Introduction

Iron sulfides Fe1−x S have a substantial deficiency at the iron sites, and at room temperature the stable phases are Fe7S8, Fe9S10, Fe10S11, Fe11S12, and FeS (Nakazawa and Morimoto 1971). The cation-deficient Fe1−x S materials have interesting magnetic properties, and can find a potential application in the nonvolatile phase-change magnetic memory devices (Takayama and Takagi 2006). The compounds Fe1−x S with 0 ≤ x ≤ 0.125, extending from the nearly stoichiometric hexagonal troilite Fe1−x S (0 ≤ x ≤ 0.05) to the monoclinic Fe7S8 (x = 0.125), have the NiAs-like crystal structures, and belong to the so called pyrrhotite group (Wang and Salveson 2005). The clustering of Fe atoms in the troilite phase and the ordering of Fe atoms and cation vacancies in the more Fe-deficient compositions lead to the superstructures. The troilite has a 2C superstructure of NiAs with the hexagonal lattice parameters \( a = \sqrt 3 A \), c = 2C, where A and C are the axes of the NiAs subcell. The appearance of vacancies reduces the symmetry of the system from hexagonal to monoclinic. The monoclinic pyrrhotite Fe7S8 has a 4C superstructure of NiAs-type which can be represented as a derivative from FeS by subtraction of one Fe per eight FeS units (Wang and Salveson 2005; Bertaut 1953). The resultant structure is composed of the Fe sites layers separated by the S layers from the layers containing the Fe sites and the cation vacancies. As to magnetic properties, the Fe1−x S compounds can be antiferromagnetic (AFM) and/or ferrimagnetic (FRM), and the magnetic behavior is strongly dependent on composition and temperature (Wang and Salveson 2005; Lotgering 1956; Zapletal 1969; Marusak and Mulay 1979, 1980; Fei et al. 1995; Li and Franzen 1996).

In this article, we present the structural and magnetic properties of the newly synthesized iron sulfide nanosheets with a NiAs-like crystal structure studied by the Mössbauer spectroscopy and magnetic measurements in a wide temperature range 78–700 K. An evidence of the vacancy redistribution over iron layers, changing essentially the magnetic properties of the compound, was established at high-temperatures. We examined the inter- and intra-exchange interactions between Fe atoms taking into account the geometry of the exchange bonds, and found a model of the vacancy redistribution which explains the magnetic anomaly observed in the experiment.

Sample preparation and characterization

The nanoparticles of iron sulfide Fe1−x S were synthesized by thermal decomposition of the mixture of iron-oleylamine (Fe-OLA) complexes and sulfur-oleylamine (S-OLA) in a three-neck flask equipped with an inlet of argon gas, condenser, magnetic stirrer, thermocouple, and heating mantle. The details of the process are described in the previous studies (Lin et al. 2009, 2010) and summarized in Table 1.

Table 1 Some details of the synthesis of the iron sulfide Fe1−x S nanoparticles. Fe-OLA ≡ iron-oleylamine complexes, S-OLA ≡ sulfur-oleylamine complexes, and Fe/S ≡ molar ratio of iron chloride tetrahydride (FeCl2·4H2O) to thiourea (NH2CSNH2), 0 ≤ x ≤ 0.125
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The crystal structure and phase purity of the samples were examined by X-ray powder diffraction (XRD). As shown in Fig. 1, all reflections can be readily indexed to the hexagonal phase with NiAs-type structure (P63/mmc). An estimation of the crystallite size by the Scherrer’s formula of the peak broadening (Langford and Wilson 1978) gives an average size ~30.5 nm.

Fig. 1
figure 1

Room temperature X-ray diffraction patterns of the Fe1−x S nanodisks recorded for the samples prepared at Fe/S = 1/2 (FS-NA1) and Fe/S = 1/1 (FS-NA2) conditions. Fe/S is the molar ratio of FeCl2·4H2O to NH2CSNH2. The reflection indexes correspond to the hexagonal NiAs-type structure (P63/mmc)

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The particles shape and size were examined by the scanning electron microscope (SEM) and transmission electron microscope (TEM). The SEM images (Fig. 2a) show the aggregative plate-like particle structure with the thickness of the sheets about 30–50 nm. The TEM images (Fig. 2b–d) display particles with the accurate shape of hexagonal plates whose characteristic size is about 200–400 nm in plane and about 30–50 nm in thickness.

Fig. 2
figure 2

SEM (a) and TEM (b, c, and d) images of the Fe1−x S nanoparticles

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The Mössbauer spectroscopy and magnetic measurement data

The Mössbauer spectroscopy was applied to examine the phase composition, structural, and magnetic properties of the nanoparticles. The 57Fe-Mössbauer spectra were recorded at temperatures between 80 and 700 K in the transmission geometry with a standard spectrometer operating in the constant accelerations regime. The gamma-ray source 57Co(Rh) was at room temperature, and the isomer shifts were measured relative to metal α-Fe at room temperature. To exclude the sample oxidation, the high-temperature measurements were performed in the vacuum and/or in argon filled furnaces.

We found that the room temperature Mössbauer spectra of all five samples prepared at different molar ratio of FeCl2·4H2O to NH2CSNH2 (see Table 1) are very similar. This supports the NiAs-type structure and implies similar magnetic behavior of the Fe1−x S nanoparticles in all the samples. The FS-NA1 and FS-NA2 samples (see Table 1) were investigated in a wide temperature range, and several Mössbauer spectra recorded at different temperatures are shown in Fig. 3. The magnetic splitting of spectra lines is gradually reduced as temperature increases from 80 to 570 K, and above 565 K the spectra transforms into a doublet typical of the paramagnetic state.

Fig. 3
figure 3

The 57Fe-Mössbauer spectra of Fe1−x S nanoparticles (FS-NA1) at different temperatures

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The spectra-line shape indicates that iron ions occupy several nonequivalent sites which can be explained by the presence of cation vacancies. We have examined several models of the spectra fitting, including plotting the distribution functions for the hyperfine parameters by the DISTRY program (Rusakov 2000), and found that the best fit can be obtained with four six-line components (shown in Fig. 4a, b) which relate to four nonequivalent iron sites. At room temperature, the values of isomer shifts (δ) for four components are in the range of 0.70–0.64 mm/s (Table 2), which shows that iron ions in all nonequivalent sites are in the valence state close to Fe2+, and the trivalent iron does not appear in our Fe1−x S pyrrhotite. At 80 K, the values of the magnetic hyperfine fields H hf for four Mössbauer components are about 335, 310, 279, and 245 kOe, and at room temperature, these values are reduced to 300, 280, 260, and 232 kOe, respectively. The values of all hyperfine parameters are given in Table 2.

Fig. 4
figure 4

The 57Fe-Mössbauer spectra of Fe1−x S nanoparticles at temperatures 300 K (a) and 473 K (b). The spectra fitting to four magnetic components attributed to nonequivalent iron sites are shown by grid-ticks above the spectra. Solid (color red) lines correspond to the calculated spectra (Color figure online)

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Table 2 Hyperfine parameters obtained from the 57Fe-Mössbauer spectra at different temperatures for the nonequivalent iron sites in the Fe1−x S nanosheets: H hf is the magnetic hyperfine field at 57Fe nuclei, δ is the isomer shift relative to α-Fe at room temperature, ε is the quadrupole shift, S is the relative line area of the spectrum component, and Γ is the half-maximum line width
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The temperature dependences of the hyperfine fields H hf for three most intensive Mössbauer components are shown in Fig. 5. From the field behavior, we estimated the value of Néel temperature to be about 565 K. We found that the relative intensities of the Mössbauer components for nonequivalent iron sites change with the temperature increase from 400 to 550 K in accordance with the magnetic properties change. Above the Néel temperature, the Mössbauer spectrum consists of a broad doublet (Fig. 3) which can be related to several overlapping components in the paramagnetic state.

Fig. 5
figure 5

The temperature dependences of the magnetic hyperfine field H hf at the 57Fe nuclei for three most intensive Mössbauer components in the Fe1−x S nanoparticles

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The magnetic measurements of the Fe1−x S nanoparticles were performed at temperatures between 300 and 700 K using the VSM-type magnetometer with the sample kept in the argon atmosphere. The hysteresis loops were measured at temperatures 300 ≤ T ≤ 650 K in an applied field sweeping from −11 to 11 kOe. We found that upon heating, the magnetization value M is rather low in the region 300–370 K, and then it increases essentially and reaches maximum at 470 K (Fig. 6a). The peak-like transition in M(T) starts at ~370 K and ends near ~560 K. Above 360 K, the hysteresis loops are typical of a ferromagnet, and the coercivity rises rapidly reaching a maximum value at 390 K, and then it decreases slowly showing a local maximum at 465 K (Fig. 6b).

Fig. 6
figure 6

Temperature dependence of magnetization M H=1.1T (a) and coercivity H C (b) obtained from hysteresis loops of Fe1−x S nanoparticles

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Discussions

The interlayer and intralayer exchange interactions

The nonequivalent iron sites in the cation-deficient Fe1−x S compounds appear due to the presence of cation vacancies in the nearest neighboring of Fe ions. In the NiAs-type structure of Fe1−x S, the Fe cations are octahedrally coordinated by six S anions (the FeS6 octahedra) (Fig. 7), and the coordination polyhedron of S is the trigonal prism created by six Fe (the SFe6 prisms) (Goodenough 1963; Wolf and Dwight 1993). Within the iron layers, the direct Fe–Fe ferromagnetic interactions J 1 connect the Fe ion with six nearest Fe neighbors (Fig. 7), but the Fe–Fe interionic distances are very large (~3.4 Å) and the J 1 exchange interaction integral should be very small (Goodenough 1963). However, beside the direct interactions, the Fe ion is connected with 6 nearest Fe neighbors of the same layer by 12 superexchange Fe–S–Fe interactions J 2, which involve three sulfur ions above and three sulfur ions below the iron layer (Fig. 7). The angle of these Fe–S–Fe bonds is about 96° and the Fe–S distances are near 2.44 Å (Wolf and Dwight 1993). The 90° superexchange Fe–S–Fe interactions are supposed to be ferromagnetic (J 2 > 0) (Goodenough 1963).

Fig. 7
figure 7

The unit cell of the NiAs-type crystal structure of Fe1−x S compound. Black (color blue) balls are the Fe cations and grey (color red) balls are the S anions. The intralayer direct Fe–Fe and 90°-superexchange Fe–S–Fe bonds are shown by dash lines with J 1 and J 2, respectively, and the interlayer 129°- and 62°-superexchange Fe–S–Fe bonds are shown by dash lines with J 3 and J 4, respectively (Color figure online)

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The interlayer superexchange Fe–S–Fe interactions connect each Fe ion with 18 Fe ions from two nearest layers (nine bonds above and nine bonds below the selected Fe-layer), however, not all these bonds are equivalent (Fig. 7). Although the length of all Fe–S bonds is nearly the same (~2.44 Å), only 12 of the 18 bonds have the Fe–S–Fe bond angle of about 129° which is effective for the AFM interaction (J 3 < 0), while six interlayer bonds (J 4) are at the angle ~62° (Fig. 7) which is not effective in the electronic d–p interaction (Goodenough 1963).

Here we note that the previous considerations of the Mössbauer and magnetic data of Fe1−x S on the basis of the 18 equivalent superexchange bonds were not correct (Levinson and Treves 1968; Ok and Lee 1973; Kim et al. 2009).

Nonequivalent iron sites

It is supposed that the magnetic structure of Fe1−x S consists of the ferromagnetic Fe layers in the c plane with an AFM coupling of the neighboring layers along the c axis (Lotgering 1956; Levinson and Treves 1968; Ok and Lee 1973, 1984; Kim et al. 2009; Ok et al. 1982). An appearance of the cation vacancies □ influences both the direct Fe–Fe and the superexchange Fe–S–Fe interactions. In general, the vacancies can be distributed randomly or orderly. In the layered NiAs structure, several types of the nonequivalent iron sites can be considered in the case of vacancy ordering (see Fig. 8a, b):

Fig. 8
figure 8

Iron layers (black balls) stacked along the c-axis in the NiAs-type crystal structure of Fe1−x S compound. Schematic location of cation vacancies □ is shown for the cases of 3C-type (a) and 2C-type (b) of the vacancy ordering. Numerals at iron cations indicate the number of the interlayer 129°-superexchange Fe–S–Fe bonds J 3 of this cation with the iron ions from neighboring layers. Arrows show the broken J 3 bonds. Sulfur anions are not shown

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(1) The Site-1 exists in some local sites of a selected Fe-layer where there are not any vacancies (in the nearest environment of some Fe sites) both in this layer and in the two nearest layers above and below the selected layer (Fig. 8a). All the intralayer and interlayer (Fe–Fe and Fe–S–Fe) bonds are preserved in this case, and the magnetic state of the iron ions is governed by the (6J 1 + 12J 2 + 12J 3) couplings. Only this type of sites should be presented in the stoichiometric FeS compound.

(2) The Sites-2 appears when the cation vacancies are in the selected Fe-layer, but there are not any vacancies in two nearest layers above and below the selected layer (Fig. 8a). In this case, vacancies can appear in each third (or in more distant) iron layer along the c-axis, and this type of the vacancies ordering we attribute to the NC superstructure with N ≥ 3. The intralayer direct Fe–□ and 90°-superexchange Fe–S–□ bonds appear in this case but all interlayer Fe–S–Fe bonds are preserved. The magnetic state of the Fe ion having one nearest vacancy in the Site-2 is governed by the (5J 1 + 10J 2 + 12J 3) coupling (Fig. 8a). Two in-layer vacancies would lead to the (4J 1 + 8J 2 + 12J 3) coupling (Fig. 8a).

(3) The Sites-3 appears when there are not any vacancies in the selected Fe-layer, but the vacancies are located in one nearest layer above or below the selected layer (Fig. 8a). In this case, all in-layer Fe–Fe and Fe–S–Fe bonds are preserved and the interlayer Fe–S–□ bonds with one neighboring layer containing vacancies appear. This type of the vacancy ordering corresponds to the NC-type superstructure with N ≥ 3. Depending on the vacancy location, two sub-sites can exist (Fig. 8a): If the Fe–S–□ bond angle is near 129°, then the (6J 1 + 12J 2 + 10J 3) couplings remain efficient. If the Fe–S–□ bond angle is near 62°, then all efficient couplings (6J 1 + 12J 2 + 12J 3) are preserved. This site is similar to the Site-1.

(4) The Sites-4 appears when there are no vacancies in the selected Fe-layer, but the vacancies are located in two nearest layers both above and below the selected layer (Fig. 8b). In this case, all intralayer Fe–Fe and Fe–S–Fe bonds are preserved and the interlayer Fe–S–□ bonds appear in two neighboring layers. In this case vacancies may appear in each second iron layer along the c-axis, and this type of the vacancy ordering we attribute to the 2C-type superstructure.

Depending on the vacancy location, there are several types of the iron sites (see Fig. 8b) in which the Fe ion experiences the (6J 1 + 12J 2 + 10J 3), (6J 1 + 12J 2 + 11J 3) or (6J 1 + 12J 2 + 8J 3) couplings with the nearest iron neighbors.

Thus, if all J 1, J 2, and J 3 interactions are taken into account, then the above considered interactions reduce to six nonequivalent Fe sites having the following exchange couplings:

$$ \begin{aligned} {\text{Site-A}}. 1= \left( { 6J_{ 1} + 1 2J_{ 2} + 1 2J_{ 3} } \right)\\ {\text{Site-A}}. 2= \left( { 5J_{ 1} + 10J_{ 2} + 1 2J_{ 3} } \right)\\ {\text{Site-A}}. 3= \left( { 4J_{ 1} + 8J_{ 2} + 1 2J_{ 3} } \right)\\ {\text{Site-B}} = \left( { 6J_{ 1} + 1 2J_{ 2} + 1 1J_{ 3} } \right)\\ {\text{Site-C}} = \left( { 6J_{ 1} + 1 2J_{ 2} + 10J_{ 3} } \right)\\ {\text{Site-D}} = \left( { 6J_{ 1} + 1 2J_{ 2} + 8J_{ 3} } \right)\\ \end{aligned} $$
(1)

It was shown that the intralayer magnetic interactions, both the direct Fe–Fe and the 90° Fe–S–Fe superexchange one, are a good deal weaker than the interlayer superexchange Fe–S–Fe interactions, i.e., J 3 ≫ J 2 > J 1 (Goodenough 1963; Hirahara and Murakami 1958; Motida and Miyahara 1970). Neglecting both the J 1 and J 2 interactions, only four nonequivalent Fe sites (with the 12J 3, 11J 3, 10J 3, and 8J 3 interactions) remain. We denote them as the Site-A(12J 3), B(11J 3), C(10J 3), and D(8J 3), respectively. As seen in Fig. 8, the A, B, and D sites maybe present with different probability in both the above mentioned superstructures NC with N = 2 and N ≥ 3, while the D site with 8J 3 interaction may not appear in the NC (N ≥ 3) superstructures.

Based on the above analysis, we conclude that in our Fe1−x S nanoparticles, the values of the magnetic hyperfine fields H hf about 335, 310, 279, and 245 kOe observed for four Mössbauer components at 80 K (see Table 2) correspond to the nonequivalent iron sites A, B, C, and D with the 12J 3, 11J 3, 10J 3, and 8J 3 exchange couplings, respectively. The corresponding room temperature values of H hf, reduced to 300, 280, 260, and 232 kOe, are in a good agreement with the values of the fields for iron ions with 0, 1, 2, and 4 nearest vacancies, respectively, found in the bulk hexagonal Fe0.909S (the sites A, B, and C) and monoclinic Fe0.881S (the sites A, C, and D) compounds (Ovanesyan et al. 1971). The probability of appearance of different type vacancies in the Fe1−x S compounds depends on the vacancy concentration x and on the methods of synthesis. The presence of all four nonequivalent A, B, C, and D iron sites in our nanoparticles at T < 300 K implies a coexistence of two types of superstructures NC with N = 2 and N ≥ 3.

The values of H hf at nonequivalent iron sites, and the supertransferred hyperfine magnetic fields

The H hf field values (of about 350–250 kOe) found in the sulfide Fe1−x S nanoparticles are much lower than the typical values in iron oxides, which are about 550 kOe for Fe3+ ions in the octahedral oxygen coordination (Lyubutin 1969; Lyubutin et al. 1967a, b). This can be explained by different sources of the field in Fe 2+ and Fe3+ ions. The magnetic hyperfine field H hf at iron nuclei is composed of three main contributions (Huang et al. 1966, 1967):

$$ H_{\text{hf}} = H_{\text{c}} + H_{\text{orb}} + H_{\text{STHF}} $$
(2)

(i) The core term H c appears from the core s-shells (of the own Fe ion) which are spin-polarized by the 3d-shell. It is so called the contact Fermi interaction (Watson and Freeman 1961). The H c value in the Fe2+ ions is lower than that in the Fe3+ ions since the d-shell spin of Fe2+ (S = 2) is lower than in Fe3+ (S = 5/2).

(ii) The orbital field H orb appears in Fe2+ from the own non-spherically symmetric 3d 6-electron shell. This term is absent in the Fe3+ ions since the 3d 5 shell is spherically symmetric and its orbital momentum is quenched. The sign of H orb is opposite to the H c term, thus the total H hf field in Fe2+ is still more reduced.

(iii) The term H STHF is so called “supertransferred hyperfine field” (STHF). In antiferromagnets, this field appears at Fe nuclei as a result of the transfer of spin density to the central cation Fe(↑) from neighboring cations having an opposite (antiparallel) spin Fe(↓) via superexchange Fe(↑)–L–Fe(↓), where L is the ligand. The mechanism of creation of the H STHF field was first suggested by Huang et al. (1966, 1967) and further developed by others (Sawatsky and Van der Woude 1974; Van der Woude and Sawatsky 1971; Moskvin et al. 1977a, b; Lyubutin 1992).

The direction of the main field H c is opposite to the iron 3d spin, i.e., the field H c is negative with respect to the iron magnetization (Watson and Freeman 1961). On the contrary, the H orb field is positive, and it reduces the total field value at iron nuclei. The direction of H STHF coincides with the H c direction increasing the total field H hf.

In the nonequivalent iron sites of Fe1−x S, the terms H c and H orb should be similar (at least, at low temperatures) but the H STHF term depends on the number of nearest iron neighbors, and thus it is different for A, B, C, and D sites. Thus, from the Mössbauer data we can conclude that the highest field H hf = 335 kOe (at 80 K) in our Fe1−x S nanoparticles corresponds to the Site-A(12J 3) without any vacancies in the nearest neighboring. One vacancy decreases the field at the Site-B(11J 3) by about 25 kOe; two vacancies reduce the field at the Site-C(10J 3) by about 55 kOe, and four vacancies reduce the field at the Site-D(8J 3) by 90 kOe. An average value of the H STHF term in Fe1−x S can be estimated as (25 ± 3) kOe per one Fe–S–Fe superexchange bond at the angle of 129°.

In oxides, the value of H STHF for Fe in the octahedral sites was evaluated as ~(10–20) kOe at 4.2 K (Lyubutin 1992; Abe et al. 1963; Petitt and Forester 1971; Boekema et al. 1979). It has been shown that the H STHF values in the chalcogen compounds must be essentially higher than in oxides due to the strong covalent bonding between paramagnetic cation and chalcogen ligand (Lyubutin 1992; Lyubutin and Dmitrieva 1975; Okada et al. 1979; Dmitrieva et al. 2007).

Magnetic structure and magnetic sublattices

It is suggested that the magnetic structure of Fe1−x S consists of ferromagnetic iron layers which are antiferromagnetically coupled to each other along the c-axis (Bertaut 1953; Lotgering 1956; Marusak and Mulay 1979, 1980). The total magnetic moment M tot appears from the competition between magnetic moments of neighboring layers, and the material can be AFM or FRM depending on the value of moments of the corresponding sublattices.

The Mössbauer measurements in the external magnetic fields revealed that in Fe7S8 (Levinson and Treves 1968), Fe9S10 (Marusak and Mulay 1979, 1980), Fe0.881S, and Fe0.900S (Ovanesyan et al. 1971) the direction of iron magnetic moments in the layers with vacancies (i.e., the site-A in our case) is opposite to the direction of moments in the layers without vacancies (i.e., the sites B, C, and D). Thus, the total magnetic moment \( M_{\text{tot}} \) of the compound appears as a result of the competition between magnetic moments \( M_{\text{A}} \) and \(\left( M_{\text{B}} + M_{\text{C}} + M_{\text{D}} \right) \) of the corresponding magnetic sublattices. At room temperature the \(\left( M_{\text{B}} + M_{\text{C}} + M_{\text{D}} \right) \) moment value is higher than the \( M_{\text{A}} \) moment, and \( M_{\text{tot}} \) is directed along the moments of the layers without vacancies.

$$ \overrightarrow{M}_{\text{tot}} = \left( {\overrightarrow{M}_{\text{B}} + \overrightarrow{M}_{\text{C}} + \overrightarrow{M}_{\text{D}} } \right) - \overleftarrow{M}_{\text{A}} $$
(3)

Figure 9 shows the most probable ordering of the iron magnetic moments in layers with and without vacancies alternating along the c-axis. The 2C type of the vacancy ordering shown in Fig. 9a provides a FRM state due to incomplete compensation of magnetic moments of the layers with and without vacancies. This type of magnetic structure is consistent with the Mössbauer data (Marusak and Mulay 1979, 1980; Levinson and Treves 1968). The AFM state appears in the 3C superstructure of Fig. 9b because of the complete compensation of the moments in layers with and without vacancies (by paired).

Fig. 9
figure 9

Schematic view of the iron magnetic layers stacked along the c-axis in the NiAs-type crystal structure of Fe1−x S compound for the cases of 2C-type (a) and 3C-type (b) of the vacancy ordering. Directions of magnetization in the layers with vacancies (dashed lines) and without vacancies (solid lines) are shown by arrows. Ferrimagnetic structures (FRM), consistent with the Mössbauer observation, are realized in the (a) case, and antiferromagnetic (AFM) structure appears in the (b) case

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Vacancy redistribution

From the line areas of the Mössbauer components at 80 K we found that the occupation of the nonequivalent iron sites A, B, C, and D are in the ratio 1:1:1:0.5, respectively. At room temperature, the occupation of the C site slightly increases at the expense of the A and B sites. Heating the sample to the temperature 470 K, where maximum magnetization was observed in the magnetic measurements, reveals a considerable redistribution of the Mössbauer line areas. An essential increase in the occupations of the site-D was observed, while the occupation of the B site is reduced, and the occupation of the A and C sites remains almost unchanged. This shows an increase in the number of Fe ions with weaker exchange interactions 8J 3 and the reduction of Fe ions with the 11J 3 interaction.

The above analysis (“Nonequivalent iron sites” section) shows that Fe ions with 11J 3 couplings at B-sites mainly exist in the superstructures where layers with vacancies are well separated from each other by two or more layers without vacancies (see Fig. 8a). We discern these type superstructures as NC type with N ≥ 3. On the other hand, the D(8J 3 ) sites may appear only in the superstructures where vacancies locate in every second iron layer along c-axis (Fig. 8b), and we discern these type of vacancy ordering as the 2C superstructure.

Thus, from the Mössbauer data we can conclude that upon heating the Fe1−x S nanoparticles to 470 K, the vacancy ordering changes from the NC (N ≥ 3) type superstructure to the 2C type. As a result of vacancy redistribution, the AFM state (Fig. 9b) transforms to a FRM state (Fig. 9a), thus increasing the magnetization of the compound. In reality, as follows from the Mössbauer data, a mixture of both coexisting phases maybe present at all temperatures with different weights.

Above the Néel temperature (T > 570 K), the Mössbauer spectrum consists of a single doublet with broaden lines (Fig. 3). The nonequivalent iron sites are not detected in the paramagnetic temperature region. From the magnetic measurements, we found that upon subsequent cooling of the sample from 600 to 300 K the magnetization almost did not change and remains negligible (Fig. 6b). Meanwhile the Mössbauer spectrum, obtained at 300 K after heating the sample to 650 K, shows hyperfine magnetic spitting of the spectral lines typical of iron magnetic ordering. These data indicate that after heating above the Néel temperature, the material becomes a pure antiferromagnet and remains in that state down to 300 K. This effect can be explained by a random distribution of vacancies (over all iron layers) at high-temperatures which leads to the total compensation of the magnetic moments in neighboring layers. A single doublet with broaden lines in the Mössbauer spectrum at 650 K supports the random distribution of vacancies. The broaden lines associated with the random distribution of vacancies were also observed in several literature (Knodoro 1999; Kruse 1990; Knodoro and Kiwanga 1997).

It was found in the previous studies of the hexagonal pyrrhotites (Li and Franzen 1996) that the value of magnetization measured in the cooling regime was higher than that at the sample heating. On the contrary, in our case the magnetization of heating branch is clearly higher than the cooling one. In the heating regime, a small increase of magnetization at temperatures above 400 K was recently observed in the Fe0.92S compound (Kim et al. 2009). This effect was explained by the rearrangement of vacancies but the Mössbauer data of the authors (Kim et al. 2009) show that the rearrangement starts at 570 K which is close to the Néel temperature. The peak-like transition behavior has been found in pyrrhotite group with composition Fe9S10 which has a hexagonal closed-packed structure, and it was explained in terms of a vacancy rearrangement (Marusak and Mulay 1979, 1980).

Conclusion

The iron sulfide Fe1−x S nanoparticles with the shape of hexagonal plates or disks were successfully prepared by thermal decomposition method. At room temperature the compounds have the NiAs-type crystal structure. The Mössbauer spectroscopy and magnetic measurements data indicate that a mixture of AFM and FRM phases with the NC (N ≥ 3) and 2C-type superstructures is present in the Fe1−x S compound at temperatures between 80 and T N. At T < 370 K, the AFM phase prevails over the FRM phase. Upon the sample heating, the redistribution of iron vacancies at T > 370 K takes place and the vacancy ordering of the NC-type (N ≥ 3) transforms to the ordering of the 2C-type which essentially increases the magnetization. Heating the sample above the Néel temperature 565 K leads to a random distribution of vacancies, and this state is quenched upon subsequent cooling of the sample to 300 K. This gives rise to a pure AFM structure with a zero magnetic moment due to the total compensation of the moments in neighboring iron layers. Thus, the high-temperature redistribution of cation vacancies leads to irreversible magnetic transitions in the Fe1−x S nanodisks. We believe that these interesting magnetic properties of the nanoparticles would find useful applications in technical devices.