Temperature-driven hidden 5f itinerant-localized crossover in heavy-fermion compound PuIn3
TTemperature-driven hidden 5 f itinerant-localized crossover in heavy-fermion compound PuIn Haiyan Lu ∗ and Li Huang Science and Technology on Surface Physics and Chemistry Laboratory, P.O. Box 9-35, Jiangyou 621908, China (Dated: February 8, 2021)The temperature-dependent evolution pattern of 5 f electrons helps to elucidate the long-standing itinerant-localized dual nature in plutonium-based compounds. In this work, we investigate the correlated electronic statesof PuIn dependence on temperature by using a combination of the density functional theory and the dynamicalmean-field theory. Not only the experimental photoemission spectroscopy is correctly reproduced, but alsoa possible hidden 5 f itinerant-localized crossover is identified. Moreover, it is found that the quasiparticlemultiplets from the many-body transitions gradually enhance with decreasing temperature, accompanied by thehybridizations with 5 f electrons and conduction bands. The temperature-induced variation of Fermi surfacetopology suggests a possible electronic Lifshitz transition and the onset of magnetic order at low temperature.Finally, the ubiquitous existence orbital selective 5 f electron correlation is also discovered in PuIn . Theseilluminating results shall enrich the understanding on Pu-based compounds and serve as critical predictions forongoing experimental research. I. INTRODUCTION
Plutonium (Pu) situates on the edge between the obviouslyhybridized 5 f states of uranium and mostly localized 5 f states of americium , signifying the itinerant-localized natureof 5 f electrons . The spatial extension of partially filled 5 f states enables the hybridization with conduction bands, facil-itating active chemical bonding and formation of abundantplutonium-based compounds. Besides the fantastic physicalproperties of Pu which are governed by the 5 f states , thePu-based compounds demonstrate novel quantum phenom-ena including unconventional superconductivity , nontriv-ial topology , complicated magnetic order , and heavy-fermion behavior , to name a few. The discovery of super-conductivity in PuCoGa with astonishingly high tran-sition temperature of 18.5 K has renewed an interest in Pu-based compounds. The unconventional superconductivity inPu-based “115” system (Pu MX , M = Co, Rh; X = Ga, In) is in-timately intertwined with 5 f electrons which manifest them-selves in plenty of ground state properties comprising mag-netism, superconductivity, and charge density wave .PuIn crystallizes in cubic AuCu structure (space group Pm -3 m ) [see Fig. 1(a)] with lattice constant 4.703 Å , whichis the parent material of PuCoIn with the insertion of theCoIn layer into the cubic structure. PuIn is a paradigm Pu-based heavy-fermion compound with an electronic specificheat coe ffi cient of 307 mJ / (mol × K ), suggesting a substantiale ff ective mass enhancement. Moreover, the measured tem-perature dependence of electrical resistivity decreases rapidlybelow 50 K, displaying representative heavy-fermion behav-ior. Since the Pu-Pu distance in PuIn is larger than the Hilllimit, the specific heat, electrical resistivity, magnetic suscep-tibility and In nuclear quadrupole resonance experimentsall indicate the onset of antiferromagnetic order (AFM) below T N = . Meanwhile, the de Haas-van Alphen (dHvA)oscillation identifies a Fermi surface pocket near the [111]direction with an enhanced cyclotron e ff ective mass both inparamagnetic phase and antiferromagnetic state . The impact of magnetism on heavy-fermion state with e ff ectivemass renormalization is another interesting issue. It is notablethat the heavy-fermion state and antiferromagnetic order areclosely related to the intricate electronic structure of PuIn .The experimental photoemission spectroscopy of PuIn above T N shows one peak around the Fermi level and the mainpeak at -1.2 eV, combined with mixed level model calcu-lation within density functional theory (DFT), implying theitinerant-localized dual nature of 5 f electrons . On the theo-retical side, the electronic structure, three-dimensional Fermisurface, dHvA quantum oscillation frequency and e ff ectiveband mass in both the paramagnetic and antiferromagneticstates of PuIn have been systematically addressed based onthe density functional theory with a generalized gradient ap-proximation . Even though great e ff orts have been made togain valuable insight into the itinerant-localized nature of 5 f states. Only one of the three calculated Fermi surfaces on thebasis of the 5 f -itinerant band model has been observed bydHvA experiment. Besides, the experimental photoemissionspectroscopy is well reproduced by employing mixed levelmodel seems not quite consistent with the subsequent cal-culations . The inconsistency might come from di ff erent ap-proximations in traditional first-principles approaches. Theitinerant degree of 5 f states is not quantitatively describedwithout rigorous treating many-body e ff ects. In addition, theground state calculation fails to access the finite tempera-ture e ff ects. It is instructive to study the evolution of elec-tronic structure as a function of temperature to probe the low-temperature magnetic state. Furthermore, large spin-orbitalcoupling and complicated magnetic ordering states make thetheoretical calculations rather di ffi cult. Accordingly, it seemstough to acquire an accurate and comprehensive picture forthe electronic structure of PuIn .In the paper, we present the electronic structure of PuIn de-pendence on temperature using the density functional theoryin combination with the single-site dynamical mean-field the-ory (DFT + DMFT). A comparative study of PuIn shall shedlight on the bonding behavior and correlation e ff ects, so as todevelop a deeper understanding of the relationships betweenelectronic structure and antiferromagnetic state. We endeavorto elucidate the itinerant-localized 5 f states. We calculate a r X i v : . [ c ond - m a t . s t r- e l ] F e b (a) (b) In Pu X M Γ R a* b* c* X FIG. 1. (Color online). (a) Crystal structure of PuIn . (b) Schematicpicture of the first Brillouin zone of PuIn . Some high-symmetry k points X [0.5, 0.0, 0.0], Γ [0.0, 0.0, 0.0], M [0.5, 0.5, 0.0], and R [0.5,0.5, 0.5] are marked. the momentum-resolved spectral functions, density of states,Fermi surface, self-energy functions and valence state fluctua-tions of PuIn . It is discovered that 5 f states become itinerantat low temperature accompanied by moderate valence statefluctuations. Moreover, the change of Fermi surface topologypossibly implies the development of antiferromagnetic order.Finally, it is found that strongly correlated 5 f electrons areorbital dependent, which seems commonly exists in Pu-basedcompounds.The rest of this paper is organized as follows. In Sec. II,the computational details are introduced. In Sec. III, the elec-tronic band structures, total and partial 5 f density of states,Fermi surface topology, 5 f self-energy functions, and proba-bilites of atomic eigenstates are presented. In Sec. IV, we at-tempt to clarify the 4 f and 5 f electrons in isostructural com-pounds CeIn and PuIn . Finally, Sec. V serves as a briefconclusion. II. METHODS
The well-established DFT + DMFT method combinesrealistic band structure calculation by DFT with the non-perturbative many-body treatment of local interaction e ff ectsin DMFT . Here we perform charge fully self-consistentcalculations to explore the detailed electronic structure ofPuIn using DFT + DMFT method. The implementation ofthis method is divided into DFT and DMFT parts, which aresolved separately by using the
WIEN2K code and the EDMFTF package .In the DFT calculation, the experimental crystal structure ofPuIn was used. Since the calculated temperature is abovethe antiferromagnetic transition temperature, the system wasassumed to be nonmagnetic. The generalized gradient approx-imation was adopted to formulate the exchange-correlationfunctional . The spin-orbit coupling was taken into accountin a second-order variational manner. The k -points mesh was15 × ×
15 and R MT K MAX = . f orbitals of plutonium were treatedas correlated. The four-fermions interaction matrix was pa-rameterized using the Coulomb interaction U = . J H = . . The fully localized limit scheme was used to calculatethe double-counting term for impurity self-energy function .The vertex-corrected one-crossing approximation (OCA) im-purity solver was employed to solve the resulting multi-orbital Anderson impurity models. Note that we not only uti-lized the good quantum numbers N (total occupancy) and J (total angular momentum) to classify the atomic eigenstates,but also made a severe truncation ( N ∈ [3, 7]) for the localHilbert space to reduce the computational burden. The con-vergence criteria for charge and energy were 10 − e and 10 − Ry, respectively. It is worth mentioning that the advantageof OCA impurity solver lies in the real axis self-energy, thedirect output Σ ( ω ) were applied to calculate the momentum-resolved spectral functions A ( k , ω ) and density of states A ( ω ),as well as other physical observables. III. RESULTS OF PUIN A. Momentum-resolved spectral functions
To ascertain the reliability of our calculations, we evaluatethe momentum-resolved spectral functions A ( k , ω ) of PuIn along the high-symmetry lines X − Γ − M − R in the irre-ducible Brillouin zone [see Fig. 1(b)] from 580 K to 14.5K. Figure 2 visualizes the temperature dependence of A ( k , ω )at two typical temperatures 580 K and 14.5 K, respectively.In comparison with the available theoretical results by C.-C.Joseph Wang et al. utilizing a generalized gradient approxi-mation , the basic feature of band structures [see Fig. 2(c)]is roughly consistent with each other. For instance, hole-likeorbit around -1 eV at Γ point and similar hole-like orbit at M point are generally identical. However, the most striking dis-crepancy is the narrow quasiparticle 5 f bands in the vicinityof the Fermi level. It should be pointed out that the enhancedspectral weight of 5 f states in the Fermi level at low temper-ature commonly exists in actinide systems . It is speculatedthat the missing of flat 5 f bands in literature is partly as-cribed to the underestimation of strong correlation among the5 f electrons without fully taking into account the many-bodye ff ects.After inspecting the detailed characteristics of A ( k , ω )shown in Fig. 2(a) and Fig. 2(c), it is identified that onlythe conduction bands intersect the Fermi level, indicating themostly localized 5 f states and incoherent quasiparticle bandsat high temperature. With gradual decreasing temperature,the overall band profiles generally remain unchanged exceptfor the emergence of flat 5 f bands around the Fermi level.In the energy range of -1 eV ∼ f states and are split byspin-orbital coupling. At low temperature, 5 f states tend tobe itinerant and form coherent bands. Along the X - Γ and Γ - M high-symmetry lines, moderate hybridization between 5 f bands and 5 p valence electrons are observed. It is guessed thatthe stripe-like patterns, c - f hybridization and coherent quasi-particle bands possibly reveal a temperature-induced localizedto itinerant crossover for 5 f states in PuIn . (a) (b) (c) (d) FIG. 2. (Color online). Momentum-resolved spectral functions A ( k , ω ) of PuIn as a function of temperature under ambient pressure obtainedby DFT + DMFT calculations. (a) 580 K. (c) 14.5 K. An enlarged view of panel (b) 580 K and (d) 14.5 K in the energy window ω ∈ [ − . , .
05] eV. In these panels, the horizontal lines denote the Fermi level. A () ( a r b . un i t s ) calc.PES1PES2 FIG. 3. (Color online). Electronic density of states of PuIn . The cal-culated and experimental data are represented by solid thick line andcircles, respectively. The calculated data is multiplied by the Fermi-Dirac distribution function. The experimental data are extracted fromRef. [28] at two photon energies of 21.2 eV (red circles) and 40.8 eV(blue circles), respectively. B. Density of states
To further explore the electronic structure of PuIn , we dis-cuss the density of states as a function of temperature in de-tail. In Fig. 3, we plot the calculated total density of statesand experimental photoemission spectroscopy together. Ev-idently, the representative peaks at the Fermi level and -1.2 eVare correctly confirmed by our results, which serve as criticalvalidation for our calculations. Then Fig. 4 shows the elec-tronic density of states at typical temperatures 580 K and 14.5K. Several features are as follows. First of all, the spectralweight at the Fermi level is low, which is almost invisible athigh temperature. Meanwhile, 5 f states are nearly localizedto form incoherent states. Besides, the broad “hump” residesfrom 0 . f orbitals and the lower Hubbard bands locate inthe energy range of − − δ -Pu and PuB . Thirdly, owingto the spin-orbital coupling , the 5 f orbitals are split into six-fold degenerated 5 f / and eight-fold degenerated 5 f / states.In Fig. 4(d), it is clear that the central quasiparticle peak ismainly constituted by the 5 f / state and a small satellite peakat -0.45 eV belongs to 5 f / state, resulting in the energy gapabout 0.45 eV. Furthermore, the peak at -1.2 eV is ascribed
580 K (a) (b)
580 K (c) (d) (e) (f) QP QP FIG. 4. (Color online). Electronic density of states of PuIn . Total density of states (thick solid lines) and partial 5 f density of states (color-filled regions) of 580 K (a), 14.5 K (b). The j -resolved 5 f partial density of states with 5 f / and 5 f / components represented by red andblue lines, respectively. 580 K (c), 14.5 K (d). (e) The evolution of 5 f density of states against temperature in the vicinity of Fermi level. (f)The height of the central quasiparticle peak h QP (5 f / ) as a function of temperature. to 5 f / state which accords with experimental photoemissionspectroscopy. It is worth mentioning that the 5 f / state re-mains insulating-like and manifests a gap in the Fermi level.Therefore, the distinguished coherent behavior of 5 f / stateand 5 f / state is orbital selective. Fourthly, as is shown inFig. 4(e), the central quasiparticle peak from 5 f / states be-comes sharp and intense at low temperature. The incrementof spectral weight of central quasiparticle peak with decreas-ing temperature implies the onset of coherent 5 f states andappearance of itinerant 5 f valence electrons. In consequence,it is roughly concluded that a localized to itinerant crossovermay occur with a decline of temperature. C. Fermi surface topology
In this subsection, we examine the Fermi surface topologyto unveil the temperature-dependent 5 f correlated electronicstates of PuIn . The three-dimensional Fermi surface and cor-responding two-dimensional Fermi surface at two character-istic temperatures 580 K and 14.5 K are visualized in Fig. 5.It is observed that two doubly degenerated bands intersect theFermi level (No. of bands: 18 and 19, 16 and 17), whichare marked by α and β , respectively. α bands resemble dis-torted spherical Fermi surfaces at each of the eight apex an-gles of the first Brillouin zone, while β bands locate at Γ pointto form ellipsoid shape. As can be seen, the Fermi surfacetopology of α and β bands agree quite well with previous the- oretical results . Particularly, β band corroborates the Fermisurface measured by dHvA experiment , demonstrating theaccuracy of our calculations again. When the temperaturegoes down, the topology of α bands nearly remains unchangedand the volumes rarely alter either. The key factors lie in β bands, which experience topology variation and volume ex-pansion. At high temperature, they cross the Γ - X line to for-mulate ellipsoid-like Fermi surfaces [see Fig. 5(c)] and theyintersect the M - X line at low temperature. So the Fermisurface topologies indeed change tremendously with decreas-ing temperature, which hints the possible Lifshitz transitionfor 5 f states and potential low-temperature magnetic order.The transformation of Fermi surface topology is intimatelyconnected with the temperature-driven localized to itinerantcrossover of 5 f correlated electronic states, which could bedetected using quantum oscillation measurements . D. Self-energy functions
As mentioned above, the 5 f electrons are strongly cor-related and the electron correlation e ff ects can be deducedfrom their electron self-energy functions . Figure 6 illus-trates the renormalized imarginary part of self-energy func-tions Z | Im Σ ( ω ) | for 5 f / and 5 f / states. Here Z means thequasiparticle weight or renormalization factor, which denotesthe electron correlation strength and can be obtained from the M X Γ M X Γ (a) (b) (c) M X Γ M X Γ (d) (e) (f) FIG. 5. (Color online). Three-dimensional Fermi surface and two-dimensional Fermi surface of PuIn calculated by the DFT + DMFT methodat 580 K (a, b, c) and 14.5 K (d, e, f). There are two doubly degenerated bands (labelled by α and β ) crossing the Fermi level. Three-dimensionalFermi surface of α and β bands are plotted in the left and middle columns, respectively. The right columns denote the two-dimensional Fermisurface on the k x - k y plane ( k z = π/
2) corresponding to β bands. real part of self-energy functions via the following equation : Z − = m (cid:63) m e = − ∂ Re Σ ( ω ) ∂ω (cid:12)(cid:12)(cid:12)(cid:12) ω = . (1)Generally, Z | Im Σ (0) | is considered as an indicator of low-energy electron scattering rate . At low temperature, Z | Im Σ f / (0) | approaches zero, demonstrating the itinerant na-ture of 5 f states. With elevating temperature, Z | Im Σ f / ( ω ) | rises swiftly, especially in the low-energy regime of [-0.5eV, 0.5 eV], and then reaches finite values. Conversely, Z | Im Σ f / ( ω ) | surges up quickly at high-energy regime ( | ω | < Z | Im Σ f / ( ω ) | becomesmore significant than that of Z | Im Σ f / ( ω ) | , which leads to thesuppression for the itinerancy of 5 f / state and explains itsenergy gap in the Fermi level. Since self-energy functionsof 5 f / and 5 f / states manifest di ff erentiated temperature-dependent patterns, it is concluded that 5 f electron correlationare orbital selective. E. Atomic eigenstate probabilities
In analogy with the archetypal mixed-valence metal δ -Pu whose average 5 f electron occupation deviated from its nom- inal value 5.0, PuIn is expected to display mixed-valence be-havior since it shares some common features like the three-peak structure in the spectral functions of δ -Pu. To inter-pret the valence state fluctuations and mixed-valence behav-ior, we attempt to obtain the 5 f electron atomic eigenstatesfrom the output of DMFT ground states. Here p Γ is adoptedto quantify the probability of 5 f electrons which stay in eachatomic eigenstate Γ . Then the average 5 f valence electronis expressed as (cid:104) n f (cid:105) = (cid:80) Γ p Γ n Γ , where n Γ is the number ofelectrons in each atomic eigenstate Γ . Finally, the probabilityof 5 f n electronic configuration can be defined as (cid:104) w (5 f n ) (cid:105) = (cid:80) Γ p Γ δ ( n − n Γ ).Figures 7(a)-(c) depict the calculated probability of 5 f n electronic configuration for PuIn , where n ∈ [3, 7] and otherprobability of electronic configurations are too small to beseen. As listed in Table I, the probability of 5 f electronicconfiguration is overwhelmingly dominant, which accountsfor 86%, followed by 5 f and 5 f electronic configurations.At 580 K, the probability of 5 f and 5 f electronic configura-tions stand at 8.6% and 4.7%, respectively. In the meantime,the occupation of 5 f electrons is approximately 4.96, whichapproaches its nominal value 5.0. Hence 5 f electrons are in-clined to stay more time at 5 f electronic configuration than5 f and 5 f electronic configurations. It means that valencestate fluctuations are not quite remarkable at relatively high (a) (b) FIG. 6. (Color online). Renormalized real-frequency self-energyfunctions of PuIn obtained by the DFT + DMFT method. (a) and(b) denote temperature-dependent Z | Im Σ ( ω ) | for the 5 f / and 5 f / states, where Z means the renormalization factor. temperature, signifying localized 5 f states. As the temper-ature lowers, the probability of 5 f electronic configurationslightly decreases, accompanied by a subtle deduction of 5 f and a minor growth of 5 f electronic configuration. Overall,the probability of 5 f n electronic configurations are not sensi-tive to varying temperature. As a consequence, the occupationof 5 f electrons keeps almost unchanged, suggesting the atyp-ical mixed-valence behavior of PuIn , which is beyond ourexpectation. In this respect, the temperature-induced local-ized to itinerant crossover of 5 f states is hidden in the atomiceigenstate probabilities. TABLE I. Probabilities of 5 f , 5 f , 5 f , 5 f , and 5 f for PuIn attemperatures 580 K and 14.5 K, respectively.Temperatures 5 f f f f f
580 K 1.106 × − × − × − × − IV. DISCUSSIONA. f electrons in CeIn and PuIn Here we concentrate on the isostructural compounds CeIn and PuIn to unravel the alluring f electrons and fascinat-ing bonding behavior. As mentioned above, CeIn and PuIn stabilize in cubic AuCu structure with similar lattice con-stant 4.689 Å and 4.703 Å , respectively. Since the ele-ment identification is regarded as the chemical substitution Cefor Pu, the electronic structure and related physical propertiesare expected to share abundant common traits. For instance, CeIn and PuIn are typical heavy-fermion compounds ,which develop antiferromagnetic order below Ne´el tempera-ture 10 K and 14.5 K , respectively.Figure 8 presents the calculated momentum-resolved spec-tral functions A ( k , ω ) of both CeIn and PuIn along the samehigh-symmetry lines in the Brillouin zone via DFT + DMFTmethod at 14.5 K. Several features are as follows. Firstly, theparallel flat bands at 0.1 eV and 0.4 eV [see Fig. 8(a)] areattributed to Ce-4 f electrons, which are split by spin-orbitalcoupling into j = / j = / f bands intersect conduction bands to form c − f hybridizationand open obvious hybridization gaps. Thirdly, the electron-like band and hole-like band only adjoin along the X - Γ line inthe angle-resolved photoemission spectroscopy experiment ,which is well reproduced by our calculation. Fourthly, theconduction bands with strong energy dispersions are mainlycontributed by In atoms. Consequently, the electron-like bandand hole-like band at Γ and M points located about -1 eV and-0.5 eV below the Fermi level, respectively.For comparison, it is significative to evaluate band structureof PuIn [see Fig. 8(b)]. First of all, the overall energy profilesseem incredibly similar for CeIn and PuIn , even though theband degeneracy at Γ point in CeIn is lifted in PuIn . Suchamazing similarity in the band structure is attributed to theconduction band of In atoms. Secondly, the dispersionless flat5 f bands mainly distribute at -0.9 eV and -0.45 eV below theFermi level, where the spin-orbital coupling energy separa-tion between j = / j = / f electrons isabout 0.45 eV. It is reasonable that the stronger spin-orbitalcoupling strength of Pu results in a larger energy separationthan that of Ce, since the atomic number of Pu is much higherthan that of Ce. Thirdly, both 4 f and 5 f states are stronglycorrelated with strikingly renormalized bands and electron ef-fective masses. Lastly, it is widely believed that 4 f states aremore localized than the 5 f states. However, 4 f states in CeIn seem to take in active chemical bonding and becomes itiner-ant at low temperature. Conversely, the 5 f states in PuIn undergoes a hidden localized-itinerant crossover at low tem-perature. In this scenario, the f electron nature in CeIn andPuIn pose archetypical prototype to gain deep understandingon the intrinsic connection between 4 f and 5 f states, so as touncover low temperature antiferromagnetic order. B. dHvA quantum oscillation dHvA quantum oscillation is known as a useful tool to de-tect the Fermi surface. The dHvA e ff ect encodes the magneticfield dependence of the quantum oscillations in magnetiza-tion and other properties owing to the change in the occupa-tion of Landau levels driven by the oscillation of the magneticfield. An oscillation frequency proportional to the extremalFermi surface cross-sectional area perpendicular to the mag-netic field direction is expressed as: F = (cid:126) π e A , (2) (a) (b) (c) (d) FIG. 7. (Color online). Probabilities of 5 f (red) (a), 5 f (blue), 5 f (green) configurations (b) and 5 f (purple), 5 f (cyan) (c), 5 f occupancyas a function of temperature (d) for PuIn by DFT + DMFT calculations. (a) (b)
FIG. 8. (Color online). The momentum-resolved spectral functions A ( k , ω ) of both CeIn (a) and PuIn (b) along the high-symmetry lines inthe Brillouin zone obtained by DFT + DMFT method at 14.5 K. The horizontal dashed lines mean the Fermi level. where F is the dHvA frequency in unit of kT, e is the ele-mentary charge, (cid:126) is the reduced Planck constant, A denotesthe extremal area. Moreover, the electron e ff ective mass av-eraged around the extremal orbits can be obtained from thedamping strength as a function of temperature. Thus thedHvA frequency and electron e ff ective mass are evaluated us-ing the numerical algorithm implemented by Rourke and Ju-lian . In comparison with dHvA experimental results, themagnetic field is chosen along the [111] direction. The cal-culated dHvA frequency together with electron e ff ective massare listed in Table II. The calculated dHvA frequency of β band is 1.91 kT, which is close to the experimental value about2.0 kT and theoretical value 2.18 kT based on 5 f -itinerant band model. However, our calculated dHvA frequency di ff ersfrom the value using a generalized gradient approximation .These discrepancies might arise from the approximations ofDFT calculation methods. Furthermore, the obtained electrone ff ective mass is 1.45 m e , approaching the previous theoret-ical value 1.56 m e . In view of the accordance between thetheoretical and experimental results, it is guessed that the elec-tronic correlations indeed a ff ects the Fermi surface and elec-tron e ff ective mass, because the discrepancy exists betweenDFT results and experimental dHvA frequencies for param-agnetic state of PuIn . Additionally, the other orbits are notdiscussed here, which might serve as critical prediction forfurther dHvA experiment. TABLE II. The calculated dHvA frequency and electron e ff ectivemass of PuIn with magnetic field along the [111] direction. h meanshole-like orbit, e denotes electron-like orbit.F (kT) m ∗ ( m e ) Type1.91 1.45 e5.33 4.62 e7.68 6.57 e9.10 7.39 h V. CONCLUSION
In summary, we studied the detail electronic structures ofPuIn by employing a state-of-the-art first-principles many-body approach. The temperature dependence of itinerantto localized crossover and the correlated electronic states were addressed systematically. As the temperature declines,the augmented itinerancy of 5 f electrons and emergenceof valence state fluctuations indicate a localized-itinerantcrossover. Especially, 5 f states manifest orbital selective elec-tron correlation, reflected by orbital-dependent electron e ff ec-tive masses and renormalized bands. Our results not only pro-vide a comprehensive picture about the evolution of 5 f corre-lated electronic states with respect to temperature, but alsogain important implications into the low temperature mag-netism in PuIn . Further studies about the other Pu-basedcompounds are undertaken. ACKNOWLEDGMENTS
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