PHYSICAL PROPERTIES OF METALLIC MAGNETIC COMPOUNDS : 5f-BAND APPROACHConditions for the appearance of magnetism in metallic actinide systems

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PHYSICAL PROPERTIES OF METALLIC MAGNETIC COMPOUNDS : 5f-BAND APPROACHConditions for the appearance of

magnetism in metallic actinide systems

C.-H. de Novion

To cite this version:

C.-H. de Novion. PHYSICAL PROPERTIES OF METALLIC MAGNETIC COMPOUNDS : 5f-

BAND APPROACHConditions for the appearance of magnetism in metallic actinide systems. Journal

de Physique Colloques, 1979, 40 (C4), pp.C4-1-C4-8. �10.1051/jphyscol:1979401�. �jpa-00218797�

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5f- BAND APPROACH

Conditions for the appearance of magnetism in metallic actinide systems

C.-H. de Novion

SESI, CEN, BP 6, 92260 Fontenay aux Roses, France

R6sum6. - Nous prhcisons les parametres gouvernant I'apparition de moments magnhtiques localishs dans les actinides B I'htat mCtallique, diluts ou concentrts. Les systkmes Kondo diluCs U,Thl-, et (UxThl-,)S, les composts de protactinium, UAI, et les composCs de structure NaCl seront plus particuliGrement discutts.

Abstract. - We review the parameters responsible for the occurrence of localized magnetic moments in dilute or concentrated metallic actinide systems, and discuss their experimental evidence. The dilute U, Thl-, and (U,Thl-,)S Kondo systems, the protactinium compounds, UA12 and the rocksalt compounds will be more specif icaHy considered.

1. Introduction.

-

Metallic actinide systems display very various electronic structures. For example, one finds temperature independent magnetic susceptibilities (U, Np, Pu), strongly temperature dependent susceptibilities without magnetic ordering (UAl,, USn,) or with high ordering temperatures (NpC) [ I , 21. The presence of Sf electrons in light actinides was first proved by the neutron scattering magnetic form factor measurements on UH, [3] for magnetically ordered systems, and by considera- tions on metallic volume [4] and crystallographic and electronic structures [S] for metals. Some time ago, H. H. Hill [6] pointed out that one may classify actinide (U, Np, Pu) metallic compounds into a magnetic and a non-magnetic group, depending on intermetallic distance d,,. Below a critical value of d,, (

-

^3.4

^A),

the overlap between Sf neighbouring wavefunctions becomes large : the Sf states delocali- ze into bands and the actinide localized moments vanish.

Since that time, considerable new information has been brought, showing that if this picture is qualitatively correct, many parameters influence the appearance of Sf magnetism in early actinides. These parameters and their experimental evidence will be discussed below. We shall focuse on two main points : actinide impurities and ordered metallic actinide systems.

2 . Dilute alloys. - 2.1 ACTINIDE IMPURITIES

IN NON-METALLIC COMPOUNDS.

-

In ionic compounds, U, Np and Pu impurities form M3' to M6' ions with open 5f shells. Their electronic structure may be, in principle, easily described by limiting the effect of the crystal to electrostatic crystal-field terms of the order of lo-' eV [7]. Except if the fundamental level is a crystal-field singlet, the impurity magnetic susceptibility will follow a C / T law : this is the case of U diluted in T h o 2 , where at low temperature the effective moment is near that of the

Sf2

r,

^triplet

[a].

In the same way, EPR measurements show that the ground state of Np diluted in Tho, is 5f3

r ,

^[9].

This behaviour is favoured by the ionic character, the energy of the Sf states falling in the wide gap between the p valence bands of the metalloid and the empty s or d actinide bands (see Fig. l a and the X-ray photoemission studies on oxides [lo]).

2.2 ACTINIDE IMPURITIES IN METALLIC SYSTEMS : THEORETICAL CONCEPTS.

-

In metals, the energies around the Fermi level are occupied by a non- vanishing electronic density of states, and the impurity Sf atomic wave-function will be admixed with the Bloch states (see Fig. 1 b). A measurement of this interaction is given by the golden rule :

Fig. 1. - 5f energy levels and conduction electron density of states in dilute actinide alloys. a : non-metallic alloy ; b : non-

magnetic metallic alloy ( U 4 A ) ; c : Kondo alloy ; d : mixed valence alloy.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979401

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C4-2 C.-H. DE NOVION

where W is the frequency of the transition from a one-electron 5f state into the conduction band, v = ( 5f I V I k ) is the average matrix element of the impurity potential V between the localized 5f orbital and Bloch states I k ), and N(E,) the e l e c t r o ~ density of states of the matrix assumed to be constant in the vicinity of E, [ l l , 121. Because the local 5f state is essentially orthogonal to the Bloch states of nor- mal or transition metals, it is well described by a ge- neralized asymetric Anderson Hamiltonian [l2] ^(I).

The magnetic susceptibility of the system described by this Hamiltonian has been recently exactly calculated by the renormalization group technique in the case of a non-orbitally degenerate local state [14, 151. The results of these calculations allow to discuss very generally the electronic structure of impurities (in particular actinide impurities) in non-magnetic metals. Assuming a non-orbitally degenerate 5f level, several parameters govern the behaviour of the system : A, U (Coulomb interaction between Sf electrons of opposite spins), T (temperature), E,, (energy of a single 5f electron on the impurity, relative t o the Fermi energy E,), and 2 D (matrix bandwidth). Depending on the relative values of these parameters, several regimes are found :

- For k , T %=- U, A, I E,, I , the number of f electrons on the impurity may fluctuate freely between 0, 1 and 2 : this is the free-orbital regime.

- If U > > A and -E,,> A (see Fig. l c ) , a local -moment regime appears in a temperature range : U, - E,, % k , T % k , T,(A, U) ; Tk( < A ) is an effective Kondo temperature. A definite configuration occupies the impurity site, and charge fluctuations occur only by virtual processes. In this temperature range, the susceptibility follows a Curie- Weiss law :

x

^=.C / ( T

+

2 T,). The Weiss constant 2 T, implies a residual coupling with the conduction electrons.

- If U

*

^{A and} ^-^E,,> A, at low temperature ( T < T,), the localized f electrons are strongly coupled to the conduction electrons via the mixing interaction A : this is the strong-coupling regime. It corresponds here to the Kondo compensated state, but extends to the Friedel-Anderson non magnetic virtual bound state when U

--

l E,, I 4 A. In this regime, when

-

E,, = U/2 and whatever the value of A /U, physical properties follow universal laws which are qualitatively predicted by the RPA theory of localized spin fluctuations [16, 391 : when T -+ 0,

x

approaches a constant value ,u

;/

k , T, ; the electronic specific heat is proportional to temperature : C , = yT, with the ratio

6

⁼x / y equal to twice the free electron value

6,

; p = poll ^-(T/T,,)'] where

(') Yet, this Hamiltonian does not describe correctly the scree- ning of the charge fluctuations which are important when

A / U < 1 . This may in principle be done by introducing the

impurity d orbitals [13].

T,,, the spin fluctuation temperature, is of the order of T,, and pg is near the unitary limit for scattering of the 1 = 3 spherical component of the conduction electrons (phase shift rr /2).

- If I E , , l S A

<

U, one has a mixed-valence regime, the impurity 5f occupation number is between 0 and 1 (see Fig. I d ) . For k , T G A,

x

^will

be of the order of p;/A [14, 15, 171.

These regimes are not sharply separated. A magnetic impurity is an impurity with low T,, i.e. large U/A (the condition for the appearance of magnetism in the Hartree-Fock description [l2]). In real actinide systems, the 5f levels are orbitally degenerate. Nevertheless, it is thought that the above description applies qualitatively if one replaces the levels labelled E,, and E,,

+

U in figure 1 by E$' and E:"' : here, E$' is the increase of impurity energy (potential

+

Coulomb repulsion) when one adds an electron to a Sfn-' configuration.

- When I E, - E$' I < A

<

E$"' - E,, i.e. if the energy of the n -th electron is the Fermi energy, the system is in an intermediate configuration (fluctuating or not) between Sfn and 5fn-'. For k , T 4 A,

x

⁼p ; / A ; for k g T >> A,

x

behaves as for a mixture of the two configurations.

- When E, - E g ' and E

2'"

^-

^E;

^>>A, one has a Kondo impurity for which

x

changes from a constant value for T 4 T, to a Curie-Weiss law when k , T , 5 k , T < E$"' - E:', displaying an apparent non-magnetic-to-magnetic transition with increasing temperature.

- When A

+

E

$ "'

^-E

'"' ,,

, one has non- magnetic impurities for which the local moment regime has disappeared and where

x

is temperature independent as long as

k,

T 4 A (in this non- magnetic virtual bound. state, the charge fluctuation rate on the impurity is A / h [I 11).

What are the values of the parameters A and U for actinide impurities in metals ? In the thorium metal matrix, one may estimate A from the Sf-6d transfer integrals : v = 0.5 to 1 eV [I81 and therefore A = 0.5 to 2 eV. For U in ThS, slightly smaller widths are found, the Sf-6d transfer integrals between U and Th neighbours, and 5f-3p between U and S being of the order of a few 10-'eV. On the other hand, the Coulomb energy for 5f electron hopping in the conduction band, E,

+

E$-" - E'"' 5f 3

has been estimated for pure metals in the range 1 to 5 eV from theoretical calculations [I91 as well as from spectroscopic and thermodynamic data [20].

Therefore, in view of these estimations of A and U, one may expect a great variety of experimental behaviours for actinide impurities in metals. These behaviours are further complicated by two features : - Crystal-field and spin-orbit coupling in the 5f states [39]. This should govern the quantitative behaviour of the alloy in the local moment regime,

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where one should take into account the coarse intraconfiguration level structure. In the case of a singlet ground state due to crystal-field (larger than k , T,), the properties of the alloy should be drasti- cally modified.

-

The presence of a 6d level of approximately the same energy as the 5f level. Because in a transition metal like Th, the 6d localized level be- longs to the Hilbert space of Bloch states, it cannot be treated by the Anderson Hamiltonian, but must be described by a local d scattering potential [21, 221.

2.3 ACTINIDE IMPURITIES IN METALLIC SYSTEMS :*

EXPERIMENTAL BEHAVIOUR.

-

Up to now, most of the data have been obtained for uranium impurities ; the only system where several actinide impurities have been studied is the Pd-actinide system [23], where the Pd matrix has a complex electronic structure. Our information is restricted to transition-like matrices, because of the low solubility of actinides in simple monovalent metals. The studied alloys contain generally

-

^{1 %}actinide content : there still could remain some long-range interactions between the impurities.

The most remarkable feature is the preferred appearance of magnetism (i.e. very low Kondo temperatures) on neptunium impurities. For example, the decrease of the superconducting temperature of lanthanum when introducing actinide impurities is largest for Np, strong for Pu and negligible for U and Am [24]. This has led Jullien et al. [25] to a model of virtual bound state broadened by 5f-6d hybridization and split by spin-orbit coupling : the j = 5/2 level is just full for Am (non-magnetic) and about half-full for Np, which is at the optimum position for appearance of magnetism.

Typical cases of non -magnetic actinide impurities are those of Ti-Pu, Y-Pu,

...

[26, 271. In such systems, the increase of magnetic susceptibility, independent of temperature, and the absence of Kondo minimum, is compatible with non-magnetic virtual bound states of widths = 1 eV.

2.4 THE Ux Th,-, A N D (U, Th,-,)S SYSTEMS. - These have been the most extensively studied (apart from PA-U [23]). Uranium metal is a Pauli parama- gnet, and US a ferromagnet below 180 K which displays a cc good >> Curie-Weiss law at larger temperatures [I] : in Hill's classification, they fall respectively in the non-magnetic and magnetic Table I

Ax (4 K) AY

uemcgs) (mJ/KZ)

-

U,Th,-, 58 4.85

(U,Th,-,)S 5 1 1.50

groups. Nevertheless, diluted in pure Th and ThS, they show strikingly similar behaviours.

Let us define AX, T A y and Ap the increments of magnetic susceptibility, electronic specific heat and electrical resistivity due to the uranium impurities.

In both systems, these quantities were found to vary proportionally to the uranium content (for x 0.02 in the metal and x s 0.06 in the sulphide) [28-311.

They are given in table I for 1 % mole uranium.

AX has a finite value at 4 K and follows a Curie- Weiss law between 100 and 300 K. In this temperature range, the apparent effective moment p is near that of the free ions SfZ or 5f3 for U,Th,-,, and near that of a 5fn ion ( n = 2,3,4) with octahedral crystal- field for (U, Th,-,)S (the same as in pure US). The C,

/

T ⁼y

+

a T Z law is well followed [29, 311. y is very large. The ratio

5

⁼AX (4 K)/Ay for sulphides falls near the value 2

5,

found for the orbitally non-degenerate Kondo impurities. For the metals, it is near the free electron value

E0,

and is more difficult to understand. In both cases, Ap follows a quadratic law below 10 K : Ap = Apo[l - ( T / Ts3'].

This is shown for (Uo.,Th0.,)S on figure 2 where the low temperature saturation is clearly visible. The values of T,, are near the 8, values deduced from the Curie-Weiss law and give the order of magnitude of the spin fluctuation (or Kondo) temperature, which here for both systems is of the order of lOOK (lo-' eV).

In conclusion, the physical properties of (U,Th,-,)S are in good agreement with the Kondo impurity model presented in § 2.2, even if this model in its present development does not include the effect of an orbital moment. The facts that the effective moment is the same as in pure US and that

Fig. 2 . - Low temperature dependence of Ap for (Uo ,Tho 94)s

(M. KonCzykowski, M. Haessler, unpublished).

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C4-4 Table I1

C.-H. DE NOVION

in ordered compounds of the same family definite crystal-field levels are found (see 9 3.4) suggest that the actinide impurity is in a strongly correlated Sfn configuration ( n = 2 probably) (*). The observation of the Kondo effect shows that the antiferromagnetic exchange integral with conduction electrons due to covalent mixing is larger than the contact integral due to the Coulomb interaction. The strong value of T,, = T, = 100 K is compatible with D = 5 eV and A ⁼0.1 U ⁼0.1 eV (see 9 2.2). It explains that spin- glass effects, which give properties which do not vary proportionally to x, occur only near the critical concentration for ferromagnetism, x = 0.43 [32].

The dilute (x G 1) solid solutions (U, Th,-,)N 1331, (U, Th,+, )Se and (U, Th,-, )Te [30] behave in much the same way as (U, Th,-,)S. Except for (U, Th,-,)Te, one finds a correlation between the spin-fluctuation temperature T,, and the intermetallic distance dMM as shown on table I1 : the largest d,,, the smallest the mixing interaction A and therefore the smallest

T,,

and

T,.

That the telluride does not fit in this correlation is certainly due to its different crystal structure (CsCl instead of rocksalt), leading to a different intraconfiguration level structure (triplet instead of singlet ground state in the case of Sf2), which influences the numerical value of T,,

.

The situation seems qualitatively similar for U, Th,_,. The much larger d,, value (3.6

A)

compared to a -uranium (3.1

h;)

explains probably the disap- pearance of magnetism in the latter.

3. Metals and metallic compounds. - 3.1 PROTACTINIUM COMPOUNDS. - There has been up to now very little information on compounds of protactinium, the first actinide where 5f electrons are thought to occur. Recent

x

measurements on PaC [34], PaAs, and PaSb, [35] have shed some light on the electronic structure of Pa in metallic systems.

The three above compounds, as well as Pa pure metal [2] display a temperature independent magnetic susceptibility which is an increasing function of dMM (see Fig. 3). The possible valences for Pa are 5 (no f electron) and 4 (one f electron) : there is no possibility of obtaining a singlet ground state by crystal field effects.

x

must be here essentially a Pauli paramagnetism. Therefore in Pa metallic

(') This is confirmed by the small variation of resistivity under pressure, less than 1 % between 0 and 10 kbars (M. Konbzykowski, M. Haessler, unpublished).

compounds, the f states are sufficiently broad to be delocalized and contribute to hybrid f-d-s bands.

When dMM is large, which is the case of PaSb2, the f bands become narrow and

x

large (for similar dMM distances, uranium compounds display localized magnetism). Conversely, in a ionic compound like PaCl,, the magnetic susceptibility follows a Curie- Weiss law characteristic of a 5f' localized configuration [I].

Fig. 3.

-

Magnetic susceptibility versus intermetallic distance for several protactinium compounds.

O

3.2 PURE METALS. - If one considers the overall actinide metal sery, the main feature is the sudden switch from a transition-metal-type behaviour (Pa, U, Np, Pu) to a rare-earth-type behaviour starting at americium [61. The magnetic properties of curium metal definitely support the picture of a localized 5f7 configuration [36]. On the contrary, the physical properties of U, Np and Pu metals are governed by hybrid 5f-6d bands, the existence of which is due to the wide spatial extent of 5f states (compared to d,,) and to the near energy of Sf and 6d atomic levels. Major evidence of this is given by the relati- vistic band calculations of Kcelling and Freeman [371 although limited up to now to simple crystal structures, and by. the interpolation cohesive energy calculations of Johansson [20] showing that the 5f contribution to cohesive energy in U , Np, Pu, amounts to 10-25 kcal/mole. The band calculations show. that the 5f bands extend in energy over several eV for early actinides, and narrow when the atomic number increases (X and y increase). The hybridization between 6d and 5f bands was shown by Jullien et al. [381 to reduce considerably the occurrence of ferromagnetism (Stoner criterion) in the 5f band, and might explain that only curium is the first magnetic actinide metal.

d M M [ i )

310 3.5f PaC 4.0

-

4.5

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One of the main defi to the understanding of the actinide metals was the anomalous thermal dependence of electrical resistivity (especially in Pu), associated with a temperature independent magnetic susceptibility. As the behaviours of the various Pu allotropic forms are very similar [40], Jullien et al. [41] assumed that this is not due to the detailed band structure, but rather to many-body effects in the narrow Sf bands. Qualitatively, these authors showed that antiferromagnetic spin fluctuations (associated with a dynamic susceptibility maximum at a wavevector q Z 0) resolved the above discrepan- cy ; it explained the anomalous thermal dependence of many physical properties in these metals, when taking into account the effective thermal dependence of

x

(q, w ) [42]. A major drawback for quantitative fitting is that the RPA theory of spin fluctuations is a perturbation type theory, and that the observed

x

and p curves in Pu need, to be fitted in this model, a very large exchange enhancement ( - 10) and a small Sf Fermi energy (

-

lo-, eV).

3.3 INTERMETALLIC COMPOUNDS.

-

The most studied systems are the Laves phases (i.e. UA1,) and the AuCu, structure compounds (i. e. URh,). We give below examples of the very various Sf behaviours observed :

-

URh, shows a temperature independent paramagnetism [2]. The band-like nature of Sf electrons was shown by de Haas-van-Alphen oscillation measurements, which agreed with the calculated band structure [43]. Strong hybridization between 6d and Sf uranium states, and 4d rhodium states, seems to be a dominant factor.

- UA1, shows probably ferromagnetic spin fluctuations (paramagnons associated to a maximum of

~ ( q , w ) at q = 0) in a narrow Sf (-6d) band. As observed by Brodsky and Trainor [44], there seems to be two characteristic temperatures, T,, = 25 K and T,, = 100 K (see Fig. 4). At very low temperatu-

Fig. 4. - Temperature dependence of magnetic susceptibility and electrical resistivity of UAI, (schematic).

res, a T 3 In T logarithmic term was found in the specific heat, and its ascription to band paramagnons confirmed by its magnetic field dependence [44]. For T 4 T,,, the low temperature quadratic dependences of p and

x

and the nuclear relaxation rate value fit well with the paramagnon theory with T, =

T,,

= 25 K [45]. Above T,,, the resistivity satu- rates to = 150 ~ f l . cm and the magnetic susceptibility is Curie-Weiss like with

8, = 2 T,, and p = 3 ^{p B}: this value of the effective moment is near the Sf2 or Sf3 free ion values ; apparently, k , T,, is suggestive of the Fermi energy of a very narrow Sf band. At T > T,, the system behaves rather like a collection of U impurities with a characteristic temperature of = 100 K. This is why Doniach 1391 proposed that when heating such a system, the scattering by the spin fluctuations becomes sufficiently large to shorten the mean free path down to the order of interatomic spacing : the U atoms are seen independent by the conduction electrons. Under a 6.5 kbar hydrostatic pressure, T,, increases by 20 % (at 40 K,

x -

^p

^;/

^T,,decreases by 20 %) [46]. This is much more than for (U, Th,-,)Se confirming that in UA1, there are much more 5f states at the Fermi level. (The energy shift of Sf levels under such pressure should be of the order of

= 0.1 eV, and the bandwidth increase negligible as the decrease of lattice parameter is = 0.01

hi).

In conclusion, a possible way of describing UA1, might be in terms of weakly coupled Kondo impurities, which condense into a Fermi liquid below 100 K.

- NpSn, may be thought as an itinerant antiferro- magnet (T, = 9.5 K) and NpOs, as an itinerant ferromagnet (T, = 7.5 K) [44]. Arguments for this are the extremely high electronic yT term in the specific heat, the small ordered moments and the very low entropies at the transition (AS, ⁴R In 2).

In NpSn,, the form of the specific heat curve agrees with the Fedders and Martin [47] model of itinerant antiferromagnetism. In NpOs,, the moments are not localized on neptunium, and the ratio between the ordered moment found by neutron diffraction and the 2 3 7 ~ p hyperfine field is smaller than the value found for localized moment systems [48].

On the same hand, the correlation between a maximum of "'Np isomer shift and a minimum of hyperf ine field in the Np(Co,-, Fe, )Si, solid solution around x = 1 [49] is a possible indication of itinerant antiferromagnetism in a hybridized 5f (actinide)-3d (transition metal) band. The study of the magnetic density in UCrS, [SS] suggests strong uniaxial delo- calization of the uranium moment.

- On the view of Mossbauer and magnetic properties, a compound such as NpAl, behaves much more as a localized Sf electron system. The transition from itinerant .to localized Sf behaviour with increasing dMM in neptunium Laves phases has been discussed by Aldred et al. [48]. Definite crystal-field

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C4-6 C.-H. DE NOVION levels have recently been put in evidence in UPd, by

inelastic neutron scattering [50].

3.4 ROCKSALT COMPOUNDS. - Because of their magnetic properties, these have generally been thought (with the exception of UC) as having well localized 5fn configuratioys [I]. Nevertheless, the high y values, the photoehission measurements on US [51] as well as the properties of the corresponding dilute alloys (see

5

2.4) put some doubt on this simple description. This is particularly the case for UN, where the relatively small d,, value (3.5

A),

the very high y, the weak ordered moment (0.75 pB) and the small entropy at TN = 52 K (AS,

-

^0.1R ln 2) strongly suggest itinerant antiferromagnetism [52].

Recently, new arguments for the localized 5fn approach have been given, especially by neutron scattering experiments. A crystal field excited level, predicted by fitting the magnetic susceptibility with that of a 5f3 configuration, has been probably observed in UAs by inelastic neutron scattering [53].

Moreover, neutron form factor measurements on a USb single crystal [54] and on 242PuP powder [56]

give good agreement with localized configuration models in the

+

3 oxidation state. On the same hand, the magnetic and NMR ( 3 1 ~ ) properties of NpP are well explained by a localized 5f4 configuration with strong crystal-field [57]. How is it possible t o reconcile these data with the dilute alloy properties ? A first correlation can be made between the electronic specific heat coefficient y in the concentrated phase UX, and the spin fluctuation temperature Tsf in the corresponding dilute alloy (U, Th,-,)X : both decrease when going

from nitrides ( y = 50 mJ/mole/K2, T,, = 500 K ) v i a sulphides (y = 23 nT, T,,

-

^{150 K)}

to selenides (y = 9 mJ, T,,

-

^{50 K).}

We suggest then the following explanation : the RKKY interaction between actinide moments (or any exchange interaction which tends to align them) competes against the spin fluctuations. I n the compounds with large d,, and therefore small T,,, the spin fluctuations are suppressed and pure localized behaviour is observed : this is the case for

selenides where T,, 4 T , = 160 K (the Curie temperature). In nitrides (and to a less extent in sulphides), k, T,, and the exchange energy are of the same order of magnitude (

-

500 K), spin fluctuations partly subsist in the ordered phase which is barely stabilized. Under high pressure [58] or when substituting carbon to nitrogen and increasing the 5f-2p hybridization [59], the ordering temperature TN decreases very rapidly. The problem of charge state and charge fluctuations in a compound such as UN is still unsolved. Important Sf-2p covalency effects in the rocksalt compounds are predicted from the available band structure calculations [60]

and from the lattice parameter values [63]. This might explain the unusual ground state and short- range spin correlations found in USb [61].

4. Conclusion.

-

U, Np and Pu pure metals, and protactinium compounds among others, have to be considered as 5f band systems with considerable hybridization with s-p-d bands. Similarly, one finds non-magnetic dilute actinide alloys such as xi-Pu, where the local 5f state is strongly mixed with the d band. But in most cases, actinide (U, Np, Pu) impurities in metallic mitrices behave as Kondo- type impurities. When increasing the concentration and going to a pure metallic compound, the single impurity Kondo coupling competes with two effects : on one hand, the exchange interactions between moments, which may stabilize their orienta- tion and lead to ordered magnetism (i.e. U s e system) ; on the other hand, coupling between the impurity levels by direct 5f-5f or indirect 5f-(d, s, p)- 5f transfer integrals, leading at 0 K to hybrid bands, the coherence of which is destroyed at rather low temperatures (i.e. UA12). Quite similar behaviours have been suggested for several cerium intermetallics [62].

Acknowledgments. - The author wishes to thank Drs. M. Haessler, J. Gal, J. M. Fournier, H. Lau- nois, M. KonCzykowski, B. Coqblin, for useful discussions.

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C.-H. DE NOVION

DISCUSSION Dr. VILLAIN.

-

You insisted on theoretical mo-

dels where magnetism is due to Coulomb repulsion.

What is the effect of intra-atomic exchange (Hund's rule) ?

C.-H. DE NOVION. - The role of intra-atomic exchange (J,,,) on the Anderson-type impurity has not been much investigated beyond the Hartree- Fock scheme. According to Caroli et al. (Phys. Rev.

Lett. 1969) it will modify the quantitative behaviour but not the gross qualitative behaviour.

Dr. W. SUSKI.

-

What is your opinion about possibility of mixed valence state in concentrate actinide systems ?

C.-H. DE NOVION. - It could appear in systems where the direct or indirect 5f-5f transfer integrals are very small, i.e. the intermetallic distance sufficiently large (for example, not the pure metals).

High pressure dependences of the properties are needed. The concept could be more understandable at high temperatures, where in some cases the compound seems to behave as a collection of actinide impurities.

Dr. B. COQBLIN. - The concept of fluctuating valence is probably misleading in actinide metals and compounds such as UAI,, because there is no well-defined configuration f n (n integer) as in rare-

earths. It is better to speak of intermediate or mixed valence, meaning that there is a non-integer number of 5f electrons in a non-magnetic (and generally close to be magnetic) state. There would be an effect of pressure in compounds such as UAI, because the spin fluctuations have the effect of enhancing the modification due to a change in the number of 5f electrons. So, actinide metals (Np, Pu) or compounds (UAI,, USn,.. .) are essentially described by the spin fluctuation model and not by the so- called fluctuating valence models, except plutonium at high temperatures which undergoes a continuous change of valence under pressure.

C.-H. DE NOVION. - I agree with the danger of the term fluctuating valence, even for high temperature plutonium delta. But systems like (U, Th,-,)S, where the 5f-5f transfer integrals are very small, display the Kondo effect and have a reasonably defined 5fn configuration. So in principle it is not ridiculous to imagine the possibility of mixed- valence system, although one has not identified unambiguously such a system in actinides.

Pr. JOHANSSON.

-

Can we at present clearly identify an actinide compound where we can say : cr this is a mixed-valence compound D ?

C.-H. DE NOVION. - No. Only presumptions in some case.

COMMENT

Dr. F. STEGLICH. - There is evidence of parama- are strongly overdamped with an inelastic line width gnons existing in UAI, at low temperature which considerably larger than the quasi-elastic line width.

seems not to confirm a mixed-valent behaviour of Finally, the temperature variation of the quasi- UAl,. Also, we have not seen any indication of CF elastic line width is strikingly different from that of excitations by inelastic neutron scattering up to canonical MV systems with RE'S like CePd,.

50 meV. Either there are no CF transitions or they