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Structural and magnetic properties of CdxInyCrzSe4
ARTICLE IN PRESS
Journal of Crystal Growth 297 (2006) 419–425 www.elsevier.com/locate/jcrysgro
Structural and magnetic properties of CdxInyCrzSe4 D. Skrzypeka,, E. Malickab, A. Waskowskac, S. Widucha, A. Cichona, T. Mydlarzd a
A. Che!kowski Institute of Physics, University of Silesia, Uniwersytecka 4, 40-007 Katowice, Poland b Institute of Chemistry, University of Silesia, Bankowa 14, 40-007 Katowice, Poland c Institute of Low Temperature and Structure Research, Polish Academy of Sciences, 50 422 Wroclaw, Poland d International Laboratory of High Magnetic Fields and Low Temperatures, 53 529 Wroclaw, Poland Received 2 June 2006; received in revised form 4 October 2006; accepted 10 October 2006 Communicated by D.W. Shaw Available online 28 November 2006
Abstract Mixed selenide spinels of (Cd)[Cr1.81In0.19]Se4 and (Cd0.745In0.255)[Cr1.94In0.06]Se4 have been studied using X-ray diffraction, magnetic measurements and ESR spectroscopy. In3+ ions accommodate both tetrahedral and octahedral sites in the spinel structure. The magnetic short-range order appears in the critical region from Tc to about 200 K for the selenide spinels. The linear temperature dependence of the resonance linewidth at T4250 K is interpreted by an occurrence of one-phonon process in a spin-lattice relaxation. r 2006 Elsevier B.V. All rights reserved. PACS: 76.30.v; 61.10.i Keywords: A1. Crystal structure; A1. X-ray diffraction; A2. Single-crystal growth; B2. Magnetic materials; B2. Semiconducting ternary compounds
1. Introduction Ternary selenide spinels, exhibiting interesting structural, magnetic and electrical transport properties have been the subject of numerous studies. It was shown that replacement of the di- or tri-valent cation by a third metal resulted in new chemical compounds with essentially changed physical properties [1–13]. However, experimental results reported in the literature so far refer mostly to polycrystalline forms of the quaternary selenides. We have prepared the Cd–In–Cr–Se4 single crystals with various In concentrations for the purpose of studying the influence of the In3+ admixtures on the cation distribution and magnetic ordering in this spinel system. The parent CdCr2Se4 crystallises in the normal spinel structure (Fd3m) [14]. Cadmium and chromium in the cubic close packing of selenium atoms are tetrahedrally (A-type sites) and octahedrally (B-type sites) coordinated, respectively. The compound is a ferromagnetic p-type semiconductor [3] with lattice parameter around 10.7 A˚ [1]. Corresponding author. Tel./fax: +48322588431.
E-mail address: [email protected] (D. Skrzypek). 0022-0248/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2006.10.104
The Curie temperature reported in literature was in the range of 128 K [15]–142 K [3]. The solid solutions CdxInyCrzSe4 were synthesised in polycrystalline form by Shabunina et al. [16]. X-ray structure determination showed that indium, In3+, could accommodate both tetrahedral and octahedral sites in the spinel structure [16]. In the present paper, we study the structural and magnetic properties of single crystals, CdCr2Se4, substituted with In ions in the A- and B-sites using X-ray diffraction, magnetic measurements and ESR spectroscopy. 2. Experimental procedure 2.1. Preparation of the substrates and crystal growth The single crystals were grown by chemical vapour transport method in closed quartz ampoules with anhydrous chromium chloride (purity 98%) as a transporting agent and with the selenides CdSe and In2Se3 as the solid phases. The starting materials, binary selenides, were synthesised from elemental cadmium, indium and selenium
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(purity 99.999%). The stoichiometric mixtures of the elements were pulverised in an agate mortar and sealed in evacuated quartz ampoules. After heating at the 1075 K for 7 days, the selenides were ground in an agate mortar and heated once more for 7 days at the same temperature as before. X-ray powder analysis showed that all products contained only the synthesised phase. The mixture of selenides with transporting agent CrCl3 was sealed in quartz tubes (length E200 mm, inner diameter d ¼ 20 mm) evacuated to E103 Pa. These ampoules were heated in a horizontal zone furnace to about 1123 K at the solution zone, maintaining the temperature gradient of 10 K along the ampoule. After 10 days, the furnace was cooled to room temperature. Growing of quaternary spinel-type chromium selenide single crystals requires special conditions of the chemical transport reactions, which are very important in the crystallisation of the spinels. The equilibrium constants of chemical transport reactions (Ka) were calculated as a function of the temperature to determine, for example, the transport ability of CrCl3. The results of transport depend on log Ka value. When the log Ka value is close to zero, one may expect great transport ability of chemical reactions, even for small temperature difference. The transporting agent CrCl3 dissociated to CrCl3, CrCl4 and Cl2 above 773 K [17]. The transporting reactions, with CrCl3, CrCl4 and Cl2 as the transporting agents, were used to calculate the equilibrium coefficients in heterogeneous system (a gas phase and some solid phases). For the CdSe–In2Se3–CrCl3 system, values of log Ka for transport reactions are similar to the equilibrium state values (log KaE0). Calculated values of log KaE0 for CrCl3 and CrCl4 confirmed that transport of CdSe and In2Se3 is carried out by these agents. The obtained single crystals with well-formed luster faces have the shape of a regular octahedron of 1–3 mm in the edge lengths (see Fig. 1). The XPS survey spectrum confirmed the presence of indium in both compounds.
Fig. 1. The single crystals of (Cd)[Cr1.81In0.19]Se4.
2.2. Experimental techniques 2.2.1. X-ray diffraction The X-ray diffraction measurements were performed with a four-circle diffractometer Xcalibur/CCD Oxford Diffraction, operating in k geometry, using graphite monochromated MoKa radiation and o-scan technique and Do step of 1.21. A set of 900 images was taken in nine runs of 100 exposures with different orientations in the reciprocal space. The exposure time per image was 30 s. Crystal and instrument stability was controlled by one image, selected as a standard and measured after each 50 images [18]. The intensity data were integrated and corrected for Lorentz and polarisation effects with the CrysAlis software [19]. Numerical absorption correction based on the crystal shape was applied [19]. 2.2.2. Magnetic measurements The high-field magnetisation measurements were carried out at T ¼ 4.2 K with a ballistic magnetometer in a Bittertype magnet. The electron spin resonance spectra were recorded with a standard EPR spectrometer operating at X-band (9 GHz) frequency, using 100 kHz field modulation. The microwave frequency was measured using Hewlett Packard 534 microwave frequency counter. The temperature-dependence measurements were performed in the temperature range from 90 to 400 K. The values of the ESR parameters: DB-linewidth and Br-resonance field were obtained on the basis of the best fit for the simulated Lorenzian profile in comparison with the experimentally observed spectra. In both methods (XRD and ESR), the same octahedral, as-grown single crystals were measured. 3. Results and discussion 3.1. Crystal structures and cation distribution Two single-crystal samples representative for the indiumsubstituted CdCr2Se4 spinel, with nominal In concentration y ¼ 0.2 and 0.25 have been selected for the X-ray diffraction measurements. The aim was to determine the location and concentration of the In ion over the tetrahedral (A) and octahedral (B) sites in the cubicclose-packed selenium sublattice. The structure refinement was performed using the SHELXL-97 program package [20]. The crystal data and the details of experimental conditions are summarised in Table 1. The crystal structures have been refined in the space group Fd3¯ m (No. 227) with the origin of the unit cell taken at the point 3¯ m. Similarly as in parent CdCr2Se4, the Cd2+ ion was located at the tetrahedral position 8a: (1/8, 1/8, 1/ 8), and Cr3+ at the octahedral position 16d: (1/2, 1/2, 1/2). The anion took the position 32e: (u, u, u). For each sample, two models have been considered: (1) indium was sharing the tetrahedral position (A) with cadmium and (2) the indium ion was substituting Cr3+ at the octahedral
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written as (Cd)[Cr1.81In0.19]Se4. The results of the structure refinement are given in Tables 2 and 3. The sample II with the nominal y ¼ 0.25, appeared to be a mixed spinel, as some portion of In can be found in octahedral sites, but majority of the indium ions have migrated to the tetrahedral sites leading to the formula (Cd0.745In0.255)[Cr1.94In0.06]Se4. The ionic radius of In with the tetrahedral coordination RIn ¼ 0.63, while for the sixfold coordination the value is R ¼ 0.80 [21]. This feature explains the fact that despite the higher value of y in this sample, the unit cell dimension is not increasing when compared with parent CdCr2Se4 having the unit cell parameter a ¼ 10.745(2) A˚ [22,23].
[B]-sites. In each model, the cations located in the same site were refined with the coupled site occupancy factors. The resulting values enabled writing the chemical formulae for the two crystals. It appeared that in the two selected samples the admixture has been accommodated in a different way. For the sample I with y ¼ 0.2 the best convergence in the structure refinement was obtained for the model 2) with In located at the [B]-sites. The chemical formula can thus be Table 1 Crystal data, experimental details and structure refinement results for the Cd–Cr–In–Se spinel system Crystal data Temperature (K) Crystal system, space group Unit cell dimensions (A˚) a Volume (A˚3) Z Calculated density (Mg/m3) Crystal size (mm) Data collection Wavelength (A˚) 2y max for data collection Limiting indices h k l Reflections collected Reflections unique Reflections 42 s (I)] Absorption coefficient (mm1) Refinement Refinement method Number of refined parameters Goodness-of-fit on F2 Final R indices [I42s(I)] R1 wR2 Extinction coefficient Largest diff. peak and hole (e A˚3)
(Cd)[Cr1.81 In0.19]Se4 297 Cubic, Fd3¯ m
(Cd0.745In0.255) [Cr1.94In0.06]Se4
10.7767(12) 1251.58(3) 8 5.716 0.08 0.08 0.09
10.7577(12) 1159.18(3) 5.274 0.08 0.08 0.09
0.71073 94.01
92.90
14, 17 14, 17 14, 17 5788 259 207 30.10
21, 15 13, 20 20, 21 6801 317 276 30.55
3.2. Magnetic and ESR studies In the chromium spinels, the Cr3+ ions always occupy the B-site of the spinel structure. The local symmetry on this octahedral site leads to a non-degenerate orbital ground state with S ¼ 32. The lattice built upon the B-site consists of tetrahedra of chromium ions. Each chromium ion is common to two tetrahedra, which are defined by the positions of their six first-nearest neighbours. The magnetic properties of CdCr2Se4 were analysed by Baltzer et al. [22] in terms of competing interactions: ferromagnetic between first-nearest neighbours and antiferromagnetic between higher-order neighbours. The field-dependent magnetic moment for both obtained crystals is shown in Fig. 2. The saturation effects have been observed at relatively low Table 3 Selected interatomic distances (A˚) and angles (deg.) for the Cd–Cr–In–Se spinel system in the tetrahedral A and octahedral B sites
Full-matrix least-squares on F2 10 0.956 0.999 0.024 0.035(4) 0.0006(4) 0.91 and 0.87
421
A–Se Cr/In–Se Se–Cr–Se Se–Cr–Se Se–Cr–Se Se–Cd–Se
0.023 0.040(5) 0.00110(5) 0.87 and 1.15
(Cd)[Cr1.81In0.19]Se4
(Cd0.745In0.255)[Cr1.94In0.06]Se4
2.5909(5) 4 2.5541(3) 6 180.00(1) 3 96.86(1) 6 83.14(1) 6 109.47(1) 6
2.5893(4) 4 2.5481(3) 6 180.00(1) 3 96.95(1) 6 83.03(1) 6 109.47(1) 6
Table 2 Atomic coordinates, site occupation factors and equivalent isotropic displacement parameters for the Cd–Cr–In–Se4 spinel system Campound
(Cd)[Cr1.81In0.19]Se4 (Cd0.745In0.255)[Cr1.94In0.06]Se4
Anion positional paramaeter (u)
0.26380(2) 0.26397(2)
Uiso (A˚2 103)
Site occupation A
B
Cd
Cr/In
Se
1.0 0.745:0.255(9)
0.905:0.095(7) 0.970:0.030(5)
14.1(1) 11.3(1)
11.5(2) 9.5(1)
12.3(1) 9.23(9)
Note: The atomic positions are as follows: Cd Cr/In Se
(A) site (B) site Anion site
8a 18 18 18 16d 12 12 12 32e (u u u)
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Fig. 2. The magnetic moment versus the external magnetic field (T ¼ 4.2). K (Cd)[Cr1.81In0.19]Se4 ; J (Cd0.745In0.255)[Cr1.94In0.06]Se4.
magnetic fields. Admixtures of In3+ only in [B]-sites affected strongly the chromium ion interactions, reducing the saturation magnetic moment. Recently, similar results for the Cd[Cr2xGax]Se4 were reported by some of us [23]. In the system (Cd0.745In0.255)[Cr1.94In0.06]Se4, when the majority of the indium ions have migrated to the tetrahedral sites, the magnetic saturation moment is close to the theoretical value of 6mB/molecule. Within the paramagnetic (PM) region, the ESR spectra of both obtained crystals showed a single Lorenzian line with g ¼ 1.99 which is attributed to Cr3+ ions. The ESR spectra for (Cd)[Cr1.81In0.19]Se4 and (Cd0.745In0.255) [Cr1.94In0.06]Se4 and their temperature evolution below T ¼ 140 K are displayed in Figs. 3 and 4, respectively. Clearly, the ESR spectra for both obtained crystals show the same varying tendency. Apart from the dramatic modifications of the spectra at low temperatures are observed: (a) deviation from Lorenzian line-shape; (b) shift of the resonance field (Br); (c) broadening of the linewidth (DB); (d) the anomalous increasing of the intensity;and (e) the splitting of the spectra. The spectral modifications also suggest that there is a structural phase transition from cubic symmetry to tetragonal or orthogonal one at Tc, in addition to the ferromagnetic transition. The plots of the temperature dependence of the linewidth and resonance field are shown in Figs. 5 and 6 for (Cd)[Cr1.81In0.19]Se4 and (Cd0.745In0.255)[Cr1.94In0.06]Se4, respectively. Starting from the T ¼ 400 K, the linewidth values linearly decreased as the temperature was reduced to T ¼ 250 K. The ESR linewidth is related to the relaxation of the spin system. For individual spins DB1/t, where t is the spin relaxation time. In a dense magnetic material, this relationship is modified since the magnetisation relaxes towards an effective field instead of the external field. The review of the mechanisms for the spin-lattice relaxation
Fig. 3. The temperature evolution (Cd)[Cr1.81In0.19]Se4 single crystal.
of
the
ESR
spectrum
of
(and associated temperature dependencies of ESR linewidths) for concentrated magnetic systems was reported by Huber and Seehra [24] and Seehra et al. [25]. For non-Sstate systems with SX1, it is expected that the relaxation of magnetisation is dominated by the phonon modulation of the crystalline field. Following the analysis in Ref. [24], the ESR linewidth of the exchange-coupled PM materials can be described by the expression: DB ¼ DBss þ DBsph , where DBss is described by the exchange narrowing theory [26]: DBss ¼ ½ðDBdd Þ2 =Bex , (i.e. is proportional to the square of the dipolar produced linewidth DBdd divided by the rate of exchange) and DBs-ph represent the contribution of the spin–phonon interaction. The linear temperature dependence of ESR linewidth, which was observed for both obtained crystals shows in accordance with [24] that one-phonon relaxation may
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Fig. 6. The temperature dependence of the ESR parameters for (Cd0.745In0.255)[Cr1.94In0.06]Se4.
Fig. 4. The temperature evolution of (Cd0.745In0.255)[Cr1.94In0.06]Se4 single crystal.
the
ESR
spectrum
of
Fig. 5. The temperature dependence of the ESR parameters for (Cd)[Cr1.81In0.19]Se4.
prevail in PM materials even at high temperatures. This effect is caused by a broad band of phonons that may participate in the spin relaxation process.
In PM state, there are the interactions between spins and by lowering of the temperature, short-range order progressively occurs, which can correspond to very small clusters. Near the transition temperature Tc, the clusters grow and coalesce to create an infinite magnetic matrix at Tc. ESR has been recognised as a powerful tool for probing the spin structure and dynamics. Its high sensitivity to both minor magnetic phases and short-range interactions permits a selective disclosure of the subtle changes in spin systems. That is why our measurements of the ESR spectra reveal (below T ¼ 160 K for (Cd)[Cr1.81In0.19]Se4 and T ¼ 140 K for (Cd0.745In0.255)[Cr1.94In0.06]Se4) apart from strong PM line, the presence of the new lines (see Figs. 3 and 4), which means the appearance of the clusters of Cr3+. It is worth noting that the short-range order, which suggests an increased magnetic inhomogeneity of the systems, is depended upon indium distribution. The confirmation of this suggestion is in the calculations, which were done by Bakrim et al. [27]. These authors calculated, from the results of the random phase approximation (RPA), the correlation functions for a Heisenberg ferromagnetic model having both nearest-neighbour (nn) and next nearest-neighbour (nnn) exchange integrals. The theoretical results obtained were used to study the PM state of spinels Cd[Cr2xGax]Se4. It can be noted that all correlation functions persist far into PM region (see Figs. 1–6 in Ref. [27]). The appearance of the short-range magnetic ordering was confirmed by the temperature dependence of the spectrum intensity. In Figs. 7 and 8, the temperature evolution of intensity of ESR spectrum for both obtained crystals is shown. The adequate values were calculated as double integration of the spectrum (DI). This defined intensity should be proportional to the spin susceptibility of the sample. It can be seen, that below T ¼ 300 K, the deviation of the inverse susceptibility from the Curie–Weiss law appears. As the temperature is reduced from about T ¼ 170 K, the values for the intensity rapidly increase.
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In addition, the ESR spectra analyses also indicate that the PM–ferromagnetic transition is incomplete and the PM phase may still survive in a certain temperature range below Tc. 4. Conclusions
Fig. 7. The relative (Cd)[Cr1.81In0.19]Se4.
ESR
susceptibility
versus
temperature
for
In this work, we presented the X-ray diffraction analysis for two types of diluted ferromagnetic CdCr2Se4 single crystals: (Cd)[Cr1.81In0.19]Se4 in which In substitutes Cr and (Cd0.745In0.255)[Cr1.94In0.06]Se4 where In substitutes Cd and Cr. The magnetic properties of the same as-grown single crystals were examined by ESR spectroscopy. ESR was found to be extremely sensitive for detecting minor magnetic phases and short-range order. In resonance spectra, the ferromagnetic clusters signals are presented: from TE160 K for Cd)[Cr1.81In0.19]Se4 and from TE140 K for (Cd0.745In0.255)[Cr1.94In0.06]Se4. The transition region appears to be broad for both obtained crystals and PM phase was still present up to T ¼ 125 K. The stronger magnetic inhomogeneity occurs for (Cd)[Cr1.81In0.19]Se4 crystal. The linear variation in resonance linewidth with temperature for T4250 K is an experimental proof of Huber’s–Seehra’s theory. It describes the occurrence of one-phonon processes up to high temperatures in spinlattice relaxation in magnetically concentrated systems. References
Fig. 8. The relative ESR susceptibility (Cd0.745In0.255)[Cr1.94In0.06]Se4.
versus
temperature
for
This rise is more marked than theoretically predicted for the Heisenberg-type ferromagnets, where magnetic susceptibility wE[(TTc)/Tc]p with p ¼ 43 [28]. The effect observed is due to the presence of external magnetic field, which orients the clusters in the field direction. The spectra below T ¼ 130 K (see Figs. 3 and 4) are attributed to the ferromagnetic resonance (FMR). In FMR equation written by Kittel [29], the contributions of the demagnetisation and magnetocrystalline anisotropy fields occur. The complexity of resonance spectra for both the obtained crystals is due to the inhomogeneity of the internal magnetic field which is caused by the demagnetising effects brought about by the octahedron sample shape [30] and due to the domain structure [31]. It can be seen, from Figs. 5 and 6, that the transition region is broad for both the obtained crystals. The original PM line broadens gradually, shifts from PM resonance and finally vanishes.
[1] P.K. Baltzer, P.J. Wojtowicz, M. Robbins, E. Lopatin, Phys. Rev. 151 (1966) 367. [2] C. Haas, A.M.J.G. van Run, P.F. Bongers, W. Albers, Solid State Commun. 5 (1967) 657. [3] H.W. Lehmann, Phys. Rev. 163 (1967) 488. [4] H.W. Lehmann, G. Harbecke, J. Appl. Phys. 38 (1967) 946. [5] A.R. von Neida, L.K. Shick, J. Appl. Phys. 40 (1969) 1013. [6] H. von Philipsborn, J. Crystal Growth 9 (1971) 296. [7] H. Hahn, K. Schroder, Z. Anorg. Allg. Chem. 269 (1952) 135. [8] N. Menyuk, K. Dwight, J. Arnott, W. Wold, J. Appl. Phys. 37 (1966) 1387. [9] J. Tang, T. Matsumoto, T. Naka, T. Furubayashi, S. Nagata, N. Matsumoto, Physica B 259–261 (1999) 857. [10] F.K. Lothering, R.P. Van Stapele, G.H.A.M. Van der Steen, J.S. Van Wiesingen, J. Phys. Chem. Solids 30 (1969) 799. [11] J. Alvarez, V. Sagredo, J. Mantilla, J. Magn. Magn. Mater. 196–197 (1999) 407. [12] J. Krok-Kowalski, J. Warczewski, T. Mydlarz, A. Pacyna, I. Okonska-Kozlowska, J. Magn. Magn. Mater. 166 (1997) 172. [13] I. Okonska-Kozlowska, E. Malicka, A. Waskowska, T. Mydlarz, J. Solid State Chem. 148 (1999) 215. [14] V.T. Kalinnikov, T.G. Aminov, V.M. Novotortsev, Inorg. Mater. 39 (2003) 1159. [15] M. Nouges, J.L. Dormann, J. Magn. Magn. Mater. 54–57 (1986) 87. [16] G.G. Shabunina, R.A. Sadykov, T.G. Aminov, Inorg. Mater. 36 (2000) 1208. [17] V. Plies, Z. Anorg. Allg. Chem. 556 (1988) 120. [18] Oxford Diffraction, Crys. Alis CCD. Data Collection software, Oxford Diffraction Ltd., Wroc"aw, Poland, 2001. [19] Oxford Diffraction, CrysAlis RED. Data Reduction program. Issue 171.26, Oxford Diffraction Ltd., 2004.
ARTICLE IN PRESS D. Skrzypek et al. / Journal of Crystal Growth 297 (2006) 419–425 [20] G.M. Sheldrick, 1999 SHELXL-99, Program for Crystal Structure Refinement, University of Go¨ttingen. [21] R.D. Shannon, Acta Crystallogr. A 32 (1976) 751. [22] P.K. Baltzer, P.J. Wojtowicz, M. Robbins, E. Lopatin, Phys. Rev. 151 (1966) 367. [23] I. Okonska-Kozlowska, E. Malicka, A. Waskowska, J. Heimann, T. Mydlarz, J. Solid State Chem. 158 (2001) 34–39. [24] D.L. Huber, M.S. Seehra, J. Phys. Chem. Solids 36 (1975) 723–725. [25] M.S. Seehra, M.M. Ibrahim, V.S. Babu, G. Srinivasan, J. Phys.: Condens. Matter 8 (1996) 11283.
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[26] A. Abragam, B. Bleaney, Electron Paramagnetic Resonance of Transition Ions, Clarendon Press, Oxford, 1970. [27] H. Bakrim, K. Bouslykhane, M. Hamedoun, A. Hourmatallah, N. Benzakour, J. Magn. Magn. Mater. 285 (2005) 327. [28] W. Zarek, Acta Phys. Pol. A 52 (1977) 657–663 and references therein. [29] C. Kittel, Phys. Rev. 73 (1948) 155; C. Kittel, Phys. Rev. 76 (1949) 743. [30] D.S. Schmool, J.M. Barandiaran, J. Magn. Magn. Mater. 191 (1999) 211. [31] R. Szymczak, A. Szewczyk, M. Baran, V. Tsurkan, J. Magn. Magn. Mater. 8 (1990) 481.
Journal of Crystal Growth 297 (2006) 419–425 www.elsevier.com/locate/jcrysgro
Structural and magnetic properties of CdxInyCrzSe4 D. Skrzypeka,, E. Malickab, A. Waskowskac, S. Widucha, A. Cichona, T. Mydlarzd a
A. Che!kowski Institute of Physics, University of Silesia, Uniwersytecka 4, 40-007 Katowice, Poland b Institute of Chemistry, University of Silesia, Bankowa 14, 40-007 Katowice, Poland c Institute of Low Temperature and Structure Research, Polish Academy of Sciences, 50 422 Wroclaw, Poland d International Laboratory of High Magnetic Fields and Low Temperatures, 53 529 Wroclaw, Poland Received 2 June 2006; received in revised form 4 October 2006; accepted 10 October 2006 Communicated by D.W. Shaw Available online 28 November 2006
Abstract Mixed selenide spinels of (Cd)[Cr1.81In0.19]Se4 and (Cd0.745In0.255)[Cr1.94In0.06]Se4 have been studied using X-ray diffraction, magnetic measurements and ESR spectroscopy. In3+ ions accommodate both tetrahedral and octahedral sites in the spinel structure. The magnetic short-range order appears in the critical region from Tc to about 200 K for the selenide spinels. The linear temperature dependence of the resonance linewidth at T4250 K is interpreted by an occurrence of one-phonon process in a spin-lattice relaxation. r 2006 Elsevier B.V. All rights reserved. PACS: 76.30.v; 61.10.i Keywords: A1. Crystal structure; A1. X-ray diffraction; A2. Single-crystal growth; B2. Magnetic materials; B2. Semiconducting ternary compounds
1. Introduction Ternary selenide spinels, exhibiting interesting structural, magnetic and electrical transport properties have been the subject of numerous studies. It was shown that replacement of the di- or tri-valent cation by a third metal resulted in new chemical compounds with essentially changed physical properties [1–13]. However, experimental results reported in the literature so far refer mostly to polycrystalline forms of the quaternary selenides. We have prepared the Cd–In–Cr–Se4 single crystals with various In concentrations for the purpose of studying the influence of the In3+ admixtures on the cation distribution and magnetic ordering in this spinel system. The parent CdCr2Se4 crystallises in the normal spinel structure (Fd3m) [14]. Cadmium and chromium in the cubic close packing of selenium atoms are tetrahedrally (A-type sites) and octahedrally (B-type sites) coordinated, respectively. The compound is a ferromagnetic p-type semiconductor [3] with lattice parameter around 10.7 A˚ [1]. Corresponding author. Tel./fax: +48322588431.
E-mail address: [email protected] (D. Skrzypek). 0022-0248/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2006.10.104
The Curie temperature reported in literature was in the range of 128 K [15]–142 K [3]. The solid solutions CdxInyCrzSe4 were synthesised in polycrystalline form by Shabunina et al. [16]. X-ray structure determination showed that indium, In3+, could accommodate both tetrahedral and octahedral sites in the spinel structure [16]. In the present paper, we study the structural and magnetic properties of single crystals, CdCr2Se4, substituted with In ions in the A- and B-sites using X-ray diffraction, magnetic measurements and ESR spectroscopy. 2. Experimental procedure 2.1. Preparation of the substrates and crystal growth The single crystals were grown by chemical vapour transport method in closed quartz ampoules with anhydrous chromium chloride (purity 98%) as a transporting agent and with the selenides CdSe and In2Se3 as the solid phases. The starting materials, binary selenides, were synthesised from elemental cadmium, indium and selenium
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(purity 99.999%). The stoichiometric mixtures of the elements were pulverised in an agate mortar and sealed in evacuated quartz ampoules. After heating at the 1075 K for 7 days, the selenides were ground in an agate mortar and heated once more for 7 days at the same temperature as before. X-ray powder analysis showed that all products contained only the synthesised phase. The mixture of selenides with transporting agent CrCl3 was sealed in quartz tubes (length E200 mm, inner diameter d ¼ 20 mm) evacuated to E103 Pa. These ampoules were heated in a horizontal zone furnace to about 1123 K at the solution zone, maintaining the temperature gradient of 10 K along the ampoule. After 10 days, the furnace was cooled to room temperature. Growing of quaternary spinel-type chromium selenide single crystals requires special conditions of the chemical transport reactions, which are very important in the crystallisation of the spinels. The equilibrium constants of chemical transport reactions (Ka) were calculated as a function of the temperature to determine, for example, the transport ability of CrCl3. The results of transport depend on log Ka value. When the log Ka value is close to zero, one may expect great transport ability of chemical reactions, even for small temperature difference. The transporting agent CrCl3 dissociated to CrCl3, CrCl4 and Cl2 above 773 K [17]. The transporting reactions, with CrCl3, CrCl4 and Cl2 as the transporting agents, were used to calculate the equilibrium coefficients in heterogeneous system (a gas phase and some solid phases). For the CdSe–In2Se3–CrCl3 system, values of log Ka for transport reactions are similar to the equilibrium state values (log KaE0). Calculated values of log KaE0 for CrCl3 and CrCl4 confirmed that transport of CdSe and In2Se3 is carried out by these agents. The obtained single crystals with well-formed luster faces have the shape of a regular octahedron of 1–3 mm in the edge lengths (see Fig. 1). The XPS survey spectrum confirmed the presence of indium in both compounds.
Fig. 1. The single crystals of (Cd)[Cr1.81In0.19]Se4.
2.2. Experimental techniques 2.2.1. X-ray diffraction The X-ray diffraction measurements were performed with a four-circle diffractometer Xcalibur/CCD Oxford Diffraction, operating in k geometry, using graphite monochromated MoKa radiation and o-scan technique and Do step of 1.21. A set of 900 images was taken in nine runs of 100 exposures with different orientations in the reciprocal space. The exposure time per image was 30 s. Crystal and instrument stability was controlled by one image, selected as a standard and measured after each 50 images [18]. The intensity data were integrated and corrected for Lorentz and polarisation effects with the CrysAlis software [19]. Numerical absorption correction based on the crystal shape was applied [19]. 2.2.2. Magnetic measurements The high-field magnetisation measurements were carried out at T ¼ 4.2 K with a ballistic magnetometer in a Bittertype magnet. The electron spin resonance spectra were recorded with a standard EPR spectrometer operating at X-band (9 GHz) frequency, using 100 kHz field modulation. The microwave frequency was measured using Hewlett Packard 534 microwave frequency counter. The temperature-dependence measurements were performed in the temperature range from 90 to 400 K. The values of the ESR parameters: DB-linewidth and Br-resonance field were obtained on the basis of the best fit for the simulated Lorenzian profile in comparison with the experimentally observed spectra. In both methods (XRD and ESR), the same octahedral, as-grown single crystals were measured. 3. Results and discussion 3.1. Crystal structures and cation distribution Two single-crystal samples representative for the indiumsubstituted CdCr2Se4 spinel, with nominal In concentration y ¼ 0.2 and 0.25 have been selected for the X-ray diffraction measurements. The aim was to determine the location and concentration of the In ion over the tetrahedral (A) and octahedral (B) sites in the cubicclose-packed selenium sublattice. The structure refinement was performed using the SHELXL-97 program package [20]. The crystal data and the details of experimental conditions are summarised in Table 1. The crystal structures have been refined in the space group Fd3¯ m (No. 227) with the origin of the unit cell taken at the point 3¯ m. Similarly as in parent CdCr2Se4, the Cd2+ ion was located at the tetrahedral position 8a: (1/8, 1/8, 1/ 8), and Cr3+ at the octahedral position 16d: (1/2, 1/2, 1/2). The anion took the position 32e: (u, u, u). For each sample, two models have been considered: (1) indium was sharing the tetrahedral position (A) with cadmium and (2) the indium ion was substituting Cr3+ at the octahedral
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written as (Cd)[Cr1.81In0.19]Se4. The results of the structure refinement are given in Tables 2 and 3. The sample II with the nominal y ¼ 0.25, appeared to be a mixed spinel, as some portion of In can be found in octahedral sites, but majority of the indium ions have migrated to the tetrahedral sites leading to the formula (Cd0.745In0.255)[Cr1.94In0.06]Se4. The ionic radius of In with the tetrahedral coordination RIn ¼ 0.63, while for the sixfold coordination the value is R ¼ 0.80 [21]. This feature explains the fact that despite the higher value of y in this sample, the unit cell dimension is not increasing when compared with parent CdCr2Se4 having the unit cell parameter a ¼ 10.745(2) A˚ [22,23].
[B]-sites. In each model, the cations located in the same site were refined with the coupled site occupancy factors. The resulting values enabled writing the chemical formulae for the two crystals. It appeared that in the two selected samples the admixture has been accommodated in a different way. For the sample I with y ¼ 0.2 the best convergence in the structure refinement was obtained for the model 2) with In located at the [B]-sites. The chemical formula can thus be Table 1 Crystal data, experimental details and structure refinement results for the Cd–Cr–In–Se spinel system Crystal data Temperature (K) Crystal system, space group Unit cell dimensions (A˚) a Volume (A˚3) Z Calculated density (Mg/m3) Crystal size (mm) Data collection Wavelength (A˚) 2y max for data collection Limiting indices h k l Reflections collected Reflections unique Reflections 42 s (I)] Absorption coefficient (mm1) Refinement Refinement method Number of refined parameters Goodness-of-fit on F2 Final R indices [I42s(I)] R1 wR2 Extinction coefficient Largest diff. peak and hole (e A˚3)
(Cd)[Cr1.81 In0.19]Se4 297 Cubic, Fd3¯ m
(Cd0.745In0.255) [Cr1.94In0.06]Se4
10.7767(12) 1251.58(3) 8 5.716 0.08 0.08 0.09
10.7577(12) 1159.18(3) 5.274 0.08 0.08 0.09
0.71073 94.01
92.90
14, 17 14, 17 14, 17 5788 259 207 30.10
21, 15 13, 20 20, 21 6801 317 276 30.55
3.2. Magnetic and ESR studies In the chromium spinels, the Cr3+ ions always occupy the B-site of the spinel structure. The local symmetry on this octahedral site leads to a non-degenerate orbital ground state with S ¼ 32. The lattice built upon the B-site consists of tetrahedra of chromium ions. Each chromium ion is common to two tetrahedra, which are defined by the positions of their six first-nearest neighbours. The magnetic properties of CdCr2Se4 were analysed by Baltzer et al. [22] in terms of competing interactions: ferromagnetic between first-nearest neighbours and antiferromagnetic between higher-order neighbours. The field-dependent magnetic moment for both obtained crystals is shown in Fig. 2. The saturation effects have been observed at relatively low Table 3 Selected interatomic distances (A˚) and angles (deg.) for the Cd–Cr–In–Se spinel system in the tetrahedral A and octahedral B sites
Full-matrix least-squares on F2 10 0.956 0.999 0.024 0.035(4) 0.0006(4) 0.91 and 0.87
421
A–Se Cr/In–Se Se–Cr–Se Se–Cr–Se Se–Cr–Se Se–Cd–Se
0.023 0.040(5) 0.00110(5) 0.87 and 1.15
(Cd)[Cr1.81In0.19]Se4
(Cd0.745In0.255)[Cr1.94In0.06]Se4
2.5909(5) 4 2.5541(3) 6 180.00(1) 3 96.86(1) 6 83.14(1) 6 109.47(1) 6
2.5893(4) 4 2.5481(3) 6 180.00(1) 3 96.95(1) 6 83.03(1) 6 109.47(1) 6
Table 2 Atomic coordinates, site occupation factors and equivalent isotropic displacement parameters for the Cd–Cr–In–Se4 spinel system Campound
(Cd)[Cr1.81In0.19]Se4 (Cd0.745In0.255)[Cr1.94In0.06]Se4
Anion positional paramaeter (u)
0.26380(2) 0.26397(2)
Uiso (A˚2 103)
Site occupation A
B
Cd
Cr/In
Se
1.0 0.745:0.255(9)
0.905:0.095(7) 0.970:0.030(5)
14.1(1) 11.3(1)
11.5(2) 9.5(1)
12.3(1) 9.23(9)
Note: The atomic positions are as follows: Cd Cr/In Se
(A) site (B) site Anion site
8a 18 18 18 16d 12 12 12 32e (u u u)
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Fig. 2. The magnetic moment versus the external magnetic field (T ¼ 4.2). K (Cd)[Cr1.81In0.19]Se4 ; J (Cd0.745In0.255)[Cr1.94In0.06]Se4.
magnetic fields. Admixtures of In3+ only in [B]-sites affected strongly the chromium ion interactions, reducing the saturation magnetic moment. Recently, similar results for the Cd[Cr2xGax]Se4 were reported by some of us [23]. In the system (Cd0.745In0.255)[Cr1.94In0.06]Se4, when the majority of the indium ions have migrated to the tetrahedral sites, the magnetic saturation moment is close to the theoretical value of 6mB/molecule. Within the paramagnetic (PM) region, the ESR spectra of both obtained crystals showed a single Lorenzian line with g ¼ 1.99 which is attributed to Cr3+ ions. The ESR spectra for (Cd)[Cr1.81In0.19]Se4 and (Cd0.745In0.255) [Cr1.94In0.06]Se4 and their temperature evolution below T ¼ 140 K are displayed in Figs. 3 and 4, respectively. Clearly, the ESR spectra for both obtained crystals show the same varying tendency. Apart from the dramatic modifications of the spectra at low temperatures are observed: (a) deviation from Lorenzian line-shape; (b) shift of the resonance field (Br); (c) broadening of the linewidth (DB); (d) the anomalous increasing of the intensity;and (e) the splitting of the spectra. The spectral modifications also suggest that there is a structural phase transition from cubic symmetry to tetragonal or orthogonal one at Tc, in addition to the ferromagnetic transition. The plots of the temperature dependence of the linewidth and resonance field are shown in Figs. 5 and 6 for (Cd)[Cr1.81In0.19]Se4 and (Cd0.745In0.255)[Cr1.94In0.06]Se4, respectively. Starting from the T ¼ 400 K, the linewidth values linearly decreased as the temperature was reduced to T ¼ 250 K. The ESR linewidth is related to the relaxation of the spin system. For individual spins DB1/t, where t is the spin relaxation time. In a dense magnetic material, this relationship is modified since the magnetisation relaxes towards an effective field instead of the external field. The review of the mechanisms for the spin-lattice relaxation
Fig. 3. The temperature evolution (Cd)[Cr1.81In0.19]Se4 single crystal.
of
the
ESR
spectrum
of
(and associated temperature dependencies of ESR linewidths) for concentrated magnetic systems was reported by Huber and Seehra [24] and Seehra et al. [25]. For non-Sstate systems with SX1, it is expected that the relaxation of magnetisation is dominated by the phonon modulation of the crystalline field. Following the analysis in Ref. [24], the ESR linewidth of the exchange-coupled PM materials can be described by the expression: DB ¼ DBss þ DBsph , where DBss is described by the exchange narrowing theory [26]: DBss ¼ ½ðDBdd Þ2 =Bex , (i.e. is proportional to the square of the dipolar produced linewidth DBdd divided by the rate of exchange) and DBs-ph represent the contribution of the spin–phonon interaction. The linear temperature dependence of ESR linewidth, which was observed for both obtained crystals shows in accordance with [24] that one-phonon relaxation may
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Fig. 6. The temperature dependence of the ESR parameters for (Cd0.745In0.255)[Cr1.94In0.06]Se4.
Fig. 4. The temperature evolution of (Cd0.745In0.255)[Cr1.94In0.06]Se4 single crystal.
the
ESR
spectrum
of
Fig. 5. The temperature dependence of the ESR parameters for (Cd)[Cr1.81In0.19]Se4.
prevail in PM materials even at high temperatures. This effect is caused by a broad band of phonons that may participate in the spin relaxation process.
In PM state, there are the interactions between spins and by lowering of the temperature, short-range order progressively occurs, which can correspond to very small clusters. Near the transition temperature Tc, the clusters grow and coalesce to create an infinite magnetic matrix at Tc. ESR has been recognised as a powerful tool for probing the spin structure and dynamics. Its high sensitivity to both minor magnetic phases and short-range interactions permits a selective disclosure of the subtle changes in spin systems. That is why our measurements of the ESR spectra reveal (below T ¼ 160 K for (Cd)[Cr1.81In0.19]Se4 and T ¼ 140 K for (Cd0.745In0.255)[Cr1.94In0.06]Se4) apart from strong PM line, the presence of the new lines (see Figs. 3 and 4), which means the appearance of the clusters of Cr3+. It is worth noting that the short-range order, which suggests an increased magnetic inhomogeneity of the systems, is depended upon indium distribution. The confirmation of this suggestion is in the calculations, which were done by Bakrim et al. [27]. These authors calculated, from the results of the random phase approximation (RPA), the correlation functions for a Heisenberg ferromagnetic model having both nearest-neighbour (nn) and next nearest-neighbour (nnn) exchange integrals. The theoretical results obtained were used to study the PM state of spinels Cd[Cr2xGax]Se4. It can be noted that all correlation functions persist far into PM region (see Figs. 1–6 in Ref. [27]). The appearance of the short-range magnetic ordering was confirmed by the temperature dependence of the spectrum intensity. In Figs. 7 and 8, the temperature evolution of intensity of ESR spectrum for both obtained crystals is shown. The adequate values were calculated as double integration of the spectrum (DI). This defined intensity should be proportional to the spin susceptibility of the sample. It can be seen, that below T ¼ 300 K, the deviation of the inverse susceptibility from the Curie–Weiss law appears. As the temperature is reduced from about T ¼ 170 K, the values for the intensity rapidly increase.
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In addition, the ESR spectra analyses also indicate that the PM–ferromagnetic transition is incomplete and the PM phase may still survive in a certain temperature range below Tc. 4. Conclusions
Fig. 7. The relative (Cd)[Cr1.81In0.19]Se4.
ESR
susceptibility
versus
temperature
for
In this work, we presented the X-ray diffraction analysis for two types of diluted ferromagnetic CdCr2Se4 single crystals: (Cd)[Cr1.81In0.19]Se4 in which In substitutes Cr and (Cd0.745In0.255)[Cr1.94In0.06]Se4 where In substitutes Cd and Cr. The magnetic properties of the same as-grown single crystals were examined by ESR spectroscopy. ESR was found to be extremely sensitive for detecting minor magnetic phases and short-range order. In resonance spectra, the ferromagnetic clusters signals are presented: from TE160 K for Cd)[Cr1.81In0.19]Se4 and from TE140 K for (Cd0.745In0.255)[Cr1.94In0.06]Se4. The transition region appears to be broad for both obtained crystals and PM phase was still present up to T ¼ 125 K. The stronger magnetic inhomogeneity occurs for (Cd)[Cr1.81In0.19]Se4 crystal. The linear variation in resonance linewidth with temperature for T4250 K is an experimental proof of Huber’s–Seehra’s theory. It describes the occurrence of one-phonon processes up to high temperatures in spinlattice relaxation in magnetically concentrated systems. References
Fig. 8. The relative ESR susceptibility (Cd0.745In0.255)[Cr1.94In0.06]Se4.
versus
temperature
for
This rise is more marked than theoretically predicted for the Heisenberg-type ferromagnets, where magnetic susceptibility wE[(TTc)/Tc]p with p ¼ 43 [28]. The effect observed is due to the presence of external magnetic field, which orients the clusters in the field direction. The spectra below T ¼ 130 K (see Figs. 3 and 4) are attributed to the ferromagnetic resonance (FMR). In FMR equation written by Kittel [29], the contributions of the demagnetisation and magnetocrystalline anisotropy fields occur. The complexity of resonance spectra for both the obtained crystals is due to the inhomogeneity of the internal magnetic field which is caused by the demagnetising effects brought about by the octahedron sample shape [30] and due to the domain structure [31]. It can be seen, from Figs. 5 and 6, that the transition region is broad for both the obtained crystals. The original PM line broadens gradually, shifts from PM resonance and finally vanishes.
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