Magnetic phase transitions in RCu2Ge2 (R = Dy − Tm) intermetallics

Intermetallics 19 (2011) 964e969

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Magnetic phase transitions in RCu2Ge2 (R ¼ Dy  Tm) intermetallics q. Gondek a, *, D. Kaczorowski b, A.P. Pikul b, A. Szytu1a c a

Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Mickiewicza 30, 30-059 Kraków, Poland W. Trzebiatowski Institute of Low Temperature and Structure Research, Polish Academy of Sciences, P.O. Box 1410, 50-950 Wrocław, Poland c M. Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 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 13 July 2010 Received in revised form 6 November 2010 Accepted 22 February 2011 Available online 21 March 2011

Magnetic and related properties of RCu2Ge2 (R ¼ Dy  Tm) intermetallics were investigated by means of magnetic susceptibility, electrical resistivity and specific heat measurements. The compounds were found to order antiferromagnetically at 6.2 K (DyCu2Ge2), 5.6 K (HoCu2Ge2), 3.0 K (ErCu2Ge2) and 3.9 K (TmCu2Ge2). Electrical transport and heat capacity data were analysed by means of appropriate models giving the Debye and Einstein temperatures estimation. By extracting purely magnetic contribution to the heat capacity the Schottky effect due to crystalline electric field (CF) was evidenced. The corresponding CF levels schemes were estimated, as well. Moreover, the magnetic entropy has been calculated for all investigated samples. Ó 2011 Elsevier Ltd. All rights reserved.

Keywords: A. Rare-earth intermetallics B. Electrical resistance and other electrical properties B. Magnetic properties B. Thermodynamic and thermochemical properties

1. Introduction The RCu2Ge2 compounds (R ¼ Gd, Tb, Dy, Ho, Er, and Tm) crystallise with the body-centred tetragonal structure (space group I4/mmm), in which the R, Cu and Ge atoms occupy 2(a), 4(d) and 4 (e) positions, respectively, and forms an alternating atomic layers sequence ReCueGeeCueR [1], which is one of the characteristic features of that structure. According to the literature, the Gd-, Tb-, Dy- and Ho-based compounds order antiferromagnetically below the Néel temperatures of 12, 15, 8 and 6.4 K, respectively, while the ErCu2Ge2 and TmCu2Ge2 phases were reported to be magneticaly non-ordered at least down to 4.2 K [2]. Neutron diffraction measurements confirmed the magnetic phase transitions in the compounds TbCu2Ge2, HoCu2Ge2 [3,4], DyCu2Ge2 [5], and evidenced commensurate antiferromagnetic structure with the same propagation vector k ¼ (½, 0, ½) for each of the latter phases. Moreover, the neutron scattering experiments revealed occurrence of the antiferromagnetic ordering (with the same magnetic structure) also in ErCu2Ge2, however the magnetic order arises below 1.9 K [6]. Temperature dependences of the magnetic peaks intensities indicated that in all four compounds (i.e. with Tb, Dy, Ho and Er) the magnetic structures are stable [3,4]. Recent detailed magnetization measurements performed on a single crystal of * Corresponding author. E-mail address: [email protected] (q. Gondek). 0966-9795/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.intermet.2011.02.017

TbCu2Ge2 revealed presence of two subsequent magnetic phase transitions: at TN ¼ 12.3 K and Tt ¼ 9.6 K [7,8]. In order to shed more light on physical properties of that family of intermetallics, we performed detailed studies of the compounds RCu2Ge2. In this paper we report on magnetization, electrical transport and specific heat measurements for DyCu2Ge2, HoCu2Ge2, ErCu2Ge2, and TmCu2Ge2, and briefly discuss the influence of the crystalline electric field on their temperature characteristics in the paramagnetic region.

2. Experimental details Polycrystalline samples of RCu2Ge2 (R ¼ La, Dy, Ho, Er and Tm; Labased sample served as an isostructural non-magnetic counterpart) were synthesised by conventional arc melting of stoichiometric amounts of high-purity constituents (R of 99.9% purity, Cu and Ge of 99.99% purity) under protective argon atmosphere. The melting was repeated several times in order to ensure good homogeneity of the pellets. Subsequently, the products were annealed in evacuated quartz tubes at 800  C for one week. Quality of the products was verified by X-ray powder diffraction at room temperature using a Philips PW e 3710 X’PERT diffractometer with CuKa radiation. The diffraction patterns were easily indexed within the expected tetragonal crystal structure of the ThCr2Si2-type with no spurious phases. The magnetic properties were studied in the temperature

Ł. Gondek et al. / Intermetallics 19 (2011) 964e969

range 1.72e400 K and in external magnetic fields up to 5 T employing a commercial Quantum Design SQUID magnetometer. The magnetic properties were studied using fixed to rotate powdered samples. The heat capacity and the electrical resistivity were measured by relaxation method and ac four-point technique, respectively. For the heat capacity a rectangular shaped bulk samples of dimensions 2.5 mm  2.5 mm  1 mm were prepared. Electrical resistivity measurements were made on bars of rectangular cross section (0.5 mm2) and length up to 4 mm. The measurements were carried out from room temperature down to 2 K or 350 mK (depending on the investigated sample) utilizing the Quantum Design PPMS platform.

Table 1 Magnetic data of investigated RCu2Ge2 compounds. TN e ordering temperature; qp e paramagnetic Curie temperature; meff e effective magnetic moment; m5T e magnetic moment at B ¼ 5 T; ND e magnetic moment derived from neutron diffraction; Bcr e critical field of metamagnetic transition. R

TN(K)

qp(K)

m(mB) meff(mB)

m5T

Dy

6.0 8 5.5 6.4 2.6 e 3.5 e

5.1(2) 15 3.2(1) 6 4.6(1) 4.5 10.6(1) 2

10.4(1) 10.6 10.3(1) 10.6 9.5 (1) 10.7 7.3(1) 7.5

8.13(5) e 7.44(4) e 7.68(4) e 2.43(3) e

Ho Er Tm

3. Results Analysis of the X-ray diffraction data has confirmed the ThCr2Si2-type of crystal structure. According to the Rietveld analysis, the lattice parameters at 300 K were found to be: a ¼ 4.025 (1) Å and c ¼ 10.279(1) Å for DyCu2Ge2 [RBragg ¼ 3.12%]; a ¼ 4.015 (1) Å and c ¼ 10.298(1) Å for HoCu2Ge2 [RBragg ¼ 3.23%]; a ¼ 4.000 (1) Å and c ¼ 10.311(1) Å for ErCu2Ge2 [RBragg ¼ 3.01%] and a ¼ 3.991 (1) Å and c ¼ 10.318(1) Å for TmCu2Ge2 [RBragg ¼ 3.30%]. The above data nicely correlates with values reported in ref. [1]. The ability of texture of the powdered samples was found to be highly dependent on grains’ sizes. For finely powdered samples (grains’ sizes distribution with maximum of about 5 mm) no significant texture was observed. The temperature and field dependencies of the magnetic susceptibility c and magnetization s measured for RCu2Ge2 (R ¼ Dy, Ho, Er and Tm) are presented in Fig. 1(aed). In the paramagnetic region all the c1(T) curves follow the CurieeWeiss law with the refined parameters (i.e. the effective magnetic moment meff and the paramagnetic Curie temperature qp) as given in Table 1. The derived qp values are intrinsically anisotropic, therefore in our experiment

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Bcr(T)

Ref.

2.5(2) e 2.0(2) e 1.0(1) e 0.41(6) e

this [2] this [2] this [2] this [2]

ND e 8.0(2) e 6.5(1) e 8.0(4) e e

work work work work

only a mean values can be found. Taking into account that a bulk samples exhibit a preferred orientation the measurements were performed on finely powdered fixed-to-rotate specimens. Lack of texture of finely powdered samples as derived from XRD data ensures the proper estimation of mean values of qp. The same holds for isothermal magnetisation studies. The values of meff are very close to the theoretical ones expected for the free R3þ ions, indicating presence of well localized magnetic moments. The negative values of qp suggest an antiferromagnetic character of the magnetic correlations in the studied compounds. Indeed, distinct cusp-like maxima were observed at low temperatures in c(T). For estimation of the Néel temperatures a d(cT)/dT plots were prepared (see the upper insets to Fig. 1(aed)), where the maximum values of d(cT)/dT are related to the Néel temperatures TN (collected in Table 1). The isothermal magnetization s(B), displayed in the lower insets to Fig. 1(aed), show clear field-induced metamagnetic phase transitions, corroborating the antiferromagnetic character of the ground states of the RCu2Ge2 compounds. The

Fig. 1. Temperature dependence of inverse magnetic susceptibility c1 of DyCu2Ge2 (a); HoCu2Ge2 (b); ErCu2Ge2 (c) and TmCu2Ge2 (d). The solid lines represent the CurieeWeiss fit. The insets show a low temperature part of c(T) and the isothermal magnetization s measured as a function of increasing and decreasing magnetic field B (closed and open symbols, respectively).

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values of magnetic moments m5T and of the critical fields Bcr are collected in Table 1. Fig. 2(aed) show temperature variations of the electrical resistivity r(T) of the investigated compounds. As seen, overall shapes of the r(T) curves are very similar to each other. In particular, the resistivity of all compounds decreases quasi-linearly from room temperature down to about 50 K and tends to saturation at lower temperatures. At TN pronounced drops of r manifest the antiferromagnetic ordering of the compounds. As can be inferred from Tables 1 and 2, the Neel temperatures estimated from the electrical properties correlates with the magnetometric data very well. In the paramagnetic region, where the spin-disorder resistivity rN may be considered as constant, the electrical resistivity can be described by the BlocheGrüneiseneMott (BGM) formula:




rðTÞ ¼ ðr0 þ rN Þ þ 4AT

T

qD

4 qZD =T 0

x5    KT 3 ðex  1Þ 1  ex

(1)

where the first term stands for the scattering of conduction electrons on static defects in the crystal lattice (the residual resistivity r0) and on disordered magnetic moments (the spin-disordered resistivity rN), the second one originates from the electron-phonon scattering (qD is the approximant of the Debye temperature [9]) and the third one accounts for interband sed scattering. Least-squares fitting of Eq. (1) to the experimental data yielded the parameters collected in Table 2. The values of all the parameters are of magnitude typical for intermetallics. It is worth noting that all four Debye temperatures are very close to each other, thus suggest similar phonon spectrum in the compounds studied, as expected for isostructural phases with similar molar masses. In order to estimate the magnetic contribution to the specific heat of the compounds studied, the specific heat of non-magnetic isostructural LaCu2Ge2 was measured as a reference. As can be inferred from Fig. 3, the temperature dependence of the specific heat of the latter compound can be described by the formula:

Table 2 Results of refinement of BMG model with ordering temperatures as derived from resistivity data for RCu2Ge2. The ordering temperature TN was estimated from point where the dr(T)/dT exhibit maxiumum. R

TN (K)

r0 þ rN (mUcm)

A (mUcmK1)

qD (K)

K (mUcmK3)

Dy Ho Er Tm

5.8(1) 6.0(1) 2.8(1) 3.6(1)

17.12(5) 12.91(4) 17.88(6) 79.10(8)

0.146(1) 0.271(2) 0.192(2) 1.858(3)

249.0(1) 248.2(1) 247.4(2) 246.7(4)

2.81(9) 3.22(8) 5.48(8) 5.73(7)

   

108 108 108 108

QD


Cphþel ¼ 9R

1 T 1  a T QD

3 ZT 0

x4 ex ðex

 1Þ2

Q 2 QEi Ei e T 1 X T þR þ gT 1  aT i  QEi 2 e T 1

(2)

where the first and the second term stand for the phonon specific heat within the Debye and Einstein models, respectively (R e gas constant, QD e the Debye temperature, QEi e the Einstein temperatures), gT is the specific heat of conduction electrons, and 1/(1eaT) is a correction for anharmonic vibrations. Since the LaCu2Ge2 compound consists of 5 atoms per f.u., one can expect presence of 15 modes in the phonon structure: 3 acoustic modes (described by the first term of Eq. (2) and 12 optical modes (the second term of Eq. (2)). In order to reduce the number of fitting parameters, the optical modes were grouped arbitrarily into 4 trifold degenerated branches. Least-squares fitting of Eq.(2) with i ¼ 4 to the experimental data (see the solid line in Fig. 3) yielded the following values of the fitting parameters: QD ¼ 195.4 K; QE1 ¼ 114.1 K; QE2 ¼ 233.2 K; QE3 ¼ 251.4 K; QE4 ¼ 325.9; g ¼ 7.1 mJ/mol K2 and a ¼ 5.95  105 1/K. The so-derived analytical formula for the non-magnetic contribution to the specific heat of

Fig. 2. Electrical resistivity r of DyCu2Ge2 (a); HoCu2Ge2 (b); ErCu2Ge2 (c) and TmCu2Ge2 (d). The upper insets display low-temperature parts of r(T), while the lower ones display dr/dT derivative. The solid lines represents the BMG fit to the experimental data (see text for discussion).

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specific heat Cmagn(T) as a distinct l-like anomaly at temperatures of 6.2, 5.6, 3.0 and 3.9 K for R ¼ Dy, Ho, Er and Tm, respectively, being in excellent agreement with the magnetic and electrical transport data. Additional anomalies observed at 2.6 K in ErCu2Ge2 and at 1.7 K in TmCu2Ge2 correspond probably to some spin reorientation in these compounds, hardly visible in reported physical characteristics. At elevated temperatures broad maxima in Cmagn(T), that can be ascribed to the Schottky anomaly due to crystal electric field effect, are well visible in each compound. The latter contribution can be described by the formula:

2

di

cmagn

LaCu2Ge2 was subsequently adapted to the particular rare-earths derivatives by modifying the characteristic temperatures QD and QEi with respect to the molar masses of the lanthanides. Fig. 4(aed) present temperature variations of the specific heat of RCu2Ge2 (R ¼ Dy, Ho, Er and Tm) together with the so-calculated nonmagnetic contributions, and Fig. 5(aed) display results of their subtraction from the respective total Cp(T) dependencies. As can be seen in Fig. 5(aed), the bulk antiferromagnetic ordering of all the compounds studied manifest itself the magnetic

di

12

6P   P 6 d2i e T B de TC B C 6 Bi ¼ 1 i C R6 i ¼ 1 B C ¼ 26  B C T 6 B P di C 6 P di @ A 6 4 e T e T i¼1

Fig. 3. Specific heat curve for non-magnetic LaCu2Ge2 reference sample. Solid line represents fit of phononic and electronic contributions.

0

i¼1

3 7 7 7 7 7 7 7 7 5

(3)

where R is the universal gas constant and di are the energies of crystal field levels (in Kelvins; d1 h 0). Since Dy and Er are Krammers ions, the ground multiplet splits into 8 doublets. In the case of Ho and Tm, being non-Krammers ions, singlets are also allowed. However, since the compounds HoCu2Ge2 and TmCu2Ge2 are magnetically ordered, their ground state must be a doublet or at least a quasi-doublet. It is worth noting, that in case of singlet CF ground state magnetic ordering is also possible, however it relays on balance between separation of the ground CF state from higher levels and strength of magnetic interactions. Magnetic entropy for all investigated samples is presented in Fig. 6. As one can notice, in each compound studied, the magnetic entropy achieves at room temperature the value Rln(2J þ 1)

Fig. 4. Temperature dependence of the specific heat of DyCu2Ge2 (a); HoCu2Ge2 (b); ErCu2Ge2 (c) and TmCu2Ge2 (d) compounds. The solid lines represent the non-magnetic contributions (see text for details).

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Ł. Gondek et al. / Intermetallics 19 (2011) 964e969

Fig. 5. Magnetic specific heat of DyCu2Ge2 (a); HoCu2Ge2 (b); ErCu2Ge2 (c) and TmCu2Ge2 (d). Solid lines denote Schottky contribution originating from crystal field levels scheme as presented in insets. In the insets to the part (a) and (c) all levels are doublets. In rest cases, there are doublets (thick bars) or singlets (thin bars) shown.

expected for the (2J þ 1)-fold degenerated multiplet suggesting full thermal population of the whole CF multiplet already at 300 K. Insets to Fig. 6(aed) present magnetic entropy in the vicinity of the magnetic phase transitions. In DyCu2Ge2 the magnetic entropy

at TN is very close to value Rln2, expected for the magnetically ordered ground CF doublet. In HoCu2Ge2 the value of Rln2 is exceeded probably due low lying higher CF levels (cf. Fig. 6b). In ErCu2Ge2 and TmCu2Ge2 the magnetic entropy is strongly reduced.

Fig. 6. Magnetic entropy of DyCu2Ge2 (a); HoCu2Ge2 (b); ErCu2Ge2 (c) and TmCu2Ge2 (d). The insets present magnetic entropy in vicinity of the ordering temperature (the ordering temperatures are marked by arrows).

Ł. Gondek et al. / Intermetallics 19 (2011) 964e969

4. Discussion and conclusions The compounds DyCu2Ge2; HoCu2Ge2, ErCu2Ge2 and TmCu2Ge2 were found to be antiferromagnetically ordered below 6.2 K, 5.6 K, 3.0 K and 3.9 K, respectively. In ErCu2Ge2 and TmCu2Ge2 the magnetic ordering is reported for the first time. Moreover, in both samples additional anomalies in ordered region were found at 2.6 K (ErCu2Ge2) and 1.7 K (TmCu2Ge2), hardly visible in other physical properties. We can tentatively ascribe those anomalies to the transitions from commensurate into incommensurate magnetic structure, which were predicted theoretically [10]. According to our preliminary neutron diffraction data (not given here), ErCu2Ge2 indeed exhibits such phase transition at 2.6 K. Evidence of spin rearrangement in isostructural RCu2Si2 and RFe2Ge2 intermetallics seems to corroborate our hypothesis [11,12]. The ordering temperatures of the investigated compounds RCu2Ge2 are slightly higher than those reported for their RFe2Ge2 analogues: (2.1 K for Dy; 1.1 K for Ho; 2.5 K for Er; no magnetic ordering for Tm) [12]. Since magnetic moment on Fe site in RFe2Ge2 is negligible, it hints at transfer of the electronic density of states (DOS) between Fe and its ligands. That may be a reason of weakening of the RKKY interactions in this family. The 169Tm Mössbauer spectroscopy data available for TmFe2Ge2 and TmCu2Ge2 indicate opposite signs of the lattice contributions to the electric field gradient Vzz for these two compounds [13]. This seems to be in agreement with the mentioned DOS transfer. Magnetic data of the investigated compounds exhibit a metamagnetic transition at critical field (defined as the B value where maximum of ds/dB occurs), which is quasi-linearly dependent on the number of the 4f electrons (cf. Table 1). The value of Bcr may be related to “stiffness” of the magnetic structure and consequently stays in a strict relation to the strength of the magnetic interactions and magnetic anisotropy. The values of the magnetic moments at 5 T are significantly lower that the ordered magnetic moments expected for the free ions. The value of the magnetic field is apparently too small to force alignment of the magnetic moments along the direction of the magnetic field as expected for antiferromagnets. Specific heat data give valuable information about magnetic entropy gained at wide temperature range. In principle, the ground CF doublet should give contribution of Rln2 to the entropy at the ordering point. However, this value might be different due to splitting of this state by molecular field or due to influence of higher CF levels, which are insufficiently separated from the ground state. In the first case, the expected value may be lowered. For the second

969

scenario, the value would be higher. In real systems both factors act simultaneously, thus the value of entropy at the ordering temperature relays on interplay of those mechanisms. This is nicely noticeable, when comparing Figs. 5 and 6, for DyCu2Ge2 (almost exact value, just one higher CF level may contribute) HoCu2Ge2 (exceeded value, three higher CF level may contribute) and ErCu2Ge2 (a little lower value, just one higher CF level may contribute). The TmCu2Ge2 is a special case as there are no contributions from higher CF levels (large energetically separation of about 90 K). Consequently, it exhibits lowered value of entropy even well above the transition temperature. The above findings are consistent with estimation made for isostructural RFe2Ge2 compounds, except for TmFe2Ge2 [12]. In cases of R ¼ Dy, Ho, Er the doublet ground state was reported to be the most probable. On the other hand, for nonmagnetic TmFe2Ge2 sample a sinlget ground state with closely lying further excited states was evidenced. The above mentioned results of the 169Tm Mössbauer measurements corroborate such significant difference in crystal electric field in TmFe2Ge2 and TmCu2Ge2 compounds [13]. A considerable crystal field effects are visible in neutron diffraction measurements reported for (TbeEr)Cu2Ge2 samples [4e6]. The direction of the magnetic moment changes from (110) for R ¼ Tb direction into (001) for R ¼ Er. It is a common assumption that the sign of the aJ Stevens factor may be responsible for preferable orientation (perpendicular or parallel to the c-axis). In case of RCu2Ge2 family this is fulfilled for Tb, Dy and Er based compounds. References [1] Rieger W, Parthé E. Monatshefte für Chemie 1969;100:444. [2] Kotsanidis PA, Yakinthos JK. Solid State Commun 1981;40:1041e3. [3] Schobinger-Papamanthellos P, Niggli A, Kotsanidis PA, Yakinthos JK. J Phys Chem Solids 1984;45:695e9. [4] Pinto H, Melamud M, Kuznietz M, Shaked H. Phys Rev B 1985;31:508e15. [5] Kotsanidis PA, Yakinthos JK, Roudaut E. Solid State Commun 1984;50:413e6. [6] Yakinthos JK. J Magn Magn Mater 1985;46:300. [7] Song C, Johnson D, Wermeille D, Goldman AI, Budko SL, Fisher LR, et al. Phys Rev B 2001;64. 224414-1-5. [8] Shigeoka T, Shiraishi M, Mitamura H, Uwatoko Y, Fujiwara T, Goto T. Physica B; 2004:112e6. 346e347. [9] Giovannini M, Michor H, Bauer E, Hilscher G, Rogl P, Ferro R. J Alloys Comp 1998;280:26. [10] Gignoux D, Schmitt D. Phys Rev B 1993;48:12682. [11] Takeda Y, Dung N, Nakano Y, Ishikura T, Ikeda S, Matsuda T, et al. J Phys Soc Jap 2008;77:104710. [12] Avila MA, Bud’ko SL, Canfield PC. J Magn Magn Mater 2004;270:51. [13] Stewart GA, Thompson PW, Cadogan JM, Li Hong-Shuo. Hyp Int 1994;90:407.