Vanishing ordered moment in the frustrated triangular lattice antiferromagnet CuNdO$_2$

We investigate the magnetic ground state of CuNdO$_2$, which is a delafossite with a triangular lattice of magnetic Nd$^{3+}$ ions that are well separated by non-magnetic Cu spacer layers. From inelastic neutron scattering measurements of the crystal electric field, we determine the strong Ising character of the pseudo-spin 1/2 Nd$^{3+}$ moments. Magnetic susceptibility and heat capacity measurements reveal the onset of long-range antiferromagnetic order at $T_N=0.78$ K. While the magnetic transition is definitively observed with muon spin relaxation, accompanied by the formation of a weakly dispersing spin wave excitation, no dipole-ordered moment is detected with neutron diffraction. We show that the apparent absence of a dipolar ordered moment is a consequence of the dominant Ising character of the antiferromagnetically coupled Nd$^{3+}$ moments, which experience extreme frustration on the triangular lattice. Consequently, the frustration in CuNdO$_2$ is relieved through in-plane ordering of the substantially smaller perpendicular component of the Nd$^{3+}$ moments into a 120\textdegree\ structure, with a nearly vanishing ordered moment.

💡 Research Summary

In this work the authors investigate the magnetic ground state of CuNdO₂, a delafossite compound in which magnetic Nd³⁺ ions form an undistorted triangular lattice that is well separated by non‑magnetic Cu⁺ layers. Bulk probes—magnetic susceptibility, heat capacity, and zero‑field muon spin relaxation (μSR)—all reveal a clear phase transition at Tₙ = 0.78 K, indicating the onset of long‑range antiferromagnetic order. However, powder neutron diffraction performed above and below Tₙ shows no new Bragg peaks, and a detailed difference analysis finds no magnetic scattering within the experimental noise. This apparent contradiction is resolved by a thorough crystal‑electric‑field (CEF) study using inelastic neutron scattering (INS). Four dispersionless CEF excitations are observed at 11.3, 17.7, 74.8 and 100.8 meV, allowing the authors to fit a Stevens‑operator Hamiltonian appropriate for the D₃d point symmetry of Nd³⁺. The resulting ground‑state Kramers doublet is a mixture of |±½⟩, |∓5/2⟩ and |±7/2⟩ components, yielding a highly anisotropic pseudo‑spin‑½ moment: an out‑of‑plane (Ising) component μ_z ≈ 1.27 μ_B and a much smaller in‑plane component μ_⊥ ≈ 0.11 μ_B. Thus each Nd³⁺ ion behaves essentially as an Ising spin with a tiny transverse component.

The strong Ising character combined with antiferromagnetic nearest‑neighbour exchange on a triangular lattice creates extreme geometric frustration. The authors argue that the system relieves this frustration not by ordering the large Ising component, but by allowing the much smaller transverse component to develop a 120° antiferromagnetic pattern within the plane. To test this hypothesis they performed low‑energy INS (E_i = 3.6 meV) at 4 K and 0.05 K. Below Tₙ a weak, nearly dispersionless excitation at ≈0.27 meV appears, consistent with a collective spin wave of a 120° ordered state. Linear spin‑wave calculations based on an XXZ Hamiltonian (J = 0.2 meV, anisotropy ε = 0.5) reproduce the observed mode and its intensity, confirming that the ordered state is indeed a 120° structure stabilized by anisotropic exchange.

μSR data provide complementary evidence for static magnetism: the asymmetry spectra develop a damped oscillatory component below Tₙ, with an internal field of roughly 60 mT. The strong damping indicates a broad distribution of local fields, consistent with the notion that the dominant Ising moments are not coherently ordered, while the transverse component produces a small but detectable static field at the muon site.

In summary, CuNdO₂ exemplifies a rare case where strong single‑ion Ising anisotropy and geometric frustration conspire to suppress the conventional dipolar order parameter. The system orders via the tiny transverse component, leading to an almost vanishing ordered moment that evades detection by neutron diffraction but is revealed by μSR and low‑energy spin‑wave excitations. This work highlights the importance of considering both crystal‑field anisotropy and exchange anisotropy when interpreting magnetic order in rare‑earth triangular lattices, and it provides a concrete experimental realization of a “hidden” ordered state where the observable dipole moment is essentially zero.