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

TL;DR

NaGdS$_2$ presents a rare triangular-lattice magnet where $S=7/2$ Gd$^{3+}$ moments experience competing Heisenberg exchange and dipolar interactions. The study combines bulk probes (magnetization, specific heat, ac susceptibility, thermal expansion, magnetostriction) and local techniques (ESR, $^{23}$Na NMR) with McPhase-inspired modeling to reveal weak exchange ($J_H vert/k_B vert hicksim 52~ ext{mK}$) and sizable dipolar effects that together suppress long-range order down to the mK regime, while fostering short-range ferromagnetic correlations that are anisotropic in the plane. The results demonstrate that dipolar interactions can dominate in large-$S$ rare-earth triangular lattices, producing an in-plane ferromagnetic tendency offset by antiferromagnetic stacking along $c$ and leading to a frustrated ground state with potential spin-liquid-like character. This highlights NaGdS$_2$ as a key platform to study the balance between exchange and dipolar couplings in frustrated magnets with minimal crystal-field anisotropy.

Abstract

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.

Figures (11)

• Figure 1: Crystal structure of NaGdS$_2$ with (a) hexagonal layers of Gd$^{3+}$ ions viewed along [001] and (b) alternating stacking of nonmagnetic and magnetic planes of NaS$_6$ and GdS$_6$ octahedra. The visualization was done in VESTAvesta3.
• Figure 2: Powder diffraction patterns of the two NaGdS$_2$ batches used in this study. Selected single crystals were ground to powder to measure the spectrum. One of the transparent single crystals is shown in the inset.
• Figure 3: Field-dependent magnetization of single-crystalline NaGdS$_2$ for $H\parallel c$ (main figure) and $H\perp c$ (left inset) as well as polycrystalline NaGdS$_2$ (right inset) at various temperatures. The solid lines show Brillouin functions.
• Figure 4: Temperature dependence of the magnetic dc susceptibility of (a) polycrystalline material and (b) single crystals of NaGdS$_2$. The left inset in (a) shows an enlargement of the data in $\mu_0H$ = 0.01 T below 2 K revealing the absence of magnetic order down to 0.5 K. The right inset in (a) and the inset in (b) show the inverse susceptibility and Curie-Weiss fits (solid lines) indicating paramagnetism and revealing a small anisotropy in the single crystal (b).
• Figure 5: Specific heat divided by $T$ vs. $T^2$ at different magnetic fields. In zero and low magnetic fields the upturn at lowest temperatures indicates magnetic contributions. At higher fields a broad Schottky-like anomaly develops. The dashed line shows the specific heat calculated for a 8-level Schottky anomaly at 12 T.