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Magnetic properties and phase diagram of NdPd5Al2
Journal of Alloys and Compounds 675 (2016) 94e98
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
Magnetic properties and phase diagram of NdPd5Al2 skova , Jan Prokleska, Petr Proschek, Pavel Javorský Jan Zuba c*, Kristina Vla Charles University in Prague, Faculty of Mathematics and Physics, Department of Condensed Matter Physics, Ke Karlovu 5, 121 16 Prague 2, Czech Republic
a r t i c l e i n f o
a b s t r a c t
Article history: Received 7 October 2015 Received in revised form 19 February 2016 Accepted 29 February 2016 Available online 2 March 2016
We have investigated a single crystal of the tetragonal intermetallic compound NdPd5Al2 by means of magnetization, specific heat and magnetoresistivity measurements. NdPd5Al2 orders antiferromagnetically below 1.3 K and exhibits a distinct magnetocrystalline anisotropy with the c-axis as the easy axis of magnetization. Magnetic phase diagram constructed on the basis of heat capacity and magnetization measurements is characterized by two different low-temperature phases and first-order phase transition in the zero field. © 2016 Elsevier B.V. All rights reserved.
Keywords: Phase diagrams Phase transitions Magnetically ordered materials Heat capacity Magnetization
1. Introduction RPd5Al2 compounds (R is rare earth element or actinide) have aroused an interest of scientific community after the discovery of a paramagnetic unconventional heavy-fermion superconductor NpPd5Al2 (Tc ¼ 4.9 K, g ¼ 200 mJ mol1 K2) by Aoki et al., in 2007 [1] and a Kondo lattice antiferromagnet CePd5Al2 [2] followed by reporting of a pressure-induced superconductivity in this compound [3]. These findings motivated further investigations of mentioned materials [4e8] as well as studies of analogous compounds also crystallizing in the tetragonal ZrNi2Al5-type structure (space group I4/mmm). UPd5Al2 reported in 2008 [9] exhibit paramagnetic CurieeWeiss behaviour and saturation of the susceptibility in low temperatures due to the non-magnetic ground state. Griveau and co-workers succeeded in a preparation of PuPd5Al2 which was found to be antiferromagnetic with TN ¼ 5.6 K but does not present a superconductivity [10]. Ribeiro et al. reported a number of rare-earth based materials RPd5Al2 (R ¼ Y, Ce, Pr, Nd, Sm, Gd) [11]. Most of them (R ¼ Ce, Nd, Sm, Gd) order magnetically, namely NdPd5Al2 shows anomaly in the heat capacity due to an antiferromagnetic transition at 1.2 K. PrPd5Al2, studied also by Nakano et al. [12], is a paramagnet with a singlet ground state showing saturation of the low-temperature
* Corresponding author. E-mail address: [email protected] (J. Zub a c). http://dx.doi.org/10.1016/j.jallcom.2016.02.256 0925-8388/© 2016 Elsevier B.V. All rights reserved.
susceptibility similarly to UPd5Al2. YbPd5Al2, originally presented by Hirose et al. [13], is presumably an antiferromagnet with the ordering temperature only 0.19 K. Recently, paper by Benndorf and his colleagues has been published to complete a family of the RPd5Al2 rare-earth compounds with until then missing members (R ¼ Tb Tm) [14], so the whole range of analogous 4f-compounds from Ce to Yb (except for Eu) and the non-magnetic analogues YPd5Al2 and LuPd5Al2 exist [15,3]. The new RPt5Al2 (R ¼ Y, GdeTm, Lu) series was prepared as well [14]. Whereas previous studies of rare-earth isostructural RPd5Al2 homologues [11,14] deal mainly with polycrystals, in our paper we aim to measurements on a single crystalline sample which is desired for a proper investigation of anisotropic physical properties. We report on magnetization, heat capacity and electrical resistivity measurements. 2. Experimental details Single crystalline samples of NdPd5Al2 have been prepared by the Czochralski method in a tri-arc furnace. Pure metals (Nd: 99.5%, Pd: 99.995%, Al: 99.9999%) were used as a starting material. In case of Nd, the initial purity was further enhanced by solid state electrotransport (SSE). Ingot (rod) of Nd was heated up close to the melting temperature (z1200 K for Nd) by electrical currents (z120 A) and kept there for 3e5 weeks for purification. A stoichiometric mixture of all constituent elements with total mass of 8 g was firstly melted into a button under a protective argon atmosphere and flipped and remelted several times for better
c et al. / Journal of Alloys and Compounds 675 (2016) 94e98 J. Zuba
homogenization. The rod was then pulled out of the melt at a translation speed of 4 mm/h using tungsten as a virtual seed. The resultant ingot was consisted of elongated plate-like stacked grains with crystallographic c direction perpendicular to the ingot. Individual crystals used for the measurement were separated from the ingot with a fine wire saw and polished. To verify homogeneity of the samples, electron-probe microanalysis was performed on the Mira Tescan scanning electron microscope (SEM) equipped with an energy-dispersive X-ray detector (EDX). No secondary phase was found. Quality of the crystals as well as their orientation was checked by the back-reflection Laue method. Powdered samples were further characterized by the Xray diffraction employing Bruker D8 diffractometer. Structural parameters were refined with Fullprof software [16] and are given in the Table 1. The low temperature (T < 2 K) magnetization was measured using the Hall probes. The sample was placed on the Hall cross on the a-c plane with the edge in the middle of the cross and magnetic field applied along the c-axis (and in plane of the Hall cross). With this geometry the Hall probe is sensitive to the stray field proportional to the c-axis magnetization, the absolute values were calculated using the reference measurement at 2 K. Further experiments were performed on the devices supplied by Quantum Design: temperature and field dependences of the magnetization were measured on the Magnetic Property Measurement System 7 T (MPMS) SQUID magnetometer; resistivity and heat capacity on the Physical Property Measurement System 9 T (PPMS) equipped with a Helium-3 refrigerator. Resistivity measurements were performed employing the four-probe method. Heat capacity was measured and evaluated using standard timerelaxation technique (temperature dependence in field applied perpendicular to the c-axis and field dependence) and dual-slope curve analysis [17] (temperature dependence in field along the caxis). The precision of the latter method is slightly worse, but it is better suited to perform measurements across first-order phase transition and follow qualitative changes e. g. with application of magnetic field. 3. Results and discussion 3.1. Susceptibility and magnetization
95
Fig. 1. The temperature dependence of the magnetic susceptibility in the field of 1 T applied along [100], [110] and [001] directions. Solid lines represent fit by the CurieeWeiss law. Please note different scales on the left y-axis.
to the CurieeWeiss law in the region 50e300 K leads to the paramagnetic CurieeWeiss temperature qp ¼ 8.6 K and the effective magnetic moment meff ¼ 3.62 mB for H k ½001, respectively qp ¼ 27.1 K and meff ¼ 3.71 mB for H k ½100 and qp ¼ 28.0 K and meff ¼ 3.68 mB for H k ½110. Values of the meff are close to the Nd3þ free-ion moment. Field dependences of magnetization in the paramagnetic state (Fig. 2) were measured for H k ½100, H k ½110 and H k ½001 and at 2 K and 10 K. In the range from 0 to 7 T all curves exhibit a linear dependence with exception of H k ½001 at 2 K which saturates at z 2.3 mB/Nd above 4 T. The data indicates caxis as the easy axis of magnetization and corroborates that there is no substantial anisotropy in the basal plane, correspondingly to our results from Ref. M/H vs. T data (Fig. 1). Fig. 3 shows M vs. H dependence for H k ½001 measured using the Hall probes. The ordered-state magnetization (T < 1.3 K) shows a rapid increase of the magnetization around 1.25 T in the 0.3 K data which further shifts to the lower fields with increasing temperature. This feature corresponds to the anomaly observed in the specific heat data and can be attributed to the magnetic transition
Temperature dependence of magnetic susceptibility is presented in Fig. 1. The data were collected in the field of 1 T applied along [100], [110] and [001] directions and in the temperature range from 300 K to 2 K, where the compound is in the paramagnetic state. At temperatures above 100 K the H/M vs. T dependences show linear CurieeWeiss-like behaviour for all three field directions. Whereas this more or less holds for the susceptibility in the field applied along the tetragonal c-axis, which is the easy direction of magnetization, also down to the low temperatures, dependences for the field applied within the basal plane (i. e. for H k ½100 and H k ½110) show a noticeable kink below 50 K which can be presumably ascribed to the crystal-field effects. The fit Table 1 Structural parameters of NdPd5Al2. I4/mmm a ¼ 4.147(2) Å c ¼ 14.865(6) Å Nd Pd (1) Pd (2) Al
(0, (0, (0, (0,
0, 0) 0, 1/2) 1/2, 0.146(1)) 0, 0.241(3))
Fig. 2. Magnetic isotherms in the paramagnetic state for two different temperatures and field applied along the significant crystallographic directions.
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c et al. / Journal of Alloys and Compounds 675 (2016) 94e98 J. Zuba
Fig. 3. Magnetic isotherms in the ordered state and paramagnetic state measured employing the Hall probes. The absolute values were calculated using the reference measurement at 2 K. The solid line represents derivative of the 0.3 K data.
from antiferromagnetic phase 1 to the phase 2 as will be discussed below. 3.2. Specific heat and phase diagram The low-temperature evolution of specific heat in the magnetic fields applied along [001] direction is presented in Fig. 4. It shows a well pronounced anomaly which is related to magnetic order below TN ¼ 1.3(1) K, in agreement with previous results [11]. The anomaly in the Cp/T vs. T plot shifts to lower temperatures with increasing field suggesting the antiferromagnetic ordering. The 0.94 T dependence reveals additionally another transition at approx. 1.2 K alongside the first one at 0.9 K. This transition is observed only as rather weak anomaly, but becomes more pronounced in higher fields where it also shifts to lower temperatures (see inset of Fig. 4). The 1.08 T dependence still features both transitions, while in higher fields only the transition at higher temperature is observable in our specific heat data. Fig. 5 presents Cp/T vs. T in magnetic fields applied
Fig. 4. Low-temperature specific heat of NdPd5Al2 plotted as Cp/T vs. T. Measurements were performed in magnetic fields applied along the tetragonal c-axis using dualeslope curve analysis. The inset depicts a detail of the Cp(T) dependence in the region where another transition appears.
perpendicular to the [001] direction. In contrast with heat capacity for H k ½001, specific heat for H⊥½001 is not significantly influenced by low magnetic fields (e. g. 0.5 T). The antiferromagnetic ordering still survives in the field of 3 T, while in 5 T, we already observe Cp/T vs. T behaviour which reflects increasing ferromagnetic component. Besides the Cp(T), we have also measured the dependence of the heat capacity on magnetic field in the ordered state. Results for the measurement at 0.8 K are presented in Fig. 6a. The data clearly demonstrate the occurrence of the two phase transitions located around 1 and 3 T and resemble Cp(H) dependences measured for e. g. Nd2RhIn8 [18]. In addition, we also present the magnetoresistivity measured above and below TN (Fig. 6b). The ordered-state data apparently differ from the paramagnetic ones by the hump between 1 and 3 T. Nevertheless, the transitions are not so pronounced in the case of magnetoresistivity as in the heat capacity data and were not used to construct the magnetic phase diagram. We note that weak magnetoresistivity effect was found also in related Nd2RhIn8 compound [19]. Temperature dependence of resistivity in zero field (inset of Fig. 6b) shows similar behaviour around the transition temperature as in previously studied Nd2TIn8 and NdTIn5 compounds [20]. The magnetic phase diagram represented in Fig. 7 summarizes our findings from specific heat and M(H) measurements in field applied along the c-axis. It features two different magnetic phases the lower-field phase 1 which is supposed to be antiferromagnetic and another field-induced magnetic phase 2. The existence of two magnetic phases resembles phase diagrams of related RTX5 and R2TX8 [21e23,19,24]. The shape of the border between both phases is similar to that found in R2CoGa8 series [24], while somewhat distinguishes from those published for RRhIn5 [21,22] and R2RhIn8 compounds [23,19]. The microscopic nature of both magnetic phases has been thoroughly studied by neutron diffraction in the case of Ho2RhIn8 [25]. In both magnetic phases, the rare-earth moments are oriented parallel along the c-axis. The ground state magnetic structure is a simple collinear antiferromagnet described by a single propagation vector. The magnetic structure in the fieldinduced phase is then a complex multi-k structure described by four propagation vectors. The transition between both phases can be simply viewed also as flipping of one quarter of the Ho magnetic moments which causes the total magnetization to be half of the
Fig. 5. Low-temperature specific heat (plotted as Cp/T vs. T) in magnetic fields applied perpendicular to the tetragonal c-axis. Data were collected using standard timerelaxation technique.
c et al. / Journal of Alloys and Compounds 675 (2016) 94e98 J. Zuba
97
Fig. 7. The magnetic phase diagram of NdPd5Al2 based on the Cp(T) (full squares), Cp(H) (empty squares) and M(H) (empty diamonds) measurements in field applied along the c-axis. The error bars were estimated from the width of the anomalies in the case of Cp(T) and M(H) data and from the step between datapoints in the Cp(H) data. The lines connecting points in the graph are just a guide for an eye. The insets show temperature vs. time dependences during the heating pulse in the field of 0 and 1.23 T demonstrating different order of the two phase transitions. The dotted line serves as a tentative phase border as discussed in the text.
Fig. 6. Specific heat as a function of magnetic field (a). Magnetoresistivity (b) expressed as the Dr/r0 ratio where Dr¼r(H,T)r0 and r0 is the resistivity in zero field. The inset of the lower figure shows the resistivity around the phase transition. Solid line represents smoothing spline interpolation of the data and is just a guide for an eye.
field-induced ferromagnetic state value [25]. In our case of NdPd5Al2, the magnetization after the first transition reaches z1.2 mB/Nd which is roughly half of the saturated value presented in Fig. 2, i.e. we observe the same behaviour as reported for R2RhIn8 compounds including Ho2RhIn8 [23,19]. Such similarity together with a closely related crystal structure indicates possibly the same nature of the phase transition between the two magnetic phases also in NdPd5Al2. The microscopic determination of the magnetic structure(s) in NdPd5Al2 by neutron diffraction is highly desirable to make a final conclusion. The insets in Fig. 7 display time dependences of the sample's temperature during the constant heating pulse and following relaxation. Their shape is clearly different when measured below 0.5 T and above 1.1 T. Whereas the low-field curves exhibit plateaus around TN indicating the first-order phase transition, the curves above 1.1 T show behaviour typical for the second-order phase transition; in the region from approx. 0.5 Te1.1 T curves gradually change their character from the former type to the latter. Firstorder phase transition in zero field is unusual for transition between paramagnetic and magnetically ordered state, but it was observed e. g. in the case of U2Rh3Si5 [26]. Another tentative explanation might be the fact that the phase 2 region in the phase diagram reaches down to the zero field (dotted line in Fig. 7) or due to possible presence of some other magnetic phase existing only in
a very narrow temperature range as in the case of Ho2RhIn8 [25]. The first-order nature of the transition seen in low fields arises then from transition between this phase (or phase 2) and phase 1. Fig. 8 shows the low-temperature magnetic heat capacity of NdPd5Al2 replotted as Cmag/T vs. T2. The magnetic specific heat was obtained by subtracting the lattice specific heat of the nonmagnetic yttrium analogue [15] from the original data, i. e. Cmag(NdPd5Al2) ¼ C(NdPd5Al2) C(YPd5Al2). Although Y is not the best analogue for Nd (LaPd5Al2 probably does not form), the lattice contribution to the specific heat of NdPd5Al2 is negligible in comparison with the magnetic specific heat in the presented temperature region, so the choice of the non-magnetic analogue does not play an important role. Further, we have fitted the data in the ordered state by the expected specific heat dependences for magnetic excitations (including a gap in the magnon spectrum) [27]: d
Cmag ¼ AT m expðD=TÞ;
(1)
where D is size of the gap, d is the characteristic dimension of the excitations and m ¼ 2 for ferromagnetic, respectively m ¼ 1 for antiferromagnetic magnons. However, we are not able to unambiguously determine whether the compound exhibits 3D or 2D antiferromagnetic magnons mainly due to the very limited fitting range, in which the experimental data can be reasonably described by both dependences as presented in Fig. 8. By integrating the temperature dependence of the Cmag/T, we have calculated the magnetic entropy. As can be seen in the inset of Fig. 8, the entropy reaches Rln2 close above TN, indicating the doublet ground state.
4. Conclusions Single crystal of NdPd5Al2 was successfully prepared and studied by means of susceptibility, magnetization, specific heat and resistivity measurements. Magnetic phase diagram derived from heat capacity measurements consists of two low-temperature phases - the zero-field antiferromagnetic phase and an additional
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c et al. / Journal of Alloys and Compounds 675 (2016) 94e98 J. Zuba
Fig. 8. Low-temperature magnetic specific heat replotted as Cmag/T vs. T2. Data were evaluated using standard time-relaxation method. The thick lines represents fits of the data by the expected dependences given by Fig. 1 for antiferromagnetic excitations. The resulting parameters obtained by the fitting in the temperature range 0.5e1.1 K are A ¼ 17.10 J mol1K4 and D¼1.55 K for the 3D AFM magnons, respectively A ¼ 44.27 J mol1K3 and D¼2.49 K for the 2D AFM magnons. The inset shows corresponding magnetic entropy as a function of temperature.
phase which appears when magnetic field is applied along the tetragonal c-axis. It has been established that the magnetic phase transition in the zero field is the first-order phase transition. Acknowledgements We would like to thank R. Tarasenko and V. Tka c for technical assistance during measurements. This study has been supported by the Czech Science Foundation (Grant No. P204-13-12227S). Experiments were performed in MLTL (http://mltl.eu/), which is supported within the Program of Czech Research Infrastructures (Project No. LM2011025). References [1] D. Aoki, Y. Haga, T.D. Matsuda, N. Tateiwa, S. Ikeda, Y. Homma, H. Sakai, Y. Shiokawa, E. Yamamoto, A. Nakamura, et al., Unconventional heavyfermion superconductivity of a new transuranium compound NpPd5Al2, J. Phys. Soc. Jpn. 76 (2007) 063701. [2] R. de Almeida Ribeiro, T. Onimaru, K. Umeo, M. de Abreu Avila, K. Shigetoh, T. Takabatake, A Kondo lattice antiferromagnet CePd5Al2, J. Phys. Soc. Jpn. 76 (2007) 123710. [3] F. Honda, M.-A. Measson, Y. Nakano, N. Yoshitani, E. Yamamoto, Y. Haga, T. Takeuchi, H. Yamagami, K. Shimizu, R. Settai, et al., Pressure-induced superconductivity in antiferromagnet CePd5Al2, J. Phys. Soc. Jpn. 77 (2008) 043701. [4] J.-C. Griveau, K. Gofryk, J. Rebizant, Transport and magnetic properties of the superconductor NpPd5Al2, Phys. Rev. B 77 (2008) 212502.
[5] K. Gofryk, J.-C. Griveau, E. Colineau, J. Sanchez, J. Rebizant, R. Caciuffo, Kondo behavior in superconducting NpPd5Al2, Phys. Rev. B 79 (2009) 134525. [6] T. Onimaru, Y.F. Inoue, K. Shigetoh, K. Umeo, H. Kubo, R.A. Ribeiro, A. Ishida, M.A. Avila, K. Ohoyama, M. Sera, et al., Giant uniaxial anisotropy in the magnetic and transport properties of CePd5Al2, J. Phys. Soc. Jpn. 77 (2008) 074708. [7] F. Honda, M. Measson, Y. Nakano, N. Yoshitani, T. Takeuchi, K. Sugiyama, M. Hagiwara, K. Shimizu, K. Kindo, N. Tateiwa, et al., Magnetic and superconducting properties of a pressure-induced superconductor CePd5Al2, Phys. B Condens. Matter 404 (2009) 3202e3205. [8] Y. Inoue, T. Onimaru, A. Ishida, T. Takabatake, Y. Oohara, T. Sato, D. Adroja, A. Hillier, E. Goremychkin, Sinusoidally modulated magnetic structure of a Kondo lattice compound CePd5Al2, J. Phys. Conf. Ser. 200 (2010) 032023. IOP Publishing. [9] Y. Haga, D. Aoki, Y. Homma, S. Ikeda, T. Matsuda, E. Yamamoto, H. Sakai, N. Tateiwa, N. Dung, A. Nakamura, et al., Crystal structure and magnetic properties of the new ternary actinide compounds AnPd5Al2 (An¼ U, Np), J. Alloys Compd. 464 (2008) 47e50. [10] J.-C. Griveau, K. Gofryk, E. Colineau, J. Rebizant, Crystal structure and physical properties of PuPd5Al2, J. Nucl. Mater. 385 (2009) 11e14. [11] R. Ribeiro, Y. Inoue, T. Onimaru, M. Avila, K. Shigetoh, T. Takabatake, Magnetic properties of RPd5Al2 (R¼ Y, Ce, Pr, Nd, Sm, Gd), Phys. B Condens. Matter 404 (2009) 2946e2948. [12] Y. Nakano, F. Honda, T. Takeuchi, K. Sugiyama, M. Hagiwara, K. Kindo, E. Yamamoto, Y. Haga, R. Settai, H. Yamagami, et al., Magnetic and Fermi surface properties of CePd5Al2 and PrPd5Al2, J. Phys. Soc. Jpn. 79 (2010) 024702. [13] Y. Hirose, N. Nishimura, K. Enoki, F. Honda, T. Takeuchi, K. Sugiyama, M. Hagiwara, K. Kindo, R. Settai, Y. Onuki, Electrical and magnetic properties of new Yb-based compound YbPd5Al2, J. Phys. Soc. Jpn. 81 (2012). SB057. [14] C. Benndorf, F. Stegemann, H. Eckert, O. Janka, New transition metal-rich rareearth palladium/platinum aluminides with RET5Al2 composition: structure, magnetism and 27Al NMR spectroscopy, Z. für Naturforsch. B 70 (2015) 101e110. k, P. Javorský, Structural and electronic properties of [15] M. Divis, P. Cerm a YPd5Al2, Phys. B Condens. Matter 407 (2012) 276e279. [16] J. Rodríguez-Carvajal, Recent advances in magnetic structure determination by neutron powder diffraction, Phys. B Condens. Matter 192 (1993) 55e69. [17] Quantum Design, PPMS Heat Capacity Option User's Manual, Part Number 1085-150, Rev. L3 ed. (San Diego, CA, USA, October 2010) [18] P. Javorský et al., submitted to J. Magn. Magn. Mater. k, Y. Skourski, A. Andreev, High[19] P. Javorský, K. Pajskr, M. Klicpera, P. Cerm a field magnetization and magnetic phase diagrams in Nd2RhIn8 and Tb2RhIn8, J. Alloys Compd. 598 (2014) 278e281. [20] P. Pagliuso, J. Thompson, M. Hundley, J. Sarrao, Crystal-field-induced magnetic frustration in NdMIn5 and Nd2MIn8(M¼ Rh, Ir) antiferromagnets, Phys. Rev. B 62 (2000) 12266. [21] N.V. Hieu, H. Shishido, T. Takeuchi, A. Thamizhavel, H. Nakashima, K. Sugiyama, R. Settai, T.D. Matsuda, Y. Haga, M. Hagiwara, K. Kindo, Y. nuki, Unique magnetic properties of NdRhIn5, TbRhIn5, DyRhIn5, and HoRhIn5, J. Phys. Soc. Jpn. 75 (2006) 074708. [22] J. Duque, R.L. Serrano, D. Garcia, L. Bufaical, L. Ferreira, P. Pagliuso, E. Miranda, Field induced phase transitions on NdRhIn5 and Nd2RhIn8 antiferromagnetic compounds, J. Magn. Magn. Mater. 323 (2011) 954e956. k, M. Kratochvílova , K. Pajskr, P. Javorský, Magnetic phase diagrams [23] P. Cerm a of R2RhIn8 (R¼ Tb, Dy, Ho, Er and Tm) compounds, J. Phys. Condens. matter Inst. Phys. J. 24 (2012) 206005. [24] D.A. Joshi, R. Nagalakshmi, S. Dhar, A. Thamizhavel, Anisotropic magnetization studies of R2CoGa8 single crystals (R¼ Gd, Tb, Dy, Ho, Er, Tm, Y, and Lu), Phys. Rev. B 77 (2008) 174420. k, K. Prokes, B. Ouladdiaf, M. Boehm, M. Kratochvílova , P. Javorský, [25] P. Cerm a Magnetic structures in the magnetic phase diagram of Ho2RhIn8, Phys. Rev. B 91 (2015) 144404. [26] B. Becker, S. Ramakrishnan, A. Menovsky, G. Nieuwenhuys, J. Mydosh, Unusual ordering behavior in single-crystal U2Rh3Si5, Phys. Rev. Lett. 78 (1997) 1347. € m, Low temperature heat capacity of the rare earth metals, [27] L.J. Sundstro Handb. Phys. Chem. rare earths 1 (1978) 379e410.
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
Magnetic properties and phase diagram of NdPd5Al2 skova , Jan Prokleska, Petr Proschek, Pavel Javorský Jan Zuba c*, Kristina Vla Charles University in Prague, Faculty of Mathematics and Physics, Department of Condensed Matter Physics, Ke Karlovu 5, 121 16 Prague 2, Czech Republic
a r t i c l e i n f o
a b s t r a c t
Article history: Received 7 October 2015 Received in revised form 19 February 2016 Accepted 29 February 2016 Available online 2 March 2016
We have investigated a single crystal of the tetragonal intermetallic compound NdPd5Al2 by means of magnetization, specific heat and magnetoresistivity measurements. NdPd5Al2 orders antiferromagnetically below 1.3 K and exhibits a distinct magnetocrystalline anisotropy with the c-axis as the easy axis of magnetization. Magnetic phase diagram constructed on the basis of heat capacity and magnetization measurements is characterized by two different low-temperature phases and first-order phase transition in the zero field. © 2016 Elsevier B.V. All rights reserved.
Keywords: Phase diagrams Phase transitions Magnetically ordered materials Heat capacity Magnetization
1. Introduction RPd5Al2 compounds (R is rare earth element or actinide) have aroused an interest of scientific community after the discovery of a paramagnetic unconventional heavy-fermion superconductor NpPd5Al2 (Tc ¼ 4.9 K, g ¼ 200 mJ mol1 K2) by Aoki et al., in 2007 [1] and a Kondo lattice antiferromagnet CePd5Al2 [2] followed by reporting of a pressure-induced superconductivity in this compound [3]. These findings motivated further investigations of mentioned materials [4e8] as well as studies of analogous compounds also crystallizing in the tetragonal ZrNi2Al5-type structure (space group I4/mmm). UPd5Al2 reported in 2008 [9] exhibit paramagnetic CurieeWeiss behaviour and saturation of the susceptibility in low temperatures due to the non-magnetic ground state. Griveau and co-workers succeeded in a preparation of PuPd5Al2 which was found to be antiferromagnetic with TN ¼ 5.6 K but does not present a superconductivity [10]. Ribeiro et al. reported a number of rare-earth based materials RPd5Al2 (R ¼ Y, Ce, Pr, Nd, Sm, Gd) [11]. Most of them (R ¼ Ce, Nd, Sm, Gd) order magnetically, namely NdPd5Al2 shows anomaly in the heat capacity due to an antiferromagnetic transition at 1.2 K. PrPd5Al2, studied also by Nakano et al. [12], is a paramagnet with a singlet ground state showing saturation of the low-temperature
* Corresponding author. E-mail address: [email protected] (J. Zub a c). http://dx.doi.org/10.1016/j.jallcom.2016.02.256 0925-8388/© 2016 Elsevier B.V. All rights reserved.
susceptibility similarly to UPd5Al2. YbPd5Al2, originally presented by Hirose et al. [13], is presumably an antiferromagnet with the ordering temperature only 0.19 K. Recently, paper by Benndorf and his colleagues has been published to complete a family of the RPd5Al2 rare-earth compounds with until then missing members (R ¼ Tb Tm) [14], so the whole range of analogous 4f-compounds from Ce to Yb (except for Eu) and the non-magnetic analogues YPd5Al2 and LuPd5Al2 exist [15,3]. The new RPt5Al2 (R ¼ Y, GdeTm, Lu) series was prepared as well [14]. Whereas previous studies of rare-earth isostructural RPd5Al2 homologues [11,14] deal mainly with polycrystals, in our paper we aim to measurements on a single crystalline sample which is desired for a proper investigation of anisotropic physical properties. We report on magnetization, heat capacity and electrical resistivity measurements. 2. Experimental details Single crystalline samples of NdPd5Al2 have been prepared by the Czochralski method in a tri-arc furnace. Pure metals (Nd: 99.5%, Pd: 99.995%, Al: 99.9999%) were used as a starting material. In case of Nd, the initial purity was further enhanced by solid state electrotransport (SSE). Ingot (rod) of Nd was heated up close to the melting temperature (z1200 K for Nd) by electrical currents (z120 A) and kept there for 3e5 weeks for purification. A stoichiometric mixture of all constituent elements with total mass of 8 g was firstly melted into a button under a protective argon atmosphere and flipped and remelted several times for better
c et al. / Journal of Alloys and Compounds 675 (2016) 94e98 J. Zuba
homogenization. The rod was then pulled out of the melt at a translation speed of 4 mm/h using tungsten as a virtual seed. The resultant ingot was consisted of elongated plate-like stacked grains with crystallographic c direction perpendicular to the ingot. Individual crystals used for the measurement were separated from the ingot with a fine wire saw and polished. To verify homogeneity of the samples, electron-probe microanalysis was performed on the Mira Tescan scanning electron microscope (SEM) equipped with an energy-dispersive X-ray detector (EDX). No secondary phase was found. Quality of the crystals as well as their orientation was checked by the back-reflection Laue method. Powdered samples were further characterized by the Xray diffraction employing Bruker D8 diffractometer. Structural parameters were refined with Fullprof software [16] and are given in the Table 1. The low temperature (T < 2 K) magnetization was measured using the Hall probes. The sample was placed on the Hall cross on the a-c plane with the edge in the middle of the cross and magnetic field applied along the c-axis (and in plane of the Hall cross). With this geometry the Hall probe is sensitive to the stray field proportional to the c-axis magnetization, the absolute values were calculated using the reference measurement at 2 K. Further experiments were performed on the devices supplied by Quantum Design: temperature and field dependences of the magnetization were measured on the Magnetic Property Measurement System 7 T (MPMS) SQUID magnetometer; resistivity and heat capacity on the Physical Property Measurement System 9 T (PPMS) equipped with a Helium-3 refrigerator. Resistivity measurements were performed employing the four-probe method. Heat capacity was measured and evaluated using standard timerelaxation technique (temperature dependence in field applied perpendicular to the c-axis and field dependence) and dual-slope curve analysis [17] (temperature dependence in field along the caxis). The precision of the latter method is slightly worse, but it is better suited to perform measurements across first-order phase transition and follow qualitative changes e. g. with application of magnetic field. 3. Results and discussion 3.1. Susceptibility and magnetization
95
Fig. 1. The temperature dependence of the magnetic susceptibility in the field of 1 T applied along [100], [110] and [001] directions. Solid lines represent fit by the CurieeWeiss law. Please note different scales on the left y-axis.
to the CurieeWeiss law in the region 50e300 K leads to the paramagnetic CurieeWeiss temperature qp ¼ 8.6 K and the effective magnetic moment meff ¼ 3.62 mB for H k ½001, respectively qp ¼ 27.1 K and meff ¼ 3.71 mB for H k ½100 and qp ¼ 28.0 K and meff ¼ 3.68 mB for H k ½110. Values of the meff are close to the Nd3þ free-ion moment. Field dependences of magnetization in the paramagnetic state (Fig. 2) were measured for H k ½100, H k ½110 and H k ½001 and at 2 K and 10 K. In the range from 0 to 7 T all curves exhibit a linear dependence with exception of H k ½001 at 2 K which saturates at z 2.3 mB/Nd above 4 T. The data indicates caxis as the easy axis of magnetization and corroborates that there is no substantial anisotropy in the basal plane, correspondingly to our results from Ref. M/H vs. T data (Fig. 1). Fig. 3 shows M vs. H dependence for H k ½001 measured using the Hall probes. The ordered-state magnetization (T < 1.3 K) shows a rapid increase of the magnetization around 1.25 T in the 0.3 K data which further shifts to the lower fields with increasing temperature. This feature corresponds to the anomaly observed in the specific heat data and can be attributed to the magnetic transition
Temperature dependence of magnetic susceptibility is presented in Fig. 1. The data were collected in the field of 1 T applied along [100], [110] and [001] directions and in the temperature range from 300 K to 2 K, where the compound is in the paramagnetic state. At temperatures above 100 K the H/M vs. T dependences show linear CurieeWeiss-like behaviour for all three field directions. Whereas this more or less holds for the susceptibility in the field applied along the tetragonal c-axis, which is the easy direction of magnetization, also down to the low temperatures, dependences for the field applied within the basal plane (i. e. for H k ½100 and H k ½110) show a noticeable kink below 50 K which can be presumably ascribed to the crystal-field effects. The fit Table 1 Structural parameters of NdPd5Al2. I4/mmm a ¼ 4.147(2) Å c ¼ 14.865(6) Å Nd Pd (1) Pd (2) Al
(0, (0, (0, (0,
0, 0) 0, 1/2) 1/2, 0.146(1)) 0, 0.241(3))
Fig. 2. Magnetic isotherms in the paramagnetic state for two different temperatures and field applied along the significant crystallographic directions.
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Fig. 3. Magnetic isotherms in the ordered state and paramagnetic state measured employing the Hall probes. The absolute values were calculated using the reference measurement at 2 K. The solid line represents derivative of the 0.3 K data.
from antiferromagnetic phase 1 to the phase 2 as will be discussed below. 3.2. Specific heat and phase diagram The low-temperature evolution of specific heat in the magnetic fields applied along [001] direction is presented in Fig. 4. It shows a well pronounced anomaly which is related to magnetic order below TN ¼ 1.3(1) K, in agreement with previous results [11]. The anomaly in the Cp/T vs. T plot shifts to lower temperatures with increasing field suggesting the antiferromagnetic ordering. The 0.94 T dependence reveals additionally another transition at approx. 1.2 K alongside the first one at 0.9 K. This transition is observed only as rather weak anomaly, but becomes more pronounced in higher fields where it also shifts to lower temperatures (see inset of Fig. 4). The 1.08 T dependence still features both transitions, while in higher fields only the transition at higher temperature is observable in our specific heat data. Fig. 5 presents Cp/T vs. T in magnetic fields applied
Fig. 4. Low-temperature specific heat of NdPd5Al2 plotted as Cp/T vs. T. Measurements were performed in magnetic fields applied along the tetragonal c-axis using dualeslope curve analysis. The inset depicts a detail of the Cp(T) dependence in the region where another transition appears.
perpendicular to the [001] direction. In contrast with heat capacity for H k ½001, specific heat for H⊥½001 is not significantly influenced by low magnetic fields (e. g. 0.5 T). The antiferromagnetic ordering still survives in the field of 3 T, while in 5 T, we already observe Cp/T vs. T behaviour which reflects increasing ferromagnetic component. Besides the Cp(T), we have also measured the dependence of the heat capacity on magnetic field in the ordered state. Results for the measurement at 0.8 K are presented in Fig. 6a. The data clearly demonstrate the occurrence of the two phase transitions located around 1 and 3 T and resemble Cp(H) dependences measured for e. g. Nd2RhIn8 [18]. In addition, we also present the magnetoresistivity measured above and below TN (Fig. 6b). The ordered-state data apparently differ from the paramagnetic ones by the hump between 1 and 3 T. Nevertheless, the transitions are not so pronounced in the case of magnetoresistivity as in the heat capacity data and were not used to construct the magnetic phase diagram. We note that weak magnetoresistivity effect was found also in related Nd2RhIn8 compound [19]. Temperature dependence of resistivity in zero field (inset of Fig. 6b) shows similar behaviour around the transition temperature as in previously studied Nd2TIn8 and NdTIn5 compounds [20]. The magnetic phase diagram represented in Fig. 7 summarizes our findings from specific heat and M(H) measurements in field applied along the c-axis. It features two different magnetic phases the lower-field phase 1 which is supposed to be antiferromagnetic and another field-induced magnetic phase 2. The existence of two magnetic phases resembles phase diagrams of related RTX5 and R2TX8 [21e23,19,24]. The shape of the border between both phases is similar to that found in R2CoGa8 series [24], while somewhat distinguishes from those published for RRhIn5 [21,22] and R2RhIn8 compounds [23,19]. The microscopic nature of both magnetic phases has been thoroughly studied by neutron diffraction in the case of Ho2RhIn8 [25]. In both magnetic phases, the rare-earth moments are oriented parallel along the c-axis. The ground state magnetic structure is a simple collinear antiferromagnet described by a single propagation vector. The magnetic structure in the fieldinduced phase is then a complex multi-k structure described by four propagation vectors. The transition between both phases can be simply viewed also as flipping of one quarter of the Ho magnetic moments which causes the total magnetization to be half of the
Fig. 5. Low-temperature specific heat (plotted as Cp/T vs. T) in magnetic fields applied perpendicular to the tetragonal c-axis. Data were collected using standard timerelaxation technique.
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Fig. 7. The magnetic phase diagram of NdPd5Al2 based on the Cp(T) (full squares), Cp(H) (empty squares) and M(H) (empty diamonds) measurements in field applied along the c-axis. The error bars were estimated from the width of the anomalies in the case of Cp(T) and M(H) data and from the step between datapoints in the Cp(H) data. The lines connecting points in the graph are just a guide for an eye. The insets show temperature vs. time dependences during the heating pulse in the field of 0 and 1.23 T demonstrating different order of the two phase transitions. The dotted line serves as a tentative phase border as discussed in the text.
Fig. 6. Specific heat as a function of magnetic field (a). Magnetoresistivity (b) expressed as the Dr/r0 ratio where Dr¼r(H,T)r0 and r0 is the resistivity in zero field. The inset of the lower figure shows the resistivity around the phase transition. Solid line represents smoothing spline interpolation of the data and is just a guide for an eye.
field-induced ferromagnetic state value [25]. In our case of NdPd5Al2, the magnetization after the first transition reaches z1.2 mB/Nd which is roughly half of the saturated value presented in Fig. 2, i.e. we observe the same behaviour as reported for R2RhIn8 compounds including Ho2RhIn8 [23,19]. Such similarity together with a closely related crystal structure indicates possibly the same nature of the phase transition between the two magnetic phases also in NdPd5Al2. The microscopic determination of the magnetic structure(s) in NdPd5Al2 by neutron diffraction is highly desirable to make a final conclusion. The insets in Fig. 7 display time dependences of the sample's temperature during the constant heating pulse and following relaxation. Their shape is clearly different when measured below 0.5 T and above 1.1 T. Whereas the low-field curves exhibit plateaus around TN indicating the first-order phase transition, the curves above 1.1 T show behaviour typical for the second-order phase transition; in the region from approx. 0.5 Te1.1 T curves gradually change their character from the former type to the latter. Firstorder phase transition in zero field is unusual for transition between paramagnetic and magnetically ordered state, but it was observed e. g. in the case of U2Rh3Si5 [26]. Another tentative explanation might be the fact that the phase 2 region in the phase diagram reaches down to the zero field (dotted line in Fig. 7) or due to possible presence of some other magnetic phase existing only in
a very narrow temperature range as in the case of Ho2RhIn8 [25]. The first-order nature of the transition seen in low fields arises then from transition between this phase (or phase 2) and phase 1. Fig. 8 shows the low-temperature magnetic heat capacity of NdPd5Al2 replotted as Cmag/T vs. T2. The magnetic specific heat was obtained by subtracting the lattice specific heat of the nonmagnetic yttrium analogue [15] from the original data, i. e. Cmag(NdPd5Al2) ¼ C(NdPd5Al2) C(YPd5Al2). Although Y is not the best analogue for Nd (LaPd5Al2 probably does not form), the lattice contribution to the specific heat of NdPd5Al2 is negligible in comparison with the magnetic specific heat in the presented temperature region, so the choice of the non-magnetic analogue does not play an important role. Further, we have fitted the data in the ordered state by the expected specific heat dependences for magnetic excitations (including a gap in the magnon spectrum) [27]: d
Cmag ¼ AT m expðD=TÞ;
(1)
where D is size of the gap, d is the characteristic dimension of the excitations and m ¼ 2 for ferromagnetic, respectively m ¼ 1 for antiferromagnetic magnons. However, we are not able to unambiguously determine whether the compound exhibits 3D or 2D antiferromagnetic magnons mainly due to the very limited fitting range, in which the experimental data can be reasonably described by both dependences as presented in Fig. 8. By integrating the temperature dependence of the Cmag/T, we have calculated the magnetic entropy. As can be seen in the inset of Fig. 8, the entropy reaches Rln2 close above TN, indicating the doublet ground state.
4. Conclusions Single crystal of NdPd5Al2 was successfully prepared and studied by means of susceptibility, magnetization, specific heat and resistivity measurements. Magnetic phase diagram derived from heat capacity measurements consists of two low-temperature phases - the zero-field antiferromagnetic phase and an additional
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Fig. 8. Low-temperature magnetic specific heat replotted as Cmag/T vs. T2. Data were evaluated using standard time-relaxation method. The thick lines represents fits of the data by the expected dependences given by Fig. 1 for antiferromagnetic excitations. The resulting parameters obtained by the fitting in the temperature range 0.5e1.1 K are A ¼ 17.10 J mol1K4 and D¼1.55 K for the 3D AFM magnons, respectively A ¼ 44.27 J mol1K3 and D¼2.49 K for the 2D AFM magnons. The inset shows corresponding magnetic entropy as a function of temperature.
phase which appears when magnetic field is applied along the tetragonal c-axis. It has been established that the magnetic phase transition in the zero field is the first-order phase transition. Acknowledgements We would like to thank R. Tarasenko and V. Tka c for technical assistance during measurements. This study has been supported by the Czech Science Foundation (Grant No. P204-13-12227S). Experiments were performed in MLTL (http://mltl.eu/), which is supported within the Program of Czech Research Infrastructures (Project No. LM2011025). References [1] D. Aoki, Y. Haga, T.D. Matsuda, N. Tateiwa, S. Ikeda, Y. Homma, H. Sakai, Y. Shiokawa, E. Yamamoto, A. Nakamura, et al., Unconventional heavyfermion superconductivity of a new transuranium compound NpPd5Al2, J. Phys. Soc. Jpn. 76 (2007) 063701. [2] R. de Almeida Ribeiro, T. Onimaru, K. Umeo, M. de Abreu Avila, K. Shigetoh, T. Takabatake, A Kondo lattice antiferromagnet CePd5Al2, J. Phys. Soc. Jpn. 76 (2007) 123710. [3] F. Honda, M.-A. Measson, Y. Nakano, N. Yoshitani, E. Yamamoto, Y. Haga, T. Takeuchi, H. Yamagami, K. Shimizu, R. Settai, et al., Pressure-induced superconductivity in antiferromagnet CePd5Al2, J. Phys. Soc. Jpn. 77 (2008) 043701. [4] J.-C. Griveau, K. Gofryk, J. Rebizant, Transport and magnetic properties of the superconductor NpPd5Al2, Phys. Rev. B 77 (2008) 212502.
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