Magnetic properties and magnetic structures of R2TGe6 (T = Ni, Cu; R = Tb, Ho and Er)

Journal of Alloys and Compounds 803 (2019) 307e313

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Magnetic properties and magnetic structures of R2TGe6 (T ¼ Ni, Cu; R ¼ Tb, Ho and Er) Bogusław Penc a, Stanisław Baran a, Andreas Hoser b, Andrzej Szytuła a, * a b

w, Poland M. Smoluchowski Institute of Physics, Jagiellonian University, Łojasiewicza 11, 30-348, Krako Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Hahn-Meitner Platz 1, D-14109, Berlin, Germany

a r t i c l e i n f o

a b s t r a c t

Article history: Received 28 March 2019 Received in revised form 31 May 2019 Accepted 4 June 2019 Available online 5 June 2019

The magnetic properties and magnetic structures of the R2TGe6 compounds (T ¼ Ni and Cu, R ¼ Tb, Ho and Er) were studied by magnetometric and neutron diffraction measurements. All compounds have an el temperorthorhombic crystal structure of the Ce2CuGe6-type and are antiferromagnetic with the Ne atures ranging from 6 K for Er2CuGe6 up to 42 K for Tb2NiGe6. Based on the neutron diffraction data the magnetic structures were determined for R2NiGe6 (R ¼ Tb, Er) and R2CuGe6 (R ¼ Ho, Er). In these compounds the magnetic moments localized on the rare earth element form a collinear commensurate magnetic structure. The magnetic unit cell is equal to the crystal one in R2NiGe6 (R ¼ Tb, Er) while it is doubled along the a-axis (propagation vector k ¼ (½, 0, 0)) in R2CuGe6 (R ¼ Ho and Er). The obtained magnetic structures are discussed on the basis of competition between the RKKY-type interactions and influence of Crystalline Electric Field (CEF). © 2019 Elsevier B.V. All rights reserved.

Keywords: Rare earth intermetallics Germanides Magnetic properties Magnetic structure Neutron diffraction

1. Introduction Compounds of rare earths with transition metals and germanium attract special attention mainly due to a wide variety of chemical composition, crystal structure and interesting magnetic properties. Magnetic properties of these compounds are in majority related to the localized magnetic moments originating from the 4f electrons of rare earth ions. Formation and stability of their magnetic structures is a result of competition between two dominant interactions: the indirect exchange interaction of the RKKY type and the interaction with Crystalline Electric Field (CEF) [1]. These two interactions depend on configuration of the 4f shell and local surrounding of rare earth ions. Nowadays the research concentrates on the compounds with complex crystal structures. One of the interesting groups are ternary compounds with general formula R2TGe6, where R is a rare earth element and T is a transition element. They crystallize in an orthorhombic structure of the Ce2CuGe6-type (Amm2 space group) [2,3]. Magnetic data for the R2NiGe6 compounds indicate an antiferromagnetic ordering at low temperatures for those with the R ¼ Pr, Nd, GdeTm. The corel temperatures range from 4 K for R ¼ Tm up to 42 K responding Ne for R ¼ Tb [4]. Temperature dependence of the electrical resistivity

* Corresponding author. E-mail address: [email protected] (A. Szytuła). https://doi.org/10.1016/j.jallcom.2019.06.027 0925-8388/© 2019 Elsevier B.V. All rights reserved.

indicates a metallic behavior in the temperature range from 5 K to 290 K for R ¼ Gd-Ho [5]. Neutron diffraction data for Ho2NiGe6 indicate that the Ho magnetic moments form an uniaxial antiferromagnetic ordering below 11 K [6]. The R2CuGe6 compounds with light rare earth elements such as Ce, Pr, Nd and Sm [2,7,8] exhibit an el temperatures not antiferromagnetic ordering with the Ne exceeding 20 K. Also the heavier germanides (R ¼ Gd e Er) show el temantiferromagnetic properties with the corresponding Ne peratures raging from 5.6 K (R ¼ Er) up to 33.1 K (R ¼ Tb) [9]. The R2CuGe6 compounds with R ¼ Y, Gd e Er exhibit metallic electrical conductivity in the temperature region 78 Ke300 K [10]. The new investigations of the electrical transport properties of R2CuGe6 (R ¼ La, Ce and Nd) confirm metallic-like behavior in the temperature range from 5 K to 290 K [5,10]. The Y2TGe6 (T ¼ Ni and Cu) germanides behave as a Pauli like paramagnet [4,10] indicating existence of a non-localized magnetic moment on T elements. In order to gain a complete physical picture of the magnetic properties of the selected R2TGe6 (R ¼ Tb, Ho and Er; T ¼ Ni and Cu) compounds, we have performed a systematic investigations on annealed polycrystalline samples by measuring DC susceptibility and magnetization (in different applied magnetic fields) as well as neutron diffraction measurements. On the basis of these data an information on the temperature dependence of magnetic properties together with parameters of the crystal and magnetic structures have been determined.

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2. Experimental details Polycrystalline samples of the R2TGe6 compounds (R ¼ Tb, Ho and Er, T ¼ Ni and Cu) were prepared by arc melting of stoichiometric amounts of the constituent elements (nominal purities: Re3 N, Ni, Cu e 4 N and Ge e 5 N) on a water cooled copper hearth under a protective Ti-gettered argon atmosphere. The samples were annealed at 870 K in evacuated quartz tube for one week and next quenched in cold water. The quality of the samples was checked by X-ray powder diffraction at room temperature with the CuKa radiation on X'Pert PRO X-ray diffractometer. Magnetic measurements were performed in the temperature range 1.9 Ke390 K on vibrating sample magnetometer (VSM) option for the Physical Property Measurement System (PPMS) by Quantum Design. Magnetic susceptibility measurements were carried in applied magnetic field of 50 Oe and 1 kOe, while the isothermal hysteresis loops were collected at 1.9 K in external field between 90 kOe and 90 kOe. Neutron diffraction patterns were obtained by means of the E6 diffractometer at the BER II reactor (BENSC, Helmholtz e Zentrum e Berlin) with the incident neutron wavelength 2.4315 Å. The diffraction patterns were collected at el temdifferent temperatures below and above the respective Ne peratures. The Rietveld-type program FullProf [11] was used for processing the diffraction data. 3. Results The X-ray diffraction patterns of the investigated compounds,

collected at room temperature, presented in Fig. S1, are very similar one to another. The analysis of the patterns showed dominant contribution originating from the 2:1:6 phase with minor amounts of impurity phases: elemental Ge and RTxGe2 whose contents are reported in Table S1. For all compounds the determined values of lattice parameters are in good agreement with the data presented in Refs. [2e4]. 3.1. Magnetic data Temperature dependences of the reciprocal magnetic susceptibilities are displayed in Fig. 1a and d for R2NiGe6 (R ¼ Tb, Er) and in Fig. 1b and c for R2CuGe6 (R ¼ Ho and Er). In broad temperature range a linear dependence, described by the Curie e Weiss formula c(T) ¼ C/(T e Qp), is observed. In this equation C is a Curie constant related to the effective magnetic moment by formula meff ¼ (C/8)½ while Qp is a paramagnetic Curie temperature. The least squares fitting of the experimental data gave values of the effective magnetic moments and the paramagnetic Curie temperatures which are listed in Table 1. The values of meff are close to those predicted for free R3þ ions while Qp are negative indicating dominant character of antiferromagnetic interactions. Magnetic susceptibility of Tb2NiGe6 has a maximum at 42 K characteristic of antiferro-to paramagnetic transition (see the upper inset in Fig. 1a). At low temperatures an additional small intensity peak at 2.4 K, related to the Tb2O3 impurity phase, is visible. Hysteresis loop measured at 1.9 K confirms antiferromagnetic properties and shows a metamagnetic phase transition at the magnetic field of 70 kOe.

Fig. 1. Temperature dependence of the reciprocal magnetic susceptibility of (a) Tb2NiGe6, (b) Ho2CuGe6, (c) Er2CuGe6 and (d) Er2NiGe6 measured at the external magnetic field of 1 kOe. The insets: the upper ones - temperature dependence of the magnetic susceptibility at low temperatures taken at 50 Oe (ZFC and FC) and at 1 kOe (ZFC); the lower ones hysteresis loop between 90 kOe and 90 kOe at T ¼ 1.9 K.

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Table 1 el temperature; Qp is the paramagnetic Curie temperature; meff - the effective magnetic moment; ms e the Magnetic data for the R2CuGe6 compounds. TN refers to the Ne moment at T ¼ 1.9 K and H ¼ 90 kOe (M) together with the one determined from neutron diffraction at the lowest temperature (ND); Hcr e critical magnetic field from magnetometric measurements and DMM e direction of the magnetic moment. Compound

TN [K]

Qp [K]

Tb2NiGe6 Ho2NiGe6a Ho2CuGe6 Er2NiGe6 Er2CuGe6

42 11 10 6.4 6

21.6 11 6.0 1.5 8.6

a

meff [mB]

ms [mB]

Exp.

Theor.

Exp. M

Exp. ND

Theor.

9.73 10.58 10.51 9.48 9.83

9.72 10.61 10.61 9.58 9.58

2.08 7.5 7.48 6.11 6.53

7.9(1) 8.16(7) 9.0(1) 7.5(1) 8.12(8)

9.0 10.0 10 9.0 9.0

Hcr [kOe]

DMM

70 14.5 16 8 7

kb kb kb ka kc

Data from Refs. [4,6].

Low temperature magnetic susceptibility data of Ho2CuGe6 evidence for antiferromagnetic ordering below 10 K (see the upper inset in Fig. 1b). This result is confirmed by hysteresis loop at 1.9 K presenting a metamagnetic transition at H ¼ 16 kOe. An antiferromagnetic ordering has also been found in Er2TGe6 (T ¼ Ni, Cu) as their respective susceptibility curves have maxima at 6.4 K (T ¼ Ni) and 6 K (T ¼ Cu) e see Fig. 1c and d. Additional anomalies found at 3 K for T ¼ Ni and at 4 K for T ¼ Cu originate from the impurity phases: ErNi0.65Ge2 [13] and ErCu0.25Ge2 [14]. Also the hysteresis loops measured at low temperatures (1.9 K) are typical of antiferromagnetic materials and indicate a metamagnetic process with the critical field of 8 kOe (T ¼ Ni) and 7 kOe (T ¼ Cu). It is worth noting that no metamagnetic transition has been detected at 5 K for Er2CuGe6. For both compounds the magnetization is not saturated at H ¼ 90 kOe. For all compounds calculated values of the magnetic moments at 1.9 K and H ¼ 90 kOe are smaller than the values predicted for free R3þ ions (see Table 1). 3.2. Neutron diffraction data Neutron diffraction pattern of Ho2NiGe6, collected above the el temperature, is shown in Fig. 2. The neutron diffraction in Ne paramagnetic state confirms that all samples have an orthorhombic crystal structure of the Ce2CuGe6-type (see Fig. 3). In this structure the crystal unit cell contains two formula units and the atoms occupy the following positions: R1, R2, Ge1 and Ge2 atoms the 2a

Fig. 3. Orthorhombic crystal unit cell of the R2TGe6 compounds.

site (0, 0, z) while T, Ge3, Ge4, Ge5 and Ge6 atoms at the 2b site (½, 0, z). In order to define origin of the coordinate system the z parameter of the R1 atom was fixed to zero during the Rietveld refinement. The determined values of the lattice parameters and atoms' positional parameters are listed in Table 2. This type of crystal structure is characterized by small values of the a and b lattice parameters (about 4 Å) and large value of the c one (~21 Å). The crystal structure of R2TGe6 can be described as a pile of atomic planes stacked along the c-axis according to the following sequence: R1 e Ge3 e Ge4 e R2 e T e Ge1 e Ge2 e R1 e Ge3 e Ge4 e R2 e T e Ge6 e Ge5 e R1 (see Fig. 3). The lattice parameters of R2NiGe6 compounds are smaller than those in R2CuGe6. Neutron diffraction pattern of Tb2NiGe6 at T ¼ 1.7 K contains a large number of additional peaks (Fig. 4a). The strong intensity Table 2 The a, b, c lattice parameters, unit cell volume V and zi positional atom parameters for R2CuGe6 (R ¼ Nd and Er) obtained from the neutron diffraction data at paramagnetic state.

Fig. 2. Neutron diffraction pattern of Ho2CuGe6 collected at 14.2 K. The squares represent the experimental points. The solid lines are for the calculated profile of the crystal structure and for the difference between the observed and calculated intensity (in the bottom of diagram). The vertical bars indicate positions of Bragg reflections for the investigated compound and elemental Ge.

T [K] a [Å] b [Å] c [Å] V [Å3] z(R2) z(T) z(Ge1) z(Ge2) z(Ge3) z(Ge4) z(Ge5) z(Ge6) RBragg [%] Rprof [%]

Tb2NiGe6

Ho2CuGe6

Er2NiGe6

Er2CuGe6

45 4.0449(7) 3.9914(7) 21.425(5) 345.9(1) 0.670(2) 0.229(1) 0.273(2) 0.388(2) 0.533(2) 0.114(2) 0.887(1) 0.767(1) 7.4 6.5

14.2 4.0841(8) 3.9751(8) 20.902(5) 339.6(1) 0.670(1) 0.237(2) 0.294(2) 0.410(1) 0.549(2) 0.128(2) 0.898(2) 0.773(2) 12.0 9.4

15.3 3.995(1) 3.941(1) 21.112(6) 332.4(2) 0.665(2) 0.238(3) 0.295(3) 0.409(3) 0.545(1) 0.126(3) 0.906(2) 0.780(2) 11.9 7.91

8.3 4.0940(9) 3.9878(9) 20.935(7) 341.8(2) 0.668(2) 0.236(2) 0.286(3) 0.404(3) 0.546(2) 0.121(4) 0.891(3) 0.770(3) 10.9 8.3

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Fig. 4. Differential neutron diffraction patterns of (a) Tb2NiGe6, (b) Ho2CuGe6, (c) Er2CuGe6 and (d) Er2NiGe6. The squares represent experimental points, the solid lines are for the calculated profiles for the crystal and magnetic structure models (as described in the text) and for the difference between the observed and calculated intensities (in the bottom of each diagram). The vertical bars indicate positions of the Bragg reflections of magnetic origin.

peaks can be indexed within a magnetic unit cell identical with the crystal one. In the crystal unit cell the rare earth atoms occupy the following positions: S1 (0, 0, 0), S2 (0, 0.5, 0.5) at the first site and S3 (0, 0, z(R2)) and S4 (0, 0.5, z(R2)þ0.5) at the second one. The best agreement between the experimental and theoretical models has been obtained for an antiferromagnetic arrangement with the sequence þþ– and the Tb magnetic moment equal to 7.9(1) mB and parallel to the b-axis (Rmag ¼ 10.2%) (Fig. 5a). Temperature depenel temperature of 42 K dence of the magnetic moment gives the Ne (see the inset in Fig. 4a). Additional peak at 2Q ¼ 17.2 comes from the TbNi0.5Ge2 impurity phase [12]. The temperature dependence el temof the corresponding magnetic moment provides the Ne perature of TbNi0.5Ge2 as equal to 26 K (see the inset in Fig. 4a). The low temperature neutron diffraction patterns of Ho2CuGe6 and Er2CuGe6 are similar one to another (Fig. 4b and c). The peaks of magnetic origin can be indexed with the propagation vector k ¼ (½, 0, 0) e the magnetic unit cell is doubled along the a-axis when compared with the crystal one. The best fit to the experimental data has been found for the þ– þ sequence of magnetic moment within the crystal unit cell. The rare earth magnetic moment equals 9.0(1) mB at T ¼ 2.2 K and is parallel to the b-axis for R ¼ Ho (Rmag ¼ 8.0%) (Fig. 5b) while it equals 6.95(11) mB at T ¼ 1.7 K and is parallel to the c-axis for R ¼ Er (Rmag ¼ 12.1%) (Fig. 5c).

Fig. 5. Magnetic structure of (a) Tb2NiGe6, (b) Ho2CuGe6, (c) Er2CuGe6 and (d) Er2NiGe6.

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Fig. 6. Temperature dependence of the a, b and c lattice parameters together with the unit cell volume V and the values of magnetic moments in (a) Tb2NiGe6, (b) Ho2CuGe6 and (c) Er2NiGe6.

An anomaly visible at ~4 K in temperature dependence of the Er2CuGe6 magnetic susceptibility (see Fig. 1c) as well as small intensity peaks at 2Q equal to ~34 and ~50 in the neutron diffraction pattern taken at 1.7 K originate from the ErCu0.25Ge2 impurity phase according to the data in Ref. [14]. Quantitative determination of the impurity phase was not possible due to strong overlapping of Bragg reflections originating from the impurity and main (Er2CuGe6) phases. Differential neutron diffraction pattern (2.5 Ke15.3 K) for Er2NiGe6 (see Fig. 4d) shows a distribution of the magnetic peaks similar to that observed for Tb2NiGe6. The Er magnetic moments equal 7.5(1) mB at T ¼ 2.5 K and form an antiferromagnetic structure with the þþ– sequence. The moments are parallel to the a-axis (Rmag ¼ 8.6%) (Fig. 5d). A broad maximum at 2Q ¼ 13.5 originates from the ErNi0.65Ge2 impurity phase [13]. 3.3. Temperature dependence of parameters of the crystal and magnetic structures For selected compounds the neutron diffraction patterns have been collected in a function of temperature. Based on these data, the temperature dependence of the a, b, c, unit cell parameters as well as the unit cell volume V has been determined and is presented in Fig. 6. Temperature dependences of the magnetic moments determined from the neutron diffraction patterns indicate el temperatures. that the magnetic structures are stable up to the Ne

For all compounds a jump in values of the lattice parameters and el temperature. unit cell volumes is observed at the respective Ne This jump clearly evidences for the magnetostriction effect (see Table 3). 4. Discussion The results presented in the work indicate that the investigated compounds are antiferromagnets with magnetic moment localized on the rare-earth atoms. The determined values of effective magnetic moments are close to those predicted for free R3þ ions while the magnetic moments in the ordered state, as found from magnetization as well as from the neutron diffraction data, are smaller than those of free R3þ ions. The macroscopic magnetic data are in agreement with the results reported previously in Refs. [3,4,7e9]. The layered magnetic structures observed in R2NiGe6 (R ¼ Tb and Er) with the sequence þþ– (see Fig. 5a and d) is characterized by ferromagnetic arrangement of the R moments within the (001) plane. Along the c-axis the short distance couplings (S1eS4 and S2eS3) are found antiferromagnetic for R2NiGe6. For the longer distance couplings (S1eS3 and S2eS4) the coupling character is reversed. In case of the R2CuGe6 (R ¼ Ho, Er) compounds their magnetic ordering within the (001) plane is different - described by the propagation vector k ¼ (½, 0, 0) and following the þ– þ sequence within the volume of crystal unit cell. The magnetic

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proportional to density of states at the Fermi level N(EF). The XPS data indicate that in rare earth intermetallics containing Ni atoms the Ni 3d states are close to the Fermi level [15] while for the Cubased compounds the 3d states are about 4 eV below the Fermi level (see Fig. 2 in Ref. [16]). Thus both the densities of states at the el temperatures Fermi level N(EF) as well as the respective Ne should be lower for the Cu-based compounds which is in agreement with the experimental results (see Fig. 3a in Ref. [9]). The role of CEF manifests itself in a reduction of magnetic moments in the ordered state in comparison with the free R3þ ion values (see Table 1) as well as in change of direction of the moments (for example: in R2NiGe6 the direction of magnetic moment changes from the b-axis for R ¼ Tb to the a-axis for R ¼ Er and in Er2CuGe6 it changes from the b-axis for R ¼ Ho to the c-axis for R ¼ Er). This change results from a change in local surroundings of the rare earth atoms. el temperature vs. de Gennes factor dependence is almost The Ne linear for the Ni compounds while some deviations from linearity are observed for the Cu compounds (see Fig. 3b in Ref. [9]). These deviations are another evidence of the CEF effect [17]. The presented results indicate that change of both the rare earth as well as transition 3d elements strongly influences the values and orientations of magnetic moments. 5. Summary

Fig. 6. (continued). Table 3 Difference between the lattice parameters (Da ¼ ao -ap) and unit cell volumes (DV ¼ Vo e Vp) where o and p refer to ordered and paramagnetic states, respectively, together with the values of magnetic moments for the selected R2TGe6 compounds. Compound

Da [Å]

Db [Å]

Dc [Å]

DV [Å3]

m [mB]

Tb2NiGe6 Ho2CuGe6 Er2NiGe6

0.01 0.0125 0.0075

0.009 0.01 0.005

0.04 0.021 0.04

2.25 2.27 2.0

7.9(1) 9.0(1) 7.5(1)

moments are parallel to the b-axis (R ¼ Ho) (Fig. 5b) or to the c-axis (R ¼ Er) (Fig. 5c). Appearance of a new interaction of long range character leads to doubling the magnetic unit cell along the [100] direction. The above results indicate influence of the non-magnetic T (3d) element on magnetic ordering in the rare earth sublattice. The differences in magnetic orderings within the (001) plane between the Ni- and Cu-based compounds can be found in Fig. 5. It is worth noting that doubling of the magnetic unit cell along the aaxis as observed in R2CuGe6 (R ¼ Ho, Er) corresponds with larger value of the a lattice parameter when compared with the values found for the Ni-based compounds (see Table 2). The interatomic R-R distances in both series of compounds are long enough to exclude any direct magnetic interaction. As the temperature dependence of electrical resistivity is typical of metallic materials [5,10], the magnetic interactions occur probably via conduction electrons as described by the RKKY theory. This prediction is supported by nearly linear dependence of the paramagnetic Curie temperatures vs de Gennes factor (see Fig. 3b in Ref. [9]). In the RKKY model the exchange interactions are

The results presented in this work confirm that the ternary R2TGe6 (R ¼ Tb, Ho, Er; T ¼ Ni, Cu) compounds crystallize in the orthorhombic Ce2CuGe6-type structure. The magnetic and neutron diffraction measurements reveal that these compounds order antiferromagnetically at low temperatures. The values of the effective magnetic moments together with the neutron diffraction data indicate that the magnetic moments are localized on the rare earth atoms. The rare earth moments in R2NiGe6 (R ¼ Tb, Er) form a simple collinear magnetic structure with the magnetic unit cell identical to the crystal one while R2CuGe6 (R ¼ Ho and Er) have a doubled magnetic unit cell (k ¼ (½, 0, 0)). Observed reduction of the magnetic moments in ordered state with respect to the free R3þ ion values together with a change of directions of the magnetic moments in function of chemical composition confirm significant influence of the CEF effect. Determined magnetic structures together with metallic character of the electric transport indicate that the RKKY-type interactions are responsible for stability of the magnetic order. el temperatures in the Anomalies found at the respective Ne temperature dependences of lattice parameters and unit cell volume evidence for the magnetostriction effect. Acknowledgement Kind hospitality and financial support extended to two of us (S. B. and A. S.) by the Berlin Neutron Scattering Center (BENSC) is gratefully acknowledged. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.jallcom.2019.06.027. References [1] D. Gignoux, D. Schmitt, Phys. Rev. B 48 (1993) 12682e12691. [2] M.B. Konyk, P.S. Salamakha, O.I. Bodak, V.K. Pecharsky, Kristallographia 33 (1988) 838e840. [3] O. Sologub, K. Hiebl, P. Rogl, O. Bodak, J. Alloy. Comp. 227 (1995) 37e39. [4] M. Konyk, L. Romaka, D. Gignoux, D. Fruchart, O. Bodak, Yu Gorelenko, J. Alloy.

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