4f and 5f based systems

The electronic structure of lanthanides and actinides is characterized by partially occupied f-electron states (4f and 5f states, respectively). Their magnetic and other electronic properties are, however, quite different. The 4f orbitals are deeply confined in the core of lanthanide ions but the 5f wave functions of actinide atoms are rather extended in space, although not as much as in d metals and situated near the Fermi energy. Actinide intermetallic compounds have therefore some characteristic features that resemble 3d, 4d, or 5d transition metals. The different behavior of 4f-5f elements is particularly striking when comparing light lanthanides with light actinides and is documented in figure 1 where the evolution of the atomic volume for transition metal elements, lanthanides and actinides is shown. The transition metals exhibit almost a parabolic dependence of the atomic volume on the number of d-electrons, having a minimum value for half-filled d shells. This dependence results from the participation of d-electrons in the chemical bonding leading to the reduction of the atomic volume as the bonding strength increases. The atomic volume of elements from the lanthanide series is much less dependent on the atomic number. It decreases only slightly as the 4f-shell is gradually filled. This is well known as lanthanide contraction and is due to the incomplete charge screening of the nuclei by 4f electrons. There are two exceptions to this contraction. The first is due to the different valence states of Eu and Yb and the second is found for Ce which behaves in many respect as actinide metals.

Figure 1: The evolution of the atomic volume for transition metal elements, lanthanides and actinides. Note a drastic change in the volume between the Pu and Am.

When inspecting the development of the atomic volume of actinide metals, one immediately sees the direct similarity between the ‘light’ actinides, up to Pu, and the transition metals on one side and the ‘heavy’ actinides and 4f-systems on the other. This suggests that the 5f- electronic states at the beginning of the 5f-series participate directly in the bonding and are more delocalized than at the end of the series, where they are more localized [1]. The clear threshold is situated between Pu and Am. The light actinides do not order magnetically and Th, Pa and U are superconductors. The linear specific-heat coefficient is increasing in the sequence Th → Pu, reaching a maximum of 22 mJmol^-1K^-1 for Pu, suggesting an increasing density of states at the Fermi level due to filling of the 5f-shell. The heavy actinides do order magnetically and the crossover is usually referred to as a Mott transition. For Am, a rather small linear specific-heat coefficient of 2 mJ*mol^-1K^-1 is found, reflecting a low density of states at the Fermi level, which indicates that 5f-electronic states were pulled below E_F and that 5f electrons are localized like in the case of 4f elements.

Because of position of 5f electrons nearby the Fermi level, a large diversity of physical properties in light-actinides and their compounds can be observed. The reason is a variable degree of the 5f-localization and the dominance of many-body phenomena in the cross-over regime between the strong and weak hybridization (caused by the energy and space overlap of 5f wavefunctions with other electronic states in the material), which give rise to exotic phenomena like heavy fermions. The second vital ingredient of actinide magnetism is the strong spin-orbit interaction, providing significant orbital polarisation of 5f-band systems and leading to a strong coupling of the direction of 5f-moments and both crystal and electronic structure. Its most apparent consequence is a huge magnetocrystalline anisotropy observed in U-intermetallics. The degree of energy and space overlap between the 5 f states with other states in a lattice determines the degree of delocalization of 5 f moment and loss of magnetism. It depends on several parameters like the geometry of the surrounding 5 f atom, the coordination, the interatomic distances, etc., which can be influenced by, e.g., external perturbation like pressure. They represent, therefore an ideal playground for systematic studies.

In the recent years a series of experiments in magnetic fields, low temperatures and hydrostatic or uniaxial pressures on various 3d, 4d, 5d and 4f and 5f model systems have been performed. The d-electron containing materials investigated at HZB were in majority systems with lower symmetry or symmetry imposing frustration of some kind [2-4]. Neutron diffraction revealed the regions of external variables at which the relevant magnetic moments built a particular phase and helped to determine the spatial arrangement and magnitude of magnetic moments involved. Majority of the 4f electron systems studied in recent years represent “classical” magnetic systems with a well defined magnetic sub-lattice [5]. Effect of magnetic field and temperature on the particular magnetic structure has been the typical application. In few case an interplay between a magnetism and superconductivity could be studied [6,7]. In many cases, the interplay between the 4f and d-electron sub-lattice have been studied, often under combined extreme conditions [8,9]. Such studies contributed in the identification of the interaction strength between the 4f and the d electrons, which, in turn led to the understanding of the magnetically anisotropic materials that are important in technical applications. From actinide elements, mainly studies on uranium and thorium based systems have been performed. The reason is obviously the radioactivity of actinides and related security issues. Nevertheless, even in these cases one could apply a moderate hydrostatic pressure and study the evolution of magnetic structures as a function of temperature and magnetic field.

References

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[2] H.K. Rønnow, M. Enderle, D.F. McMorrow, L.-P. Regnault, P. Dhalenne, A. Revcolevschi, A. Hoser, K. Prokeš, P. Vorderwisch, and H. Schneider, Phys. Rev. Lett. 84, 4469 (2000)

[3] N. Qureshi, H. Fuess, H. Ehrenberg, T.C. Hansen, C. Ritter, K. Prokeš, A. Podlesnyak, D. Schwabe, Phys. Rev. B 74, 212407 (2006)

[4] T. Nakajima, S. Mitsuda, T. Inami, N. Terada, H. Ohsumi, K. Prokeš, and A. Podlesnyak, Phys. Rev. B 78, 024106 (2008)

[5] S. Lee, A. Podlesnyak, K. Prokeš, V. Sikolenko, A. Ermolenko, E. Gerasimov, Yu. Dorofeev, A. Vokhmyanin, J.-G. Park, A. Pirogov, JETP Letters 34 (2005)

[6] H.J. Kang, P. Dai, J.W. Lynn, M. Matsuura, J.R. Thompson, Shou-Cheng Zhang, D.N. Argyriou, Y. Onose, Y. Tokura, Nature 423 ,522 (2003)

[7] A. Jensen, K.N. Toft, A.B. Abrahamsen, D.F. McMorrow, M.R. Eskildsen, N.H. Andersen, J. Jensen, P. Hedegård J. Klenke, S. Danilkin, K. Prokeš, V. Sikolenko, P. Smeibidl, S.L. Bud’ko, P.C. Canfield, Phys. Rev. B 69 ,104527 (2004)

[8] O. Prokhnenko, J. Kamarád, K. Prokeš, Z. Arnold, A.V.Andreev, Phys. Rev. Lett. 94, 107201 (2005)