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Spin, orbital, and total magnetic moments ͑ Bohr magnetons ͒ as obtained from the (GGA ϩ OP) calculation of fcc Am.
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Density-functional electronic structure calculations have been used to investigate the high pressure behavior of Am. At about 80 kbar (8 GPa) calculations reveal a monoclinic phase similar to the ground state structure of plutonium (α-Pu). The experimentally suggested α-U structure is found to be substantially higher in energy. The phase transition...
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... fcc (GGA ϩ OP) calculation gives an equilibrium volume too low compared to the experimental dhcp equilibrium volume. For comparison, we corrected for this discrepancy in the equilibrium volume by shifting the total energy curve so that B and B Ј were unchanged but the equilibrium volume was identical to the experimental value 29.3 Å 3 ͑ not shown ͒ . In this case, the Mott transition already occurs at about 44 kbar and the volume collapse increases to about 40%. Hence, correction for this discrepancy does not improve our theoretical agreement with experiment. It is unclear how to compare our theoretical transition pressure ͑ 80 kbar ͒ with experimental data because there is a large hysteresis in the experiments. It may be interpreted that our transition occurs too early at 80 kbar. This might be due to an underestimated total energy gain associated with the localization of the 5 f electrons in our calculations. Therefore, in another comparison, we arti- ficially lowered the total energy curve for the (GGA ϩ OP) calculation by 14 mRy ͑ 0.2 eV ͒ and this resulted in a transition pressure close to 150 kbar ͑ 15 GPa ͒ with, still, a considerable 20% volume collapse. The calculated ͑ GGA ͒ zero- temperature equilibrium volumes of Ce and light actinides 24,25 ͑ Th–Pu ͒ are on average about 7% smaller than measured room temperature data. It therefore seems likely that the itinerant monoclinic phase ͑␣ -Pu ͒ of Am also has too low a calculated equilibrium volume in the present calculations. The equilibrium volume is calculated to be 16.9 Å 3 . If we introduce a correction so that the monoclinic phase obtains a 7% larger equilibrium volume, we instead obtain a transition pressure of about 100 kbar ͑ 10 GPa ͒ and a volume collapse of about 18%. This correction gives a somewhat better agreement with experiment for the transition pressure, whereas the calculated volume collapse is rather insensitive to this correction. Experimentally 8,11 an orthorhombic ͑␣ -U ͒ structure at about 150 kbar ͑ 15 GPa ͒ was proposed in Am. In our calculation this orthorhombic structure ͑ with b / a , c / a , and atomic coordinate y set equal to their equilibrium values for ura- nium ͒ is substantially higher in energy than the monoclinic phase, and provided our description of the electronic structure is accurate, we therefore rule out the orthorhombic phase in the high pressure/low temperature phase diagram of Am. If, hypothetically, a transition to the ␣ -U phase took place, completely neglecting the monoclinic ͑␣ -Pu ͒ phase, the transition is calculated to occur at about 200 kbar ͑ 20 GPa ͒ ac- companied by a volume collapse of about 21%. In Table I we summarize our EOS data for the calculated crystal structures. The Murnaghan fit of fcc Am gave a bulk modulus ͑ B ͒ of about 430 kbar ͑ 43 GPa ͒ and a B Ј equal to 2.9. The equilibrium volume is too low, only 25.1 Å 3 compared to the observed volume of 29.3 Å 3 , but the bulk modulus is in rather good agreement with experiment. Our calculations underestimate the equilibrium volume by about 14%, which may indicate that the 5 f contribution to the chemical bond is overestimated in our GGA ϩ OP scheme at lower pressures. The large discrepancy for the equilibrium volume is a serious failure of the theory, but is consistent with the results found for Pr recently, 18 where the difference between theory and experiment for the equilibrium volume was about 14%. It is possible to remove most of the 5 f bonding by putting these electrons ad hoc as core electrons. In Fig. 3 we compare calculations for fcc Am (GGA ϩ OP) with nonpo- larized ͑ GGA ͒ calculations with the 5 f electrons treated as core electrons (5 f in core ͒ . The (5 f in core ͒ calculation is shifted down an amount 0.17 Ry ͑ 2.3 eV ͒ to allow a clearer comparison between the two energy curves. The equilibrium volume for the (5 f in core ͒ calculation is in somewhat better agreement, 26.6 Å 3 , but still almost 10% too low compared to experiment. The corresponding bulk modulus is about 460 kbar ͑ 46 GPa ͒ , in rather close agreement with our (GGA ϩ OP) calculation. B Ј is also in good agreement with the (GGA ϩ OP) theory, 3.4 compared to 3.0. From Fig. 3 we conclude that for the volume range close to equilibrium the two theoretical treatments (GGA ϩ OP) and (5 f in core ͒ are in relatively good agreement, with a small discrepancy of about 4% in their respective equilibrium volumes. Notice, however, that for compressed volumes the total energy curves begin to separate between the two calculations. This is certainly expected because the (5 f in core ͒ treatment should become less satisfactory at higher pressures. We an- ticipate an increased overlap at smaller volumes between the 5 f orbitals, which eventually will form band states. At this point, it would of course be grossly inaccurate to treat them as core states. This effect is inherent in the (GGA ϩ OP) theory where a suppression of the magnetic moments signals delocalization. In Fig. 4 we show the spin, orbital, and total magnetic moments as a function of atomic volume for fcc Am calculated using the (GGA ϩ OP) approach. The symbols represent the calculations, the full line here is a guide for the eye only. The orbital moment is enhanced by the orbital polarization of the 5 f orbitals and at the equilibrium volume it is about Ϫ 0.85 Bohr magnetons. The majority contribution to the orbital moment is traced to the 5 f spin-down states ͑ Ϫ 0.93 ͒ with a small contribution also from the 6 d spin- down ͑ 0.13 ͒ and spin-up ͑ Ϫ 0.05 ͒ states. With the orbital polarization switched off the orbital moment is smaller in magnitude ͑ Ϫ 0.65 Bohr magnetons ͒ . The 5 f band is less than half full and therefore the sign of the spin-orbit coupling ͑ corresponding to Hund’s third rule of an open-shell atom ͒ turns the orbital moment antiparallel to the spin moment. The total and spin magnetic moments slowly decrease in magnitude with volume, whereas the orbital moment is almost constant until about 17 Å 3 where both spin and orbital moments collapse to zero. This signals a complete 5 f delocalization in Am, and 5 f band states that contribute to the chemical bonding between atoms. At this volume the 5 f states in Am are itinerant, as in the lighter actinides, Th–Pu. Magnetic calculations for Am in the ␣ -Pu structure collapse to nearly zero magnetic moment ͑ not shown ͒ , confirming this picture. Consequently, in this paramagnetic regime ͑ Fig. 1 ͒ , fcc Am is the most unfavorable structure and instead the monoclinic ͑␣ -Pu ͒ structure has the lowest energy. This result confirms the simple model calculations carried out by S ̈ derlind et al. 12 who showed that for a 5 f band occupation of about six, the ␣ -Pu structure should be lower in energy than both the ␣ -U and fcc structures. The orbital polarization energy, the 1/2 E 3 L 2 term, was of the order of 2–7 mRy throughout the volume range studied. The Racah parameter E 3 is a linear combination of Slater integrals and was in our calculations for Am of the order of 4–6 mRy. Calculations without orbital polarization gave a somewhat lower transition pressure ͑ 65 kbar ͒ and a somewhat larger volume collapse ͑ 28% ͒ . We have studied six crystal structures of Am with a first- principles method using the (GGA ϩ OP) scheme. The total energy for five of these structures ͑ bcc, bcm, ␣ -U, ␣ -Np, and ␣ -Pu ͒ was calculated assuming spin degeneracy whereas for the fcc structure, this requirement was lifted. At 80 kbar we calculate a transition from fcc Am to monoclinic Am and a volume collapse of 25%. We interpret this transition as a Mott transition; the onset of a low symmetry crystal structure is prompted by delocalization of the 5 f electrons in Am. The low density fcc phase is also modeled by a calculation with the 5 f electrons occupying core states. For low pressures this rather ad hoc approximation is in relatively good agreement with the (GGA ϩ OP) calculations, with a very similar B and B Ј but a 4% larger equilibrium volume. With increasing pressure the treatment with 5 f electrons in the core becomes gradually inappropriate, with an inaccurate total energy as a result. Calculations of the transition pressure between fcc and monoclinic Am are sensitive to the accuracy of the total energy for both the localized and the itinerant phase. The transition pressure would be considerably higher and the volume collapse smaller if the equilibrium volume for the monoclinic phase was 5–10 % larger. This is certainly within the usual error associated with a GGA calculation for an f -electron metal. The transition pressure would also increase considerably upon a small downward shift ͑ 0.1–0.2 eV ͒ of the energy curve for the low density fcc phase. Thus, inac- curacies in the calculations could easily explain the fact that we calculate a transition pressure somewhat lower than the values reported for this transition. A large volume collapse, however, seems relatively insensitive to possible inaccura- cies in the total energy calculations and we therefore have confidence in this result. We appreciate the difficulties in- volved in determine the correct crystal structure from high pressure experiments and the necessary fitting that has to be done. Also, the hysteresis in the experimental results make it hard to directly compare our results with experiment. We believe, however, that Fig. 2 is clear evidence that our tech- nique is able to describe the correct physics of the high pressure transitions in Am. To get a more accurate description overall the exchange/correlation functional needs to be improved. In the present paper we have investigated the total energy of two different configurations: delocalized 5 f states and localized, chemically inert 5 f states. Provided there are no complications involving other electronic configurations, such as mixed valence, Kondo behavior, and so on, we rule out the ␣ -U structure as the high pressure phase of Am. ...
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Citations
... To complement the single-site model treatment of the Am magnetism, we have performed density functional theory (DFT) calculations of AmFe 2 using the DFT þ U method. The results are summarized in the Supplemental Material [45][46][47][48][49][50][51][52][53][54]. Calculations employing the around mean-field approach [46] with low values of U < 1 eV provided XAS and XMCD spectra having qualitatively the same shape as the measured ones. ...
Trivalent americium has a nonmagnetic (J ¼ 0) ground state arising from the cancellation of the orbital
and spin moments. However, magnetism can be induced by a large molecular field if Am3þ is embedded in
a ferromagnetic matrix. Using the technique of x-ray magnetic circular dichroism, we show that this is the
case in AmFe2. Since hJzi ¼ 0, the spin component is exactly twice as large as the orbital one, the total Am
moment is opposite to that of Fe, and the magnetic dipole operator hTzi can be determined directly; we
discuss the progression of the latter across the actinide series.
... To complement the single-site model treatment of the Am magnetism, we have performed density functional theory (DFT) calculations of AmFe 2 using the DFT+U method. The results are summarized in the Supplementary Material [45][46][47][48][49][50][51][52][53][54]. An improved treatment of AmFe 2 , whose electronic structure involves an interplay of strong correlation effects with exchange fields from the ordered Fe sublattice, and strong spin-orbit interaction of Am, could require a computational scheme going beyond the present static DFT+U approach. ...
Trivalent americium has a non-magnetic ($J$ = 0) ground state arising from
the cancelation of the orbital and spin moments. However, magnetism can be
induced by a large molecular field if Am$^{3+}$ is embedded in a ferromagnetic
matrix. Using the technique of x-ray magnetic circular dichroism, we show that
this is the case in AmFe$_2$. Since $\langle J_z \rangle$ = 0, the spin
component is exactly twice as large as the orbital one, the total Am moment is
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... Americium metal has received considerable attention in the past and recently because of the unique changes in electronic and crystal structure that occur as functions of pressure. [7][8][9][10][11][12][13][14][15] At ambient conditions the 5f electrons are localized but with increasing pressure they begin to participate in bonding and delocalize. This change in character has a substantial effect on the equation of state as well as phase stability and transformations. ...
... The early reports concluded that Am went through transitions from its ground-state dhcp AmI phase to a face-centered-cubic (fcc) AmII, monoclinic AmIII, and eventually face-centered-orthorhombic α-uranium-type AmIV. 7 The latter two structural assignments were questioned first by theory 9 and later determined to be face centered and primitive orthorhombic, respectively. 10 Only the AmIII → AmIV showed 10 a significant volume collapse of 7%. ...
We have conducted electronic-structure calculations for Am metal under pressure to investigate the behavior of the 5f-electron states. Density-functional theory (DFT) does not reproduce the experimental photoemission spectra for the ground-state phase where the 5f electrons are localized, but the theory is expected to be correct when 5f delocalization occurs under pressure. The DFT prediction is that peak structures of the 5f valence band will merge closer to the Fermi level during compression indicating the presence of itinerant 5f electrons. Existence of such 5f bands is argued to be a prerequisite for the phase transitions, particularly to the primitive orthorhombic AmIV phase, but does not agree with modern dynamical-mean-field theory (DMFT) results. Our DFT model further suggests insignificant changes of the 5f valence under pressure in agreement with recent resonant x-ray emission spectroscopy, but in contradiction to the DMFT predictions. The influence of pressure on the 5f valency in the actinides is discussed and is shown to depend in a nontrivial fashion on 5f-band position and occupation relative to the spd valence bands.
... It has been suggested [9,10] that the 5f electrons of the actinides before Am participate in bonding while the 5f electrons of the actinides after Pu become localized and non bonding. As a result, several experimental and theoretical works have been done in recent years to gain insight into the structural and electronic properties of Am [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. Central to the questions concerning Am are the phase transitions with increasing pressure, localization/delocalization behavior of the 5f electrons, and possible magnetism of Am. ...
Ab initio total energy calculations within the framework of density functional theory have been performed for atomic hydrogen
and oxygen chemisorption on the (0001) surface of double hexagonal packed americium using a full-potential all-electron linearized
augmented plane wave plus local orbitals method. Chemisorption energies were optimized with respect to the distance of the
adatom from the relaxed surface for three adsorption sites, namely top, bridge, and hollow hcp sites, the adlayer structure
corresponding to coverage of a 0.25 monolayer in all cases. Chemisorption energies were computed at the scalar-relativistic
level (no spin-orbit coupling NSOC) and at the fully relativistic level (with spin-orbit coupling SOC). The two-fold bridge
adsorption site was found to be the most stable site for O at both the NSOC and SOC theoretical levels with chemisorption
energies of 8.204eV and 8.368eV respectively, while the three-fold hollow hcp adsorption site was found to be the most stable
site for H with chemisorption energies of 3.136eV at the NSOC level and 3.217eV at the SOC level. The respective distances
of the H and O adatoms from the surface were found to be 1.196Åand 1.164Å. Overall our calculations indicate that chemisorption
energies in cases with SOC are slightly more stable than the cases with NSOC in the 0.049–0.238eV range. The work functions
and net magnetic moments respectively increased and decreased in all cases compared with the corresponding quantities of bare
dhcp Am (0001) surface. The partial charges inside the muffin-tins, difference charge density distributions, and the local
density of states have been used to analyze the Am-adatom bond interactions in detail. The implications of chemisorption on
Am 5f electron localization-delocalization are also discussed.
... to fit the total energy curve and obtain the equilibrium lattice constant and the bulk modulus. We have listed these results together with some of the available theoretical and experimental results [7, 14,27282930 inTable 1. ...
The electronic and geometrical properties of bulk americium and square and hexagonal americium monolayers have been studied with the full-potential linearized augmented plane wave (FP-LAPW) method. The effects of several common approximations are examined: (1) non-spin polarization (NSP) vs. spin polarization (SP); (2) scalar-relativity (no spin-orbit coupling (NSO)) vs. full-relativity (i.e., with spin-orbit (SO) coupling included); (3) local-density approximation (LDA) vs. generalized-gradient approximation (GGA). Our results indicate that both spin polarization and spin orbit coupling play important roles in determining the geometrical and electronic properties of americium bulk and monolayers. A compression of both americium square and hexagonal monolayers compared to the americium bulk is also observed. In general, the LDA is found to underestimate the equilibrium lattice constant and give a larger total energy compared to the GGA calculations. While spin orbit coupling shows a similar effect on both square and hexagonal monolayer calculations regardless of the model, GGA versus LDA, an unusual spin polarization effect on both square and hexagonal monolayers is found in the LDA results as compared with the GGA results. The 5f delocalization transition of americium is employed to explain our observed unusual spin polarization effect. In addition, our results at the LDA level of theory indicate a possible 5f delocalization could happen in the americium surface within the same Am II (fcc crystal structure) phase, unlike the usually reported americium 5f delocalization which is associated with crystal structure change. The similarities and dissimilarities between the properties of an Am monolayer and a Pu monolayer are discussed in detail. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006
... The localization of the 5f electrons is due to strong correlations between them that are not accurately treated by density functional calculations (DFT) with a local density approximation (LDA), and many attempts have been made to solve this problem. In the case of Am the localization of the 5f electrons at atmospheric pressure was simulated successively by a ferromagnetic (FM) configuration [1, 2], by putting the 5f electrons in the atomic core [3], by decoupling them from the other band electrons [4, 5], by the self-interaction corrected (SIC) LDA [6, 7], and by a disordered local moment picture [8] within the LDA and the coherent potential approximation. With the methods used in345, of constrained LDA type, it is not possible to determine ab initio localized–delocalized transitions because the total energies calculated in constrained LDA and LDA are not comparable. ...
... With the methods used in345, of constrained LDA type, it is not possible to determine ab initio localized–delocalized transitions because the total energies calculated in constrained LDA and LDA are not comparable. In12345678, except in [3], the calculations were simplified by the use of a face-centred cubic (fcc) structure instead of the double hexagonal close packed (dhcp) structure of ambient conditions. Moreover, in [1] and [8] the spin–orbit coupling was neglected, which is a rough approximation for a highly relativistic metal such as Am. ...
... Independently of the real physical meaning of magnetism in δ-Pu, which is as yet an open question, this is a way to model the localization of the 5f electrons because it gives rise to a band splitting which reduces the bonding, resulting in an increased lattice constant and reduced bulk modulus. In the same way, Am is NM because of the cancellation between the spin and the orbital moments, which cannot be reproduced theoretically [2], but allowing magnetism in the theory permits a band splitting to simulate the localization of the 5f electrons. Generally speaking, the LDA fails to give the correct orbital moment when the orbital contribution to the magnetism is important, as in magnetic actinides, since the approximate treatment of exchange is not orbital dependent; even with the so-called 'orbital polarization' correction this cannot be rectified [2]. ...
Density-functional electronic calculations have been used to investigate the high-pressure behaviour of americium. The phase transitions calculated agree with the recent sequence obtained experimentally under pressure: double hexagonal close packed face-centred cubic face-centred orthorhombic primitive orthorhombic (Pnma). In the first three phases the 5f electrons are found localized; only in the fourth phase (Am IV) are the 5f electrons found delocalized. The localization of the 5f electrons is modelled by an anti-ferromagnetic configuration which has a lower energy than the ferromagnetic ones. In this study the complex crystal structures have been fully relaxed.
... This "partial localization" of the 5f states is found in many actinide intermetallic compounds. The underlying microscopic mechanism is an area of active current research (Lundin et al. 2000, Söderlind et al. 2000. LDA calculations show that the hopping matrix elements for different 5f orbitals vary. ...
In this review article we present a survey of unconventional superconductors and their coexistence behaviour with magnetism. We focus on Ce- and U-based heavy fermion superconductors, in addition we discuss the rare earth borocarbide and skutterudite superconductors. We show that heavy fermion behaviour in Ce- and U- compounds should be described differently. While the Kondo-lattice model with localised 4f-electrons is appropriate for Ce-compounds, dual models including localised and itinerant 5f-electrons are necessary for U-compounds. We demonostrate that this leads to consistent results for Fermi surface topology and mass enhancement in various U-compounds. We also show that virtual exchange of localised 5f-electron excitations provides a new mechanism for unconventional superconductivity in addition to the known itinerant spin-fluctuation exchange mechanism. We discuss symmetry properties and coexistence of unconventional superconducting and density wave (hidden) order parameters and methods for their detection, notably the new angle resolved magntetotransport methods. The latter have been very succesful for the investigtion of gap anisotropies in the nonmagnetic borocarbide superconductors. Recent results on the new multiphase Pr-skutterudite superconductor are also reviewed. Comment: REVIEW ARTICLE to be published in `Handbook on the Physics and Chemistry of Rare Earths' (Elsevier) 186 pages, 66 figures
... Also, the high pressure phases of Am have been succesfully described by the standard LSD theory. [17,18] Recently, the SIC-LSD method was applied to the series of actinide metals [19] from Np to Fm, correctly describing the itinerant nature of Np, the trivalency of Am, Cm, Bk and Cf, and the shift to divalency in Es and Fm. Pu turns out to be the most delicate case, being situated on the borderline between the itinerant and well localized actinides. ...
The electronic structures of several actinide solid systems are calculated using the self-interaction corrected local spin density approximation. Within this scheme the $5f$ electron manifold is considered to consist of both localized and delocalized states, and by varying their relative proportions the energetically most favourable (groundstate) configuration can be established. Specifically, we discuss elemental Pu in its $\delta$-phase, PuO$_2$ and the effects of addition of oxygen, the series of actinide monopnictides and monochalcogenides, and the UX$_3$, X= Rh, Pd, Pt, Au, intermetallic series.
... There is a small volume discontinuity of 2% at this transition, which is followed by a much larger collapse of 7%, when Am adopts the orthorhombic, Pnma structure at 16 GPa. There is little doubt that these combined phase transitions represent delocalization of 5f states in Am [16][17][18][19][20]. ...
The structural behaviour of the actinide metals with pressure is being studied using diamond-anvil cells and the high-brilliance and angle-dispersive techniques now available at the ID30 beamline of the European Synchrotron Radiation Facility. A review is given of recent work at room temperature and up to 100 GPa. The results illustrate clearly the difference between the earlier metals (Pa, U) and those further across the actinide series (Am, Cm, and Cf). The complex structures at atmospheric pressure of the lighter actinides are a consequence of itinerant 5f electrons, and these metals show less compressibility (i.e. exhibit larger bulk moduli) and few (if any) phase transitions under pressure. In contrast, the transplutonium metals do not have 5f electrons contributing to their cohesive energies at atmospheric pressure, are therefore 'soft' (have lower bulk moduli), and show multiple phase transitions before their 5f electrons become itinerant. After delocalization of their 5f electrons due to pressure, they acquire structures displayed by the light actinides.
... Without SO splitting, single group notation, the corresponding representation is Γ 15 , Γ v 15 , and Γ c 15 . All bands along [110] are split by the SO interaction, and for small k (i.e. near Γ) we can use the k · p theory to estimate the third–order [18,16] term: ...
... The split states for k along [110] belong to either of the two nondegenerate representations Σ 3 and Σ 4 , and ∆E in eq. (17) is E(Σ 4 ) − E(Σ 3 ). ...
... They have been measured in magneto–optical[36] and polariton scattering experiments.[37,38] They result in a slight shift of the position of the top of the heavy– ( 3 2Table 2 Values of the coefficient of the spin splitting proportional to k 3 of Γ 1 – conduction band for k [110] as obtained with the LMTO method, the k · p 16 × 16 Hamiltonian, and k · p perturbation theory (PT). Experimental data are from Refs. ...
This chapter describes some aspects of how relativistic effects manifest themselves in the quantum theory of solids. Although examples are mentioned where the energy shifts of energy bands relative to each other influence the physical properties, we mainly discuss the combined effects of crystal symmetry and spin-orbit coupling. In crystals without inversion symmetry this leads to a spin splitting of the bands which in particular for compound semiconductors produce interesting optical properties which also may be of technological importance. Also the properties of magnetic metals are influenced by relativistic effects, again mainly due to the spinorbit coupling. A quantitative description of spin polarization and spinorbit coupling is essential for materials where the spin-and orbital moments are comparable in magnitude. Often such materials also are those where simple (local) implementations of the density functional theory are not sufficiently accurate. Strong electron correlations require other theoretical methods, self-interaction corrections, ”LDA+U”, for example. Magnetooptical effects (Kerr effect, circular dichroism), magneto-elastic effects and magnetostriction are fields of great importance, in basic as well as applied solid state research. An understanding of the relation between magnetic properties of layered structures and spin dependent transport properties is essential for the explanation of the Giant Magnetoresistance (GMR) effect, and thus for the development for novel recording and storage devices.
