Nodal-line-enhanced quantum geometric effects: anomalous and nonlinear Hall effects in the parity-mixed antiferromagnet NbMnP

TL;DR

The paper investigates intrinsic anomalous and nonlinear Hall effects in NbMnP, a parity-mixed antiferromagnet with coexisting $B_{3g}$ (even) and $B_{2u}$ (odd) magnetic components. By combining first-principles calculations with Wannier interpolation, it shows that SOC-induced gaps along nodal lines on the $k_y=0$ mirror plane strongly enhance Berry curvature and Berry-connection polarization dipole, yielding a large AHE and a sizable NHE. The anomalous Hall conductivity reaches approximately $-366\ \mathrm{S/cm}$ near the Fermi level, while the nonlinear Hall conductivities $\sigma^{\rm NHE}_{y;xx}$ and $\sigma^{\rm NHE}_{y;zz}$ are of the order of a few mS/V at EF, both arising from intrinsic (geometric) mechanisms. The work highlights NbMnP as a prototypical system to study nodal-line–driven transport in parity-mixed antiferromagnets and clarifies how symmetry-breaking components contribute to distinct Hall responses.

Abstract

The anomalous Hall effect has been understood in terms of the geometric nature of Bloch bands and impurity scattering, and has been observed in a wide variety of magnetic materials such as ferromagnets and antiferromagnets. Recently, a large anomalous Hall effect was reported in the noncollinear antiferromagnetic metal NbMnP whose magnetic order is a mixture of the even-parity and the odd-parity magnetic components. Such a magnetic structure is expected to exhibit the anomalous Hall effect and the nonlinear Hall effect from the symmetry breaking of the antiferromagnet ordering. Here, we theoretically investigate the intrinsic anomalous and nonlinear Hall effect of NbMnP induced by the quantum geometry of Bloch band using the first-principles calculation and the Wannier interpolation method. We found that the intrinsic Hall response of NbMnP is predominantly governed by the strongly enhanced Berry curvature and Berry-connection-polarization dipole on a specific mirror plane. These enhanced geometric quantities originate from the spin-orbit-coupling-induced gap openings along the nodal lines. Our results indicate that NbMnP serves as a model system for investigating transport phenomena originating from nodal-lines in parity-mixed antiferromagnets.

Figures (4)

• Figure 1: (a) Schematic of the NbMnP with the noncollinear AF structure. (b) Decomposition of the noncollinear AF state into $B_{3g}$ and $B_{2u}$ irreducible representations. The magnetic order in NbMnP is a mixture of these two even- and odd-magnetic components. This figure is created by using the vesta software Momma:db5098.
• Figure 2: (a) Magnetic-Brillouin zone for the orthorhombic lattice of NbMnP. Area painted in light blue represents the $k_y=0$ plane. (b) Energy bands of NbMnP in the noncollinear AF magnetic state from the first-principles calculation (red lines) and the tight-binding model (green lines).
• Figure 3: (a) Chemical potential dependence of the anomalous Hall conductivity $\sigma_{yz}$. Fermi level is set to zero on the horizontal axis. (b) $k_y$-dependence of area integral of $\mathcal{B}^{yz}_{\bm k}$ over the $k_x$-$k_z$ plane. (c) Electronic bands of NbMnP with and without SOC. (d) Nodal lines on the $k_y=0$ plane. The line color represents the energy level of the nodal lines. (e) Berry curvature summed over the occupied states, $\mathcal{B}^{yz}_{\bm k}$, on the $k_y=0$ plane. Black lines represent the Fermi surface.
• Figure 4: (a)(b) Chemical potential dependence of the intrinsic nonlinear Hall conductivity $\sigma^{\rm{NHE}}_{y;\,xx}$ and $\sigma^{\rm{NHE}}_{y;\,zz}$, respectively. (c)(d) Area integral of $\Lambda^{\alpha\beta\gamma}_{\bm k}$ over the $k_x$-$k_z$ plane. (e)(f) BCP dipole summed over the occupied states, $\Lambda^{yxx}_{\bm k}$ and $\Lambda^{yzz}_{\bm k}$, on the $k_y=-0.005(2\pi/b),~0,~0.005(2\pi/b)$ planes. Black lines represent the Fermi surface.