changes in remanence, coercivity and domain state at low temperature in magnetite

Changes in remanence, coercivity and domain state atlow temperature in magnetite

Oë zden Oë zdemir a;*, David J. Dunlop a, Bruce M. Moskowitz b

a Department of Physics, University of Toronto at Mississauga, Mississauga, ON, Canada L5L 1C6b Institute for Rock Magnetism, University of Minnesota, Minneapolis, MN 55455, USA

Received 17 July 2001; received in revised form 18 October 2001; accepted 19 October 2001

Abstract

Submicron magnetite crystals with mean sizes of 0.037, 0.10 and 0.22 Wm undergo major changes in hysteresisproperties and domain states in crossing the Verwey transition (TVW120 K). The 0.037 Wm crystals are single-domain(SD) both in the cubic phase at room temperature T0 and in the monoclinic phase below TV. The 0.10 and 0.22 Wmcrystals have a mixture of SD and two-domain (2D) states at room temperature T0, but mainly SD structures below TV,in agreement with micromagnetic calculations. Coercive force Hc increases on cooling through TV, by a factor 3^5 inthe submicron magnetites and 40 in a 1.3 mm single crystal, because of the high crystalline anisotropy andmagnetostriction of monoclinic magnetite. As a result, domain walls and SD moments are so effectively pinned belowTV that all remanence variations in warming or cooling are reversible. However, between W100 K and T0, remanencebehavior is variable. Saturation remanence (SIRM) produced in monoclinic magnetite at 5 K drops by 70^100% inwarming across TV, with minor recovery in cooling back through TV (ultimate levels at 5 K of 23^37% for thesubmicron crystals and 3% for the 1.3 mm crystal). In contrast, SIRM produced in the cubic phase at 300 K decreases5^35% (submicron) or s 95% (1.3 mm) during cooling from 300 to 120 K due to continuous re-equilibration of domainwalls, but there is little further change in cooling through TV itself. However, the submicron magnetites lose a further 5^15% of their remanence when reheated through TV. These irreversible changes in cycling across TV, and the amounts ofthe changes, have potential value in determining submicron magnetite grain sizes. The irreversibility is mainly caused by2DCSD transformations on cooling through TV, which preserve or enhance remanence, while SDC2Dtransformations on warming through TV cause remanence to demagnetize. ß 2002 Elsevier Science B.V. All rightsreserved.

Keywords: magnetite; hysteresis; magnetic domains; coercivity; remanent magnetization

1. Introduction

There has been much recent interest in the

properties of magnetite at low temperatures, par-ticularly in cycling through the Verwey transition(TVW120 K), where magnetite transforms fromcubic to monoclinic structure [1^10]. Most pub-lished data (e.g. [2,4,11,12]) are for remanencesproduced in cubic magnetite at room temperatureT0, then cooled through TV and warmed back toT0. Only rarely (e.g. [13], Fig. 7; [14], Fig. 2; [8],

0012-821X / 02 / $ ^ see front matter ß 2002 Elsevier Science B.V. All rights reserved.PII: S 0 0 1 2 - 8 2 1 X ( 0 1 ) 0 0 5 6 2 - 3

* Corresponding author. Tel. : +1-905-828-3829;Fax: +1-905-828-5425.

E-mail address: [email protected] (O. Oë zdemir).

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Fig. 5) have companion data been measured forremanences produced in the monoclinic phase be-low TV, then warmed through TV to T0 andcooled back through TV to the original temper-ature. Very few of these data are for submicronmagnetites or large single crystals. One purpose ofthe present study was to produce high-qualityhysteresis and remanence cycling data for thesevery small and very large magnetites.

Despite the wealth of published work, it is stillunclear what controls the transformation of rema-nence across the cubic^monoclinic phase transi-tion, or indeed what is the domain structure ofmonoclinic magnetite below TV. Moloni et al.[3] were successful in imaging domains between77 and 110 K on the {110} plane of discs cutfrom a large synthetic single crystal of magnetite,using a novel low-temperature magnetic forcemicroscope. They found two types of domains,both typical of substances with strong uniaxialanisotropy. Lamellar domains without closurestructures characterized parts of the crystal wherethe monoclinic c-axis (the easy axis of magnetiza-tion) lay in the plane of view, while intricate wavypatterns appeared in twinned regions where the c-axis intersected the viewing plane. Structures un-fortunately faded from view around 110 K, butreappeared on cooling. Pinning of a wall by atopographic feature was observed in one case.No observations were possible of domains aboveTV, nor of how structures transform or are re-nucleated between the cubic and monoclinicphases.

There are no domain observations at low tem-peratures for smaller magnetite crystals, but Mux-worthy and Williams [15,16] have made micro-magnetic calculations of the structures of modelmagnetite cubes ranging in size from 0.08 to 0.6

Wm at temperatures down to 100 K. Modeling atlower temperatures was limited by fragmentaryknowledge of the governing physical constants.One important prediction of their work is thatthe critical SD size increases from 0.07 Wm inthe cubic phase at T0 to 0.14 Wm in the mono-clinic phase at 110 K, just below TV. Thus wewould expect to see a marked change in magneticproperties such as hysteresis parameters of mag-netites in the 0.07^0.14 Wm size range in crossingthe Verwey transition. Testing this prediction isanother purpose of our work.

2. Sample characterization

We studied three ¢ne-grained magnetites withmedian particle sizes of 0.037, 0.10 and 0.22 Wm.Their basic properties have been described byDunlop [17,18]. The cube-shaped crystals weregrown from aqueous solution and were initiallysurface oxidized. We therefore heated the magne-tites in a mixture of 80% CO2 and 20% CO for 120h at 395³C to reduce the surface layer and thenstored them in a desiccator until beginning experi-ments. Experimental samples were 2% by weightdispersions of magnetite in non-magnetic CaF2.

Susceptibility curves measured with a Kappabridge gave magnetite Curie temperatures of575^580³C. X-ray unit cell edges determined usinga Debye-Scherrer camera with Cu-KK radiationwere 8.393 þ 0.008, 8.399 þ 0.005 and 8.400 þ0.005 Aî for the 0.037, 0.10 and 0.22 Wm samples,respectively. These values are characteristic of stoi-chiometric magnetite. Saturation magnetizationMs values of 85.8, 89.2 and 89.4 Am2/kg (Table1) also indicate nearly stoichiometric Fe3O4.

For comparison, we studied a 1.3 mm single

Table 1Values of hysteresis parameters measured at room temperature and at low temperature

Grain size Measurements at 295 K Measurements at W15 K

(Wm) Ms Mrs/Ms Hc Hcr/Hc Ms Mrs/Ms Hc Hcr/Hc

(Am2/kg) (mT) (Am2/kg) (mT)

0.037 þ 0.015 85.8 0.276 17.5 1.61 91.5 0.517 89.7 1.450.10 þ 0.03 89.2 0.219 13.3 1.64 95.4 0.406 50.2 1.280.22 þ 0.04 89.4 0.126 8.8 2.69 94.0 0.389 37.1 1.271300 90.7 0.003 0.13 45 ^ 0.013 1.1 ^

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crystal of magnetite from Richmond County, QC,Canada. The Curie temperature of 577³C, spinelunit cell edge a = 8.397 Aî , and room temperatureMs of 90.7 Am2/kg indicate stoichiometric mag-netite with no major impurities.

3. Low-temperature hysteresis

Hysteresis loops were measured in a maximum¢eld of 1.5 T at selected temperatures from W15K to 295 K using a Princeton Measurements Cor-poration AGFM (MicroMag Model 2900) with aliquid He cryostat. Condensation and icing on thecryostat interfered with measurements below W15K. Hysteresis measurements on the 1.3 mm crys-

tal used a Quantum Design MPMS-2 SQUIDmagnetometer at Kyoto University, Japan.

Table 1 summarizes 295 K and W15 K valuesof the saturation magnetization Ms, saturationremanence to saturation magnetization ratioMrs/Ms, coercive force Hc, and remanent to ordi-nary coercive force ratio Hcr/Hc. At W15 K, thethree submicron samples have parameters ap-proaching those of single-domain (SD) grains:Mrs/Ms = 0.389^0.517 and Hcr/Hc = 1.27^1.45. At295 K, on the other hand, Mrs/Ms values aremuch below 0.5 and depend strongly on grainsize, while Hcr/Hc increases to 1.6^2.7. Hc valuesare a factor 4^5 higher at W15 K than at roomtemperature.

Values of Hc for the submicron magnetites atintermediate temperatures are plotted in Fig. 1.Between room temperature and the onset of the

Fig. 1. Coercive force Hc measured in 1.5 T hysteresis loopsat temperatures from W15 to 295 K. Hc is almost tempera-ture independent above TV, then increases sharply in crossingthe Verwey transition for all submicron magnetites.

Fig. 2. Remanence ratios Mrs/Ms measured at low tempera-tures. Above TV, Mrs/Ms is constant, indicating no change indomain state. Below TV, all the submicron magnetites showsharp increases in Mrs/Ms, reaching SD-like values of 0.39^0.52 at W15 K.

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Verwey transition at TVW120 K, Hc is almostconstant. Only for the 0.037 Wm sample is therea slight increase, from 17.5 mT at 295 K to 19.0mT at 130 K. This small gradual increase in Hc

may re£ect residual non-stoichiometry in the sur-face layers of these ultra¢ne magnetite crystals.The 0.037 Wm sample had slightly lower Ms valuesthan those of the other magnetites (Table 1), in-dicating some surface oxidation.

At the Verwey transition, all the submicronmagnetites showed an increase in coercive force.The largest increase in Hc, from 20 mT at 125 K

to 70 mT at 100 K, was for the 0.037 Wm sample.Below 100 K, Hc continued to increase but moreslowly, ultimately reaching 90 mT for the 0.037Wm sample at 20 K.

Mrs/Ms changes somewhat di¡erently at lowtemperature (Fig. 2). As with Hc, Mrs/Ms valuesare almost temperature independent between 300K and TV. However, Mrs/Ms then increases verystrongly and rapidly over the narrow temperaturerange 120^110 K, but unlike Hc, changes verylittle between 100 and 20 K for all the submicronsamples. Mrs/Ms approximately doubled in cross-

Fig. 3. Low-temperature hysteresis parameters of the 0.10 and 0.22 Wm magnetites on a Day plot of Mrs/Ms vs. Hcr/Hc. Thedata follow PSD type curves [20] quite closely. Changes from more MD-like to SD-like parameters occur between 100 and 120K (Verwey transition).

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ing the Verwey transition for the 0.037 Wm sam-ple. The change in Mrs/Ms was largest of all forthe 0.22 Wm sample: from 0.136 at 120 K to 0.34at 100 K.

The changing domain structure at low temper-ature is traced in Fig. 3 on a Day et al. [19] plot ofMrs/Ms vs. Hcr/Hc. The three type curves, calcu-lated by mixing experimental data from SD (or¢ne-grained, F) and small multidomain (MD)end members, ¢t measured values for sized pseu-do-single-domain (PSD) magnetites quite well[20]. The largest change in domain structure isfor the 0.22 Wm sample. At 150^295 K, Mrs/Ms = 0.126^0.128 and Hcr/Hc = 2.66^2.69, charac-teristic of moderately large PSD magnetites (70^75% MD mixtures), while at 14^71 K, Mrs/Ms = 0.380^0.389 and Hcr/Hc = 1.27^1.31, closeto SD values. Mrs/Ms and Hcr/Hc hardly changeon cooling through the isotropic temperatureTiW130 K, where the ¢rst magnetocrystalline ani-sotropy constant K1 changes sign and momentar-ily vanishes, in spite of the change at Ti fromG111f to G100f easy axes which must cause somereorganization of the domains. Mrs/Ms and Hcr/

Hc change mainly between 120 and 90 K, withW75% of this change (measured along the Dayplot curves) occurring between 110 and 100 K.Changes in domain structure are therefore mainlya result of the decreasing lattice symmetry (cubicspinelCmonoclinic) and accompanying large in-crease in crystalline anisotropy in crossing theVerwey transition. The changes in Mrs/Ms andHcr/Hc are less dramatic for the 0.10 Wm samplebut again occur almost entirely at and below TV,not around Ti.

The room temperature hysteresis curve of the1.3 mm magnetite crystal is ramp-like and typicalof large MD grains. Room- temperature hystere-sis parameters are consistent with truly MD be-havior: Ms = 90.7 Am2/kg, Hc = 0.13 mT, Mrs/Ms = 0.003 and Hcr/Hc = 45. The temperature de-pendence of coercive force during cooling from300 to 15 K is shown in Fig. 4. In contrast tothe behavior of the submicron magnetites, Hc de-creased on cooling, reaching a minimum at theisotropic temperature Ti = 130 K. In crossing theVerwey transition, Hc increased more than an or-der of magnitude, from 35 WT to 1.1 mT. The

Fig. 4. Coercive force Hc measured in 0.4 T hysteresis loops for the 1.3 mm crystal of magnetite at temperatures from 10 to300 K.

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change was much sharper than for the submicronmagnetites, occurring mainly in a 6 10 K intervalbelow 120 K. In cooling from 110 to 15 K, Hc

remained essentially constant, again in contrast tothe submicron magnetites.

4. Isothermal remanence cooling (300CC5 K) andwarming (5CC300 K) curves

We measured temperature dependence of rema-nence with an MPMS-2 SQUID magnetometer atthe Institute for Rock Magnetism, University ofMinnesota, Minneapolis, MN, USA. Sampleswere given a saturation isothermal remanent mag-netization (SIRM) in a ¢eld of 2.5 T at roomtemperature, then cooled in zero ¢eld to 5 Kand back to 300 K. The SIRM cooling and warm-ing curves for the submicron magnetites areshown in Fig. 5. The SIRM cooling curve forthe 0.037 Wm sample is almost £at between 300and 150 K. In further cooling across the Verweytransition, the remanence dropped to 95% of theoriginal SIRM, but this was not a permanent de-

magnetization. SIRM cooling and warmingcurves were reversible for the monoclinic phasein the range 5^90 K, with all but 2% of the initialSIRM intensity being recovered at 5 K. Warmingthrough the Verwey transition resulted in a per-manent remanence loss, however, with W85% ofthe original SIRM remaining at 300 K.

In cooling from 300 K to TV, the remanence ofthe 0.10 Wm magnetite decreased in much thesame way as that of the 0.037 Wm magnetite. AtTV, 10% of initial SIRM had apparently beendemagnetized but all but 2% of this remanencewas recovered in cooling to 5 K. The remanenceretraced the cooling curve in warming from 5 to100 K, then decreased sharply at the mono-clinicCcubic phase transition. The memory atroom temperature was about 80% of the initialSIRM.

The zero ¢eld cooling and warming curves ofSIRM for the 0.22 Wm sample had many of thesame features as those of 0.037 and 0.10 Wm mag-netites but the decrease in remanence with coolingto TV was larger. At the phase transition, theremanence was only 63% of the initial SIRM

Fig. 5. Normalized temperature variation of saturation isothermal remanence (SIRM) of submicron magnetites during zero ¢eldcooling from 300 to 5 K and zero ¢eld warming back to 300 K. SIRM was produced in a ¢eld of 2.5 T at 300 K. Open circles,triangles and squares represent the 0.037, 0.10 and 0.22 Wm magnetites, respectively.

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and there was little recovery in cooling to 5 K.The cooling and warming curves below TV resem-ble those of the 0.037 and 0.10 Wm samples. Inwarming from 90 to 120 K, the remanence de-creased a further W15%, then increased slightlywith further warming. At 300 K, the survivingremanence was 55% of the original SIRM.

For all submicron magnetites, SIRM coolingand warming curves are irreversible for the high-temperature cubic phase but completely reversibleat all temperatures below 90 K for the low-tem-perature monoclinic phase. The remanence de-crease across the Verwey transition during thewarming half cycle becomes more marked withincreasing grain size. The permanent remanenceloss at 300 K after a complete cycle also increaseswith increasing grain size.

SIRM cooling and warming curves for the 1.3mm magnetite crystal appear in Fig. 6. The rema-nence decreased steadily with cooling to the Ver-wey transition, as for the 0.22 Wm magnetite, butthe changes were much larger. By 120 K, only 3%of the original SIRM remained. The remanencethen increased sharply in cooling across TV, fol-lowed by a smaller more gradual decrease be-

tween 110 and 100 K. In warming from 10 K toTV, the behavior was completely reversible, butabove TV, the remanence did not retrace the cool-ing curve but increased slightly until 150 K andthen became almost temperature independent.The SIRM memory at room temperature wasW10%.

5. Isothermal remanence warming (5CC300 K) andcooling (300CC5 K) curves

The submicron magnetites were cooled to 5 Kin zero ¢eld, where they were given a 2.5 T SIRM,and then warmed to 300 K in zero ¢eld. Theshapes of the remanence curves between 5 and90 K and also across the Verwey transition werebasically the same for all samples, but the amountof remanence lost at TV increased with increasinggrain size (Fig. 7). In warming from 5 K, therewas a slight drop in remanence extending up to35 K for all the submicron magnetites. Similarbehavior has been observed for a large naturalsingle crystal of magnetite by Oë zdemir et al. [1],ruling out remanence unblocking in ultra¢ne par-

Fig. 6. Normalized zero ¢eld cooling (300C5 K) and warming (5C300 K) curves for SIRM produced at 300 K in the 1.3 mmcrystal of magnetite.

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ticles as a cause. The remanence drop may berelated to a 30^35 K transition, marked by asharp peak in the quadrature susceptibility kQ atthis temperature [21,22]. Following major dropsat the Verwey transition, the remanence remainedconstant or decreased slightly in warming above

TV. In recooling across the Verwey transition,there was little recovery of low-temperature rema-nence. The SIRM memories for the 0.037, 0.10and 0.22 Wm samples at 5 K were 37, 31 and23% of the original monoclinic SIRM, respec-tively.

Fig. 7. Normalized zero ¢eld SIRM warming curves from 5 to 300 K for submicron magnetites. SIRM was produced in mono-clinic magnetite in a ¢eld of 2.5 mT at 5 K. The open circle, triangle and square at 5 K are SIRM memories after a completewarming^cooling cycle.

Fig. 8. Normalized zero ¢eld SIRM warming curve from 10 to 300 K for the 1.3 mm crystal of magnetite. The single point at10 K is the SIRM memory of monoclinic magnetite after cooling from 300 to 10 K.

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The SIRM warming curve for the 1.3 mm mag-netite crystal (Fig. 8) di¡ers in several ways fromthe submicron magnetite curves. The remanencewas almost temperature independent between 10and 100 K. At the crystallographic phase transi-tion, the remanence decreased abruptly over onlytwo temperature steps to practically zero, where itremained from TV to 300 K. Thus SIRM pro-duced in monoclinic magnetite of this size is com-pletely demagnetized in the transition to the cubicphase. Almost no memory of the initial SIRMwas recovered in recooling through the Verweytransition.

6. Discussion

6.1. Domain states at room temperature andlow temperature

Magnetite in 0.037 Wm cubes should have SDstructure both above and below TV. We measuredMrs/Ms = 0.517 at W15 K, but at 295 K, Mrs/Ms

was only 0.276 (Table 1). A major factor in thisdi¡erence is superparamagnetism. Particles have adistribution of sizes about the mean and thesmaller particles are thermally unstable or super-paramagnetic (SP) at 295 K [17]. They contributeto Ms but not to Mrs, thereby lowering the Mrs/Ms ratio. At 15 K, most of these particles arestable SD because thermal energy kT is 20 timessmaller. Mrs/Ms thus increases to more SD-likevalues. SP behavior at room temperature is prob-ably responsible also for the rather high Hcr/Hc

value of 1.61 [20].Two factors in£uence the SD value of Mrs/Ms :

`£owering' of the spins at the corners of SD grains[23,24] and the number of easy axes of anisotropy.The £owering factor is 0.92 for 0.1 Wm magnetitecubes [15] and increases with decreasing size [23].More signi¢cant is the di¡erence between uniaxialand multiaxial anisotropy. Perfect cubes at 295 Kwould have purely magnetocrystalline anisotropywith four equivalent G111f easy axes, leading to anexpected Mrs/Ms of 0.866 ([25], Ch. 11). However,high-temperature hysteresis [26] suggests thatthere is su¤cient elongation of our submicroncubes to make uniaxial shape anisotropy impor-

tant; Mrs/Ms = 0.5 is expected for uniaxial aniso-tropy. Experimentally (Fig. 2) there is no obviouschange in Mrs/Ms for any of the submicron mag-netites in passing the isotropic temperatureTi = 130 K, where K1 momentarily vanishes andthe spins in perfect SD cubes would rotate toG100f easy axes, with Mrs/Ms = 0.832. Shape ani-sotropy is probably responsible.

The evolving domain structures of the 0.1 and0.22 Wm magnetites are well displayed in Fig. 3.At room temperature, both have PSD values ofMrs/Ms and Hcr/Hc which change to almost SDvalues at 15^50 K. Because 0.1 Wm is above thecritical SD size d0 for cubic magnetite but belowd0 for monoclinic magnetite [15], this is the ex-pected trend for our 0.1 Wm magnetite. The trendfor our 0.22 Wm magnetites is not as expected,however. Such grains are well above the predictedd0 of 0.14 Wm at 110 K and should not have Mrs/Ms and Hcr/Hc values almost identical to those ofthe 0.1 Wm magnetites at 15^50 K. Perhaps, as theHc values in Fig. 1 suggest, the anisotropy ofmonoclinic magnetite increases enough with cool-ing from TV to 50 K to push d0 above 0.22 Wm.Of course, the Mrs/Ms values of 0.406 and 0.389at 15 K are distinctly lower than Mrs/Ms = 0.517of the 0.037 Wm sample, so there must be somecompromise with SD structure in the largergrains, likely an admixture of two-domain (2D)states.

Values of Mrs/Ms and Hcr/Hc at room temper-ature and down to 150 K indicate quite di¡erentstructures for 0.1 Wm compared to 0.22 Wm mag-netites, but not as di¡erent as recent micromag-netic theories predict. In early modeling, Dunlop[17,27,28] proposed from several independentlines of evidence that 0.1 Wm magnetites have es-sentially SD structure, whereas 0.22 Wm magne-tites have 2D structure with a broad domain wallthat ¢lls a substantial fraction of the grain. Re-cent micromagnetic models come to similar con-clusions. The SIRM state predicted for 0.1 Wmcubes is essentially SD both above and belowTV, with only a slight di¡erence in the degree of£owering, while 0.3 Wm cubes have room temper-ature SIRM of 0.09^0.17U(Mrs)SD [15]. The ob-served 150^295 K values of Mrs/Ms are 0.219^0.223 for the 0.1 Wm sample, lower than predicted,

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and 0.126^0.128 for the 0.22 Wm sample, higherthan predicted. Both samples have wide size dis-tributions. Probably the smaller grains in eachsample are SD and the larger ones are in 2D/vor-tex states. The fraction of SD grains will be muchgreater in the 0.1 Wm sample; hence its higherMrs/Ms.

In all three submicron magnetites, most of thechange in domain structure is accomplished overa very narrow temperature range and is clearlyassociated with the cubicCmonoclinic phasechange at the Verwey transition, not with thechange of easy axes in the cubic phase at Ti.This is also the case for the 1.3 mm crystal,although there are smaller-scale minima in Hc

and Mrs/Ms at Ti associated with the minimumin crystalline anisotropy at the isotropic point(Fig. 4).

Because of self-demagnetization, any change inHc in an MD ferromagnet is expected to producea proportional change in Mrs through adjustmentof domain wall positions: Mrs = Hc/N, where N isdemagnetizing factor ([25], Ch. 5). This is approx-imately true even for the profound changes inmagnetic properties and domain structure thatoccur in crossing the Verwey transition [3,29].From Table 1, Hc for our 1.3 mm crystal in-creases from 0.13 to 1.1 mT between 295 andW15 K, while Mrs/Ms increases by a similar fac-tor, from 0.003 to 0.013. The ratio between Hc

and Mrs (both expressed in A/m, 15 K data) is0.18, which is comparable to N = 0.33 for an equi-dimensional crystal.

6.2. Low-temperature coercive force

From the temperature dependence of coerciveforce Hc, one can deduce the relative contribu-tions of magnetocrystalline, magnetoelastic andshape anisotropies and hence what factor or fac-tors control the stability of low-temperature rema-nence and room temperature memory. Shape ani-sotropy is indicated by Hc(T)OMs(T). Formagnetocrystalline and magnetoelastic anisotro-pies the coercivity has a K1/Ms or Vs/Ms temper-ature dependence (Vs is the isotropic magneto-striction), leading to a variation Hc(T)OMn

s (T)with ns 1.

Bilogarithmic plots of Hc vs. Ms for our sub-micron samples in the range 120^300 K werestraight lines with slopes n = 1.71, 1.45 and 1.74for the 0.037, 0.10 and 0.22 Wm magnetites, re-spectively. The value of n = 1.71 for the 0.037Wm magnetite is not a reliable indicator of aniso-tropy because Hc is greatly a¡ected by the re-versed moment of the SP fraction. For the 0.10and 0.22 Wm magnetites, the variationsHc(T)OM1:45

s (T) and M1:74s (T) re£ect some combi-

nation of shape, magnetocrystalline and magne-toelastic anisotropies. At the isotropic pointTi = 130 K, Hc values for the three samples were19.6, 14.5 and 9.8 mT, respectively, indicating alarge contribution from shape and magnetoelasticanisotropies. If magnetocrystalline anisotropywere the main source of coercivity, Hc wouldhave very small values at Ti, where K1 becomeszero, as was the case for the 1.3 mm crystal(Fig. 4).

Cooling the submicron samples through theVerwey transition resulted in large increases inHc, as much as a factor 3 for the 0.037 Wm mag-netite (Fig. 1). Increases in Hc in the vicinity ofTV have been observed previously [6,9,30^32],although the changes were only sharp for grainsizes v 0.25 Wm. Hc increases because of the largechanges in magnetocrystalline and magnetoelasticanisotropies when magnetite deforms to mono-clinic structure at TV. Magnetocrystalline aniso-tropy constants, Ka, Kb, Ku, Kaa, Kbb and Kab ofmonoclinic magnetite below TV are much largerthan K1 of cubic magnetite [33]. Magnetostrictionand magnetoelastic constants also increase discon-tinuously in the vicinity of TV [34].

Muxworthy and Williams [16] used three-di-mensional micromagnetic simulations to predictHc values for 0.08^0.3 Wm magnetites between100 and 300 K. Below TV, for all grain sizes mag-netization reversals were by coherent rotation inthe monoclinic easy plane. Very large Hc valueswere predicted for monoclinic magnetite. For 0.1Wm grains at 100 K, the model gave HcW200 mT.This theoretical value is 10 times larger than ourexperimental value of 20.8 mT at 100 K for thesame grain size (Fig. 1). The disagreement be-tween the experimental and theoretical valuesmight be due to simpli¢cations in the theoretical

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model, for example, neglecting magnetostrictiveand magnetoelastic anisotropies.

The temperature dependence of Hc for the 1.3mm crystal is quite di¡erent from that of the sub-micron magnetites (Fig. 4). Hc decreases withcooling from 300 K to a minimum of 0.035 mTaround Ti = 130 K. Recent work on natural singlecrystals of magnetite has shown that Hc varieswith temperature as Vs/Ms between 300 and 170K, indicating the importance of magnetoelasticanisotropy over this temperature range [7].Coarse-grained magnetites behave similarly [35].Below 170 K, the coercivity is controlled by mag-netocrystalline anisotropy as well [7], and this ac-counts for the marked minimum at 130 K. Incrossing the Verwey transition, Hc increases verysharply by almost a factor 40.

6.3. Low-temperature cycling of SIRM

The variation of remanence during a low-tem-perature cycle depends strongly on the tempera-ture at which the remanence was produced andthe consequent direction of approach to TV. Inboth our submicron and mm size crystals of mag-netite, if SIRM is given to the monoclinic phase atlow temperature and TV is approached from be-low, a major part of the remanence is lost at thephase transition (Figs. 7, 8). Most of the decreaseat TV is permanent, with almost no recovery inthe second crossing of the Verwey transition inthe cooling half of the cycle for the 1.3 mm crystaland 23^37% recovery for the submicron magne-tites. The shape of the curves is almost independ-ent of grain size, except for the memories. On theother hand, if SIRM is imparted to the cubicphase at room temperature T0 and TV is ap-proached from above, the memories and theshapes of the demagnetization curves are stronglydependent on the domain state and grain size(Figs. 5, 6).

The temperatures at which demagnetization oc-curs are also strongly controlled by the type oflow-temperature cycling. For example, if theSIRM is induced at low temperatures and TV isapproached from below, almost total demagneti-zation occurs at TV. In this case, the isotropicpoint Ti is unimportant (Figs. 7, 8). If SIRM is

induced at T0 and TV is approached from above,Ti and TV both play an important role in the de-magnetization mechanism [2,5]. The ¢rst demag-netization occurs at Ti because the isotropic pointmust be passed on the way to TV. This is partic-ularly important for remanences carried by PSDand MD magnetites, in which magnetocrystallineanisotropy controls a major part of the rema-nence.

There are two reasons to expect di¡erences be-tween the results of cooling^warming and warm-ing^cooling cycles. First, the domain structure ofmonoclinic magnetite below TV is di¡erent fromthat of cubic magnetite above TV [3,29]. BelowTV, spins lie along the [001] c-axis, domains arelamellar without closure structures, and walls arestrongly pinned by crystal defects because of thehigh magnetostriction and crystalline anisotropy.Many submicron grains lack domain walls en-tirely, as Table 1 and Fig. 3 attest. Above TV,spins have a choice of six or eight easy directionsevenly distributed in space, promoting sets of do-mains with di¡erent orientations linked by closurestructures, and walls are less strongly pinned, par-ticularly near Ti. Thus the starting remanence hasvery di¡erent properties. Second, as mentionedabove, in cooling^warming cycles domains mustpass Ti before reaching TV, whereas in warming^cooling cycles, profound changes have already oc-curred at TV before Ti is reached.

We will discuss ¢rst the results of our cooling^warming cycles of SIRM. This process is oftenreferred to as low-temperature demagnetization(LTD), although it has seldom been used as aroutine paleomagnetic cleaning technique [36^39]. There is some ambiguity in what is meantby magnetic memory in low-temperature cycling.In the ¢rst passage of the Verwey transition, acertain fraction of the initial remanence survives(or is recovered after a dip at TV itself) : this is the`¢rst memory'. The fraction of the initial rema-nence remaining after the second passage of TV

is the `second memory'. When LTD is done forpaleomagnetic purposes, usually only the secondmemory is measured. King and Williams [9] arguethat a more logical de¢nition of memory is thefraction of room-temperature remanence recov-ered after a complete cycle, i.e. second memory3

EPSL 6060 3-1-02


¢rst memory (their Fig. 10). For our results (Figs.5 and 6), this quantity is negative: on secondpassage of TV, there is a further loss of rema-nence, not a recovery, and the second memorycannot be taken as a baseline remanence that isuna¡ected by passage through TV. Yet there isremanence recovery, as shown by dips and recov-eries at TV in one or both passages (Figs. 5, 6).

6.4. Cooling+ warming cycles of SIRM

Cooling through the Verwey transition has littlee¡ect on room-temperature SIRM for the 0.037Wm magnetite sample, apart from a minor dip andrecovery at TV itself (Fig. 5), probably becausethe SD remanence in this sample is controlledmainly by shape anisotropy. For the 0.10 and0.22 Wm magnetites, at least some of which con-tain walls or wall-like vortex structures above TV,there are increasing remanence losses in coolingfrom T0 to TV but these are not localized nearTi. Wall unpinning is likely responsible becausethe demagnetization is much less in the 0.10 Wmgrains than in the 0.22 Wm grains where 2D struc-tures are more prevalent. However, there is noimportant change in remanence in the ¢rst cross-ing of the Verwey transition apart from a mildrecovery which is most marked for the 0.10 Wmgrains. In cooling and rewarming below TV, theremanence is constant until around 90 K, when asubstantial further demagnetization occurs in thesecond passage of TV.

The behavior of the 1.3 mm crystal is di¡erentin several respects (Fig. 6). The amount of demag-netization in cooling from T0 to TV is much great-er (s 90%) and there is an in£ection around 130K matching the minimum in Hc at the same tem-perature (Fig. 4). These di¡erences are a naturalconsequence of progressive wall unpinning. Thenumerous domain walls in this large crystal havemuch more freedom of movement than the singlewalls in submicron grains. Another di¡erence isthe large and sudden increase in remanence oncooling through TV, which is matched by an equaldecrease in rewarming through the transition. Inthe submicron magnetites, reversible changes werecon¢ned to temperatures below 90 K and behav-ior across TV was highly irreversible.

The contrasting responses of large and smallmagnetites in crossing the Verwey transitionmay be related to monoclinic twinning. As a mag-netite crystal cools through TV, the unit cell dis-torts from cubic to monoclinic. If all parts of thecrystal have the same monoclinic c-axis, the entirecrystal must distort. To reduce such megascopicstrain, di¡erent parts of the crystal tend to formtwins with di¡erent c-axes [40,41] and contrastingdomain patterns [3]. Strain is accommodated atthe boundaries between twinned regions, whichare consequently under stress [42]. The spacingbetween twin boundaries, dictated by the require-ment that overall crystal strain be minimized, isbetween 0.3 and 2 Wm. Thus below TV, our 1.3mm crystal contains numerous monoclinic twinswhereas the submicron magnetite crystals areprobably untwinned.

The stressed twin boundaries and twin junc-tions (where twins oriented at right angles meet)act as strong pinning sites for magnetic domainwalls. In crossing the Verwey transition, domainwall thickness decreases sharply because of theabrupt increases in magnetocrystalline and mag-netostriction constants [5] and this increases thee¤ciency with which the walls are pinned [43,44].In recrossing the Verwey transition, the crystalreverts to cubic structure, the twin boundariesdisappear and the remanence decreases reversiblyto its original level in the 1.3 mm crystal (Fig. 6).Submicron magnetites are untwinned and lackthis lock-in mechanism ensuring reversible behav-ior in cycling across the transition.

Why do the submicron magnetites scarcelychange their remanence intensity in coolingthrough TV but lose substantial remanence onrewarming through TV ? First, pinning of wallsto crystal defects such as dislocations which existboth above and below TV increases on coolingthrough the transition but decreases on warming.Demagnetization associated with wall unpinningwill occur on warming, not cooling. Second, SDstructures predominate in all submicron samplesin the monoclinic phase. In the 0.037 Wm grains,both cubic and monoclinic phases are SD, andshape anisotropy evidently bridges the transition(Fig. 5). In the 0.10 and 0.22 Wm grains, judgingby their higher n values, shape anisotropy is less

EPSL 6060 3-1-02


in£uential. In cooling, the easy axis above TV,which lies within a cone around the SIRM direc-tion, becomes the SD c-axis below TV and rema-nence is preserved (or could even increase if2DCSD, accounting for the dip and recoveryphenomenon). On rewarming through TV inzero ¢eld, the choice of multiple easy axes dis-perses the remanence of grains that remain SD,while those grains that nucleate a wall demagnet-ize. With increasing grain size, the role of multi-axial anisotropy grows and the proportion of 2Dgrains increases, with the result that remanenceloss across the transition increases (Fig. 5).

Micromagnetic simulations of SIRM cooling^warming curves for model 0.3 Wm magnetite cubesby Muxworthy and Williams ([15], Fig. 14) repro-duce many of the features of our 0.22 Wm results.The progressive demagnetization in cooling fromT0 to TV is predicted to be W60%, whereas weobserve W35% loss for our somewhat smallergrains. There is a small dip and recovery ofremanence in crossing the transition, and constantreversible behavior in cooling and rewarming be-low W100 K, both as observed. The warmingcurve across the transition has a further irrevers-ible loss of remanence, but the magnitude is onlyone half of the 15% we observe. Finally there isonly minor recovery above TV : both their theo-retical and our experimental remanence curves arealmost £at from 120 K to T0. This good agree-ment between theory and observations is mostencouraging.

6.5. Warming+ cooling cycles of SIRM

The behavior of SIRM of monoclinic magnetitein warming^cooling cycles across TV is quite un-like that of SIRM of cubic magnetite in cooling^warming cycles. Room temperature SIRM de-magnetizes in cooling to TV, by amounts that in-crease with increasing grain size (Figs. 5, 6) butSIRM imparted at 5 K scarcely changes withheating until TV is reached, and the curves aregrain size independent (Figs. 7, 8). The stronguniaxial anisotropy of monoclinic magnetitemust be responsible for pinning domain walls inthe larger grains and SD moments in small grains.The 2.5 T ¢eld applied at 5 K aligns spins along

the monoclinic c-axis in each submicron crystaland the spins are locked in along [001] when the¢eld turned o¡.

In crossing the phase transition, permanent de-magnetization of all the magnetites occurs at TV

when the crystal structure changes from mono-clinic to cubic. The amount of demagnetizationfor the submicron magnetites is much greaterthan the corresponding demagnetization of roomtemperature SIRM memory when it was warmedacross TV (Figs. 5, 7). In warming through andabove TV, there is no dip and recovery of rema-nence like that seen in cooling the room temper-ature SIRM through TV. The Verwey transition isall important in warming monoclinic SIRM; thereis no expression of Ti in the remanence variation.Furthermore, the large amounts of demagnetiza-tion that occurred in cooling the room tempera-ture SIRM of the submicron magnetites from T0

to TV are completely lacking in the monoclinicSIRM memory over the same range.

All these observations force us to the conclu-sion that the memory of cubic phase SIRM belowthe Verwey transition has a domain state entirelydi¡erent from that of SIRM produced directly inthe monoclinic phase at low temperature. Theconverse is equally true: memory of monoclinicSIRM transformed to the cubic phase is not atall equivalent in its properties to SIRM impartedto the cubic phase above TV.

Although we do not yet understand the domainstructure of monoclinic magnetite well enough tointerpret these di¡erences in detail, the contrast-ing magnetic properties of SIRM warming^cool-ing cycles and cooling^warming cycles could beuseful in diagnosing the presence and grain sizeof magnetite in natural materials such as sedi-ments and soils. Warming curves of low-temper-ature monoclinic phase SIRM are routinely usedto detect magnetite in environmental studies, andthey clearly provide a very sharp indication of theVerwey transition (Figs. 7, 8). On the other hand,cooling^warming curves of room-temperature cu-bic phase SIRM provide a wealth of details notpresent in the monoclinic warming curves (Fig. 5,6), including several key indicators of grain sizeand domain structure.

The ¢rst size indicator is the second memory,

EPSL 6060 3-1-02


which ranges from 86% for 0.037 Wm grains to80% for 0.10 Wm and 55% for 0.22 Wm grains.The second indicator is the loss of remanence incooling from T0 to TV, which is 5% for 0.037 Wm,10% for 0.10 Wm and 35% for 0.22 Wm grains.Finally, the change in remanence in warmingacross TV (approximately equal to ¢rst memory3second memory) is W5% for 0.037 Wm, W12% for0.10 Wm, and W15% for 0.22 Wm grains. The cor-responding range of memories for monoclinicSIRM is 23^37% (Fig. 7), o¡ering less potentialsize resolution.

7. Conclusions

Submicron magnetites undergo importantchanges in their hysteresis properties and domainstates in crossing the Verwey transition. Oursmallest crystals (0.037 Wm) are SD/SP at roomtemperature T0 (Mrs/Ms = 0.276, Hc = 17.5 mT)but thermally stable SD at 15 K (Mrs/Ms = 0.517, Hc = 90 mT) (Table 1, Figs. 1, 2).Larger crystals have PSD parameters at T0 (Mrs/Ms = 0.219, 0.10 Wm; Mrs/Ms = 0.126, 0.22 Wm)but almost SD properties at 15 K (Mrs/Ms = 0.406, 0.10 Wm; Mrs/Ms = 0.389, 0.22 Wm)(Fig. 3), and probably contain a mixture of SDand 2D/vortex states. These observations are inapproximate agreement with micromagnetic pre-dictions [15,16].

Coercive force Hc increases by factors of 3^40between 120 and 100 K, and continues to increasewith further cooling in the submicron magnetites(Table 1, Figs. 1, 4). The increases re£ect the largeincreases in magnetocrystalline anisotropy andmagnetostriction in the cubicCmonoclinic phasetransition. Although the increases are large, forthe submicron magnetites they are only W10%of the increase in Hc predicted by micromagneticmodeling [16].

Low-temperature cycling results are very di¡er-ent depending on whether SIRM is produced inthe monoclinic phase and heated through TV orproduced in the cubic phase and cooled throughTV. One reason is the di¡erent domain structuresof monoclinic and cubic magnetites, and transfor-mations between the structures across TV (e.g.

SDC2D in warming, 2DCSD in cooling). An-other reason is the very high anisotropy and co-ercivity below TV, which pins both domain wallsand SD moments tightly, compared to the weakeranisotropy above TV, which permits continuousre-equilibration of domain walls during coolingfrom T0.

There are some novel features in cooling^warm-ing cycles of cubic phase SIRM which have notbeen previously reported. There is only a slightdip and recovery of remanence between 120 and100 K in cooling, but a major permanent loss ofremanence in rewarming from 100 to 120 K,which increases with increasing grain size. Onecause is the change of crystalline anisotropyfrom uniaxial to multiaxial in the mono-clinicCcubic transformation, which dispersesthe remanence. Even more important is theSDC2D/vortex transformation across the transi-tion. In our 1.3 mm crystal, there are large rema-nence changes across the transition but these areperfectly reversible because domain walls are¢rmly locked in place by c-axis twin boundariesin the monoclinic phase.

Warming^cooling cycles of monoclinic phaseSIRM are simpler, with s 50% loss of remanencein the ¢rst crossing of the Verwey transition, al-most constant remanence above TV, and only mi-nor recovery in the second crossing. The verylarge permanent remanence losses in submicrongrains are not easy to explain in view of themuch smaller and very size-dependent lossesseen in the cooling half cycle of the cubic phaseSIRM. The monoclinic and cubic SIRMs mustinvolve entirely di¡erent domain structures, evenafter transformation across TV.

Although warming curves of monoclinic SIRMare conventionally used to identify magnetite inrocks, sediments and soils, cooling^warmingcycles of cubic phase SIRM o¡er three grainsize diagnostic indicators for submicron magne-tites. These are remanence loss in cooling from300 to 120 K, further remanence loss in warmingfrom 100 to 120 K (second crossing of TV), andultimate remanence level or memory after a com-plete 300C10C300 K cycle. Monoclinic SIRMmemory is a less sensitive indicator of submicrongrain sizes.

EPSL 6060 3-1-02


Acknowledgements

We are grateful to Prof. M. Torii for help withthe measurements at Kyoto University. The Insti-tute for Rock Magnetism, University of Minneso-ta, Minneapolis, MN, USA is operated with sup-port from NSF and the Keck Foundation. The1.3 mm magnetite crystal was kindly donated byM. Back of the Royal Ontario Museum, Toronto,ON, Canada. We thank Subir Banerjee, GuntherKletetschka and Valera Shcherbakov for helpfulreviews. This research was supported by NSERCCanada through grant A7709 to D.J.D.[RV]

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changes in remanence, coercivity and domain state at low temperature in magnetite

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