Disorder- and Topology-Enhanced Fully Spin-Polarized Currents in Nodal Chain Spin-Gapless Semimetals

Recently discovered high-quality nodal chain spin-gapless semimetals $M{\mathrm{F}}_3$ ($M=\mathrm{Pd}$, Mn) feature an ultraclean nodal chain in the spin up channel residing right at the Fermi level and displaying a large spin gap leading to a 100% spin polarization of transport properties. Here, we investigate both intrinsic and extrinsic contributions to anomalous and spin transport in this class of materials. The dominant intrinsic origin is found to originate entirely from the gapped nodal chains without the entanglement of any other trivial bands. The side-jump mechanism is predicted to be negligibly small, but intrinsic skew scattering enhances the intrinsic Hall and Nernst signals significantly, leading to large values of respective conductivities. Our findings open a new material platform for exploring strong anomalous and spin transport properties in magnetic topological semimetals.

Figure 1

Nodal chain spin gapless semimetals (NCSGSMs) and their fully spin-polarized currents. (a) The crystal structure of $M{\mathrm{F}}_3$ ($M=\mathrm{Pt}$, Mn), and the view of (111) plane. The blue spheres are magnetic $M$ atoms, whereas yellow spheres are nonmagnetic F atoms. The red arrows label the spin magnetization aligned along [111] direction. The pink lines denote three mirror planes. The sketch of the Brillouin zone is shown in (b), and (c) shows spin-polarized band structure without SOC, where the inset is a close-up of the bands near the $Z$ point. The horizontal violet dashed lines mark the considered energy range of anomalous and spin transport. (d) Schematic illustration of fully spin-polarized Hall current induced by AHE (SHE) and ANE (SNE) in a NCSGSM (indicated with a hexagonal petal), when an electric field or a temperature gradient field is applied along the longitudinal direction.

Figure 2

Large spin-pure AHC and ANC. (a) AHC ${\sigma }_{xy}$ versus ${\sigma }_{xx}$ for ${\mathrm{PdF}}_3$ at the true Fermi energy $E_f$ and at $E_f-0.04\mathrm{eV}$, with the magnetization $\mathbf{M}$ along the $z$ or $x$ direction, ranging across intrinsic from dirty to clean regimes. Note that when $\mathbf{M}\parallel x$, the nonzero component of AHC is ${\sigma }_{yz}$. The data of ${\mathrm{MnF}}_3$ for $\mathbf{M}\parallel z$ are also plotted. In the plot, data for various ferromagnets are shown for comparison, as reported in previous works [108, 109, 110]. (b), (c) Disorder-related contributions to the AHC (${\sigma }_{xy}^{\mathrm{int}}$, ${\sigma }_{xy}^{\mathrm{isk}}$, ${\sigma }_{xy}^{\mathrm{sj}}$, and the total ${\sigma }_{xy}$) as a function of ${\sigma }_{xx}$ (at $E_f$) and energy, respectively. In (c), the intrinsic AHC is calculated at the clean limit, while the extrinsic AHC is evaluated by incorporating a Gaussian disorder potential with a weak disorder parameter ($1.83{\mathrm{eV}}^2{\mathrm{bohr}}^3$) [85], corresponding to ${\sigma }_{xx}=2.12\times {10}^5\mathrm{S}/\mathrm{cm}$, where the extrinsic ${\sigma }_{xy}$ reaches a plateau, indicated by a vertical dashed line in (b). (d), (e) Disorder-related contributions to the ANC (${\alpha }_{xy}^{\mathrm{int}}$, ${\alpha }_{xy}^{\mathrm{isk}}$, ${\alpha }_{xy}^{\mathrm{sj}}$, and the total ${\alpha }_{xy}$) for various temperatures $T$ and energy, computed at $E_f$ and for $T=200\mathrm{K}$, respectively.

Figure 3

The underlying physical origin of large AHC and ANC. (a) The band structure of ${\mathrm{PdF}}_3$ with SOC, with the inset zooming into the bands near the $Z$ point. (b) Berry curvature ${\mathrm{\Omega }}_{xy}$ along high symmetry lines (singular value at $Z$ point reaches $0.46\times {10}^5{\mathrm{bohr}}^2$). (c) The distribution of nodal lines in the Brillouin zone, and (d) projected on $k_x\text{−}{k}_y$ plane. (e) ${\mathrm{\Omega }}_{xy}$ and nodal lines in the Brillouin zone, and (f) projected to the $k_x\text{−}{k}_y$ plane where ${\mathrm{\Omega }}_{xy}$ is integrated along the $k_z$ direction, i.e., $\int {\mathrm{\Omega }}_{xy}(k_x,k_y,k_z)d{k}_z$. To present main features in the distribution of ${\mathrm{\Omega }}_{xy}$, the values of less than $200{\mathrm{bohr}}^2$ are not shown.

Figure 4

Anisotropic AHC and ANC. (a),(b) Total AHC and ANC ($T=200$ K) for ${\mathrm{PdF}}_3$ when the magnetization $\mathbf{M}$ is aligned along the $z$ and $x$ axes.