MAGNETORESISTANCE OF FeS1.14 SINGLE CRYSTALS FOR B // c

HAL Id: jpa-00229087

https://hal.archives-ouvertes.fr/jpa-00229087

Submitted on 1 Jan 1988

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of

sci-entific research documents, whether they are

pub-lished or not. The documents may come from

teaching and research institutions in France or

abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est

destinée au dépôt et à la diffusion de documents

scientifiques de niveau recherche, publiés ou non,

émanant des établissements d’enseignement et de

recherche français ou étrangers, des laboratoires

publics ou privés.

MAGNETORESISTANCE OF FeS1.14 SINGLE

CRYSTALS FOR B // c

E. Vitoratos, S. Sakkopoulos

To cite this version:

JOURNAL DE PHYSIQUE

Colloque C8, Supplement au no 12, Tome 49, decembre 1988

MAGNETORESISTANCE OF

FeS1.14

SINGLE CRYSTALS FOR

B

//

c

E. Vitoratos and S. Sakkopoulos

Department of Physics, University of Patras, GR-261 10, Patras, Greece

Abstract. - Measurements of the transverse magnetoresistance on natural single crystals of pyrrhotite FeS1.14 revealed a phenomenon of the order The shape of the curves Ap/ p (0) vs. B for different temperatures is explained and the magnitude of the magnetoresistance can be adequately forseen by the s-d model.

T h e o r y a n d material

A quantitative theory of magnetoresistance in heavily-doped antiferromagnetic semiconductors has been developed by Nagaev et al. based on the s-d

model [I, 21. The basic idea is that indirect exchange via the conduction electrons tends to establish a ferro- magnetic ordering a fact that differenciates the mag- netization of regions of unequal electron concentration due t o impurities 131. These spatial fluctuations of magnetization cause a particularly strong scattering of the carriers.

This theory predicts that,

(1)

for B << B,, where B, is the magnetic field which po- larizes completely the electron-spins. A is the s-d ex- change parameter, p is the Fermi energy of the carriers, nA the critical concentration of electrons at which the antiferromagnetic order becomes unstable, n the con- centration of carriers and M is the crystal magnetic moment per atom. We have that M = (B.S)

/

BF where B is the magnetic field, S the spin of the Fe atom and BF the saturation magnetic field, at which both sublattices of the antiferromagnet become paral- lel to each other. For B

>

B, the magnetoresistance

ceases to be a function of the field, reaching a satura- tion value given by the equation:

The two equations above predict a magnetoresis- tance which is negative for n

<

0.1 nA and positive for n

>

0.125 nA in all magnetic fields B

<

BF. For intermediate carrier densities 0.1 nA

<

n

<

0.125 n ~ ,

Ap

/

p ( 0 ) is negative for B

<<

B, becoming posi- tive as B approaches B,. After reaching saturation

for B N

B,,

the magnetoresistance becomes negative again for B

>

BF.

Experimental data on the rare earth compounds EuSe, EuS, EuTe [4, 51 and Gd2S3 [6] are in excellent agreement with this theory. It is not known though if this is also true for transition element semiconducting compounds, because magnetoresistance data are lack- ing. This prompted us to carry out magnetoresistance measurements on natural single crystals of pyrrhotite.

Natural pyrrhotite FeS1.14 is a heavily-doped [7, 81 ferrimagnetic semiconductor with a distorted NiAs structure, in which successive planes perpendicular to the c-axis are occupied exclusively by iron atoms with their magnetic moments antiferromagnetically aligned. The iron vacancies are ordered in every second plane forming a superstructure [9] and making the compound ferrimagnetic.

Spectroscopical data give the value A = 0.25 eV for the s-d exchange parameter in high-spin Fe, from which an A S = 0.5 eV is concluded. On the other hand, from Hall effect and thermopower measurements a Fermi energy /I = 0.14 eV was deduced for pyrrhotite

[lo,

111, which is less than half the s-d exchange energy. Measurements a n d results

The transverse magnetoresistance was measured by the four probe DC method for temperatures ranging from 88 to 607 K, beyond the N6el point TN 600 K of pyrrhotite and for magnetic fields from 0 to 7 000 G in 500 G intervals with B

//

c. Three typical curves at different temperatures are presented in figure 1. Discussion and conclusions

The critical carrier concentration n~ is given by the equation, nA = ( 4 k T ~ )

/

AS^^) where k is the Boltz-

mann constant and a the distance between nearest atoms in the lattice [3]. For pyrrhotite, where TN

-

600 K, S = 2, A = 0.25 eV and a = 3.1

x

lo-'

cm, the last equation gives nA = 3.0

x

lo2'

crnW3.

According to the theory, the magnetoresistance is negative for low magnetic fields, becoming positive for higher fields, only if the carrier concentration n lies in

C8 - 194 JOURNAL DE PHYSIQUE

Fig. 1. - Transverse magnetoresistance for B

//

c, as a function of B at three temperatures. The experimental uncertainties are indicated. The first three experimental points for weak magnetic fields of the curves at T = 308 K and T = 376 K are fitted by equation (1) with n = 3.8 x

lo2' cm-3 and n = 4.0 x 10"

the range 0.1 n A

<

n

<

0.125 n A . For n A = 3.0 x

10'' ~ m - ~ this shape of the magnetoresistance curve must be observed only for 3.0

x

1021

<

n

<

3.8 x

10'' ~ m - ~ .

From Hall effect measurements on natural single crystals of pyrrhotite, a carrier concentration n =

3

-

8 x

loz1

~ m - ~ was determined [12, 131. Besides, the shape of the magnetoresistance curves at T = 308

and 376 K in figure 1 suggests that n must lie in the range 3.0 - 3.8 x 10'' ~ m - ~ , as it is predicted by the theory above. Taking into account the approximate character of n A and n calculation, we can say that the

shape of the magnetoresistance curves agrees well with the experimentally deduced carrier concentration.

The theory gives the exact shape of the magnetore- sistance curves either for B

<<

B, or B

>

B,. In the

intermediate region, in which the majority of our ex- perimental points lies, the shape of the curves is not analytically given. According to the theory [14], B, =

2 2 / 3 C 1 ~ ~

/

AS. For pyrrhotite, which is characterized

by a high magnetic anisotropy [15], BF = 100 kG, for

B

//

c and BF = 30 kG, for B l c and the last equation

gives B, = 50 kG and 17 kG for the two orientations respectively. In both cases the maximum B = 7 kG

used in the experiments, is too weak t o reach satura- tion.

Equation (1) fits very well the first experimental points of the curves a t T = 308 K and 376 K with n = 3.8 and n = 4.0 x 10'' cme3 respectively. More- over, the fact that the magnetoresistance takes higher values for higher temperatures a t B

<<

B,, can be ex-

plained as a result of an increase of n and BF with

temperature, according to equation (1).

The fact that the shape of the magnetoresistance curves is sensitive to the carrier concentration, can give a possible explanation of the oscillatory shape of the curve at T = 606 K. Because of the strong s-d exchange interaction, the change of magnetization induced by a magnetic field can affect appreciably the splitting of energy bands into sub-bands of

+

and - spins, leading to a corresponding change of n with B.

In conclusion we see that the theory outlined above can predict the magnitude of the magnetoresistance and in most cases the exact shape of the curves, for

FeS1.14.

[I] Kashin, V. A. and Nagaev, E. L., JETP Lett. 21

(1975) 56.

[2] Zil'bervarg, V. E. and Nagaev, E. L., Sov. Phys.

Solid State 18 (1976) 1460.

[3] Kashin, V. A. and Nagaev, E. L., Sou. Phys.

JETP 39 (1974) 1036.

[4] Shapira, Y., Foner, S., Oliveira, N. F., Jr. and Redd, T. B., Phys. Rev. B 10 (1974) 4765. [5] Shapira, Y., Kautz, R. L. and Reed, T. B., Phys.

Lett. 47A (1974) 39.

[6] Andrianov, D. G., Drozdov, S. A. and Lazareva,

G. V., Sow. Phys. Solid State 21 (1979) 1253. [7] Sakkopoulos, S., Vitoratos, 'E. and Argyreas, T.,

J. Appl. Phys. 55 (1984) 595.

[8] Gosselin, J. R., Townsend, M. G . and Tremblay, R. J., Solid State Commun. 19 (1976) 799. [9] Tokonami, M., Nishiguchi, K. and Morimoto, N.,

Am. Mineral. 57 (1972) 1066.

[lo] Sakkopoulos, S. and Theodossiou, A., 'J. Appl.

Phys. 45 (1974) 5379.

[ l l ] Tsatis, D. and Theodossiou, A., J. Phys. Colloq.

France 41 (1980) C5-371.

[12] Theodossiou, A., Phys. Rev. 137 (1965) A1321. [13] Pomoni, K. and Theodossiou, A., J. Appl. Phys.

53 (1982) 8835.

[14] Nagaev, E. L., Physics of Magnetic Semiconduc-

tors (Mir Publishers, Moscow) 1983, pp. 63, 234. [15] Sato, K., Yamada, M. and Hirone, T., J. Phys.