Magnetic anisotropy and dipolar interactions in the frustrated triangular-lattice magnet NaGdS_2

In this comprehensive study, we present results of bulk measurements (magnetization, specific heat, ac susceptibility, thermal expansion, and magnetostriction) combined with local methods such as nuclear magnetic resonance (^23Na NMR) and electron spin resonance (ESR) and simulations (McPhase) on polycrystalline and single-crystalline NaGdS_2 samples. The rare-earth delafossite NaGdS_2 is a triangular-lattice magnet with S = 7/2 spin-only Gd^3+ moments with suppressed single-ion anisotropy. In our study, we estimate that NaGdS_2 has a weak antiferromagnetic exchange (J_H/k_B is about 52mK) and signs of long-range magnetic order are absent down to lowest temperature. However, indications of short range magnetic order are found below 180 mK in the ac susceptibility and thermal expansion. Our results indicate an interplay of Heisenberg-type and dipolar exchange. Due to the large moment of the Gd^3+ ions, one expects a strong impact of the dipolar coupling in NaGdS_2, in contrast to the related NaYbS_2. ESR and ^23Na NMR measurements, indeed, indicate the formation of short-range ferromagnetic correlations. NaGdS_2 appears to be a rare system, in which magnetic order is suppressed by a competition between Heisenberg and dipolar interactions.

💡 Research Summary

In this work the authors present a comprehensive investigation of the magnetic properties of NaGdS₂, a rare‑earth delafossite in which spin‑only Gd³⁺ ions (S = 7/2) form a perfect two‑dimensional triangular lattice. High‑quality polycrystalline and single‑crystal samples were synthesized by a Na‑flux method and characterized by X‑ray diffraction, confirming the centrosymmetric R 3̅ m structure. Bulk measurements (magnetization, specific heat, ac susceptibility, thermal expansion, magnetostriction) were combined with local probes (^23Na nuclear magnetic resonance and electron spin resonance) and with McPhase simulations to elucidate the interplay of exchange and dipolar interactions.

Magnetization data down to 0.5 K reveal no sign of long‑range order; the Curie–Weiss analysis yields a small negative Weiss temperature (θ ≈ ‑2 K) and a saturation moment close to the free‑ion value (≈ 7 μB), indicating a weak antiferromagnetic Heisenberg exchange J/kB ≈ 52 mK. A subtle anisotropy is observed: θ∥ = ‑2.2 K (field ‖ c) versus θ⊥ = ‑1.5 K (field ⟂ c). Because Gd³⁺ has a large magnetic moment, dipolar coupling (∝ μ²) becomes comparable to J and is responsible for the observed anisotropy, rather than crystal‑field effects that dominate in Yb‑based delafossites.

Specific‑heat measurements show an upturn in C/T below 4 K at zero field, signalling the onset of magnetic correlations. In applied fields ≥ 1 T a broad Schottky‑type anomaly appears, well described by an eight‑level Zeeman‑split model for the S = 7/2 manifold, confirming that the dominant field‑induced contribution is the Zeeman splitting of the Gd³⁺ levels.

Electron‑spin‑resonance spectra (X‑band, 9.4 GHz) are weak but observable up to ~60 K. The lines are broad and highly anisotropic; the effective g‑factor for H‖c is ≈ 2.6 at 60 K, while H⊥c shows a different value. Upon cooling the linewidth ΔH increases and the resonance field shifts, reflecting growing internal fields caused by short‑range ferromagnetic correlations.

^23Na NMR, performed between 2 K and 295 K, detects a pronounced change in shift and spin‑lattice relaxation below ~180 mK, indicating the development of short‑range ferromagnetic clusters. No sharp transition is observed, consistent with the absence of long‑range order.

McPhase simulations that incorporate both the weak antiferromagnetic Heisenberg exchange (J ≈ 52 mK) and the dipolar interaction reproduce the experimental observations: long‑range order is suppressed, while short‑range ferromagnetic correlations emerge below ~180 mK. The competition between exchange and dipolar terms places NaGdS₂ among the rare systems where dipolar interactions are energetically comparable to exchange, leading to a “dipolar‑frustrated” ground state distinct from the quantum spin‑liquid behavior seen in Yb‑based delafossites.

Overall, the study demonstrates that in NaGdS₂ the large Gd³⁺ moment makes dipolar coupling a decisive factor, competing with a very weak Heisenberg antiferromagnetism. This competition prevents conventional magnetic ordering down to the lowest measured temperatures, while allowing short‑range ferromagnetic correlations to develop. The material thus provides a valuable platform for exploring the interplay of dipolar and exchange interactions on a geometrically frustrated triangular lattice.