Specific heat and magnetic susceptibility of single-crystalline ZnCr2Se4 spinels doped with Ga, In and Ce

Materials Chemistry and Physics 131 (2011) 142–150

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Specific heat and magnetic susceptibility of single-crystalline ZnCr2 Se4 spinels doped with Ga, In and Ce b c ´ ˛ E. Malicka a,∗ , T. Gron´ b , A. Slebarski , A. Gagor , A.W. Pacyna d , R. Sitko a , J. Goraus b , T. Mydlarz e , J. Heimann b a

University of Silesia, Institute of Chemistry, ul. Szkolna 9, 40-006 Katowice, Poland University of Silesia, Institute of Physics, ul. Uniwersytecka 4, 40-007 Katowice, Poland c Institute of Low Temperature and Structure Research, Polish Academy of Sciences, P.O. Box 1410, 50-950 Wrocław, Poland d The Henryk Niewodnicza´ nski Institute of Nuclear Physics, Polish Academy of Sciences, ul. Radzikowskiego 152, 31-342 Kraków, Poland e International Laboratory of High Magnetic Fields and Low Temperatures, ul. Gajowicka 95, 53-529 Wrocław, Poland b

a r t i c l e

i n f o

Article history: Received 28 January 2011 Received in revised form 23 June 2011 Accepted 29 July 2011 Keywords: Chalcogenides X-ray photo-emission spectroscopy (XPS) Magnetic properties Specific heat

a b s t r a c t The crystal structure, X-ray photoelectron spectra (XPS), dc magnetic isotherm, ac magnetic susceptibility and specific heat measurements for antiferromagnetic and semiconducting ZnCr2 Se4 spinel diluted with Ga, In and Ce are presented. For all the studied spinels the XPS spectra exhibit the Cr 2p3/2 splitting of 1 eV characteristic for the 3d3 electron configuration of the chromium ions. A correlation between the second critical field Hc2 of the helix to paramagnetic transition and the magnetic specific heat C-peak was found in (Zn0.86 Ce0.08 )[Cr2 ]Se4 . This correlation weakens for (Zn0.99 )[Cr1.92 Ga0.06 ]Se4 and disappears for (Zn0.83 In0.11 )[Cr1.73 In0.14 ]Se4 as the saturation magnetic moment rapidly decreases in the sequence Ce, Ga and In. The magnetic contribution to the specific heat displays a sharp peak at TN and is maximal at the spin fluctuation temperature of 40 K, which is related to the maximum of the magnetic susceptibility at the same temperature and at 50 kOe in the spin fluctuation region, evidenced by the entropy exceeding 90% of the entropy calculated classically for the complete alignment of the Cr spins, Sm = R ln(2S + 1). These effects are considered within the cation–anion distances in octahedral sites, the cation deficiency and the spin state of 3d Cr3+ ions in t2g orbital. © 2011 Elsevier B.V. All rights reserved.

1. Introduction It is well known in literature that ZnCr2 Se4 spinel is a matrix for various diluted systems where the effects of the site disorder, lattice frustration and random distribution of spin interactions create novel potential applications in the spin-based electronic technology. ZnCr2 Se4 orders antiferromagnetically (AFM) at Néel temperature TN = 20 K but high positive Curie–Weiss  CW = 115 K [1,2] evidences strong ferromagnetic (FM) interactions. The magnetic order is accompanied by structural transformation from cubic ¯ to tetragonal I41 /amd symmetry with a small contraction Fd3m along the c axis [3,4]. Neutron-diffraction investigations [1,2] have shown the helical AFM spin structure below TN , which results from a strong ferromagnetic (FM) spin arrangement in the planes perpendicular to the [0 0 1] direction of the orthorhombic cell. The spin orientation between the planes changes by the angle 42◦ , and the spin propagation vector along the [0 0 1] is incommensurate.

∗ Corresponding author. Permanent address: Chemistry Department, University of Silesia, ul. Szkolna 9, 40-006 Katowice, Poland. Tel.: +48 323591627. E-mail address: [email protected] (E. Malicka). 0254-0584/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.matchemphys.2011.07.080

The specific heat and thermal expansion studies evidenced a strong effect of the external field [5]. The sharp first-order anomalies in the specific heat appearing at the AFM transition suggested a spin-driven origin of the transition, however, the suppression of the negative thermal expansion by the external magnetic fields might have pointed to the role of the spin–lattice coupling. In the same investigation a metamagnetic transition in the critical field Hc1 of about 10 kOe and T = 2 K, the breakdown of the helical spin arrangement in the critical field Hc2 of about 65 kOe for T = 2 K, and the full saturation magnetization of about 6 ␮B per molecule above Hc2 in the FM state are revealed. The differences between the zero-fieldcooling (ZFC) and field-cooling (FC) susceptibilities indicated a spin frustration effect [5]. The studies of the complex ac dynamic magnetic susceptibility in external magnetic fields in polycrystalline ZnCr2 Se4 spinel [6] and the fitting procedure of the Curie–Weiss law [7] have shown a parallel spin coupling in FM clusters in the range between TN = 20.7 K and  CW = 55.1 K visible in a broad maximum at 34 K for H = 40 kOe and at 43.5 K for H = 50 kOe in the real part of ac magnetic susceptibility characteristic for magnetic fluctuations. Numerous papers described also the influence of various cationic admixtures on physical properties of ZnCr2 Se4 spinel

E. Malicka et al. / Materials Chemistry and Physics 131 (2011) 142–150

[8–17]. The magnetic and electrical measurements carried out for Zn1−x Ga2x/3 Cr2 Se4 poly- and single crystals in the compositional range 0.0 ≤ x ≤ 0.5 have shown AFM order below the Néel temperature (22 K ≥ TN ≥ 12 K) [8–10] and the thermally activated p-type conduction [9–12]. The increase of the Ga ion content resulted in a decrease of TN [9,10], Curie–Weiss temperature (118 K ≥  CW ≥ 62) [8–10] and also of the effective magnetic moment (5.49 ␮B ≥ eff ≥ 5.27 ␮B ) [8–10]. In addition, a disappearance of the critical fields has been observed [13]. The characteristics of ZnCr2−x Inx Se4 single crystals in the compositional range 0.0 ≤ x ≤ 0.14 exhibited AFM order with the metamagnetic phase transitions below the Néel temperature (22 K ≥ TN ≥ 16 K) [14,15] and the thermally activated p-type conductivity [16,17] for x ≤ 0.07. With higher In content (x > 0.07) and above room temperature a change of the sign of the Seebeck coefficient from negative to positive has occurred [17]. With In concentration of x = 0.14 a decrease of TN to 16 K with  CW ∼ 49 K and the critical fields (Hc1 ∼ 8 T and Hc2 ∼ 11 T) [14] was observed together with unusually high value of the effective magnetic moment [16,17], eff ∼ 6.82 ␮B that has been explained by the presence of Cr2+ ions [14,15]. However, the saturation moment of 4.36 ␮B /f.u. [14], smaller than in pure ZnCr2 Se4 (∼6 ␮B /f.u.) [14] did not confirm the presence of bivalent chromium. Recently, the structural, electron spin resonance and magnetic properties of the single-crystalline spinel system ZnCr2−x Inx Se4 showed that the magnetic moment of 5 ␮B /f.u. at 2 K and at 8 T was almost independent on the In-substitution and also excluded the presence of the magnetic ions in a different valence state: Cr2+ and Cr4+ besides the main state: Cr3+ [18]. The present paper reports in more detail the magnetic and specific heat properties of ZnCr2 Se4 diluted with nonmagnetic ions of Ga and In and magnetic Ce ion. We are expecting to find a correlation between the critical fields, specific heat behaviour and spin configuration in the Cr3+ d-orbital. With this aim the XPS spectra were measured to evidence the electronic state of Cr ion at room temperature. Subsequently, the dc magnetization and complex ac dynamic magnetic susceptibility measurements were performed to investigate the effect of external magnetic field on the spin driven origin of the transition. Finally, the specific heat versus temperature was measured at different external fields for the purpose of the spin–phonon coupling observations. 2. Experimental description 2.1. Synthesis and crystal structure Starting materials for single crystal growth of Znx Cry Mez Se4 (Me = Ga, In, Ce) were the binary selenides ZnSe, Ga2 Se3 , In2 Se3 and elementary cerium (purity 99.99%) and selenium (purity 99.99%). The crystals were obtained by a chemical vapour transport reaction using anhydrous chromium chloride CrCl3 (purity 95%) as a transporting agent. The binary selenides were synthesized from elemental zinc, gallium, indium and selenium, all with the stated purities better than 99.99%. The stoichiometric mixtures of the elements were pulverized in an agate mortar and sealed in evacuated quartz ampoules. The synthesis was repeated several times at 1073 K in order to obtain good homogeneity of the selenides. Mixtures of the starting materials were sealed in quartz ampoules (length ∼200 mm, inner diameter 20 mm) evacuated to ∼10−3 Pa. For single crystals of Znx Cry Gaz Se4 and Znx Cry Inz Se4 the temperature of crystallization zone was 1120 K and 1155 K, while the temperature of melting zone was 1200 and 1230 K, respectively. The growth of Znx Cey Crz Se4 single crystals was carried out at temperatures between 1250 K and 1150 K. The furnace was slowly cooled to room temperature after 3 weeks of heating. The obtained single crystals had a regular octahedral shape and well-formed regular (1 1 1) faces with edge length of about 0.5 ÷ 5 mm. Chemical compositions of the single crystals were determined nondestructively by energy-dispersive X-ray fluorescence spectrometry (EDXRF) [19]. The samples were excited by an X-ray beam from the air-cooled side-window Rh target of the X-ray tube with Be window of 125 ␮m thickness and nominal focal spot size of ca. 100 ␮m of (XTF 5011/75, Oxford Instruments, USA). The X-ray tube was supplied with XLG high-voltage generator (Spellman, USA). The pinhole collimator was placed in front of the X-ray tube to reduce the size of analyzed area. The X-ray spectra emitted by the samples were collected by a thermoelec-

143

trically cooled Si-PIN detector (XR-100CR Amptek, Bedford, MA, USA) of 6 mm2 active area, 500 ␮m crystal thickness and 12.5 ␮m Be window thickness. The resolution of the Si-PIN detector cooled to the temperature of ca. −55 ◦ C was 145 eV at 5.9 keV. The detector was coupled to a multichannel analyzer (PX4 Amptek, Bedford, MA, USA). The quantitative EDXRF analysis was performed using the fundamental parameter method based on the Sherman equation [20] and Pella et al. algorithm [21,22] to calculate the X-ray tube spectrum. Each single crystal was measured five times at various positions. The average values of determined concentrations together with calculated stoichiometry of synthesized single crystals are presented in Table 1. A single-crystal X-ray data collection was performed with Kuma KM4CCD diffractometer equipped with CCD detector and using Mo K␣ radiation. The CrysAlis. Software, version 1.170.32 [23] was used for data processing. An empirical absorption correction was applied using spherical harmonics implemented in Scale3 Abspack scaling algorithm. The structure was refined by the full-matrix leastsquares method by means of SHELX-97 program package [24]. In order to determine the positions and site occupation factors (SOFs) for the cations two different procedures were used in the least-square refinements depending on the dopant type. In ZnCr2 Se4 doped with In3+ and Ce3+ SOFs for all cations were treated as free variables since the scattering factors for Ce3+ and In3+ differ remarkably from those for Zn2+ and Cr3+ [International Tables For Crystallography, Vol. C, Tables 4.2.6.8 and 6.1.1.4]. In order to avoid correlations between SOFs for two atoms located at the same position, at the first stage of the refinement SOFs for individual cations were treated alternatively as the free parameters. In the last cycles all parameters were refined together as free variables. In ZnCr2 Se4 doped with Ga3+ a slightly different procedure was used since the scattering factors for Ga3+ and Zn2+ are almost equal. Firstly, the presence of Ga3+ was tested at Cr3+ site, SOFs for Cr3+ and Ga3+ were set free together with Zn2+ to estimate the number of vacancies on A site. Secondly, the difference between the Ga3+ concentration obtained from EDXRF analysis and amount of Ga3+ at B site was calculated. Since the remaining Ga3+ content (equal to 0.01) was within the estimated standard deviation of EDXRF analysis the Ga3+ ions were excluded from tetrahedral sites. The results of crystal structure refinement and the interatomic distances for all compounds are given in Tables 2–4. 2.2. X-ray photoelectron spectroscopy (XPS) The XPS spectra were taken using a PHI 5700/660 Physical Electronic spectrometer with monochromated Al K␣ radiation. The photoelectron spectra were analyzed with a hemispherical mirror assuring energy resolution of about 0.3 eV. In order to obtain free of contamination fresh surface, the samples were scraped in situ in 10−10 hPa vacuum. The binding energy in the range −2 to 1400 eV and the core-level characteristic peaks for Cr 2p have been measured. The background was subtracted using the Tougaard’s approximation. 2.3. Magnetic and specific heat measurements Magnetization and ac magnetic susceptibility with real ( ) and imaginary ( ) components were measured in the zero-field-cooled mode using a vibrating sample magnetometer with a step motor [25] at 4.2 K and in applied magnetic fields up to 150 kOe and a Lake Shore 7225 ac susceptometer up to 60 kOe in the temperature range 4.2–300 K, respectively. System accuracy: calibration constants (both ac and dc) are accurate within ± 1.0%. Ac susceptibility sensitivity to 2 × 10−8 emu in terms of equivalent magnetic moment and dc moment sensitivity: 9 × 10−8 emu. Specific heat was measured with a Quantum Design Physical Properties Measurement System (QD-PPMS) with heat capacity option in temperature range 1.8–300 K and at magnetic field up to 70 kOe.

3. Results and discussion 3.1. Crystal structure and cation distribution ZnCr2 Se4 crystallizes in the cubic spinel structure with the space ¯ (No. 227). In a normal spinel structure Zn2+ group symmetry Fd3m ions are located at 8a (1/8, 1/8, 1/8) (A site) with tetrahedral coordination whereas the Cr3+ ions, that are known for a strong octahedral site preference [26], occupy octahedrally coordinated position 16d: (½, ½, ½) (B site). The Se2− ions are located at 32e Wyckoff site. The incorporation of In3+ , Ce3+ or Ga3+ into the ZnCr2 Se4 does not change the crystal symmetry. The spinel structure is very flexible in respect to the cations it can incorporate. In particular A2+ and B3+ cations can mix or even replace forming inverted spinel. It also seems that the growth conditions are essential for stabilization of the certain cation distribution, e.g. Ga3+ in ZnCr2 Se4 matrix may substitute for Cr or/and Zn [27]. In3+ ions

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Table 1 The chemical composition of single crystals expressed in wt%. Spinel

Zn

In

Ga

Ce

Cr

Se

Zn0.83 ± 0.04 In0.25 ± 0.01 Cr1.73 ± 0.06 Se4 Zn0.99 ± 0.02 Ga0.06 ± 0.01 Cr1.92 ± 0.04 Se4 Zn0.86 ± 0.02 Ce0.08 ± 0.01 Cr2.0 ± 0.04 Se4

11.1 ± 0.5 13.4 ± 0.3 11.6 ± 0.3

5.9 ± 0.2 – –

– 0.9 ± 0.1 –

– – 2.4 ± 0.2

18.4 ± 0.6 20.6 ± 0.4 21.3 ± 0.4

64.6 ± 0.9 65.1 ± 0.8 64.7 ± 0.9

Table 2 Crystal data, experimental details and crystal structure refinement results at 295 K for I: (Zn0.83 In0.11 )[Cr1.73 In0.14 ]Se4 , II: (Zn0.99 )[Cr1.92 Ga0.06 ]Se4 , III: (Zn0.86 Ce0.08 )[Cr2 ]Se4 . Spinel Crystal data Crystal system, space group Mr (g mol−1 ) a (Å) V (Å3 ), Z Crystal size (mm) Data collection 2 max for data collection Tmin , Tmax  (mm−1 ), Rint No. of measured, independent and observed [I > 2(I)] reflections Refinement R[F2 > 2(F2 )], wR(F2 ), S No. of reflections No. of parameters No. of restraints max , min (e A˚ −3 )

I

II

III

¯ Cubic, Fd3m 490.40 10.5093(3) 1160.70(6), 8 0.15 × 0.1 × 0.08

¯ Cubic, Fd3m 484.62 10.4971(2) 1156.67(4), 8 0.2 × 0.15 × 0.08

¯ Cubic, Fd3m 484.40 10. 4937(2) 1155.55(3), 8 0.21 × 0.15 × 0.08

36.18 0.03, 0.08 32.53, 0.057 4802, 164, 153

36.18 0.005, 0.070 32.92, 0.088 4696, 165, 147

36.19 0.01, 0.07 32.912, 0.063 4801,165,157

0.014, 0.029, 1.149 164 12 0 1.322, −0.635

0.017, 0.042, 1.422 165 11 0 0.641, −0.739

0.013, 0.032, 1.357 165 11 0 0.594, −0.549

Table 3 Anion parameters (u), site occupation factors and equivalent isotropic displacement parameters (Uiso ) at 295 K for I: (Zn0.83 In0.11 )[Cr1.73 In0.14 ]Se4 , II: (Zn0.99 )[Cr1.92 Ga0.06 ]Se4 , III: (Zn0.86 Ce0.08 )[Cr2 ]Se4 . (A) and (B) are the tetra- and octahedral sites, respectively. Spinel

u

I II III

0.25940(2) 0.25933(2) 0.25944(2)

Uiso (Å2 × 104 )

Site occupation factors A

B

A

B

Se

0.832(2): 0.111(2) 0.987(3) 0.864(4): 0.076(3)

0.867(3): 0.071(2) 0.962(5): 0.031(4) 1.005(3)

98(2) 97(2) 96(2)

66(2) 66(2) 54(2)

66(1) 70(1) 58(1)

Table 4 Interatomic distances at 295 K for I: (Zn0.83 In0.11 )[Cr1.73 In0.14 ]Se4 , II: (Zn0.99 )[Cr1.92 Ga0.06 ]Se4 , III: (Zn0.86 Ce0.08 )[Cr2 ]Se4 . Spinel

Zn/In–Se

Cr/In–Se

Zn–Se

Cr/Ga–Se

Zn/Ce–Se

Cr–Se

I II III

4× 2.4467(4) – –

6× 2.5322(7) – –

– 4× 2.4425(4) –

– 6× 2.5301(2) –

– – 4× 2.4434(4)

– – 6× 2.5283(2)

were also found in octahedral and/or tetrahedral sites [18,28]. Thus, for all compositions the tetrahedrally coordinated A as well as octahedrally coordinated B positions were tested as a potential sites for dopants. The most stable and convergent refinements were obtained for the atom positions and SOFs presented in Table 3. In3+ as well as Ce3+ replaced for Zn2+ in tetrahedral sites introduce an increase of the overall positive charge in the crystal that has to be compensated. In the case of In3+ dopant the compensation comes from cation vacancies that appear at both A and B sites. In (Zn0.83 In0.11 )[Cr1.73 In0.14 ]Se4 there is 6% vacant cation A sites and 6.5% B sites. In (Zn0.86 Ce0.08 )[Cr2 ]Se4 6% of vacancies is observed only at A position. (Zn0.99 )[Cr1.92 Ga0.06 ]Se4 has much smaller number of cation-deficient sites (1% vacant A and B sites) due to the fact that A sites are occupied exclusively by Zn2+ ions. The cubic lattice parameter of the ZnCr2 Se4 phase is equal to ˚ The incorporation of Ga3+ ions into the crystal struca = 10.497(1) A. ture does not influence the mean unit cell parameter that is equal to 10.4971(2) A˚ for (Zn0.99 )[Cr1.92 Ga0.06 ]Se4 . The result is not unexpected if we compare the ionic radius (ri ) of Ga3+ to Cr3+ and Zn2+ . At octahedrally coordinated position ri Ga3+ = 0.76 A˚ [29] is almost

˚ Consequently, this substitution does not identical to ri Cr3+ = 0.755 A. affect unit cell dimensions. In (Zn0.83 In0.11 )[Cr1.73 In0.14 ]Se4 crystals a equals to ˚ The increase of lattice parameter compared to 10.5093(3) A. ZnCr2 Se4 may be attributed to the presence of In3+ in B site. Ionic radius of In3+ in octahedral coordination equals to ri In3+ = 0.94 A˚ ˚ In3+ at tetrahedral site that remarkably differs from ri Cr3+ = 0.755 A. ˚ has similar ionic radius as Zn2+ at the same position (ri In3+ = 0.76 A, ri Zn2+ = 0.74 A˚ [29]) consequently, In3+ occupying A site should not affect the a value. Concerning (Zn0.86 Ce0.08 )[Cr2 ]Se4 , there is a striking decrease in the unit cell dimension after incorporation of large Ce3+ ion on A site (ri Ce3+ = 1.15 A˚ in the tetrahedral coordination). The effect cannot be elucidated in terms of ionic radii values. One of the explanations may be the large number of vacant A sites that is comparable to the Ce3+ concentration (6% vacancies vs. 8% of Ce3+ ) that prevents unit cell elongation. It is also worth noting that in some spinels lattice parameters do not obey the Vegard’s law even if dopants significantly differing in ionic radius are introduced into the crystal structure, e.g. in Znx Cry Alz Se4 spinels the substitution of Cr3+ for smaller Al3+ cations leads to the increase of the lattice parameter [30].

E. Malicka et al. / Materials Chemistry and Physics 131 (2011) 142–150

145

6

ZnCr2Se4 (Zn0.99)[Cr1.92Ga0.06]Se4

(Zn0.83In0.11)[Cr1.73In0.14]Se4

5

(Zn0.86Ce0.08)[Cr2]Se4

σ (μB/f.u.)

Intensity [a.u.]

4

1eV

3

(Zn0.99)[Cr1.92Ga0.06]Se4 2

Cr 2p3/2

(Zn0.83In0.11)[Cr1.73In0.14]Se4

Cr 2p1/2

(Zn0.86Ce0.08)[Cr2]Se4 1

570

575

580

585

590

Binding Energy [eV]

0 0

Fig. 1. Cr 2p – XPS spectra of the ZnCr2 Se4 single crystals diluted with Ga, In and Ce. The XPS spectrum for the ZnCr2 Se4 matrix was taken from Ref. [31] for comparison.

90

120

150

Fig. 2. Magnetization, , vs. magnetic field H at 4.2 K for (Zn0.99 )[Cr1.92 Ga0.06 ]Se4 , (Zn0.83 In0.11 )[Cr1.73 In0.14 ]Se4 and (Zn0.86 Ce0.08 )[Cr2 ]Se4 .

The ac magnetic susceptibility versus temperature and external magnetic field is shown for (Zn0.99 )[Cr1.92 Ga0.06 ]Se4 in Figs. 3 and 4, for (Zn0.83 In0.11 )[Cr1.73 In0.14 ]Se4 in Figs. 5 and 6 and for (Zn0.86 Ce0.08 )[Cr2 ]Se4 in Figs. 7 and 8, respectively. The spinels with mainly octahedral coordination of Ga and In ions show fuzzy peaks in  (T) and the  (T) signal oscillating around zero. The spinel with tetrahedrally coordinated Ce shows sharp peaks formed both in the real part,  (T), and the imaginary part,  (T), of magnetic susceptibility. The peaks in  (T) dependencies, measured in the field 0 and ∼10 kOe are broad indicating the second order transition from AFM to paramagnetic (PM) state. The corresponding energy 0

20

40

60

80

100

1,6

Hac = 1 Oe f = 120 Hz Hdc:

1,2

-3

3

χ' [10 cm /g]

TN

0 kOe 10 kOe 30 kOe 50 kOe

0,8

0,4

Tm 0,0 4

(Zn0.99)[Cr1.92Ga0.06]Se4

3 2

3.3. Magnetic properties The magnetic isotherms for the three spinels are shown in Fig. 2 exhibit zero coercivity and remanence as well as a lack of hysteresis. In the field above 70 kOe the three samples reach a saturation. For (Zn0.83 In0.11 )[Cr1.73 In0.14 ]Se4 the marked lowering of the saturation moment ( sat = 1.04 ␮B /f.u. at 4.2 K and at 136 kOe) was noticed. Smaller reduction was observed for (Zn0.99 )[Cr1.92 Ga0.06 ]Se4 ( sat = 4.56 ␮B /f.u. at 4.2 K and at 136 kOe) and only for (Zn0.86 Ce0.08 )[Cr2 ]Se4 the saturation moment is close to the theoretical value of 6 ␮B /f.u. in the high-spin (HS) state. These results are the main reason for looking at the spin configuration of the 3d3 t2g orbital in more detail.

-4

3

Fig. 1 shows the Cr 2p XPS spectra for (Zn0.99 )[Cr1.92 Ga0.06 ]Se4 , (Zn0.83 In0.11 )[Cr1.73 In0.14 ]Se4 and (Zn0.86 Ce0.08 )[Cr2 ]Se4 single crystals and for comparison ZnCr2 Se4 [31]. All the spectra exhibit the spin–orbit separation of 9.5 eV between the Cr 2p3/2 and Cr 2p1/2 states. The Cr 2p3/2 states itself are split into two peaks at 574.2 and 575.2 eV. The peak separation with the binding energy difference E of about 1 eV is typical of the 3d elements. Such a value of E was reported for a number of chalcogenide spinels [31,32], i.e. metallic ferromagnet CuCr2 Se4 , semiconducting ferromagnet Hg(Cd)Cr2 Se4 , semiconducting ferrimagnet Fe(Mn)Cr2 S4 , insulating ZnCr2 S4 and semiconducting antiferromagnet ZnCr2 Se4 . This energy difference was also reported for Mn and Cr-based Heusler alloys with localized magnetic moments larger than 4 ␮B /f.u. [33,34] for which a linear relationship between the magnitude of the splitting of the 2p3/2 core levels and the valence state of the 3d transition metals has been observed [33]. Based on these findings, especially taking into account a variety of macroscopic magnetic and electrical properties of the chalcogenide spinels mentioned above, it can be concluded that the splitting of the Cr 2p3/2 level in the single crystals under study is determined by the symmetry and bonding properties of the ligand field [35,36]. The Ga, In and Ce ions, built into the spinel structure with the concentrations given by chemical formula of the present crystals did not change the cubic symmetry of the room temperature phase, thus the ligand field around Cr ions remains octahedral. Therefore the direct influence of the substitution on E is not observed.

60

H (kOe)

χ'' [10 cm /g]

3.2. X-ray photoelectron spectroscopy (XPS)

30

1 0 -1 -2 -3 -4

0

20

40

60

80

100

T [K] Fig. 3. Real  and imaginary  components of ac magnetic susceptibility vs. temperature T recorded at Hac = 1 Oe with f = 120 Hz taken at different external magnetic fields for (Zn0.83 In0.11 )[Cr1.73 In0.14 ]Se4 . The Néel TN and Tm temperatures are indicated by arrows.

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E. Malicka et al. / Materials Chemistry and Physics 131 (2011) 142–150

1,8

1,5

Hc2

Hac = 1 Oe

χac [10 cm /g]

-3

Hac = 1 Oe f = 120 Hz 4.3 K 10 K 18.1 K 21.5 K

0,6

0,3

1,2

Hc1

3

Hc1

0,9

-3

3

χac [10 cm /g]

f = 120 Hz 4.3 K 9.8 K 15.9 K 18.2 K

1,5

1,2

0,9

0,6

0,3

(Zn0.99)[Cr1.92Ga0.06]Se4

(Zn0.83In0.11)[Cr1.73In0.14]Se4

0,0

0,0 0

10

20

30

40

50

60

0

10

20

30

H [kOe]

40

50

60

H [kOe]

Fig. 4. Ac magnetic susceptibility, ac , vs. static magnetic field H recorded at internal oscillating magnetic field Hac = 1 Oe with internal frequency f = 120 Hz taken at different temperatures for (Zn0.99 )[Cr1.92 Ga0.06 ]Se4 . The critical fields Hc1 and Hc2 are indicated by arrows.

Fig. 6. Ac magnetic susceptibility, ac , vs. static magnetic field H recorded at internal oscillating magnetic field Hac = 1 Oe with internal frequency f = 120 Hz taken at different temperatures for (Zn0.83 In0.11 )[Cr1.73 In0.14 ]Se4 . The critical fields Hc1 and Hc2 are indicated by arrows.

loss anomalies in  (T), are also broad and have low intensities. In higher magnetic fields of 30, 40 and 50 kOe all peaks in  (T) and  (T) curves are anomalously sharp, suggesting the structural phase transition of the first order. This idea, of course, requires confirmation by the X-ray and neutron diffraction studies in magnetic fields. For the three considered cation substitutions,  (T) and  (T) dependencies show broad maximum at Tm in the magnetic field ≥ 40 kOe, indicating the FM order persisting in the PM region. In Figs. 4, 6 and 8 are shown the ac magnetic susceptibilities versus external magnetic field, ac (H), measured at different temperatures of the range 4.3–22 K. For the crystals admixed with

Ga and Ce there are seen two critical fields denoted by Hc1 and Hc2 . With increasing temperature, the critical field Hc1 , connected with the metamagnetic transition and breakdown of the spiral spin structure [3,5] decreases only slightly, whereas Hc2 , related to the breakdown of the conical spin arrangement [5,6] decreases significantly. Above TN both critical fields disappear. With increasing external magnetic field the critical field Hc1 remains almost unchanged because it is related to the AFM order in the tetragonal structure, while Hc2 is shifted toward the higher fields. Therefore the FM order may exists far above TN in the cubic (spinel) structure

0

20

40

60

80

0

100

2,0

TN

3

χ' [10 cm /g]

0,8

0,5

6

Hac = 1 Oe

5

f = 120 Hz Hdc:

3

χ'' [10 cm /g]

0 kOe 12.5 kOe 30 kOe 40 kOe 50 kOe

4

-5

3

(Zn0.86Ce0.08)[Cr2]Se4

0,0

(Zn0.83In0.11)[Cr1.73In0.14]Se4

10

-4

100

Tm Tm

0,0

χ'' [10 cm /g]

80

1,0

0,4

0

60

-3

0 kOe 10 kOe 30 kOe 50 kOe

-3

3

f = 120 Hz Hdc:

1,2

5

40

TN

Hac = 1 Oe

1,6

χ' [10 cm /g]

20

1,5

-5 -10

3 2 1

-15

0 0

20

40

60

80

100

T [K] Fig. 5. Real  and imaginary  components of ac magnetic susceptibility vs. temperature T recorded at Hac = 1 Oe with f = 120 Hz taken at different external magnetic fields for (Zn0.83 In0.11 )[Cr1.73 In0.14 ]Se4 . The Néel TN and Tm temperatures are indicated by arrows.

0

20

40

60

80

100

T [K] Fig. 7. Real  and imaginary  components of ac magnetic susceptibility vs. temperature T recorded at Hac = 1 Oe with f = 120 Hz taken at different external magnetic fields for (Zn0.86 Ce0.08 )[Cr2 ]Se4 . The Néel TN and Tm temperatures are indicated by arrows.

E. Malicka et al. / Materials Chemistry and Physics 131 (2011) 142–150

147

200

1,4

(Zn0.86Ce0.08)[Cr2]Se4

Hc2

1,2

experiment Debye fit ΔC

160

C [J/(mol·K)]

0,8

Hc1

-3

3

χac [10 cm /g]

1,0

0,6

Hac = 1 Oe f = 120 Hz 4.3 K 6K 11.9 K 20.2 K 22.2 K

0,4

0,2

10

80

40

(Zn0.83In0.11)[Cr1.73In0.14]Se4

0

0,0 0

120

20

30

40

50

0

60

50

100

150

H [kOe] Fig. 8. Ac magnetic susceptibility, ac , vs. static magnetic field H recorded at internal oscillating magnetic field Hac = 1 Oe with internal frequency f = 120 Hz taken at different temperatures for (Zn0.86 Ce0.08 )[Cr2 ]Se4 . The critical fields Hc1 and Hc2 are indicated by arrows.

reaching some maximum at Tm . It means that external magnetic fields extends the temperature range of the FM order and on the other hand it shifts the AFM arrangement toward the lower temperature. In particular, (Zn0.86 Ce0.08 )[Cr2 ]Se4 , where the Ce admixture is tetrahedrally coordinated, the Hc1 and Hc2 anomalies are sharp and at temperature 4.3 K the critical field Hc2 is shifted toward the higher magnetic fields. Similar trend in the field dependence is seen in the case of (Zn0.99 )[Cr1.92 Ga0.06 ]Se4 although the Hc1 and Hc2 peaks are not sharp, that can be explained with the random distribution of Cr–Se and Ga–Se bonds in the octahedral sites, whereas for (Zn0.83 In0.11 )[Cr1.73 In0.14 ]Se4 the Hc2 peak does not occur. 3.4. Specific heat studies Fig. 9 displays specific heat in zero-magnetic field vs. temperature in wide T-range for (Zn0.83 In0.11 )[Cr1.73 In0.14 ]Se4 . Above ∼100 K the temperature dependence of the specific heat for the all investigated compounds can be well approximated by the Debye expression [37]:

D 0

x 4 ex (ex − 1)2

dx,

250

300

Fig. 9. Specific heat C vs. temperature T in zero magnetic field for (Zn0.83 In0.11 )[Cr1.73 In0.14 ]Se4 and the best fit of Debye expression (dashed red line), C(T ) = 9RnD



D /T 2

(x4 ex /(ex − 1) ) dx, to the experimental data denoted

D 0

acteristic for the spin fluctuations. The evidence for the magnetic phase transition (strongly field dependent) give either the magnetic (cf., Figs. 3, 5 and 7) or specific heat data presented below, whereas the component  (T) of the ac magnetic susceptibility clearly shows the broad maxima at Tm ∼ 40 K, which support the high energy spin fluctuations in the all investigated samples. Fig. 10 shows the specific heat for (Zn0.99 )[Cr1.92 Ga0.06 ]Se4 with sharp peak at TN , which is strongly shifted to much lower temperatures in the applied magnetic fields. We found that

40

(Zn0.99)[Cr1.92Ga0.06]Se4

35

(1)

where R is the universal constant, nD is the number of atoms in the formula unit and  D is the Debye temperature. As an example, the specific heat data in Fig. 9 are compared with the calculated C(T) dependence. The least-square fit of Eq. (1) to the experimental data yield the values of Debye temperature  D of 368 K, 337 K, and 290 K, for the ZnCr2 Se4 samples doped with Ga, In, and Ce, respectively, and a number of atoms in formula unit nD is very closed to 7. We note, that  D of (Zn0.86 Ce0.08 )[Cr2 ]Se4 is distinctly lower then  D obtained for the remaining compounds, it will be discussed. The C(T, H = 0) data obtained for the investigated samples are very similar to that obtained for (Zn0.86 Ce0.08 )[Cr2 ]Se4 , therefore, they are not presented here. In the temperature region T < ∼100 K the deviation observed between the measured and calculated C(T) data can be addressed to the magnetic ordering state at T < TN ≈ 22 K and high energy spin fluctuations. The difference C = Cexp − C also shown in Fig. 9 has a distinct maximum at ∼40 K, which well correlates with the maximum of the ac susceptibility  (cf., Figs. 3, 5 and 7) char-

 T 3

as Cexp (green solid circles). With blue line a magnetic contribution C = Cexp − C to the specific heat vs. temperature T is marked. In the temperature region T < TN , C(T) expresses magnetic contribution C ∼ T3 exp(−Eg /kB T) due to anisotropic spiral structure with an activation gap in magnon dispersion and the spin fluctuation contribution C ∼ ıT3 ln(T/Tsf ), with the spin fluctuation temperature Tsf = ∼40 K. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

H=0 10 kOe 30 kOe 50 kOe 70 kOe

30

C [J/(mol·K)]

C(T ) = 9RnD

T

3 

D /T

200

T [K]

25 20 15 10 5 0 0

3

6

9

12

15

18

21

24

27

30

T [K] Fig. 10. Specific heat, C, vs. temperature T taken at different external magnetic fields for (Zn0.99 )[Cr1.92 Ga0.06 ]Se4 .

148

E. Malicka et al. / Materials Chemistry and Physics 131 (2011) 142–150

1,0

2,0

1,6

(Zn0.86Ce0.08)[Cr2]Se4 Debye fit 2

C/T [J/(mol·K )]

1,2

(Zn0.83In0.11)[Cr1.73In0.14]Se4

0,8

H=0 10 kOe 30 kOe 50 kOe 70 kOe

1,4

C/T [J/(mol·K2)]

(Zn0.99)[Cr1.92Ga0.06]Se4

(Zn0.86Ce0.08)[Cr2]Se4

1,8

1,0 0,8

0,6

0,4

0,6 0,2 0,4 0,2 0

3

6

9

12

15

18

21

0,0

24

0

5

10

T [K]

15

20

25

30

T [K]

Fig. 11. Temperature dependence of the specific heat of (Zn0.86 Ce0.08 )[Cr2 ]Se4 plotted as C/T vs. T.

the field of 70 kOe fully removes the magnetic peak-anomaly at the lower temperatures, however, C(T)/T measured in this field is slightly increasing when T → 0 below ∼6 K, that suggests some “magnetic behaviour” induced by the magnetic field. A very similar C(T)/T dependencies induced by the field of 70 kOe are also observed for (Zn0.86 Ce0.08 )[Cr2 ]Se4 (in Fig. 11) and for (Zn0.83 In0.11 )[Cr1.73 In0.14 ]Se4 (in Fig. 12). We therefore suggest that the increasing of C/T in the low-T region can be attributed to the inhomogeneous magnetic phase (e.g., of spin-glass-type). The C(T) and C(T)/T data displayed in Fig. 12 also suggest complex magnetic structure in (Zn0.83 In0.11 )[Cr1.73 In0.14 ]Se4 (e.g., mixed or low-spin (LS) states) in reference to the remaining compounds. The double structure of the C(T) and C(T)/T peaks suggests the coexistence of two type of magnetic ordering, one at TN = 17.5 K, while the second broad maximum indicates the magnetic transition at ∼16.3 K, probably due to short-range magnetic ordering. Fig. 13 compares the C(T)/T data at H = 0 for the investigated samples. The C/T displays a sharp maximum at TN . In the case of ZnCr2 Se4 doped with Ga or Ce, C(T) can be well fitted by the

Fig. 13. Temperature dependence of the specific heat per Cr ion of the spinels under study plotted as C/T vs. T. The Debye fit is marked by dashed black line.

expression for an anisotropic spiral structure with an activation gap in magnon dispersion [38]: Cm ∼ T3 exp(−Eg /kB T), the spin fluctuation contribution to the specific heat: Csf = ıT3 ln(T/Tsf ), with the spin fluctuation temperature Tsf = ∼30 K and the lattice contribution: Cph = ˇT3 , in the figure we present the fit of C(T)/T = (Cph + Cm + Csf )/T to the experimental data for the sample (Zn0.99 )[Cr1.92 Ga0.06 ]Se4 , the fit was not possible for (Zn0.83 In0.11 )[Cr1.73 In0.14 ]Se4 due to the more complex magnetic structure of this compound probably connected with LS states.

T

Figs. 14–16 show entropy S(T ) =

(C(T )/T ) dT calculated at dif0

ferent magnetic fields. For all of the magnetic and phonon the ordering temperature and for the samples with Ce or In

samples investigated the value contribution to the entropy at at H = 0 is only ∼4.5 J mol−1 K−1 doping, and about 6 J mol−1 K−1

10 1,0

(Zn0.99)[Cr1.92Ga0.06]Se4

(Zn0.83In0.11)[Cr1.73In0.14]Se4 8

H=0 5 kOe 10 kOe 30 kOe 50 kOe

0,6

H=0 10 kOe

S [J/(mol·K)]

C/T [J/(mol·K2)]

0,8

30 kOe 6

50 kOe 70 kOe

4

TN

0,4

2

0,2

0 0

3

6

9

12

15

18

21

0

24

Fig. 12. Temperature dependence of (Zn0.83 In0.11 )[Cr1.73 In0.14 ]Se4 plotted as C/T vs. T.

5

10

15

20

25

30

T [K]

T [K] the

specific

heat

of

Fig. 14. Entropy S per Cr ion vs. temperature T at different magnetic fields H for (Zn0.99 )[Cr1.92 Ga0.06 ]Se4 .

E. Malicka et al. / Materials Chemistry and Physics 131 (2011) 142–150

149

TN, Cm [K]

6 0

15

20

25

30 70

(Zn0.86Ce0.08)[Cr2]Se4 Ferro

50

TN

2

Hc1

40

Hc2 TN

30

Cm

20

Conical

60

Spin fluctuations

60

Hc1, Hc2 [kOe]

S [J/(mol·K)]

3

10

Helimagnet

H=0 10 kOe 30 kOe 50 kOe 70 kOe

4

5

70

50 40 30

H [kOe]

(Zn0.86Ce0.08)[Cr2]Se4 5

20

Metamagnetic treshold

1

10

10

Spiral 0 0

5

10

15

20

0

0

25

T [K]

0

6

(Zn0.83In0.11)[Cr1.73In0.14]Se4 5

H=0 5 kOe S [J/(mol·K)]

4

10 kOe 30 kOe 50 kOe

3

TN

2

1

0 0

5

10

15

20

25

T [K] Fig. 16. Entropy S per Cr ion vs. temperature T at different magnetic fields H for (Zn0.83 In0.11 )[Cr1.73 In0.14 ]Se4 .

10

15

20

25

30

T [K]

Fig. 15. Entropy S per Cr ion vs. temperature T at different magnetic fields H for (Zn0.86 Ce0.08 )[Cr2 ]Se4 .

for Ga dopant, i.e., much lower than the magnetic contribution Sm = R ln(2S + 1) = 11.52 J mol−1 K−1 calculated per one Cr3+ atom with S = 3/2. It is clearly shown that application of magnetic fields strongly suppresses the magnetic transition in the doped ZnCr2 Se4 (the same effect has been observed for pure ZnCr2 Se4 [5]) and shifts the peak in C/T to lower temperatures. The TN -anomaly is fully suppressed by the field of 70 kOe, however, the specific-heat data C/T indicates the remnant magnetic order at the highest magnetic fields. To estimate the magnetic contribution to entropy S, we calculated the magnetic entropy S at TN , by integrating [C(T, ␮0 H = 0) − C(T, ␮0 H = 70 kOe)]/T over the transition region. At TN , S is only ∼8% of the full magnetic entropy per one Cr atom expected for the complete alignment of the Cr spins. Very similar result has been obtained recently [5] for ZnCr2 Se4 . In Ref. [5] the S-anomaly was interpreted as a result of spin fluctuations in the paramagnetic regime, well visible in the ac data. Our specific heat

5

Fig. 17. The phase diagram for (Zn0.86 Ce0.08 )[Cr2 ]Se4 : critical fields Hc1 and Hc2 vs. temperature T, Néel temperature TN vs. magnetic field H and temperature position of specific heat peak Cm vs. magnetic field H.

data fully confirm this explanation. Fig. 17 shows the standard procedure with metamagnetic transitions to plot the phase diagram Hc vs. T, TN vs. H and Cm vs. H for (Zn0.86 Ce0.08 )[Cr2 ]Se4 . Metamagnetic threshold connected with the first critical field Hc1 does not depend on temperature below TN and it does not correlate with specific heat. On the other hand, this diagram shows a strict correlation between the second critical field Hc2 , Néel temperature TN and the temperature position of specific heat peak Cm suggesting that the structural instability can be removed by an external magnetic field. In case of the Ga and In rich samples the Hc1 (T) dependence is very similar to the Ce reach one, therefore is not presented here, while Hc2 (T) relation was not clearly visible especially for the In rich sample. Summarizing these observations it can be noticed that in comparison with two other compositions the (Zn0.83 In0.11 )[Cr1.73 In0.14 ]Se4 spinel exhibits: the most strongly lowered saturation moment, the largest non-stoichiometry (i.e., the largest cation deficiency) and the largest bond frustration resulting from the random distribution of Cr–Se and In–Se bonds in the octahedral sites which are related to the disappearance of the second critical field and broadening of the specific heat peak. On the contrary to these indications, in earlier reported the stoichiometric spinel systems (Zn)[Cr2−x Alx ]Se4 with x = 0.15 and 0.23 [30,39,40] and (Zn)[Cr2−x Inx ]Se4 with x = 0.08, 0.12 and 0.21 [18], such large lowering of the saturation moment was not noticed. Hypothetically, some of the moments in (Zn0.83 In0.11 )[Cr1.73 In0.14 ]Se4 might still be anti-parallel or even perpendicular to the field, similarly as in the MnCr2 S4 matrix [41]. However, the ZnCr2 Se4 matrix of the spinels under study fully saturates [5]. Another possibility (caused both by the elongation of the cation–anion distances in octahedral sites and/or the cation deficiency observed in this case) is the transition from high-to-low spin state in the 3d3 t2g orbital of the chromium ions. Similar, albeit weaker effects might be occurred for (Zn0.99 )[Cr1.92 Ga0.06 ]Se4 . 4. Conclusions The XPS spectra taken at room temperature indicate that local magnetic moments induced by the Ga, In and Ce ions admixed in ZnCr2 Se4 spinel are not influencing the 3d3 electronic configuration

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E. Malicka et al. / Materials Chemistry and Physics 131 (2011) 142–150

of Cr ions in cubic phase of the spinels. However, the anomalies in the ac magnetic susceptibility and specific heat observed close to TN , show magnetic fluctuations for which the spin configuration of the 3d3 t2g orbital of Cr3+ becomes strongly dependent on the stoichiometry and interatomic distances in the octahedral sites. These effects may be responsible for the HS–LS transitions, finally leading to the lowering of the saturation moment. Acknowledgment The work was supported by the Ministry of Science and Higher Education by the Grant No. N N204 145938. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.matchemphys.2011.07.080. References [1] F.K. Lotgering, Proceedings of the International Conference on Magnetism, Nottingham, 1964, London, Institute of Physics, 1965. [2] R. Plumier, J. Phys. (Paris) 27 (1966) 213. [3] R. Kleinberger, C.R. de Kouchkovsky, Acad. Sci. Paris, Ser. B 262 (1966) 628. [4] F. Yokaichiya, A. Krimmel, V. Tsurkan, I. Margiolaki, P. Thompson, H.N. Bordallo, A. Buchsteiner, N. Stüßer, D.N. Argyriou, A. Loidl, Phys. Rev. B 79 (2009) 064423. [5] J. Hemberger, H.A. Krug von Nidda, V. Tsurkan, A. Loidl, Phys. Rev. Lett. 98 (2007) 147203. ´ E. Malicka, A.W. Pacyna, Physica B 404 (2009) 3554. [6] T. Gron, ´ A.W. Pacyna, E. Malicka, Solid State Phenom. 170 (2011) 213. [7] T. Gron, ´ [8] S. Juszczyk, J. Krok, I. Okonska-Kozłowska, T. Mydlarz, A. Gilewski, J. Magn. Magn. Mater. 46 (1984) 105. [9] A.A. Zhukov, Ya.A. Kesler, V.F. Meshceriakov, A.V. Rozancev, Sov. Phys. Solid State (USA) 26 (1984) 1. ´ ´ J. Krok, T. Mydlarz, Mater. Res. Bull. [10] I. Okonska-Kozłowska, H.D. Lutz, T. Gron, (1984) 1. ´ H. Duda, J. Warczewski, Phys. Rev. B 41 (1990) 12424. [11] T. Gron, ´ H. Duda, J. Warczewski, J. Magn. Magn. Mater. 83 (1990) 487. [12] T. Gron, ´ [13] S. Juszczyk, I. Okonska-Kozłowska, P. Byszewski, Phase Trans. 4 (1984) 291.

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