Magnetic ordering of Mn2GeS4 single crystals with olivine structure

Journal Pre-proofs Magnetic ordering of Mn2GeS4 single crystals with olivine structure M. Solzi, C. Pernechele, G. Attolini, G.E. Delgado, V. Sagredo PII: DOI: Reference:

S0304-8853(19)32390-X https://doi.org/10.1016/j.jmmm.2019.166164 MAGMA 166164

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Journal of Magnetism and Magnetic Materials

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6 August 2019 8 October 2019 15 November 2019

Please cite this article as: M. Solzi, C. Pernechele, G. Attolini, G.E. Delgado, V. Sagredo, Magnetic ordering of Mn2GeS4 single crystals with olivine structure, Journal of Magnetism and Magnetic Materials (2019), doi: https:// doi.org/10.1016/j.jmmm.2019.166164

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Magnetic ordering of Mn2GeS4 single crystals with olivine structure M. Solzi1,2, C. Pernechele1, G. Attolini2, G.E. Delgado3, V. Sagredo4 1 Department

of Mathematical, Physical and Computer Sciences, University of Parma, Parco Area delle Scienze 7/A, 43124 Parma (Italy) 2 IMEM-CNR Institute, Parco Area delle Scienze 37/A 43124, Parma (Italy) 3 Laboratorio de Cristalografía, Departamento de Química, Facultad de Ciencias, Universidad de los Andes, Mérida (Venezuela) 4 Laboratorio de Magnetismo, Departamento de Física, Facultad de Ciencias, Universidad de los Andes, Mérida (Venezuela)

Abstract Single crystals of Mn2GeS4 were grown by chemical vapor transport. X-ray powder diffraction data show a single phase. Rietveld refinement results indicated that Mn2GeS4 crystalize in an olivine-type structure. The magnetic properties of the compound have been studied by means of DC magnetometry and AC susceptibility measurements. The system shows two different phase transitions on decreasing temperature, a first one at about 90 K, leading the system from the paramagnetic to an antiferromagnetic state and a second at about 25 K, corresponding to the onset of a weak ferromagnetic behavior superimposed to the underlying antiferromagnetic order. No evidence of a possible spin-glass behavior in the intermediate temperature region has been found.

Keywords: transition metal alloys and compounds; crystal growth; magnetization; phase transitions; magnetic measurements Corresponding author: M. Solzi, Department of Mathematical, Physical and Computer Sciences, University of Parma, Parco Area delle Scienze 7/A, 43124 Parma (Italy); [email protected]

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1. Introduction Magnetic semiconducting materials have interesting semiconducting properties and have received attention since long time because of their potential application in optoelectronic and magnetic devices [1,2]. The more frequently studied materials are known as semi-magnetic semiconductors, obtained from the derivatives of the II-VI binaries with tetrahedral coordination [3]. One of these families is II2-IV-VI4, which belongs to one of the four possible families of the fourfold defect derivatives of the II-VI binary semiconductors [4]. Concerning the crystal structure, it is important to mention that these materials generally crystallize in the olivine structure type with the VI anions forming a hexagonal close packing, and the cations in tetrahedral (IV) and octahedral (II) coordination [5]. In particular, the transition metal containing olivine compounds have been considered in the past for possible application as multifunctional magnetic materials [6]. To this aim, the sulphide Mn2GeS4 [7], selenide Mn2GeSe4 [8,9] and telluride Mn2GeTe4 [10] compounds have been studied and a detailed structural analysis has been described in each case. From the point of view of their magnetic structure and properties, A2BX4 (A = Mn, Fe, Ni; B = Si, Ge; X = S, Se, Te, O) chalcogenide olivines, where the A atoms form a saw-tooth lattice, represent interesting examples of frustrated lattices of magnetic atoms determining complex magnetic excitations [11,12]. This is an attractive topic in quantum correlated systems, mainly because the ground state of the spin-half saw-tooth chain is understood exactly [13], corresponding to an antiparallel alignment of each ferromagnetic saw-tooth chain with all spins along the b-axis. Due to their peculiar magnetic structure, these compounds have been considered as good model systems to study multicritical phenomena [14-16] and, to this aim, in-depth studies on the magnetic structure and the magnetic behaviour of systems as Mn2BS4 (B= Ge, Si) [17,18] have been performed. In particular, (H-T) magnetic phase diagrams for the spin-flop transition have been traced based on high-field measurements on single crystals, highlighting the presence of spontaneous weak ferromagnetism at low temperature. In recent years, saw-tooth compounds have been proposed as potential materials for application in magnonics [19]. Moreover, multicomponent magnetic structures found in magnetically frustrated materials like the olivine compounds represent an interesting way to obtain multiferroic systems. For example, Mn2GeO4 has been found to exhibit both a ferroelectric polarization and a ferromagnetic magnetization that are directly coupled and point along the same direction [20]. Materials belonging to this family of olivine-type 2

compounds have found important new application also for thermoelectric power generation, owing to peculiar band structure features [21,22] and as cathode materials for batteries [23]. Motivated by the recent renewed interest in this family of compounds, we focused our attention on a particular compound of this family, Mn2GeS4, which has been synthetized in form of single crystals by means of CVT (Chemical Vapour Transport). The aim of this work was to evaluate the detailed magnetic behaviour, in particular at low magnetic fields and in dynamic conditions, of Mn2GeS4 by trying to explain it in correlation with the crystal and the magnetic structure. We performed then a thorough series of magnetic measurements in low and high DC magnetic field, and in low AC magnetic field on both random powder and single crystals, together with a morphologic and structural characterization of the realized crystals.

2. Materials and methods Mn2GeS4 crystals were obtained by CVT method in closed ampoule. 5N pure elements have been used as starting material for the crystal growth. The transport agent was iodine with a concentration in the ampoule of 4 mg/cm3. A mass of 1.5 g polycrystalline starting materials were prepared by mixing stoichiometric amounts of the pure elements and pre-reacted in evacuated quartz ampoules, 180 mm length with internal diameter of 18 mm. The ampoule was placed in a two-zone furnace with the charge at 850°C (with the opposite side at higher temperature) for three days while increasing the temperature by 20 °C/h to prevent explosion. To obtain crystals, the source and the crystallization zone were kept at 850/800°C respectively, for a growth time of ten days. After reaching the room temperature, the ampoule was opened, the crystals removed and rinsed with ethyl alcohol. The resulting crystals showed a dark colour and had typical dimensions of about 2021.2 mm3 (see Fig. 1 upper), with highly reflecting surfaces and faceting (see Fig. 1 lower). X-ray powder diffraction patterns (XRD) were obtained at room temperature by using a Siemens D5005 diffractometer, with a Bragg-Brentano geometry in / reflection mode and CuK radiation ( = 1.54059 Å). Data were collected by steps of 0.02° (2) over the angular range of 10-80°, with a counting time of 20 s per step. Quartz was used as external standard. Magnetic characterization was performed by means of a Quantum Design MPMS-XL SQuID magnetometer equipped with ac susceptometer. The temperature range that can be explored is

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2400K, while the magnetic field can be varied from 0 up to 50 kOe. Hysteresis loops were measured at different temperatures (5 K, 50 K, 100 K) from 50kOe to 50kOe. Magnetic AC

a

b

Figure 1: (a) Morphology of the as grown crystals; (b) SEM image shows faceting and reflecting surfaces of a single crystal. (Color online only)

susceptibility characterization was performed as a function of temperature at three different frequencies (1 kHz, 300 Hz and 70 Hz), with a maximum modulating field of 4 Oe and without a superimposed DC field. The magnetic characterization of Mn2GeS4 were first performed on powder pressed in gel capsules and then on some larger single crystals. The powder sample consists of a randomly oriented ensemble of small crystals (with average size around 200-300 m), directly obtained during the synthesis process together with the larger needle-shaped crystals shown in Fig. 1.

3. Results 3.1 Structural analysis X-ray diffraction experiments were carried out in order to check the stoichiometry of the sample and to determine the arrangement of the cations in the lattice structure. The X-ray data confirm the presence of a single phase. Structural studies, including the cation distribution, were performed by the Rietveld refinement method [24] using the FullProf program [25]. Atomic coordinates reported by Julien-Pouzol et al. [7] were used as a starting model. The final figures of merit were: Rp= 6.3%, Rwp= 10.8%, Rexp= 8.6% and χ2= 2.5, for 4001 step intensities and 45 independent reflections. The definitions of these figures were 4

taken from Ref. [24]. The observed, calculated and difference profile for the final refinement are shown in Fig. 2. Figure 3a shows the unit cell diagram for Mn2GeS4.

Figure 2: Rietveld refinement plot for Mn2GeS4. (Color online only)

Mn2GeS4 crystals display orthorhombic symmetry, space group Pnma, and unit cell parameters: a= 12.7632(3) Å, b= 7.4336(2) Å, c= 6.0268(2) Å, while the cell volume is V = 571.80(3) Å3. Mn2GeS4 crystallizes in an olivine-type structure, which consists of a threedimensional arrangement of distorted MnS6 octahedra and GeS4 tetrahedra connected by common faces. This olivine structure can be described as a hexagonal close packing of S2 anions with the Mn+2 cations occupying half of the octahedral sites and the Ge+4 cations occupying one eighth of the tetrahedral sites. Figure 3b shows how the octahedra and tetrahedra share faces.

a

b

Figure 3. (a) Unit cell diagram for Mn2GeS4. (b) Unit cell projection showing the arrangement of MnS6 octahedra and GeS4 tetrahedra along the [100] direction. (Color online only)

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3.2 Magnetization measurements on powder samples A first basic characterization of the magnetic properties of Mn2GeS4 was performed on a powder sample (mass 38 mg) by means of (T) magnetization curves (Fig. 4), in the temperature range 5-300 K, according to the standard zero-field cooling (ZFC) and fieldcooling on cooling (FCC) protocol, by applying a magnetic field of 10 Oe and 100 Oe. Both the low-field ZFC and FCC curves display the presence of two main transition temperatures, at T1= 24 K and T2= 87 K (Fig. 4a and inset). These transitions are evident both at 10 Oe and at 100 Oe (Fig. 4b and inset) and may be further highlighted in the temperature dependence of inverse mass susceptibility (Fig. 5b). The Curie-Weiss fitting of the latter measurements above T2 allowed the extrapolation of the Curie-Weiss constant, the sign and intensity of which are related to the exchange interaction: in this case, it turns out to be θCW = 213 K, whose sign is indicative of anti-ferromagnetic coupling. Thus, one may interpret the highest

Figure 4: Temperature dependence of mass magnetization in zero field cooling (ZFC, closed symbols) and field cooling (FCC, open symbols), measured at (a) 10 Oe and (b) 100 Oe for a powder Mn2GeS4 sample.

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transition temperature T2 as the Néel temperature corresponding to the onset of such antiferromagnetic long-range order. The ZFC-FCC (T) measurements performed at 10 Oe (figure 4a) show below T1 the onset of a “ferromagnetic-like” order. Indeed, the ZFC curve (closed dots in Fig. 4a) increases from 5K up to 20 K and crosses the FCC curve at ≈ 22K, indicating that the lowest critical temperature (T1) corresponds to the bifurcation of ZFC-FCC curves, a typical marker of irreversibility phenomena. In Figure 5a, the mass susceptibilities of the two series of measurements (10 and 100 Oe) are compared. The applied magnetic field seems to play a crucial role in determining the characteristics of the “ferromagnetic-like” behavior. In fact, the mass susceptibility at 5 K is reduced by a factor 3 from χm= 6×103 emu/g Oe at 10 Oe to χm= 2×103 emu/g Oe at 100 Oe. The measurements performed at 100 Oe (Fig. 4b) show below T1 a steep increase not only in the FCC curve, but also in the ZFC curve, thus

Figure 5 (a) Comparison of the temperature dependence of mass susceptibility in zero field cooling (ZFC) and field cooling (FCC), measured at 10 Oe (closed and open dots) and 100 Oe (closed and open triangles) for a powder Mn2GeS4 sample. (b) Temperature dependence of the inverse of mass susceptibility in field cooling (FCC), measured at 10 Oe (open dots) and at 100 Oe (open triangles) for the same sample. The arrows indicate the critical temperatures.

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indicating that an applied field of 100 Oe is large enough to almost saturate the sample at 5 K. This aspect will be further discussed in the following, with reference to the hysteresis loops. Isothermal magnetization measurements as a function of the applied field were performed at different temperatures (5K, 50K, 100K) from 50kOe to 50kOe, in order to investigate the three different regimes that are evidenced by the two transition temperatures (T1 and T2). At T= 100 K, the temperature at which the hysteresis loop is measured is higher than T2 and, according to Figure 5b, the system should be described by the Curie-Weiss law (that is, it should be paramagnetic, with null coercivity and remanent magnetization). Figure 6a confirms this basic concept. In the temperature range between the two transition temperatures, for example at T= 50 K, the system shows an overall paramagnetic-like behavior, as confirmed by figure 6b. Coercivity Hc and specific magnetization remanence r are zero within the experimental error. Below T1, at the lowest temperature at which a net magnetic moment was inferred from Fig. 4, the hysteresis loop opens, as it is evident in Fig. 7a-b for the curve at 5 K. The opening

Figure 6: Hysteresis loops measured at (a) 100 K and (b) 50 K for a powder Mn2GeS4 sample.

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of the hysteresis loop confirms the onset of a net magnetic moment observed and discussed with reference to Figure 4. The loop is characterized by a coercivity field of 4010 Oe and a specific magnetization remanence σr = 0.200.05 emu/g that corresponds to a very small value of the magnetic moment, about 0.01 B/FU. In the high field region of figure 7a, there is a strong paramagnetic-like contribution due to the part of the sample anti-ferromagnetically ordered below 87 K, that is why a not saturated behavior and a large high-field susceptibility is observed. According to figure 7b, it is clear now the reason of the almost superimposed ZFC-FCC curves measured at 100 Oe: such field value is indeed higher than the reversal one at 5 K and thus the weak ferromagnetic contribution of the sample is almost saturated. Thus, it is not surprising that the measured remanence at 5 K is in agreement with the specific magnetization measured with a 100 Oe applied field at the same temperature in the ZFC-FCC curves of fig. 5. From Fig. 7a, the

Figure 7: (a) Hysteresis loop measured at 5 K for a powder Mn2GeS4 sample. (b) The zoom of the low-field part clearly evidences the small opening of the loop.

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almost linear (H) curve up to 5 T allows to deduce the DC molar susceptibility at 5 K: it turns out to be 0.048 emu/mol Oe. AC-susceptibility measurements have been performed on the Mn2GeS4 powder sample in the temperature range 5-100 K at three different frequencies (1 kHz, 300 Hz, 70 Hz). The basic idea of this series of measurements was to check the possible presence of a spin-glass behavior, as hypothesized for example to occur in the isostructural manganite olivines Mn2GeO4 and Mn2SiO4 [11] and also in the parent compound Mn2GeTe4 [26]. In Fig.s 8a-b, the AC characterization up to 100 K is reported. The peak position at T1 (both in the real and the imaginary part of AC susceptibility) is unaffected by the change in AC field frequency, as well as the underlying area. Moreover, even the drop of the real part of the AC susceptibility at T3 turns out to be not influenced by the change in frequency (see Fig. 9). Therefore, we can conclude that no trace of a spin-glass behavior is evident from these measurements, at least in the explored frequency range. The presence of the transitions at T1 and at T2 is confirmed also through the results of AC-susceptibility measurements (Fig. 9).

Figure 8: (a) Real and (b) imaginary part of AC susceptibility measured for a powder Mn2GeS4 sample by applying a modulating AC field of 4 Oe at the three frequencies 1 kHz, 300 Hz, 70 Hz, in the temperature region around T1.

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Figure 9: Real part of AC susceptibility measured for a powder Mn2GeS4 sample by applying a modulating AC field of 4 Oe at the three frequencies 1 kHz, 300 Hz, 70 Hz, in the temperature span 5-100 K. Inset: zoom of the high temperature region of the real part of AC susceptibility. The imaginary part is close to zero in the same temperature region.

3.3 Magnetization measurements on single crystals A series of ZFC-FCC magnetization measurements have been performed on a needle-shaped single crystal of Mn2GeS4 (mass 4.5 mg), with the magnetic field applied along different crystallographic axes. With a field of 100 Oe applied along the a-axis, the curves clearly show the presence of the two main transition temperatures at T1= 24 K and at T2= 87 K (Fig.s 10a and 10b). However, the same measurements performed with the field applied along the band the c-axis show apparently only the transition at T1= 24 K, while that at higher temperatures turns out to be still detectable but with a weaker anomaly (Fig.s 10a and 10b). It has to be noticed that the low-field DC susceptibility at 5 K after ZFC is strongly dependent on the direction of the applied field: it is indeed very low in the case of field applied along the a-axis, while it is about 16 and 38 times larger if the field is applied along the b-axis and the c-axis, respectively. This fact clearly means that the magnetic response of the system to a small external magnetic field is sensibly stronger if the field direction lies in the plane perpendicular to the a-axis. Hysteresis loops have also been measured at 5 K along distinct crystallographic directions: they look very different, as can be noticed from Fig.s 11a and 11b. If observed on a

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Figure 10: (a) Comparison of the temperature dependence of mass DC susceptibility in zero field cooling (ZFC) for a single crystal of Mn2GeS4, with a 100 Oe magnetic field applied along different crystal axes; inset: low-temperature zoom for H||a; (b) hightemperature zoom.

wide scale, the loop measured with the field along the a-axis is indeed almost linear and paramagnetic-like, while that with the field along the b- or the c-axis shows a clear remanence and a curved shape. Moreover, a zoom in the low-field region put in evidence that only the loop along the b- and the c-axis is open, with a coercivity of 28 Oe and 14 Oe, respectively (see Table 1), in agreement with the value obtained for the powder sample. On the contrary, the loop measured along the a-axis does not show any trace of hysteresis, at least within the experimental error. The values of the specific magnetization remanence at T= 5 K are also reported in Table 1, corresponding to about 5103 B/Mn2+ for the field applied along

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Figure 11: (a) Hysteresis loop measured at 5 K for a single crystal of Mn2GeS4, with the magnetic field applied along different crystal axes; (b) low-field zoom.

Table 1: Magnetic properties of the Mn2GeS4 single crystal along different crystal axes and of the Mn2GeS4 powder sample. Coercivity, magnetization remanence and susceptibility were measured at T = 5 K; DC molar susceptibility was measured at an applied field of 20 kOe, initial DC mass susceptibility at 100 Oe. Field direction H||a H||b H||c Random (powder)

mol

m

00.05 0.170.05 0.180.05

(emu/mol Oe) 4.3×102 4.9×102 5.0×102

(emu/gOe) 1.3×104 2.1×103 4.9×103

Cm (emu K/g Oe) (2.680.07)×102 (3.00.1)×102 (3.20.1)×102

peff (B) 5.80.1 6.10.2 6.30.2

θCW (K) 238 230 254

2.80.1 2.70.1 2.90.1

0.200.05

(4.760.02)×102

2×103

(2.710.03)×102

5.80.1



2.50.1

Hc (Oe) 05 285 142

r (emu/g)

4010

f

the b- or the c-axis, while it is about zero for the field applied along the a-axis. The molar susceptibility values at 5 K, deduced by a linear fit of the high-field portion of the hysteresis 13

loop with a magnetic field up to 20 kOe applied along a, b and c directions, are reported in Table 1. These values turn out to be in agreement with that obtained for the powder sample and have to be compared with the values of M/H = 0.040.05 emu/mol Oe measured in a Mn2GeS4 single crystal by applying a magnetic field of 1030 kOe along the different cell directions at 5 K in Ref. [18]. With the purpose of deducing the intensity of antiferromagnetic exchange coupling along the different crystallographic axes, a series of measurement of the temperature dependence of specific magnetization has been performed with an applied magnetic field large enough to rule out any low-field “ferromagnetic-like” phenomenon (H= 1000 Oe). The Curie-Weiss fitting of such curves above T2 allowed the extrapolation of slightly different values of the Curie-Weiss constant measured along different crystallographic axes, as reported in Table 1. It turns out that the strongest interaction occurs along the c-axis.

4. Discussion The above-described results allow to interpret the highest transition temperature T2 as the onset of a long-range anti-ferromagnetic ordering. This is confirmed by the negative sign of the Weiss constant extrapolated from the Curie-Weiss fitting of the (T) curves for the powder sample and for the single crystal (see Table 1): the obtained values are noticeably larger than the value 201 K reported in Ref. [18]. The transition at T2 can then be seen as a Néel temperature TN and the ratio f = |θCW|/TN = 2.50.1 for the powder sample (2.72.90.1 for the single crystal along different directions, see Table 1), which is larger than unity, measures the degree of magnetic frustration. Most anti-ferromagnets exhibit some frustration, arising from the incompatibility of the lowest-energy anti-ferromagnetic state with the crystal lattice. The f value obtained in this case is however relatively small with respect to that observed for a parent system which is a strongly geometric frustrated anti-ferromagnet, for example Mn2SiO4 [11]. Moreover, it has to be noticed that the values of θCW and f obtained by applying the magnetic field along different crystal axes turn out to be slightly different, reflecting the different intensity of interactions and, as a consequence, of the degree of magnetic frustration. This fact could be correlated to the different Mn-Mn distance along different directions in the unit cell. The shortest distances between Mn2+ ions are indeed: 3.73 Å (4a-4a), 3.97 Å (4a-4c) and 4.83 Å (4c-4c) [15]. 14

The actual nature of the transition at the critical temperature T1 deserves a specific discussion, although the conclusions remain rather speculative. The observed divergence at T1 between ZFC and FCC low-field magnetization (Fig. 4a) and the observed opening of the hysteresis loop below T1 (Fig. 7b) represent the key elements that allow to describe this transition as a transformation to a ferromagnetic-like behavior (weak ferromagnetism), coexisting with the underlying anti-ferromagnetic order. A collinear antiferromagnetic ordering at 4.2 K has been observed indeed by powder neutron diffraction experiments in Mn2GeS4 [15]. This interaction is supposed to couple the spins of Mn2+ on the sites 4a and 4c in Cy modes, that correspond to a ground state characterized by an antiparallel alignment of each ferromagnetic saw-tooth chain with all spins along the b-axis. For comparison, the parent compound Mn2GeTe4, which has a Néel temperature TN of about 135 K, shows mainly antiferromagnetic behavior with a very weak superimposed ferromagnetic component that has been attributed to spin canting [26]. It was reported that Mn2SiS4 shows a weak ferromagnetic behavior only in a very narrow temperature region (83–86 K) just below TN [6,16], differently from Mn2GeSe4, for which this behavior persists down to low temperature [9]. The presence of a first para-antiferromagnetic transition followed by a second transition at lower temperature to a partially canted arrangement is typical also of Fe2GeS4 [27] and of other compounds isomorphic to olivines, like the Mn- and Fe-orthosilicates [28]. In the case of Mn2SiSe4, from a combined study of magnetometry and powder neutron diffraction [29] it has been possible to infer the onset at low temperature of a short-range order involving a canting away from the strict c-axis orientation of the spins. The observed weak remanent magnetization has been associated in this case with imperfect compensation upon summing over very small (2-3 nm) regions of coherence, in which there are such short-range ferroand/or ferri-magnetic arrangements of the canted spin components. The obtained result of weak ferromagnetism below T1 is in contrast with that of Ref. [18], which reports an apparent absence of spontaneous magnetization at low temperature. However, the analysis reported in ref. [18] is mainly based on high-field measurements and the minimum applied field of 1000 Oe is likely large enough to mask any evidence of weak ferromagnetism. We have indeed demonstrated that a magnetic field as high as 100 Oe is enough to almost saturate the weak ferromagnetic contribution. Moreover, our result of a very small magnetization remanence at 5 K with H||c may explain the difficulty of detecting a spontaneous magnetization (see the inset of Fig. 2(h) in Ref. [18]). On the other hand, Ref. [18] reports also a significant enhancement of susceptibility at low temperature if H||c, that is in agreement with our results (Fig. 10a). 15

The actual physical origin of the observed weak ferromagnetic contribution below T1 in Mn2GeS4 can be hardly identified merely basing on magnetometric measurements. By analogy with systems similar to Mn2GeS4 and from previous studies, one can say that the weak ferromagnetic behavior may result from local non-zero components that do not sum up in the overall magnetic structure. However, to obtain the evidence of a possible short-range order like in the case of Mn2SiSe4 would require the execution of dedicated neutron diffraction experiments.

5. Conclusions The grown Mn2GeS4 crystals present an olivine-type structure, as it results from X-ray diffraction measurements. From the point of view of the magnetic behavior, the system shows two different phase transitions on decreasing temperature. The first one, at about 90 K, corresponds to a paramagnetic to anti-ferromagnetic transformation, while that at lower temperature (about 25 K) refers to the onset of a weak ferromagnetic behavior superimposed to the underlying anti-ferromagnetic order, likely to be ascribed to spin canting due to a geometrical frustration. No evidence of a possible spin-glass behavior in the intermediate temperature region has been found on the basis of AC susceptibility measurements.

Declaration of Competing Interest Authors declare no conflict of interest.

Acknowledgments Funding: this research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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18

Figure Captions Figure 1: (a) Morphology of the as grown crystals; (b) SEM image shows faceting and reflecting surfaces of a single crystal. (Color online only) Figure 2: Rietveld refinement plot for Mn2GeS4. (Color online only) Figure 3. (a) Unit cell diagram for Mn2GeS4. (b) Unit cell projection showing the arrangement of MnS6 octahedra and GeS4 tetrahedra along the [100] direction. (Color online only) Figure 4: Temperature dependence of mass magnetization in zero field cooling (ZFC, closed symbols) and field cooling (FCC, open symbols), measured at (a) 10 Oe and (b) 100 Oe for a powder Mn2GeS4 sample. Figure 5 (a) Comparison of the temperature dependence of mass susceptibility in zero field cooling (ZFC) and field cooling (FCC), measured at 10 Oe (closed and open dots) and 100 Oe (closed and open triangles) for a powder Mn2GeS4 sample. (b) Temperature dependence of the inverse of mass susceptibility in field cooling (FCC), measured at 10 Oe (open dots) and at 100 Oe (open triangles) for the same sample. The arrows indicate the critical temperatures. Figure 6: Hysteresis loops measured at (a) 100 K and (b) 50 K for a powder Mn2GeS4 sample. Figure 7: (a) Hysteresis loop measured at 5 K for a powder Mn2GeS4 sample. (b) The zoom of the low-field part clearly evidences the small opening of the loop. Figure 8: (a) Real and (b) imaginary part of AC susceptibility measured for a powder Mn2GeS4 sample by applying a modulating AC field of 4 Oe at the three frequencies 1 kHz, 300 Hz, 70 Hz, in the temperature region around T1. Figure 9: Real part of AC susceptibility measured for a powder Mn2GeS4 sample by applying a modulating AC field of 4 Oe at the three frequencies 1 kHz, 300 Hz, 70 Hz, in the temperature span 5-100 K. Inset: zoom of the high temperature region of the real part of AC susceptibility. The imaginary part is close to zero in the same temperature region. Figure 10: (a) Comparison of the temperature dependence of mass DC susceptibility in zero field cooling (ZFC) for a single crystal of Mn2GeS4, with a 100 Oe magnetic field applied 19

along different crystal axes; inset: low-temperature zoom for H||a; (b) high-temperature zoom. Figure 11: (a) Hysteresis loop measured at 5 K for a single crystal of Mn2GeS4, with the magnetic field applied along different crystal axes; (b) low-field zoom.

Table caption Table 1: Magnetic properties of the Mn2GeS4 single crystal along different crystal axes and of the Mn2GeS4 powder sample. Coercivity, magnetization remanence and susceptibility were measured at T = 5 K; DC molar susceptibility was measured at an applied field of 20 kOe, initial DC mass susceptibility at 100 Oe.

Field Hc Cm r mol m direction (Oe) (emu K/g Oe) (emu/g) (emu/mol Oe) (emu/gOe) H||a 05 00.05 4.3×102 1.3×104 (2.680.07)×102 H||b 285 0.170.05 4.9×102 2.1×103 (3.00.1)×102 H||c 142 0.180.05 5.0×102 4.9×103 (3.20.1)×102 Random 4010 0.200.05 (4.760.02)×102 2×103 (2.710.03)×102 (powder)

peff θCW f (K) (B) 5.80.1 238 2.80.1 6.10.2 230 2.70.1 6.30.2 254 2.90.1 5.80.1  2.50.1

Table 1

20

Figure 1

a

b

21

Figure 2

22

Figure 3

a

b

23

Figure 4

0.075 0.0012

 (emu/g)

0.050 0.0008 60

0.025

0.000

ZFC 10 Oe FCC 10 Oe

0

25

 (emu/g)

0.2

50

T (K)

100

a

75

100

0.010

0.008 60

0.1

0.0

80

80

ZFC 100 Oe FCC 100 Oe

0

25

50

75

100

b 100

T (K)

24

Figure 5

m (emu/g Oe)

6.0x10-3 ZFC 10 Oe ZFC 100 Oe FCC 10 Oe FCC 100 Oe

4.0x10-3 2.0x10-3 0.0

a 0

50

T (K)

150

100

1m (emu/g Oe)1

1.5x104

1.0x104

5.0x103

0.0

b 0

50

T (K)

100

150

25

Figure 6

 (emu/g)

4 2 0 -2

a

-4 -60000

-30000

0 H (Oe)

30000

60000

6

 (emu/g)

4 2 0 -2

b

-4 -6 -60000

-30000

0

30000

60000

H (Oe)

26

Figure 7

 (emu/g)

8 4 0 -4

a

-8 -60000

-30000

0

30000

60000

H (Oe)

 (emu/g)

0.4

0.0

b

-0.4 -1000

0

1000

H (Oe)

27

Figure 8

1x10-3 ' (emu/g Oe)

1 kHz 300 Hz 70 Hz

a

5x10-4

0

0

10

20

30

40

T (K)

'' (emu/g Oe)

4x10-3

b

1 kHz 300 Hz 70 Hz

2x10-3

0

0

10

20

T (K)

30

40

28

Figure 9

' (emu/g Oe)

8x10-4

1.0x10-4

6x10-4

7.5x10-5 60

80

4x10-4

100 1 kHz 300 Hz 70 Hz

2x10-4

0

0

20

60

40

80

100

T (K)

29

Figure 10

 (emu/g Oe)

5.0x10-3 4.0x10-3

1.2x10-4

3.0x10-3 8.0x10-5 0

-3

2.0x10

20

40

a

1.0x10-3 0.0

0

20

40

60

80

b

1.2x10-4

 (emu/g Oe)

100

1.0x10-4 H||c H||b H||a

8.0x10-5 60

70

80

90

100

T (K)

30

Figure 11

 (emu/g)

4 2

H||c H||b H||a

0 -2

a

-4

 (emu/g)

-20000 0.50 0.25

-10000

0

10000

20000

H||c H||b H||a

0.00

-0.25

b

-0.50 -200

-100

0 H (Oe)

100

200

31

Highlights     

single crystals of Mn2GeS4 were grown by chemical vapor transport a thorough magnetic characterization was performed on a needle–shaped single crystal a weak ferromagnetic behavior is superimposed to a dominant antiferromagnetic order a geometrical frustration is the likely origin of spin canting no evidence of a possible spin-glass behavior has been found

32