⇦Chinese Physics Letters, 2023, Vol. 40, No. 12, Article code 127501 Highly Anisotropic Magnetism and Nearly Isotropic Magnetocaloric Effect in Mn$_{3}$Sn$_{2}$ Single Crystals Jianli Bai1,2, Qingxin Dong1,2, Libo Zhang1,2, Qiaoyu Liu1,2, Jingwen Cheng1,2, Pinyu Liu1,2, Cundong Li1,2, Yingrui Sun1,2, Yu Huang1,2, Zhian Ren1,2, and Genfu Chen1,2,3* Affiliations 1Institute of Physics and Beijing National Laboratory for Condensed Matter Physics, Chinese Academy of Sciences, Beijing 100190, China 2School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China 3Songshan Lake Materials Laboratory, Dongguan 523808, China Received 8 October 2023; accepted manuscript online 21 November 2023; published online 20 December 2023 *Corresponding author. Email: gfchen@iphy.ac.cn Citation Text: Bai J, Dong Q, Zhang L et al. 2023 Chin. Phys. Lett. 40 127501    Abstract Mn$_{3}$Sn$_{2}$ has been proposed as an ideal material for magnetic refrigeration. It undergoes two successive ferromagnetic transitions ($T_{\rm C1} = 262$ K and $T_{\rm C2} = 227$ K) and one antiferromagnetic transition ($T_{\rm N} = 192$ K). Herein we report, for the first time, the preparation of single crystals of Mn$_{3}$Sn$_{2}$ from Bi flux. The resultant anisotropic magnetic properties and magnetocaloric effect are investigated along the three principal crystallographic directions of the crystal. Significant anisotropy of magnetic susceptibility and multiple field-induced metamagnetic transitions were found at low fields, whereas the magnetocaloric effect was found to be almost isotropic and larger than that of the polycrystalline one. The maximum magnetic entropy change amounts to $-\Delta S_{\rm M} = 4.01$ J$\cdot$kg$^{-1}\cdot$K$^{-1}$ near $T_{\rm C1}$ under a magnetic field change of $\mu_{0}\Delta H = 5$ T along the $c$-axis, with the corresponding refrigerant capacity of 1750 mJ$\cdot$cm$^{-3}$. Combined with a much wider cooling temperature span ($\sim$ $80$ K), our results demonstrate Mn$_{3}$Sn$_{2}$ single crystal to be an attractive candidate working material for active magnetic refrigeration at low temperatures.
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 DOI:10.1088/0256-307X/40/12/127501 © 2023 Chinese Physics Society Article Text The magnetocaloric effect (MCE) and its most straightforward application, magnetic refrigeration, have sparked intense research interest due to the potential improvement in energy efficiency of cooling and temperature control systems in combination with other environmental benefits associated with a technology that does not rely on the compression/expansion of harmful gases.[1-3] Good magnetocaloric materials are usually characterized by large values of isothermal magnetic entropy change $-\Delta S_{\rm M}$ and adiabatic temperature change $\Delta T_{\rm ad}$ when subjected to a change in the external magnetic field.[1] In practice, MCE in paramagnetic materials has been widely used to achieve very low temperatures, while magnetic refrigerant materials are commonly used to operate at a higher temperature. Magnetocaloric refrigeration near room temperature (RT) has the widest application prospects. The heavy lanthanide metals and their compounds are always considered to be the best potential magnetocaloric materials because they have the largest available magnetic entropy resulting from the largest magnetic moment. Pure Gd in particular is still one of the best magnetocaloric materials and is regarded as the reference material for near RT applications because of its large $-\Delta S_{\rm M}$ ($\sim$ $80$ mJ$\cdot$cm$^{-3}\cdot$K$^{-1}$ for $\Delta H = 5$ T).[4,5] Actually, it has been shown that there are no clear advantages of a giant MCE material replacing Gd or Gd-based solid solution alloys.[3] However, the high price of rare earth metals makes it difficult for related materials to be widely adopted. Therefore, related research is turning to the $3d$ transition metals, especially Mn, Fe, and Co. For instance, intermetallic compounds Mn(As$_{1- x}$P$_{x}$),[6] Mn(As$_{1- x}$Sb$_{x}$),[7] and Heusler alloys Ni$_{2}$MnGa[8,9] also show a giant MCE. However, the intermetallic Mn-based refrigerants containing As and/or P both have high vapor pressures and are not environmentally friendly. Thermal hysteresis may be a potential problem for magnetic refrigeration because the first-order magnetic/structural transition will lead to a significant reduction in the efficiency of energy conversion during the magnetic refrigeration cycle. Additionally, these huge effects are usually restricted to narrow temperature intervals of 5–15 K and are not suitable for practical applications.[10] Although hybrid materials involving multiphases with different transition temperatures offer the possibility of solving this problem, they also pose greater difficulties in terms of preparation processes and technological design.[11,12] The best scenario for material selection is to use a single material whose profile closely matches the ideal curve.[13] Unfortunately, there are still no low-priced magnetocaloric materials with good properties that can be widely used near RT. Mn$_{3}$Sn$_{2}$ of the Ni$_{3}$Sn$_{2}$ type (space group Pnma) has been proposed as an ideal material for magnetic refrigeration near RT,[14,15] and there have been numerous studies on the effect of doping on the MCE.[16,17] However, all these studies are based on polycrystalline samples, probably because Mn$_{3}$Sn$_{2}$ is only formed below 480 ℃.[18,19] Nevertheless, for magnetocaloric materials, investigations on single crystals have greater theoretical and practical significance: they not only provide a new insight into the magnetic structure and reveal more physical details than polycrystalline samples,[20] but also avoid grain boundary effects and structural and stoichiometric inhomogeneity found frequently in polycrystals.[14,21] Additionally, the single-crystal approach enables us to explore the strength of the MCE anisotropy. As an important part of the study of the MCE, MCE anisotropy can facilitate finding new, constructive solutions for developing magnetic refrigerators.[22] In the presence of obvious magnetocrystalline anisotropy, a larger MCE in a single crystal for specific crystallographic directions than in polycrystals can be obtained. For example, compared with polycrystals, $-\Delta S_{\rm M}$ of single crystals can be improved by about 17% in Cr$_{5}$Te$_{8}$,[23] 40% in ErGa$_{2}$,[24] 46% in ErMnO$_{3}$,[25] 50% in MnFe$_{4}$Si$_{3}$,[20] and 70% in HoMn$_{2}$O$_{5}$.[26] As a result of the significant anisotropic MCE, magnetic entropy change can even reach a large value by just rotating the magnetization vector in specific crystallographic surfaces. This is known as the rotating MCE and has received a lot of attention.[25-30] For instance, a large rotating MCE ($-\Delta S_{R, {\max}} = 12.43$ J$\cdot$kg$^{-1}\cdot$K$^{-1}$ for 7 T) can be obtained simply by rotating the single crystal HoMn$_{2}$O$_{5}$ within the $cb$ plane in a constant magnetic field.[26] However, the working temperature of most materials with a giant rotating MCE is limited to low temperatures due to low $T_{\rm C}$ values. Inspired by powder neutron diffraction and $^{119}$Sn Mössbauer spectroscopy experiments that illustrated a high $T_{\rm C}$, complex magnetic arrangements and striking anisotropy among different crystallographic directions in Mn$_{3}$Sn$_{2}$,[31] and with the aim of gaining more insight into its real potential in magnetic cooling, in this work, we have synthesized single crystals of Mn$_{3}$Sn$_{2}$ for the first time and report on the anisotropic magnetic and magnetocaloric properties of Mn$_{3}$Sn$_{2}$ single crystals for magnetic fields applied along the $a$, $b$, and $c$ axes, respectively. We have found that the susceptibility and magnetization exhibit significant anisotropy at low fields, but the MCE is essentially isotropic. A larger magnetic moment and the corresponding MCE better than those reported for polycrystals have been also observed. Experimental Methods. Single crystals of Mn$_{3}$Sn$_{2}$ were grown in Bi flux. High-purity Mn (99.95%) powder, a Sn (99.999%) ingot and Bi (99.999%) shots were used as reagents. A mixture of the starting material was put into an alumina crucible with a molar ratio of Mn : Sn : Bi = $6\!:\!5\!:\!35$ and sealed in an evacuated quartz tube. The quartz tube was slowly heated to 550 ℃, held for 20 h, and then slowly cooled to 400 ℃ at a rate of 1 ℃/h. At this temperature the flux was removed by centrifugation. Finally, the residual Bi flux was etched away from the crystalline facets in diluted HNO$_{3}$. The obtained single crystals were in the form of strips with a length of about 2 mm, as shown in Fig. 1(d).
cpl-40-12-127501-fig1.png
Fig. 1. (a) The single-crystal energy-dispersive x-ray (EDX) pattern of a Mn$_{3}$Sn$_{2}$ sample at room temperature. Inset: enlarged view of the (600) Bragg peak. (b) The crystal structure of Mn$_{3}$Sn$_{2}$ at room temperature. Yellow and red spheres represent Sn and Mn atoms, respectively. (c) EDX spectroscopy of Mn$_{3}$Sn$_{2}$. (d) Optical image of as-grown single crystals on a millimeter grid. AC: atomic concentration, WC: weight concentration.
The chemical composition was analyzed by an EDX spectrometer equipped on a Phenom scanning electron microscope operated at 15 kV. The EDX analysis yielded the atom molar ratio Mn : Sn = $59.5\!:\!40.5$, consistent with the formula Mn$_{3}$Sn$_{2}$. No foreign elements were detected within the limitation of instrumental resolution, as shown in Fig. 1(c). Structural parameters were refined at 273 K by single-crystal x-ray diffraction (XRD). Magnetic properties were characterized by a Quantum Design vibrating sample magnetometer. Results and Discussion. Figure 1(b) shows the crystal structure of Mn$_{3}$Sn$_{2}$ which crystallizes in an orthorhombic structure with space group Pnma (No. 62). The structure of Mn$_{3}$Sn$_{2}$ was solved by a direct method and refined by full matrix least-squares based on F2 using a SHELXTL program package. The refinement results are shown in Table 1. The lattice parameters at room temperature are $a = 7.5605$ Å, $b = 5.4946$ Å, and $c = 8.5890$ Å, in good agreement with those reported in Ref. [18]. The low values of $R1$ (0.0388) and $wR2$ (0.0913) under $I > 2\sigma (I)$ indicate a good structural solution. Figure 1(a) presents the single-crystal XRD pattern. All the peaks can be identified as ($h$00) reflections. The sharp Bragg peaks and better resolved $K_{\alpha 1}$ and $K_{\alpha 2}$ diffraction peak splitting indicate the high quality of the single crystal.
Table 1. Crystal data and structure refinement for Mn$_{3}$Sn$_{2}$.
Parameters Data
Chemical formula Mn$_{3}$Sn$_{2}$
Formula weight 402.24 g$\cdot$mol$^{-1}$
Temperature 273(2) K
Wavelength (Mo $K_{\alpha}$) 0.71073 Å
Crystal system Orthorhombic
Space group Pnma
Unit cell dimensions $a = 7.5605$(14) Å
$b = 5.4946$(11) Å
$c = 8.5890$(17) Å
$\alpha = 90^{\circ}$
$\beta = 90^{\circ}$
$\gamma = 90^{\circ}$
Volume 356.80(12) Å$^{3}$
$Z$ 4
Density (calculated) 7.487 g$\cdot$cm$^{-3}$
Absorption coefficient 23.856 mm$^{-1}$
$F$ (000) 700
$\varTheta$ range for data collection 3.59–28.54$^{\circ}$
Index ranges $-10 \le h \le 9$, $-7 \le k \le 7$, $-10 \le l \le 11$
Reflections collected 3064
Independent reflections 496 ($R_{\rm int} = 0.0538$)
Coverage of independent reflections 99.0%
Absorption correction Multi-scan
Structure solution technique Direct methods
Refinement method Full-matrix least-squares on $F^{2}$
Function minimized $\sum w(F_{0}^{2} - F_{\rm c}^{2})^{2}$
Data/restraints/parameters 496/0/28
Goodness-of-fit on $F^{2}$ 1.321
Final $R$ indices [$I > 2\sigma (I)$] $R1 = 0.0388$
$wR2 = 0.0904$
$R$ indices (all data)$^{\rm a}$ $R1 = 0.0400$
$wR2 = 0.0913$
Largest diff. peak and hole 2.707 and $-$4.395 $e$Å$^{-3}$
RMS deviation from mean 1.042 $e$Å$^{-3}$
$^{\rm a}$ $R=\sum||F_0|-|F_{\rm c}||\Big/\sum|F_0|$, $wR=\Big\{\sum\big[w(|F_0|^2-|F_{\rm c}|^2)^2\big]\Big/\sum\big[w(|F_0|^4)\big]\Big\}^{1/2}$,
$~~~w = 1/[\sigma^{2}(F_{0}^{2}) + (0.0444P)^{2} + 1.9544P]$, with $P = (F_{0}^{2} + 2F_{\rm c}^{2})/3$.
In order to explore the magnetism of Mn$_{3}$Sn$_{2}$, we first performed anisotropic temperature-dependent magnetization measurements with selected magnetic fields parallel to the $a$, $b$, and $c$ axes using zero-field-cooled mode, as shown in Figs. 2(a)–2(c). For different directions, three magnetic transitions arise, two of which are ferromagnetic (FM) with transition temperatures $T_{\rm C1} = 262$ K and $T_{\rm C2} = 227$ K, and one (the left one) is antiferromagnetic (AFM) with transition temperature $T_{\rm N} = 192$ K. All are in good agreement with the previously reported data.[14,15] There is significant anisotropy among $M_{a}(T)$, $M_{b}(T)$ and $M_{c}(T)$ at low fields; specifically, the AFM transition is more pronounced in $M_{b}(T)$ while the second FM transition at 227 K is more obvious in $M_{a}(T)$ and $M_{c}(T)$. Interestingly, they are essentially the same at higher magnetic fields, indicating that the magnetic moment is easily saturated. Then, we performed isothermal magnetization measurements for three directions from 2 K to 300 K. All show the overall soft FM characteristics which guarantee an almost reversible MCE, and the differences are mainly found in the low-field range, as shown in Figs. 2(d)–2(f). The full saturation moment $M_{\rm S}$ attained in small magnetic fields ($\mu_{0}H < 1$ T) increases with decreasing temperature, well consistent with the temperature dependence of the $M(T)$ curve at $\mu_{0}H = 1$ T. Unlike typical FM polarization, when $H$ is parallel to the $b$-axis with $\mu_{0}H < 0.6$ T and $T < T_{\rm N}$, two sharp metamagnetic transitions occur at $\mu_{0}H_{1}$ and $\mu_{0}H_{2}$, both of which gradually decrease with increasing temperature and finally disappear [see the insets of Fig. 2(e)]. This is due to the polarization of the two different arrangements of spins to the $b$-axis induced by the external fields.[28,31] When $H$ is parallel to the $a$-axis with $\mu_{0}H < 0.8$ T and $T < T_{\rm N}$ or to the $c$-axis with $\mu_{0}H < 0.1$ T and $T_{N } < T < T_{\rm C2}$, similar weak metamagnetic transitions also exist. We note that none of these low-field transitions were observed in polycrystals.[14] We also note that at temperatures between $T_{\rm N}$ and $T_{\rm C1}$, the magnetic moment saturates much more quickly with $H//b$ consistent with the $M$–$T$ curves, indicating that the $b$-axis is the easy magnetization axis, which is consistent with the results of neutron diffraction.[31] The average magnetic moments of each Mn atom at 2 K are approximately 2.00 $\mu_{\scriptscriptstyle{\rm B}}$ (where $\mu_{\scriptscriptstyle{\rm B}}$ is the Bohr magneton), 1.93 $\mu_{\scriptscriptstyle{\rm B}}$ and 2.04 $\mu_{\scriptscriptstyle{\rm B}}$ for $a$, $b$, and $c$ directions, respectively. The effective magnetic moment of a single crystal in this work is larger than that of a polycrystal (1.8 $\mu_{\scriptscriptstyle{\rm B}}$) from reported data, probably due to the presence of heterogeneous phases in the polycrystal.[14]
cpl-40-12-127501-fig2.png
Fig. 2. Magnetization $M(T)$ and $M(\mu_{0}H)$ of Mn$_{3}$Sn$_{2}$. (a)–(c) Temperature-dependent zero-field-cooled magnetization $M(T)$ at various magnetic fields with $\mu_{0}H$ parallel to the $a$, $b$, and $c$ axes, respectively. Insets of (a) and (c) show $M(T)$ under 0.01 T. (d)–(f) Isothermal magnetization $M(\mu_{0}H)$ measured for $\mu_{0}H$ parallel to the $a$, $b$, and $c$ axes, respectively, in the temperature range 2–320 K. The vertical coordinates represent the total magnetic moment of each chemical formula (Mn$_{3}$Sn$_{2}$). Insets present $M(\mu_{0}H)$ at low fields under several selected temperatures.
To explore the MCE of Mn$_{3}$Sn$_{2}$ single crystal, we measured the magnetization curves in the temperature range 100–320 K (with steps of 3 K for 220–235 K and 265–270 K, and steps of 5 K for other ranges). Then the isobaric–isothermal magnetic entropy change $\Delta S_{\rm M}$ induced by a field change can be calculated from the Maxwell relation[32] \begin{align*} \Delta S_{\rm M} (T,\,H)=\mu_{0} \int_0^H {\Big(\frac{\partial S}{\partial H}\Big)_{T} dH=} \mu_{0} \int_0^H {\Big(\frac{\partial M}{\partial T}\Big)_{H} dH}. \end{align*} As shown in Figs. 3(a)–3(c), $-\Delta S_{\rm M}$ of Mn$_{3}$Sn$_{2}$ is characterized by two peaks of similar magnitude centered around $T_{\rm C1}$ and $T_{\rm C2}$ for all three directions, while no anomaly is visible at $T_{\rm N}$ as reported.[14] As anticipated from the weak magnetic anisotropy of Mn$_{3}$Sn$_{2}$ in high fields, $\Delta S_{\rm M}$ is weakly anisotropic, too. For $H//c$, $-\Delta S_{\rm M}$ reaches maxima of 4.01 J$\cdot$kg$^{-1}\cdot$K$^{-1}$ and 5.2 J$\cdot$kg$^{-1}\cdot$K$^{-1}$ near $T_{\rm C1}$ for field changes of $\Delta H=5$ and 7 T, respectively. By contrast, the corresponding values of $-\Delta S_{\rm M}$ are 3.96 J$\cdot$kg$^{-1}\cdot$K$^{-1}$ and 4.99 J$\cdot$kg$^{-1}\cdot$K$^{-1}$ for $H//a$, and 3.85 J$\cdot$ kg$^{-1}\cdot$K$^{-1}$ and 4.8 J$\cdot$kg$^{-1}\cdot$K$^{-1}$ for $H//b$, which are just slightly smaller. It is worth noting that these values are about 10% larger than that for a polycrystal (3.6 J$\cdot$kg$^{-1}\cdot$K$^{-1}$ for $\Delta H=5$ T) from the data reported in Refs. [14,15] and consistent with the larger magnetic moment mentioned above. $\Delta S_{\rm M}$ of Mn$_{3}$Sn$_{2}$ is about one third of that of the best magnetic refrigerants near RT, such as Gd and Gd$_{5}$Si$_{4- x}$Ge$_{x}$ families,[2] which makes it a potential magnetocaloric material. In addition to $\Delta S_{\rm M}$, another important parameter to characterize the MCE is the magnetocaloric refrigerant capacity (RC), which means the numerical integration of the area under the $-\Delta S_{\rm M}$ curve between $T_{1}$ and $T_{2}$, i.e.,[2] \begin{align*} q=-\int_{T_{1} }^{T_{2} } {\Delta S_{\rm M} (T)dT}, \end{align*} where $T_{1}$ and $T_{2}$ refer to the temperatures at the half-height width of the peaks [see Fig. 3(d)]. The value of RC provides an estimate of the amount of heat that can be transferred between the cold and hot reservoirs. As shown in Fig. 3(d), the differences in RC among the three directions are not significant and increase essentially linearly with increasing magnetic field. Obviously, the existence of two consecutive FM transitions in Mn$_{3}$Sn$_{2}$ makes its cooling temperature region ($\Delta T_{\rm cooling}$) much wider than common materials with a single magnetic phase transition. Thus a large range of cooling is expected on single-phase Mn$_{3}$Sn$_{2}$ rather than using a combination of materials with different transition temperatures, which is desired for the Ericsson cycle applied to high-temperature magnetic refrigeration. In the meantime, its magnetocaloric refrigerant capacity RC is thus greatly increased: for $\mu_{0}\Delta H = 5$ T, RC ($\approx 1750$ mJ$\cdot$cm$^{-3}$) is just over a half of that of Gd ($\sim$ $3160$ mJ$\cdot$cm$^{-3}$).[2] Actually, RC and $\Delta T_{\rm cooling}$ are more relevant parameters when evaluating the technological interest of a refrigerant material. When compared with typical second-order phase transition (SOPT) magnetocaloric materials with a Curie temperature $T_{\rm C}$ between 210 K and 300 K, Mn$_{3}$Sn$_{2}$ exhibits a large $\Delta S_{\rm M}$ and excellent refrigerant capacity, as shown in Fig. 3(e). To our knowledge, it is also the best SOPT Mn-based magnetocaloric material in this temperature region.
cpl-40-12-127501-fig3.png
Fig. 3. MCE of Mn$_{3}$Sn$_{2}$. (a)–(c) Magnetic entropy change $-\Delta S_{\rm M}$ calculated for $\mu_{0}H$ parallel to the $a$, $b$, and $c$ axes, respectively, in the temperature range 100–320 K. (d) Magnetocaloric refrigerant capacity as a function of $\mu_{0}H$ for different directions. (e) $|\Delta S_{\rm M}|$ and refrigerant capacity RC$_{\rm FWHM}$ [defined as $|\Delta S_{\rm M}|_{{\max} }\times$ ($T_{2} - T_{1}$)] for different SOPT magnetocaloric materials.[1,14]
Actually, Mn$_{3}$Sn$_{2}$ has great potential for applications in low and ultra-low temperature refrigeration (usually $-$80 ℃ to $-$10 ℃), which is important for biomedical technology research, drugs, food, and medical supply storage. For instance, the recommended storage temperature for high-quality long-term storage of fish is $-$35 ℃,[33] most complex compounds for biomedical research need to be stored in refrigerators at $\sim$ $-20$  ℃ or below.[34] Even though a lot of effort has been made to achieve efficient cooling to $-$60 ℃ and even $-$80 ℃, the results are still unsatisfactory as the traditional compression/expansion of gases is still the main method of cooling.[35-39] Furthermore, it is possible to adjust the initial cooling temperature region ($\sim$ $203$–283 K) to a higher or lower one by doping to meet additional needs.[16,17] The excellent magnetocaloric properties of Mn$_{3}$Sn$_{2}$, in addition to the very low material cost, make it an attractive candidate material for commercial magnetic refrigeration. In summary, we have reported on the anisotropic magnetism and large nearly isotropic MCE in Mn$_{3}$Sn$_{2}$ single crystal for the first time. We also observed multiple field-induced metamagnetic transitions that did not occur in the polycrystalline material. Magnetization at low fields reveals the presence of complex magnetic arrangements in Mn$_{3}$Sn$_{2}$. Despite the fact that the $b$-axis is the easy magnetization axis, the magnetic moments in different directions are all easily saturated, thus leading to an almost isotropic MCE. The MCE for $a$, $b$, and $c$ directions is essentially slightly larger than that reported for polycrystal. Our results, from the single-crystal perspective, demonstrate that Mn$_{3}$Sn$_{2}$ is a promising magnetocaloric material with great application potential in low-temperature refrigeration. In addition, due to the high FM transition temperature and highly anisotropic magnetism, it is of interest to further check whether there are obvious anomalous Hall effect and anomalous Nernst effect and anisotropy in the magneto-transport properties of Mn$_{3}$Sn$_{2}$. Recently, relevant theoretical calculation has suggested that Mn$_{3}$Sn$_{2}$ should be a new kind of magnetic topological material with a coexisting essential nodal line and nodal surface.[40] The single crystal reported here can also provide a platform to prove whether the topological non-trivial energy band structures exist in Mn$_{3}$Sn$_{2}$, by performing measurement such as angle-resolved photoelectron spectroscopy. Acknowledgements. This work was supported by the National Natural Science Foundation of China (Grant No. 12274440), the Strategic Priority Research Program (B) of Chinese Academy of Sciences (Grant No. XDB33010100), National Key R&D Program of China (Grant No. 2022YFA1403903), and the Synergetic Extreme Condition User Facility (SECUF). 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