Structural chemistry and magnetic properties of R11M4In6 (R = Gd, Tb, Dy, Ho, Er, Y; M = Si, Ge) compounds

Intermetallics 25 (2012) 18e26

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Structural chemistry and magnetic properties of R11M4In6 (R ¼ Gd, Tb, Dy, Ho, Er, Y; M ¼ Si, Ge) compounds Yu. Tyvanchuk a, R. Duraj b, T. Jaworska-Go1a˛b c, S. Baran c, *, Ya.M. Kalychak a, J. Przewo znik d, A. Szytu1a c a

Analytical Chemistry Department, Ivan Franko National University of Lviv, Kyryla and Mephodiya 6, 79005 Lviv, Ukraine Institute of Physics, Technical University of Cracow, Podchora˛ z_ ych 1, 30-084 Kraków, Poland c M. Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland d Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Mickiewicza 30, 30-059 Kraków, Poland b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 27 May 2011 Received in revised form 7 February 2012 Accepted 9 February 2012 Available online 15 March 2012

Crystal structure and magnetic properties of R11M4In6 compounds (R ¼ Gd, Tb, Dy, Ho, Er, Y; M ¼ Si, Ge) were investigated by means of X-ray diffraction and magnetometric measurements. The compounds crystallize in the tetragonal Sm11Ge4In6-type crystal structure (an ordered version of the Ho11Ge10-type; space group I4/mmm). Gd11Ge4In6, Tb11Ge4In6 and Tb11Si4In6 order antiferromagnetically at low temperatures. For the compounds with Dy, Ho and Er magnetic phase transitions to noncollinear magnetic structures with a ferromagnetic component were observed. The magnetocaloric effect, in terms of the isothermal magnetic entropy change DSm, was observed for Dy11Si4In6. Both yttrium compounds are Pauli paramagnets. Ó 2012 Elsevier Ltd. All rights reserved.

Keywords: A. Magnetic intermetallics A. Rare-earth intermetallics B. Crystallography B. Magnetic properties F. Diffraction (X-ray)

1. Introduction The ReMeIn ternary systems (R e a rare earth element, M ¼ Si, Ge) have been recently studied searching for new intermetallic compounds and investigating the influence of the chemical bonding on the physical properties. Isothermal (at 870 K) sections of the phase diagrams have been reported for the ReSieIn systems with R ¼ Y [1], La [2], Ce [3], Sm [4], Gd [5], Yb [6], Lu [7] and for the ReGeeIn systems with R ¼ Y [8], La [2], Ce [3], Nd [9], Sm [4], Gd [10], Yb [6] and Lu [11]. In the ReSieIn systems the compounds: R3SiIn (R ¼ La, Ce; La3GeInetype; I4/mcm) [2,3] and R11Si4In6 (R ¼ Y, Gd, Tb, Ho, Er; Sm11Ge4In6etype; I4/mmm) [1, 5] were found. In the ReGeeIn systems the compounds with the compositions: R3GeIn (R ¼ LaeNd, Sm, Gd; La3GeIn-type; I4/mcm) [2e4,9,12,13], R3GeIn4 (R ¼ LaeNd; La3GeIn4etype; I4/mcm) [2,3,9,12,14], R11Ge4In6 (R ¼ Y, La, Ce, Sm, Gd; Sm11Ge4In6etype; I4/mmm) [2,4,8e10,14,15] and R11Ge8In2 (R ¼ GdeTm; Gd11Ge8In2-type; I4/mmm) [13], EuGeIn (own type; Pnma) [16], R2Ge2In (R ¼ Y, LaeYb; Mo2FeB2-type; P4/ mbm) [17e20] were obtained. The solid solutions R2Ge2xSixIn (R ¼ LaeNd; 0  x  1) were also reported [21]. * Corresponding author. Tel.: þ48 126635686; fax: þ48 126337086. E-mail address: [email protected] (S. Baran). 0966-9795/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.intermet.2012.02.005

For some of these compounds magnetic properties were determined. In the R2Ge2In family of compounds La2Ge2In is diamagnetic, the compounds with R ¼ Ce, Pr and Nd exhibit localized magnetism of R3þ ions with complex magnetic behavior hinting at canted antiferromagnetism or spin-glass freezing at the lowest temperatures [18], the compounds with R ¼ Sm, Gd, Tb and Ho are antiferromagnets with the Néel temperature equal to 25, 42, 51 and 23 K, respectively, and Yb2Ge2In is a Pauli paramagnet [20]. Ce3GeIn4 is paramagnetic down to 1.72 K, whereas Ce11Ge4In6 orders ferromagnetically at Tc ¼ 7.5 K [14]. R11Ge8In2 (R ¼ GdeTm) order ferromagnetically at low temperatures and for the Gd-, Tb- and Tm-samples a magnetocaloric effect was observed with the largest magnetic entropy change of DSm ¼ 10.6 J/kg K in Tm11Ge8In2 [13]. In this work the results of X-ray diffraction and magnetometric measurements of the ternary intermetallics R11M4In6 (R e heavy rare earth element, M ¼ Si or Ge) are reported. Based on these data the crystal structure parameters of the compounds are determined and magnetic properties are characterized including information on their phase situation, type of magnetic order, values of temperatures of magnetic phase transitions and magnetic moments in the ordered as well as in the paramagnetic state.

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of 1 kOe (to determine the value of the effective magnetic moment meff and the paramagnetic Curie temperature qp) and finally the magnetization curves were measured up to 90 kOe at 1.9 K (to determine the value of the magnetic moment in the ordered state). For Dy11Si4In6 additional measurements of magnetization curves in the temperature range 10e86 K (the temperature step DT ¼ 4 K) were carried out. To state precisely the temperatures of the phase transitions, the temperature dependence of the AC magnetic susceptibility cAC ¼ c0  ic00 were measured at several chosen frequencies between 10 Hz and 10 kHz in the temperature range 2e80 K. For Dy11Si4In6 additional measurements of the AC magnetic susceptibility at 2, 4, 6, 8 and 10 kOe were performed.

3. Results and discussion Fig. 1. X-ray diffraction pattern of Tb11Ge4In6: the observed (solid circles), the calculated (solid line) and the difference pattern (in the bottom of the figure). The vertical bars indicate the positions of the Bragg reflections for Tb11Ge4In6 (the upper row) and the reflections originating from the impurity phase Tb5Ge3 (the lower row).

2. Experimental details R11Si4In6 (R ¼ Tb, Dy, Ho, Er) and R11Ge4In6 (R ¼ Gd, Tb, Ho, Er) samples, each of the total weight of 1 g, were prepared by argon arc-melting of the stoichiometric amounts of the elements. Ingots of the rare earth elements (the purity better than 99.85 wt. %) and germanium, silicon and indium (the purity better then 99.99 wt. %) were used as the starting material. The samples were annealed at 870 K for 4 weeks to improve homogeneity. X-ray powder diffraction patterns were recorded at room temperature using a PANalytical X’Pert PRO MPD diffractometer (CuKa radiation, Bragg-Brentano geometry; Institute of Physics, Jagiellonian University, Kraków, Poland), HZG-4a (CuKa radiation, Bragg-Brentano geometry; Ivan Franko National University of Lviv, Ukraine), STOE STADI P diffractometer (CuKa1-radiation, linear position sensitive detector, curved Ge(111) monochromator, transmission geometry; Ivan Franko National University of Lviv, Ukraine). The data were analyzed using the Fullprof program [22] based on the Rietveld method. The magnetic measurements were carried out using a vibrating sample magnetometer (VSM) and an AC susceptometer option of the Quantum Design PPMS platform (Institute of Physics, Jagiellonian University, Kraków, Poland). Three types of DC magnetic measurements were performed: at low temperatures in a magnetic field equal to 50 Oe (to determine magnetic phase transition temperatures), then a scan from 1.9 up to 300 K in a magnetic field

3.1. Crystal structure The X-ray diffraction pattern of Tb11Ge4In6 is plotted in Fig. 1. Similar patterns were obtained for the other investigated samples. The reflections of strong intensities correspond to the main tetragonal phase and can be indexed in the Sm11Ge4In6-type crystal structure (an ordered version of the Ho11Ge10-type structure, space group I4/mmm) [15]. Some additional reflections of small intensities are related to the R5M3 impurity phase and free indium. The crystal structure of R11M4In6 compounds was solved in single crystal studies of Sm11Ge4In6 [4] and La11Ge4In6 [15]. The structure was found to be a ternary derivative of the binary Ho11Ge10-type. In the parent crystal structure of the Ho11Ge10 compound the HoeHo pairs and three types of Ge atoms were described [23]: 1 e isolated atoms (at 8j, 4d and 4e), 2 e pairs of atoms (at 16m) and 3 e square clusters of four atoms (at 8h). The HoeHo interatomic distances in Ho11Ge10 are much shorter then in a metallic Ho and the germanium atoms of type 2 and 3 form a 3Dnet where GeeGe distances are equal to 2.543 Å and 2.584 Å, respectively, which is typical for compounds with GeeGe chains [18,23]. In the Sm11Ge4In6-type structure the indium atoms occupy the above mentioned 2- and 3-type positions (16m and 8h) despite of significantly larger atomic size (Fig. 2a), whereas the germanium atoms occupy the isolated positions. It means that germanium atoms are surrounded by Sm atoms which either form double trigonal prisms connected with joint vertices (Fig. 2b) or tetrahedra and empty octahedra (Fig. 2c). The 16m site in the cerium compound is occupied by a mixture of In and Ge atoms, that leads to the composition Ce11Ge4.74In5.26 [14] while for heavy rare earths (R ¼ GdeTm) the 16m site is fully occupied by Ge resulting in the stoichiometry R11Ge8In2 [13].

Fig. 2. Crystal structure of Sm11Ge4In6: (a) 3D-network of indium, (b) trigonal prisms of [Ge1Sm24Sm32], (c) stacking of [Ge2Sm14] tetrahedra and empty [Ge3Sm14Sm4] octahedra (notation corresponding to Table 2).

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Table 1 Crystal structure data refinements for R11Si4In6 (R ¼ Tb, Dy, Ho, Er, Y). Parameters

Tb11Si4In6

Dy11Si4In6

Ho11Si4In6

Er11Si4In6

Y11Si4In6

M [g/mol] 2Theta range [deg] Step size in 2Theta [deg] Scanning time/step [s/step] a [Å] c [Å] V [Å3] R1 at 16n (0, y, z)

2549.44 10e130 0.03 17 11.5194 (7) 16.146 (1) 2142.5 (4) 0.2562 (4) 0.3140 (3) 0.3438 (4) 0.1013 (3) 0.3275 (4) 0.1690(7) 0.155 (3) 0.390 (3) Not refined 0.2044 (3) 0.1699 (4) 0.1304 (5) 0.21 (3) 5.3 2.6

2588.76 10e130 0.03 17 11.4889 (5) 16.1070 (9) 2126.0 (3) 0.2567 (4) 0.3161 (3) 0.3469 (4) 0.1010 (3) 0.3269 (4) 0.1691(6) 0.150 (3) 0.393 (3) Not refined 0.2054 (3) 0.1674 (4) 0.1262 (5) 0.19 (5) 8.0 4.4

2615.51 15e90 0.03 20 11.3655 (5) 16.015 (1) 2068.7 (2) 0.2569 (4) 0.3153 (4) 0.3431 (5) 0.1029 (3) 0.3263 (4) 0.1745(9) 0.154 (3) 0.390 (3) Not refined 0.2049 (3) 0.1694 (4) 0.1303 (5) 1.82 (4) 5.5 3.0

2641.14 15e90 0.03 20 11.3387 (5) 15.975 (1) 2053.9 (2) 0.2551 (4) 0.3149 (3) 0.3434 (5) 0.1034 (3) 0.3254 (4) 0.1718(8) 0.151 (3) 0.393 (3) Not refined 0.2042 (3) 0.1693 (4) 0.1271 (6) 1.22 (4) 4.9 7.0

1779.29 15e95 0.05 10 11.486 (1) 16.175 (2) 2134.2 (5) 0.253 (1) 0.314 (1) 0.344 (1) 0.102 (1) 0.331 (1) 0.166(2) 0.147 (5) 0.387 (5) Not refined 0.206 (1) 0.169 (1) 0.128 (1) 0.60 (3) 7.2 4.9

R2 at 16n (0, y, z) R3 at 8h (x, x, 0) R4 at 4e (0, 0, z) Si1 at 8j (x, ½, 0) Si2 at 4e (0, 0, z) Si3 at 4d (0, ½, ¼) In1 at 16m (x, x, z) In2 at 8h (x, x, 0) Bover [Å2] RBragg [%] RF [%]

Table 2 Crystal structure data refinements for R11Ge4In6 (R ¼ Gd, Tb, Ho, Er, Y). Parameters

Gd11Ge4In6

Tb11Ge4In6

Ho11Ge4In6

Er11Ge4In6

Y11Ge4In6

M [g/mol] 2Theta range [deg] Step size in 2Theta [deg] Scanning time/step [s/step] a [Å] c [Å] V [Å3] R1 at 16n (0, y, z)

2709.03 11e120 0.05 10 11.532 (1) 16.307 (2) 2168.3 (7) 0.249 (1) 0.314 (1) 0.346 (2) 0.099 (1) 0.335 (1) 0.160 (3) 0.156 (4) 0.392 (4) Not refined 0.212 (1) 0.174 (1) 0.126 (2) 0.75 (9) 11.4 1.7

2727.54 10e130 0.03 17 11.5131 (5) 16.225 (1) 2150.6 (4) 0.2524 (4) 0.3120 (3) 0.3457 (5) 0.1001 (4) 0.3295 (5) 0.1676 (9) 0.154 (2) 0.390 (2) Not refined 0.2052 (4) 0.1720 (5) 0.1281 (6) 0.54 (3) 5.7 3.8

2793.59 10e130 0.03 17 11.4373 (7) 16.131 (1) 2110.1 (4) 0.2529 (4) 0.3141 (4) 0.3432 (5) 0.1012 (4) 0.3266 (4) 0.1679 (9) 0.150 (2) 0.390 (2) Not refined 0.2047 (3) 0.1724 (4) 0.1296 (6) 0.30 (5) 4.2 2.4

2819.22 10e130 0.03 17 11.3817 (7) 16.064 (1) 2081.0 (4) 0.2529 (4) 0.3138 (3) 0.3435 (4) 0.1024 (3) 0.3271 (4) 0.1696 (7) 0.156 (2) 0.391 (2) Not refined 0.2061 (3) 0.1722 (4) 0.1275 (5) 0.21 (2) 4.2 2.4

1957.28 20e130 0.05 10 11.489 (1) 16.265 (2) 2147.1 (4) 0.2497 (6) 0.3124 (6) 0.3448 (8) 0.1009 (6) 0.3282 (7) 0.1654 (14) 0.151 (2) 0.395 (2) Not refined 0.2075 (3) 0.1712 (5) 0.1308 (7) 0.21 (3) 3.8 2.3

R2 at 16n (0, y, z) R3 at 8h (x, x, 0) R4 at 4e (0, 0, z) Ge1 at 8j (x, ½, 0) Ge2 at 4e (0, 0, z) Ge3 at 4d (0, ½, ¼) In1 at 16m (x, x, z) In2 at 8h (x, x, 0) Bover [Å2] RBragg [%] RF [%]

In the R11M4In6 compounds studied the rare earth atoms occupy the Wyckoff positions 16n, 8h and 4e, the Ge or Si atoms are located at 4d, 4e and 8j whereas In atoms at 8h and 16m. The determined lattice parameters and the positional atom parameters are listed in

Table 1 (for R11Si4In6) and Table 2 (for R11Ge4In6). They are in good agreement with the ones published previously [1,5,10]. The values of the a and c lattice parameters and the unit cell volume V decrease with increasing atomic number (Z) of the rare earth element.

Table 3 Magnetic properties of R11Si4In6 and R11Ge4In6: the Néel or Curie temperature (TN, TC), the paramagnetic Curie temperature (qp), experimental (exp.) and theoretical (theor.) values of the effective magnetic moment (meff) and of the magnetic moment in the ordered state (m) at T ¼ 1.9 K and H ¼ 90 kOe and the magnetic critical field (Hcr). Compound

TN [K]

TC [K]

qp [K]

meff [mB] Exp., theor.

m [mB] Exp., theor.

Hcr [kOe]

Tb11Si4In6 Dy11Si4In6 Ho11Si4In6 Er11Si4In6 Gd11Ge4In6 Tb11Ge4In6 Ho11Ge4In6 Er11Ge4In6

63 e e e 36 38 e e

e 52 19 20 e e 26 26

3.7 23.7 8.0 11.4 51.6 14.3 15.8 7.7

9.94, 9.72 10.61, 10.65 10.66, 10.61 9.55, 9.58 7.99, 7.92 9.96, 9.72 10.69, 10.61 9.74, 9.58

3.8, 5.0, 7.2, 6.2, 3.9, 3.8, 7.5, 6.0,

34.3 6.4 1.4 5.1 11.1 46.8 1.1 9.6

9.00 10.0 10.0 9.0 7.0 9.0 10.0 9.0

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Fig. 3. Temperature dependence of the real component of the AC (a) and the DC (b) magnetic susceptibility of Gd11Ge4In6 (1), Tb11Ge4In6 (2) and Tb11Si4In6 (3) below 90 K.

3.2. Magnetic properties

H [kOe]

0 8

20

b

6

40

60

80

100

Tb 11 Ge4 In6 Ho 11 Ge4 In6 Er 11 Ge4 In6 Gd 11 Ge4 In6

4

3+

magnetic moment per R [µB]

The magnetic data obtained for the investigated compounds, namely the values of the critical temperatures of magnetic origin (TN, TC), the paramagnetic Curie temperatures (qp), the effective magnetic moments (meff), the magnetic moments in the ordered state (m) determined at T ¼ 1.9 K and H ¼ 90 kOe and the critical field values (Hcr) are collected in Table 3. Groups of compounds with similar magnetic properties are discussed in details below. Gd11Ge4In6, Tb11Ge4In6 and Tb11Si4In6 order antiferromagnetically at low temperatures. Their AC and DC magnetic susceptibility plots (Fig. 3) show maxima characteristic of the phase transition from an antiferro- to a paramagnetic state at 36 K, 38 K and 63 K, respectively. The antiferromagnetic order is also confirmed by the magnetization curves measured at 1.9 K (Fig. 4). The reciprocal magnetic susceptibility obeys the CurieeWeiss law above the appropriate critical temperature. For Tb11Si4In6 an additional anomaly at 38 K is observed. In these compounds metamagnetic phase transitions (with hysteresis) are observed while increasing magnetic field. The temperature dependences of the c0 component of the AC magnetic susceptibility and the DC magnetic susceptibility at 50 Oe of Dy11Si4In6 are plotted in Fig. 5. Above 10 K both of them increase with increasing temperature to reach their maxima about 49 K and then sharply decrease at 52 K. This gives an evidence for a longrange ferromagnetic-like order with the Curie temperature of 52 K. The values of c0 slowly decrease with increasing frequency (Fig. 5a). The reciprocal magnetic susceptibility obeys the CurieeWeiss law at high temperatures. The temperature dependence of c00 recorded at f ¼ 10 Hz is similar to the one described above and decreases to zero at 52 K. The magnetic transition temperature determined by c00 is frequency dependent and changes from 52 K for f ¼ 10 Hz to 50.3 K for f ¼ 10 kHz. For frequencies higher than 50 Hz two maxima, at T1 ¼ 2.5 K and T2 ¼ 19 K, are observed (Fig. 5b). The values of T1 and T2 increase with increasing frequency suggesting that the process is dynamical and a change in the orientation of the Dy magnetic moments takes place. The relation of 1/f versus 1/Ti was analyzed by the formula s ¼ soexp(Ea/kBT), where s0 is a characteristic time and Ea is an

2 T= 1.9 K

0

a

8

Ho11Si4In6 Er11Si4In6 Tb11Si4In6 Dy11Si4In6

6

4

2 T= 1.9 K

0 0

20

40

60

80

100

H [kOe] Fig. 4. Magnetization curves measured at 1.9 K for (a) R11Si4In6 (R ¼ Tb, Dy, Ho, Er) and (b) R11Ge4In6 (R ¼ Gd, Tb, Ho, Er).

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Fig. 5. Magnetic susceptibility of Dy11Si4In6: (a) the real c0 and (b) the imaginary c00 component of the AC magnetic susceptibility versus temperature for the frequency varied between 10 Hz and 10 kHz, the temperature dependence of the DC magnetic susceptibility measured at H ¼ 50 Oe (c) and H ¼ 1 kOe (the inset in (d)) and the reciprocal DC susceptibility at H ¼ 1 kOe (d) versus temperature.

Fig. 6. Temperature dependence of the (a) real c0 and (b) imaginary c00 component of the AC magnetic susceptibility of Dy11Si4In6 measured at 2, 4, 6, 8 and 10 kOe.

Fig. 7. Magnetization isotherms measured for Dy11Si4In6 between 10 and 86 K (a) and the appropriate magnetic entropy change calculated as described in Section 3.2 (b).

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Fig. 8. Magnetic susceptibility of Ho11Si4In6: (a) the real c0 and (b) the imaginary c00 component of the AC magnetic susceptibility versus temperature for the frequency varied between 10 Hz and 10 kHz, (c) the temperature dependence of the DC magnetic susceptibility measured at H ¼ 50 Oe and (d) at H ¼ 1 kOe (inset) and (d) the reciprocal DC susceptibility (at H ¼ 1 kOe) versus temperature.

activation energy, yielding the following values: s0 ¼ 1.9  106 s and Ea ¼ 24(2) K for T1 and s0 ¼ 1 108 s and Ea ¼ 243(22) K for T2. Below 10 K both the real c0 and imaginary c00 part of the AC magnetic susceptibility of Dy11Si4In6 hardly depend on the amplitude of the magnetic field while c00 significantly depends on the magnetic field value in the temperature range 20e50 K (Fig. 6), which confirms a ferromagnetic component in this temperature region. The magnetization curve of Dy11Si4In6 collected at 1.9 K (full circles in Fig. 4a) exhibits a metamagnetic character with Hcr ¼ 6.4 kOe and strong hysteresis. The magnetic moment at 1.9 K and H ¼ 90 kOe, equals 5.0 mB, and is twice smaller than the free Dy3þ ion value (10 mB).

The magnetization curves measured in the temperature range 10e86 K are collected in Fig. 7a. Below and about TC ¼ 52 K they have a ferromagnetic component and do not saturate in the magnetic field up to 90 kOe. On the basis of these data, the isothermal entropy changes were calculated using the Maxwell relation approximated by the expression:

DSm ðT; DHÞ ¼

X Miþ1  Mi i

Tiþ1  Ti

DHi

where DH is the change in the magnetic field value, Mi and Miþ1 are the values of magnetization at temperatures Ti and Tiþ1,

Fig. 9. Magnetic susceptibility of Ho11Si4In6: (a) the real c0 and (b) the imaginary c00 component of the AC magnetic susceptibility versus temperature for the frequency varied between 10 Hz and 10 kHz, (c) the temperature dependence of the DC magnetic susceptibility measured at H ¼ 50 Oe and (d) at H ¼ 1 kOe (inset) and (d) the reciprocal DC susceptibility (at H ¼ 1 kOe) versus temperature.

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Fig. 10. Magnetic susceptibility of Er11Si4In6: (a) the real c0 and (b) the imaginary c00 component of the AC magnetic susceptibility versus temperature for the frequency varied between 10 Hz and 10 kHz, (c) the temperature dependence of the DC magnetic susceptibility measured at H ¼ 50 Oe and (d) at H ¼ 1 kOe (inset) and (d) the reciprocal DC susceptibility (at H ¼ 1 kOe) versus temperature.

respectively ([24,25] and references therein). The biggest values of such calculated entropy changes were obtained at the Curie temperature (Fig. 7b). The maximum magnetic entropy change of 16.5 J/kg K is higher than the one reported for Tm11Ge8In2 [13], Gd3NiSi2 [26], Gd3CoSi2 [27], Gd6Co4.85 [28] but lower when compared to 36 J/kg K found for Gd5Si2Ge2 [29] or 24.4 J/kg K for LaFe11.6Si1.4 [30]. A large magnetocaloric effect is observed also in NieGdeAl metallic glasses [31]. Temperature and frequency dependence of the real c0 and imaginary part c00 of the AC susceptibility and the temperature

dependence of the DC magnetic susceptibility measured at 50 Oe and 1 kOe are plotted for Ho11Si4In6 (Fig. 8), Ho11Ge4In6 (Fig. 9), Er11Si4In6 (Fig. 10) and Er11Ge4In6 (Fig. 11). In all cases broad maxima in c0 and c00 are observed and then c00 decreases to zero suggesting disappearance of ferromagnetic order. A slow displacement of the maximum in c00 is observed while changing frequency. Above the magnetic phase transition temperatures the reciprocal magnetic susceptibilities obey the CurieeWeiss law. The magnetization curves collected at 1.9 K do not saturate at H ¼ 90 kOe (Fig. 4) suggesting complex magnetic order at low

Fig. 11. Magnetic susceptibility of Er11Ge4In6: (a) the real c0 and (b) the imaginary c00 component of the AC magnetic susceptibility versus temperature for the frequency varied between 10 Hz and 10 kHz, (c) the temperature dependence of the DC magnetic susceptibility measured at H ¼ 50 Oe and (d) at H ¼ 1 kOe (inset) and (d) the reciprocal DC susceptibility (at H ¼ 1 kOe) versus temperature.

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Fig. 12. Stacking of trigonal prisms in R11Ge4In6 (a) and R2Ge2In (b).

temperatures. The magnetic moment values at the ordered state are smaller than the appropriate free rare earth ion values. The magnetic susceptibility of Y11Si4In6 and Y11Ge4In6 is temperature independent and equal to 8.2  104 and 0.9  104 cm3/mol, respectively. The reported magnetic properties result from the complex crystal structure of the studied compounds in which the rare earth atoms occupy four distinct sublattices. The interactions between the rare earth moments at different sublattices lead to different magnetic orderings. Trying to explain the above-described magnetic properties of the R11M4In6 compounds one has to take into account that two competing temperature dependent mechanisms come into play below TC. With decreasing temperature, the thermal fluctuations in the spin systems are reduced and thereby magnetization increases but simultaneously the movement of domain walls slows down which in turn results in a decrease of magnetization. These two opposing processes give rise to the peaks observed in magnetic susceptibility of the Dy-, Ho- and Ercompounds. The critical temperatures of the magnetic ordering determined here for R11Ge4In6 are close to those found for R11Ge8In2 [13] and R2Ge2In (R ¼ Gd, Tb, Ho) [18,20]. The former family of compounds

crystallizes in just the same tetragonal crystal structure as R11Ge4In6 does and with similar values of the lattice parameters. In both groups of compounds the rare earth atoms occupy the same crystallographic sites. The difference is in the occupation of the 16m site, which in the R11Ge8In2 group is occupied by Ge and in the R11Ge4In6 compounds by In atoms. These atoms occupy the positions in the polyhedral coordination of the rare earth atoms and influence the magnetic properties observed experimentally. There is especially interesting to compare properties of the R11Ge4In6 and R2Ge2In compounds as both crystal structures could be visualized as a pile of double trigonal prisms (Fig. 12) connected with joint faces (for R2Ge2In) or with joint vertices (for R11Ge4In6). The GeeGe distances in the double prisms are rather similar in Sm2Ge2In (2.508 Å, [20]) or much longer in Sm11Ge4In6 (3.506 Å, [4]) while compared with the ones in the elemental germanium (2.45 Å). According to the interatomic distance analysis, the GeeGe and GeeR interactions are the strongest ones in R2Ge2In (GeeGe ¼ 2.508 Å and GeeSm ¼ 2.993 Å for Sm2Ge2In [20]) whereas in R11Ge4In6 the strongest interactions are the IneIn, ReR and GeeR ones (IneIn ¼ 2.936 Å, SmeSm ¼ 3.275 Å and GeeSm ¼ 2.841 Å for Sm11Ge4In6 [4]). The R2Ge2In (R ¼ Gd, Tb, Ho) compounds are antiferromagnets while R11Ge8In2 are ferromagnets. For Tb11Ge8In2 and Dy11Ge8In2 a change in the magnetic ordering is observed below the Curie temperature. The temperature dependence of electrical resistivity of R2Ge2In (R ¼ La, Ce, Pr, Nd [5] and Sm, Gd [7]) are typical for metallic conductivity. This suggests that the interactions between the rare earth moments are of the RKKY-type. For RKKY-type interactions the dependence of the critical temperature of the magnetic ordering is a function of the de Gennes factor (gJ  1)2J(J þ 1), where gJ is the Lande splitting factor and J is the total angular momentum of the corresponding magnetic ion. The de Gennes scaling is not fulfilled in the discussed families of compounds (Fig. 13) which means that an another mechanism influences also the stability of their magnetic ordering. The observed reorientation process indicates an influence of various ReR bonds or of the crystal electric field. 4. Summary and conclusions

Fig. 13. Ordering temperatures versus the de Gennes factor (gJ  1)2J(J þ 1) for the studied compounds R11M4In6 (R ¼ GdeEr; M ¼ Si, Ge) and two isostructural families of compounds: R11Ge8In2 (R ¼ GdeTm) [14] and R2Ge2In [20].

The work reports data concerning the R11M4In6 compounds, where R is a heavy rare earth element and M is Si or Ge. These compounds crystallize in a tetragonal crystal structure (the Sm11Ge4In6-type; space group I4/mmm). The rare earth elements occupy four, M e three and In e two nonequivalent Wyckoff positions. The parameters of the crystal structure are determined.

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The investigated compounds exhibit complex magnetic behavior. No drastic change in magnetic behavior for compounds with M ¼ Si and Ge was observed. At high temperatures the magnetic susceptibility obeys the CurieeWeiss law with positive (except Tb11Si4In6) values of the paramagnetic Curie temperature qp and the effective magnetic moments meff (the average value for all crystallographic sites of R ions) close to the values for free R3þ (see Table 3) At T ¼ 1.9 K the magnetization curves do not saturate up to H ¼ 90 kOe and the values of the magnetic moments determined on their basis are significantly smaller than the free R3þ ones. These suggest a noncollinear order or a partial disorder in the studied compounds at low temperatures. The positive values of the paramagnetic Curie temperature suggest that ferromagnetic interactions are dominant but at low magnetic fields an antiferromagnetic order is observed in Gd- and Tb- compounds. The paramagnetic Curie temperature values smaller (except Gd11Ge4In6) than the temperatures of the onset of magnetic ordering indicate that antiferromagnetic correlations are present in these compounds. The competition between the ferromagnetic and antiferromagnetic interactions may be the reason of a magnetic frustration. The magnetic ordering with a ferromagnetic component is confirmed by the imaginary component of the AC magnetic susceptibility of Dy-, Ho- and Ercompounds diminishing to zero at temperatures marked as TC and by the shape of the magnetization curves of Dy11Si4In6 in the temperature region 10 K e TC. Not saturated magnetization curves suggest ferrimagnetic or noncollinear magnetic structures with a ferromagnetic component within this temperature range. The magnetization curves have metamagnetic character at low temperatures. This may suggest antiferromagnetic or spin-glasstype ordering but the observed fluctuation process point rather to the latter. For Dy11Si4In6 the isothermal entropy changes (DSm) have been evaluated about the Curie temperature and the largest value of 16.5 J/kg K was obtained. To clarify the points raised above further investigations are necessary, particularly additional specific heat measurements and neutron diffraction studies to determine the magnetic structures and their temperature induced changes.

Acknowledgements Yu. Tyvanchuk would like to acknowledge kind hospitality of the Institute of Physics of the Jagiellonian University and the financial support from the Józef Mianowski Fund (Foundation for Promotion of Science).

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