Electronic structure of 3d impurities in ferromagnetic iron

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Electronic structure of 3d impurities in ferromagnetic iron

P. Léonard, N. Stéfanou

To cite this version:

P. Léonard, N. Stéfanou. Electronic structure of 3d impurities in ferromagnetic iron. Journal de

Physique, 1982, 43 (10), pp.1497-1502. �10.1051/jphys:0198200430100149700�. �jpa-00209531�

Electronic structure of 3d impurities ⁱⁿ ferromagnetic ^iron

P. Léonard and N. Stéfanou

Laboratoire de Magnétisme ^et de Structure Electronique ^{des Solides} (*), Université Louis Pasteur, 4, ^{rue Blaise} Pascal, ⁶⁷⁰⁷⁰ Strasbourg Cedex, ^France

(Reçu ^{le 17} février 1981, révisé le 17 mai, accepté ^{le 10} juin 1982)

Résumé. 2014 Nous présentons les résultats du calcul de la structure électronique ^des impuretés (Ti, V, Cr, Mn, Co, Ni, Cu) ^diluées dans le fer ferromagnétique ^obtenus par la méthode des combinaisons linéaires d’orbitales ^« muffin- tin » dans l’approximation ^{de la} sphère atomique (LMTO-ASA). ^{Les moments locaux et les} champs hyperfins

sur l’impureté ainsi que les changements ^de coefficient de chaleur spécifique électronique ^sont comparés ^aux

résultats expérimentaux.

Abstract.

We present the results of the calculation of the electronic structure of impurities (Ti, V, Cr, Mn, Co, Ni, Cu) diluted in ferromagnetic iron obtained by the method of linear combination of « muffin-tin » orbitals in the atomic sphere approximation (LMTO-ASA). ^{The local moments and the} hyperfine ^{fields on the} impurity

and the electronic specific ^heat coefficient charges ^are compared ^{with the} experimental ^data.

Classification Physics ^Abstracts

71. 20

1. Introduction.

The study of the electronic structure of iron alloys with transitional impurities

has been the subject ^{of numerous} experimental ^and

theoretical works. The electronic structure of the

alloys ^{of a weak} ferromagnet ^{such as iron is not as}

well understood on the whole as the electronic structure of the alloys ^of strong ferromagnet ^{such as}

Ni or Co. The quantitative theoretical study ^{of the}

dilute iron alloys requires ^{therefore a} precise ^know- ledge ^{of the structure of the} ferromagnetic ^iron

where the s-d mixing ^{and the} splitting of the sub- bands are essential. Moreover, the method used must be able to take into ^account the scattering

of the Bloch waves of the matrix by ^the impurity.

It has been shown recently ^{how the LMTO-ASA}

method extended to the case of dilute alloys [1, 2]

allows these requirements ^{to be met without} requiring

excessive numerical calculations while taking fully

account of the spectrum of the valence electrons of the matrix.

In section 2, ^{we recall} briefly how the electronic structure of the impurities is obtained with the LMTO- ASA method and in section 3, the results for the Ti, V, Cr, Mn, Co, Ni, ^Cu impurities diluted in iron are

presented ^{and discussed.}

Section 4 is devoted to the conclusion.

2. Electronic structure of dilute alloys Ee(Ti, V, Cr, Mn, Co, Ni, Cu).

^{2.1 GENERAL} DESCRIPTION OF THE MODEL.

It has been shown recently ^how

the LMTO-ASA method can be extended to the

case of dilute alloys [1, 2]. ^The impurity potential ^is

localized on the impurity ^{cell and we take into account} fully the self-consistent electronic structure of the matrix. In the LMTO method, the electronic density

on the impurity ^{site is} given by :

(*) ^{LA au C.N.R.S. no 306.}

In this formula, ^all primed quantities ^{refer to the} impurity.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198200430100149700

1498

-

nL(E) ^{is the} partial density ^{of states of the matrix} relating ^{to the} representation ^L

{ 1, m } ^{of the} symmetry point group of the crystal;

-

RL (r, E) is the normalized wave function,

solution of the Schrodinger equation ^{in the} impurity cell ;

where the derivative is taken at the « muffin- tin » sphere ;

, where ^the energy Ef is defined by DI(E*) I - ^{1. In the}

atomic sphere approximation (ASA), the « muffin- tin » sphere ^is replaced by ^the Wigner-Seitz sphere.

In this formulation, ^{the main} advantage ^{on the}

Green’s function method is that the quantities ^which depend ^{on the} energy, such as the wave functions and their logarithmic derivatives at the atomic

sphere, ^{are evaluated} by ^a restricted expansion ^from

the parameters ^{of the} potential determined once

for all [3].

The change of the number of states between the

alloy and the matrix is, ^{for an} energy smaller than E,

where

-1 17; (0) andItl,(O) ^{are the} numbers of bound

7C l( ) _7T ( )

states of L symmetry ^{for the} impurity ^{and matrix} potential ;

If Az is the difference between the atomic numbers of the impurity and matrix atoms, the Friedel screening

rule is :

where EF is the Fermi level.

In the formulae for p’(r, E) ^and AZ(E), ^the spin

index is dropped.

2.2 THE ELECTRONIC STRUCTURE OF IRON AND THE IMPURITY POTENTIAL.

The self-consistent elec- tronic structure of iron, calculated by ^{the LMTO-}

ASA method, has been described previously [4, 1].

In order to determine the impurity potential, ^first

we consider a fictitious non-magnetic crystal ^with

the body centred cubic structure. Its parameter ^is that of ferromagnetic ^{iron. It} is built of atoms of the

same chemical species ^{as the} impurity. ^{Thus, we}

calculate the self-consistent ^« muffin-tin » potential ^V

of this metal in the canonical version of the LMTO- ASA method which neglects ^the hybridization ^{of the}

different symmetry ^{states. In this} way, ^we take partial

account of the surrounding ^{of the} impurity ^{in the} alloy. ^The impurity potentials ^seen by the electrons of different spins ^{are obtained} by ^the simple ^addition

of constants :

These constants are adjusted ^to satisfy the Friedel

screening ^rule

and the change of the observed saturation magneti-

zation

where c is the atomic concentration of impurities.

With these constants, the effect of the polarization

on the impurity ^{site due to} surrounding electrons of different spins is taken into account. Even though

our impurity potentials ^{are localized on the} impurity cell, they ^are determined by ^a self-consistent condition which takes into account the electronic screening

inside and outside the impurity cell. Our results are

given ^{in the table I for the} Ti, V, Cr, Mn, ^Cu impurities.

For these impurities, ^{we have} represented ^the partial (T25 ^and F12 symmetries) and total densities of states

on the figures ^{1, 2 and 3.}

3. Analysis ^{of the} results and discussion.

3.1 Fe(Ti, V, Cr, Mn, Cu).

^The comparison ^bet-

ween the total densities (Fig. 1) ^{and the} partial (F’ 25

and F12) ^densities (Figs. ^{2 and} 3) displays ^the impor-

tance of the d states for the screening ^{of the} impurities.

Results obtained may be analysed ^{as follows :}

-

The screening ^is essentially realized in the T

sub-band for the impurities ^on the left of iron in the periodic ^{table, so that :}

and the _average magnetization ^{of the} alloy ^{can be}

written approximatively

We find again ^the phenomenological law deduced from the measured magnetizations for these impu-

rities. For Cu impurity, ^the screening ^{is built in} the 1 ^sub-band.

-

The impurity ^{d states} appear ^as peaks ^{in the}

Table I.

Screening of ^the impurities for ^the alloys Fe(Ti, V, Cr, Mn, Cu). Caption : ^{C : constant} potential.

ns, np, ^nd, Nimp : ^{numbers of electrons with, s, p,} d symmetry ^{and total} number of ^{electrons in the} impurity ^cell.

Zs(EF), AZp(EF), AZD(EF) : ^s, p, d components of ^the impurity charge. dj:tjdc Ic-0 : change of saturation magne- tization per impurity.

local density ^{of states on the} impurity site. These

peaks ^are located either below (e.g. Cu 1) ^{or in} (e.g.

Cr 1) ^{or above} (e.g. Ti) ^{the band.}

For the T12 symmetry, ^the peaks ^{of the} density

of states T ^{are located, on} both sides of the Fermi level (EF = ^0.702 Ryd.) ; ^{Ti 0. 8} Ryd. ;

V 0.74 Ryd.; ^{Cr and Mn :. rr 0.70} Ryd.;

Cu 0.6 Ryd. The densities of states I present

two peaks : ^one peak ^{has an} energy in the vicinity

of the maximum of the iron density ^{and another} peak lies in the vicinity of the bottom of the band

(Ti, V, Cr, Mn) ^{or below} (Cu).

For the F’ 25 symmetry ^{and for} the T sub-band,

we observe also resonant states in the vicinity ^{of the}

Fermi level (Ti, V, Cr, Mn). ^For the I sub-band,

the common salient feature is a very weak density

of states at the Fermi level for each impurity. ^Other

resonances are also present. One, ⁱⁿ particular,

located at about 0.56 Ryd., ^{is related to a hole of} density in the matrix.

-

In each _case, as it should be, ^{one observes a}

shift of the states towards the lower energies ^{when the} potential ^{becomes more and more} attractive.

By subtracting the number of T and I ^electrons

on the impurity, ^we calculate the local moments

These are essentially ^{due to the} polarization ^{of the d}

electrons and it is remarkable that they ^are in very

good agreement with the measured moments even

though ^the impurity potential ^is being ^determined only by ^the average magnetization ^{and the} screening

rule.

1500

Fig. ^1.

T25 partial densities of states for iron and its

alloys.

Once the impurity potential ^is determined, ^the

contribution to -the contact interaction to the hyper-

fine field on the impurity for the band states is calculat- ed :

Though ^{it is not} possible ^to neglect ^the polarization

of the deep ^{states of the} impurity, ^it appears that the calculated field has the correct magnitude compared

with the measured field (Table ^{II and} Fig. 5).

In the case of Cu where the local ^moment is zero

and where it is expected that the contribution of the band states is dominant, the calculated and observed fields are very close. Our calculated hyperfine ^field

in the case of Cu is comparable ^{to the value obtained} by Yoshida et al. [15] who determined the electronic structure of non-magnetic impurities diluted in ferro-

magnetic ^iron by KKR method.

The measurement of the electronic specific ^heat

Fig. ^2.

F12 partial densities of states for iron and its

alloys.

of the alloy gives ^the density ^of states at the Fermi level. Effectively, ^the change Any of the coefficient of electronic specific ^heat y is, ^{for a} concentration c of

impurities,

where n(E) is the electronic density ^{of iron. The}

presence of _very narrow resonant states in the vicinity

of the Fermi _energy is responsible ^{for the} large ^observed

variations of _y (Table ^{II and} Fig. 6). ^{For the} impurities

to the left of iron, the variation of the displaced charge

with the _energy is _very important ⁱⁿ the T ^{sub-band :}

it results from the competition between the large

contribution of the T2 5 ^states with the contribution of the F12 ^{states which} changes ^the sign ^{when these}

states go ^across the Fermi level. Due to very large

variations of the generalized phase ^{shifts at the}

Fermi level, ^our quantitative results should be

considered with care. Nevertheless, ^we think that the

Fig. ^3.

Total densities of states for iron and its alloys.

Fig. ^4.

^{Local moments on the} impurity site in iron

alloys : A theoretical values; ⁰ experimental ^values.

large variations of _{y are} really ^{related to the} presence of the F, 2 ^and F2’5 resonant states in the T ^sub-band

at the vicinity ^of EF.

Fig. ^5.

Hyperfine ^{fields on the} impurity site in iron

alloys : A theoretical values; ⁰ experimental ^values.

Fig. ^6.

Change of the electronic specific heat coefficient in iron dilute alloys : ^A theoretical values; 0 experimental

values.

3.2 Fe(Co, Ni).

^{In the case of Co and Ni, it is}

not possible ^to satisfy the conditions of _average

magnetization (d/1/dc [_o - I JlB/at.) ^and screening

with a couple ^{of constants C t and C I} coherent with those of the other impurities. Consequently, ^{it is not} possible ^{to find a local} screening for Co and Ni intermediate between Mn and Cu. It follows that the modification of the potential ^{due to the} impurity

must be extended to its near neighbours. ^{This modi-}

1502

Table II.

Hyperfine fields ^and change of ^the electronic specific ^heat coefficient ^{in iron} alloys.

fication is furthermore suggested by the deviation to the local neutrality obtained for the other impurities (in electrons) ; ^{Ti :} 0.3 5 ; ^{V :} 1.21; ^{Cr :} 1. 54; ^{Mn :} 1.57;

Cu : - 0.21 (Table I). The effect of the perturbation

on the near neighbour ^sites will be the subject ^{of a} forthcoming ^work.

4. Conclusion.

We have calculated the electronic structure of alloys Fe(Ti, V, Cr, Mn, Co, Ni, Cu) by ^the LMTO-ASA method taking ^{account of the}

self-consistent electronic structure of the ferromagne-

tic iron and of localized impurity potentials. ^The impurity potentials ^are adjusted ^{in order to} satisfy

the screening ^{rule and to} give the measured _average

magnetization. ^It follows that the calculated values

of the local moments and hyperfine ^{fields on the} impurity and the coefficients of the electronic specific

heat are comparable with the measured values.

The electronic structure is dominated by the presence of resonant d states.

The case of Co and Ni cannot be studied in the

approximation of localized potentials ^and requires

consideration of the extension of the potential ^outside

the impurity ^cell.

In conclusion, taking ^account of the results obtained elsewhere for the alloys Fe(Al, ^{Si, P, Ga) [1], our}

model gives, ^{on the} whole, ^{a rather} good ^under- standing ^{of the structure of} s-p and d impurities

diluted in ferromagnetic ^iron provided ^the screening

of the impurity ^{is localized on its site.}

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