Condensed Spin Excitation of Quantized Dirac Fermions in the Quasi-Two-Dimensional semimetal BaMnBi$_2$

Abstract

Dirac semimetals provide a new platform for the quantum Hall effect at low magnetic fields. In the presence of strong spin-orbit coupling, a spin-split Landau level is expected to enhance the bulk quasiparticle excitation. Here we report NMR spectroscopy that site-selectively probes dynamic spin susceptibility on the magnetic semimetal BaMnBi$_2$. We find that spontaneous staggered fields from antiferromagnetic Mn moments are completely canceled at the Bi layer hosting Dirac fermions. The nuclear spin-lattice relaxation rate $1/T_1$ follows the cubic temperature dependence down to low temperatures under the in-plane field, manifesting the chemical potential close to the Dirac point. $1/T_1$ becomes constant below 20 K under the out-of-plane field, where the well-separated Laudau level appears. The strong anisotropy of $1/T_1$ exceeding 100 suggests spin-split Landau levels in the quantum Hall regime.

Figures (4)

• Figure 1: (a) Dirac cone along the $\Gamma$-M line in BaMnBi$_2$ryu2018Zn. (b) Spin-split Landau levels under spin-orbit and Zeeman coupling for one of the four valleys. The red and blue lines denote energy levels with opposite spins. (c) Crystal structures of BaMnBi$_2$ (tetragonal $I4/mmm$), including two Bi sites: Bi(1) forms a square-net layer on the mirror plane li2016Biryu2018Zn, and Bi(2) bridges localized Mn ions. The arrow on Mn denotes the magnetic moment below $T_{\rm N}$lee2013Sr. (d) $^{209}$Bi ($I=9/2$) NMR spectra under the out-of-plane (${\bf B} \parallel {\bf c}$) and in-plane (${\bf B} \parallel ab$ plane) magnetic field.
• Figure 2: (a) Temperature $T$ dependence of $^{209}$Bi Knight shift $K$ defined as the relative frequency shift $K = (\omega - \omega_0)/\omega_0$ ($\omega_0 = \gamma_{\rm n} H$) in a magnetic field parallel or perpendicular to the $c$ axis in BaMnBi$_2$. (b) Magnetic susceptibility obtained from the bulk magnetization measurement for magnetic field along the $c$ axis or the $ab$ plane.
• Figure 3: (a) $^{209}$Bi nuclear spin-lattice relaxation rate $1/T_1$ measured under magnetic field (8.51 T) parallel (open circles) and normal (closed circles) to the $ab$ plane in BaMnBi$_2$. A dotted line represents a guide of $T^3$. A red curve represents a fitting by the gapped spin-wave excitation in addition to Dirac fermions. (b) Density of states $\rho(E)$ linear to $|E|$ in the absence of magnetic field (i), where the chemical potential $\mu$ is located slightly above (or below) the Dirac point. Quantized density of states following Eq.(2) with $\mu$ crossing the second Landau level (ii) and between Landau levels (iii). A small band gap $\Delta/k_{\rm B} = 1.4$ K is assumed. (c) Temperature dependence of $1/T_1$ calculated using Eq.(1) under the in-plane magnetic field without the Landau quantization (i, black), under magnetic field along $c$ axis with $\mu/k_{\rm B} = 20$ K (ii, red), and for $\mu/k_{\rm B} = 10$ K located in between the Landau levels (iii, blue).
• Figure 4: Angular dependence of $1/T_1$ for BaMnBi$_2$ at $1.5$ K and $8.5$ T, where the magnetic field is tilted from the $c$ axis. (b) Numerical calculation of $1/T_1$, based on Eq.(\ref{['DOS_Landau']}) for quantized 2D Dirac fermions, as a function of the out-of-plane component of magnetic field for $v_{\rm F} = 1.6 \times 10^5$ m/s sharapov2004Diracli2016Bi. (c) Magnetic field dependence of $1/T_1$ for BaMnBi$_2$ at $T=1.5$ K. (d) $1/T_1$ calculated for $\mu/k_{\rm B} =$ 20 K and the damping factor $\Gamma/k_{\rm B} = 0.2$ K.