Non affinity of Fe2+ for B sites in iron thiochromites and compared band structures of oxides and sulfides spinels

NON AFFINITY OF Fe*+ FOR B SITES IN IRON THIOCHROMITES AND COMPARED BAND STRUCTURES OF OXIDES AND SULFIDES SPINELS Luc BROSSARD,LEON GOLDSTEIN,PIERRE GIBARTand JEAN-LOUISD~RMAN Laboratoire

de Magnktisme,

C.N.R.S..

92190 Bellevue, France

(Received 5 January 1978; accepted in revised fom

18 July 1979)

Abstract-fkparture from stoichiometry in vapor grown Fe&S, was studied using Mossbauer spectroscopy. The paramagnetic Mbssbauer spectra give evidence of two singlets and two doublets which correspond respectively to A site Fe** ++ Fe3+, Fen in Td symmetry and in symmetrylowerthan Td.The following ionic distribution has been deduced:

Compounds in the system Fer+,Cr2_,S4 have been studied for 0 GX ~0.1. The spectra are solved assuming Fe” in A site with Td symmetry, A site Fen with lower symmetry and B site Fe’+. No Fe*’ appears in B site. These features are discussed in terms of schematic band structures implying single electron narrow bands. The non-affinity of Fez+ for B sites of iron thiochromites is discussed in relation with B site C?’ level.

1. lNTRODWlTON

Magnetic and electric properties of compounds in the system Fer+,Crz-,O, (0 c x c 2) have been interpreted assuming affinity of Fe’+ for the E sites[l,2]. The sub stitution of iron to chromium can be fairly well described by the following ionic distributions: 0~~~0.69

Fe*+(Cr:t,FeylO,

0.69~~ G 1.38 (Fe:‘,Fe:‘)ICr:‘,Fe2rz,Fe:;‘lo, with y = x - 0.69 1.38cx ~2.00

(Fe:‘xl,Fe~~)(Cr:~.Fef”‘JO1.

These formulas show the appearance of B sites hopping conduction from x = 0.69 to x = 2 (magnetite). More recently, through analysis of Mbssbauer spectra the following site distribution has been established[3]:

temperature and of the saturation magnetic moment, they suggested the ionic distribution:

specially for the compositions x = 0.4 and 0.5. This excludes the presence of any Fe” and therefore of any hopping conduction on E sites. Moreover, resistivity measurements [41 give evidence of metallic conduction for x - 0.5 in contrast with the semiconducting properties of FeCr2S,[S]. Finally, room temperature Seebeck measurements show p type carriers for 0 d x < 0.4, while for x = 0.5 composition having regions of p type and some of n type are formed. Likewise, electric and magnetic properties[S] and room temperature Mijssbauer spectra[5.6] of non stoichiometric FeCr2S, have been interpreted by assuming the following ionic distribution[S]: (Fe:‘,Fe),‘)lCr:~,Fe2,‘IS4-,0,

with 22 =x - y. (1)

Details on magnetic and electric properties of these This formula shows the absence of A site Fe*+. For compounds can be found elsewhere[5]. They are p type x< 1.70 (for high values of x), small but increasing semiconductors with a low mobility of carriers. It is numbers of Fe*’ ions move to A sites as x approaches believed that conduction results from d holes[7]: never1.5. theless correlations are important, the macroscopic Robbins et 01.[4] extended their preceding work[ I] on magnetic properties (c~, u) are rather close to a purely the system Fe,+,Cr2_IS,. They studied the electronic ionic model. Then, Fe and Cr d electrons are better and magnetic properties of the compounds of this system described in a narrow d-band model than in a single ion for 0 bx ~0.5 and tentatively interpreted the results crystal field theory. Sulfur annealing slightly lowers the using the same scheme as in Fer+,Cr2-X04. Using the x resistivity p whereas hydrogen annealing increases p by dependence of the unit cell parameter o, of the Curie almost two orders of magnitude. A maximum in @jpT v.c.r.-4,16-I 669

670

I ,. BROSSARD et al.

appears

at

Tc as it does

further

raising

of r,

These

properties their

the A site

d electron.

exchange

interaction

than the Fe”(A)-Cr”‘(B) These

results

Watanabe[8] the

energy of

influenced

previous

by

the

heat

that

the

anomalous

FeCr2S4

may

Watanabe

rather

in the temperature

carrier

concentration

such as p type conductivity

These

recent

narrow

varies

ACrZSe4

is due

results[9]

of FeCr&

object

other

Indeed, a

of

and electric

described

affinity

for

previous

B sites of iron thiochromites assumptions[4-6]:

similar

spine1 for

Fe” proved

this

oxichromites[

in a

B

sites

of

is

iron

the compounds

show clearly

netic

(x = 0) of Fe*’

singlet

characteristic

Evidence

doublet

for x ~0.2.

following:

and isomer

=

for of

was

on (0~

of

Fe”

in E

parameters

to

quadrupole

In Section In

eQVzZd( I + $/3)

FeCr&

non

The

two

absorber

mylar

foils

In order

samples

spectra

the number

6. IOh at room 9.10”.

parameters magnetic)

the

be pointed

small

out.

For

level

is

at T = 77 K it is more

In this

case,

(mainly

at T = 77 K where data

the

accuracy

at the ground

while

fit of a lot of hype&e

takes

not be the case

the spectra

a physical

with

a poor

are

meaning.

ratio

This

of signal

to

noise.

Spectra the

were fitted using a least squares convolution

sorption

of

Lorentzian

lines: the general

p(u)

written

on

to the stoichiometry,

should

of counts

temperature

to the

statistical

a great

with respect

of the

instance,

would

with

of FeCr&

the quality

broadenings

at low temperature

[ 121.

to study

deviations

or linewidth

been found

for a given

form

routine

emission

describing

velocity

based

and

ab-

the absorption

u of the source

can be

as [ 131:

(2)

fY and f’ are the Mossbauer

part: preparation

Miissbauer

spectra

stoichiometric

3 a tentative between

explanation

oxide a

and

of

and com-

FeCr2S4

and

on

of relative

the f’ factor

intensities

and sulfide

single

is proposed band

solid

model

solutions

of the source

a, (i = 1,.

for

is sug

2. EXPERIMENTAL

and

Fe sites

. . , N) are assumed to be

Each peak k of each site i is defined intensity

Bit = I, for a doublet

&:

by its position

for a singlet

n = 2 and /?e = l/2.

r, and UT, are the experimental

chromium-spinels.

electron

FeInCr2-IS,

for the

factors

for the N different

identical.

sorption broadening

linewidths factor

T=(vlf’)t, samples

(I,

of the absorption

where contain

same

and

respectively.

ab

v is a

linewidth.

t is the effective the

. ..

emission

= 0.10 mm/s)

&

n = 1 and

thickness.

quantity

of

All our

“Fe

atoms

elsewhere[l4]:

the

(IO mgFe/cm2).

single crystals As

signal).

in

transducer

are the

2.1 Generalities method[S].

of “Co

velocity

between

splittings

and its normalized

Fei+,Crz-,S*

a linear

velocity

a conventional

source

= 3.00 mm/s

the experimental

on

gested.

with

In this expression:

experimental

conclusion,

the ap-

of this dou-

if existing

Fel+,Cr2-,S.+ difference

single phase

shows

splitting

2

2 reports

results

taken

temperature by

have

of the absorber:

puted

to obtain analysis

synand S.

any glue to avoid any strain in A site: local strain

induced

on

by direct

of iron, Cr&

site.

6 = 0.76 mm/s vs iron metal. Section

transport

has been

shift

the samples,

were

cold-pressed

on A site Fe*+

depth

of the paramag-

a doublet

was

prepared

X-rays

room

triangular

first

spectra

( Td symmetry)

in B site of FeCr&

quadrupole

2r

(x > 0.2)

to

case

Feln,Cr2-,Sd

in A site

The hyperfme

Fe”

the

Mossbauer

of such

has no

non-affinity

thiochromites

the evolution

of the absence

blet of dilute

not

of the solid solution

x G 2). They

Fe*’

in contrast

I, 31. This

[ 1I] by room temperature

found

that

The

(symmetrical

than is to show

des-

out on as grown

phase.

is moved

without

were

were necessary

Pd (5OmC)

in

band.

that the 3d electrons

heat

are

is the same in all crys-

mixtures

spectra

glue powdered

chalcogenide Hg, Cu)[lO]

than

by the same

CrlFe

samples

of a second

powder

cm-’

in valence

lower

different

or Hz which

obtained

for x >O.l,

Miissbauer

for the magnetic

of this work

crystals

annealings

spectrometer.

found

&

in Ref. [S]) were carried

appropriated

of

I to 2. lOI

and then are better

Several pearence

much

sec. This is much

(A: Cd,

from

polycrystals:

on an as grown

from

to holes

confirm

are accountable

and

thesis

He

K. They

under

So, the ratio

samples.

mobility.

cm*/V

in the

of

of the carrier

effect

is slightly

tals.

band approach.

The

the

single

experiment.

which

of sulfur vacancies,

(annealing

behaviour

the

range 77-200

observed

spinels

properties

of

Hall

of 0.2-0.3

which

A site Fe2’

FeCr&

Fe”’

is

due to a change

which

mobility that

from

the

FeCr&

than of the carrier

sample

than

in details

temperature

electrical

er al.191 measured

smaller

cribed

to be larger

the

in

treatment

be mainly

and a carrier

holes or

of resistivity

from

resistivity

suggests

concentration

treatments

suggestions

that the order deduced

the

the number

Fel+xCr2-xS4

with

who found

dependence

is known

and a ratio Cr/Fe

2. To modify

that Fe”

band arising

In addition,

deficiency

one.

agree

activation

A

annealing.

This creates

in the narrow

sixth

materials.

sulfur assuming

into Fe”‘.

number

Fe”

(A)-C’?“(B)

with

are well understood

in A sites are converted increases

in all magnetic

is observed

grown

were grown crystals

by vapor

display

transport

a slight

sulfur

More exponential

details

can

exp u

be in

the

found

preceding

expression

is

Non affinity of Fe” for B sites in iron thiochromites

expanded in a power serie to the second order in Ic(exp u - 1 taut bu?. Each term of the expansion is weighted by factors a and b close to 1 and 0.5 in order to describe the exponential by an accurate expansion up to second order terms. Integration is then done term by term. Iteration is done with V, ai and with the S,k values which are related to the hyperfine parameters S, H and V,,. Moreover, it is possible to assign different broadening factors vi to the subspectra i. 2.2 Non stoichiometric FeCr& (a) Room temperature Fe” Miissbauer spectra on non stoichiometric FeC& with three different heat treatments (as grown, sulfur and hydrogen annealed) are reported in Fig. 1. They look like a singlet whose isomer shift S is -0.58 mm/s. but with a rather large experimental line width r, (-0.4Omm/s).’ Moreover, some asymmetric shoulders can be seen near the base of the spectra. Experimental points as well as calculated ones are shown as the result of the superposition of two singlets and two

Non stokhiometric As grown I%x I 0.41 rnrrv3 Nr, = 7.2 IO%ounts Pmax = 16.5%

Non storhiometnc s* ameolcd rex = O.&Omm/s Nan = 6.106cc4mts PrrxIx 5 21%

H2annealed rex s 0.36mrnb Nm

s

6.106caunls

Pmax = 22%

0

Fig.

I. Room

0.2

0.4

0.6

06

I

Vmm/s

temperature Miissbaucr spectra of non stoi(as grown, sulfur and hvdroaen annealed). The solid curves (narrow line) correspond td the-different do;blcts as computed, the lower solid line the adjusted fit arising from these doublets and the points the experimental data.

chiometric Fe&S,

671

doublets. This four site solution gives a much lower mean quadratic error than that obtained in a previous paper(S]. The latter was found upon a three site reproduction ahd suggested the presence of B site Fe”; but its hyperfine parameters are not in agreement with those obtained in the system Feln,Crz-XSs which are reported in Section I. Furthermore, the absence of such a B site Fe” doublet suggests the presence of B site vacancies instead of B site iron excess as it will be discussed later on. Finally, the hyperfine parameters e, S and the normalized intensities a of the four sites are given in Table I, where r,, is the experimental linewidth. Ikcussion. The first singlet (Vzz = 0, 8 - 0.40 mm/s) is related to an equal number of Fe” and Fe3+ ions in A site, which undergo a hopping. Such a A site Fe2,” singlet has been already mentionedI I] and the frequency of the electronic relaxation between ferrous and ferric behaviour is greater than the inverse of the nuclear excited state lifetime Q+ Therefore the proportion of A site Fe3’ is equal to a,/2 and its variation with heat treatment agrees well with resistivity data. At lower temperatures (T = 77 K), electronic relaxation frequency becomes lower than 7~’ and A site Fe” characteristic hyperline magnetic sextuplet appears when computing the experimental data. The intensity of this sextublet is equal to a,/2 with the three different heat treatments (see (b)). The second singlet (V, = 0,8- 0.58 mm/s) is typical of Fe” in regular tetrahedron (Td local symmetry): in a single ion crystal field approach, it is well knownIl that the degeneracy of ground electronic state ‘E is lifted by second order spin-orbit coupling. In the absence of magnetic exchange interaction, ‘E is split into five equally separated levels, i.e. a singlet A,, a doublet E,a triplet T,, . . .. In the case of rapid electronic relaxation on each of these levels, the mean value of the electric field gradient (E.F.G.) operators is zero. This gives a Boltzmann’s thermal average value of Vzz also equal to zero. In fact, the single ion crystal field theory is good for very dilute ions and a valid approximation for insulators (spine1 oxides for example). In the present case, the semiconducting properties of FeCr& make a sixth 3d electron narrow band to be more suitable for describ ing them[7]. This is especially true in the temperature region where the compound shows its carrier’s concentration maxima (90< T< T, and T> 250 K). To our knowledge, theoretical calculations of the temperature dependence of the mean value of hyperfine parameters (hyperline magnetic field H, principal component V,, and asymmetric parameter 11 of the E.F.G.) in a single electron narrow band model have never been performed so far. These calculations should explain the cancelling at T> T, of the Vzz created by the sixth 3d electron narrow band of Fe” in Td local symmetry, in a similar fashion as done for Fe2+ ion with the crystal field theory. The two doublets (S - 0.56 and 0.62 mm/s) are related to those Fe” in A site whose local symmetries are lower than rd: these iron atoms are surrounded by the non cubic configurations (4s and I ICI-‘+, 3s and 12Cr”. . . ). These different local configurations around A site Fe” are simulated by these two doublets.

L. BROSSARDet al.

672

Table I. Hypertineparametersand normalisedintensitiesof non stoichiomet~cFeCr& at room temperaturewith: 6 = (eQV,&4)\/[I + ($/3f); 6 = isomer shift/iron metal (unit = mm/s); f’, is the experimental linewidth measured at half depth of the spectra: (*cl = 0 and cz = 0 have been imposed during the fits)

T = 300

FeCr254

K as grown

r ex MS

0.40

Ii2 annealed 0.36

.oo

.oo

.37:.02

.40~.01

.38+.02

.05+.01

.08+*Ol

.03+.01

4

.CO

.oo

.oo

i

.584+.005

.590+.005

.!j84+.005

.670+.005

.630+.005

.i300+.005

.12+.02

.11+.02

.13:.02

.61+.01

.62,.3i

.f2+.Ol

.16+.01

.ii+.Ol

.101.01

.37+.X

.35+.02

.38+.G2

.56+.01

.57T.3’ *

.57:.Cl

iZc.31

:Zy.Oi

.G71Jl

6. 1

a1

Fe:'

annealed

.oo

G Fe'.!j+ A

S

0.41

2

Tdsymnetry "2

Fe;+ SYm

lower than 'd

‘4 E4 =4

The fits reported on Table 1 give the least quadratic error and can be considered to the best: the reliability of our fit Function F(B) is a chi-squared (x2) Function with m-n degrees of Freedom, with m and n: the number of channeis and of independent parameters [ 141.For m-n z 100, x2 Function can be approximated by the normal Function D: D = {F(b) -(m - n)}/Vt2tm - n)). In the fits reported here, D is divided by about 3 compared with previously reported results[S]. Our results suggest the existence of Fe’+ and F$” in A site, of sulfur vacancies and even of cations vacancies. The general Formula is written:

with 2z=3x-2g-2~. The experimental values of the intensities a~ and a~ (Table 1) can be related with x, y and w through the binomial law assuming a statistical distribution of the ions and vacancies a,=2y a2 = (I- cr,)P,

with

POOis the probability of finding 45 and 12C?+ as nearest neighbours and next nearest neighbours of A site Fe For the corresponding values of x and w. This gives x = 0.03?0.01, z =0.02-0.035~0.01 and w =O.Ol~O.Ol. In the remaining discussion w will be omitted. This conclusion of an absence of B site Fe*+ in iron thiochromites is supported by the Fact that sulfospinels containing metal vacancies are easy to prepare[l6]. Moreover B site vacancies have been also advanced to explain Miissbauer spectra of non stoichiomet~c Fe301[17] and Fe&[ IS]. (b) Low temperature Miissbauer spectra. The three typical samples were studied at 77 K. The spectra are shown in Fig. 2 with the unsoured spectrum 2d of stoichiometric sample For comparison. Before discussing the fit results reported on Table 2 it is necessary to remind those obtained on stoichiometric FeCr2S,,. More details can be found elsewhere[I9]. The main suggestions are the following: in order to take into account the differences between the linewidths of the peaks as well as the deviations between the experimental and the calculated nuclear transition probabilities, two subspectra of equal intensity and of equal isomer shift 0.72 mmls are necessary to fit the spectra at ‘I’5 77 K. They correspond respectively to:

and eQVzz = + 0.23 mm/s 4

Non affinity of

673

Fe*’ for B sites in iron thiochromites quadrupole

96

interaction

e,,,

-0.215 mm/s in the magnetic

state, with 94

eQVZZ

lln =8-(3cosZB-ltnsin2Bcos2~). 92 97

95

97

95

‘97

192

167 -6

-4

-2

0

2

4

6Vmn

Fii. 2. Compared Mossbauer spectra of non stoichiometric and stoichiometric FeCr& at ‘F = 77 K. (a: as grown, b and c: sulfur and hydrogen annealed: d: stoichiometric). Solid curve correspond to the adjusted fit and points to the experimental data.

for the first one and

and eQvzz - -0.19mmls -4 for the second. This leads to observe the same nuclear

The two subspectra have different magnetic hyperfine held H (204 and 210 kOe). This fit can be interpreted with the aim of the sixth 3d electron narrow band picture of Td local symmetry Fe” in connection with a slow relaxation model of this electron between the (x2 - y’) and the hybridized (see Section 3.1) (3z2- 3) orbitals leading to the two preceding subspectra. Now we can discuss the results of the fits of the non stoichiometric samples (Table 2). Four groups of sites were necessary to fit the experimental spectra: The two first sites correspond to Fe” with Td local symmetry in the first neighbour shell. Their hyperfine parameters are equal to those of stoichiometric Fe&S. The intensities of these two sites have been assumed to be equal when computing the spectra. The following site has a magnetic hyperfine field lower than Fe” A in r, symmetry. From the intensity values of this site (see further discussion), it is believed that it represents probably Fe” A in Td symmetry with Fe” ions as nearest neighbours. The following three sites have magnetic hypertine fields greater than Fe” A in Td symmetry. Moreover, their linewidth r, is much larger than for the first site group. This probably indicates that these sites should more conveniently be described by a distribution of hypertine parameters due to a statistical repartition of sulfur vacancies or/and Cr vacancies. They induce an axial symmetry which lowers the Td symmetry and increases the values of H compared to the first site[20]. The last site with the highest magnetic hypertine field corresponds to Fe” A. It is supposed that at 77 K, the A site hopping is almost completely quenched.

Table 2. Hypertine parameters and normalised intensities of non stoichiometric FeCr,S, at T = 77 K with c, = (eQVJ8)43 co? 0 - 1 t n sin’ Bcos 2~) where 11 is the asymmetry parameter of the E.F.G. and 0 and cp are the polar angles of the hypertine magnetic field H in the principal axis of the E.F.G.

L. BROSSARD et al.

674

The intensities a of Table 2 are consistent with the room temperature data (see ai values in Table 1). First of all, the total intensity of the three sites of Fe” A in symmetry lower than Td has been imposed to be equal to the total intensity (a3+ a4) of the two corresponding sites at room temperature. Then, the intensity of the Fe” A site has been chosen so that the outerpart of the spectra is fitted at best. With y as the fraction of Fe3’ A site, the respective intensities of Fe” A group in Td symmetry without and with Fe3’ n.n. have been assumed proportional to (1 - y)’ and (1 - (I - y)“). It should be pointed out that the three sites of Fe” A with symmetry lower than r, simulate in fact a distribution since the adjustment of the less intense sub spectra at the left hand side of the spectra is relatively poor. Then, these fits are only one of many possible interpretations. But, these fits lead to the best mean value of the quadratic error, thus it is the best self consistent solution. Moreover, they are in agreement with the room temperature data. Since both sets of data at 77 and 300K are consistent, they can give a formal basis to the distribution of Fe”, Fe” and vacancies in non-stoichiometric FeCr& 2.3 Miissbauer study of Fel+xCr2-rS4 (x ~0.1) The absence of B site Fe*+ doublet is once more obvious in the room temperature Miissbauer spectrum of Fe,.,Cr,.& (Fig. 3): this constitutes an extension of the preceding study and allows us to suggest the non affinity of Fe*+ for B sites of iron thiochromites which will be interpreted later on (see Section 3.1). Thus, we must look to give a reliable analysis of the Massbauer spectra compatible with the magnetic and electric properties of Fel+xCr2_xS4[4]. The substitution of iron to chromium can occur in two ways a pion’: The first one supposes that Fe*’ and Fe” are in B site, and that hopping between them occurs as observed in Fel+,Cr2-,Oa for 0.69 zzx z~2.00[1]. If it is so, we get

(Fe:‘~2Fe:;)(Cr:‘,Fe~.~+lS,.

(3)

In order to reproduce the experimental variation of the saturation magnetic moment ~[4], we can use the neutron diffraction data on FeCr2Sa[21] and Fe,.2Crl.sS~[221 which give: p(FeZ,‘) = 4.2~~

and

AC&)

= 2.9~~.

By assuming &Fe3+) = SC(~,we obtain U= = (1.52 t I .34x)p,. This formula describes satisfactorily the experimental values of u= only for x 5 0.1; for x > 0.1 it is necessary to take into account additional B site vacancies. The second one assumes the presence of Fe3’ and vacancies in the E site instead of Cti+; on this basis the solid solution can be described as (Fe:‘3,Fe::)lCr:‘,-,Fe~+O~lS~.

It will be seen now that this ionic distribution is the mbit probable in connection with the experimental[4] variations of U_ and with the tendency to metallic behaviour as x increases. The variations with x of V- lead to the following variations of y and of the ions concentrations in the two sites (Table 3). It must be noticed that this ionic distribution gives an exact reproduction of the saturation moment variations for all X; this was not the case for the distributionL41 assuming B site Fe”. Moreover, for x = 0.5, IFe’+J,, = IFe2+IA.This is in agreement with metallic conduction and with the fact that regions of compound are of p type and some others of n type: this can be interpreted by assuming that the sixth 3d electron narrow band of A site Fe*’ is half-filled for x = 0.5 and that substitution of Fe to Cr lowers the Fermi level.

Fe,,%% T amb N,*3.6 06cps Pmox=Il5%

.;: _

0 Fig.

0.2

04

(4)

0.6

06

I.0

Vmm/s

3. Room temperature Miissbauer spectrumof Fel~lCrl.&4.m experimental data, and 3 = calculated subspectra.

X =

theoretical curve. I, 2

615

Non affinityof Fe” for B sites in iron thiochromites Table 3. Variations

with x of ions concentration

1.762

1.884

in Fe,.,C&,Sc

1 .L85

1.629

1.333

Table 4. Calculated intensities (I, of the elementary Mijssbauer spectra in Fe I.rCr2-IS~ (x = 0.05,O.l). are deduced from the binomial law assuming a statistical distribution

Theoretical intensities

x =

0.05

x =

0.1

I

Ol

I

C.65

I

I

=

3Y

I+X

and

ad=-

I

0.42

I

I tx’

Figure 3 shows the fit between the room temperature experimental and calculated Mossbauer spectra of the Fe,.,Cr,.& composition obtained by the superposition of three elementary spectra corresponding to the following hyperhne parameters (Table S(a)). Iteration steps did not accept a fourth singlet of A site Fe*.” or a slight doublet or a singlet of A site Fe3’ whose isomer shift should be equal to -0.18mmls; the agreement between the experimental and calculated intensities of A site Fe2’ should be noticed. In order to conlinn these results we have performed a Miissbauer spectrum of Fe,.iCr,.& in the paramagnetic region at T = 225 K. The spectrum is very similar to that obtained by Van Diepen er a/.[21 at the same temperature on Fe,.&ri.&. Table 5(b) gives the values of the hypertine parameters and relative intensities of the computed spectrum. The strong variation with temperature of the quadrupole interaction of the low symmetry Fe’+ A is related with the Boltzman occupation of

a3

I 0.45

I

0.02

0.28

I

Now, the binomial law assuming statistical distribution of ions leads to the following calculated intensities ai of the four elementary Miissbauer spectra (Table 4) with

a3

a2

I

The values

a4 0.05

I o.c4

I

0.09

the multielectronic levels. On the other hand, the ab sence of a temperature dependance of the quadrupole interaction of the B site Fe3+ shows its origin from the lattice. At 77 K. the magnetic spectrum is very complicated due to the presence of Fe3+ B and enhanced effect of nearest and next nearest neighbours. Nevertheless, Fe” B can be clearly distinguished (a =0.13*0.03), l,,, = -0.04 * 0.03, S = 0.42 2 0.03, H = 322 * 4 kOe). These results favour the presence of Fe” and vacancies in the B site of the system Fel+XCr2_XS4.They constitute a coherent extension of the preceding study of non stoichiometric FeCr& which is characterised by B site vacancies. It should be emphasized the difference existing between the oxide spine1 Fel+,Crz-,O., and the preceding system characterised by a mixing of spine1 and NiAs phases for x ~0.5: contrary to the first solid solution, there is no continuity with x between FeCr& and Fe3S.+ Therefore hopping on the B site suggested to explain the properties and Mossbauer spectra of Fe3&[17] has no physical reason to exist in Fel,,Crz-,S,. Moreover, it is plausible that the B site vacancies are accountable of the phases mixing for x > O.S-and of our difficulty to obtain single phase compound-as soon as the B site vacancies amount becomes important and greater than -8%. 3. INTERPRETATlON 3.1 Non ajinity of Fe” for B sites of iron thiochromites In oxide spinels, the magnetic and electric properties of insulators are generally well described on the basis of

676

L. BROSSARDet al. Table 5. Experimental

values of hyperfine parameters and relative intensities of the elementaries spectra of Fe,&, & (Sa: Tirmht5b at T = 225 K)

Miissbauer

(al T

amb

x = 0.1

clml/s E mn/s

:

Experimental Intensities

3+

Fez+ A Td symnetry

Fe B

1

Lower synrmetry

3.00

0.35 2 .a2

i).1e* .02

0.58+.02

0.55t.02

3.302.02

0.42: .02

0.46~ .02

3.12+ .32

1

T = 225°K x =

0.1

cmn/;

Experimental intensities

Fe: Td symneti-y

0.00

0.45 _ + 0.2

the single ion crystal field theory. Multielectronic states indicate that 3d electrons are localized on each atomic site. From this point of view, it is well known[23] that the “T2, level of R site Fe2+ is lower in energy than the ‘E level of A site Fe*+; the energy difference between them is equal to 2AJ15, where As is the cubic crystal field splitting observed at the B site (AB- lO’cm-’ in oxides). Such a trend explains the experimental tendency of Fe2+ to occupy the_ B sites of the solid solution Fe&&,Oa. On the other hand, the non affinity of Fe2+ for B sites of Fel+,Cr2-,S, and of FeIn,Cr2-XS4 (x ~0.2) requires some explanations; moreover it should be emphasized that the difference between these systems and Fe&,-in which Fe2’ is present on B sites-is due to the presence--or absence+f chromium on these sites. If insulating properties of FeIn2S. justify localised d electrons on B site Fe2’, the semiconducting properties of preceding solid solutions derived from FeCr2& suggest a small mobility of the carriers for A site Fe2’: these 3d electrons can be described in a suitable way by one electron narrow band[24] including the 3d degenerate case; its bandwith W is proportional to the product of the z number of B site n.n. (z = 12) with the transfer energy I from A to B site of the sixth 3d electron. Its tendency of delocalisation has been shown[7] and these transfers between A through B sites can be real or virtual: in the case of FeCr2S* they are real when the mobility is non zero in the temperature region where the

Lower synsnetry

0.49 + -02

0.17 + 0.2

3.42 _ + FJ.2

resistivity is minimum. These transfers can be realised by the following superexchange interaction Fe(A)-S-WBtS-Fe(A).

(5)

Indeed, Baltzer et a/.[251 have shown using high temperature expansion of the susceptibility that in ternary spine1 two kinds of interaction do exist: the positive Cr-SCr interaction and the negative Cr-S-Fe-S-Cr. Existence of more distant exchange interaction gives rise to different types of magnetic order: ferromagnetism (CdCr2S4),helimagnetism (HgCr2S,), antiferromagnetism (ZnCr&). The importance of these more distant interactions has been experimentally proved by supertransferred hyperfine fields on A site. In the present case, the interaction[S] insures the antiparallel coupling between the net moments of Fe” and Cr”‘. Moreover the sixth 3d electron of A site Fe” can be transferred in B site without changing its spin direction. Indeed ifs spin is parallel to the resulting one of 0”’ and its transfer therefore promotes a ‘E, CiL’ high spin excited state in weak octahedral field[26]. The relative ionic energy levels of such ion states in some thiospinels can be considered in Fig. 4. They have been obtained on the basis of optical absorption or activation energies deduced from resistivity measurements. Let us consider the ground state of our system, obtained in absence of electronic transfer: it is constituted by single electron narrow bands centered on ‘E

671

L. BROSSND et al. Energy

site A

b)

T siteB

@_____ B site

A site Fe”

_______- lop of s*valence band. -2.0

I

LA2g Cr3+

Fig. 4. Energy of ground state multielectronic levels of some cations in thiospinels(from Ref.1241).

A site Fe*+ and ‘AZ, B site Cr’+ levels; the excited state is obtained by transferring the sixth A site Fe” 3d electron in the narrow band centered on ‘E, C? level; let us label U the energy difference between the ‘E level of A site Fe*’ and ‘E,\B site C?. U has been estimated by Goodenough [7] to about 0.08 eV which results from the activation energy 0.04eV measured by Bouchard et al.[27] with sintered sample. A perturbation treatment involves an energy lowering of the ground state of the system by its coupling with the excited one, the energy diminution being equal to -(f*/U), with t 4 U. This approach is in fact a simplification of our physical prob lem since the d narrow bands are not rigorously single electron one but are doubly degenerated; one can simulate this by the following picture, where dashed lines represent preceding excited configuration:

Nevertheless, the following assumptions can be done: (a) U can be sufficiently weak so that the narrow band centered on ‘E level of A site Fe*’ should be lower than the ‘T,, E site Fe*’ level: to support this assumption, it is necessary that B site Fe” should be described by multielectronic levels implying that Fe*’ 3d electrons (if they exist) remain localised on B site; if this was not the case, they should be described by a narrow band whose energy lowering by mixing with excited C?+ band should be similar to that obtained presently in A site. In such a case, the two narrow bands centered on the ‘E and ‘Tt Fe*+ levels should be affected by an analogous energy decrease and the oxide situation should be encountered. (b) If U is much more smaller, the A site Fe*+ narrow band can hybridize with the B site Cr*’ one. It seems that it is necessary to put forward such a model to explain the low temperature Mossbauer spectra of stoichiometric FeCr2S., ([ 191and Refs. therein) specially on both sides of the second order phase transition temperature (IO K). In conclusion, we can assume that the presence of C?+ on B site of semiconducting iron thiospinels lowers sufficiently the sixth 36 electron narrow band of A site Fe*‘, so that Fe*’ has no affinity for B sites. 3.2 Single electron narrow band structures of solid SOL lions Fer+XCr2-XS4and FeIn,Cr2-IS4 These single electron narrow band structures are derived from the preceding assumption and are coherent with the band structure of the system Fe, .,Cu,CrzS4 (0 d x d I) [7,28] which interpret satisfactorily the magnetic[29] and electric measurements and Miissbauer spectra[30,31] too. The Fig. 5(a) shows the band structure of the solid

XLO.2

x,0.2 Fe In,, Cr2_x S4

Fig. 5. Band structure of

Cr”

Fer+,Cr2_,S4and FeIn,Cr2_xS,(‘F> r,).

x,2

678

L. BROSSMD et al.

solution Fel+XCr2_xS4: the Fermi level EF decreases with x, so that Fe” are going in B site; for x = 0.5, the A site Fe” band is half-filled as expected from the metallic behaviour of the compound. The Fig. 5(b) shows on the contrary that the Fermi level of the system FeIn,Crz_,S4 is increasing with x: for x > 0.2, Fe*+ appears in B site; the band structure is coherent with the fact that the compounds are of p type for x < 0.2, of n type for x = 0.2 and insulating for x = 2. These figures are drawn for T > T,; for T< r,, the magnetic order splits the valence band and those of the magnetic cations. These band structures are based on the assumption of intrinsic conduction. Non stoichiometric FeCr2S4 study (section 2.2) has shown that electric properties are modified in a quantitative fashion by method of preparation: possible additional vacancies levels lying between the one electron narrow bands of A site Fe*+ and E site C?’ are not taken into account in the preceding description. Acknowledgement-The authors wish to express their thanks to Dr. P. Lederer and M. Heritier for helpful discussions.

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