A theoretical model in Sm1-xMxS alloys

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A theoretical model in Sm1-xMxS alloys

I. Aveline, J. Iglesias-Sicardi

To cite this version:

I. Aveline, J. Iglesias-Sicardi. A theoretical model in Sm1-xMxS alloys. Journal de Physique Colloques, 1979, 40 (C5), pp.C5-354-C5-355. �10.1051/jphyscol:19795124�. �jpa-00218909�

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JOURNAL DE PHYSIQUE Collogue C5, supplement au n° 5, Tome 40, Mai 1979, page C5-354

A theoretical model in Sm^JVLJS alloys

]. Aveline and J. R. Iglesias-Sicardi

Instituto de Fisica, Universidade Federal do Rio Grande do Sul, 90000 Porto Alegre, RS, Brasil

Résumé. — Nous présentons un modèle pour expliquer le changement, en fonction de la concentration, de la valence du Samarium dans les alliages Sitii _^XM^XS, où M est un métal de transition. Nous supposons que la bande 4f du Sm est une bande de largeur nulle avec une interaction Coulombienne {/finie. La bande d de l'alliage est traitée en CPA et un terme d'hybridation entre les électrons f et d est inclus. Nous obtenons un bon accord avec les résul- tats expérimentaux.

Abstract. — We present a model to explain the change of the Samarium valence in Sm^^M^S alloys, where M is a transition metal, as a function of the concentration x. The model considers the 4f-band of Samarium as a zero- width band with a finite Coulomb repulsion U. The d-band of the alloy is treated in CPA and an hybridization term between f- and d-electrons is included. A good agreement with experimental results is obtained.

Recent experiments performed on Sm1_xMJCS alloys [1] with M = Y, Pr, Gd, Tb, Dy, Ho, show that when the concentration x is increased the number of 4f electrons on the Samarium atoms goes from 6 (for x = 0) to about 5.3 (for x £ 0.3).

A previous theoretical calculation for Sm^^Y^S alloys, including a Vd{ hybridization between the narrow 4f band of Sm and the d band of the alloy, treated within the Coherent Potential Approximation (CPA) [2], was able to explain the Samarium valence for x < 0.3, but failed for higher concentrations.

We present below a theoretical model to explain the Samarium valence over all concentration range, taking into account a finite Coulomb repulsion between the 4f-electrons.

We consider alloys of the type Sn^ _ Jvi^S, where M is a transition metal. In those alloys, only the Sm atoms have occupied 4f states. We treat the 4f states as forming a zero width band, with a finite Coulomb interaction U. The Hamiltonian for the f-band is of the Hubbard type :

The d-band of SmS is above the 4f band. Thus SmS is a semiconductor with a full 4f band and an empty 5d band. We assume that the d band of MS overlaps the 4f band. A transfer of 4f electrons to the d band occurs for x > 0 via an hybridization term :

Hd{ = I (Fkf e** 41 4 + V* e-'k* eg <£). (4)

kiff

The Hamiltonian of the system is the sum of (1), (2) and (4) :

3Z = Hl + Hd + Hdf. (5) Using the Green's functions technique, decoupling

them in Hubbard's approximation [4], we obtain the densities of states of the d- and f-bands (full details will be given elsewhere [5]) :

The Hamiltonian for the d-band of the alloy is

where gjj are the energies of the d-electrons calculated in CPA [3]

Z(z) is the concentration- and energy-dependent CPA self energy, and a(k) is the dispersion relation for the d-density of states.

where

and

Here p°(E) is the d-density of states of each of the components :

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19795124

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THEORETICAL MODEL IN Sm,-,M,S ALLOYS C5-355

3 .O The number of f-electrons at each concentration

n,, is calculated integrating eq. (6b) up to the Fermi level, which is determined by the condition :

where nfsm is the number of f electrons of SmS and ^/ ndM the number of d electrons of MS. As p," and p;

are functions of n,-,, the integration must be done in z a self-consistent way and both magnetic and non- magnetic solutions are obtained. The non-magnetic are energetically more stable.

We have computed the density of states and the number of f-electrons per atom of Samarium as a

function of the concentration for Sm,-,Y,S alloys. ₁_/ Figure 1 shows p, and p, for a typical concentration, /

x = 0.4. We can see that the alloy is a conductor with ^2.0

'

¹ ^I ¹ ^I

0.0 0.2 0.4 0.6 0.8 a high density of f-states at the Fermi level.

CONCENTRATION

Fig. 2. - The full line is the Samarium valence, as a function of the concentration x, in the alloys Sm, -,Y,S. The broken line shows the valence after substracting the d-electrons of character f as explained in the text.

The full line of figure 2 shows the Sm valence, as a function of the concentration, calculated as :

References 4.0

3.0

2.0

1.0

[l] PENNEY, T. and HOLTZBERG, F., Phys. Rev. Lett. 34 (1975) 322;

JAYARAMAN, A., DERNIER, P. and ~ N G I N O T T I , L. D., P h y ~ . Rev. B 11 (1975) 2783 ;

TAO, L. J. and HOLTZBERG, F., Phys. Rev. B 11 (1975) 3842 ; AVIGNON, M., GHATAK, S. K. and Corn, J. M. D., J. Magn.

Magn. Mat. 3 (1976) 88 ;

GUNTHERODT, G., MELCHER, R. L., PENNEY, T. and HOLTZ- BERG, F., J . Magn. Magn. Mat. 3 (1976) 93 ;

POHL, D. W., Phys. Rev. B 15 (1977) 3855 ;

GRONAU, M. and METHFESSEL, S., Physica 86-88B (1977) 218 ; HEDMAN, L., JOHANSSON, B. and RAO, K. U., Physica 86-88B

(1977) 221 ;

OHASHI, M., KANEKO, T., YOSHIDA, H. and ABE, S., Physica 86-88B (1977) 224 and

SURYANARAYAMAN, R., Physica 86-88B (1977) 227.

[2] IGLESIAS-SICARDI, J. R., GOMES, A. A,, JULLIEN, R., COQ- BLIN, B. and DUCASTELLE, F., Physica 86-88B (1977) 515.

[3] VELICKY, B., KIRKPATRICK, S. and EHRENREICH, H., Phys.

Rev. 175 (1968) 747.

[4] HUBBARD, J., Proc. R. SOC. (London) A 276 (1963) 238 and KISHORE, R. and Josni, S. K., Phys. Rev. B 2 (1970) 141 1.

[5] AVELINE, I. and IGLESIAS-SICARDI, J. R., J. LOW Temp. Phys.

35 (1979) in press.

1.0

;

being the fraction of d-electrons below the gap, for

- ' e

2 E, E, Eo+U OaO any concentration. In this way we obtain the broken line in figure 2 for the effective Sm valence, which

Fig. 1. - The full line is the f-density of states of Sm,-,Y,S, and Can explain qualitatively the for

the broken line the d-density of states, for x = 0.4. Sm, -,Y,S alloys [I].

-

I

Zsm = 2

+

Cnfsm - (n,,

+

n , J l . (10) We see that, placing E, near the bottom of the d- band and E,

+

U near the middle of the YS d-band, , ^...

-- .,

the f-level at E,

+

U hybridizes strongly with the

\

1 ^/' \ d-band, and the valence increases rapidly as a function

I \

\ ^\\ of We have computed n,, simply by integrating x. For x 2 0.5 the valence saturates to Zsm

-

^3.p,,

'1 but, because of the d-f hybridization, a large fraction

\

\ of d electrons are of character f (compared with a relatively small fraction o f f electrons of character d).

\

\ This d electrons which are essentially localized must

\

\ be subtracted from Zsm. We estimate this number as

# k I