Magnetism and Low-Temperature Magnetocaloric Effect in Gd₇(BO₃)(PO₄)₂O₆ Compound with Monoclinic Lattice

Abstract

The development of magnetic refrigerants with both low-field responsiveness and a large magnetic entropy change in the sub-Kelvin temperature range remains a critical challenge for advancing cryogenic technologies. This study focuses on the monoclinic compound Gd₇(BO₃)(PO₄)₂O₆, in which high-density Gd³⁺ ions form magnetic frustrated structures within the bc-plane and stack along the a-axis direction. The combination of a high magnetic ion density and frustrated magnetic configuration enables the coexistence of a low magnetic transition temperature and excellent magnetocaloric effects. Magnetic susceptibility measurements reveal an antiferromagnetic-to-paramagnetic phase transition below 2 K. The maximum magnetic entropy change reaches 35.2 J kg⁻¹ K⁻¹ under a varying magnetic field of 0–7 T. This study highlights the potential of frustrated magnetic interactions in monoclinic lattices with a high Gd³⁺ content for achieving superior cryogenic magnetocaloric performance.

1. Introduction

The pursuit of efficient cooling technologies has positioned cryogenic magnetic refrigeration as a promising field, with applications spanning from quantum computing and space exploration to advanced medical diagnostics [1]. This approach presents distinct advantages over traditional cooling methods, offering superior efficiency, reduced environmental impact, and capabilities to reach extremely low temperatures [2]. At its core, this technology exploits the magnetocaloric effect (MCE)—a phenomenon where magnetic materials undergo temperature changes when exposed to varying magnetic fields. During magnetization, the ordering of magnetic moments decreases magnetic entropy; during demagnetization, their randomization increases entropy and produces cooling [3]. For effective sub-Kelvin refrigeration, materials must demonstrate substantial magnetic entropy changes alongside minimal adiabatic temperature variations [4]. The development of such specialized magnetic refrigerants remains a central challenge in advancing this technology.

In recent years, considerable efforts have been devoted to exploring novel magnetocaloric materials with enhanced performance in the ultra-low-temperature regime [5,6]. Among the various material families, rare-earth-based compounds have emerged as promising candidates, owing to their large magnetic moments and diverse magnetic interactions [7,8,9,10]. Gadolinium-based compounds have attracted significant interest due to the high magnetic moment of Gd³⁺ ions (7.94 ${\mu }_B$) and their potential for achieving large MCE [11,12,13,14,15]. Chen et al. reported on the GdF₃ compound, which features high spin, high-density structure, and weak ferromagnetic interactions [16]. This compound exhibits a maximum magnetic entropy change of up to 528 mJ·cm⁻³ K⁻¹ under a varying magnetic field of 0–9 T. Zhang et al. investigated the magnetism and magnetocaloric effect of the Gd₂CuTiO₆ compound with a double perovskite structure [17]. Due to the exchange interactions between the Gd-4f and Cu-3d magnetic sublattices, this compound demonstrates enhanced low-temperature magnetocaloric effects, achieving a maximum magnetic entropy change of 51.4 J kg⁻¹ K⁻¹ under a magnetic field change of 0–7 T. Chen et al. studied the magnetic properties and magnetocaloric effect of NaGd₉(SiO₄)₆O₂ single crystals [18]. The high magnetic density and relatively weak exchange interactions in this compound lead to a magnetic ordering transition at 2.6 K, with a volumetric magnetic entropy change of 382.8 mJ·cm⁻³ K⁻¹ under a magnetic field of 0–7 T. Therefore, gadolinium-based compounds with a high magnetic density are promising candidates for further exploration in the quest for high-performance cryogenic magnetic refrigerants.

Frustrated magnetic systems, characterized by competing magnetic interactions that cannot be simultaneously satisfied, have been identified as a fertile ground for realizing low-temperature magnetocaloric materials [19,20,21,22]. These frustrated magnetic configurations often exhibit enhanced MCE due to the presence of low-energy magnetic excitations [23]. In this work, we focus on the Gd₇(BO₃)(PO₄)₂O₆ compound with monoclinic crystal, which combines a high density of Gd³⁺ ions with a frustrated magnetic structure. The unique arrangement of Gd³⁺ ions within the bc-plane and their stacking along the a-axis direction gives rise to competing magnetic interactions, making it an ideal platform for investigating low-temperature magnetocaloric effects. Through a comprehensive study of magnetic properties and MCE, we demonstrate the potential of Gd₇(BO₃)(PO₄)₂O₆ as a promising cryogenic magnetic refrigerant.

2. Materials and Methods

A high-quality polycrystalline sample of the Gd₇(BO₃)(PO₄)₂O₆ compound was synthesized using a high-temperature solid-state reaction method. The starting materials used for the synthesis were NH₄H₂PO₄ (99.99%), Gd₂O₃ (99.99%), and H₃BO₃ (99.99%). Prior to the mixing process, all raw materials should be subjected to drying in an oven for 24 h to eliminate any adsorbed moisture. Additionally, weighing should be conducted in an inert nitrogen environment to avoid hydration. These reagents were mixed in stoichiometric proportions and thoroughly ground in an agate mortar. To compensate for the volatilization of NH₄H₂PO₄ and H₃BO₃ at high temperatures, an excess of these precursors was added. After sufficient grinding, the mixture was initially heated at 773 K for 5 h. Subsequently, the sample was heated at 1473 K for 10 h, then removed from the furnace and reground. The grinding and heating process at 1473 K was repeated until a pure phase was obtained. All heating processes involve placing the sample in an alumina crucible and are carried out in air. The crystal structure of the synthesized compound was analyzed at room temperature by powder X-ray diffraction (XRD) using a diffractometer with Cu Kα radiation (λ = 1.5406 Å). The XRD data were collected over a 2θ range of 10° to 60° with a step size of 0.02° and a scanning speed of 2° per minute. To investigate the magnetic properties of the compound, temperature-dependent magnetization measurements were performed using a Quantum Design Physical Properties Measurement System (PPMS-9) equipped with a vibrating sample magnetometer (VSM) option. The measurements were carried out in the temperature range of 2–300 K under an applied magnetic field of 0.05 T. Field-dependent magnetization measurements were also conducted at various temperatures using the VSM option of the PPMS-9, with applied magnetic fields up to 7 T.

3. Results

3.1. Crystal Structure

The crystal structure of the Gd₇(BO₃)(PO₄)₂O₆ compound is shown in Figure 1a, where each Gd³⁺ ion is surrounded by seven oxygen atoms, forming a polyhedral structure. Figure 1b presents the crystal structure from different perspectives, clearly revealing the layered stacking feature along the a-axis direction. It is worth noting that the nearest-neighbor distance between the stacked Gd³⁺ ions along the a-axis direction is 3.79 Å, indicating the presence of complex three-dimensional magnetic interactions in this compound. To better illustrate the uniqueness of the crystal structure, Figure 1c provides a magnified view of the local structure. The black dashed lines serve as a visual guide to observe the occupancy characteristics of Gd³⁺ ions in the lattice. The neighboring Gd³⁺ ions form a magnetically frustrated structure, with the distances between adjacent Gd³⁺ ions ranging from 3.68 to 3.88 Å. This unique structure leads to disorder and competition among the magnetic moments, which is expected to result in a lower magnetic ordering temperature. Figure 2 presents the refined powder X-ray diffraction (XRD) pattern of the Gd₇(BO₃)(PO₄)₂O₆ compound at room temperature. The compound crystallizes in a monoclinic structure with space group No. 14 (P2₁/c). The lattice parameters are determined to be a = 6.6924 Å, b = 17.2453 Å, and c = 12.1073 Å. The refined experimental diffraction peaks are in good agreement with the standard peaks, and the corresponding refinement parameters R_P, R_WP, and R_F are 13.07%, 14.699%, and 0.886%, respectively. The detailed crystal structure information is summarized in

Table 1. Crystallographic information of Gd₇(BO₃)(PO₄)₂O₆ compound.

Compound	Gd7(BO3)(PO4)2O6
Space group	P21/c (No. 14)
a (Å)	6.6924
b (Å)	17.2453
c (Å)	12.1073
V (Å3)	1285.0881
RP (%)	13.07
RWP (%)	14.699
RF (%)	0.886

.

3.2. Magnetic Properties

To determine the magnetic properties of the Gd₇(BO₃)(PO₄)₂O₆ compound, the temperature-dependent magnetic susceptibility M (T) was measured in the temperature range of 2–300 K under an applied magnetic field of 0.01 T using both zero-field-cooled (ZFC) and field-cooled (FC) modes, as shown in Figure 3a. With decreasing temperature, the magnetic susceptibility gradually increases, and no inflection point is observed down to 2 K, indicating that the magnetic ordering temperature of this compound is below 2 K. The dM/dT curve also confirms that no magnetic ordering transition occurs in the compound above 2 K. The Curie–Weiss fitting of the magnetic susceptibility data in the temperature range of 2–300 K yields an effective magnetic moment of 8.1 ${\mu }_B$ for Gd³⁺, which is close to the theoretical value (7.96 ${\mu }_B$) [24]. Furthermore, the fitted paramagnetic Curie temperature (θ) is −8.17 K, indicating that the Gd³⁺ ions exhibit typical antiferromagnetic characteristics. However, the magnetic measurements collected above 2 K did not observe a magnetic ordering temperature. When considering only the nearest-neighbor interactions ($J_1$) of Gd³⁺, the Hamiltonian for the Gd₇(BO₃)(PO₄)₂O₆ compound can be expressed as $H_{\mathrm{ex}}=J_1{\sum }_{〈i,j〉}{S}_i·S_j$. Hence, the magnitude of the $J_1$ can also be used to evaluate the magnetic ordering temperature. For the Gd₇(BO₃)(PO₄)₂O₆ compound, with z = 4 and S = 7/2, the experimental fit of the Curie-Weiss temperature is −8.17 K, which leads to a $J_1$ value of 390 mK through ${\theta }_{\mathrm{CW}}=-J_1\mathit{zS}(S+1)/3k_B$. Since the magnetic transition temperature in magnetic materials is significantly influenced by $J_1$, the magnetic transition temperature in is below 2 K. To further understand the magnetism of the Gd₇(BO₃)(PO₄)₂O₆ compound, the dM/dT results of its susceptibility as a function of temperature under different magnetic fields are presented in Figure 3b. At magnetic fields below 3 T, no inflection point is observed in the dM/dT curves. As the magnetic field increases, the inflection point appears and moves to higher temperatures. Therefore, based on the present results, several characteristics of the Gd₇(BO₃)(PO₄)₂O₆ compound can be inferred: the magnetic transition temperature is below 2 K; and an induced transition from antiferromagnetic to ferromagnetic states occurs in magnetic fields exceeding 3 T.

Figure 4a shows the isothermal magnetization curves M (H) of the Gd₇(BO₃)(PO₄)₂O₆ compound at different temperatures under magnetic fields ranging from 0 to 7 T. As the magnetic field increases, the magnetization intensity increases almost linearly and does not reach saturation even at a high field of 7 T, which can be attributed to the typical frustrated structure in this compound. In Figure 4b, the Brillouin function for a free Heisenberg spin of S = 7/2 at T = 2 K is plotted. A significant difference can be clearly observed between the Brillouin function and the M (H) curve of Gd₇(BO₃)(PO₄)₂O₆ compound at 2 K. Relatively speaking, the Brillouin function curve tends to saturate at lower magnetic fields, indicating that the magnetic interactions in this compound are dominated by superexchange or dipolar antiferromagnetic interactions. Moreover, the M (H) curves measured at 2 K using increasing and decreasing magnetic fields exhibit good reversibility, suggesting that the current compound undergoes a second-order magnetic phase transition from an antiferromagnetic state to a paramagnetic state.

3.3. Magnetocaloric Effect

Although the compound exhibits a high saturation magnetization of 180 Am²/kg, a significant portion of the magnetic entropy (${–\Delta S}_M$) is lost due to strong antiferromagnetic interactions. Magnetic entropy change is an important parameter for evaluating the magnetocaloric effect. Based on the Maxwell relation, it is given by [25]. The temperature dependence of the magnetic entropy change ${–\Delta S}_M\left(T\right)$ for the Gd₇(BO₃)(PO₄)₂O₆ compound under different magnetic fields is shown in Figure 5. As the magnetic field increases, the peak value of the ${–\Delta S}_M$ appears to gradually shift towards higher temperatures, which is particularly evident under 7 T. This suggests that the compound may undergo a field-induced metamagnetic transition from an antiferromagnetic state to a ferromagnetic state under the influence of the magnetic field. This conclusion is obtained because the peak value of the ${–\Delta S}_M$ in ferromagnetic materials shifts towards higher temperatures with an increasing magnetic field. Although the compound has an antiferromagnetic ground state, the results of the ${–\Delta S}_M$ are sufficient to prove the correctness of this hypothesis, and similar results have also been observed in other compounds with antiferromagnetic interactions [26].

Under a varying magnetic field of 0–7 T, the maximum magnetic entropy change ($–\Delta S_M^{max}$) of the compound reaches 35.2 J/kg K, exhibiting a relatively excellent low-temperature magnetocaloric effect. However, based on the theoretical magnetic entropy change calculation formula $–\Delta S_M^{max}$ = nRln(2S + 1)/M, where n is the number of magnetic ions, R is the ideal gas constant, S is the spin quantum number of the magnetic ions, and M corresponds to the molar mass of the compound, the calculated theoretical magnetic entropy change is as high as 83.0 J/kg K. This is significantly higher than the currently observed experimental value. As mentioned above, due to the strong frustration, the magnetization increases linearly with the magnetic field, resulting in a significant reduction in ${–\Delta S}_M$.

The refrigerant capacity (RC) and temperature-averaged magnetic entropy change (TEC) are also important parameters for evaluating the magnetocaloric effect, as obtained from Equations (2) and (3) [27,28], where $T_{hot}$ and $T_{cold}$ correspond to the temperatures at half of the |$–\Delta S_M^{max}$|, respectively. For the Gd₇(BO₃)(PO₄)₂O₆ compound, $T_{cold}$ is determined to be 2.5 K, ${\Delta T}_{lift}$ is the desired temperature lift, and $T_{mind}$ is the center temperature at which the maximum TEC is expected to be obtained. Under a varying magnetic field of 0–7 T, the TEC (3) and RC of the Gd₇(BO₃)(PO₄)₂O₆ compound are 33.2 J/kg and 288.6 J/kg, respectively.

Table 2. Comparison of magnetocaloric parameters between Gd₇(BO₃)(PO₄)₂O₆ compound and other candidate materials with similar magnetic transition temperatures.

Compounds	${\mathit{T}}_{\mathit{N}}$$/{\mathit{T}}_{\mathit{C}}$ (K)	${\mathit{\mu }}_0$∆H (T)	${-\Delta \mathit{S}}_{\mathit{M}}^{\mathit{m}\mathit{a}\mathit{x}}$ (J/kg K)	RC (J/kg)	Reference
Gd7(BO3)(PO4)2O6	$<$2	7	35.2	288.6	This work
GdCrO3	2.3	7	37.0	542.0	[30]
Gd2GeMoO8	1.4	7	41.2	257.4	[31]
GdVO4	2.4	5	41.1	*	[32]
GdAlO3	3.9	9	40.9	271.0	[33]
LiGd(MoO4)2	$<$2	7	33.6	*	[34]
DyBO3	1.01	5	22.0	*	[35]

* Indicates that the relevant data are not available in the referenced.

compares the magnetocaloric parameters of other low-temperature magnetic refrigerant materials with similar magnetic transition temperatures. It should be emphasized that although the magnetocaloric effect of the current compound is not outstanding, its theoretical magnetic entropy changes of up to 83.0 J/kg K indicate that excellent magnetocaloric effects can be expected and achievable through further optimization. From the crystal structure of the Gd₇(BO₃)(PO₄)₂O₆ compound, it can be observed that Gd³⁺ forms a magnetic frustrated structure in the ab-plane, creating a two-dimensional structure, and these layers are stacked along the c-axis direction. Therefore, if partial non-magnetic ions occupy the Gd³⁺ sites, it could disrupt some of the frustrated structures. Although introducing non-magnetic ions into the system would reduce the magnetic density of the compound, if the magnetization can tend to saturate at lower magnetic fields while slightly reducing the saturation magnetization, a more superior magnetocaloric effect compared to the current one would be obtained, especially at low magnetic fields. B.Y. Kang et al. investigated the magnetically frustrated system R_1−xY_xB₄ (R = Tb and Dy) and found that the substitution of non-magnetic Y³⁺ ions for R³⁺ ions leads to two phenomena: a decrease in the magnetic transition temperature is observed; the substitution results in a weak ferromagnetic transition, which is precisely due to the disruption of the magnetically frustrated state [29]. Additionally, it is noteworthy that the frustrated structures are connected by oxygen atoms, which generate interlayer interactions. Thus, replacing some of the oxygen atoms with other molecular ligands can also significantly modulate the crystal structure, such as further increasing the interlayer spacing to achieve a lower magnetic transition temperature.

$$\Delta S_M\left(T,H\right)=S_M\left(T,H\right)-S_M\left(T,0\right)={\int }_0^H{\left\{{\displaystyle \frac{\partial M(T,H)}{\partial T}}\right\}}_{H}dH,$$

(1)

$$RC={\int }_{T_{cold}}^{T_{hot}}\left|\Delta S_M\left(T\right)\right|dT$$

(2)

$$TEC(\Delta T)={\displaystyle \frac{1}{{\Delta T}_{lift}}}\left\{{\int }_{T_{mid}-{\displaystyle \frac{{\Delta T}_{lift}}{2}}}^{T_{mid}+{\displaystyle \frac{{\Delta T}_{lift}}{2}}}{{\Delta S}_M\left(T\right)}_{\Delta H,T}dT\right\}$$

(3)

4. Discussion

It is important to emphasize that although the current magnetocaloric effect of the compound is not outstanding, its theoretical magnetic entropy change reaches as high as 83.0 J/kg K, indicating its potential to achieve superior low-temperature magnetocaloric effects. The fitted nearest-neighbor interaction $J_1$ as low as 390 mK indicates that the Gd₇(BO₃)(PO₄)₂O₆ compound likely has a low magnetic transition temperature. Results of temperature-dependent susceptibility curves (dM/dT) under different magnetic fields suggest that although this compound has antiferromagnetic interactions, these antiferromagnetic interactions can flip to a ferromagnetic state in magnetic fields exceeding 3 T. Additionally, due to the magnetically frustrated structure in the Gd₇(BO₃)(PO₄)₂O₆ compound, its magnetization exhibits an almost linear increase with the magnetic field, which is the main reason for the significant suppression of magnetic entropy. However, it is noteworthy that this compound has a high rare earth content, which means that the partial substitution of Gd³⁺ with non-magnetic ions could disrupt some of the magnetic frustration structure, making the magnetization more easily saturated with an increasing magnetic field. Although this would weaken the magnetic ion content of the system, causing a slight decrease in saturation magnetization, an overall enhancement in the magnetocaloric effect can be expected.

In addition, the geometric arrangement of magnetic ions in magnetically frustrated materials leads to competitive interactions between spins, resulting in lower magnetic transition temperatures. However, replacing some of the magnetic ions with non-magnetic ions can disrupt the frustrated structure, which is a double-edged sword for the development of ultra-low-temperature magnetic refrigeration materials. Specifically, the substitution of non-magnetic ions can eliminate some of the frustrated structures in the lattice, allowing the magnetization to saturate at lower magnetic fields and thus releasing more magnetic entropy. However, this could also lead to an increase in the magnetic ordering temperature. Therefore, it is particularly important to optimize the amount of non-magnetic ion substitution to balance the magnetocaloric effect and the magnetic transition temperature.

5. Conclusions

In conclusion, we have investigated the crystal structure, magnetic properties, and magnetocaloric effects of the monoclinic-lattice-structured Gd₇(BO₃)(PO₄)₂O₆ compound. This compound is characterized by a high density of Gd³⁺ ions arranged in a unique frustrated magnetic structure within the bc-plane and stacked along the a-axis direction, exhibiting promising magnetocaloric properties. Magnetic susceptibility measurements reveal an antiferromagnetic-to-paramagnetic phase transition occurring below 2 K. Based on the shift of the temperature corresponding to the magnetic entropy change peak towards higher temperatures with an increasing magnetic field, it can be inferred that the compound undergoes a field-driven metamagnetic transition from an antiferromagnetic to a ferromagnetic state. Most notably, the compound exhibits a significant magnetic entropy change of 35.2 J kg⁻¹ K⁻¹ under a magnetic field variation of 0–7 T. The results of this study emphasize the substantial potential of utilizing frustrated magnetic interactions in monoclinic lattices with a high concentration of Gd³⁺ ions. However, due to the strong magnetic frustration, the magnetization remains unsaturated even under a magnetic field as high as 7 T. In future work, the focus should be on tuning the magnetic frustration to enhance the magnetocaloric effect.