H. PARKER and C. J. TINSLEY : Electrical Conduction in Magnetite 189

phys. stat. eol. (a) 88, 189 (1976)

Subject classification: 14.3; 18.3; 22.6

Portsmouth Polytechnic, England

Electrical Conduction in Magnetite BY

R. PARKER and C. J. TWSLEY

At elevated temperatures magnetite behaves as a semiconductor. Although the material exhibita no reaistivity anomaly a t the Curie point, the unusual complexity of the e-T curve down to the Verwey temperature is demonstrated to be an immediate consequence of magnetic order. Magneto-resistance coefficients can be predicted from these curves in conjunction with aunceptibility data.

Im Hochtemperaturgebiet lessen eich am Magnetit Halbleitereigenschaften nachweisen. Trotz jeglicher Abweaenheit einer Wideratandnanomalie bei der Curietemperatur l a B t aich democh zeigen, d a B der komplizierte Verlauf der p-T-Kurven bie hinunter zur Verwey- temperatur allein auf der megnetiechen Ordnung beruht. Die Koeffizienten dor Wider- standsiinderung im Magnetfeld sind aus dieeen Kurven mit Hilfe von Suezeptibilitiits- daten berechenbar.

1. Introduction Magnetite (F%O,) exhibits an unusually complex variation of electrical

resistivity e as a function of temperature and various attempts have recently been made (see for example (1 to 31 where reference to other work will also be found) to interpret this feature in terms of models that have proved useful in other situations. The present paper is concerned with some recently obtained results which are not accounted for by any of the models that have been proposed so far, and for which an adequate theoretical treatment still remains to beformu- lated. The remainder of this section briefly outlines some relevant features of magnetite that are already well established. The following section deals with our experimental investigations in the context of results available from other sources, and in the final sections attention is drawn to some hitherto neglected features of the conductivity data.

At elevated temperatures magnetite has a spinel-type crystal structure, the iron atoms fitting into the tetrahedrally (A-sites) and octahedrally (B-sites) co-ordinated interstices of the oxygen-lattice in the ratio of 1 to 2. Ionic bonding predominates and the ionic formula may be written as Fe3+[FeP+Fe3+]0:, where the brackets signify B-sites. The material becomes spontaneously magnet- ized below 851 K and exhibits ferrimagnetic order as a result of anti-parallel alignment of the 3d-electron spins of the iron ions on the two dissimilar types of crystal site. The magnetic moment per formula unit, when extrapolated to 0 K , is close to 4pB, the spin-only value for the Fe*+ ion. Below 119 K , referred to aa the Verwey temperature T,, the crystal structure becomes orthorhombi- cally distorted. An associated ro-operative ordering of ferrous ions on the B-sites was first postulated by Verwey et al. [4,5] to account for a large discontinuity in e a t this temperature. While certain detailed features of the ordering mech- anism have subsequently been questioned by Cullen and Callen [6], the essential validity of the Venvey hypothesis has been demonstrated by means of neutron diffraction (71 and by Mossbauer spectroscopy [8].

190 R. PARXEB and C. J. TWSLEY

Below T, magnetite exhibits certain semiconducting properties though tho reeistivity-temperature relationship can only be deacribed by a conventional semiconductor equation with the msumption of a continuously variable acti- vation energy of the conductivity [9]. As the temperature increases through T,, the resistivity drops by about 2 orders of magnitude to approximately 10-2 Qcm and a t higher temperatures e exhibits a much more gradual but complex varia- tion with T which encompasses regions with negative temperature coefficients, reminiscent of metallic conductivity. Consistent also with a mechanism of metal- lic conduction is the fact that both thermo-electric power and Hall coefficient measurements indicate a constant number of charge carriers approximately equal to that of Fez+ ions present. However quite untypical of metallic conduc- tion is the observation that up to perhaps 600K both the value of e and the shapes of e vs. T curvesare largely determined by impurity content or deviations from stoichiometry of the order of 1% [9]. Also uncharacteristic of metallic conduction is the fact that the material exhibits no anomalous temperature coefficient of conductivity in the temperaturo range within a few degrees of tho Curie point [ 10, 111. It is now well established [4 ,6,8] that electrical conduc- tion reaulta from the transfer of electrons between octahedrally co-ordinated Fez+ and FeS+ ions.

2. Measurements and Resnlta

Four-terminal measurements of resistivity, thermo-electric power and mag- neto-resistance have been made on a series of specimens of spinel oxides in the composition range Me,FeS-,O, (Me = Ni or Zn). The object was to determine the trend of the electrical propertiqs as a function of temperature, magnetization and composition. Results here relevant are thoso with compositions a t , and close to, z = 0. Unless otherwise stated samples were polycrystalline and prepared from spectroscopically pure ferric oxide powder according to stctndard ceramic techniques. However the sintering atmosphere was controlled for those materials that were otherwise liable to suffer oxidation to ferric oxide or irreversible over- reduction. A number of materials were selected for reeistivity measurement at various frequencies up to 6MHz and no significant dispersion effects were found. Magneto-resistance coefficients A& quoted here are those associated with in-

trinsic or spontaneous magnetization after correction for any contribution by domain effects. For convenience Ae/e was measured in transverse fields after it had been estab- lished for some materials that resulta are unaffected by the magnetic field direction.

Fig. 1. Reaiativity-temperature relationehip for several epeoimenn of magnetite. (a) Stoichiometric sinile crystal. FqO,, (b) oxygen-deficient poly- cryetalline epecimen. FqOs.oee, (c) etoichiometric polycrystalline specimen, FqO,, (d) aingle orgetal

apecimen acoording to [12]

Electrical Conduction in Magnetite 191 "i--"' Fig. 2. A& vcrnun applied msgnetio field fl at 453.5 K for Fe,O,

% -84 i -01 , /' n i i i d s 6 7 a

HfkOeJ - - Some typical resistivity-temperature curves for single crystal and polycrys-

talline magnetite are displayed in Fig. 1. It was found that a t , and above the Curie point To the resistivity is very well described by the semiconductor relationship

e = A T exp (A) with A and q constant up to the highest temperatures of measurement (1600 K). For the etoichiometric material A = 2.06 x lO-'RcmK-l and q = (99 f 3) x x 10-8 eV. According to (1) this corresponds to a conductivity maximum in the neighbourhood of 1100 K and this emerges clearly from the graphs. Roughly 30 K below T,, e begins to drop below the value indicated by (1) and the diver- gence increases progressively with the lowering of temperature.

Below about 600 K the e vs. T relationship becomes sensitive to the detailed composition of specimens. Stoichiometric materials exhibit a fairly flat resistivity minimum around 400K. Curves reported in the literature can generally be reproduced reasonably well by the preparation of specimens with an appro- priate deficiency in oxygen content; this is illustrated in Fig. 1 by the similarity in shape between our curve for Fe&.om and that of Smith [12].

From their work with other ferrite systems the authors had formed the im- pression [ 131 that, although magnetite displays no Curie point anomaly in resis- tivity, the departure from (1) a t a somewhat lower temperature is nevertheless a direct consequence of the ordering of the ionic magnetic moments. This assumption can be tested by comparing resistivity changes due to the advent of spontaneous magnetization with those where the intrinsic magnetization is induced by the application of an external field H. Accordingly Aele was mea- sured aa a function of H at various temperatures, and in the range from room temperature to about 200 "C a linear relationship between Ae/e and H was obtained and a(Ae/e)/aH determined. A typical result is shown in Fig. 2 for measurements at 463.6 K. The points below about 2 kOe fall into the region of the technical magnetization curve and the influence of the demagnetization factor and are not therefore of concern to the present discussion. To compare the two sets of results information is still required concerning the variation of the magnetization I with T and H respectively, and this problem will be con- sidered in the next section.

3. The Spin-dependent Resietivity

It is a fairly general feature of magnetic materials that their resistivity below the Curie point tends to fall below that extrapolated from the paramagnetic region and that in such a case Ae/e is proportional to ( A I ) z , where AI is a field- induced increment in the intrinsic magnetization [ 141. Although it was not pos- sible to teat this relationship for pure magnetite on account of its high Curie

192 R. PARK= and C. J. "INSLEY

temperature, the validity could be confirmed for a range of appropriately zinc- substituted compositions.

It is instructive to express the relative contribution of the spontaneous spin order in a reduced form:

I n (2) @F, T represents the actual reaistivity, pp, T that extrapolated from the paramagnetic regionsand the term within the square brackets denotea the reduced spontaneous B-sublattice magnetization, all at temperature T. Fig. 3 shows the temperature dependence of eF, T (full curve) and ep, T (broken line) derived from the results in Fig. 1 for stoichiometric magnetite: the latter line was cal- culated using equation (1) to repreeent the relationship between e and T for the spin-disordered phase.

If the resistance decrement (@F, T - gp, T) is due solely to the advent of mag- netic order on the B-sublattice, values of Q ( T ) calculated from (2) and (1) will be related to measurements of Aele made a t the same temperature by

G(T) = O*(T) , where

(3)

The experimental relationship between reduced resultant magnetization and reduced temperature 6 (= TIT,) has been eatabliehed by the authors. Neutron

e -

Fig. 3 Fig. 4

Fig. 3. Comparison of extrapolated and calculated paramagnetic resistivities for F40,. Full line measured values of (1O3/T) lg ey, T; broken line (lO'/T) Ig ep, T by extrapolation from T > T,; ( 0 ) calculeted valuea of (1P/T) Ig ep, T assuming Ae/e proportional to A [ Z ( H . T)/Z(O, O)]*; (0) calculated value8 of (lo'/?') Ig e p , T assuming A& proportional to

d[IB(H. T ) / I R ( O , o)]' Fig. 4. The dependence of reduced magnetization on reduced temperature in FqO,. (0) measured values of reduced resultant magnetization, I (0 , T)/I(O, 0) ; line calculated values of Z(0, T) I ( O . 0 ) ; (0). (m) measured values of A-and B-sublattice reduced magnetizations.

l ~ ( 0 , T)/IA(O, 0) and IB(O, T)/ZB(O, 0) (Riste and Tenzer [Is])

Electrical h d u c t i o n in Magnetite 193

diffraction measurements have also been reported of the correaponding sublattice magnetizations [ 151 ; these results are shown in Fig. 4.

In order to demonstrate the validity of (3) i t is first neceaaary to establish values of the magnetic siisceptibility beyond tech- nical saturation a t the temperatures in ques- tion. There appear to be no relevant data in the published literature, and the facilities available to the authors for measurements of susceptibility were limited so that results could be obtained only in a restricted range around T,, i.e., 0.991 < O < 1.04. In this region a(Ae/e)/aH is not merely undetectable, but is actually predicted to be zero accor- ding to (1) and (2), any divergence between e F , T and g p . ~ appearing only a t somewhat lower temperature. However the susceptibi- lity measurements within the range (0.991 to 1.04). T,are described very well by the X8el molecular field theory [ 161, extended to the case of two dissimilar magnetic ions with a choice of molecular field coefficients as fol- lows:

I- -I-

- I

Y

I

- I

JBB , p = - = + O . 8 5 , JAA a = - = - 0.10 JAB JAB

(5)

where the J, are interaction energies of neighbouring cationspaire on the appropriate sublattices. It is evident from Fig. 4 that these valuea lead also to a very satisfactory fit of the experimental Z(0, T)/Z(O, 0) vs. 8 curve. The parameters in (5) have therefore been used to calculate the susceptibility a t the temperature of the magneto-resistance measurements. Resultant, as well as R-sub- lattice susceptibilities have been computed and are recorded in Table 1, together with measured values of a(Ae/e)/aH. The physical identity expressed by, equation (3) was tested by calculating e p , T, expressed, according to (2) and (4) as

194 R. PARKER and C. J. TINSLEY: Electrical Conduction in Magnetite

and the results are given in Table 1 and displayed in Fig. 3. It is evident that ep, T, aa determined from magneto-resistance measurements, agrees well with the values obtained from the extrapolated e VB. T curves if i t is assumed that the conductivity is determined by the degree of ordering of the B-sublattice rather than by the resultant magnetization.

4. Conclueion Magnetite behaves as a semiconductor near and above its Curie point; in

this temperature region the electrical properties suggest that conduction is due to the transfer of electron8 from Fez+ to Feat ions on the B-sublattice by means of a thermally activated hopping mechanism. Somewhat below To a spin-order- induced increase in conductivity sets in which extends down to the Verwey temperature and simulates certain properties appropriate to metallic conduction. Realistic theoretical models need to account for the sensitivity of the ,p vs. T curves to small changes in etoichiometry and for the dominant role played by the B-sublattice magnetization in determining the conduction mechanism.

Acknowledgement

The authors wish to thank Dr. J. R. Drabble for the loan of a single crystal specimen.

Reierencee [l] W. HAUBENBEISEEB, phye. stat. eol. 1,819 (1961). [2] J. R. CULLEN, B. CEAUDHURY, and E. R. CALLEN, Phys. Letters A 58, 113 (1972). [3] B. LOBENZ and D. IELE, phys. stat. sol. (b) 69,451 (1975). [4] E. J. W. VHIWEY and P. W. HMIJXAN, Physica 8, 979 (1941). 161 E. J. W. VERWEY, P. W. HUMAN, and F. C. R~MKIJN, Chem. Phye. 16, 181 (1947). [6] J. R. CULLEN and E. R. CALLEN, Phye. Rev. B 7, 397 (1973). [7] W. C. HAMILTON. Phys. Rev. 110, 1069 (1958). 181 W. KUNDIQ and R. 6. Ha~omvr, Solid State Commun. 7,223 (1989). [9] B. G R ~ T H , D. ELWELL, and R. PARKER, Phil. Mag. 22. 163 (1970). [lo] P. A. MILES, W. B. WEE-, and A. VON HLP~EL, Rev. mod. Phye. 2% 279 (1967). [ll] R. PABKER and C. J. TINSLEY, Ferritee, Proc. Inter. Conf., Univ. Tokyo Press 1971

[12] D. 0. S m , Prog. Rep. Lab. h u l a t i o n Research M.I.T. 11, 63 (1952). 1131 C. J. TINSLEY. Ph.D. Thesis, Univ. London 1976. [14] R. PABUW. Magnetic Oxides, Ed. D. CRAIK, Wiley & Sons, New York 1975 (Chap. 8). [la] T. RISTE and L. TBNZEB, J. Phye. Chem. S o l i b 19, 117 (1981). [18] L. N k n . Ann. Phys. (France) 12. 167 (1948).

(p. 591).

(Rcccivcd October 15, 1975)