Growth and Magnetocaloric Properties of Co(NH₄)₂(SO₄)₂·6H₂O Crystal

Abstract

Co(NH₄)₂(SO₄)₂·6H₂O single crystal was grown via slow solvent evaporation at room temperature. The magnetic and magnetocaloric properties were investigated. The results show that Co(NH₄)₂(SO₄)₂·6H₂O exhibits paramagnetic behavior across 2–300 K. The maximum magnetic entropy change (−ΔS_M) of 13.90 J kg⁻¹ K⁻¹ under conditions of 2 K and μ₀ΔH = 5 T approaches the theoretical value of 14.58 J kg⁻¹ K⁻¹. In addition, the variation of −ΔS_M with temperature is relatively flat, suggesting a wide working temperature range for magnetic refrigeration, which provides the possibility for the application of Co²⁺-based compounds in the field of low-temperature magnetic refrigeration.

1. Introduction

Cryogenic environments play a pivotal role in achieving breakthroughs in quantum computing, superconductivity, and spaceborne detector systems through precise control of low-temperature states [1,2,3]. The predominant technologies include adsorption refrigeration, dilution refrigeration, and adiabatic demagnetization refrigeration (ADR) [4]. Among these, the first two technologies require the expensive and scarce isotope helium-3 (³He). Comparatively, ADR based on magnetocaloric effect (MCE) has attracted increasing attention due to its low cost, high efficiency, and ability to operate independently of gravity without the need for scarce ³He [5], which has become an important approach for achieving ultra-low temperatures [6].

To achieve efficient cooling in sub-Kelvin temperature ranges, magnetic refrigerants, as the key material of ADR, must exhibit a large magnetic entropy change (−ΔS_M) and a sufficiently low magnetic ordering temperature [7]. Paramagnetic compounds are particularly suitable for such applications due to their large magnetic moments and intrinsically low ordering temperatures [1,2]. Currently, anhydrous paramagnetic salts, such as GGG(Gd₃Ga₅O₁₂) and GLF(GdLiF₄), are frequently employed as magnetic refrigerants near 4 K because of their high magnetic moment density [8]. Hydrated paramagnetic salts, such as CPA (KCr(SO₄)₂·12H₂O) and FAA (NH₄Fe(SO₄)₂·12H₂O), exhibit lower magnetic ordering temperatures due to the presence of water molecules in their crystal lattice. These hydrated salts are often used in the final stage of the ADR system to achieve extremely low temperatures of 10 mK and 30 mK, respectively [9,10].

Another representative compound, Mn(NH₄)₂(SO₄)₂·6H₂O (MAS), has garnered attention as a low-temperature magnetic refrigerant because of its substantial theoretical entropy change, reaching Rln(6) [11]. However, the phase transition temperature of MAS (175 mK) [12] is considerably higher than those of CPA (10 mK) [9] and FAA (30 mK) [10], which prevents it from achieving lower temperatures. In recent years, Co²⁺-based compounds have been regarded as promising candidates for low-temperature magnetic refrigeration. For example, the maximum magnetic entropy change (−ΔS_M) of La₂Co₃(NO₃)₁₂·24H₂O (LCoN) reaches 9.45 J·kg⁻¹·K⁻¹ at 4 K and μ₀ΔH = 7T. This compound exhibits weak antiferromagnetic interactions and a low magnetic ordering temperature [13]. Other Co²⁺-containing compounds, such as CoCl₂ [14] and CoSO₄·7H₂O [15], have also demonstrated MCE performance. If Mn²⁺ ions in MAS are substituted by Co²⁺ ions, potential refrigerants with improved performance may be obtained. This motivates further exploration of hydrated Co²⁺-based paramagnetic salts as magnetic refrigerants. In this work, Co(NH₄)₂(SO₄)₂·6H₂O crystal was grown and its magnetocaloric properties were investigated.

2. Experiment

2.1. Crystal Growth

Co(NH₄)₂(SO₄)₂·6H₂O single crystal was obtained through slow evaporation. A total of 7.56 g (30 mmol) Co(NO₃)₂·6H₂O and 7.93 g (60 mmol) (NH₄)₂SO₄ with purity of 99.9% were weighed and dissolved in a clean 250 mL glass beaker using 150 mL deionized water to prepare a 0.2 mol/L solution. The solution was stirred at a constant temperature of 60 °C in a water bath for 1 h to ensure complete reaction, resulting in a purple–red, clear, and transparent solution. The beaker was placed on an evaporating dish to allow for slow evaporation of the solvent at room temperature, leading to the formation of abundant crystals. The small and well-shaped single crystals without visible defects were selected as seed crystals. The seed crystal was placed at the bottom of a clean 150 mL glass beaker containing the above solution. The beaker was then sealed with a layer of parafilm, and approximately 20 evenly distributed small holes were pierced in the parafilm using a needle with a diameter of 1 mm. The solvent was allowed to evaporate slowly at room temperature, ultimately yielding a large size (20 × 15 × 9.5 mm³) single crystal, as shown in Figure 1.

2.2. Characterization

The powder X-ray diffraction analysis of the single crystal was performed at room temperature using a Bruker D8 X-ray diffractometer equipped with Cu Kα radiation (λ = 1.5418 Å) over the range 10° ≤ 2θ ≤ 70°. The step size and scan rate were 0.02° and 0.1 °/step, respectively.

A transparent single crystal was selected and ground into a 14.24 mg powder sample for magnetic measurements. A superconducting quantum interference device (SQUID) magnetometer was employed to perform zero-field cooling (ZFC), field cooling (FC), and isothermal magnetization (M(μ₀H)) measurements. The M(T) curves were measured at a sweep rate of 1 K/min in the temperature range 2–300 K, while the M(μ₀H) curves were recorded from 0 to 9 T in the temperature range 2–10 K.

3. Results and Discussion

3.1. Crystal Structure

Figure 2a shows the experimental and calculated XRD patterns of Co(NH₄)₂(SO₄)₂·6H₂O crystal. The experimental results are in good agreement with the reference pattern (ICSD No. 14347). Co(NH₄)₂(SO₄)₂·6H₂O crystallizes in the monoclinic space group P2₁/c. Rietveld refinement of the powder XRD data was performed using the GSAS-II software version 5.4.6, and the relevant parameters are listed in

Table 1. Crystallographic data of Co(NH₄)₂(SO₄)₂·6H₂O obtained by powder diffraction, where Z is the number of chemical formulas in a unit cell, ${\rho }_{calc}$ is the density, and R is the residual factor.

Empirical Formula	CoH20N2O14S2
Formula weight (g mol−1)	395.21
Temperature (K)	296.15
Crystal system	Monoclinic
Space group	P21/c
a (Å)	6.2437 (49)
b (Å)	12.5259 (44)
c (Å)	9.2560 (95)
α (°)	90
β (°)	73
γ (°)	90
Volume (Å3)	692.1 (73)
Z	2
${\rho }_{calc}$ (g cm−3)	1.876
Radiation	Cu Kα (λ = 1.5418 Å)
2θ range for data collection (°)	10–70
Final R indexes (all data)	R1 = 0.0288, wR2 = 0.0369

. The compound shares the same structure as Mn(NH₄)₂(SO₄)₂·6H₂O (MAS), belonging to the Tutton salt family with the general formula [M^I₂M^II(SO₄)₂·6H₂O]. In its structure, Co²⁺ and NH₄⁺ ions occupy distinct lattice sites and are linked to sulfate groups and water molecules through ionic and hydrogen bonding. Each Co²⁺ ion is surrounded by six H₂O molecules to form [Co(H₂O)₆]²⁺ octahedra, while NH₄⁺ groups share oxygen atoms with sulfate tetrahedra, providing interlayer connections. Within the unit cell, SO₄²⁻ anions form a three-dimensional hydrogen-bond network with Co²⁺ ions and water molecules through oxygen atoms [16,17]. The distance between magnetic Co²⁺ ions is 6.23 Å, which is shorter than that of Mn²⁺ ions (6.26 Å) in MAS.

Structurally, Co(NH₄)₂(SO₄)₂·6H₂O is isomorphous with other M²⁺ Tutton salts (M = Mn, Fe, Ni, and Cu), all crystallizing in the monoclinic P2₁/c (or equivalent P2₁/a) symmetry with similar hydrogen-bonding frameworks [18]. The thermal decomposition and dehydration behavior of this class of salts, including the cobalt analogue, have been investigated previously by thermogravimetric analysis [19,20]. Figure 2b illustrates the structure of Co(NH₄)₂(SO₄)₂·6H₂O.

3.2. Magnetic Measurements

The temperature-dependent magnetic susceptibility (χ) of Co(NH₄)₂(SO₄)₂·6H₂O was measured under zero-field-cooled (ZFC) and field-cooled (FC) protocols in the range of 2–300 K with an external field of μ₀H = 1 T, as shown in Figure 3a. The complete overlap of the ZFC and FC curves demonstrates negligible thermal hysteresis, and no clear signatures of magnetic phase transitions are detected within this temperature interval, confirming the paramagnetic nature of the compound. To further elucidate the magnetic ground state, the inverse susceptibility χ⁻¹(T) was analyzed according to the Curie–Weiss law,

$${\chi }^{-1}=(T-{\theta }_P)/C$$

where C is the Curie constant, and ${\theta }_P$ is the Curie–Weiss temperature. The effective magnetic moment was derived from the fitted Curie constant using the following:

$${\mu }_{eff}=\sqrt{{\displaystyle \frac{3k_{B}C}{N_A{\mu }_B^2}}}=\sqrt{8C}$$

with C in emu·K·mol⁻¹ and ${\mu }_{eff}$ in Bohr magnetons (${\mu }_B$). A linear fit in the low-temperature region (2–10 K), shown in Figure 3b, yields a Curie–Weiss temperature of ${\theta }_P$ = −0.60 K, indicative of weak antiferromagnetic interactions. The Curie constant obtained from the fit is C = 2.03 emu·K·mol⁻¹, from which the effective magnetic moment is calculated as ${\mu }_{eff}=4.03{\mu }_B$. This value slightly exceeds the theoretical spin-only moment of 3.87 ${\mu }_B$ expected for a high-spin Co²⁺ ion with a $3d^7$ electronic configuration (n = 3 unpaired electrons, $S=3/2$). Such an enhancement is commonly attributed to the residual orbital angular momentum that is only partially quenched by the octahedral crystal field. Similar behavior has been observed in other Co²⁺ systems, where ${\mu }_{eff}$ values exceed the spin-only prediction due to unquenched orbital contributions and spin–orbit coupling effects [21].

The dashed line in Figure 4a represents the theoretical M(H) curve at 2.0 K, calculated using the Brillouin function. At this temperature, the saturation magnetic moment of Co(NH₄)₂(SO₄)₂·6H₂O is 2.23μ_B per Co²⁺ ion, corresponding to 74.3% of the theoretical value of 3 μ_B expected for a system of non-interacting Co²⁺ ions with J = 3/2 and g = 2. The reduction relative to the ideal paramagnetic value can be ascribed either to the presence of a small fraction of non-magnetic impurities or to net antiferromagnetic interactions among Co²⁺ ions. Figure 4b shows the isothermal magnetization curves M(H) recorded between 2 and 10 K under applied fields up to 9 T. At 2.0 K, the magnetization increases continuously and approaches saturation at around 4 T, suggesting the existence of weak magnetic coupling in the system. With an increasing temperature above 8.5 K, the M(H) curves become nearly linear, reflecting that thermal fluctuations dominate and the applied field is insufficient to fully align the magnetic moments [22].

The magnetocaloric effect (MCE) of Co(NH₄)₂(SO₄)₂·6H₂O is characterized by the magnetic entropy change (−ΔS_M), calculated from isothermal magnetization curves using the Maxwell equation.

$$-\Delta S_M(T,{\mu }_0\Delta H)={\mu }_0{\int }_{0T}^{{\mu }_0{H}_{max}}{\left[{\displaystyle \frac{\partial M\left(T,{\mu }_0{H}^{’}\right)}{\partial T}}\right]}_{ {\mu }_0{H}^{’}}d{H}^{’}$$

Figure 5 presents the −ΔS_M −T curves for selected ΔH values. As the temperature decreases, −ΔS_M gradually increases, reaching a maximum value of −ΔS_M = 13.90 J kg⁻¹ K⁻¹ at T = 2 K and μ₀ΔH = 5 T. For paramagnetic systems containing Co²⁺ ions, the theoretical maximum entropy change ($∆S_M^{Max}$) can be determined by the formula:

$$∆S_M^{Max}=S_J=N{k}_B\ln \left(2J+1\right)=nRln(2J+1)$$

where $n$ is the number of magnetic ions, $R$ is the gas constant, and $J$ is the angular momentum quantum number. For Co(NH₄)₂(SO₄)₂·6H₂O, the theoretical upper limit is 14.58 J kg⁻¹ K⁻¹, and the experimental −ΔS_M value achieves 95% of this theoretical maximum. The discrepancy between the experimental and theoretical values may be attributed to the presence of AFM coupling. Furthermore, Figure 5 indicates that the −ΔS_M value shows relatively small variation with temperature under a fixed magnetic field, suggesting that the magnetic refrigeration system based on Co²⁺ ions has abroad operational temperature ranges. From

Table 2. Comparison of the relevant parameters for Co(NH₄)₂(SO₄)₂·6H₂O with the abovementioned hydrated salts, where T_t is the temperature at which the maximum magnetic entropy change is achieved during the experimental process, and $∆S_M^{Max}$ is the maximum magnetic entropy change. Data compiled from Refs. [12,13,14].

Materials	Tt (K)	μ0H	$∆{\mathit{S}}_{\mathit{M}}^{\mathit{M}\mathit{a}\mathit{x}}\left({\mathbf{J} \mathbf{k}\mathbf{g}}^{-1}{\mathbf{K}}^{-1}\right)$	Ref.
CoCl2	27.0	7	11.5	[14]
LCoN	4.0	7	9.45	[13]
CMN	1.8	—	7.5	[23]
CoSO4·7H2O	1.2	10	11.5	[16]
MAS	0.2	—	38.1	[12]
Co(NH4)2(SO4)2·6H2O	2.0	5	13.9	This work

, the maximum magnetic entropy change of Co(NH₄)₂(SO₄)₂·6H₂O is higher than that of CoCl₂, CoSO₄·7H₂O, and LCoN, exhibiting potential application prospect.

Belov–Arrott plots and the field exponent n are widely employed to determine the order of magnetic phase transitions. Figure 6a presents the Belov–Arrott curves obtained from the M²-H/M relations in the temperature range of 2–10 K. None of the curves intersect the origin, indicating that the critical temperature lies outside the investigated window, and, thus, no phase transition occurs within the measured range. According to Banerjee’s criterion [24], all the curves exhibit positive slopes, suggesting that if a transition occurs at lower or higher temperatures, it should be of second-order character. In addition, Law [25] proposed another method to determine the type of magnetic phase transition, which is to calculate the field exponent n to determine the order of the magnetic phase transition. Figure 6b illustrates the distribution of the exponent n in the temperature range of 2–9 K. The magnetic entropy change (ΔS_M) as a function of the applied magnetic field (H) can be described by a power-law relation:

$$∆S_M\propto H^n$$

where the exponent n is a parameter that depends on both temperature and magnetic field. Its calculation formula is given by the following:

$$n(T, H) ={\displaystyle \frac{\mathrm{d} \ln |\Delta S_M|}{\mathrm{d} \ln H}}$$

Previous studies have demonstrated that the temperature dependence of n provides a quantitative criterion for identifying the type of magnetic phase transition. For a second-order phase transition (SOPT), n approaches one well below the Curie temperature and tends toward two well above it. As shown in Figure 6b, the maximum value of n remains below two across the entire investigated temperature range, and no overshoot beyond this threshold is observed. This behavior is consistent with the scenario expected for a second-order transition, suggesting that although no critical point is reached within the measured 2–9 K window, the eventual transition of Co(NH₄)₂(SO₄)₂·6H₂O should be of second-order character. Compared with FOPT materials, SOPT materials generally exhibit smaller thermal hysteresis, which enhances the stability of the refrigeration cycle and allows for a broader operating-temperature range [26].

4. Conclusions

In summary, a Co(NH₄)₂(SO₄)₂·6H₂O single crystal with the size of 20 × 15 × 9.5 mm³ was successfully grown by the slow evaporation method at room temperature. Magnetic susceptibility measurements revealed that Co(NH₄)₂(SO₄)₂·6H₂O exhibits paramagnetic behavior within the measured temperature range, and the fitted Curie–Weiss temperature was ${\theta }_P$ = −0.60 K, indicating weak antiferromagnetic (AFM) interactions among the magnetic ions in this compound at low temperatures. The maximum magnetic entropy change was 13.90 J kg⁻¹ K⁻¹ at 2 K and 5 T, which is close to the theoretical prediction of 14.58 J kg⁻¹ K⁻¹ and exceeds those reported for CMN and LCoN under similar conditions. Additionally, the smooth temperature dependence of −ΔS_M suggests a broad operational temperature window for magnetic refrigeration, thereby enhancing its application potential. This work indicates that the Co²⁺-based compounds may be promising candidates for low-temperature magnetic refrigeration.