Research ArticleCONDENSED MATTER PHYSICS

The valence-fluctuating ground state of plutonium

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Science Advances  10 Jul 2015:
Vol. 1, no. 6, e1500188
DOI: 10.1126/sciadv.1500188
  • Fig. 1 Visualization of the valence-fluctuating ground state of δ-Pu by means of neutron spectroscopy.

    (A) Above a characteristic Kondo temperature TK, the f-electron wave function in f-electron materials such as Pu is typically well localized, resulting in the formation of a magnetic moment (red). (B) For temperatures T < TK, the conduction electrons (black) tend to align their spins antiparallel with respect to the magnetic moment that in turn becomes quenched, resulting in hybridization of the f electron with the conduction electrons. (C) On the basis of our DMFT calculations for δ-Pu (see the text), this leads to a strongly modified electronic density of states (DOS) that then includes the electronic f level as a “quasiparticle resonance” with a width of kBTK (kB is the Boltzmann constant) at the Fermi level EF. The DMFT calculation shows that the hybridization of 5f and conduction electrons drives a quantum mechanical superposition of different valence configurations, where the 5f electrons are continuously hopping into and out of the Fermi sea via the quasiparticle resonance, resulting in virtual valence fluctuations. Here, we use the spin fluctuations that arise from the repeated virtual ground state reconfiguration of the Pu ion from a magnetic (A) to a nonmagnetic (B) state to visualize the valence fluctuations by measuring the dynamic magnetic susceptibility χ″(ω) of δ-Pu by means of neutron spectroscopy. (D) χ″(ω) obtained from our measurements carried out at room temperature (T = 293 K) shows a maximum at the energy Embedded Image (black dashed line) that is determined by the characteristic spin fluctuation energy Esf = kBTK and the lifetime τ of the fluctuations via τ = /2Γ. The red solid line is a fit χ″(ω) to Eq. 1 as described in the text. The broken blue line was calculated via DMFT. The vertical black bar represents the energy resolution of the experiment. (E and F) Full energy (hω) and momentum transfer (Q) dependence of the magnetic scattering as observed in our experiment and calculated by DMFT, respectively. The vertical and horizontal dash-dotted lines in (E) denote the integration ranges used for the energy and momentum transfer cuts shown in (D) and Fig. 2, respectively. The white solid line in (F) denotes the boundary beyond which no experimental data are available. f.u., formula units; a.u., arbitrary units.

  • Fig. 2 The magnetic form factor for δ-Pu.

    The black squares and open circles denote the magnetic form factor for δ-Pu as determined by our neutron spectroscopy experiment carried out at room temperature (T = 293 K) and with incident neutron energies Ei = 250 and 500 meV, respectively. The solid and dashed red lines are tabulated magnetic form factors for 5f4 and 5f5 electronic configurations in the intermediate coupling regime. The dash-dotted red line is a mix of both according to the 5f4 and 5f5 occupation as determined by RXES (see Table 1). The solid blue line was calculated via DMFT (11).

  • Table 1 Average occupation of the 5f states in δ-Pu.

    The occupation of the 5f states in δ-Pu is shown as calculated by DMFT and measured by RXES (13) and core-hole photo-emission spectroscopy (CHPES) (12), respectively. We also list the corresponding effective moment μeff of the three 5f states based on the intermediate coupling scheme (21).

    δ-Pu 5f statef4f5f6
    Occupation (DMFT) (%)126621
    Occupation (RXES) (%)8(2)46(3)46(3)
    Occupation (CHPES) (%)6(1)66(7)28(3)
    Effective moment μeffB)2.881.2250
  • Table 2 The various contributions to the magnetic susceptibility of δ-Pu.

    Embedded Image denotes the magnetic susceptibility associated with the magnetic 5f4 and 5f5 states of δ-Pu at room temperature as determined by our neutron spectroscopy measurements. Embedded Image gives the temperature-independent Van-Vleck contribution Embedded Image of the nonmagnetic 5f6 that is estimated from the published magnetic susceptibility of Am (see the text). The error bar for Embedded Image was estimated from the various values of the occupation of the 5f6 state of δ-Pu determined by different experiments (Table 1). The sum of both reproduces the static magnetic susceptibility χBulk of δ-Pu as measured by magnetic susceptibility reasonably well (22). All quantities are given in units of 10−4 cm3/mol.

    Embedded ImageEmbedded ImageEmbedded ImageχBulk
    0.8(3)3.1(15)3.9(15)5.3

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/1/6/e1500188/DC1

    Fig. S1. A neutron powder diffraction profile of the δ-Pu sample enclosed in a double-wall Al can used for the experiments reported here is shown.

    Fig. S2. Visual method of adjusting the analytically calculated self-shielding factor SSFPu for δ-Pu.

    Fig. S3. Analytical method of adjusting the analytically calculated self-shielding factor SSFPu for δ-Pu.

    Fig. S4. The dynamic magnetic susceptibility of δ-Pu measured via neutron spectroscopy for incident neutron energies of Ei = 500 meV (A) and 250 meV (B), respectively.

    Fig. S5. Theoretical fluctuating magnetic moment of δ-Pu defined in eq. S16.

    Fig. S6. Summary of the main results of our DMFT calculation.

    Table S1. Isotopics and coherent and absorption neutron cross sections of the δ-Pu sample used for the experiment described in this report.

    Table S2. Self-shielding factors SSF for the δ-Pu and Th samples for both used incident energies Ei = 250 and 500 meV obtained via eqs. S3 to S6.

    Table S3. Results of the sum rule analysis for both the fluctuating magnetic moment 〈μz〉 (eq. S13) and the static susceptibility χ′(0) (eq. S14) are provided for incident energies Ei = 250 and 500 meV.

    References (3545)

  • Supplementary Materials

    This PDF file includes:

    • Fig. S1. A neutron powder diffraction profile of the δ-Pu sample enclosed in a double-wall Al can used for the experiments reported here is shown.
    • Fig. S2. Visual method of adjusting the analytically calculated self-shielding factor SSFPu for δ-Pu.
    • Fig. S3. Analytical method of adjusting the analytically calculated self-shielding factor SSFPu for δ-Pu.
    • Fig. S4. The dynamic magnetic susceptibility of δ-Pu measured via neutron spectroscopy for incident neutron energies of Ei = 500 meV (A) and 250 meV (B), respectively.
    • Fig. S5. Theoretical fluctuating magnetic moment of δ-Pu defined in eq. S16.
    • Fig. S6. Summary of the main results of our DMFT calculation.
    • Table S1. Isotopics and coherent and absorption neutron cross sections of the δ-Pu sample used for the experiment described in this report.
    • Table S2. Self-shielding factors SSF for the δ-Pu and Th samples for both used incident energies Ei = 250 and 500 meV obtained via eqs. S3 to S6.
    • Table S3. Results of the sum rule analysis for both the fluctuating magnetic moment 〈μz〉 (eq. S13) and the static susceptibility x'(0) (eq. S14) are provided for incident energies Ei = 250 and 500 meV.
    • References (35–45)

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