D. S. CHAPIN,J. A. KAFALAS, AND J. M. HONIG
1402
Electrical Properties of Ferromagnetic CrO, (1.89 < IX: < 2.02)
by D. S. Chapin, J. A. Kafalas, and J. M. Honig Lincoln Laboratory, 1 Massachuaetta Institute of Technology, Lexington, Maasachuaetta (Received November 20,1064)
The resistivity ( p ) and Seebeck coefficients ( a ) of hot-pressed CrO, (1.89 < 2 < 2.02) have been determined in the temperature (7’)range 0-450°K. p increased slightly with rising T; no significant anomaly was encountered a t the Curie point of the samples. Plots of a us. T exhibited four types of temperature dependence. Both a and p change only slightly with 2 . The data are interpreted in terms of a band scheme recently proposed by Goodenough.
In this paper we report on measurements of the electrical properties of CrO, (1.89 < 2 < 2.02). This study was motivated in part by the striking physical properties of CrOz. The oxide is ferromagnetic and quasi-metallic.2a Also, above 200OK. the thermal expansion coefficient along the c axis of the rutile structure is negative, while that along the a axis is positive, so that the volume expansion coefficient remains nearly independent of temperature.2b The only systematic electrical measurements to date seem to be those of Kubota and H i r ~ t a who , ~ observed an anomalous resistivity maximum near the Curie temperature of 119’. It seemed highly desirable to check their work and to extend the measurements over a wider range of conditions, in the hope that this might clarify the conduction mechanism which was not ~ n d e r s t o o d . ~The data cited below are examined in terms of a model recently proposed by Goodenough5 for a systematic interpretation of the electrical properties of metallic oxides. A review of the physical properties and methods of preparations of CrOz has been provided by Kubota and Hirota6 (KH); further information is provided by the duPont g r o ~ p . ~While ,~ single crystals have been grown by hydrothermal methods, the resulting specimens were too small for use in electrical measurements by conventional techniques. Our attempts to grow large single crystals of CrOz were likewise unsuccessful. Therefore, all measurements presented here were carried out on hot-pressed polycrystalline material. CrOz begins to decompose above 250°8; this sets an upper limit to the temperature range in which measurements could be carried out. The Journal of Physical Chdst~stry
Experimental Preparation of CrO,. Mallinckrodt CrOl and Baker or Kern Cr208 powders were mixed in appropriate quantities to produce CrO, with 2 = 2, placed in a cylindrical 0.96 X 2.5 cm. boron nitride cell with a Pt foil liner, and subjected to a pressure of 20 kbars a t approximately 400’. I n a typical case, the resulting ferromagnetic pellet had a density of 4.81 g./cc., compared to a literature value of 4.80 g./cc., and to a density of 4.90 g./cc. calculated from lattice parameters. Analyses of the resulting specimens for impurity content were made on a CEC 21-10 spectrograph and are tabulated in Table I. Parallelepiped specimens approximately 8 X 6 X 3 mm. in dimensions were cut and measured to the nearest 0.01 mm.; two holes, 0.76 mm. in diameter, were ultrasonically drilled through the sample perpendicular both to the long axis and to the (1) Operated with support from the U. S. Air Force. (2) (a) J. B. Goodenough, “Magnetism and the Chemical Bond,” F. A. Cotton, Ed., John Wiley and Sons, Inc., New York, N. Y., 1963; (b) K. Siratori and S. Iida, J . Phys. Soe. Japan, 15, 2362 (1960); 17, 208 (1962). (3) B. Kubota and E. Hirota, ibid., 16, 345 (1960). (4) J. B. Goodenough, ref. 2a, p. 243. (5) J. B. Goodenough, paper submitted to International Colloquium of CNRS on Oxygen Compounds of Transition Elements in the Solid State, Bordeaux, Sept. 1964. (6) B. Kubota and E. Hirota, Natl. Tech. Rept. (Osaka), No. 4, 372 (1961) (translation available OTS,SLA). (7) T. J. Swoboda, P. Arthur, Jr., H. L. Cox, J. N. Ingraham, A. L. Oppegard, and M.S. Sadler, J . AppE. Phya., 3 2 , 3745 (1961). (8) F. J. Darnell and W. H. Cloud, paper submitted to International Colloquium of CNRS on Oxygen Compounds of Transition Elements in the Solid State, Bordeaux, Sept. 1964.
ELECTRICAL PROPERTIES OF FERROMAGNETIC CrO,
largest faces and placed approximately 4 mm. apart to accommodate thermocouples. Seebeck Coefiients. The standard four probe technique was used to determine the Seebeck coefficients (a),initially with reference to platinum for the -50 to 200' region, and later with reference to copper for lowtemperature measurements. The voltage outputs of four Pt-Pt-10% Rh (or copper-constantan) thermocouples, numbered 1 through 4 from bottom to top of the sample, were read with a Leeds and Northrup K-3 potentiometer. The four platinum (or Cu) leads of the couples served as contacts for the thermal e.m.f. measurements. Thermocouples 2 and 3 were butt welded and extended straight through the specimen; Eccobond silver epoxy cement was used to make electrical and thermal contacts. Each end of the specimen was in contact successively with silver dust, a platinum (or Cu) disk to which a thermocouple was welded (no. 1 or 4),a quartz disk, a massive silver (or Cu) block, a second quartz disk, and finally, a lavite (or stainless steel) pedestal. The vertical assembly was spring loaded and enclosed in a stainless steel shield which was wound with two electrical trimming heaters (or, in the case of copper, heaters were embedded in a re-entrant well in the Cu block). The whole assembly could be surrounded either with a large vertical clam furnace or with a vessel having a re-entrant well in the bottom so that the annular space could accommodate a Dry Icealcohol bath. For the low-temperature measurements, the setup was transferred to a second cell in which the assembly could be surrounded with liquid Nz or He. Gaseous helium a t a pressure of a few centimeters was used as the heat transfer medium. The e.m.f. between any two positions on the sample was found to be proportional to the corresponding temperature difference (AT). Plots of e.m.f. us. AT were made for each average sample temperature; the straight line through the points passed quite close to the origin in most cases. The slopes of these lines were corrected for the contributions from the platinum or copper leads, using the data of Cusack and Kendall,gor of the Landolt-Bornstein tables. lo Resistance Measurements. Resistances were determined with a Keithley 503 milliohmmeter which was connected to the four Pt (or Cu) thermocouple leads. The four probe measurements were carried out a t a frequency of 100 C.P.S. X-Ray Analysis. Powder photographs were obtained with a 3-7 hr. exposure in a DebyeScherrer camera using Cu radiation with a Ni filter.
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(9) N. Cusack and P . Kendall, Proc. P h y s . SOC.,22, 898 (1958). (10) "Landolt-Bornstein Tabellen," Vpl. 11, Part 6, SpringerVerlag, Berlin, 1959, p. 931.
Volume 69, N u m b e r 4
April 1966
D. S. CHAPIN,J. A. KAFALAS, AND J. A I . HONIG
1404
Stoichiometry. Chromium content (and therefore z), in CrO, was determined by oxidation-reduction titration of the oxidized chromium in solution with standardized ferrous ammonium sulfate to a precision of 1 part in 1000 or better. I n some runs, Cr was also determined from the weight loss on calcination of Cr02 to Cr203at 800’. The two sets of determinations differed by less 1han 1% in every case.
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1
(a)
Results Resistivity Measurements. Because of the polycrystalline nature of the specimens, measurements of resistivity ( p ) as a function of temperature (2’) were frequently erratic. In the worst cases, severe hysteresis effects were encountered, which could not be eliminated; however, in many runs, readings tended to stabilize after subjecting the sample to several cycles. The results of two relatively good runs for x = 1.904 and x = 2.013 are shown in Figure 1. In Figure l a , the initial p measurements lay above the remainder and passed through a flat maximum near the Curie temperature of T , = 119”; the remaining points fell on a nearly straight line, with no visible anomalies near T,, and with no difference in readings taken for ascending or descending temperatures. Figure l b shows the resistivities for Cr02013 taken with rising temperature. Here, the slight dependence of p on T is again noteworthy. If these data can be taken a t face value, there is an initial decrease of p as T rises from 4 to 50’K. and a rather shallow maximum in p some 40’ below the Curie point; the slight discontinuity near 100’K. may be fortuitous. These data are representative of measurements obtained on the CrO, system for 1.89 < z < 2.02. All resistivities fell in the range of 2-75 mohm-cm., which is relatively low for metallic oxides a t these temperatures. Data taken with Cr01.994,and CrOz,ol3 down to liquid helium temperatures showed no evidence for a transition to semiconductor characteristics. For x < 2, p increased slightly with T , the temperature variation becoming less and less pronounced as z approached 2 . For x > 2, the change of p with T was nonsystenistic and did not exceed +12% of the mean. Any maxirna observed by us during initial heating of the sample were relatively flat, extended over a considerable temperature range, and did not necessarily peak at the Curie point. Measurements of this type on polycrystalline samples are always subject to criticism; however, while no reliance can be placed on the numerical values, the qualitative features and trends should be of significance. Temperature Dependence of Seebeck C o e f i i e n t . Since Seebeck coefficients (CY) are determined, as nearly as The Journal (of Physical Chemistry
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Figure 1. Representative plots of resistivity us. temperature for two CrO, samples: (a) z = 1.994; the upper portion of the curve represents the initial results; the lower portion, the measurements obtained in later cycles with increasing or diminishing temperatures; ( b ) r = 2.013; data taken on the first cycle with rising T only.
possible, under conditions of no electric current Aow, these measurements should not be as drastically affected by the polycrystalline nature of the sample as the resistivity measurements. Indeed, the fluctuations in a were generally much less than those in p. For the Sommerfeld model of a metal, the expression for a due to diffusion effects is given by” r 2 k2T
= z-
-
3 ecl
(1)
where k is Boltzmann’s constant, e the electronic charge, z = f1 depending on whether one deals with a p- or n-
type metal, and F is the Fermi level taken relative to the appropriate band edge. For the other extreme of an extrinsic semiconductor conforming to the simple Wilson model, the relation of interest reads11.12 (11) A. H. Wilson, “The Theory of Metals,” Cambridge University Press, London, 1953, Chapter VIII. (12) R. W. Ure, Jr., “Thermoelectricity: Science and Engineering,” R. R. Heikes and R. W. Ure, Jr., Ed., Interscience Publishers, Inc., New York, N. Y., 1961, pp. 46, 53.
ELECTRICAL PROPERTIES OF FERROMAGNETIC CrO,
z a = - (2kT
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-
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in which the second term generally dominates the first. Thus, plots of a us. T or of a us. 1 / T should show the dependence of p on T . Representative graphs of this type are shown for Cr01.906in Figure 2. A similar graph of a us. T for the lower temperature range is shown in Figure 3 for CrOl.sgr. It is seen that a,which is negative and small relative to most oxidic materials, changes little with T < 24OoK., and then increases numerically with rising T . From an examination of these data as well as those for other samples (not shown here) one can distinguish four temperature regions: T < 240'K.; 240 < T < 323'K.; 323 < T < 389'K.; and T > 392'K. The sharp break separating the a us. 1 / T plots into two linear regions near T = 50' is particularly noteworthy. Galvano-Thermomagnetic Measurements. Experiments were carried out a t the Massachusetts Institute
T
(OK)
Figure 3. Representative plots of Seebeck coefficients us. T for Cr01.994 in the temperature range below the Curie point.
of Technology National Magnet Laboratory to determine magneto-resistivity, Hall, magneto-Seebeck, Nernst, and Ettingshausen-Kernst effects in steady magnetic fields up to 100 kgauss. S o effects could be detected in any of the attempted measurements.
Discussion
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The Goodenough Model. Any model adopted for Cr02 must provide an understanding as to why the material : (a) is ferromagnetic, (b) is a relatively good electrical conductor, and (c) does not display galvano-thernzomagnetic effects. To date, only the model proposed by Goodenoughs seems to provide a basis for understanding these facts; the pertinent features are outlined below. Beginning with the separated atoms, as indicated on the extreme left and right of Figure 4, one draws the atonic energy levels for the cation and anions. I n the rutile structure for Cr02, each Cr is surrounded approximately octahedrally by 0, and each 0, approximately trigonally by Cr. In the crystal fields referred to above,13 the d levels of Cr are first split into two e, and three tzgsublevels; moreover, because of the distinction between the c and a axes i n rutile structures, a further splitting of the tz, states into a tZgi' and two tZgLlevels takes place. The relative stability of these sets of levels depends on the c / a axial ratio of the crystal. The crystal field acting on the 0 splits each of the three p states into one pr and two pc levels. The centers of gravity of the cationic and anionic atomic levels are separated by a distarwe E M - ET on the energy scale, where E Mand E I refer, respectively, to the bladelung and the ionization energies for the "effective" charges on the ions.
-30
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Figure 2. Representative plots of Seebeck coefficients ( a ) us. T or ( b ) us. 1 / T for CrOl.ws.
(13) L. E. Orgel, "An Introduction to Transition-Metal Chemistry," Methuen and Co. Ltd., London, 1960.
Volume 69,Number 4
April 1966
D. S.CHAPIN, J. A. KAFALAS, AND J. 31. HONIG
1406
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