Tilted $p$-wave magnet candidate CeNiAsO

Abstract: The unexpectedly small ordered moments of CeNiAsO, a candidate for correlated $p$-wave magnet, have posed a serious challenge to the precise determination of its magnetic structure, hindering the understanding of its fundamental properties. By leveraging the high sensitivity to local internal fields, our $<sup>{75}$As nuclear quadrupole / magnetic resonance experiments reveal a commensurate antiferromagnetic order with a small out-of-plane moment $m_z\approx0.05$ $μ_{\mathrm{B}}$. This tilted magnetic configuration not only rotates the spin polarization axis away from the crystallographic $\mathbf{c}$-axis, but also enhances the non-relativistic spin splitting. We refer to this rare paradigm as a \textit{tilted $p$-wave magnet}.

• The paper establishes that CeNiAsO is a tilted, coplanar commensurate antiferromagnet with an out-of-plane Ce moment of approximately 0.05 μB, using detailed 75As NQR/NMR analysis.
• The finite canting preserves Tτ but breaks C2zᶳT, rotates the altermagnetic spin-polarization axis, and can enhance non-relativistic spin splitting by up to 23% at an optimal canting angle near 32°.
• High-field NMR and Hall measurements link moment reorientation above approximately 13 T to the emergence of anomalous Hall loops, while leaving the microscopic origin of the two observed loops unresolved.

The heavy-fermion compound CeNiAsO has been proposed as a candidate for a $p$-wave magnet, a class of odd-parity magnets that preserve the combined time-reversal and translation symmetry $\mathcal{T}\tau$ while exhibiting non-relativistic spin splitting. A central obstacle to confirming this assignment has been the compound's anomalously small ordered moment ($\sim 0.37~\mu_\text{B}$/Ce), which made the out-of-plane component $m_z$ of the Ce moments—and hence the fate of the ${C}_{2z}^s\mathcal{T}$ symmetry—impossible to resolve with neutron diffraction. This work resolves that ambiguity using $^{75}$As nuclear quadrupole resonance (NQR) and nuclear magnetic resonance (NMR), establishing that the ground state is a tilted, coplanar commensurate antiferromagnet (CAFM) with $m_z \approx 0.05~\mu_\text{B}$, and demonstrating through first-principles calculations and high-field transport that this tilting reconstructs the spin-group symmetry and reorients the altermagnetic spin polarization axis (2608.19856).

Motivation and open questions

CeNiAsO crystallizes in the tetragonal ZrCuSiAs-type structure ($P4/nmm$), isostructural to 1111 iron-based superconductors. Its Ce moments order antiferromagnetically at $T_\text{N1}\sim9$ K and $T_\text{N2}\sim7$ K; below $\mathcal{T}\tau$0 neutron scattering and $\mathcal{T}\tau$1SR established a commensurate AFM order with propagation vector $\mathcal{T}\tau$2 and $\mathcal{T}\tau$3 Kramers doublet character, preserving both $\mathcal{T}\tau$4 and $\mathcal{T}\tau$5 symmetries with spin polarization along $\mathcal{T}\tau$6—the configuration proposed to realize $\mathcal{T}\tau$7-wave magnetism.

Three puzzles motivated the reinvestigation. First, the ordered moment is far below the value expected for a $\mathcal{T}\tau$8 doublet and well below the $\mathcal{T}\tau$9/Ce observed in the structural analog CeFeAsO. Second, the magnetization is exceptionally hard: the $\sim 0.37~\mu_\text{B}$0-axis moment reaches only $\sim 0.37~\mu_\text{B}$1/Ce at 58 T. Third, whether the moments are strictly coplanar directly determines whether $\sim 0.37~\mu_\text{B}$2 survives—a question bearing on the broader issue of how canting affects symmetry-enforced spin splitting in altermagnets. Kondo hybridization as an explanation for the small moment is ruled out by the large magnetic entropy release ($\sim 0.37~\mu_\text{B}$3) at $\sim 0.37~\mu_\text{B}$4 and by ARPES evidence that Ce-$\sim 0.37~\mu_\text{B}$5 electrons are highly localized.

Determining the internal field via NQR/NMR

The analysis proceeds in two stages. Zero-field $\sim 0.37~\mu_\text{B}$6As NQR spectra ($\sim 0.37~\mu_\text{B}$7, $\sim 0.37~\mu_\text{B}$8 MHz) show a single peak above $\sim 0.37~\mu_\text{B}$9, broadening in the intermediate incommensurate AFM phase, and splitting into two peaks below $m_z$0—the signature of CAFM order. Because the internal field ($m_z$1 T) is comparable to the quadrupole interaction, neither term can be treated perturbatively; the authors diagonalize the full Hamiltonian comprising Zeeman, internal-field, and quadrupole terms, computing transition frequencies and probabilities exactly.

Fitting the calculated spectra to experiment yields an internal field at the As site of $m_z$2 T oriented at $m_z$3 relative to the EFG principal axis, with azimuthal angle $m_z$4 uniquely determined from the NMR central-peak splittings for both $m_z$5 and $m_z$6. The single-crystal NMR results reproduce the earlier aligned-powder data, validating the approach.

Refined magnetic structure: tilted CAFM$m_z$7

The internal field is modeled via transferred hyperfine coupling from six neighboring Ce ions (four nearest neighbors plus two next-nearest neighbors along $m_z$8), using hyperfine tensors constrained by the experimental coupling constants $m_z$9 T/${C}_{2z}^s\mathcal{T}$0 and ${C}_{2z}^s\mathcal{T}$1 T/${C}_{2z}^s\mathcal{T}$2, together with the neutron-derived moment magnitude ${C}_{2z}^s\mathcal{T}$3. Minimizing the residual between calculated and measured in-plane hyperfine constants over all moment orientations gives ${C}_{2z}^s\mathcal{T}$4 and ${C}_{2z}^s\mathcal{T}$5.

Two points strengthen confidence in this refinement: the derived azimuthal angle agrees closely with the neutron value of ${C}_{2z}^s\mathcal{T}$6, and the resulting out-of-plane component ${C}_{2z}^s\mathcal{T}$7 lies within the neutron uncertainty (${C}_{2z}^s\mathcal{T}$8)—explaining why it escaped detection. The sign of ${C}_{2z}^s\mathcal{T}$9 alternates along $^{75}$0, so net ferromagnetism is avoided and $^{75}$1 remains intact. Geometrically, the four distinct moments are shown rigorously to be coplanar, defining a new spin plane whose normal is tilted away from the crystallographic $^{75}$2-axis to $^{75}$3.

Consequences for spin-group symmetry and band structure

The finite canting breaks $^{75}$4 but preserves $^{75}$5, so the spin-group symmetry is reconstructed into $^{75}$6 about the new normal $^{75}$7. DFT+$^{75}$8 calculations ($^{75}$9 eV, $m_z \approx 0.05~\mu_\text{B}$0 eV, appropriate for localized Ce-$m_z \approx 0.05~\mu_\text{B}$1) confirm two key results. First, the non-relativistic odd-parity spin-split bands survive the tilting, but their spin polarization axis rotates from $m_z \approx 0.05~\mu_\text{B}$2 to $m_z \approx 0.05~\mu_\text{B}$3—a reorientation of altermagnetic spin texture beyond what crystallographic symmetry alone would dictate. Second, the spin splitting $m_z \approx 0.05~\mu_\text{B}$4 depends non-monotonically on the canting angle: it increases with $m_z \approx 0.05~\mu_\text{B}$5, reaching a maximum near $m_z \approx 0.05~\mu_\text{B}$6 where it is enhanced by 23% relative to the non-canted case, then vanishes at $m_z \approx 0.05~\mu_\text{B}$7. This establishes magnetic tilting as an active control parameter for tuning the non-relativistic Edelstein effect, not merely a perturbation.

Regarding the anomalous Hall effect (AHE): $m_z \approx 0.05~\mu_\text{B}$8 enforces $m_z \approx 0.05~\mu_\text{B}$9, so zero-field AHE is forbidden in the CAFM$P4/nmm$0 state, consistent with the calculations. Simulating a partially polarized FM$P4/nmm$1 configuration (relevant under high field) yields a significant $P4/nmm$2.

High-field Hall effect and field-induced moment reorientation

Experimentally, high-precision Hall measurements with $P4/nmm$3 reveal loop-structured AHE signals confined strictly to the CAFM phase: they vanish immediately above $P4/nmm$4 and are absent in both the ICAFM and paramagnetic regimes. The ordinary Hall contribution is fitted with linear plus quadratic terms (the latter needed because $P4/nmm$5 fails at high field), giving a small Hall coefficient $P4/nmm$6 m$P4/nmm$7/C consistent with good metallicity.

Field-dependent NMR provides the microscopic link: the central-peak splitting $P4/nmm$8 is nearly constant below 12 T but drops rapidly beyond 13 T—an onset field coinciding with the first AHE loop. Since a static structure would predict only a slight decrease, this drop signals field-induced reorientation of the Ce moments toward a FM$P4/nmm$9-like state that breaks $T_\text{N1}\sim9$0 and permits the AHE. The authors note that the extremely hard magnetization implies this reorientation is slow or quasi-continuous, likely unresolvable in pulsed-field magnetization.

Limitations and open questions

Several caveats temper these conclusions. The refinement assumes the magnetic structure is robust up to 10 T, justified by linearity of $T_\text{N1}\sim9$1 to 58 T and constancy of $T_\text{N1}\sim9$2 below 13 T, but the analysis cannot capture the field-induced reorientation regime itself. The fitting also requires assuming slightly different effective quadrupole frequencies between NMR and NQR, attributed to subtle field-induced EFG modifications—an assumption not independently verified. Most notably, the origin of the two separate AHE loops observed at low temperature remains unexplained; the authors explicitly leave this open, suggesting higher-field NMR as the needed probe. Finally, the conjecture that the AHE arises specifically from a field-generated net $T_\text{N1}\sim9$3 breaking $T_\text{N1}\sim9$4 is supported by the correlation of onset fields but not yet demonstrated microscopically.

Conclusion

This work revises the magnetic structure of CeNiAsO to a tilted coplanar CAFM with $T_\text{N1}\sim9$5, resolving a long-standing ambiguity in a candidate $T_\text{N1}\sim9$6-wave magnet. The tilting preserves $T_\text{N1}\sim9$7 while breaking $T_\text{N1}\sim9$8, rotating the spin polarization axis off the crystallographic $T_\text{N1}\sim9$9 direction and enhancing the non-relativistic spin splitting by up to 23% at optimal canting—defining a "tilted $T_\text{N2}\sim7$0-wave magnet" paradigm. The avoided zero-field AHE and its field-induced emergence, correlated with NMR evidence of moment reorientation near 13 T, connect magnetic-symmetry reconstruction directly to topological transport. Beyond CeNiAsO, the NQR/NMR methodology developed here offers a route to determining magnetic structures in other small-moment systems, including under extreme conditions where neutron techniques fall short.