Internal Fields Observed by Heavy Itinerant Electrons in the Superconducting Ferromagnet UGe2

Abstract

There are fascinating classes of materials called heavy fermions which contain a periodic array of localized f electrons interacting with itinerant conduction electrons. Owing to both the strong Coulomb correlation within f shell and the mixing of f -electron and itinerant-electron wave functions, a heavy fermion state is formed at low temperatures, where the electronic specific heat coefficient can be enhanced by several orders of magnitude over that of ordinary transition metals. Among them, some uraniumbased intermetallic compounds have attracted much attention due to the unusual coexistence of superconductivity and magnetism. In particular, the interplay between superconductivity and ferromagnetism in UGe2 is an interesting topic in the solid-state physics. As shown in a schematic phase diagram of UGe2 (see an inset in Fig. 1), a Curie temperature (TFM) monotonically decreases with increasing pressure (P), and collapses to zero temperature at around 1.5GPa. In the ferromagnetic phase, there seems to be another phase transition or crossover at TX, where a magnetic Bragg peak intensity exhibits a steep increase (see Fig. 1). This characteristic temperature TX also decreases with increasing pressure and becomes suppressed to zero at a critical pressure PX ( 1:2GPa). Since the superconducting transition temperature (TSC) shows a maximum at around PX, it has been speculated that the critical point PX plays an important role of the superconductivity (see, for example, refs. 2 and 3). Recently, Nakane et al. provided a supporting evidence for the conjecture by means of ac magnetic susceptibility measurements. In general, superconductivity and magnetism would be antagonistic ground states, because of the competitive nature between the Meissner effect and internal fields generated by magnetic orderings. In contrast with the case of an antiferromagnet, ferromagnetic internal fields can not be cancelled out in the range of the superconducting coherence length, which raises a question of why such nonvanishing internal fields do not destroy the superconducting Cooper pairs. This has motivated us to evaluate the magnitude of the internal fields in UGe2. In a previous paper, Aso et al. reported the temperature dependence of magnetic Bragg peak intensities [IBðTÞ] under pressure, and showed that IBðTÞ below TX can be explained by a conventional Stoner model, a typical example at P 1⁄4 1:1GPa being illustrated in Fig. 1. Furthermore, they argued that the system lies in a perfectly polarized state in a pressure region below PX. In the present Short Note, we show that this simple model also provides useful information about the internal fields observed by itinerant electrons which may carry superconducting currents. The characterization of single crystals grown by the Czochralski pulling method is seen in refs. 4 and 6. Experimental details of the elastic neutron scattering under pressure were reported in ref. 5, and will be given elsewhere. According to the Stoner model, the low temperature magnetization M in the case of the perfectly polarized state is expressed as follows (see, for example, ref. 8), M 1⁄4 M0f1 T expð =TÞg; ð1Þ