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Novel Valence Transition in Elemental Metal Europium around 80 GPa

Valence transition could induce structural, insulator-metal, nonmagnetic-magnetic and superconducting transitions in rare-earth metals and compounds, while the underlying physics remains unclear due to the complex interaction of localized 4f electrons as well as their coupling with itinerant electrons. The valence transition in the elemental metal europium (Eu) still has remained as a matter of debate. Using resonant x-ray emission scattering and x-ray diffraction, we pressurize the states of 4f electrons in Eu and study its valence and structure transitions up to 160 GPa. We provide compelling evidence for a valence transition around 80 GPa, which coincides with a structural transition from a monoclinic (C2/c) to an orthorhombic phase (Pnma). We show that the valence transition occurs when the pressure-dependent energy gap between 4f and 5d electrons approaches the Coulomb interaction. Our discovery is critical for understanding the electrodynamics of Eu, including magnetism and high-pressure superconductivity.


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Valence transition could induce structural, insulator-metal, nonmagnetic-magnetic and superconducting transitions in rare-earth metals and compounds, while the underlying physics remains unclear due to the complex interaction of localized 4f electrons as well as their coupling with itinerant electrons. The valence transition in the elemental metal europium (Eu) still has remained as a matter of debate. Using resonant x-ray emission scattering and x-ray diffraction, we pressurize the states of 4f electrons in Eu and study its valence and structure transitions up to 160 GPa. We provide compelling evidence for a valence transition around 80 GPa, which coincides with a structural transition from a monoclinic (C2/c) to an orthorhombic phase (Pnma). We show that the valence transition occurs when the pressure-dependent energy gap between 4f and 5d electrons approaches the Coulomb interaction. Our discovery is critical for understanding the electrodynamics of Eu, including magnetism and high-pressure superconductivity. 3 Understanding the behaviors of 4f electrons is key to elucidating the paradigmatic physical phenomena in lanthanide elemental metals and compounds but remains a long-standing challenge in many-body quantum physics for electron correlated materials [1][2][3][4][5][6][7]. The valence transition induced by the changes of external parameters is predominantly associated with the changes of 4f electron states [8][9][10], providing a unique opportunity to investigate the electrodynamics of 4f electrons [11,12].
concluded that Eu retains divalent up to 87 GPa [24][25][26]. Both Eu and Yb show superconductivity around 80-90 GPa [22,27]. The origin of the superconductivity in Yb can be attributed to the valence fluctuation-induced magnetic instabilities [22,28], whereas it remains perplexing to understand how the magnetic collapse and superconductivity could coexist with the strong local spin moments in the divalent Eu metal [25][26][27]29]. This problem motivated us to further investigate the valence state of Eu at higher pressure.
In this Letter, we probed the valence transition in Eu using resonant x-ray emission spectroscopy (RXES) up to a record high pressure of ~160 GPa [21,[30][31][32][33][34]. In addition, x-ray powder diffraction (XRD) was also carried out to study if the structural changes are correlated with the valence transitions. As a result, we unveil a novel pressure-induced valence transition in Eu at 4 around 80 GPa, being concomitant with a volume-collapsed structural transition from monoclinic symmetry (C2/c) to orthorhombic symmetry (Pnma). The valence transition is attributed to the pressure-induced promotion of 4f electrons to the 5d band, and the valence instability could also explain the origin of the possible superconducting transition occurring around this transition pressure. Details of the experimental settings are provided in the Supplemental Materials (SM) [35].
In our RXES measurements, an electron from the 2p 3/2 core level is photoexcited to an empty 5d 5/2 state (L 3 absorption), followed by the decay of an electron from 3d 5/2 state to fill the 2p 3/2 core hole (L α emission). According to the Anderson impurity model [55][56][57][58] the cross section of this twostep core-core resonant inelastic scattering is proportional to the unoccupied density of 5d states that is convoluted with a many-body expectation value including 2p and 3d core holes. Even though the 4f states are not directly involved in the excitations, the core hole in the 3d state modifies the total energy of the localized 4f electrons [57,58]. When more than one 4f n configuration is mixed in the initial state, the modification splits 4f n configurations in the absorption edge to yield valence histogram information [57,58]. Due to the 3d core-hole effects, two peaks are identified in RXES at around 1128 and 1135 eV with an energy separation of ~ 7 eV, which are associated with the final states 3d 9 4f 7 5d 1 (labeled as 4f 7 ) and 3d 9 4f 6 5d 1 (labeled as 4f 6 ) [59], respectively. As peak 4f 6 shows a more prominent line-shape at E i = 6970 eV, we use this RXES spectrum to monitor how the valence of Eu evolves at high pressure in this study.
Figure 2(a) shows ten RXES spectra collected with E i = 6970 eV from 11 to 160 GPa. The spectra are normalized to the peak 4f 7 maximum intensity. Analysis with the Gaussian peak fitting yields the intensity of peaks 4f 7 and 4f 6 . The valence is estimated using the conventional formula (1) for RXES, and XANES [23] measurements, 6 6 7 (4 ) 2 (4 ) (4 ) where I(4f 7 ) and I(4f 6 ) are the area integrated intensities of 4f 7 and 4f 6 peaks, respectively [21,60,61]. Figure 2(b) shows the resulting valence state. The errors are primarily due to statistics of total counts and fitting errors, which are estimated to be within ~5%. It is worth noting that a valence jump appears around 80 GPa and then gradually increases up to 160 GPa, indicating that a valence transition begins around 80 GPa.
In addition, we performed XRD up to 153 GPa to investigate the structural changes. The results ( Fig. 3) show that Eu experiences a phase transition from a body-center-cubic (bcc) to a hexagonalclosed-packing (hcp) structure at ~ 12 GPa, with a ~ 3% volume collapse, in agreement with previous studies [24,[62][63][64]. Eu remains stable in the hcp phase from 12 GPa up to 30.1 GPa and then transforms into an incommensurately modulated monoclinic crystal structure with symmetry of C2/c, as reported by Husband et al. [64]. When pressure exceeds 78 GPa, a new reversible structural phase transition with a 3.2% volume collapse occurs. The new phase is stabilized in an orthorhombic crystal structure with symmetry of Pnma, according to the structural refinement of the XRD pattern at 96 GPa ( Fig. 3(b)). peak below 87 GPa to pure 5d states and conclude Eu retains in a nearly divalent state up to 87 GPa [25]. We confirmed these findings with PYF XAS measurements (Fig. S4): the 4f 7 peak is entirely suppressed below 52 GPa, while the 4f 6 peak grows very slightly below 80 GPa.
In the previous studies of lanthanide compounds [66][67][68][69], the decrease of the 4f 7 peak commonly results in a corresponding increase of the 4f 6 peak, and the total weight of the 4f 7 peak and 4f 6 peak in the transitions remains approximately constant [30,70]. This association between the 4f 7 and 4f 6 peaks validates the use of formula (1)  The intensity of the L 3 -edge white line, which overlaps with the 4f 7 state in the XANES measurements, is dominated by the density of 5d states (due to the selection rule) and thus strongly influenced by the change of 5d states rather than 4f 7 state. Furthermore, the intensity of the white line is sensitive to changes in sample thickness, defects, inhomogeneity, as well as pressure gradient. As a result, the change in intensity of the white line alone is insufficient to evince a valence transition. In addition, the step-function-like background above the absorption edge and a strong fluorescence background in the PYF XAS above absorption edge may cause uncertainties in resolving the 4f 6 peaks. 7 In contrast, the RXES spectra measured below the absorption edge avoid the problems arising from white line and fluorescence background and are regarded as a superior probe for studying the valence transition of rare-earth metals and compounds at high pressure [21,60,61,71]. In our RXES measurements, the sum of I(4f 7 ) and I(4f 6 ) remain nearly a constant at high pressure up to 160 GPa, showing a clear correlation between 4f 7 and 4f 6 peaks (Fig. S3) Consequently, Eu's phase space can be divided into four zones (from I to IV) based on its crystal structures and valence states, as shown in Fig. 2 [76]. However, as no Kondo effect is observed in Eu and the local magnetic moment remains nearly the same [26], the Mott transition model is also unsuitable for explaining the valence transition. Considering 5d state is dominant at the Fermi level [17], and the 4f state locates about 2 eV below the Fermi level at ambient pressure [77], it is likely that the 4f state approaches 5d states and induces the valence transition at ~ 80 GPa, fitting into the promotional model.
If we only consider the conducting 5d orbital and the localized 4f orbital bands in the valence transition, we can understand the valence transition using a Hund-Heisenberg-like model [78],    [27]. Recently, it has been pointed out that the U fd may drive the quantum criticality observed in other strongly correlated electron systems such as Ce and Yb compounds [79][80][81]. Thus 10 our work provides the important information of the physics underlying the unconventional superconductivity in the strongly correlated electron systems.
In summary, using RXES, we have studied the valence transition in Eu as a function of pressure up to 160 GPa and discovered a new valence transition occurred at around 80 GPa, which is nearly committed with the phase transition from C2/c to Pnma and the superconductivity transition. The valence transition is driven by the promotion of 4f electrons to 5d bands. We gave the transition value of the pressure-dependent energy gap between 4f and 5d electrons which is close to their Coulomb interaction. RXES (dark blue solid circles) from this study, and XANES (blue hollow circles) from Ref. [23] and dotted line from Ref. [25], along with the magnetic ground states of Eu from Refs. [25,27].
The different colors represent different structures of bcc, hcp, monoclinic and orthorhombic as determined by XRD in this study, respectively, which will discuss later. The dashed line is a guide for the eye, where the increase valence around 80 GPa is highlighted by the red zone.