Ba₃BiPbREO(BO₃)₄ (RE = Pr, Nd, Gd, and Dy): two-dimensional rare-earth antiferromagnets with a geometrically-perfect triangular lattice directed by a triangular BO₃ unit

Abstract

The synthesis of novel two-dimensional (2D) triangular frustrated compounds is important for providing various platforms to investigate exotic quantum magnetism. Here, we successfully synthesised a series of RE-based magnetic compounds Ba₃BiPbREO(BO₃)₄ (RE = Pr, Nd, Gd, and Dy) with a geometrically-perfect 2D triangular lattice directed by the triangular BO₃ unit. These compounds stabilise 2D layered structures in the hexagonal (P6₃/mmc) crystal system, where magnetic ions are linked by BO₃ to form a perfect triangular frustrated lattice. The magnetisation susceptibility results show that all synthesised compounds Ba₃BiPbREO(BO₃)₄ exhibit dominant antiferromagnetic (AFM) interactions, with no long-range order (LRO) down to 2 K, which is further confirmed by specific heat measurements. Additionally, their thermal stability and attenuated total reflectance Fourier-transform infrared (ATR-FTIR) and ultraviolet-visible-near-infrared (UV-Vis-NIR) diffuse reflectance spectra are also reported. This work provides a series of RE-based magnetic compounds with a two-dimensional triangular frustrated lattice, offering novel model materials for further investigation on rare-earth-based frustrated magnetism.

---

Introduction

Two-dimensional (2D) frustrated antiferromagnets have attracted intense research interest due to their unusual quantum phenomena like quantum spin liquids (QSLs), fractional excitations, relationship to superconductivity, and potential applications in quantum computing.^1–7 Common 2D frustrated systems mainly focus on the triangular lattice, the Kagomé lattice, and the honeycomb lattice.^8–15 Among them, the triangular lattice is the most representative system for predicting the realisation of the two-dimensional quantum spin liquid state.^16–18 Typical examples of two-dimensional transition metal magnetic compounds with a triangular lattice include κ-(BEDT-TTF)₂Cu₂(CN)₃,¹⁹ Cs₂CuBr₄,²⁰ Na₂BaCo(PO₄)₂,²¹ Sr₃NiTa₂O₉,²² NiGa₂S₄,²³ Ba₃NiSb₂O₉,²⁴ and so on.

In addition to transition-metal-based magnetic frustrated systems, RE-based frustrated materials have also been widely investigated over the past decade due to their strong spin–orbit coupling and the crystal field effects of 4f electrons, which can lead to high magnetic anisotropy and a wide variety of magnetic phenomena.^25,26 So far, several RE-based antiferromagnets with 2D triangular lattices have been studied, such as YbMgGaO₄,²⁷ REZnAl₁₁O₁₉ (RE = Pr, Nd, and Sm–Tb),²⁸ REMgAl₁₁O₁₉ (RE = Pr and Nd),²⁹ CsRESe₂ (RE = La–Lu),³⁰ Ba₆RE₂Ti₄O₁₇ (RE = Nd, Sm, Gd, and Dy–Yb),¹⁸ and so on. Meanwhile, novel quantum phenomena have been observed in some of these magnetic compounds. For example, spin glass states exist in YbZnGaO₄ ³¹ and CsDySe₂;³⁰ the Berezinskii–Kosterlitz–Thouless (BKT) phase has been found in TmMgGaO₄³² and so on. However, the chemical synthesis of such magnetic models with specific frustrated lattices is random in experiments. Therefore, it is crucial to rationally design and systematically synthesise more novel rare-earth magnetic compounds with a triangular lattice for exploring their quantum magnetism.

Generally, in order to design and synthesize new magnetic compounds, various basic building units, including VO₄, PO₄, IO₃, SeO₃ and BO₃ groups, have been used to mediate magnetic ions, such as K₃Yb(VO₄)₂,³³ SrMn₂(VO₄)₂·(H₂O)₂,³⁴ Rb₃Yb(PO₄)₂,³⁵ γ-Co₂(PO₄)(OH),³⁶ MIO₃F (M = Co and Ni),³⁷ CaNi₂(SeO₃)₃·2H₂O,³⁸ Ba₂M(SeO₃)₂Cl₂ (M = Cu, Ni, Co, and Mn),³⁹ BaCuB₂O₅,⁴⁰ KBaRE(BO₃)₂ (RE = Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, and Yb),⁴¹ and so on. Recently, our group have successfully synthesised transition metal-based magnetic triangular systems KMB₄O₆F₃ (M = Co, Fe, and Ni) using the triangular BO₃ group.^42–44 Meanwhile, Xuean Chen and Xiaoyan Song et al. reported the interesting luminescence properties of Ba₃BiPbEuO(BO₃)₄ ⁴⁵ and its isostructural compound Ba₄BiPbTbO(BO₃)₄.⁴⁶ In these structures, RE³⁺ ions are connected by the BO₃ group to form a two-dimensional triangular lattice, making them ideal models for studying frustrated magnetism. In this work, we have successfully synthesised a series of rare earth-based magnetic compounds with the formula Ba₃BiPbREO(BO₃)₄ (RE = Pr, Nd, Gd, and Dy) and investigated their magnetic properties. Magnetic susceptibility results show no long-range order (LRO) down to 2 K for all four compounds, which is further confirmed by heat capacity results, probably owing to the spin frustration in the triangular lattice. Additionally, their thermal stability, ATR-FTIR spectra and UV-Vis-NIR diffuse reflectance spectra are also reported.

Experimental

Synthesis

The starting materials of praseodymium oxide (Pr₆O₁₁, 99.9%, Shanghai Aladdin Biochemical Technology Co., Ltd), neodymium oxide (Nd₂O₃, 99.99%, Shanghai Aladdin Biochemical Technology Co., Ltd), dysprosium oxide (Dy₂O₃, 99.99%, Shanghai Aladdin Biochemical Technology Co., Ltd), gadolinium oxide (Gd₂O₃, 99.99%, Shanghai Aladdin Biochemical Technology Co., Ltd), bismuth oxide (Bi₂O₃, 99.99%, Shanghai Aladdin Biochemical Technology Co., Ltd), lead oxide (PbO, 99.97%, Shanghai Aladdin Biochemical Technology Co., Ltd), barium carbonate (BaCO₃, 99%, Sinopharm Chemical Reagent Co. Ltd), and boric acid (H₃BO₃, 99.5%, Shanghai Aladdin Biochemical Technology Co., Ltd) were used as received.

Powder samples of Ba₃BiPbREO(BO₃)₄ (RE = Pr, Nd, Gd, and Dy) were prepared by a solid-state reaction. The raw materials were mixed thoroughly according to the stoichiometric ratio, pressed into pellets, and preheated in an alumina crucible at 500 °C for 12 h. For Ba₃BiPbPrO(BO₃)₄, the product was ground again and pressed into a pellet and then sintered in an alumina crucible at 750 °C for 48 h. For Ba₃BiPbREO(BO₃)₄ (RE = Nd, Gd, and Dy), the products need to be sintered at 850 °C for 48 h to obtain the pure-phase powder samples.

Large single crystals of Ba₃BiPbREO(BO₃)₄ (RE = Pr and Gd) were grown in a platinum crucible by melting a mixture of BaCO₃ (6.0 mmol), Bi₂O₃ (4.2 mmol), PbO (4.2 mmol), Gd₂O₃ (1.2 mmol), Pr₆O₁₁ (0.4 mmol), and H₃BO₃ (9.6 mmol). The powder was heated to 800 °C for 48 h, followed by programmed cooling at a rate of 20 °C h⁻¹ to room temperature. As shown in Fig. S1, millimetre-sized green transparent crystals of Ba₃BiPbPrO(BO₃)₄ and colourless transparent crystals of Ba₃BiPbGdO(BO₃)₄ were obtained in the platinum crucible, respectively, and their structures were determined by single-crystal X-ray diffraction. The single crystal samples of the other two compounds are ongoing.

Crystallographic determination

Powder X-ray diffraction data were recorded using a Rigaku SmartLab SE powder X-ray diffractometer with Cu Kα radiation (λ = 1.54184 Å) over a 2θ range of 5–120°. The single-crystal X-ray diffraction experiments for the Ba₃BiPbREO(BO₃)₄ compounds (RE = Pr and Gd) were conducted at room temperature using a Rigaku XtaLAB mini II with Mo Kα radiation (λ′ = 0.71073 Å) and the data were processed using the CrysAlisPro program. All the reflection intensities were corrected by multi-scan methods, and the structure was solved by intrinsic phasing followed by refinement using full-matrix least-squares techniques with the SHELXL crystallographic program within Olex 2 software.⁴⁷ The atomic occupancies of Bi and Pb were refined using the EXYZ and SUMP instructions, and there was occupancy disorder of Bi and Pb, which has also been reported in other compounds such as Ba₃BiPbEuO(BO₃)₄,⁴⁵ Pb₃BiV₃O₁₂,⁴⁸ PbBi₂Nb₂O₉,⁴⁹ and so on. In addition, the O2 and B2 atoms in Ba₃BiPbPrO(BO₃)₄ were modelled using the geometric constraint ISOR. The main crystallographic data and structure refinement information of Ba₃BiPbPrO(BO₃)₄ and Ba₃BiPbGdO(BO₃)₄ are shown in Table 1. The structures of all four compounds Ba₃BiPbREO(BO₃)₄ (RE = Pr, Nd, Gd, and Dy) were refined by the Rietveld method based on the crystallographic information files using the FullProf program package.⁵⁰ The crystal structure of Ba₃BiPbGdO(BO₃)₄ was used as the initial model for Rietveld refinements of Ba₃BiPbNdO(BO₃)₄ and Ba₃BiPbDyO(BO₃)₄, since single-crystal samples were not obtained. All Rietveld refinement results are listed in Table S1. The crystallographic data of all four compounds have been deposited into the CCDC database (CCDC 2466013–2466016).

Table 1 Crystal data and structure refinements for Ba₃BiPbPrO(BO₃)₄ and Ba₃BiPbGdO(BO₃)₄

a R 1 = ∑||Fo| − |Fc||/∑|Fo| and wR2 = {∑w[(Fo)^2 – (Fc)^2]^2/∑w[(Fo)^2]^2}^1/2.
Formula	Ba3BiPbPrOB4O12	Ba3BiPbGdOB4O12
Formula weight (g mol^−1)	1220.34	1236.68
Temperature (K)	298	298
Crystal system	Hexagonal	Hexagonal
Space group	P63/mmc	P63/mmc
a (Å)	5.3940(12)	5.4387(4)
b (Å)	5.3940(12)	5.4387(4)
c (Å)	26.940(7)	26.384(2)
α (°)	90	90
β (°)	90	90
γ (°)	120	120
V (Å^3)	678.8(3)	675.88(11)
Z	2	2
Max. θ (°)	24.968	29.970
λ′ (Mo Kα) (Å)	0.71073	0.71073
ρ calc (g cm^−3)	5.970	6.077
μ (mm^−1)	37.418	38.882
F (000)	1032.0	1042.0
R int	0.0749	0.0553
R 1, wR2 [I ≥ 2σ(I)]^a	0.0524, 0.1082	0.0587, 0.1291
R 1, wR2 [all data]	0.0861, 0.1175	0.0745, 0.1376
Goodness-of-fit	1.068	1.140

---

Scanning electron microscopy

The elemental distributions of samples were characterised by energy-dispersive X-ray spectroscopy (EDS-mapping) analyses using a Tescan Mira LMS.

Thermal analysis

The thermogravimetric measurements were performed with a PerkinElmer STA8000 TG analyser using an Al₂O₃ crucible. The samples were heated at a rate of 10 °C min⁻¹ under a N₂ atmosphere from ambient temperature to 980 °C.

ATR-FTIR spectra and UV-Vis-NIR diffuse reflectance spectra

The ATR-FTIR spectra were collected using a Bruker Vertex 70 FTIR spectrometer in the range of 400–4000 cm⁻¹. UV-Vis-NIR diffuse reflectance spectra were collected using a Shimadzu UV-3600 spectrophotometer in the diffuse reflectance range of 200–2400 nm.

Magnetic measurements

The magnetic measurements were performed with a Quantum Design MPMS superconducting quantum interference device (SQUID) magnetometer. The temperature-dependent magnetic susceptibility data were collected between 2 and 300 K at 0.1 T. The magnetic-field dependent magnetisation data were collected between −7 and 7 T at 2 K. The magnetic susceptibilities were corrected by subtracting the diamagnetic contribution estimated from Pascal's constants.⁵¹

Specific heat

The specific heat was measured in the temperature range between 2 K and 30 K at 0 T using a Physical Property Measurement System (PPMS-9 T). The samples were pressed into pellets from the powder samples.

Results and discussion

Structural descriptions

The purity of the isostructural compounds Ba₃BiPbREO(BO₃)₄ (RE = Pr, Nd, Gd, and Dy) was confirmed by PXRD patterns, and the crystal structures have been refined by the Rietveld refinement method, as shown in Fig. 1. The Ba₃BiPbREO(BO₃)₄ compounds (RE = Pr, Nd, Gd, and Dy) are isostructural; therefore, only the crystal structure of Ba₃BiPbGdO(BO₃)₄ is described below. Ba₃BiPbGdO(BO₃)₄ crystallizes in the hexagonal space group P6₃/mmc (no. 194) with unit cell parameters of a = 5.4387(4) Å, c = 26.384(2) Å, and Z = 2 (Table 1). The crystal structure of Ba₃BiPbGdO(BO₃)₄ consists of two-dimensional [Gd(BO₃)₂]³⁻ layers in the ab plane, which are separated by the cations of Bi³⁺, Pb²⁺, and Ba²⁺ and anions of (BO₃)³⁻ and O²⁻ along the c axis (Fig. 2a). The Bi³⁺ and Pb²⁺ cations occupy in the same 4e Wyckoff site. In the [Gd(BO₃)₂]³⁻ layers, the magnetic Gd³⁺ ions are bridged by triangular BO₃ groups and form a triangular lattice of Gd³⁺, as shown in Fig. 2b and c. The shortest intralayer Gd⋯Gd distance in the triangular lattice is 5.4387(3) Å, while the shortest interlayer Gd⋯Gd distance is 13.192(1) Å. Each magnetic Gd³⁺ cation is equally coordinated by six O²⁻ ions from the triangular BO₃ groups and forms a GdO₆ octahedron with Gd–O bond lengths of 2.265(12) Å (Fig. 2d). The EDS mapping results (Fig. S2) indicate the compounds only contain the constituent elements of Ba, Bi, Pb, RE, B and O with uniform distributions. It is worth noting that, due to the low atomic numbers and low energy, boron atoms cannot be accurately measured, as reported in Ba₄BiTbO(BO₃)₄ ⁴⁶ and other borates.^52,53

Fig. 1 Rietveld refinement results of Ba₃BiPbREO(BO₃)₄. (a) Ba₃BiPbPrO(BO₃)₄; (b) Ba₃BiPbNdO(BO₃)₄; (c) Ba₃BiPbGdO(BO₃)₄; and (d) Ba₃BiPbDyO(BO₃)₄.

Fig. 2 Crystal structure of Ba₃BiPbGdO(BO₃)₄. (a) View along the b axis; (b) the stacking of the Gd³⁺ triangular lattice along the c axis; (c) the [Gd(BO₃)₂]³⁻ triangular lattice in the ab plane; and (d) local coordination environment of the magnetic Gd³⁺ ion.

Thermal analysis

Fig. 3 shows the TG curves of Ba₃BiPbREO(BO₃)₄ (RE = Pr, Nd, Gd, and Dy). Ba₃BiPbPrO(BO₃)₄ exhibits good thermal stability up to 850 °C and then begins to decompose. Interestingly, for Ba₃BiPbREO(BO₃)₄ (RE = Nd, Gd, Dy), there is no significant weight loss up to 900 °C, indicating their excellent thermal stability.

Fig. 3 TGA curves of Ba₃BiPbREO(BO₃)₄ (RE = Pr, Nd, Gd, and Dy).

ATR-FTIR spectra

The isostructural compounds Ba₃BiPbREO(BO₃)₄ (RE = Pr, Nd, Gd, and Dy) show similar infrared spectra in the range of 400–4000 cm⁻¹ (Fig. S3). Generally, all the absorption peaks in the range of 500–1400 cm⁻¹ are due to the planar triangular BO₃ group. The peaks at 566 cm⁻¹, 596 cm⁻¹ and 648 cm⁻¹ can be assigned to the in-plane bending of B–O (ν₄), the peaks at 716 cm⁻¹ and 772 cm⁻¹ arise due to the out-of-plane bending of B–O (ν₂), the weak peaks at 899 cm⁻¹ and 955 cm⁻¹ are attributed to the symmetric stretching of B–O (ν₁), and the obvious broad absorption peaks at 1148 cm⁻¹, 1208 cm⁻¹ and 1264 cm⁻¹ originate from the B–O asymmetric stretching (ν₃) of the BO₃ group,^42,54–56 as shown in Fig. 4.

Fig. 4 FTIR spectra of Ba₃BiPbREO(BO₃)₄ (RE = Pr, Nd, Gd, and Dy) in the range of 400–1500 cm⁻¹.

UV-Vis-NIR diffuse reflectance spectra

The UV-Vis-NIR spectra of Ba₃BiPbREO(BO₃)₄ (RE = Pr, Nd, Gd, and Dy) are shown in Fig. 5. For Ba₃BiPbPrO(BO₃)₄, the electronic transition from the 4f² configuration in the ³H₄ ground state leads to distinct absorption bands in the visible range of the UV spectrum, at 442–480 nm and 590 nm, corresponding to transitions from ³H₄ to ³P_0,1,2 and ¹D₂.^57,58 This is in good agreement with the green colour of the sample. Meanwhile, three absorption bands in the near-infrared region, at 1402 nm, 1482 nm, and 1835 nm, correspond to transitions from ³H₄ to ³F_4,3,2.^59,60 In the UV spectrum of Ba₃BiPbNdO(BO₃)₄, six absorption bands are observed at 528 nm, 587 nm, 682 nm, 745 nm, 806 nm, and 879 nm, corresponding to the transitions of Nd³⁺ 4f electrons from the ground state ⁴I_9/2 to other excited states ²K_13/2 + ⁴G_9/2 + ⁴G_7/2, ⁴G5/₂ + ⁴G_7/2, ⁴F_9/2, ⁴F_7/2 + ⁴S_3/2, ⁴F_5/2 + ²H_9/2, and ⁴F_3/2.^58,61,62 For Ba₃BiPbGdO(BO₃)₄, no significant absorption bands were observed in the 200–2400 nm region; therefore, the crystal is colourless. However, the UV spectrum of Ba₃BiPbDyO(BO₃)₄ shows four absorption bands observed at 795 nm, 890 nm, 1084 nm, and 1262 nm, which can be attributed to the transitions occurring between specific energy levels, namely the transitions from ⁶H_15/2 to ⁶F_5/2, ⁶F_7/2, ⁶F_9/2 + ⁶H_7/2, and ⁶F_11/2 + ⁶H_9/2,^63,64 respectively.

Fig. 5 UV-Vis-NIR spectra of (a) Ba₃BiPbPrO(BO₃)₄; (b) Ba₃BiPbNdO(BO₃)₄; (c) Ba₃BiPbGdO(BO₃)₄; and (d) Ba₃BiPbDyO(BO₃)₄. The insets show the direct band gap of Ba₃BiPbREO(BO₃)₄ (RE = Pr, Nd, Gd, and Dy).

In addition, the optical band gap was calculated using Tauc's formula^65,66αhν = A(hν − E_g)ⁿ, where h is Planck's constant, ν is the frequency of light, A is a proportional constant, E_g is the band gap, and n denotes the type of optical transition (n = 2 and 1/2 correspond to indirect and direct band gap transitions). Here, the coefficient α was replaced with the absorbance obtained from the UV-visible spectra, and the (αhν)^1/n − hν relationship was plotted.^46,57 As shown in the inset of Fig. 5 and Fig. S4, the results indicate that the Ba₃BiPbREO(BO₃)₄ compounds (RE = Pr, Nd, Gd, and Dy) show direct band gaps with values of 3.42 eV, 3.31 eV, 3.51 eV, and 3.48 eV, respectively.

Magnetic properties

Ba₃BiPbPrO(BO₃)₄. The magnetic susceptibility of Ba₃BiPbPrO(BO₃)₄ measured at 0.1 T is shown in Fig. 6a. The χ(T) curve increases upon cooling and no anomaly is observed, indicating that no magnetic LRO occurred down to 2 K. No divergence between the zero-field cooling (ZFC) and field cooling (FC) curves rules out the possibility of spin glass and spin canting behaviours. The Curie–Weiss fitting is performed in the high-temperature range of 200–300 K, leading to an effective magnetic moment μ_eff(HT,Pr) of 3.99(1)μ_B and a Weiss temperature θ_(HT,Pr) of −90.94(9) K (Fig. 6b and Table 2). The effective magnetic moment μ_eff(HT,Pr) value is close to the expected theoretical value of 3.58μ_B for free Pr³⁺ ions. The slope of the χ⁻¹(T) curve changed below 5 K, suggesting changes in the magnetic moment and spin–spin interactions in the low-temperature region, which are related to the crystal electric field (CEF) effects.^28,67 In the low-temperature range of 2–3 K below the temperature region, the Curie–Weiss fitting gives an effective magnetic moment μ_eff(LT,Pr) of 1.88(3)μ_B and a Weiss temperature θ_(LT,Pr) of −15.76(37) K. The θ value at low temperatures is considerably larger than those reported for PrMgAl₁₁O₁₉ (θ = −6.4 K)²⁵ and PrZn Al₁₁O₁₉ (θ = −9.9 K)²⁶ with a triangular lattice, as well as that for Pr₂Be₂GeO₇ (θ = −3.6 K)¹² with a Shastry–Sutherland lattice. This may be interesting for further investigation, particularly in a large single-crystal sample. The negative Weiss temperature reveals the dominant antiferromagnetic (AFM) interactions between the spins of magnetic Pr³⁺ ions. The χT(T) value at room temperature is 1.53 emu K mol⁻¹ and then decreases upon cooling, further confirming the dominant AFM exchange interactions.

Fig. 6 Magnetic susceptibilities of Ba₃BiPbREO(BO₃)₄ (RE = Pr, Nd, Gd, and Dy) measured at 0.1 T. (a, c, e and g) ZFC (red) and FC (blue); (b, d, f) and h) χ⁻¹ (blue) and χT (green) of Ba₃BiPbREO(BO₃)₄ (RE = Pr, Nd, Gd, and Dy). The red line of χ⁻¹ shows Curie–Weiss fitting. The insets of (b), (d), (f) and (h) show χ⁻¹ in the low-temperature region.

Table 2 The spin number (S), total angular momentum (J), effective magnetic moments (μ_eff) and Curie–Weiss temperatures (θ) of Ba₃BiPbREO(BO₃)₄ (RE = Pr, Nd, Gd, and Dy). These fittings were performed in high-temperature (HT) and low-temperature (LT) regions

RE	S	J	μ J/μB	HT fit	θ/K	μ eff/μB	LT fit	θ/K	μ eff/μB
Pr	1	4	3.58	200–300 K	−90.94(9)	3.99(1)	2–3 K	−15.76(37)	1.88(3)
Nd	3/2	9/2	3.62	200–300 K	−19.39(16)	3.32(1)	2–5 K	−0.24(1)	2.25(1)
Gd	7/2	7/2	7.94	200–300 K	−7.75(14)	8.71(1)	2–5 K	−0.56(1)	8.36(1)
Dy	5/2	15/2	10.65	200–300 K	−13.60(19)	11.04(1)	2–5 K	−1.30(2)	8.41(2)

---

The magnetic-field-dependent magnetisation for Ba₃BiPbPrO(BO₃)₄ is measured at 2 K, as shown in Fig. 7a. The M(H) curve linearly increases with increasing magnetic field up to 7 T, confirming the antiferromagnetic ground state. The magnetisation value at 7 T is 0.24μ_B, which is relatively small and far from full saturation.

Fig. 7 Field-dependent magnetisations measured at 2 K between −7 T and 7 T for (a) Ba₃BiPbPrO(BO₃)₄; (b) Ba₃BiPbNdO(BO₃)₄; (c) Ba₃BiPbGdO(BO₃)₄; and (d) Ba₃BiPbDyO(BO₃)₄.

Ba₃BiPbNdO(BO₃)₄. As displayed in Fig. 6c, the χ(T) curve for Ba₃BiPbNdO(BO₃)₄ increases upon cooling and no anomaly is observed, indicating that no magnetic LRO occurred down to 2 K. Similarly, there is no divergence between the ZFC and FC curves, suggesting that the possibility of a spin glass state and spin canting behaviour is ruled out. In the high-temperature region between 200 and 300 K, the Curie–Weiss fitting is applied, yielding an effective magnetic moment μ_(HT,Nd) of 3.32(1)μ_B and a Weiss temperature θ_(HT,Nd) of −19.39(16) K, as shown in Fig. 6d and Table 2. The effective magnetic moment μ_(HT,Nd) value is close to the expected theoretical value of 3.62μ_B for free Nd³⁺ ions. In the low-temperature range of 2–5 K, the Curie–Weiss fitting gives an effective magnetic moment μ_(LT,Nd) of 2.25(1)μ_B and a Weiss temperature θ_(LT,Nd) of −0.24(1) K. The magnetic moment is smaller than that of a free Nd³⁺ ion due to the influence of the CEF effect, which causes more electrons to occupy the lowest-lying Kramers doublet states at lower temperatures. Similar observations have been reported in other frustrated Nd³⁺ compounds, such as Ba₆Nd₂Ti₄O₁₇,¹⁸ Nd₃Sb₃Zn₂O₁₄,⁶ and so on. The negative Weiss temperature indicates that the dominant magnetic exchange interaction in Ba₃BiPbNdO(BO₃)₄ is AFM. The value of χT(T) at room temperature is 1.29 emu K mol⁻¹, and then gradually decreases upon cooling, further confirming the dominant AFM exchange interactions.

Fig. 7b shows the magnetic-field-dependent magnetisation measured at 2 K for Ba₃BiPbNdO(BO₃)₄. At the beginning, the M(H) curve linearly increases below 3 T with a magnetisation of M_{3 T} = 0.97μ_B, and then increases slowly with the trend to be saturated. The experimental magnetisation of 1.20μ_B at 7 T is close to half of the saturated magnetisation, which is a typical characteristic of powder averaging of Ising spins as observed in other Nd³⁺ systems.^12,28,68

Ba₃BiPbGdO(BO₃)₄. As shown in Fig. 6e, the χ(T) curve of Ba₃BiPbGdO(BO₃)₄ increases upon cooling and no anomaly is observed, indicating that no magnetic LRO occurred down to 2 K. No divergence between the ZFC and FC curves is observed, ruling out the possibility of a spin glass state and spin canting behaviour. The Curie–Weiss fitting is performed in the high-temperature range of 200–300 K, leading to an effective magnetic moment μ_(HT,Gd) of 8.71(1)μ_B and a Weiss temperature θ_(HT,Gd) of −7.75(14) K (Fig. 6f and Table 2). In the low-temperature range between 2 K and 5 K, the Curie–Weiss fitting gives an effective magnetic moment μ_(LT,Gd) of 8.36(1)μ_B and a Weiss temperature θ_(LT,Gd) of −0.56(1) K. The negative Weiss temperature indicates that the dominant magnetic exchange interactions in Ba₃BiPbGdO(BO₃)₄ are AFM. The χT(T) value at room temperature is 9.25 emu K mol⁻¹ and then decreases upon cooling, further confirming the dominant antiferromagnetic exchange interactions.

The magnetic-field-dependent magnetisation for Ba₃BiPbGdO(BO₃)₄ is measured at 2 K, as shown in Fig. 7c. At the beginning, the M(H) curve linearly increases below 2 T, confirming the AFM ground state. Then it tends to be saturated at 7 T with a magnetisation value of 8.60μ_B, which is larger than the theoretical saturated magnetisation of Gd³⁺. Similar phenomena have been reported in other Gd-based compounds Gd₃BWO₉,⁶⁹ RbBaGd(BO₃)₂,⁷⁰ and GdZnAl₁₁O₁₉.²⁸ The underlying mechanism requires further investigation in the future using other techniques, particularly for a large single-crystal sample.

Ba₃BiPbDyO(BO₃)₄. The magnetic susceptibility of Ba₃BiPbDyO(BO₃)₄ is measured at 0.1 T, as shown in Fig. 6g. The χ(T) curve increases with no anomaly when decreasing the temperature down to 2 K, suggesting no magnetic LRO for Ba₃BiPbDyO(BO₃)₄. There is no divergence between the ZFC and FC curves, suggesting no spin glass state and spin canting behaviour. The Curie–Weiss fitting performed between 200 K and 300 K gives an effective magnetic moment μ_(HT,Dy) of 11.04(1)μ_B and a Weiss temperature θ_(HT,Dy) of −13.60(19) K (Fig. 6h and Table 2). The effective magnetic moment μ_(HT,Dy) value is close to the expected theoretical value of 10.65μ_B for free Dy³⁺ ions. The slope of χ⁻¹ varies below 5 K due to CEF effects.^17,71 In the low-temperature range, the Curie–Weiss fitting performed between 2 and 5 K gives an effective magnetic moment μ_(LT,Dy) of 8.41(2)μ_B and a Weiss temperature θ_(LT,Dy) of −1.30(2) K. The negative Weiss temperature indicates that the dominant magnetic exchange interactions in Ba₃BiPbDyO(BO₃)₄ are also AFM. The χT(T) value at room temperature is 14.56 emu K mol⁻¹ and then decreases upon cooling, which further confirms the dominant antiferromagnetic exchange interactions.

The magnetic-field-dependent magnetisation for Ba₃BiPbDyO(BO₃)₄ is measured at 2 K, as shown in Fig. 7d. At the beginning, the M(H) curve linearly increases below 1.5 T and then gradually tends to saturation. The magnetisation value at 7 T is 6.14μ_B, which is slightly larger than half of the fully polarised Dy³⁺ moments of 10μ_B due to powder averaging of Ising spins, as reported in Dy₂Be₂GeO₇,¹² Dy₂O₂CN₂,⁶⁸ Dy₃BWO₉,⁶⁹ and RbBaDy(BO₃)₂.⁷⁰

To better investigate the two-dimensional magnetism of the Ba₃BiPbREO(BO₃)₄ compounds, we evaluated the magnitudes of superexchange magnetic interactions and intra/inter-layer dipolar interactions. Here, to evaluate the energy scale of magnetic interactions, the strengths of superexchange interaction (J_nn) between local RE³⁺ moments are estimated by the mean field approximation using J_nn = 3θ/[zS(S + 1)],^18,72,73 where S denominates the total spin number (for rare earth, S is represented by the total angular momentum J), z is the number of nearest-neighbor spins (z = 6), and θ is the Weiss temperature from low-temperature fitting. Considering the significant spin–orbit coupling, varying crystal electric field (CEF) effects and spin types of RE³⁺, the quantum number J = |L ± S| and effective spin S_eff = 1/2 were adopted for estimating the nearest-neighbour exchange J_nn. For Ba₃BiPbREO(BO₃)₄ (RE = Nd, Dy), S_eff = 1/2 is particularly appropriate because electrons occupy the low-lying Kramers doublet at low temperatures. The dipolar interactions D are calculated using D = μ₀μ_eff²₂/[4π(R_nn)3k_B],^18,68,72,73 where R_nn represents intra-layer and inter-layer nearest-neighbour RE–RE distances (D_intra and D_inter) and μ_eff is the effective moment from low-temperature fitting. The calculated superexchange interaction and dipolar interactions are listed in Table 3. Evidently, the intra-layer dipolar interactions (D_intra) are approximately 15 times larger than the inter-layer counterpart (D_inter). Structurally, superexchange via the intra-layer RE–O–B–O–RE path significantly exceeds that via the inter-layer RE–O–Bi/Pb–O–Bi/Pb–O–RE path. All estimated interactions indicate that Ba₃BiPbREO(BO₃)₄ realizes quasi-two-dimensional magnetism.

Table 3 The estimated superexchange interaction (J_nn), intralayer dipole–dipole interactions (D_intra) and interlayer dipole–dipole interactions (D_inter) for Ba₃BiPbREO(BO₃)₄ (RE = Pr, Nd, Gd, and Dy)

RE	D (K)		J nn (K)
	D intra	D inter	Using J	Using Jeff = 1/2
Pr	0.0140(5)	0.00090(3)	−0.39(1)	—
Nd	0.0200(2)	0.00130(1)	−0.0048(2)	−0.16(1)
Gd	0.2706(8)	0.01892(5)	−0.0178(3)	—
Dy	0.2736(8)	0.01920(5)	−0.0102(2)	−0.87(2)

---

Heat capacity

To confirm no occurrence of LRO in Ba₃BiPbREO(BO₃)₄ (RE = Pr, Nd, Gd, and Dy), especially at low temperature, the heat capacity measurements were performed from 30 K down to 2 K (Fig. 8). The C_p(T) curve decreases upon cooling and no sharp peak is observed down to 2 K, indicating that no LRO occurred for Ba₃BiPbREO(BO₃)₄ (RE = Pr, Nd, Gd, and Dy). These are in good agreement with the magnetic susceptibility results. The slight increases below 5 K (Fig. S5) for Ba₃BiPbGdO(BO₃)₄ and Ba₃BiPbDyO(BO₃)₄ should be Schottky anomalies, despite that LRO below 2 K cannot be ruled out at this moment. Further investigations using other techniques, such as specific heat and neutron scattering measurements below 2 K, will be performed by collaborating with physicists later, particularly for the large single crystal sample.

Fig. 8 Specific heat for Ba₃BiPbREO(BO₃)₄ (RE = Pr, Nd, Gd, and Dy).

Conclusions

In conclusion, a series of isostructural rare-earth-based magnetic compounds Ba₃BiPbREO(BO₃)₄ (RE = Pr, Nd, Gd, and Dy) with a geometrically-perfect triangular magnetic lattice have been successfully synthesised. The magnetisation susceptibility results indicate that dominant interactions between RE³⁺ moments are antiferromagnetic in all four compounds and exhibit no LRO down to 2 K, as further confirmed by specific heat measurements. These RE-based magnetic compounds with a two-dimensional triangular frustrated structure provide a platform for exploring more physical phenomena in rare-earth-based spin-frustrated materials.

Author contributions

Yun Lv: synthesis of samples, formal analysis, data curation, and writing – original draft. Yanhong Wang: writing – review & editing and formal analysis. Nian Shi: data curation and formal analysis. Keke Huang: writing – review & editing and funding acquisition. Jinkui Tang: writing – review & editing and funding acquisition. Hongcheng Lu: writing – review & editing, supervision, resources, funding acquisition, and conceptualization.

Conflicts of interest

There are no conflicts to declare.

Data availability

All experimental procedures and associated data are included in the article and its supplementary information (SI). Supplementary information is available. See DOI: https://doi.org/10.1039/d5dt03066h.

Other data are available upon request from the corresponding author.

CCDC 2466013–2466016 for Ba₃BiPbREO(BO₃)₄ (RE = Pr, Nd, Gd, and Dy) contain the supplementary crystallographic data for this paper.^74a–d

Acknowledgements

This work was supported by the National Natural Science Foundation of China (NSFC No. 22271107 and 22422111), the National Key Research and Development Program (No. 2023YFA1406500), and the Open Funds of the State Key Laboratory of Rare Earth Resource Utilization (RERU2023011).

References

1. L. Balents, Nature, 2010, 464, 199–208.
2. M. Hering, H. Yan and J. Reuther, Phys. Rev. B: Condens. Matter Mater. Phys., 2021, 104, 064406.
3. C. Broholm, R. J. Cava, S. A. Kivelson, D. G. Nocera, M. R. Norman and T. Senthil, Science, 2020, 367, eaay0668.
4. D. E. Freedman, R. Chisnell, T. M. McQueen, Y. S. Lee, C. Payen and D. G. Nocera, Chem. Commun., 2012, 48, 64–66.
5. Y. She, Y. Wang, S. Li, T. Wang and H. Lu, Nano Res., 2022, 16, 3552–3557.
6. M. B. Sanders, J. W. Krizan and R. J. Cava, J. Mater. Chem. C, 2016, 4, 541–550.
7. A. Li, Y. Wang, H. Tian, A. Yalikun, Y. Journaux, M. Luo and H. Lu, Chin. Chem. Lett., 2023, 35, 108780.
8. F. H. Aidoudi, D. W. Aldous, R. J. Goff, A. M. Z. Slawin, J. P. Attfield, R. E. Morris and P. Lightfoot, Nat. Chem., 2011, 3, 801–806.
9. R. S. Dissanayaka Mudiyanselage, T. Klimczuk, D. Ni, R. J. Cava and W. Xie, Inorg. Chem., 2022, 61, 18010–18018.
10. A. F. Albuquerque, D. Schwandt, B. Hetényi, S. Capponi, M. Mambrini and A. M. Läuchli, Phys. Rev. B: Condens. Matter Mater. Phys., 2011, 84, 024406.
11. N. Shannon, T. Momoi and P. Sindzingre, Phys. Rev. Lett., 2006, 96, 027213.
12. M. Ashtar, Y. Bai, L. Xu, Z. Wan, Z. Wei, Y. Liu, M. A. Marwat and Z. Tian, Inorg. Chem., 2021, 60, 3626–3634.
13. J. T. Chalker, P. C. W. Holdsworth and E. F. Shender, Phys. Rev. Lett., 1992, 68, 855–858.
14. R. Moessner and S. L. Sondhi, Phys. Rev. Lett., 2001, 86, 1881–1884.
15. J. E. Greedan, J. Mater. Chem., 2001, 11, 37–53.
16. W. Liu, Z. Zhang, J. Ji, Y. Liu, J. Li, X. Wang, H. Lei, G. Chen and Q. Zhang, Chin. Phys. Lett., 2018, 35, 117501.
17. Y. Gao, L. Xu, Z. Tian and S. Yuan, J. Alloys Compd., 2018, 745, 396–400.
18. F. Song, A. Liu, Q. Chen, J. Zhou, J. Li, W. Tong, S. Wang, Y. Wang, H. Lu, S. Yuan, H. Guo and Z. Tian, Inorg. Chem., 2024, 63, 5831–5841.
19. Y. Saito, T. Minamidate, A. Kawamoto, N. Matsunaga and K. Nomura, Phys. Rev. B, 2018, 98, 205141.
20. J. Alicea, A. V. Chubukov and O. A. Starykh, Phys. Rev. Lett., 2009, 102, 137201.
21. J. Sheng, L. Wang, A. Candini, W. Jiang, L. Huang, B. Xi, J. Zhao, H. Ge, N. Zhao, Y. Fu, J. Ren, J. Yang, P. Miao, X. Tong, D. Yu, S. Wang, Q. Liu, M. Kofu, R. Mole, G. Biasiol, D. Yu, I. A. Zaliznyak, J.-W. Mei and L. Wu, Proc. Natl. Acad. Sci. U. S. A., 2022, 119, e2211193119.
22. M. Liu, H. Zhang, X. Huang, C. Ma, S. Dong and J. Liu, Inorg. Chem., 2016, 55, 2709–2716.
23. S. Nakatsuji, Y. Nambu, H. Tonomura, O. Sakai, S. Jonas, C. Broholm, H. Tsunetsugu, Y. Qiu and Y. Maeno, Science, 2005, 309, 1697–1700.
24. Y. Shirata, H. Tanaka, T. Ono, A. Matsuo, K. Kindo and H. Nakano, J. Phys. Soc. Jpn., 2011, 80, 093702.
25. S. Das, S. Hossain, A. Dey, S. Biswas, J.-P. Sutter and V. Chandrasekhar, Inorg. Chem., 2014, 53, 5020–5028.
26. J. Goura, J. P. S. Walsh, F. Tuna and V. Chandrasekhar, Inorg. Chem., 2014, 53, 3385–3391.
27. Y. Li, H. Liao, Z. Zhang, S. Li, F. Jin, L. Ling, L. Zhang, Y. Zou, L. Pi, Z. Yang, J. Wang, Z. Wu and Q. Zhang, Sci. Rep., 2015, 5, 16419.
28. M. Ashtar, M. A. Marwat, Y. X. Gao, Z. T. Zhang, L. Pi, S. L. Yuan and Z. M. Tian, J. Mater. Chem. C, 2019, 7, 10073–10081.
29. M. Ashtar, Y. X. Gao, C. L. Wang, Y. Qiu, W. Tong, Y. M. Zou, X. W. Zhang, M. A. Marwat, S. L. Yuan and Z. M. Tian, J. Alloys Compd., 2019, 802, 146–151.
30. J. Xing, L. D. Sanjeewa, J. Kim, G. R. Stewart, M. H. Du, F. A. Reboredo, R. Custelcean and A. S. Sefat, ACS Mater. Lett., 2020, 2, 71–75.
31. Z. Ma, J. Wang, Z. Dong, J. Zhang, S. Li, S. Zheng, Y. Yu, W. Wang, L. Che, K. Ran, S. Bao, Z. Cai, P. Čermák, A. Schneidewind, S. Yano, J. S. Gardner, X. Lu, S. Yu, J. Liu, S. Li, J. Li and J. Wen, Phys. Rev. Lett., 2018, 120, 087201.
32. Z. Hu, Z. Ma, Y.-D. Liao, H. Li, C. Ma, Y. Cui, Y. Shangguan, Z. Huang, Y. Qi, W. Li, Z. Y. Meng, J. Wen and W. Yu, Nat. Commun., 2020, 11, 5631.
33. U. K. Voma, S. Bhattacharya, E. Kermarrec, J. Alam, Y. M. Jana, B. Sana, P. Khuntia, S. K. Panda and B. Koteswararao, Phys. Rev. B, 2021, 104, 144411.
34. S.-Y. Zhang, W.-B. Guo and Z.-Z. He, Dalton Trans., 2019, 48, 65–71.
35. S. Guo, R. Zhong, K. Górnicka, T. Klimczuk and R. J. Cava, Chem. Mater., 2020, 32, 10670–10677.
36. M. Cui, N. Wang, S. Chen, X. Huang and Z. He, J. Alloys Compd., 2019, 785, 1009–1014.
37. H. Liu, Y. Wang, Y. Zhou, S. Li, Y. Dou, T. Wang and H. Lu, Inorg. Chem., 2022, 61, 17838–17847.
38. X. Huang, Z. Zhao, M. Zhang and Z. He, CrystEngComm, 2021, 23, 3126–3132.
39. A. Yalikun, Y. Wang, Y. Lv, Y. Dou, H.-J. Koo, J. Cao, W. Qi, K. Huang, M.-H. Whangbo, Z. Ouyang and H. Lu, Inorg. Chem., 2024, 63, 14354–14365.
40. Z. He and W. Cheng, Solid State Commun., 2009, 149, 236–238.
41. M. B. Sanders, F. A. Cevallos and R. J. Cava, Mater. Res. Express, 2017, 4, 036102.
42. Y. Wang, S. Li, Y. Dou, H. Li and H. Lu, Dalton Trans., 2023, 52, 13555–13564.
43. H. Li, S. Li, Y. Wang, Y. Dou and H. Lu, J. Solid State Chem., 2025, 341, 125052.
44. C. Tao and R. Li, Chem. – Eur. J., 2020, 26, 3709–3712.
45. X. Chen, R. Bian, W. Xiao and X. Song, Dalton Trans., 2022, 51, 9454–9466.
46. X. Chen, X. Yuan, W. Xiao and X. Song, RSC Adv., 2024, 14, 6270–6284.
47. G. M. Sheldrick, Acta Crystallogr., 2015, 71, 3–8.
48. P. P. Sahoo, E. Gaudin, J. Darriet and T. N. Guru Row, Mater. Res. Bull., 2009, 44, 812–816.
49. H. Xie, X. Chang, W. Yang, Y. Jiang and Y. Zhao, Synth. React. Inorg. Met.-Org. Chem., 2016, 46, 1090–1094.
50. J. Rodríguez-Carvaja, Phys. B, 1993, 192, 55–69.
51. G. A. Bain and J. F. Berry, J. Chem. Educ., 2008, 85, 532–536.
52. L. Vijayalakshmi, K. Naveen Kumar and J. D. Baek, J. Mater. Sci.:Mater. Electron., 2022, 33, 11938–11945.
53. L. Vijayalakshmi, K. Naveen Kumar, G. Srinivas, P. Hwang and J. Choi, Optik, 2021, 227, 166025.
54. R. Liu, H. Wu, H. Yu, Z. Hu, J. Wang and Y. Wu, Chem. Mater., 2021, 33, 4240–4246.
55. A. B. Kuznetsov, K. A. Kokh, N. Sagatov, P. N. Gavryushkin, M. S. Molokeev, V. A. Svetlichnyi, I. N. Lapin, N. G. Kononova, V. S. Shevchenko, A. Bolatov, B. Uralbekov, A. A. Goreiavcheva and A. E. Kokh, Inorg. Chem., 2022, 61, 7497–9505.
56. Y. Chen, P. Gong, R. Guo, F. Fan, J. Shen, G. Zhang and H. Tu, Inorg. Chem., 2023, 62, 15584–15592.
57. P. Chen, M. M. Murshed and T. M. Gesing, J. Mater. Sci., 2020, 56, 3639–3652.
58. Y. Li, W. Liu, Y. Li, X. Li, Y. Gao, Z. Tian and M. Wang, Solid State Sci., 2025, 169, 108095.
59. D. Gelija, H.-a. Kim and W. J. Chung, Opt. Mater., 2025, 167, 117251.
60. N. Kawano, K. Shinozaki, D. Nakauchi, H. Kimura, G. Okada and T. Yanagida, Mater. Res. Bull., 2023, 158, 112081.
61. A. D. Sontakke and K. Annapurna, Mater. Chem. Phys., 2013, 137, 916–921.
62. M. A. Marzouk, F. H. ElBatal, Y. M. Hamdy and H. A. ElBatal, Appl. Phys. A, 2023, 129, 505.
63. N. Yaduvanshi, C. Basavapoornima, A. S. Alqarni, U. K. Kagola, T. Uthayakumar, A. Madhu and N. Srinatha, Opt. Mater., 2024, 151, 115359.
64. Q. Chen, M. Zhang, Q. Ma and Q. Wang, J. Non-Cryst. Solids, 2019, 507, 46–55.
65. J. Tauc, R. Grigorovici and A. Vancu, Phys. Status Solidi B, 1966, 15, 627–637.
66. X. Xu, C. L. Hu, B. X. Li and J. G. Mao, Chem. – Eur. J., 2016, 22, 1750–1759.
67. Z. Ma, S. Zheng, Y. Chen, R. Xu, Z.-Y. Dong, J. Wang, H. Du, J. P. Embs, S. Li, Y. Li, Y. Zhang, M. Liu, R. Zhong, J.-M. Liu and J. Wen, Phys. Rev. B, 2024, 109, 165143.
68. Y. Lv, Y. Wang, Y. Dou, A. Li, J. Tang, O. S. Volkova, A. N. Vasiliev and H. Lu, Cryst. Growth Des., 2025, 25, 2446–2455.
69. M. Ashtar, J. Guo, Z. Wan, Y. Wang, G. Gong, Y. Liu, Y. Su and Z. Tian, Inorg. Chem., 2020, 59, 5368–5376.
70. S. Guo, T. Kong, W. Xie, L. Nguyen, K. Stolze, F. A. Cevallos and R. J. Cava, Inorg. Chem., 2019, 58, 3308–3315.
71. P. Mukherjee, A. C. Sackville Hamilton, H. F. J. Glass and S. E. Dutton, J. Phys.: Condens. Matter, 2017, 29, 405808.
72. E. C. Koskelo, C. Liu, P. Mukherjee, N. D. Kelly and S. E. Dutton, Chem. Mater., 2022, 34, 3440–3450.
73. Q. Zeng, H. Ge, M. Wu, S. Ruan, T. Li, Z. Wang, J. Li, L. Ling, W. Tong, S. Huang, A. Liu, J. Zhou, Z. Xia, J. Sheng, L. Wu and Z. Tian, Chem. Mater., 2024, 36, 2867–2879.
74. (a) CCDC 2466013: Experimental Crystal Structure Determination, 2026,  DOI:10.5517/ccdc.csd.cc2ns2tc; (b) CCDC 2466014: Experimental Crystal Structure Determination, 2026,  DOI:10.5517/ccdc.csd.cc2ns2vd; (c) CCDC 2466015: Experimental Crystal Structure Determination, 2026,  DOI:10.5517/ccdc.csd.cc2ns2wf; (d) CCDC 2466016: Experimental Crystal Structure Determination, 2026,  DOI:10.5517/ccdc.csd.cc2ns2xg.

---