Emergent Weyl Fermion Excitations in TaP Explored by ${}^{181}\mathrm{Ta}$ Quadrupole Resonance

The ${}^{181}\mathrm{Ta}$ quadrupole resonance [nuclear quadrupole resonance (NQR)] technique is utilized to investigate the microscopic magnetic properties of the Weyl semimetal TaP. We find three zero-field NQR signals associated with the transition between the quadrupole split levels for Ta with $I=7/2$ nuclear spin. A quadrupole coupling constant, ${\nu }_Q=19.250\mathrm{MHz}$, and an asymmetric parameter of the electric field gradient, $\eta =0.423$, are extracted, in good agreement with band structure calculations. In order to examine the magnetic excitations, the temperature dependence of the spin-lattice relaxation rate ($1/T_{1}T$) is measured for the $f_2$ line ($\pm 5/2\leftrightarrow \pm 3/2$ transition). We find that there exist two regimes with quite different relaxation processes. Above $T^{*}\approx 30\mathrm{K}$, a pronounced $(1/T_{1}T)\propto T^2$ behavior is found, which is attributed to the magnetic excitations at the Weyl nodes with temperature-dependent orbital hyperfine coupling. Below $T^{*}$, the relaxation is mainly governed by a Korringa process with $1/T_{1}T=\text{const}$, accompanied by an additional $T^{-1/2}$-type dependence to fit our experimental data. We show that Ta NQR is a novel probe for the bulk Weyl fermions and their excitations.

Figure 1

Typical ${}^{181}\mathrm{Ta}$ NQR spectra in TaP obtained from the spin-echo real part integration at 40 (a) and 4.2 K (b). The data were taken in 0.1 MHz steps across the spectrum. The lines $f_1$, $f_2$, and $f_3$ correspond to $\pm 3/2\leftrightarrow \pm 1/2$, $\pm 5/2\leftrightarrow \pm 3/2$, and $\pm 7/2\leftrightarrow \pm 5/2$ transitions, respectively.

Figure 2

Recovery of the nuclear magnetization $M_n(\mathrm{t})$ measured by the NQR intensity after saturation to the thermal equilibrium value for the $f_2$ line at 100 (a), 50 (b), and 4.25 K (c), the $f_1$ line at 4.25 K (d), and the $f_3$ line at 4.25 K (e). The red curves are the least-squares fit of the data derived using Eq. (1). The perfect fit in all cases demonstrates the fact that the relaxation is governed by magnetic fluctuations.

Figure 3

(a) The temperature dependence of $1/T_{1}T$ of TaP along with the schematics of the band structure. At $T^{*}\approx 30\mathrm{K}$, the relaxation process crosses over between two different regimes. (b) Schematic illustration of Eq. (5): Curves (1), (2), and (3) are expected temperature dependence from the second term (Weyl nodes) not including the exponent, while curve (4) includes the exponent. The $T^{-1/2}$ dependence associated with the conventional bands is depicted by curve (5). The magenta curve is the total relaxation behavior expected from Eq. (5) and matches the experimental results.