Effect of temperature on hybridization and magnetism in U2Pd2Sn and U2Ni2In

Effect of temperature on hybridization and magnetism in U2Pd2Sn and U2Ni2In

Journal of Alloys and Compounds 369 (2004) 273–276 Effect of temperature on hybridization and magnetism in U2 Pd2 Sn and U2 Ni2 In H. Nakotte a,∗ , S...

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Journal of Alloys and Compounds 369 (2004) 273–276

Effect of temperature on hybridization and magnetism in U2 Pd2 Sn and U2 Ni2 In H. Nakotte a,∗ , S. El-Khatib a , A. Christianson b , R.B. Von Dreele b , K. Prokes c , V. Sechovsky c , L.C.J. Pereira d , J.C. Spirlet d , J. Rebizant d a

Physics Department MSC3D, New Mexico State University, Las Cruces, NM 88003, USA b Los Alamos National Laboratory, Los Alamos, NM 874545, USA c Charles University, 12116 Prague 2, Czech Republic d European Commission, Institute for Transuranium Elements, 76125 Karlsruhe, Germany

Abstract We report on the temperature variation of the interatomic distances in isostructural U2 Ni2 In and U2 Pd2 Sn, both of which order antiferromagnetically at low temperatures. Both compounds exhibit complex non-collinear arrangements of the magnetic moments confined to the tetragonal basal plane, which is perpendicular to the shortest interuranium distance along the c-axis at low temperatures. The different temperature dependencies of the shortest interatomic links between uranium and the transition metal (Ni or Pd) provide evidence for the dual nature of 5f–d hybridization in these two compounds. We argue that magnetic ordering in U2 Pd2 Sn arises due to increased 5f–d hybridization (promoting stronger exchange) while the reduced hybridization in U2 Ni2 In allows for the formation of stable U magnetic moments. © 2004 Elsevier B.V. All rights reserved. Keywords: Intermetallics; Neutron scattering/diffraction; Heavy fermions

1. Introduction The magnetism in uranium compounds is governed by two delocalization mechanisms: firstly, the direct overlap of 5f wave functions of neighboring U-atoms, which explains the importance of the inter-uranium spacing dU–U as proposed by Hill [1], and secondly, the 5f-ligand hybridization, which is particularly important in compounds with larger U–U distances [2]. On the other hand, the strong hybridization of the f states with the p and d states of the ligand atoms not only causes delocalization of the f electrons (leading to a reduction of the magnetic moments), but it may also contribute to stronger inter-site exchange interactions (promoting a magnetic ground state). As a consequence, many uranium compounds exhibit magnetic ordering with a magnetic moment that is substantially reduced from the uranium free-ion value. Isostructural groups of uranium compounds are well suited for systematic studies of such delocalization mechanisms because the geometry of the U-ion surroundings is



Corresponding author. Tel.: +1-505-6462459; fax: +1-505-6461934. E-mail address: [email protected] (H. Nakotte).

0925-8388/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2004.01.015

unchanged. In the past decade, many studies focussed on isostructural U2 T2 X compounds (T: transition metal, X: Sn, In), which crystallize in the tetragonal U3 Si2 structure [3]. These compounds offer a new perspective on the relationship between magnetic anisotropy and the geometrical arrangement of the elements, because (unlike most other uranium compounds) two approximately equal shortest interuranium distances are found. Previous magnetization experiments inferred an antiferromagnetic ground state for U2 Ni2 In, U2 Pd2 In, U2 Ni2 Sn, U2 Rh2 Sn, U2 Pd2 Sn and U2 Pt2 Sn, while the other U2 T2 X compounds do not order magnetically [4]. Among the ‘non-magnetic’ compounds, U2 Pt2 In is of interest as it exhibits non-Fermi-liquid scaling at low temperature [5]. The occurrence of a magnetic ground state in U2 T2 X compounds is consistent with the results of simple tight-binding calculation [6], and the moment magnitude follows the trends expected from 5f-ligand hybridization [4]. The magnetic structures of all U2 T2 X antiferromagnets have been resolved by neutron diffraction: U2 Ni2 In, U2 Pd2 In, U2 Pd2 Sn and U2 Pt2 Sn exhibit non-collinear configurations of U moments, while the magnetic structures of U2 Ni2 Sn and U2 Rh2 Sn are collinear [4]. However, each U2 T2 X antiferromagnet exhibits its own magnetic structure that differs from other counterparts. The

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direction of the magnetic moments depends critically on relatively ‘small’ changes in the 5f-ligand hybridization within the U2 T2 X series. Here, we consider two antiferromagnetic members of the U2 T2 X family, namely U2 Pd2 Sn and U2 Ni2 In. U2 Pd2 Sn orders at TN = 40 K and U2 Ni2 In orders at TN = 14 K [4]. Previous studies revealed non-collinear in-plane moment configurations for both compounds [7,8]. However, the magnetic structures of these two compounds differ mostly in the fact that the exchange interaction along the c-axis is ferromagnetic in U2 Pd2 Sn whereas it is antiferromagnetic in U2 Ni2 In [8].

2. Experimental We performed neutron diffraction experiments on the same polycrystalline U2 Pd2 Sn and U2 Ni2 In samples that were used in previous studies [7,8]. The experiments were performed on powders of about 20 g of material, which were encapsulated under helium atmosphere in vanadium tubes. The samples were then mounted onto the cold finger of a displex with the capability to control the temperature between 10 and 300 K. Most of the data presented here were taken using the High Intensity Powder Diffractometer (HIPD) the Manuel Lujan jr. Neutron Scattering Center, Los Alamos National Laboratory. The HIPD spectrometer at Los Alamos has eight detector banks at ±14, ±40, ±90 and ±153◦ . Data were taken at various temperatures in the available temperature range between 10 K and room temperature. For each temperature, we counted for at least 4 h. For the analysis of U2 Ni2 In, we have included the low-temperature data at 1.8 and 4.2 K previously taken at the Intense Pulsed Neutron Source, Argonne National Laboratory [8]. Using the Rietveld refinement program package GSAS [9], we determined the structural parameters of both compounds taking into account reflections with d spacings up to 1 Å found in the highest-angle detector banks. This procedure was chosen to avoid potential contamination of the results due to magnetic contributions to the diffraction pattern (especially at below the ordering temperatures) as the magnetic form factor of U3+ is almost zero for such low d spacings [10]. Then, GSAS was taken to refine the magnetic moments using only reflections above 1 Å assuming the published moment configurations and the structural parameters determined earlier.

3. Results Our neutron-diffraction results confirm that U2 Pd2 Sn and U2 Ni2 In crystallize in the tetragonal U3 Si2 structure. In this structure, the U-atoms occupy the 4h positions with parameters (xU , xU + 1/2, 1/2), the transition metals T (Pd or Ni) occupy the 4g positions with parameters (xT , xT + 1/2, 1/2) and the p-electron elements X (Sn or In) occupy the

Fig. 1. Temperature dependence of (a) the uranium magnetic moment; (b) the shortest interuranium distances dU–U (1) and dU–U (2); and (c) the shortest U–Pd distance for U2 Pd2 Sn.

2a positions with parameters (0, 0, 0). In good agreement with previously published results, we find room-temperature structural parameters of a = 7.593 Å, c = 3.785 Å, xU = 0.1761, xPd = 0.3733 and a = 7.375 Å, c = 3.572 Å, xU = 0.1787, xNi = 0.3745 for U2 Pd2 Sn and U2 Ni2 In, respectively. These parameters can be taken to calculate all interatomic distances of interest for this paper, i.e. dU–U (1), dU–U (2) and dU–T . At room temperature, the in-plane interuranium distance dU–U (2) is only slight shorter than dU–U (2) in U2 Pd2 Sn, while the c-axis interuranium distance dU–U (1) is much shorter than dU–U (2) in U2 Ni2 In. Upon cooling, U2 Pd2 Sn exhibits a monotonous decrease of the lattice parameters a and c (∼0.2–0.3%) until it orders magnetically at TN = 40 K, below which the a parameter increases slightly and c remains constant within error bars. The position parameter xU increases and xPd decreases with decreasing temperature, until below TN both parameters show a sudden increase. The absolute variation of the x parameters is small (it occurs only on the fourth significant digit), but it is well outside the experimental error of about 0.0001. Using the structural parameters at any given temperature, we calculated dU–U (1), dU–U (2) and dU–Pd for U2 Pd2 Sn and the results are displayed in Fig. 1 together with the temperature variation of the magnetic moment determined from refinement of the magnetic structure. We

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4. Conclusions

Fig. 2. Temperature dependence of (a) the uranium magnetic moment; (b) the shortest interuranium distances dU–U (1) and dU–U (2) and; (c) the shortest U–Ni distance for U2 Ni2 In.

find that there is a crossover of the shortest interuranium distance at about 200 K, which is consistent with previous claims in ref. [7]. All three interatomic distance decrease with decreasing temperature until there is a sudden increase in dU–U (2) at temperatures right below TN . At temperatures below TN , there is little (if any) temperature variation for any of the interatomic distances considered here. Similar to U2 Pd2 Sn, U2 Ni2 In exhibits a monotonous decrease of a and c by about 0.2–0.3% until reaching TN = 14 K, but then there is a sudden drop in c while a remains constant within error bars. Contrary to the behavior in U2 Pd2 Sn, xU decreases and xNi increases initially and both parameters suddenly drop for temperatures below TN . Furthermore, the absolute change in the x parameters is larger than in U2 Pd2 Sn as it occurs on the third significant digit. In Fig. 2, we display the calculated interatomic distances dU–U (1), dU–U (2), dU–Ni and the magnetic moment for U2 Ni2 In. We find that the interuranium distances in this compound decrease monotonically with decreasing temperature, while dU–Ni increases. At TN , there are sudden changes in dU–U (2) and dU–Ni . Unlike U2 Pd2 Sn, there is a slight variation of the interatomic distances for temperatures below TN although a tendency toward saturation is found.

The most instructive observation in our experimental study is that, in the paramagnetic range, the dU–T distance in U2 Pd2 Sn decreases while it increases in the case of U2 Ni2 In (unlike other interatomic distances) with decreasing temperature. This behavior is due to opposite rotation of atom positions in respective planes containing the uranium or transition metal atoms. The atom-position parameters for U and T move away from each other in U2 Pd2 Sn while they move closer in the case of U2 Ni2 In. The dU–T distance is inversely proportional to the 5f–d hybridization (shorter separation will allow a larger overlap of respective wavefunctions), which is the dominant contribution to the total hybridization in U2 T2 X compounds [6]. Therefore, the 5f–d hybridization increases in U2 Pd2 Sn and it decreases in U2 Ni2 In. Keeping in mind the dual nature of the 5f–d hybridization, one can argue that at elevated temperatures hybridization effects in U2 Pd2 Sn are not yet strong enough to effectively mediate long-range magnetic exchange between the almost localized 5f moments while they are so large in U2 Ni2 In that these moments are completely suppressed. Subsequently, the increased 5f–d hybridization in U2 Pd2 Sn allows for long-range magnetic ordering and the decreased 5f–d hybridization in U2 Ni2 In allows for the formation of stable moments at low temperatures. An additional supporting argument for such scenarios is found in the fact that (compared to other uranium compounds) the ground-state moment in U2 Pd2 Sn is large (∼2.0µB per U-atom) and it is small (∼0.6µB per U-atom) in U2 Ni2 In. Finally, it is worthwhile to note that for both compounds the moments are perpendicular to the shortest interuranium distance, a feature that is found for the vast majority of uranium compounds [4].

Acknowledgements This work was supported by the NSF (grant number: DMR-0094241) and the BES program of the US Department of Energy. The work of V. Sechovsky and K. Prokes is a part of the research program MSM 113200002 financed by the Department of Education of the Czech Republic.

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