and ${\chi }_c$, respectively). The single crystal was cooled in zero field and measured in an applied field strength of 1 T. (b) Temperature dependence of the integrated intensity of the (001), (002), and (100) peaks. The red line is a power law fit to the temperature dependence of the (100) reflection which gives a transition temperature of $T_{\text{N}}=290\left(1\right)\mathrm{K}$. (c) Measured intensity of the (001) peak, together with lines calculated for tilt angles of $0^{\circ }$, $5^{\circ }$, and ${10}^{\circ }$. The inset shows the variation of ${\chi }^2$ with tilt angle.

Figure 3

Constant-energy maps in the $\left(h0l\right)$ plane in reciprocal space, illustrated in Fig. 1, at various $\mathrm{\Delta }E$, plotted in reduced lattice units (r.l.u.). In each panel, the top half and bottom half correspond to the data and model, respectively.

Figure 4

Constant-energy maps in the $\left(hk0\right)$ plane in reciprocal space, illustrated in Fig. 1, at various $\mathrm{\Delta }E$. In each panel, the left half and right half correspond to the data and model, respectively.

Figure 5

The observed and calculated spin-wave spectra of the Mn spins in ${\mathrm{YbMnBi}}_2$ along high-symmetry directions, as defined in Fig. 1. The calculated magnon spectrum is in good agreement with the measured spin-wave dispersion (red markers), which was obtained from constant-energy cuts through the intensity maps in the $\left(h0l\right)$ and $\left(hk0\right)$ planes.