Effect of anion substitution onto structural and magnetic properties of chromium chalcogenides

Progress in Solid State Chemistry 37 (2009) 226–242

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Effect of anion substitution onto structural and magnetic properties of chromium chalcogenides Joseph Wontcheu a, c, Wolfgang Bensch a, *, Sergiy Mankovsky b, Svitlana Polesya b, Hubert Ebert b a

Institute of Inorganic Chemistry, Christian-Albrechts-University Kiel, Max-Eyth-Str. 2, D-24118 Kiel, Germany Department of Chemistry, LMU Munich, Butenandstr. 3-13, D-81377 Munich, Germany c Department of Chemistry, University of Montreal, 2900 Boulevard Edouard-Montpetit, Montreal, QC, H3T 1J4, Canada b

a b s t r a c t Keywords: Chromium chalcogenides Anion substitution Rietveld refinement Magnetic properties Spin-glass SPR-KKR Band-structure calculations

We investigated experimentally and theoretically the effect of the substitution of Te by Se onto the structural, magnetic and electronic properties of ferromagnetic Cr5xTe8 as parent material. Whereas Cr5Te8 is dimorphic crystallizing in a monoclinic and trigonal modification, Se substituted samples crystallize in two different trigonal modifications depending on the synthesis conditions. One of the modifications can be viewed as self-intercalated dichalcogenides Cr1þxQ2 (Q ¼ Te, Se) and the other is a superstructure which is isostructural to one of the Cr5xTe8 modifications. For the Se richest samples (Te:Se ¼ 1:7) a new modification is identified which was formerly reported for Cr3þxSe4. For a distinct Cr content the replacement of Se by Te induces a reduction of the unit cell volumes, of the Cr-Cr and Cr-Te/ Se distances. Increasing the Cr content for a constant Te:Se ratio has the opposite effect. The results also suggest that the homogeneity range extends to more Cr rich compounds with decreasing Te content. For a given Cr content the substitution of Te by Se weakens the ferromagnetic exchange interactions and strengthens the antiferromagnetic exchange. With increasing Cr content and a fixed Te:Se ratio ferromagnetic properties become more pronounced. The low temperature magnetic behavior is characterized by spin-glass, spin-glass like or cluster-glass properties depending on the Cr content and the Te:Se ratio. Electronic structure calculations done within the framework of LSDA (local spin density approximation) gave a detailed insight into the electronic and magnetic properties of the investigated systems supporting the interpretation of the achieved experimental results. This applies in particular for the calculated exchange coupling constants that provided the necessary input for Monte Carlo simulations used for theoretical investigations on the magnetic properties at finite temperatures. Ó 2009 Elsevier Ltd. All rights reserved.

Contents 1. 2.

3.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 Overview about the influence of the substitution of Te by Se in Cr5þxTe8-ySey on the structural and magnetic properties with focus on compounds with y¼1–3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 2.1. Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 2.2. Theoretical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 Structural and magnetic properties of Cr1þxTe0.75Se1.25 (x¼0.3, 0.33, 0.37) and Cr1þxTe0.25Se1.75 (x¼0.36 and 0.40) with Te:Se ratios 3:5 and 1:7 . . 234 3.1. Experimental details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 3.1.1. Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 3.1.2. Composition analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 3.1.3. X-ray powder diffraction and Rietveld refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 3.1.4. Magnetic measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 3.2. Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 3.2.1. Structures of Cr1þxTe0.75Se1.25 (x¼0.3, 0.33, 0.37) and Cr1þxTe0.25Se1.75 (x¼0.36 and 0.40) with Te:Se ratios 3:5 and 1:7 . . . . . . . . . . . . 236

* Corresponding author. Present address: Christian-Albrechts-University zu Kiel, Institut fur Anorganische Chemie, Olshausenstr.40-60, 24098 Kiel, Germany. Tel.: þ49 431 880 2091; fax: þ49 431 880 1520. E-mail address: [email protected] (W. Bensch). 0079-6786/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.progsolidstchem.2009.11.001

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3.2.2. Magnetic properties of Cr1þxTe0.75Se1.25 (x¼0.3, 0.33, 0.37) and Cr1þxTe0.25Se1.75 (x¼0.36 and 0.40) with Te:Se ratios 3:5 and 1:7 . . 237 3.2.3. Theoretical investigations of Cr1þxTe0.75Se1.25 (x¼0.3, 0.33, 0.37) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 Summary and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240

1. Introduction The motivation to investigate the structural and magnetic properties of anion substituted chromium chalcogenides was inspired by several interesting observations. The structures of the chromium chalcogenides are simple and may be derived from the NiAs type structure by ordered removal of Cr atoms according to distinct compositions. A distorted hexagonal close packing of Te atoms contains Cr atoms in octahedral interstices. The Cr vacancies occur in every second metal layer, and thus the metal-deficient and metal-full layers stack alternatively along the c-axis. The CrQ6 octahedra share common edges within the fully occupied layers, the octahedra in neighbored layers share common faces. This connection scheme results in relatively long Cr-Cr separations within the layers and short distances between Cr atoms in the face sharing octahedra. The magnetic properties of the Cr chalcogenides are governed by the actual chemical composition, i.e., the presence of Cr2þ (d4), Cr3þ (d3) and/or Cr4þ (d2). The superexchange interaction via Cr-Q-Cr predominates within the full metal atom layers whereas direct exchange interactions can be expected across the face sharing CrQ6 octahedra. The strength of the magnetic exchange interactions is related to the electronic configuration of the Cr ions and the size of the anions which increases from S2- to Te2-. For some compositions the crystal symmetry is reduced from the hexagonal symmetry of NiAs. Most Cr sulfides, selenides and tellurides crystallize in very similar structures with only a few exceptions (see below). The main structural and physical properties of the chromium chalcogenides are shortly summarized in the next section. Special attention is drawn on Cr5Te8 because this phase is the parent material where the effects of anion substitution were investigated in detail. The main results of the substitution of Te by Se are presented after the short review of the properties of the chromium chalcogenides. The monosulfide Cr1-xS crystallizes monoclinic in a narrow composition range and for T < 623 K [1,2]. A superstructure of the NiAs type structure is observed for Cr5S6 [1,3] and Cr7S8 exists in a narrow homogeneity range [1,4]. Monoclinic Cr3S4 crystallizes in the 2c type of the Fe3S4 structure [1,5]. The sesqui-sulfide Cr2xS3 is dimorphic with a trigonal and rhombohedral modification [1] and the transition from one to the other modification depends on x [1]. The monoclinic Cr5S8 can only be prepared under high temperature and high pressure conditions [6,7]. Amorphous CrS3 crystallizes in a Patronite like structure [8]. For Cr5S6 ferrimagnetic properties with a Tc of about 300 K are observed. Interestingly, below 160 K the spontaneous magnetization disappears and a helical spin arrangement occurs with antiferromagnetic behavior [4,9,10]. The magnetization strongly depends on the synthesis procedure and quenching the sample from the reaction temperature reduces the spontaneous magnetization by one order of magnitude [11]. For Cr7S8 ferrimagnetic properties dominate between 280 and 125 K with an antiferromagnetic component being also present [4]. Cr3S4 shows metallic properties and exhibits a Ne´el-temperature TN between 200 K and 280 K strongly depending on the actual composition and thermal history [12–14]. The sesqui-sulfide Cr2S3 is ferrimagnetic (Tc z 130 K) with a broad maximum of the magnetization at about 80 K (Tm) [15]. Below Tm a normal

ferrimagnetic structure results and for T > Tm the magnetic moments are slightly canted [16]. Minute deviations from the stoichiometric ratio 2:3 in Cr2S3 lead to colossal magnetoresistance behavior [17]. In contrast to the sulfide, the Cr deficient Cr1-xSe phase crystallizes with hexagonal symmetry [18,19], Cr7Se8 is dimorphic with a hexagonal [20] and a monoclinic modification [19,21,22]. Stoichiometric Cr2Se3 crystallizes in a rhombohedral structure and trigonal symmetry is found for non-stoichiometric samples [16,19,21–25]. Monoclinic Cr3xSe4 [12,19,21,22,27–31] exhibits a relatively large homogeneity range and was reported to be stable for about x  0.20 [29,30]. Like the analogous sulfide, Cr5Se8 (monoclinic symmetry) can only be synthesized under high-pressure and high-temperature conditions [6]. Using a metathesis reaction, CrSe2 with the typical layered dichalcogenide structure can be prepared using KxCrSe2 as starting material [32]. Two phase transitions at about 164 K and 186 K were reported which are accompanied by a periodic charge density wave (CDW) transition [32]. Cr1-xSe and Cr7Se8 are conductors whereas Cr3Se4 and Cr2Se3 are semiconductors with small electronic band gaps Eg [20]. Cr-rich Cr3þxSe4 exhibit a temperature dependence of the conductivity typical for a poor metal [29]. For the semiconductor Cr2Se3 Eg is about 0.84 meV between 80 and 150 K and increases to 2.64 meV between 150 and 250 K [33]. For Cr3þxSe4 with x > 0 antiferromagnetic ordering is observed whereas for x < 0 metaor ferromagnetism occurs [29]. In the Cr rich region the introduction of Cr2þ(d4) ion leads to a static Jahn-Teller distortion and the total magnetic moment exhibits an appreciable contribution of the orbital momentum of the Cr2þ ions [29]. The Ne´el temperature of Cr2Se3 is between 47 K [24] and 43 K [8,15,17]. Neutron scattering experiments revealed that an antiferromagnetic low-temperature structure (LTAF) and an antiferromagnetic high temperature structure (HT-AF) exists, with the transition temperature at about 45 K. The LT-AF structure is characterized by a non-collinear arrangement of the spins and the resulting monoclinic structure can be described as a 24 layer structure. The HT-AF phase exhibits a collinear arrangement with all axes of the magnetic cell being doubled compared to the nuclear cell [26]. Monoclinic Cr3Se4 is a metal [33] and finally, metallic behavior was reported for Cr5Se8 [6]. Only little is known about the magnetic properties of the latter compound. The susceptibility curve passes a broad maximum indicating strong short-range antiferromagnetic exchange interactions [6]. The investigations of chromium tellurides started in the 1930s when ferromagnetism of ‘CrTe’ was discovered [34,35]. Several well characterized phases with compositions Cr1-xTe, Cr3Te4, Cr2Te3, and dimorphic Cr5Te8 are known [36–43]. There are also reports about the existence of Cr5Te6 (monoclinic) [40,44], Cr7Te8 (monoclinic) [45,46] and hexagonal Cr7Te8 (hexagonal) [46]. But according to the Cr-Te phase diagram the existence of these phases is questionable [36]. All these compounds crystallize in the NiAs-type structure with ordered metal vacancies [38–43] and the distribution patterns of Cr vacancies depend on the Cr concentration and on the thermal history. All Cr tellurides are ferromagnetic with the Curie temperatures Tc varying between 180 and 340 K, which decreases under high pressure [34,35,47–52]. The values for Tc sensitively depend on the composition and for Cr3Te4 they range from 315 to about 350 K [12,14,41,47,52–56].

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The magnetic moments of the Cr tellurides in the composition range CrTe to Cr2Te3 estimated from saturation magnetization measurements are smaller than the moments calculated using an ionic model. Several explanations like spin canting [40–42,57–59], non-collinear spin arrangement [52], or a canted antiferromagnetism [53] were given. Band-structure calculations [2,52] demonstrate that the Cr 3d–Te 5 p covalency and the Cr 3d2z -Cr 3d2z overlap along the c-axis are the most important interactions in CrTe, Cr3Te4 and Cr2Te3. They show also metallic conductivity [2,60]. The two Te rich phases CrTe2 (hexagonal) [61] and CrTe3 (monoclinic) [62] were also reported. Both structures are layered and the latter compound is a polytelluride with Cr3þ. Contrary to Cr5S8 and Cr5Se8, the analogous telluride Cr5Te8 is dimorphic and can be prepared in a high temperature reaction without applying pressure. The monoclinic variant m-Cr5Te8 (space group: F2/m; 61.54 at% Te) is stable at low synthesis temperatures whereas the trigonal modification tr-Cr5Te8 (space group: P-3m1 [43]) is formed by quenching the samples from about 1075 K to room temperature [36]. According to different studies the homogeneity range of tr-Cr5Te8 is between 61.8 and 62.5 at% Te [63] or 61.8 and 63.6(6) at% Te [64], i.e. in the Cr poor region of the phase diagram. In contrast to many other transition metal chalcogenides with composition M5Q8 (M ¼ V, Ti, Cr; Q ¼ S, Se, Te) [6,7,65–72], Cr5Te8 is dimorphic and the monoclinic modification does not crystallize in the monoclinic V5S8 structure type. In m-Cr5Te8 four unique metal atom sites are present whereas in V5S8 only three unique sites were found (see Fig. 1, top). The sites M2 and M3 are fully occupied whereas M1 and M4 are only partially occupied. In the structure of tr-Cr5Te8 the Cr centers occupy also four different unique sites with M2 and M3 being fully occupied and M1 and M4 are only partially (Fig. 1, bottom). In m-Cr5Te8 the chalcogen atoms are distributed over three crystallographically unique sites and in tr-Cr5Te8 over four sites. As mentioned above all Cr chalcogenides are characterized by long Cr-to-Cr distances within the fully occupied layers and short Cr-Cr separations are found between Cr centers of face sharing CrQ6 octahedra. The magnetic properties of m- and tr-Cr5Te8 are of special interest. Above 300 K the susceptibilities follow a Curie–Weiss law with large positive values for the Weiss constant and magnetic moments in accordance with a Cr3þ 3d3 spin configuration. Below room temperature both phases undergo a transition into the ferromagnetic state with a Curie temperature Tc sensitively depending on the Cr content. For Cr rich m-Cr5.016Te8 the value for Tc is about 190 K whereas for the Cr poor sample tr-Cr4.876Te8 Tc is with 245 K remarkable higher [73]. It was assumed that less effective superexchange interactions and a larger amount of antiferromagnetically coupled Cr centers are responsible for these findings. Later on a neutron scattering study performed on m-Cr5Te8 revealed the coexistence of ferromagnetic and antiferromagnetic long range order [74]. At about 180 K ferromagnetic order sets in with the magnetic moments being directed along the c-axis. A canted magnetic structure with a ferromagnetic component along the c-axis and an antiferromagnetic component in the ab-plane occurs below 70 K [74]. A highly anisotropic temperature behavior of the lattice parameters and of the thermal expansion tensor of m-Cr5Te8 suggests a strong correlation between the bulk and microscopic magnetic properties. The c-axis exhibits a remarkable contraction with decreasing temperature whereas the a- and b-axes show a small expansion. The contraction of the c-axis leads to a shortening of the Cr-Cr distance between Cr atoms of face-sharing CrTe6 octahedra indicating stronger bonding interactions [74]. Low temperature magnetization experiments show the typical behavior of soft ferromagnets with saturation at low field and low values for the remanences as well as for the coercitive fields [73]. The values for the

Fig. 1. The structure of m-Cr5Te8 (top) and of tr-Cr5Te8 (bottom). Note that all Cr atoms are in an octahedral environment of Te atoms. Only two CrTe6 polyhedra are drawn showing the face-sharing connection of the polyhedra located in neighbored metal atom layers. For further details see text.

saturation magnetization are only 72% and 65% for m-Cr5Te8 and trCr5Te8, respectively. On the basis of the neutron scattering experiments these low values can partially be explained on the basis of antiferromagnetically coupled Cr(III) d3 centers. We note that photoemission experiments performed on a Cr5Te8 sample indicate that this material is an itinerant ferromagnet [75]. Interestingly, the sample investigated showed trigonal symmetry with lattice parameters a ¼ 3.924 and c ¼ 6.008 Å, which are typical values of dichalcogenides. Since a few years there is a renewed interest in Cr chalcogenides, especially metastable compounds are in the focus of interest. For CrTe in the zinc-blende modification half-metallic ferromagnetism was predicted making this compound interesting for spintronics applications [76]. Very recently this metastable modification could be prepared as a thin film [77]. 2. Overview about the influence of the substitution of Te by Se in Cr5DxTe8-ySey on the structural and magnetic properties with focus on compounds with y [ 1–3 2.1. Experimental results In several publications we reported on the influence of the partial substitution of Te by Se in Cr5þxTe8 on the crystal structure and the magnetic properties [78–80]. In the present section we

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summarize the results obtained until now and proceed presenting new structural and magnetic data acquired for more Se rich compounds. All samples with Te:Se ratios 7:1, 6:2, and 5:3 were prepared applying the desired amounts of elemental Cr, Te, and Se [78–80]. The syntheses were performed in evacuated and sealed quartz ampoules. Despite a large number of syntheses using different temperatures, reaction times, heating and cooling rates, the monoclinic variant of Cr5Te8 could not be obtained. Instead two different trigonal modifications were identified. One modification crystallizes in a trigonal basic cell which can be regarded as the high temperature (HT) modification. The structure of these compounds can be viewed as a self-intercalated dichalcogenide. This situation is described by the formula Cr1þxQ2 (Q ¼ Te, Se) (see Fig. 2). For the preparation of these compounds the mixtures were heated to 1223– 1273 K with a heating rate of 100 or 20 K/h. The samples were held at this temperature for 4 to 6 days and they were then cooled to 1073 K with 100 K/h. At this temperature the compounds were either annealed for another two days or were directly quenched into cold water. The second modification is isostructural with tr-Cr5Te8 and the general formula of this low temperature modification (LT) is Cr5þxQ8. The samples were obtained by heating the compounds Cr1þxQ2 to 1223 K (heating rate: 100 K/h), held at this temperature for 2 days followed by a cooling to 723 K (cooling rate: 16 or 20 K/h). After annealing at this temperature for 6 days the samples were quenched into a water bath. All products were carefully examined with X-ray powder diffractometry and the chemical compositions were determined with ICP-OES. The structures were refined with the Rietveld method (technical details were reported in [78–80]). In the HT modification of the compounds there is only one crystallographic position for the chalcogenide atoms and two for the Cr atoms (Fig. 2). Therefore, the Q atoms are statistically distributed over the unique site. According to the results of the Rietveld refinements of the X-ray powder patterns one of the Cr positions is fully occupied (Cr1) and the second site Cr2 hosts the additional x Cr atoms, i.e., with increasing concentration x Cr2 is successively filled. This experimentally observed finding with the preferable complete occupation of Cr1 sites in Cr1þxQ2 and with an incomplete occupation of Cr2 sites has been studied by performing electronic structure calculations for systems with different Te:Se ratios [78,79]. Within this theoretical work in particular ab-initio total energy calculation were performed. As an example the result

of the calculations for Cr1.27Te1.5Se0.5 (Te:Se ratio ¼ 6:2) is shown in Fig. 3. Note that the energy calculations were done with a fixed Cr content. To find an equilibrium distribution for the Cr atoms distributed over the two unique crystallographic sites (see Fig. 2) the occupancy of the two sites was continuously varied. The initial state was the state with a fully occupied Cr1 site 1 and a partial occupation of Cr2 with 0.27 Cr atoms. The other configurations considered were obtained by transferring of a distinct amount d Cr from site Cr1 to site Cr2. As can be seen from Fig. 3 even the transfer of d ¼ 0.05 Cr increases the total energy of the system making it energetically less favorable. The results of the calculations are in full agreement of the experiments demonstrating that the most stable configuration is that with a fully occupied Cr1 site. In the structure of tr-Cr5þxQ8 (see Fig. 1, bottom) the Cr atoms occupy four different sites and the Q atoms are distributed over four unique positions. Careful examination of the X-ray powder patterns with the Rietveld method gave no hints for any ordering of the Te and Se, i.e., they are statistically distributed keeping in mind the accuracy of the Rietveld approach. As noted above the two metal atom sites Cr2 and Cr3 are fully occupied whereas the remaining two positions are only partially filled by Cr atoms. With increasing Cr content x the two partially occupied sites are successively filled. Substitution of the large Te by the smaller Se atom leads to a contraction of the unit cell volume. For instance, comparing the lattice parameters of Cr1.37Te1.25Se0.75 (Te:Se ¼ 5:3) with those of Cr1.36Te1.5Se0.5 (Te:Se ¼ 6:2) shows a net decrease with increasing Se content. The values for the lattice parameters a, c and V are 3.843, 6.046 Å and 77.32 Å3 for Cr1.36Te1.5Se0.5 (Te:Se ¼ 6:2) and 3.800, 6.029 Å, and 75.41 Å3 for Cr1.37Te1.25Se0.75 (Te:Se ¼ 5:3). On the other hand, the unit cell volumes and the lattice parameters exhibit a linear increase with increasing Cr content for Te:Se ¼ 7:1 and 6:2 [78,79], whereas slight discontinuities were observed for Te:Se ¼ 5:3 [80]. This non-linear behavior for the latter series of compounds may be caused by the increasing occupancy of the partially occupied Cr sites. The Cr content of the phases extends to larger values with increasing Se content. For Te:Se ¼ 7.1 only three samples Cr1þxQ2 with x ¼ 0.23, 0.26 and 0.30 could be prepared as phase pure materials. Changing the ratio to 6:2 the upper limit increased to x ¼ 0.36. Finally, for Te:Se ¼ 5:3 a sample with x ¼ 0.43 could be synthesized as phase pure material. Analogously, the maximal Cr content in Cr5þxQ8 increased to x ¼ 0.72 for Te:Se ¼ 5:3.

Fig. 2. The unit cell of Cr1þxQ2 showing two face-sharing CrQ6 octahedra.

Fig. 3. Change in total energy DE with the number of Cr atoms dCr moved from sublattice Cr1 to Cr2 for Cr1.27(Te,Se)2 (Te:Se ¼ 6:2). dCr ¼ 0 corresponds to a complete occupation of site Cr1, while dCr ¼ 0.365 corresponds to an equal occupation of both sites. Reprinted from Ref. [79] with permission from Elsevier, Copyright 2009.

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In the formal ionic picture the 16 negative charges in Cr5Te8 must be balanced by 1 Cr4þ (d2) and 4 Cr3þ (d3) cations. It is assumed that Cr5S8 and Cr5Se8 can only be prepared under highpressure and high-temperature conditions because Cr4þ is unstable in an S2-/Se2- environment. Cr5Te8 can be synthesized without high-pressure but the existence of a Cr4þ cation in the presence of Te2- is highly unlikely. However, it is was demonstrated in several contributions that Te-Te distances as long as about 3.8 Å may lead to weak bonding interactions [81,82]. In m-Cr5Te8 and tr-Cr5Te8 the Te-Te separations are significantly shorter than 3.8 Å. Such Te-Te interactions may reduce the negative charge on the Te anions, i.e., the top of the Te sp bands having some antibonding character is depopulated and the Te-Te distances are shortened. In addition, the Te-Te contacts may suggest an electron transfer from the sp anion to the d cation electronic states. Short Cr-Cr distances of about 3 Å are also indicative for weak metal-metal bonds which further reduce the positive charge on the Cr cations. In all compounds Cr-Cr distances between Cr atoms located in face-sharing CrQ6 tetrahedra range from about 3 to 3.10 Å with a tendency to an elongation with increasing Cr content. Applying again the ionic picture for Cr1þxQ2 and Cr5þxQ8 phases with x > 0.333 the presence of Cr2þ (d4) must be postulated. The detailed analysis of the geometric parameters give no hints that this Jahn-Teller ion is localized on one of the metal atom sites. However, there is a tendency for longer average Cr-Q bond lengths with increasing Cr content for a given Te:Se ratio. The ionic radius of Cr2þ is larger than that of Cr3þ and the elongation of the Cr-Q bonds may be regarded as a hint for the introduction of Cr2þ. One should stress that the formalism of ionic valences seems to be inadequate approach for the description of the bonding situation in the present samples. considerations often help to get some hints for the explanation of structural changes and of alterations of physical properties when the composition of a compound is changed. Partial charge transfer from Q to Cr and pronounced p-d hybridization may better account for the real electronic situation. The main findings of the structural changes introduced by the substitution of Te by Se may be summarized as follows:  Even in the Cr rich region the monoclinic modification of Cr5Te8 could not be prepared  For a given Cr content the lattice parameters and unit cell volumes decrease with increasing Se content  For a distinct Te:Se ratio the axes and the unit cell volumes are enlarged with increasing Cr concentration

 The maximal Cr content increases with increasing Se concentration  The Cr-Q bond lengths slightly increase with increasing Cr content for a distinct Se concentration  The Cr-Cr distances between Cr atoms in face-sharing CrQ6 octahedra are also enlarged with increasing Cr content for a distinct Te:Se ratio The magnetic properties chromium tellurides are strongly influenced by the replacement of Te atoms by Se atoms and the Cr content. Furthermore, significant differences are also found between compounds crystallizing in the HT or LT modification. All phases show a Curie-Weiss behavior in the high temperature region with effective magnetic moments being larger than expected for pure spin-only contributions, i.e., the experimentally determined meff/Cr exceeds 3.87 mB. But this result is not surprising because for many Cr chalcogenides the value for meff per Cr atom strongly deviates from the spin-only values [83]. Such an enlarged magnetic moment was explained by an electron transfer from Q to Cr via d-p hybridization [75]. The Weiss constant q can be seen in a first approximation as a measure of the sum of the nearest neighbor exchange interactions, P q ¼ SðS þ 1Þ=3kB zi Ji with zi being the number of nearest neighi bors interacting with exchange Ji. The change of q as function of the Te:Se ratio, the Cr content and the crystal structure reflects the influence of these three parameters on the magnetic properties of the samples. With increasing Se content the values for q become less positive indicating stronger antiferromagnetic exchange interactions. The substitution of Te by Se shortens the distance between neighbored Cr centers being located in CrQ6 octahedra sharing common faces (Cr1-Cr3 and Cr2-Cr4 in the HT case and Cr1-Cr2 in the LT compounds, see Figs. 1 and 2) thus strengthening the antiferromagnetic exchange interactions. On the other hand for a distinct Te:Se ratio the value for q becomes more positive with increasing Cr content due to stronger ferromagnetic exchange interactions. An example for the change of the value of the Weiss constant q with increasing Cr content is shown in Fig. 4. The values for q drastically decrease from about -43 K for Cr1.25Te1.25Se0.75 to 175 K for the most Cr-rich sample Cr1.43Te1.25Se0.75 [80]. The analogous data for the samples crystallizing in the LT modification differ only slightly from those determined for the HT compounds (-47 to 179 K). The change of the sign of q as function of the Cr content in the samples is a clear indication for a shift from predominant antiferromagnetic exchange for compounds with a lower Cr concentration

200 C r(1 +x)T e1 .2 5S e0 .7 5 C r(5 + x)T e 5S e0 .7 5

150

θ /K

100

50

0

-5 0 0.25

0.30

0.35

0.40

0.45

C r c o n te n t x in C r(1 +x)T e1 .2 5 S e0 .7 5 a n d C r(5 + x)T e 5S e 3 Fig. 4. Evolution of the q value with in creasing Cr content for the substitution series with Te:Se ¼ 5:3. Reprinted from Ref. [80] with permission from Elsevier, Copyright 2009.

J. Wontcheu et al. / Progress in Solid State Chemistry 37 (2009) 226–242

0.07

second cation and a doubly occupied p orbital of the anion are involved. The strength of the ferromagnetic interaction depends on the angle Cr-Q-Cr and values near 90 yield stronger interactions. Because both the direct antiferromagnetic and the indirect ferromagnetic exchange are simultaneously present in the compounds, the final magnetic properties are governed by the Te/Se as well as the Cr content and the crystal structures due to the different interatomic distances and Cr-Q-Cr angles in the HT and LT modifications. For canonical spin-glasses the fc curve below the glass or freezing temperature Tf is almost flat [84] whereas a continuous rise of the fc trace below Tf indicates the presence of larger magnetic clusters and the magnetic behavior of such compounds is better described as a cluster-glass [85]. Fig. 5 shows the susceptibility curves for the two compounds Cr5.12Te5Se3 and Cr1.28Te1.25Se0.75 for which the Weiss constant q is near zero, i.e., ferromagnetic and antiferromagnetic exchange interactions are nearly compensating. Analyzing the curves in Fig. 5 several experimental findings are obvious. The magnetization of the LT material is lower than for the HT modification. The temperature where the irreversibility occurs is higher for the HT than for the LT compound and below the freezing temperature the fc curves are almost flat indicating of spin-glass behavior. Above the irreversibility the ZFC and FC curves match perfectly which is another indication for spin-glass or spin-glass like properties of the compounds. The ZFC curve of Cr1.28Te1.25Se0.75 shows a relatively sharp cusp whereas for Cr5.12Te5Se3 the ZFC trace is rounded (Fig. 5). Such different shapes of the curves may be a result of differing interatomic interactions defining the magnetic ground state of the frustrated systems. Ac susceptibility measurements are a powerful method for the study of spin systems in more detail. Assuming a spin-glass state, the curves of the real (c’) and imaginary part (c’’) of the ac susceptibility should present a sharp and frequency dependent cusp around the freezing temperature. Ac susceptibility measurements performed on such compounds exhibit the typical frequency dependence of the freezing temperature Tf. As an example the c’ curves measured at different frequencies in a field of 5 Oe are displayed in Fig. 6 for Cr5.12Te5Se3 (left) and Cr1.28Te1.25Se0.75 (right). The curves for the two compounds exhibit different shapes where the triangle-like shape observed for Cr1.28Te1.25Se0.75 is more consistent with a so-called canonical spin-glass [84]. In addition the maximum in the c’ vs. T curves occur at higher temperatures for Cr1.28Te1.25Se0.75 (Tf z 47 K, 1000 Hz) than for Cr5.12Te5Se3 (Tf z 24 K, 1000 Hz). This remarkable difference of the freezing temperature reflects the strong influence of the crystal structure on the magnetic ground state because both samples have an identical Cr:Te:Se ratio. Assuming that the maximum in the c’ curves defines the freezing

Cr1.28Te1.25Se0.75 (ZFC) Cr1.28Te1.5Se0.75 (FC)

0.06

M (emu Oe/g)

Cr5.12Te5Se3 (ZFC)

0.05

Cr5.12Te5Se3 (FC)

0.04 0.03 0.02 0.01 0

20

40

60

80

231

100

T (K) Fig. 5. Zero field cooled (ZFC) and field cooled (FC) magnetization curves for the two compounds Cr5.12Te5Se3 and Cr1.28Te1.25Se0.75. The magnetic data were measured at an external field of 0.1 T. Reprinted from Ref. [80] with permission from Elsevier, Copyright 2009.

to ferromagnetic exchange interaction for the Cr richer materials. This observation can be explained analyzing the alteration of the Cr– Cr distance between metal atoms located in adjacent layers: for the Cr1þxTe1.25Se0.75 series an increase from 2.99 to 3.03 Å for x ¼ 0.25 to x ¼ 0.43 and for Cr5þxTe5Se3 from 3.05 to 3.12 Å (x ¼ 0.00 to x ¼ 0.72) was observed [82]. Because such short Cr–Cr contacts favor antiferromagnetic exchange interactions the elongation with increasing Cr content weakens this interaction. We note that similar experimental findings were made for the other Te:Se ratios investigated so far [78,79]. The low temperature magnetic properties of all samples are characterized by an irreversibility in the zero field cooled (ZFC) and field cooled (FC) magnetization curves. All compounds with low Cr contents display a spin-glass or spin-glass like behavior irrespective of the Te:Se ratio. The spin-glass state of a material is caused by structural disorder and competing antiferromagnetic and ferromagnetic exchange interactions leading to magnetic frustration. In the Se substituted Cr tellurides a partial disorder of Cr atoms over the different crystallographically independent sites which are partially occupied and a statistical distribution of Te and Se atoms over the unique sites are observed. The replacement of Te by Se changes the Cr-Cr distances across the CrQ6 octahedra sharing common faces introducing a stronger antiferromagnetic exchange interaction competing with the Cr-Q-Cr superexchange which is ferromagnetic in nature. In such a superexchange interaction a partly-filled t2g orbital of one cation, an empty eg orbital of the

7.0 4.2 6.5 6.0

3.8

10 Hz 100 Hz 1000 Hz

3.6

-4

χ ' (10 emu/g)

4.0

3.4

5.5

10 Hz 100 Hz 1000 Hz

5.0

3.2

4.5

3.0 10

15

20

25

30

T (K)

35

40

45

50

30

35

40

45

50

55

60

T (K)

Fig. 6. Frequency dependence of the real part of the ac susceptibilities of Cr5.12Te5Se3 (left) and Cr1.28Te1.25Se0.75 (right) measured at different frequencies (see insets) in a field of 5 Oe. Reprinted from Ref. [80] with permission from Elsevier, Copyright 2009.

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Fig. 7. Frequency dependence of 1/Tf for Cr1.28Te1.25Se0.75 (top) and for Cr5.12Te5Se3 (bottom). Reprinted from Ref. [80] with permission from Elsevier, Copyright 2009.

temperature Tf, the frequency dependence of Tf is usually characterized by the term DTf/[Tf$D(logn)] (n is the frequency applied). For Cr1.28Te1.25Se0.75 the value is 0.011 and for Cr5.12Te5Se3 z 0.07 which are both in the range 0.004–0.080 reported for spin-glasses [84]. The spin-glass character of the two compounds Cr1.28Te1.25Se0.75 and Cr5.12Te5Se3 is further evidenced by the frequency shift following the empirical Vogel-Fulcher law with a significantly larger frequency dependence on 1/Tf for Cr5.12Te5Se3 than for Cr1.28Te1.25Se0.75 (Fig. 7). The Vogel-Fulcher law is widely accepted to describe spin-glasses with magnetically interacting clusters thus distinguishing the spin-glass behavior from that of a superparamagnetic material [see for instance: [86] The Cr rich samples are characterized by cluster-glass or ferromagnetic behavior. Coming from the high temperature side the magnetization steeply increases with decreasing temperature and then exhibit only a moderate increase with decreasing temperature. In Fig. 8 the susceptibility curves for Cr1.37Te1.25Se0.75 and

Cr5.48Te5Se3 are displayed showing the different behavior to the Cr poorer samples presented above. An explanation for the rapid increase of the magnetic susceptibility below a distinct temperature may be the occurrence of finite-range ferromagnetic ordering forming spin-clusters at a distinct temperature which are then randomly frozen with decreasing temperature. In the magnetization saturation experiments performed at low temperatures saturation is only achieved for compounds with larger Cr contents, i.e., for samples showing properties of clusterglasses or ferromagnetism. The saturation magnetization curves for Cr1.28Te1.25Se0.75 (top) and Cr1.37Te1.25Se0.75 (bottom) are shown in Fig. 9. In the complete magnetization loops a small hysteresis can be seen with small values for both the coercitive fields and the remanences. Such low values suggest the presence of soft ferromagnetic domains with larger domains present in the Cr richer compound. While the magnetization curve of Cr1.37Te1.25Se0.75 is nearly saturated at 9 T that of Cr1.28Te1.25Se0.75 is far from saturation, which is another hint for the presence of spin-glass or spin-glass like properties. The compounds with lower Se contents exhibit a similar behavior [78,79]. Summarizing shortly: for very similar Cr concentrations the magnitude of the Curie temperature Tc decreases with increasing Se content. The comparison of the magnetic properties of the HT and LT phases reveals some remarkable differences: (i) independent from the Te:Se ratio and for similar Cr contents the magnetization of the HT phases is always significantly higher than that of the LT phases which can rationalized by the more regular Cr-Q-Cr angles providing a more effective superexchange interaction; (ii) the values for the Weiss constant q are more positive for the HT than for the LT phases. This behavior indicates more effective dominating ferromagnetic exchange interactions in the HT than in the LT modification. 2.2. Theoretical results As a first step in a theoretical study of the magnetic properties of Cr1þx(Te,Se) with Te:Se ¼ 7:1, Te:Se ¼ 6:2 and Te:Se ¼ 5:3 total energy calculations were performed for parallel and anti-parallel alignments of the Cr1 and Cr2 spin magnetic moments. We found that the antiferromagnetic alignment of the two sub-lattices in all compounds is energetically favored over the ferromagnetic one [78–80]. An analysis of the calculated exchange coupling parameters JCr1-Cr2 (see Fig. 10 for phases Te:Se ¼ 5:3) between Cr1 and Cr2

Fig. 8. The magnetic susceptibility measured in a field of 0.1 T as function of temperature for Cr1.37Te1.25Se0.75 and Cr5.48Te5Se3. Note that only the region below 200 K is displayed. Reprinted from Ref. [80] with permission from Elsevier, Copyright 2009.

Fig. 9. Magnetic field dependence of the magnetizations of for Cr1.28Te1.25Se0.75 (top) and Cr1.37Te1.25Se0.75 (bottom). Reprinted from ref. [80] with permission from Elsevier, Copyright 2009.

Fig. 10. Calculated exchange coupling parameters Jij as a function of the Cr-Cr distance Rij (shown in units of the lattice parameter a) for the compounds Cr1þx(Te,Se)2 for Te:Se ¼ 5:3 for three different compositions: Cr1.25(Te,Se)2, Cr1.34(Te,Se)2 and Cr1.41(Te,Se)2. The panels from the left to the right give results for Cr1-Cr1, Cr1-Cr2 and Cr2-Cr2 pairs. Reprinted from Ref. [80] with permission from Elsevier, Copyright 2009.

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Fig. 11. Experimental and theoretical critical temperatures vs. Cr concentrations, obtained by Monte Carlo (MC) simulations. The various panels show from left to right results for Cr1þx(Te,Se)2 compounds for Te:Se ¼ 7:1, Te:Se ¼ 6:2 and Te:Se ¼ 5:3. Reprinted from Ref. [80] with permission from Elsevier, Copyright 2009.

atoms shows that this effect is a result of the antiferromagnetic coupling between the Cr1(Cr2) and second Cr2(Cr1) neighboring atoms, while the ferromagnetic coupling between the first Cr1-Cr2 neighbors is stronger but does not give a large contribution because of the small number of neighbors. The temperature dependent magnetic properties have been investigated using Monte Carlo (MC) simulations. The exchange interactions within the fully occupied Cr1 sub-lattice (see Fig. 10) lead to an antiferromagnetic order within this sub-lattice [79], while the incomplete Cr2 sub-lattice with random distribution of Cr atoms does not exhibit any magnetic order down to the temperature T ¼ 0 K. This means that a spin-glass or cluster-glass behavior of the compounds can indeed be caused by the magnetic properties of the Cr2 sub-lattice. The spin-glass behavior of this sub-lattice at small Cr content caused by structural disorder changes to a cluster-glass behavior when the Cr concentration increases. In this way the number of ferromagnetically coupled Cr atoms in the Cr2 sublattice increases. Comparing the results of calculations of the exchange coupling parameters for the compounds with Te:Se ¼ 7:1 and Te:Se ¼ 6:2 and Te:Se ¼ 5:3 we found a small variation in their absolute values, that leads also to a corresponding variation of the critical temperatures (see Fig. 11), which was also found in experiment. To explain the experimentally observed unexpected rapid increase of the critical temperature upon increase of Cr concentration in the samples with Te:Se ¼ 5:3 (Fig. 11c), we investigated the dependence of the exchange coupling parameters on different structural imperfections [80]. As an example, Fig. 12 shows the dependence of the exchange coupling parameter Jij on the number of vacancies in the Te-Se sub-lattice. Using the results of these studies we assign the unexpected behavior in these alloys to features of their structure, as e.g. lattice distortions, which are not accounted for by the CPA alloy theory that was used to describe the non-stoichiometry of the investigated systems. We found also that the non-monotonous behavior of the critical temperature as a function of the Cr content in the compounds with Te:Se ¼ 7:1 and Te:Se ¼ 6:2 (Fig. 11 a, b) is related to the nonmonotonous variation of the exchange coupling parameters upon changes of the Cr concentration (Fig. 12). The main findings of the magnetic and theoretical studies can be shortly summarized as follows:  The substitution of Te by Se strongly reduces the dominating ferromagnetic exchange interactions by introducing antiferromagnetic interactions  In the high temperature region the susceptibility follows the Curie-Weiss law with values for q becoming less positive with increasing Se content  Competing ferromagnetic and antiferromagnetic interactions as well as structural disorder induce magnetic frustration occurring as spin-glass or spin-glass like phenomena

 Larger Cr contents leads to cluster-glass or ferromagnetic behavior  Theoretical investigations performed on compounds crystallizing in the HT modification strongly supports experimental findings 3. Structural and magnetic properties of Cr1DxTe0.75Se1.25 (x [ 0.3, 0.33, 0.37) and Cr1DxTe0.25Se1.75 (x [ 0.36 and 0.40) with Te:Se ratios 3:5 and 1:7 3.1. Experimental details 3.1.1. Synthesis The compounds Cr1þxTe0.75Se1.25 (x ¼ 0.30, 0.33, 0.37) and Cr1þxTe0.25Se1.75 (x ¼ 0.36, 0.40) have been prepared by direct solid state reactions. Mixtures of Cr (99.99%, Heraeus), Te (99.5%, Retorte), and Se (99.99%, Retorte) in the corresponding proportions were heated in evacuated sealed silica tubes to 950  C at a rate of 100  C/h and held at this temperature for six days, followed by subsequent cooling to 800  C at a rate of 100  C/h and held at this temperature for 2 days, and finally quenched to room-temperature in a water bath.

Fig. 12. Comparison of the exchange coupling parameters for Cr1þx(Te,Se)2 (Te:Se ¼ 5:3) with fully occupied (Te, Se) sub-lattice (solid lines) and with 5% vacancies in the (Te, Se) sub-lattice (dashed lines). The inter-atomic distances are shown in units of the lattice parameter a. Reprinted from Ref. [80] with permission from Elsevier, Copyright 2009.

J. Wontcheu et al. / Progress in Solid State Chemistry 37 (2009) 226–242

3.1.2. Composition analysis The chemical compositions of the samples were determined first with EDX. The presence of all three elements corresponding to the average compositions: Cr1.30Te0.75Se1.25, Cr1.33Te0.75Se1.25, Cr1.37Te0.75Se1.25, Cr1.36Te0.25Se1.75, and Cr1.40Te0.25Se1.75, was proved with an estimated standard deviation (10 measurement points) of 0.01. Finally, the compositions were confirmed by means of Inductively Coupled Plasma analysis (ICP) with an accuracy of about 3%. 3.1.3. X-ray powder diffraction and Rietveld refinement Phase purity was checked with X-ray powder diffraction analyses performed on a STOE Stadi-P diffractometer in transmission mode equipped with a linear position sensitive detector (PSD) and Ge monochromater using CuKa radiation (l ¼ 1.54056 Å). The angular range of 2q was 10–90 with 2q step size of 0.01 and

235

a counting time of 90 s for each step. The structure refinement was carried out with the Rietveld method [87–90] using the program Fullprof [91]. The results confirm that all samples are homogeneous. The background of the experimental data was interpolated linearly between selected points. Examples of the final Rietveld refinement plots are shown in Fig. 13 for trigonal Cr1.30Te0.75Se1.25 (top) and monoclinic Cr1.40Te0.25Se1.75 (bottom). The shape of the reflections was modeled with a pseudo-Voigt function. Preferred orientation was treated using March’s function. The atomic coordinates were refined without constraints, whereas the atomic displacement parameters Biso for Cr and all Te/Se atoms were tied during the refinement. In the trigonal compound, the refinement was performed based on two crystallographically independent Cr sites (Cr(1) at 1a and Cr(2) at 1b) and chalcogen atoms were statistically distributed over the 2d sites with the ratio of Te:Se fixed to 3:5. The isotropic displacement parameters for Cr(1) and

Fig. 13. Rietveld refinement plots of Cr1.30Te0.75Se1.25 (top) and Cr1.36Te0.25Se1.75 (bottom). X-ray data with peak markers and difference plot at the bottom.

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Cr(2) were constrained to be the same in order to adjust the occupation factor of Cr(2). The occupancy of Cr(1) as well as that of Te/Se was not refined. For the monoclinic samples, the starting values for the atomic coordinates were those of the Cr3þxSe4 structure in the unconventional space group B2/m [29]. We carefully analyzed whether Te and Se atoms exhibit a preference for one of the four independent sites. Initially, refinements were performed only either with Te or Se to obtain the Biso for these atoms giving hints for a site preference. Within the limits of the Rietveld method and the strong correlation between several parameters (Biso, site occupation factors, absorption, texture) no significant differences of the Biso could be detected. Therefore, refinements were done in the following way: Te and Se were statistically distributed over the four sites with the assumption that the Te:Se ratio is equal to 3:5 and 1:7, respectively, on each site. The results of the refinements are summarized in Tables 1 and 2. Selected interatomic distances are listed in Table 3. Note that standard deviations of the refined parameters have been multiplied by the Be´rar-Lelann factor [92]. 3.1.4. Magnetic measurements Magnetic measurements were conducted with a PPMS magnetometer (Quantum Design). The dc susceptibilities were measured in the temperature range of 4.2 K  T  300 K with a field of 0.1 T. The zero-field cooled (ZFC) and field cooled (FC) magnetizations MZFC and MFC were recorded at 0.01 T as follows. The system was cooled in zero field to 4.2 K, a corresponding field was set immediately after T ¼ 4.2 K was reached, and MZFC data taken on warming from 4.2 K to 300 K; finally MFC data were recorded upon cooling from 300 K to 4.2 K with a field. The ac susceptibilities were measured in an applied field of 5104 T at 10, 100 and 1000 Hz. Hysteresis loops were recorded at 15 K varying the field up to 9 T. 3.2. Results and discussion 3.2.1. Structures of Cr1þxTe0.75Se1.25 (x ¼ 0.3, 0.33, 0.37) and Cr1þxTe0.25Se1.75 (x ¼ 0.36 and 0.40) with Te:Se ratios 3:5 and 1:7 The compounds Cr1þxTe0.75Se1.25 (x ¼ 0.30, 0.33, 0.37) crystallize in the trigonal basic cell (Fig. 2) with two crystallographically independent Cr atoms being octahedrally coordinated by the Q2(Te/Se) anions. The Cr2 sub-lattice is only partially occupied. The Cr1Q6 octahedra within the fully occupied metal layers share common edges with Cr1-Cr1 distances ranging from 3.699 to 3.793 Å (Table 3). Along the c axis the Cr1Q6 octahedra share common faces with the Cr2Q6 octahedra and the resulting Cr1-Cr2 separations are between 2.953 and 2.999 Å much shorter than the Cr1–Cr1 distances. The Cr1Q6 and Cr2Q6 octahedra are slightly distorted with Cr–Q bonds ranging from 2.589 to 2.657 Å (Cr1) and 2.604 to 2.657 Å (Cr2; Table 3). The geometrical values are in accordance with available literature data. The a and c lattice parameters and the unit cell volume increase with x (Table 1) in

Table 1 Crystal data and structure refinement results for trigonal Cr1þxTe0.75Se1.25 Formula

Cr1þxTe0.75Se1.25

(1þx) Crystal system Space group a(Å) c(Å) V(Å3) Z RF/%

1.30 trigonal P-3m1 3.6992(1) 5.9060(1) 69.990(3) 1 4.09 1.41 4.52

c2 RBragg/%

1.33

1.37

3.7028(1) 5.9140(2) 70.224(2)

3.793(1) 5.998(1) 74.725(4)

3.36 1.20 3.37

5.29 1.93 5.36

Table 2 Crystal data and structure refinement results for monoclinic Cr1þxTe0.25Se1.75. Formula

Cr1þxTe0.25Se1.75

(1þx) Crystal system Space group a(Å) b(Å) c(Å) g(grd) V(Å3) Z RF/%

1.36 monoclinic B 2/m 13.1709(1) 6.2914(1) 3.6089 117.580(1) 265.061(1) 4 2.69 1.50 5.77

c2 RBragg/%

1.40

13.1876(1) 6.3016(2) 3.6149(1) 117.633(1) 266.155(1) 2.96 3.74 10.5

a non-linear manner. This non-linear behavior may be due to the mixture of Cr4þ (rCr4þ ¼ 0.55 Å)/Cr3þ (rCr3þ ¼ 0.615 Å) and Cr3þ/ Cr2þ (rCr2þ ¼ 0.73 Å) [93] in Cr poor and Cr rich compounds, respectively. Overall, there is a slight increase in Cr–Q bond lengths with increasing x, which is consistent with the presence of larger Cr2þ instead of smaller Cr4þ. The crystal structure of m-Cr1þxTe0.25Se1.75 (x ¼ 0.36 and 0.40) is shown in Fig. 14. The lattice parameters slightly increase with increasing Cr content. In contrast to the more Te rich samples the present compounds crystallize in a monoclinic unit cell with the non-conventional setting B2/m, which was reported for non-stoichiometric Cr3þxSe4 [29]. The structure is related to the hexagonal NiAs cell by the relations amono z [(ahex31/2)2 þ 2c2hex]1/2, bmono z ahex31/2 and cmono z ahex. The Cr atoms occupy two different sites: Cr1 (site 2a) is partially occupied and Cr2 (site 4i) is fully occupied. Every metal atom is in an octahedral environment of 6 Q2- (Te/Se) anions. The Cr1 centered octahedra are joined within the b-c-plane via common edges leading to relatively long Cr-Cr distances of 3.609 and 3.615 Å, respectively, for m-Cr1.36Te0.25Se1.75 and m-Cr1.40Te0.25Se1.75. Octahedra of neighboring layers share common faces in the [100] direction. The resulting Cr1–Cr2 distances (2.964 and 2.989 Å, respectively) are significantly shorter but match perfectly with metal-to-metal distances found in many chromium chalcogenides [22–29,78–80]. The covalent interactions thus generated between the Cr atoms across the face-sharing octahedra may be important for stabilizing these compounds. The Cr–Q bonds range from 2.504 and 2.599 Å and can be subdivided into two parts, three short on the one side and three ones on opposite faces of the octahedron leading to a rather distorted polyhedron (Table 3). We note that the Cr-Q bond lengths are in the typical range reported in literature [22–29].

Table 3 Selected interatomic distances (Å) for tr-Cr1þxTe0.75Se1.25 and m-Cr1þxTe0.25Se1.75. Estimated standard deviations are given in parentheses.

Cr(1)–Cr(1) Cr(2)–Cr(2) Cr(1)–Cr(2) Cr(1)–Q(1) Cr(2)–Q(1)

Cr(1)–Cr(1) Cr(2)–Cr(2) Cr(1)–Cr(2) Cr(1)–Q(1) Cr(1)–Q(2) Cr(2)–Q(1) Cr(2)–Q(2)

Cr1.30Te0.75Se1.25

Cr1.33Te0.75Se1.25

Cr1.37Te0.75Se1.25

3.699(4) 3.699(4) 2.953(1) 2.589(2) 2.604(2)

3.703(3) 3.703(3) 2.957(1) 2.593(2) 2.606(2)

3.793(4) 3.793(4) 2.999(2) 2.651(3) 2.657(3)

Cr1.36Te0.25Se1.75

Cr1.40Te0.25Se1.75

3.609(2) 3.609(2) 2.964(1) 2.534(2) 2.575(2) 2.504(1) 2.583(2)

3.615(1) 3.615(1) 2.989(2) 2.570(3) 2.586(2) 2.563(3) 2.599(1)

J. Wontcheu et al. / Progress in Solid State Chemistry 37 (2009) 226–242

Fig. 14. The structure of the monoclinic compounds Cr1þxTe0.25Se1.75 (x ¼ 0.36 and 0.40). Two face-sharing CrQ6 octahedra (orange) and two edge-sharing octahedra (green) are displayed.

3.2.2. Magnetic properties of Cr1þxTe0.75Se1.25 (x ¼ 0.3, 0.33, 0.37) and Cr1þxTe0.25Se1.75 (x ¼ 0.36 and 0.40) with Te:Se ratios 3:5 and 1:7 In Fig.15 the reciprocal susceptibilities, 1/cm, between 4 and 300 K (B ¼ 0.1 T) for tr-C1þxTe0.75Se1.25 and m-Cr1þxTe0.25Se1.75 are displayed. 200

Cr1.30Te0.75Se1.25 Cr1.33Te0.75Se1.25 Cr1.37Te0.75Se1.25

120

80

-1

χ (mol Cr/emu)

160

40

0 0

50

100

150

200

250

300

T (K) 240

Cr1.36Te0.25Se1.75

200

−1

χ (mol Cr/emu)

Cr1.40Te0.25Se1.75 160

120

80

40

0 0

50

100

150

200

250

300

T (K) Fig. 15. Temperature dependence of the inverse magnetic susceptibility of tr-Cr1þxTe0.75Se1.25 (top) and m-Cr1þxTe0.25Se1.75 (bottom) measured in a field of 0.1 T.

237

The high temperature part of the susceptibility curves were fitted with a Curie-Weiss law yielding effective magnetic moments per Cr atom between 3.78 and 4.33 mB. Some of the values are larger than expected for Cr3þ d3 (expected spin-only value: 3.87 mB) but are in agreement with data reported in the literature for chromium chalcogenides as for example: Cr5S4.8Se3.2 (4.08 mB) [6], Cr4TiSe8 (4.1 mB) [94], KCr4TiSe8 (4.46 mB) [95], Tl0.33Cr5Se8 (3.96 mB) [96] and TlCr5S8-ySey (3.92 mB) [83]. Shimada et al. attributed such enlarged magnetic moments to an electron transfer from Q to Cr via d-p hybridization [75]. Despite the fact that the Cr-Te bonds are covalent the concept of charge neutrality holds and a formal ionic picture requires for Cr poor phases a coexistence of Cr4þ (d2) and Cr3þ (d3), while Cr3þ and Cr2þ (d4) should coexist for Cr richer phases. Thus magnetic moments should be lower or larger than the expected value of 3.87 mB for Cr3þ depending on the actual Cr content. As was explained above direct Cr-Cr and indirect Cr-Q-Cr superexchange interactions are responsible for the magnetic properties. The direct exchange interaction takes place through the overlap of t2g orbitals of neighbored Crnþ ions. In case of neighbored Cr3þ cations the exchange is antiferromagnetic. If the exchange occurs between Cr3þ-Cr2þ/4þ the resulting magnetic exchange is ferromagnetic (Zener double-exchange mechanism). For the Cr cations located on adjacent layers the direct overlap of t2g orbitals might be expected due to short Cr1–Cr2 contacts (Table 3). The longer Cr1–Cr1 and Cr2–Cr2 distances (Table 3) within layers might invoke an overlap of t2g orbitals with a half-filled p orbital of the Q2anions giving rise to a superexchange coupling. These observations are consistent with the interpretation of the model of spinexchange interactions among Cr3þ moieties as stated by Goodenough and Kanamori [97–99]. The Weiss constants for the trigonal samples show a marked increase from negative values (q ¼ -134 and–113 K for Cr1.30Te0.75Se1.25 resp. Cr1.33Te0.75Se1.25, predominant antiferromagnetic interactions) to a slightly positive value for Cr1.37Te0.75Se1.25 (q ¼ 42 K, ferromagnetic exchange is dominating). In both monoclinic phases antiferromagnetic exchange interactions are dominating and even for x ¼ 1.40 a negative value for the Weiss constant is obtained (q ¼ -60 K for Cr1.36Te0.25Se1.75 and –9.5 K for Cr1.40Te0.25Se1.75). Below about 150 K the reciprocal susceptibility curves of both monoclinic samples show some remarkable deviations from linearity which may be caused by short-range antiferromagnetic correlations. Measurements with magnetic fields up to 9 T showed no alterations of the susceptibility curves which is another hint for the assumed antiferromagnetic short-range order. We note that in the 1/c curves of the two Cr poor trigonal samples also slight deviations from linearity occur below about 150 K. But these deviations are less pronounced than for the monoclinic compounds. A comparison of the magnetic properties of samples with almost the same Cr content and different Se concentrations in the series Cr1þxTe2-ySey shows that the successive exchange of Te by Se leads to a net decrease of the value for the Weiss constant q, i.e. larger Se contents strengthen the antiferromagnetic exchange interactions. For instance, q amounts to 133 K for Cr1.30Te1.75Se0.25 [78] versus -134 K for Cr1.30Te0.75Se1.25 [this work]; 111 K for Cr1.36Te1.5Se0.5 [79] versus -60 K for Cr1.36Te0.25Se1.75 [this work]; and 123 K for Cr1.37Te1.25Se0.75 [80] against 42 K for Cr1.37Te0.75Se1.25 [this work]. Since the oxidation state of Cr remains constant in these samples, only the significant alterations of the Cr–Cr distances as well as the Cr–Q–Cr angles when Te is replaced by Se must be the essential structural feature determining the magnetic behavior. From the above remark it is evident that in the Se-rich samples direct Cr–Cr exchange interactions may dominate. In order to study the low temperature behavior of these samples the ZFC/FC magnetizations were recorded at relatively low field (B ¼ 0.01 T, see Fig. 16). The ZFC and FC curves split for all samples

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below 50 K and if we define the cusp in the ZFC curve as freezing temperatures, Tf, the actual value depends on Cr concentrations and the Se content. For tr-Cr1.30Te0.75Se1.25, Cr1.33Te0.75Se1.25 and Cr1.37Te0.75Se1.25 Tf amount to 35, 33 and 30 K, respectively. The values for the monoclinic samples are much lower and are 12 K for m-Cr1.36Te0.25Se1.75 and 22 K for Cr1.40Te0.25Se1.75, respectively. Above these temperatures both curves match perfectly. Such behaviors are an evidence of a disordered spin-state (spin-glass like state) provoked by disorder and competing ferro- and antiferromagnetic exchange interactions leading to frustration. 0.012

The strong increase of the magnetization below the freezing temperature for the Cr richest trigonal compound and both monoclinic samples is not observed for canonical spin-glasses. It is more in line with the properties of a ferri- or ferromagnetic material with the relatively broad trace in the FC curve originating from domain reorientations when the temperature approaches the transition temperature from below. Such a rapid rise may be associated with the occurrence of finite range ferromagnetic ordering forming spinclusters near Tf, and the clusters are randomly frozen as T is further reduced. Materials showing such a behavior are often called clusterglasses, and similar properties were observed for the Cr rich members of compounds with Te:Se ratios of 7:1, 6:2, and 5:3 [78–80].

ZFC Cr1.30Te0.75Se1.25

0.010

0.0012

ZFC Cr1.33Te0.75Se1.25

0.008

Fc

0.0010

Cr1.33Te0.75Se1.25 χ' (emu/g)

M (emu/g)

FC Cr1.30Te0.75Se1.25

0.006

Cr1.37Te0.75Se1.25

0.0008

10 Hz 100 Hz 1000 Hz

0.0006

0.004

0.0004 0.002 0

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0.0002 30

T [K]

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T (K)

0.40

3.5

0.35 0.30

χ' (10 emu/mol)

FC Cr1.37Te0.75Se1.25

0.25 0.20

-4

M (emu/g)

3.0

ZFC Cr1.37Te0.75Se1.25

0.15

Cr1.36Te0.25Se1.75

2.5

10 Hz 100 Hz 1000 Hz

2.0 1.5

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T (K)

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T (K)

10

0.12

8

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0.08

FC Cr1.40Te0.25Se1.75

-4

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χ' (10 emu/mol)

0.10

ZFC Cr1.36Te0.25Se1.75

0.06

FC Cr1.36Te0.25Se1.75

6

Cr1.40Te0.25Se1.75

4

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2

0.04

0

0.02

10

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20

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T (K)

T (K) Fig. 16. Field cooled (FC) and zero-field cooled (ZFC) magnetization of samples given in the inset measured at a field of 0.01 T.

Fig. 17. Frequency dependence of the real part of the ac susceptibility of tr-Cr1.37Te0.75Se1.25, m-Cr1.36Te0.25Se1.75 and m-Cr1.40Te0.25Se1.75 measured at frequencies as indicated in the inset.

J. Wontcheu et al. / Progress in Solid State Chemistry 37 (2009) 226–242

trigonal and monoclinic samples can be understood on the basis of both the different Te:Se ratio and differing structural details like CrCr separations and Cr-Se-Cr angles.

2.0

T = 15.0 K Cr1.37Te0.75Se1.25

1.5

M (μB/Cr-atom)

1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -10

-8

-6

-4

239

-2

0

2

4

6

8

10

H (T) Fig. 18. Magnetic field dependence of the magnetizations of tr-Cr1.37Te0.75Se1.25 measured at 15 K.

However, a single dc susceptibility experiment can not conclusively identify a spin-glass. Better evidences are provided with neutron diffraction experiments [100] or the occurrence of a peak in the frequency-dependent ac susceptibility. For tr-Cr1.37Te0.75Se1.25, m-Cr1.36Te0.25Se1.75 and m-Cr1.40Te0.25Se1.75 the real part of the ac susceptibility curves are shown in Fig. 17. In all curves broad maxima occur between 10 and 50 K showing different shapes for the different samples. Moreover, the magnitude of the ac susceptibilities depends on the frequency below 50 K and this dependency disappears above 50 K as is typical for spin-glasses or spin-glass like materials. In addition the maximum displays a frequency dependent shift which is more pronounced for the two monoclinic samples. Analyzing the frequency dependence of Tf with the term DTf/[Tf$D(logn)] (n is the frequency applied) a value of z 0.06 is obtained for m-Cr1.40Te0.25Se1.75 which is in the range 0.004-0.080 reported for spin-glasses [84]. The field dependence of the saturation magnetization (Fig. 18) for tr-Cr1.37Te0.75Se1.25 shows a rapid increase of the magnetization at low fields. However, full saturation of the magnetization is not observed even at 9 T which is another indication for a magnetically frustrated system. In the hysteresis loop a very small coercitive field of 0.035 T and 0.1 mB/Cr atom are seen indicating the presence of very soft ferromagnetic domains. The results of dc and ac magnetic susceptibility measurements and the saturation behavior of Cr1.37Te0.75Se1.25 evidence that the magnetic ground state is characterized by spin-glass like or cluster-glass behavior. The differences of the magnetic properties of the

3.2.3. Theoretical investigations of Cr1þxTe0.75Se1.25 (x ¼ 0.3, 0.33, 0.37) As was mentioned above, an increase of the Se content in the phases is accompanied by an increase of deviations between theoretical and experimental results that can be explained by the structural features not accounted for in the calculations. In the case of compounds for which the Te:Se ratio is equal to 3:5 the important role of the lattice structure for their magnetic properties become much more pronounced. As was found in experiment for samples with a Cr concentration of 1 þ x ¼ 1.3 and 1 þ x ¼ 1.33, the Te and Se atoms are shifted in the direction of the fully occupied Cr1 layers from their ideal position corresponding to the NiAs structure, while for 1 þ x ¼ 1.37 the shift occurs in the direction of partially occupied Cr2 layers. According to the results of the total energy calculations this should lead to a strong non-monotonous dependence of the lattice parameters on Cr concentrations that was not observed in the experimental study. The structural features in the alloys with Cr content of 1 þ x ¼ 1.3 and 1 þ x ¼ 1.33 have also a crucial effect on their magnetic properties. The exchange coupling parameters JCr1-Cr1, JCr1-Cr2 and JCr2-Cr2 for Cr1.3Q2 are presented in Fig. 19. One can observe the difference to the results obtained for the compounds with Te:Se ¼ 7:1, 6:2, Te:Se ¼ 5:3 (see Fig. 10), that leads to the differences in the magnetic properties. According to the result for the exchange coupling parameters, the compound has two critical points. Upon cooling down to the first critical temperature, the total magnetic moment increases slowly reaching the maximum in the vicinity of critical temperature T ¼ 150 K. A further decrease in temperature is accompanied by a decrease in the spin magnetic moment related to an increase of magnetic order in the system with the two sub-lattices exhibiting the antiferromagnetic (AFM) alignment of their magnetic moments. Thus, one can consider the first critical temperature as a transition point to the AFM structure with a non-compensated magnetic moment because of the different occupation of two sub-lattices. The second transition observed in MC calculations around T ¼ 40 K is related to the formation of a non-collinear structure within the Cr1 sub-lattice, while the Cr2 atoms keep antiferromagnetically aligned with respect to the neighboring Cr1 atoms. As a result, the total magnetic moment below Tc2 falls down to z 0 upon further cooling. Thus, in contrast to previous results for samples with Te:Se ratios 7:1, 6:2 and 5:3, when Te:Se ¼ 3:5 the decrease of the magnetic moment upon cooling is not connected to a pure spinglass or cluster-glass transition but to the formation of noncollinear structure in the Cr1 sub-lattice. Note also that such

Fig. 19. Calculated exchange coupling parameters Jij as a function of the Cr-Cr distance Rij (shown in units of the lattice parameter a) for the compounds Cr1.3(Te,Se)2 for Te:Se ¼ 3:5. The panel from left to right gives results for Cr1-Cr1, Cr1-Cr2 and Cr2-Cr2 pairs.

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a behavior upon cooling occurs only at the relatively small occupation of Cr2 sub-lattice (1 þ x ¼ 1.3 - 1.33), when strong AFM coupling between the neighboring Cr1 and Cr2 atoms can be compensated by the sub-lattice. MC simulations using the same exchange parameters but with increased amount of Cr2 atoms leads to the formation of a collinear magnetic structure with an anti-parallel alignment of Cr1 and Cr2 magnetic moments and with a non-compensated total magnetic moment. 4. Summary and conclusions The structural and magnetic properties of the ferromagnetic parent materials m-Cr5Te8 and tr-Cr5Te8 are significantly altered when Te is substituted by Se. The replacement of Te by Se suppresses the formation of the monoclinic structure type. Instead two different trigonal modifications are obtained depending on the heat treatment. Quenching the samples from high temperatures (HT modification) yields compounds with a structure closely related to self-intercalated dichalcogenides Cr1þxQ2 (Q ¼ Te, Se). A slow cooling procedure (LT modification) led samples crystallizing in the tr-Cr5Te8 structure type which may be viewed as a superstructure of the Cr1þxQ2 type structure. In the structures fully and partially occupied metal atom layers alternate along the crystallographic c axis. For the Se richest compounds (Te:Se ratio ¼ 1:7) a different structural variant is observed which was earlier reported for Cr3þxSe4 samples, i.e. for compounds with a Cr:Se ratio smaller than 1.33. In the present case this ratio is larger than 1.33 and amounts to 1.47 and 1.43. The reason is not understood and one can only speculate that the presence of Te stabilizes this structure type for Cr poor samples. In addition, the stability range of the compounds seems to be extended to higher Cr contents with increasing Se content. With increasing Se content and a comparable Cr concentration the Cr-Q bond lengths and the Cr-Cr contacts are shortened, whereas an increase of the Cr content leads to an enlargement of the interatomic distances. These structural changes are reflected in the magnetic properties. Increasing the Se concentration strengthens the antiferromagnetic exchange interactions and for the Cr richer samples the negative value for the Weiss constants indicate dominating antiferromagnetic exchange. The low temperature behavior of most samples is complex and spin-glass, spin-glass like and cluster-glass properties are observed. Some of the Cr richest compounds show typical magnetic properties of soft ferromagnets. The spin-glass or spin-glass like behavior is caused by competing ferromagnetic and antiferromagnetic exchange interactions and by structural disorder. For a given Cr content and Te:Se ratio the HT compounds show stronger magnetizations and the values for the Weiss constant q are more positive for the HT than for the LT phases indicating more effective ferromagnetic exchange interactions. These properties can be explained on the basis of more regular CrQ-Cr angles in the HT structures than in the LT structures. Until now the effects of cation substitution onto the crystal structures and resulting physical properties were mainly studied. Only little attention was paid on research of the effects of anion substitution in chalcogenide compounds. The results of the present studies encourage us to explore other chalcogenide systems with interesting physical properties. Acknowledgements The financial support by the Deutsche Forschungsgemeinschaft (DFG) within the frame SPP1136 is gratefully acknowledged. Many thanks to Dr. R. K. Kremer (MPI Stuttgart) for helpful discussions about the magnetic data interpretation and to Fr. E. Bru¨cher (MPI Stuttgart) for some magnetic data measurements.

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