Magnetic properties of the magnetite-spinel solid solution ...rruff.info/doclib/am/vol80/AM80_213.pdf · Magnetic properties of the magnetite-spinel solid solution: Saturation magnetization

American Mineralogist, Volume 80, pages 213-221, 1995

Magnetic properties of the magnetite-spinel solid solution: Saturationmagnetization and cation distributions

Rrcn lRD J. H,unrsoN, Awonrw PtmvsDepartment of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, U.K.

Ansrnlcr

Magnetic hysteresis properties of the FerOo-MgAlrO4 solid solution have been measuredat 4.4 K and in fields up to 12 T. The trend in saturation magnetization, M"(4.4 K), as afunction of composition is consistent with the cation distribution model of Nell and Wood(1989) and suggests tlllat M, (4.4 K) changes sign at a composition of 30 mol9o FerOo. Thechange in sign of M"(4.4 K) at this composition is correlated with an anomalous peak incoercivity of over 700 mT. This effect has been explained in terms of fluctuations in bothcomposition and the degree of nonconvergent cation order, which lead to fine-scale mag-netic domains with antiferromagnetic exchange coupling.

Ixrnoouc-rrox

Magnetic minerals exist with a wide range of micro-structures associated with oxidation, subsolidus exsolu-tion, or cation ordering (Haggerty, l99l). In magneticspinel solid solutions, the processes ofnonconvergent cat-ion ordering and phase separation occur concurrently,both ofwhich lead to heterogeneities in composition, cat-ion distribution, and strain. Microstructures associatedwith these heterogeneities occur almost universally insamples and may be responsible for the unusually highcoercivities observed in coarse-grained material (Tuckerand O'Reilly, 1980; Shive and Butler, 1969;Price, 1980;Evans and Wa;'man, 1974). Microstructures associatedwith convergent cation ordering in the system hematite-ilmenite have been shown to interact strongly with mag-netic properties, leading to domain-wall pinning and self-reversed thermoremanent magnetization (Nord and Law-son, 1989, 1992; Brown et al., 1993; Hoffman, 1992;Varea and Robledo, 1987). An understanding of the mag-netic properties of heterogeneous systems is thereforefundamental to the interpretation of remanent magneti-zations and their stability over geological time.

Studying the development ofheterogeneous spinels andthe consequences for magnetic properties requires a spi-nel solid solution with a high-temperature miscibility gapso that exsolution may be induced on a laboratory timescale. Although magrretism in titanomagnetites is the mostimportant cause of remanence in natural rocks, such ex-periments are not possible with the titanomagnetite solidsolution because ofthe low temperatures required for spi-nodal decomposition (Price, I 98 I ). The solid solution be-tween magnetite (Fe3O4) and spinel (MgAl,O,) is a moresuitable system in that it consists of magnetic and non-magnetic end-members, there is a large variation in Curietemperature across the solid solution (Nishitani, l98l),the chemical solvus has a consolute point near 1000'C(Mattioli and Wood, 1988), and there are extensive

0003404x/95/0304-02 l 3$02.00

changes in the degree of nonconvergent cation orderingas a function of temperature (Nell and Wood, 1989; Nellet al., 1989). Previous experimental work on this binaryincludes measurements of lattice parameters, magnetiteactivity, Curie temperature, room-temperature low-fieldmagnetization, and cation distribution vs. composition(Mattioli et al., 1987; Mattioli and Wood, 1988; Nishi-tani, l98l; Nell et al., 1989).

The magrretic properties of a ferrimagnetic solid solu-tion are dependent on the cation distribution (Stephen-son, 1969, 1972a,1972b; Readman and O'Reilly,1972).In the case of spinel solid solutions, general formulaAB2O4, the important factor is the distribution of para-magnetic ions between tetrahedral (A) sites and octahe-dral (B) sites, the net magnetization of the spinel beingthe difference between the A and B sublattice magneti-zations (Brown et al., 1993). In complex Fe-Mg-Al spi-nels, a complete experimental determination of the cationdistribution is made difficult by the existence of four cat-ions on both octahedral and tetrahedral sites. The distri-butions of Fe2+ and Fe3* ions between sites may be de-termined by combinations of thermopower, conductivi-ty, and Mdssbauer techniques (Nell et al., 1989; Trest-man-Matts et al., 1983; Schmidbauer, 1987). For theFe.Oo-MgAlrOo binary, a theoretical determination oftheAl distribution is required, in addition to thermopowerand conductivity measurements, to determine the cationdistribution completely (Nell et al., 1989). Measurementsof saturation magrretization, however, provide a sensitiveindication oftrends or changes in cation distribution andmay therefore be used as experimental tests for modelsof cation distributions or oxidation mechanisms (Aki-moto, 1954; Readman and O'Reilly,1972). As a prelim-inary to a complete study of microstructural developmentand magnetic properties, this work presents the results oflow-temperature, high-field magnetic hysteresis measure-ments on synthetic samples of the magnetite-spinel solidsolution, quenched from above the solvus.

213

2t4 HARRISON AND PUTNIS: MAGNETITE-SPINEL MAGNETIC PROPERTIES

E>rpnnrtvrnxr,lr, AND ANALyTTCAL pRocEDUREs

Synthesis

The starting materials for all syntheses were 99.90lo pureFe,O, and MgO (Aldrich Chemicals) and AlrO. preparedby fir ing AlCl3.6HrO for 2 h at 400'C, 5 h at70O"C,and I h at 900 t. MgO and AlrO, were stored in a muffiefurnace at 400 .C to prevent hydration and cooled in adesiccator prior to weighing. MgO and AlrO, were weighedout in equimolar proportion and varying amounts of FerO,added to yield compositions at approximately l0 molo/ointervals along the binary. Oxides were ground togetherunder absolute alcohol for 20 min with an agate mortarand pestle and then pressed into a pellet.

Pellets were wrapped in Pt foil, suspended in a Pt buck-et, and fired at 1400 "C and log fo, : -4.2 for periodsbetween 3 and 5 d in a vertical-tube gas-mixing furnace(Nafziger et al., 197l). The value of fo,: -4.2 was cho-sen to yield stoichiometry in the magnetite component ofthe solid solution (Deickmann, 1982). Oxygen fugacitywas controlled by the ratio mixing of CO, and H, gassesusing Tylan General FC-260 gas flow controllers, factory-calibrated to 4o/o accuracy for CO, and Hr. Oxygen fu-gacity was monitored with an yttria-stabilized zirconiasolid electrolyte O, probe (Sato, l97l). The accuracy ofthe probe was checked between 1000 and 1300 "C withreference to the wiistite * magnetite buffer (Myers andEugster, 1983) and found to be accurate to within 0.4 logunit. Measured values of the /o, during synthesis were inagreement to within 0.4 log unit of tabulated values(Deines et al., 1974).

Samples were quenched from 1400 "C by dropping di-rectly from the furnace into water. The quench time isestimated to be << I s. Samples SP3, SP5, SPl0, and SPl2were reground, re-pressed, and fired for an additional pe-riod at 1400'C. Only a few samples were reground inthis way so that systematic differences between sampleshaving undergone one or two synthesis steps couldbe determined.

X-ray diffraction

X-ray diffractometer traces of the synthesized materialwere recorded using CuKa radiation and a scan rate of0.5" 20/min. Results suggest single-phase homogeneousspinels (based on peak sharpness and splittingof Kar-Ka,peaks), with no unreacted oxides being detected by thismethod. Lattice parameters were measured from X-raypowder diffraction patterns from a Guinier camera. Aninternal Si standard was used to correct for film shrink-age. Peak positions were measured with a vernier scaleto an accuracy of +0.01" 20.latIice parameters were thendetermined using around nine reflections in a least-squaresprocedure.

Detailed peak profiles of the 3l I and, 440 reflectionswere recorded using a Seifert automated step-scan dif-fractometer, with a step width of 0.01" 20 and a countingtime of 2 min per step (CuKa radiation). Backgroundintensity was modeled with a straight-line fit by least

squares. The 3l I profile was fitted with the sum of twoGaussian functions. The 440 profile was fitted with thesum of three Gaussian functions to take account of theKa, and Ka, peaks.

Electron microprobe analysis

Samples were mounted in epoxy resin and polishedusing a minimum of 0.25 pm of SiC. The general polishquality was poor, although regions with a diameter > l0pm were good enough to probe without encountering po-rosity. Energy-dispersive analysis was performed using abeam current of 15 nA and a beam diameter ofapprox-imately 2 p.m. Analyzed elements were Mg, Fe, and Al,using standards MgO, pure Fe metal, and AlrOr, respec-tively. O was calculated by difference and the final anal-yses were normalized to a formula unit containing fourO atoms and three cations. This procedure yields com-positions in good agreement with the expected values.

Scanning elecffon microscopy

Sintered chunks and crushed grains were mounted andAu coated for examination using secondary electron im-aging. Estimates of the grain size using this method in-dicate that the majority of grains are in the range 0.5-2pm with fewer grains with a diameter of up to l0 pm.Polished sections were C coated and examined usingbackscattered electron imaging to check sample homo-geneity. A second phase of a Si-rich material was detectedin samples SP3 and SP5. This second phase comprisesaround 5-l0o/o of the sample surface and fills the spacesbetween polished spinel regions. Two possible sources ofSi in the sample preparation are polishing with SiC orgrinding with an agate mortar and pestle. If the secondphase is a polishing artifact, then it does not affect theresults. Ifit is derived during regrinding, then its presencethroughout the sample may affect calculated values of thesaturation magretization. There is no systematic varia-tion in the results to suggest this is the case, however. Forexample, M.(4.4 K) for samples SPI I (x: 0.508, groundonce) and SPl2 (x:0.51, ground twice) differ by only0.05 pr per formula unit.

Rrsur,rs oF sAMpln ctrARAcrERrzATroN

Electron microprobe analyses of the synthetic samplesare presented in Table l. The composition of the sampleswith respect to the FerOo-MgAlrO4 binary is illustratedin Figure l. Approximate compositions of the samplesare defined in terms of the ideal solid solution(FerOo),(MgAlrOo),-,, where x is calculated from theanalysis by dividing the analyzed Fe content per formulaunit by three. The standard deviation in x is typically<0.01 for the 20 analyses, and the samples do not appearto be zoned. The single-phase nature of the samples hasbeen confirmed by TEM investigation. Figure 2 showsthe variation in lattice parameter vs. composition. Thereis good agreement with previous results for the stoichio-metric solid solution (Mattioli et al., 1987).

Peak profiles of the 3l I and 440 reflections in sample

HARRISON AND PUTNIS: MAGNETITE-SPINEL N{AGNETIC PROPERTIES

TABLe 1. Electron microprobe analyses of synthetic spinels

Sample MgO (wt%) Al,O3 (wt%) FeO (wt74 Total (wt%) Mg' Fe'

2t5

Al/Mg

sP2 24.98(0.67)sP3 2't.29(O.211sP4 28.24(0.931sPs 18.87(0.11)sP6 17.25(0.17)sPg 13.75(0.28)sP10 15.31(0.27)sP11 10.84(0.51)sP12 10.69(0.22)sP13 8.10(0.32)

60.72('t.23)55.43(0.57)67.72(1.87)48.s2(O.23)42.63(0.36)33.74(O.47138.08(0.65)27.O2(O.94)26.78(0.39)20.55(1.48)

13.24(0.58)22.98{0.1 9)0.012(0.02)31 .06(0.13)37.9q0.23)s0.40(0.44)44.7s(0.32159.1q0.9s)59.1 7(0.23)67.s4{1.53)

98.9s(1.65)99.70(0.73)95.96(2.79)98.45(0.26)97.84(0.59)97.90(0.77)98.14(0.70)96.98(0.51)96.64(0.70)e6.20(0.38)

0.93(0.01)0.82(0.004)1.04{0.006)0.76(0.003)0.72(0.004)0.60(0.008)0.65(0.006)0.s0(0.01)0.49(0.006)0.39(0.01)

1.79(0.01)1.69(0.00s)1.96(0.006)1.s4(0.005)1.40(0.00s)1.16(0.01)1.28(0.01)0.98(0.03)0.98(0.007)0.78{0.05)

0.28(0.01)o.s0(0.006)

0(0)0.70(0.005)0.88(0.006)1.2q0.013)1.07(0.02)1.52(0.03)1.5q0.01)1.8q0.003)

0.092(0.005)0.1 65(0.002)

0(0)0.23q0.002)0.295(0.002)0.412(0.m4)0.356{0.005)0.s08(0.01)0.510(0.004)0.609(0.02)

1.92(0.03)2.06(0.01)1.90(0.015)2.03(0.01)1.95(0.013)1.94(0.03)1 .97(0.015)1.97(0.04)1.98(0.02)2.00(0.09)

Nofe.' numbers in parentheses are one standard deviation.' Based on a formula unit with three cations per four O atoms.

SPI I are shown in Figure 3. Both reflections show sig-nificant diftrse scattering at the base of the main peak.Pure positional or compositional disorder in a solid so-lution produces difftrse scattering, which contributes onlyto the general background (Guinier, 1963). Il however,the disorder consists ofcorrelated changes in lattice spac-ing and structure factor (i.e., coupled compositional andpositional disorder), then difihse scattering may concen-trale at the diffraction peaks. The effect may be enhancedby short-range ordering or clustering of cations prior toexsolution. Hence the observed diffuse scattering is con-sistent with, but does not necessarily require, the presenceof heterogeneities in composition or degree of cat-ion order.

MgAlrO*

1.0

0.8

0.6

0.4

o.2

0.0 0.2 0.4 0.6 0.8 1.0

Oxidized

++

q

oo

oo

o0

€J

8 . 4 0

8 . 3 5

8 . 3 0

8 . 2 s

8 . 2 0

8 . 1 5

8 . 1 0

8 . 0 s

0.

0 . 0 o . 2 0 . 4 0 . 6 0 . 8

Mole traction magnetite

1 . 0

Fe.OoFerOo

Fig. 2. Lattice parameters of synthetic samples (plus signs)as a function of magnetite content (x). Dashed lines are the re-sults of Mattioli et al. ( I 987) for the stoichiometric and oxidizedsolid solution.

MgFerOo

Fig. l. Compositions of synthesized samples (Xs) in termsof the quaternary system FerOo -FeAlrOo -MgAlrO.-MgFerOo, asdetermined by electron microprobe analysis. The solid line rep-resents compositions on the ideal Fe.Oo-MgAl.Oo binary join.

FeAlrOo MgAlrOu

M.lcxBrrc MEASUREMENTs

Magnetic hysteresis loops were measured at 4.4 K ardin fields up to l2 T, vrith an Oxford Instruments vibratingsample magnetometer, equipped with a superconductingmagnet. Sintered chunks with a mass of 0.007-0.026 gand a diameter of 3-5 mm were placed on the end of aplastic sample holder and held in place with several layersof PTFE tape. The temperature of the sample was heldnear 4.4 K by balancing the output from a resistive heaterwith a flow of He gas through the superconducting mag-net bore. Temperature was measured with a thermocou-ple to an accuracy of +0. I K and varied between 4.3 and5 K during the time taken to measure each hysteresis loop(=50 min). Magnetization lvas measured as a function ofapplied field with a field ramp rate of 20 mT/s. The highramp rate was necessary to complete measurements in a

216 HARRISON AND PUTNIS: MAGNETITE-SPINEL MAGNETIC PROPERTIES

) s o o oq

o

- 2 0 0 0

TraLe 2. Saturation magnetization, M" (4.4 K) and coercivity,H", of synthetic spinels

Composition (x) M. (4.4 K) (p,) H. (mT)

0.09o.170.230.30.360.410.510.510.610.8'1

0.350.28o.270.260.360.390.840.891.272.233.92

539

235.7715.6392.4169.945.85 1 . 128.31 01 0

20 ( ' )

Fig. 3. Step-scan diffractometer peak profiles ofthe 31 I (a)and 440 (b) reflections in sample SPI I (x : 0.5). The solid lineis the resultant fit to the raw intensity data (plus signs), using thesum oftwo Gaussians for reflection 3ll and the sum ofthreeGaussians for reflection 440. The individual Gaussian compo-nents are shown as dashed lines.

reasonable time. The estimated error in magnetizationmeasurements is < l0-8 Am2.

The value of the saturation magnetization (i.e., mag-netization in an inf,nite applied field) was determined byfitting the high-field portion of the initial magnetizationcurve (from 4 to 12 T), with an equation of the form M: M.(l - a/m + kH, where M" is the saturation mag-netization, 11 is the applied field, and a and k are con-stants (Brown et al., 1993). The kH term is due to theforced magnetization in very high fields. Excellent fits tothe magnetization curves were possible.

Rnstnrs oF MAGNETTC MEAstREMENTS

Eleven hysteresis loops for samples of various com-position along the binary were measured, four of whichare presented in Figure 4. There is a clear transition inthe characteristic shape ofthe hysteresis loops toward the

. Apparent composition

spinel-rich end ofthe solid solution. In particular, thereis a large variation in the field required to reduce themagrretization to zero (i.e., the coercivity). Magnetite-richsamples have low coercivities and are fully saturated infields >2 T. Spinel-rich samples have extremely largecoercivities and do not appear to saturate, even in themaximum field of 12 T. The values of the saturationmagrretization per formula unit and the coercive force arepresented in Figure 5. Our confidence in the results forM" (4.4 K) is high because of the low errors involved inthe measurement of magnetization and the ideal condi-tions under which they were obtained. The error in thegiven value of the coercive force is large, however, be-cause of the poor resolution achieved with a field ramprate of 20 mT/s.

The saturation magnetization for the pure magnetiteend-member, given in Table 2, is 3.9 pb per formula unit(l po : 9.27 x 10-24 Am2), compared with an ideal valueof 4.1 po. This may suggest some degree of nonstoichiom-etry in this sample (Readman and O'Reilly, 1972). M"(4.4 K) falls to a minimum of 0.26 rrb pfu as the com-position varies between x : I and -x : 0.3. It then risesto a maximum of 0.35 pb at x : 0.09 before falling tozero in the pure spinel end-member. The minimum inthe M" (4.4 K) curve at x : 0.3 is correlated with a peakcoercivity of over 700 mT.

DrscussroxThermodynamics and cation disfributions

The variation in saturation magnetization as a functionof composition must be accounted for in terms of thedistribution of Fe3+ and Fe2+ ions between octahedraland tetrahedral sites. The equilibrium cation distributionhas been calculated for this solid solution as a functionof temperature and composition using an existing ther-modynamic model, calibrated for the Fe-Mg-Al quater-nary (Nell and Wood, 1989). Calculations were per-formed by solving numerically the three nonlinear si-multaneous equations given by Nell and Wood (1989)for the quaternary system, with compositions restrictedto the FerOo-MgAlrO4 binary (see Eqs. 25-27, Nell andWood, 1989). The expected saturation magnetization was

0 r3 4

2 0 ( ' )

o

o ' - - '

6 4 56 4 06 3 . 00 L

100 molo/o magnetlte

ra

)

HARRISON AND PUTNIS: MAGNETITE-SPINI]L' MAGNETIC PROPERTIES 2 t 7

1 5

' t 0

5o

J

' e osE

:- e o

E- 5

- t 0

- 1 5

1 5

1 0t 0

5

J* e ocE .

- 5

:' E o

€- 5

41 mol% magnetite' b

- 50

- t 0 0

0I (r)

- 8 - 4 0 4 5 1 2

B (T)

then derived directly from the calculated cation distri-bution, assuming a spin-only moment of 4 p.o for Fe2+ions and 5 po for Fe3+ ions. One Bohr magneton is themagnetic dipole moment associated with a single un-paired electron spin (l pr:9.27 x 10-24 Am'z). Resultsfor a temperature of 1200 'C are given in Figure 6. Themagnetization measured at 4.4 K is lower than that ofthe theoretical magnetization because of the effects of or-der-parameter saturation at low temperature (Salje et al.,I 99 I ). Magnetic order-parameter saturation is a quantumeffect, causing dM"(T)/dT to approach zero as T ap-proaches zero. The effect has been observed in the tita-nohematite system (Brown et al., 1993). The comparisonbetween observed and calculated magnetizations in Fig-ure 6 is hence intended only as an indicator ofthe trendin magnetization vs. composition.

The thermodynamic model predicts that, for magne-tite-rich compositions, the solid solution is ferromagneticwith the B sublattice magnetization greater than the Asublattice magnetization (M" is positive). At some inter-mediate composition, x", there is a compensation pointwhere the solid solution is antiferromagnetic with the Aand B sublattice magnetizations equal. For more spinel-rich compositions the solid solution becomes ferromag-

- 1 0

Fig. 4. Magnetization per unit mass, M(Am'zlkg), vs. applied fleld, A (T), for samples (a) SPl5, O) SP9, (c) SP6, and (d) SP3.

- 1 2 - 8 - 4 0 4 8 1 2

B (T)

netic with the A sublattice magnetization greater than theB sublattice magrretization (M" is negative). In this con-text, the sign of the saturation magnetization indicateswhether the net magnetization of the sample is parallelor antiparallel to the B sublattice magnetization. Themagnetization experiments measure only the modulus ofM", as indicated by the dashed line in Figure 6. The com-pensation point shifts toward more magnetite-rich com-positions with decreasing temperature. An exact compen-sation point exists only for an ideal structural state, wherethe composition and degree ofnonconvergent cation or-der remain homogeneous. A real crystal is heterogeneouson some scale and hence has a value of M" that is anaverage over all compositional and ordering fluctuations.In this case, we would expect to see M" fall to a minimumat x.. Hence the experimental results presented here areconsistent with the existence of a compensation point atx" = 0.3, samples with x < x" having their net magneti-zation reversed with respect to those with x > x".

Coercive force at the compensation point: Speculation

The grain size of all samples is mostly in the range of0.5-2 prn. There is no systematic variation in the averagegrain size across the solid solution. At room temperature

30 mol"/o magnetlte ,4 16.5 mol% magnet i te

218

r 0 0 0

8 0 0

6 0 0

Fig. 5. Saturarion ff;;:;.-t" ",it, M" (4.4

K) (pJ, and coercive force, fI" (mT), vs. composition. The com-pensation point, x", corresponds to the minimum in the satu-ration magnetization curve at x : 0.3 (30 mol% magnetite); 1pa:9.27 x l0 2o Am2.

we would expect the grains to display multidomain orpseudo-single-domain properties (Dunlop, 1990). Theexpected magnetic domain state at 4.4 K depends on thetemperature variation of anisotropy constants, exchangeconstants, and magnetostriction. In general, the equilib-rium number of domain walls decreases with tempera-ture, and hence it is likely that samples are either singledomain or contain very few conventional magnetic do-main walls.

The origin of coercivity in many magnetic materials isstill a subject of much debate in the literature. Currenttheories on coercivity mechanisms in permanent magnetmaterials were reviewed by Livingston (1981) and Zijls-tra (1982). In the present case, we must consider coerciv-ity mechanisms that operate in single-phase material con-taining fluctuations in composition or degree of cationordering. Such a mechanism must account for both themagrritude and compositional dependence of f1". Typicaltheories deal with the pinning of conventional magneticdomain walls by strain or by fluctuations in the magneticanisotropy and exchange constants (Jatau and Della Tor-re, 1993a, 1993b, 19941. Jatau et al., 1994). Such fluctu-ations change the energy of a domain wall locally, eitherpinning the wall or providing a barrier to wall motion.Calculation of the expected coercivity from such a mech-anism is not possible without knowledge of the compo-sitional dependence of anisotropy and exchange con-stants and information about the wavelength and ampli-tude of the fluctuations.

Giant intrinsic coercivities have been observed in manyhighly magnetic anisotropy materials at cryogenic tem-

HARRISON AND PUTNIS: MAGNETITE-SPINEI- MAGNETIC PROPERTIES

F

E

3 s F

x . 9e F

coG=o

- 6

6o

t . 00 . 80 . 60 . 20 . 0

litote flacrion magnetire lxl

Fig. 6. Predicted variation in saturation mametization vs.composition, using the cation distribution model of Nell andWood (1989) and spin-only moments of 4 po for Fe2+ and 5 pofor Fe3+. The cation distribution is calculated in intervals of l0molo/o for a temperature of 1200 qC. The solid line is the pre-dicted saturation magnetization. The dashed line is the modulusof predicted magnetization, i.e., the quantity measured in thehysteresis experiments. The triangles are our measured valuesfor the saturation magnetization.

peratures (Oesterreicher, 1978). An example is Sm-Co,

"Ni,, which has a maximum intrinsic coercivity of

23 T at 4.2 K. This results from the fact that the widthsof magnetic domain walls in highly anisotropic materialsare of the same order of magrritude as the lattice spacing.For these thin walls, the energy of the wall is larger whenthe center of the wall coincides with an atomic planerather than lying just either side of it (Zijlstra, 1982). Thisleads to a large intrinsic resistance to wall motion (anal-ogous to the Peierls stress experienced by dislocations).The high coercivity in SmCo, ,Ni, is extremely depen-dent on composition, with a pronounced peak in thecoercivity spectrum at x : 4. The compositional depen-dence may be interpreted in terms of fluctuations in theexchange constant. A possible explanation for the largeincrease in coercivity at the compensation point is pro-posed below.

If the above model for the cation distribution is correct,then fluctuations in composition, close to x", will lead toadjacent domains of opposed magnetization. The sameeffect results from a sample of homogeneous compositionbut fluctuating degree ofcation order, due to the shiftingposition of the compensation point. The chemical fluc-

HARRISON AND PUTNIS: MAGNETITE-SPINEL MAGNETIC PROPERTIES 219

tuation hence produces a fine-scale magnetic domain wall.The size of the domain wall is identical to that of thefluctuation, typically 100-200 A. A schematic model forsuch a domain wall is shown in Figure 7.1-ateral motionof these domain walls is impossible without cooperativecation migration. Saturating the sample hence requiresovercoming the strong exchange coupling between adja-cent domains. The mechanism by which this might occurinvolves the nucleation of reverse magnetic domains withdomain-wall widths smaller than the wavelength of thefluctuation. These thin walls would be easily pinned bystrain or the fluctuations in exchange and anisotropy con-stants, which result from heterogeneities in compositionand cation order. This, together with the high numberand fine scale of the domains, leads to the anomalouslyhigh coercivities observed in samples near rc.

It is interesting to compare the magnitude of the co-ercive force measured here with that observed in the he-matite-ilmenite system (Brown et al., 1993). This systemdisplays exchange-dominated pinning of domain walls bytransition induced domain boundaries (Nord and Law-son, 1989, 1992). Brown et al. (1993) gave values for thecoercive force varying between 100 and 320 mT for thetemperature range 298-77 K. By linear extrapolation oftheir data, we obtain a coercive force of approximately400 mT at 0 K, in samples containing a high density ofdomain boundaries. In samples with low densities of do-main boundaries they observe coercivities of around 20mT. There is an excellent correlation between the mag-nitude of the coercive force in the titanohematite systemand the magnetite-spinel system. In both cases chemicalheterogeneities lead to magnetic domain walls that arepinned by strong exchange interactions. The higher co-ercive force observed in the magnetite-spinel system maybe accounted for by the extremely fine scale of the fluc-tuations responsible for the effect.

Fluctuations in composition or degree of cation orderare to be expected in samples quenched from 1400 "C.Significant cation reordering has been observed in spinelsquenched from temperatures above 1000 .tC (Wood et al.,1986; Milliard et al., 1992). Such nonequilibrium behav-ior may give rise to kinetic microstructures (Carpenterand Salje, 1989), whereby local regions in the crystal or-der at a faster rate than others, enhancing any preexistingheterogeneities. Some degree of cation clustering may alsobe expected on account ofthe high-temperature solvus.

The results presented here suggest that flne-scale het-erogeneities are present in spinel solid solutions quenchedfrom high temperatures. This suggestion has significantconsequences for the thermodynamic description of suchsystems. In particular, the assumption that the entropyof disordering in complex spinels is purely configuration-al (O'Neill and Nawotsky,1984; Sack and Ghiorso, l99l;Nell and Wood, 1989) is inappropriate. This factor maycontribute to some of the quantitative diferences in ourobserved and calculated variations in cation distribution.A free energy expansion of the Landau-Ginzburg typemay be more appropriate in describing nonconvergent

A B

F\g. 1. Schematic model for the magnetic domain state in asample of bulk composition .x: .16., containing a compositionalfluctuation between magnetite-rich (Mag) and spinel-rich (Sp)regions. Solid arrows represent the magnitude and direction oftetrahedral (A) and octahedral (B) sublattice magnetizations.Shaded arrows represent the direction of net magnetization ineach region ofthe compositional fluctuation.

ordering and kinetics in heterogeneous systems (Carpen-

ter and Salje, 1989), since this approach takes account ofboth nonconfigurational entropy and fluctuations in thedegree oforder.

Mechanism for self-reversed thermoremanentmagnetization

Self-reversed thermoremanent magnetization resultsfrom the antiferromagnetic coupling between a stronglymagnetic, low Z" phase and a weaker, high 4 phase (Dun-lop, 1990). When cooled through the high-temperatureCurie point, the weakly magnetic phase obtains a mag-netization aligned parallel to the applied field. Because ofthe negative coupling between the two phases, the stron-ger magnetic phase obtains a magnetization antiparallelto that of the weaker phase when cooled through the low-temperature Curie point. Hence the net magnetization isreversed with respect to the applied field. The couplingmechanism may be either magnetostatic or exchangebased (McClelland and Goss, 1993), exchange couplingbeing the more effective. The most common example ofnatural self-reversal is in the titanohematite system (Ish-ikawa and Syono, 1963). Self-reversal in synthetic tita-nohematites of composition 300/o hematite and 700/o il-menite have been observed experimentally (Nord andLawson, 1992). Here the high-4 phase consists of Fe-enriched twin domain boundaries, which form during theR3c to R3 cation ordering transition. Self-reversal insamples with compositions < 500/o ilmenite may be causedby exsolution of a hematite-rich phase (Carmichael, l96l;Hoffman, 1975).

A mechanism for self-reversal in homogeneous ironspinels containing significant amounts of nonmagneticions has been proposed previously (Verhoogen, I 956) be-cause of changes in the equilibrium cation distribution'The mechanism operates for certain compositions whenthe magrretization associated with the low-temperatureordered distribution is reversed with respect to the high-temperature disordered state. A sample that is given amagnetization in the high-temperature state will obtain a

A B

I+l. V

ffivS p

o

--200 A -----+A B A B A B

M a g S p M a g

A B

++NDi.iiF'l

vS p

l r

lvAr$H

M a g

220

reversed magnetization after subsequent annealing at thelower temperature. This mechanism is appropriate to sys-tems where a significant degree of cation disorder remainsat the Curie temperature.

The magnetic domain structure in the FerOo-MgAlrOosolid solution at compositions near x. provides an idealmechanism for self-reversed thermoremanent magneti-zalion. There is a large variation in Curie temperaturewith the composition in this system. The variation of Z.with degree of cation order is unknown but is likely to beless pronounced (Moskowitz, 1987). In either case, thefluctuations in composition or cation order, which areresponsible for the anomalous coercivity near x., produc-es adjacent regions with different Curie temperatures andstrong negative exchange coupling. Depending on the rel-ative amounts of magnetite-rich and spinel-rich domains,we would expect self-reversed or partial self-reversedthermoremanent magnetization to occur on coolingthrough the magnetic ordering temperature in an appliedfield. This is an important example of a self-reversingmechanism where the detailed nature of the negative ex-change coupling is known, in contrast to many other pro-posed mechanisms, where only the presence of the secondmagnetic phase could be accounted for (Hoffman, 1975).

Acrxowr,rcncMENTs

The authors would like to thank Charles Dewhurst, at the Interdisci-plinary Research Centre in Superconductivity, Cambridge, for his help inmaking the magnetic measurements and for the use of the 12 T vSM.Many thanks to E. McClelland for her comments on an earlier version ofthe manuscript and to the reviewers G.L. Nord, Jr. and N.E. Brown fortheir useful comments and suggestions. R.J.H. acknowledges the receiptofa grant from the Natural Environment Research Council.

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Mem;scnrrr RECETvED Jvw24, 1994

MaNuscrrrr AccEprD Noveusen 21, 1994