Coercive forces and coercivity spectra of submicron magnetites

288

Earth and Planeta(v Science Letters. 78 (1986) 288-295 Elsevier Science Publishers BN., Amsterdam - Printed in The Netherlands

15]

Coercive forces and coercivity spectra of submicron magnetites David J. D u n l o p Geophysics Laboratory, Department of Physics, Universi O, of Toronto, Toronto, M5S I A 7 (Canada) Received August 31, 1985; revised version received February 7, 1986 Remanent coercivity spectra have been determined for four dispersions of magnetite with mean particle sizes of 0.04-0.22 #m using four different methods: (1) acquisition of isothermal remanent magnetization (IRM) in continuous fields: (2) stepwise reversal of saturation IRM by opposite-polarity continuous fields: (3) stepwise alternating-field (AF) demagnetization of saturation IRM; and (4) AF demagnetization of weak-field thermoremanent magnetization (TRM). Alternating-field methods gave narrower distributions with lower median coercivities than continuous-field (CF) methods. The two CF spectra are offset: the remanent coercive force, H R, which is the median coercivity determined by CF reversal of saturation remanence, is always less than the median coercivity, H(~, determined from 1RM acquisition. The median destructive field of saturation IRM, /tl/2, the median coercivity determined by AF demagnetization, is less than either H R or H~,. The relation reported by Dankers [1], H~ +/)1/2 ~- 2HR, is obeyed for these samples and for a companion suite of single-domain magnetites and maghemites. Ordinary coercive force. H c, is substantially affected by reversible magnetization and is a poor indicator of the median coercivity of remanence. H c. is much smaller than /)1/2, HR or H~ and varies in a different way with particle size.

1. Introduction

It has long been known that rocks and analog dispersions of ferrimagnetic particles have broad spectra of microscopic coercive forces, and that measured spectra and spectral-average coercive forces depend on the experimental technique used [1-13]. Three techniques are in general use in rock magnetism and paleomagnetism. Universally used is alternating-field (AF) demagnetization, which can be applied to remanences of thermal, isothermal or other more complicated origins, and which serves to progressively randomize or "clean" the softer (i.e., lower coercivity) fractions of the spectrum. In this paper, AF decay curves of strong-field isothermal remanence (IRM), Jir, and weak-field thermoremanence (TRM), Jtr, will be reported. The normalized intensity decay curves J ( H ) and Jtr(/~), where H is peak AF, are equivalent to cumulative or integrated coercivity distributions. The differential spectrum can be obtained numerically if desired [6]. Continuous-field (CF) methods are less commonly used for spectral determinations because they do not clean a sample's remanence but instead replace it with increasingly large IRM's. 0012-821X/86/$03.50

,v 1986 Elsevier Science Publishers B.V.

Fhey cannot be used with weak-field starting remanences because these are swamped in intensity by the added IRM's. The back-field CF technique (often called " D C demagnetization" [21]) consists of applying reverse-polarity fields of increasing magnitudes to a starting remanence, usually saturation IRM, Jr~- The cumulative coercivity spectrum is the back-field or descending branch, Jr(- H), of the remanent hysteresis curve, Jr(H)The other CF technique is determination of the IRM acquisition curve (also called the induction curve or static remanence curve), the initial ascending branch of the remanent hysteresis curve, starting from zero remanence. It is measured by applying incrementally increasing fields to an initially demagnetized sample and noting the IRM produced. The cumulative coercivity spectrum is Jir(H).

Although complete CF coercivity distributions are not usually determined, average coercivities are frequently reported. The remanent coercive force H a, the zero crossing point of the remanent hysteresis curve, is the back field that reverses one-half of an initial saturation IRM. It is the median value of the back-field CF spectrum. The analogous coercive force H~ is the field required

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to create an IRM equal to ½Jrs in a previously demagnetized sample. It represents the median value of the CF acquisition spectrum. The coercive force He, the zero crossing point of the ordinary hysteresis curve J(H), is also frequently cited. It is the field necessary to reverse one-half of the induced magnetization, starting from a saturated state, and is not directly comparable to coercivities of remanent magnetization. Finally, the commonest measure of average coercivity of remanence is the median destructive field (MDF), /)1/2, which is the AF necessary to reduce a starting remanence to one-half its initial value. The M D F is thus the median value of the AF coercivity spectrum. A general observation has been that H c < H1/2 < H R < H~, the differences being substantial. Dankers [1] and Hartstra [10] established numerical relations among the various coercive forces for magnetite, titanomagnetite and hematite grains > 5 /zm in size. The present paper reports analogous relations and compares entire coercivity spectra for submicron magnetite and maghemite particles. 2. Samples and experimental methods The four principal samples used in this work were 1% by volume dispersions of magnetite in an inert kaolin matrix. Clusters of magnetite particles were broken up as much as possible by prolonged working of the dry dispersion with mortar and pestle before adding water and binder. The samples were cylindrical, with 7 : 1 length : width ratios.

Fields were applied and all remanences were measured parallel to the long axis of each sample. The low magnetite concentration and elongate form of the samples were chosen to minimize axial selfdemagnetizing fields. The samples contained narrowly-sized, singlecrystal cubes of magnetite with mean dimensions ranging from 0.037 to 0.22 ktm (Table 1). The finest particles are just below the critical singledomain (SD) threshold, do, of 0.05-0.06 ~m [14,15]. The largest crystals are well above d o and seem to have two-domain (2D) or three-domain (3D) structures at ordinary temperatures [16,17]. They thus fall at the lower end of what Stacey [18] calls the pseudo-single-domain (PSD) range. The preparation and detailed properties of these magnetites have been described elsewhere [16]. For comparison, the properties of four similar dispersions of SD magnetites and maghemites are quoted in this paper (Table 1). These samples, labelled SD1-SD4, are the same as samples 1-4 of Dunlop and West [5]. Before measurements began, both PSD and SD suites of samples were vacuum annealed at ~ 650°C to stabilize their magnetic properties. Hysteresis and remanent hysteresis curves were measured with a ballistic magnetometer using fields H < 2400 Qe (0.24 T) supplied by an oilcooled solenoid. Jir in 2400 Oe was practically equal to Jrs in 15,000 Oe, but the induced magnetization J in 2400 Oe was 10-15% less than the saturation magnetization J~. Single-axis AF demagnetization to peak fields of 3000 Oe (0.3 T) was carried out using the same solenoid. An ap-

TABLE 1 Basic properties and measured average coercivities of the PSD and SD suites of samples Sample No.

Magnetic material

Particle size ( ~ m )

HC (Oe)

HR (Oe)

H~. (Oe)

1 2 3 4

Fe304 Fe304 Fe304 Fe304

0.22 + 0.04 0.10_+0.03 0.076_+0.025 0.037_+0.015

100 153 178 218

266 279 308 396

387 413 423 520

SD1 SD2 SD3 SD4

yFe203 Fe304 Fe304 yFe203 + 5% Co

0.01-0.10 a 0.03 × 0.20 0.05

113 254 305 874

217 471 505 1130

271 648 677 1415

HR/Hc

H{~/HR

/~1/2/HR

175 182 193 296

2.66 1.76 1.73 1.82

1.45 1.48 1.37 1.31

0.659 0.652 0.626 0.748

157 285 434 955

1.92 1.85 1.66 1.29

1.25 1.38 1.34 1.25

0.725 0.605 0.860 0.845

/41/2 (Oe)

H¢ and H R are ordinary and remanent coercive forces respectively; H~. is the field required to produce Jir = 0"5Jr~; /ll/z is the M D F of saturation IRM. Ranges quoted for particle sizes are + lo. a 0 . 5 - 5 0 / ~ m titanomagnetites subdivided by ilmenite lamellae.

290 I0

proximately zero-field environment for AF cleaning was achieved by orienting the coil axis along the magnetic meridian in the low-magnetic-noise laboratory at Erindale College and cancelling transverse and residual longitudinal earth's field components with nulling coils.

08

3. Experimental results Partial remanent hysteresis ( J r - H ) curves of the PSD samples 1-4 and of an annealed sample M containing "Mapico Black" magnetite (mean particle size { d ) = 0.21 /xm [8]) are illustrated in Fig. 1. Each IRM acquisition curve has an initial parabolic portion, described by the relation Jir = B H 2 / 2 ( B is the quadratic coefficient in the Rayleigh relation, J = A H + B H 2 [19]), followed by a fairly linear increase between 200 and 1000 Oe, and an approach to saturation above 1000 Oe. At low fields, Jir is largest in sample 1 ({d) = 0.22 /am) and smallest in sample 4 ( { d ) = 0.037/tm), a reflection of their respectively softer and harder coercivity spectra. At fields > 500 Oe, the roles are reversed because of the greater remanence-carrying capacity of fine particles. The back-field curves are featureless by comparison with the acquisition curves. The remanent coercive force H R required to reverse one-half of Jr~ is similar in samples 1, 2, 3 and M, and is considerably less dk- j r_L2f. . . . . . . . . . . . . . . . .

/ {)09. . . . . . . . 4i /

/

/

/ . . . . .

s" . . - "

50

Apphed held, H JOe/

Fig. 1. Partial remanent hysteresis curves for the PSD suite of samples. Sample M ( { d ) = 0,21 /tin) is similar in particle size and magnetic properties to sample 1 ( { d ) = 0.22 ttm). Samples 2, 3 and 4 have { d ) - 0.10, 0.076 and 0.037 ~tm respectively.

i

o6

';~ o4 i

/

23

4

$ 0.2{_ 00 -

200

400

I

6;0

i

8001 __

Apphed field,H(Oe) Fig. 2. Normalized I R M acquisition curves J i r ( H ) , with superimposed values of H c , t t R and H~, (arrows). IRM continued to be acquired up to 2400 Oe, the m a x i m u m field used, but the curves are about 90% saturated by 800 Oe.

than the field H~, needed to induce one-half of Jr,In Fig. 2, each induction curve has been normalized to saturation remanence. The coercivity spectra can now easily be compared. Although finer grains have larger coercivities on average than coarser grains, sample 1 ( ( d ) = 0.22/xm) has a small fraction of coercivities higher than any found in finer-grained samples. As an estimate of spectral width, let us arbitrarily select for minimum and maximum coercivities the fields H l and H 2 at which Ji,- is respectively 15% and 85% saturated. Then it is clear that sample 4 ( { d ) = 0.037 Fm), with H 1 = 325 Oe, H 2 = 7 9 0 Oe, H ~ / H 2 = 0.41 has a considerably narrower spectrum than sample 1, with H~ = 200 Oe, H a - 770 Oe, H 1 / H 2 = 0.26. In each PSD sample, a field equal to the ordinary coercive force H c produces irreversible changes from the demagnetized state only in the softest 3 6% of the particles. H c is thus a poor indicator of average coercivity of remanent magnetization. H R and H~ are also substantially different (Fig. 2, Table 1), the ratio H~,/H~, ranging from about 1.3 to 1.5 for the PSD samples and

291 I0 ~

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Sample/

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\ \

~.~IRM

#lduct,on,Jtp{Hj

06

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~

\

4

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xw~- ,~F detr~gnet,2cthgtlof

04 0.2

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, 200 400 600 800 Direct or olternot/)~jheld,H or H(Oe)

%

~o ' 44)0 eoo x~lternot/;~g f/e/d, H (Oe peak/

~oo

Fig. 3. Normalized decay curves Jr(/~) for A F demagnetization of an initial saturation remanence Jrs, with superimposed values of He-, /tl/2 and H R indicated by arrows. The A F coercivity spectrum is narrower and softer in each case than the corresponding CF spectrum of Fig. 2.

from about 1.25 to 1.4 for the SD samples. A F demagnetization of saturation I R M ' s of the PSD samples is illustrated by the normalized intensity decay curves of Fig. 3. As was the case for CF induction, average coercivity decreases steadily with increasing particle size. Sample 1 ( ( d ) = 0.22 /~m) again has a broader coercivity spectrum than the other samples. An A F of peak value equal to H c is sufficient to erase the remanence of only the softest 25 35% of the particles, so that H c is an inadequate indicator of A F as well as CF coercivity. An A F equal to H R would erase 70-80% of the saturation remanence. Particle remanences and domain structures are therefore more vulnerable to reorientation by a repeatedly reversing field than by a reversed field applied once only. Ratios [-I1/2/H R are 0.625-0.75 for the PSD samples and 0.60-0.85 for the SD samples. Various measures of the cumulative coercivity spectrum of sample 1 are compared in Fig. 4. The other samples have similar trends. Since the backfield ( " D C demagnetization") curve uses negative fields and spans a remanence range Jrs t o - - J r s , it

Fig. 4. A comparison of cumulative coercivity spectra determined by different A F and CF methods. The CF curves have been rescaled and reflected or inverted for comparison with the AF curves (see text). Although all spectra have generally similar shapes, the AF spectra are narrower and softer than the C F spectra. There are offsets between the CF induction and back-field spectra and between the AF spectra of weak-field T R M and of saturation IRM. Both offsets are interpreted as being due to internal fields.

must be scaled down by a factor 2, reflected, and shifted into the positive-field sector before being compared with AF demagnetization results. IRM acquisition curves simply need to be inverted for comparison. Formal relations among the various spectra have been given by Wohlfarth [3], from which the equivalence in principle of the curves Jr(/])/Jrs, 1 - J ~ ( H ) / J r s and 0.511 + J r ( - H ) / J r s ] is easily shown. CF back-field and acquisition curves that have been redrawn in this way (Fig. 4) are similar in form but are offset from each other. In 1RM acquisition, all coercivities seem to be augmented by a threshold field that is absent in I R M reversal. The A F demagnetization curves of saturation 1RM and of weak-field TRM are similar in form, and are likewise offset with respect to each other, a fact used to advantage in the Lowrie-Fuller [20] test of domain state. The initial plateau in the T R M (or other weak-field remanence) demagnetization curve reflects a threshold field that must be overcome before even the softest particles will

292 TABLE 2 Comparison of observed values of H R and H R / H c with values predicted from the Gaunt [21] relations, H R = ( I l I + H2)/3.71, 1 1 R / H c = 2.02(1 + H 1 / H 2 ) / ( 1 + 2.5H I / H 2), for a coercivity distribution with lower and upper limits H 1 and H 2 respectively Sample

H~ a

H2 ~

No.

(Oe)

(Oe)

1 2 3 4

200 240 260 325

770 685 685 790

Hj/H 2

0.26 0.35 0.38 0.41

H R (Oe)

HR/H c

pred.

obs.

pred.

obs.

260 250 255 300

266 279 308 396

1.54 1.45 1.43 1.41

2.66 1.76 1.73 1.82

~' Experimental values for H 1 and H 2 are the fields at which the 1RM is respectively 15% and 85% of its saturation value.

reorient their remanences. This threshold field is not seen when demagnetizing strong-field remanences. The CF and AF curves have rather different shapes. AF demagnetization yields a narrower and generally softer spectrum than DC methods. Domains obviously react differently to repeated hysteresis cycles than they do to repeated fields of a single polarity, whether parallel or opposed to Jr~. 4. Discussion 4. l. H,¢ and

H R/ H C

Gaunt [21] has calculated H R and the ratio H R / H c for coherently reversing independent SD

particles with a level distribution of coercivities between minimum and maximum values H l and H 2. The relations are H R = ( H 1 + H2)/3.71 and H R / H c = 2.02(1 + H ~ / H 2 ) / ( 1 + 2 . 5 H J H 2 ) . Although samples 1 - 4 do not for the most part contain coherently reversing SD particles but somewhat larger particles with probably more complex modes of magnetization change, it is interesting to see whether their distributions of coercivities lead to significant trends in H a and H R / H c according to the Gaunt relations. The fields at which the I R M is 15% and 85% saturated are again used as estimates of H1 and H 2. Results of the calculations appear in Table 2. HR is predicted to increase from 260 to 300 Oe as the particle size decreases from 0.22 to 0.037 /,m. The observed increase is more pronounced, from 266 to 396 Oe. H R / H c ratios, as predicted, decrease more or less steadily in going from larger to smaller particle sizes, but the predicted range (1.54-1,41) and observed range (2.66-1.73) of val-

ues do not overlap. It is well known that H ¢ / H c depends on domain state [22], and the high observed values undoubtedly reflect the non-SD state of most of the experimental particles. 4.2. Coerciue force H c

H c values for all four samples are at the low end of the spectrum of coercivities indicated by CF or AF methods. In the case of I R M acquisition curves (Fig. 2), H c corresponds to the field required to induce the softest 3-6% of Jr,,, starting from a demagnetized state. In the case of CF back-field curves (Fig. 1) or AF demagnetization curves (Fig. 3), a field equal to H c reverses or randomizes only the softest 15-20% or 25-35% respectively of Jr,~The explanation of these results is that H c is determined jointly by reversals of remanent moments and by negative induced magnetization, due to displacements of soft domain walls for example. In principle, if the susceptibility X0 is large enough, the entire saturation remanence Jr~ could be balanced by negative reversible magnetization - X o H c induced by the field - H c , without any irreversible change in Jr~ occurring. The present results show that some irreversible magnetization does occur in a field - H c, but reversible induced magnetization dominates. It is only because of the intimate relation between susceptibility and coercivity, as revealed in the fairly constant ratios between H c and other measures of coercive force, that H c variations over broad size ranges can be taken as representative of coercivity trends. Numerically, H c is a poor measure of coercivity of irreversible magnetization changes at any par-

293

ticle size.

4.3. H,~/ H n and ~I1/2/H R

single-axis CF acquisition and reversal of magnetization. Dankers [1] found that for all his magnetite, titanomagnetite and hematite samples, H(~ + H1/2 2 H R. In other words, H R was approximately the average of H i and the MDF/~1/2- Cisowski [23] noted an analogous relation: the crossover point of IRM acquisition and AF demagnetization curves approximately equals H R. Despite the different method of AF demagnetization used in the present study, Dankers' relationship is approximately obeyed. For seven of the eight entries in Table 1, the last two columns (H(~/H R and Itl/2/HR) sum to 2.0-2.1 and in the eighth case (sample SD3), the sum is 2.2. ~

Acquisition of IRM from an initially randomized state generally requires larger fields than demagnetization or remanence reversals that approach a demagnetized state, since the internal demagnetizing field Hd in multidomain grains or the interaction field Hin t in SD particle arrays tend to oppose increases in net magnetization and to aid in demagnetization (e.g. [5,11,23]). Dankers [1] demonstrated the role of Hin t by showing that in SD hematite, which is so weakly magnetic that interactions should be negligible, H R - H R. In magnetite, H(~/HR= 1.25-1.38 (average 1.30) for the SD samples in the present study and 1.31-1.48 (average 1.40) for the PSD samples (Table 1). Internal field effects are clearly important. Dankers [1] and Hartstra [10] found ratios in the range 1.5-1.8 (averages 1.70 [1] and 1.60 [10]) in MD magnetites 10-200 /~m is size. Although the average value of H{~/H R increases in going from SD to PSD to MD size grains, Hartstra observed no clear size dependence within the MD range and Dankers reported a steady decrease in H(~/H R as grain size increased from 10 to 200/~m. It is not obvious why /ql/2 < HR, since AF demagnetization amounts to repeated DC demagnetization and remagnetization (i.e., alternately positive and negative fields) to a peak level that diminishes gradually over many cycles. Rimbert [4] reported that during prolonged AF demagnetization, coercivities decreased roughly as the logarithm of time or number of cycles of the field, suggesting a viscous origin. The differences observed in the present study are rather large to have a viscous origin, however. Ratios of [-I1/2/H R are 0.625-0.75 for samples 1-4 and 0.605 0.86 for samples S D 1 - S D 4 (Table 1). Dankers [1] and Hartstra [10] reported even more extreme contrasts, ~I1/2/H ~ being 0.35-0.45 approximately for 2-200 /~m magnetites. Their values tend to increase with decreasing particle size, but there is a residual disagreement with the values reported here, probably because Dankers and Hartstra AF demagnetized their samples along three orthogonal axes in succession. Multi-axis demagnetization is more efficient than the single-axis demagnetization used here, but the process is not equivalent to P

4.4. Offsets between spectra Offsets between AF demagnetization curves of weak-field and strong-field remanences have been interpreted [11] to be a result of the larger values of H d in multidomain particles with strong remanences, although there may be fundamental differences also between coercivity spectra of weakfield TRM's and strong-field 1RM's [24]. Offsets between CF forward-field and back-field curves can be explained similarly, H~ or Hin t opposing creation of IRM and aiding in its reduction. The fact that AF spectra are consistently narrower than DC spectra probably has a similar root cause. AF demagnetization proceeds toward an eventual state of zero net magnetization, whereas both DC induction and back-field methods eventually approach a state of saturation remanence and thus require stronger fields to overcome demagnetizing or interaction fields. 5. Conclusions

(1) For small PSD particles of magnetite, different measurement techniques yield different remanent coercivity spectra, as has been reported previously for magnetites of other grain sizes and for other minerals [1-13]. The spectrum with the sharpest concentration of coercivities and the one that is least affected by internal demagnetizing or interaction fields is that determined by AF demagnetization of a weak-field remanence, e.g. weakfield TRM or anhysteretic remanence. AF demagnetization of a strong-field remanence, such as

294

s a t u r a t i o n I R M or T R M , yields a softer s p e c t r u m for p a r t i c l e s of this size (cf. [4,5,20,25]), w h i l e c o n t i n u o u s - f i e l d ( C F ) m e t h o d s yield b r o a d s p e c t r a e x t e n d i n g to h i g h e r fields. (2) D i f f e r e n c e s a m o n g c o e r c i v i t y s p e c t r a of s a t u r a t i o n I R M d e t e r m i n e d by A F a n d by forw a r d - f i e l d a n d b a c k - f i e l d C F m e t h o d s are m a i n l y d e t e r m i n e d by i n t e r n a l fields a n d are largely indep e n d e n t of p a r t i c l e size. F o r e x a m p l e , the r a t i o b e t w e e n the m e d i a n coercivities H~, a n d H R f r o m C F a c q u i s i t i o n a n d b a c k - f i e l d m e t h o d s respectively is in the r a n g e 1 . 2 5 - 1 . 5 for all S D a n d P S D s a m p l e s in this s t u d y a n d in the r a n g e 1 . 5 - 1 . 8 for m u c h larger m a g n e t i t e s [1,10]. (3) T h e r e l a t i o n s h i p H~, + / t w 2 = 2 H R , w h e r e / t b 2 is m e d i a n d e s t r u c t i v e a l t e r n a t i n g field, is o b e y e d for f i n e - p a r t i c l e m a g n e t i t e s , as it was for the m u c h c o a r s e r m a g n e t i t e s a n d t i t a n o m a g n e t i t e s s t u d i e d by D a n k e r s [1]. T h e f u n d a m e n t a l signific a n c e of this r e l a t i o n s h i p and an a n a l o g o u s o n e r e p o r t e d b y C i s o w s k i [23] is unclear, h o w e v e r . (4) T h e o r d i n a r y c o e r c i v e force He. is det e r m i n e d m o r e by r e v e r s i b l e m a g n e t i z a t i o n (i.e., by the s u s c e p t i b i l i t y X0) t h a n by irreversible c h a n g e s in s a t u r a t i o n r e m a n e n c e . It is a p o o r n u m e r i c a l i n d i c a t o r of a v e r a g e r e m a n e n t c o e r c i v ity. Since H c has a d i f f e r e n t o r i g i n a n d d i f f e r e n t particle-size dependence than remanent coercivities like H R or /I~/2, the ratios b e t w e e n these q u a n t i t i e s a n d H c are size d e p e n d e n t a n d c a n be u s e d as i n d i r e c t i n d i c a t o r s of d o m a i n state. H a / H c is the o n l y r a t i o c o m m o n l y u s e d for this p u r p o s e at present.

Acknowledgements I a m g r a t e f u l to J e a n R o y , N a o j i Sugiura, O z d e n O z d e m i r , F r a n z H e i d e r , R a n d y E n k i n a n d o n e of the referees for s u g g e s t i n g i m p o r t a n t i m p r o v e m e n t s to the p a p e r . T h i s w o r k was s u p p o r t e d by NSERC Operating Grant A7709 and a Canada Council Killam Research Fellowship.

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