Physics of the Earth and Planetary Interiors, 26 (1981) 1—26 1

Elsevier Scientific Publishing Company, Amsterdam — Printed in The Netherlands

The of fine particles David J. Dunlop

Geophysics Laboratory, Department ofPhysics, University of Toronto, Toronto, Ontario M5S IA 7 (Canada)

(Accepted forpublication November, 1980)

Dunlop, D.J., 1981. The of fine particles. Phys. Earth Planet. Inter., 26: 1—26.

This state-of-the-art review is a selective rather than an exhaustive survey of currently active areas in fine-particle rock magnetism. The topics considered are domain structure transitions, pseudo-single-domainmechanisms, diagnostic tests of domain structure, chemical, detrital, thermal and viscous processes, and magnetostatic interac- tion. Proposed future directions for research include: high-temperature thermoremanence and magnetic viscosity measurements and domain observations to examine the detailed magnetizationblocking process; hysteretic~andthermal properties measurements and domain structure observations in the 0.25—1 ~sm(small multidomain) size range of for comparison with domain structure calculations; experimental calibration of the time or cooling-rate dependence of blocking temperature; and systematicstudy of theparticle size, field and processdependencesof detrital and chemical .

I. Introduction Magnetic properties therefore remain the key to interpreting domain structure. Many simple iso- For the rock magnetist, domain structure, rather thermal parameters and testshave diagnostic value. than particle size per Se, is the defining character- They are evaluated and compared in Section 3. istic of a fine particle. A 10 ~&mhematite particle Subtle domain structures that may bridge the gap and a 400 A magnetite particle are analogs, in the between single - domain and multidomain be- sense that they are both single-domained. For the haviour are also considered in this section. purposes of this review, small multidomain par- Once domain structure is established with some tides with enhanced and single-domain confidence, one can begin to codify magnetic -like stability and hardness will also be treated as properties that have paleomagnetic significance. fine particles. Chemical remanence (Section 4), detrital rema- Domain structures in fine particles are usually nence (Section 5), thermoremanence (Section 6) known indirectly, either by reference to size- and viscous changes (Section 7) are discussed in dependent magnetic properties (with or without this paper. Domain structure and magnetic prop- appeal to theoretical calculations), or else as a erties change, sometimes profoundly, if magneto- reasonable extrapolation from domain observa- static interaction among particles is strong. Such tions in larger particles. The evidence is reviewed interaction is the subject of Section 8. in Section 2. More refined methods of probing The present review is a brief treatment of ultrafine particles may be developed in the future selected topics in fine-particle magnetism. More (e.g., Brecher and Cutrera, 1976; Newberry et aL, comprehensive accounts with alternative points of 1980), but short-wavelength “pseudo-single- view are found in a number of recent reviews or domain” regions and similar fme structure will collections of papers: Kneller (1969) on fine- probably never be resolvable, particle theory; Shcherbakov (1978) and Mosko-

0031-9201/8I/0000—0000/$02.50 © 1981 Elsevier Scientific Publishing Company 2 witz and Banerjee (1979) on domain structure the data indicate some compromise with stable SD transitions; Merrill (1975) on chemical remanence; behaviour. The explanation may lie in particle-size Verosub (1977) and Barton et al. (1980) on detrital dispersion, as Kneller and Luborsky assume, or in magnetization; the “Origin of TRM” volume collective behaviour of interacting SP particles (Dunlop, 1977a, 1978) on thermoremanence and (Radhakrishnamurty et al., 1973; Deutsch et al., domain structure; Dunlop (1973a) on viscous ef- 1981, this issue). fects; and Wohlfarth (1978) and Day (1979) on SD particles only slightly larger than d 3 have fine-particle magnetism generally. remanence ~rs = ~ .~1 (-‘s is saturation magnetization), a value that is maintained up to d0, the SD—MD transition size. Coercive force, 2. Domain structures on the other hand, remains well below the expected microscopic coercive force (H~)m~,,up to 2.1. Domain structure transitions d = 5d~at least, testifying to the importance of thermal fluctuations even in SD volumes 100 times Figure 1 reproduces some of Kneller and the critical SP volume (Néel, 1949; Dunlop, 1976). Luborsky’s (1963) data for nearly spherical particles. The data are a classic illustration of the subdivision into superpara- TABLE I magnetic (SP), single-domain (SD) and multido- Experimental and theoretical domain-structure transition sizes main (MD) size ranges. SP particles (particle size d, (SP—SD) and d0 (SD—MD) at 20°C(equidimensional par- d< d5, the SP—SD transition size) have, theoreti- tides assumed) cally, zero remanence and coercive force, although

Mineral . SP threshold Critical SD size, d, (~sm) size, d0(~m) ~rs”~s 0.5 Iron <0.008 a 0.023 a k 0.026” I 04 Magnetite 0.025—0.030 c.d.e 0.05—0.06 d,f 0.08~

I N . .3 Maghernite 006h Titanornagnetite 0.08 0.2k

Hc/(Hc)rp~x .2 (x=0.55—0.6) .

.0 ,,... -~. Titanomaghemite I _,e’( (x0.6,z0.4) O.O5~ 0.75’ 08 7~ \ (x=0.6, z=0.7) 0.09~ ~—___J / 0 0.025—0.030’~” l51.m 0.6 7 Pyrrhotite 1.6° 04 1 Kneller and Luborsky (1963), experimental (see Fig.4). JO b Butler and Baneijee (I975a), theoretical (see Fig. 2). / ‘... C. McNab et al. (1968), experimental. 02 / — ~ 0 d Dunlop (1973b), experimental (see Fig. 4). Dunlop and Bina (1977), experimental. 0 ...a...L.....J Evans (1972), theoretical. 05 lb g Butler and Banerjee (1975b), theoretical(see Fig. 2). Reduced pcrt,cle diameter d/d Momsh and Yu (1955), theoretical. $ Soffel (1971), experimental (see Fig. 3). Fig. I. Measurements of saturation remanence (upper, right-, Moskowitz (1980), theoretical (see Fig. 12). hand scale) and coercive force (lower, left-hand scale) of essen- k Bando et al. (1965), experimental. tially spherical electrodeposited iron particles at 207 K. corn- tmBanerjeeChevallier(1971),and Mathieuexperimental(1943),(seeexperimentalFig. 4). (see Fig. 4). paredafter Knellerwith SDandtheoryLuborsky(solid curves:(1963). eq. 4 of the text). Redrawn “ Soffel (I977a), experimental (see Fig. 3). 3

0,000 10,000 Magnet/te Iron 6000

4000 two domain

~ 2000 000 circular

~l000 ~dornain b-domain 600

.~ 400

2p0 superparamognetic

100 I I I I I _I I 02 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 Ratio of minor to major axis, b/c Fig. 2. Calculated SP, SD and MD fieldsfor magnet te parallelepipeds and ellipsoidal iron particles of various elongations. Theupper and lower SP—SD transition curves are for 4.5 x lO~y and lOOs relaxation times respectively. After Butler and Baneijee (l975a,b).

The onset of MD behaviour in particles larger crease with temperature, d5 more rapidly than d0. than d0 is marked by gradual, rather than abrupt, A direct MD— SP transition is a distinct possibility decreases in J~and H~.Empirically, the size de- pendences of both quantitieslie between d 05 and I d — ~, These “laws” are not well explained theoreti- 0 T/tono.’nogne//te cally, but they are of basic importance~in rock 6 x 055 magnetism because thermoremanence (Section 6) ::~. follows a similar “law”. Table I summarizes our present knowledge of d, 2 and d0 in commonly occurring magnetic . - Critical SD volumes span about 9 orders of magrn- I ‘00 G,wn at~,meter,a’ (#m) tude. The figures in Table I were arrived at in one .~ 30 of three ways: 20 (1) theoretical calculations; 5 Pyrrhoi/te (2) extrapolations from observed MD struc- ‘h o 150ffI tures; ‘~ 6 (3) transitions in measured magnetic properties. ~ 4 As an example of the first approach, Fig. 2 3 shows the results of some of Butler and Banerjee’s 2 (I 975a,b) calculations of critical sizes in magnetite ______I’’’’ and iron as a function of particle elongation. [See I 0 100 Kirschvink (1979) for an indirect confirmation of 6mm thcmeter d(#m) the magnetite calct~lations.]Time is relatively inef- Fig. 3. Observations of numbers of domains in natural titanomagnetite and pyrrhotite particles of various sizes. The fective in changing critical sizes: the 100 s and SD—2 D transition is observed in pyrrhotite and estimated by 4.5 X lO~y SP— SD curves are similar. Tempera- extrapolation in titanomagnetite. Redrawn after Soffel (1971, ture is important, however. Both d5 and d0 in- l977a). 4 at high temperatures. In fact, for equidimensional data on titanomagnetites of compositions other iron particles, an MD—SP transition is predicted than x = 0.4, see Day et a!. (1977)]. Thermal agi- at room temperature although the data (Fig. 1) tation results in a size-dependent coercive force in contradict this prediction. Slight departures from SD particles. Very large SD particles, or any SD 1K~the micro- equidimensionality are enough to ensure a distinct particle at 0 K, would have H~= j SD range at ordinary temperatures in all the scopic coercive force arising from shape or crystal- minerals listed in Table I. line anisotropy. But at T> 0 K in an applied field The extrapolation approach is exemplified by H(< HK), the magnetization of an SD particle Soffel’s (1971, 1 977a) work, reproduced in Fig. 3. ensemble is not perfectly constant ~ut instead [SeeHalgedahl and Fuller (1981) and Soffel (1981) relaxes from an initial disequilibrium with a re- (both this issue) for further domain structure ob- laxation~time‘r (Nêel, 1949) servations.] These experimental observations are of — E particular value in reminding us that real particles =f~exp~, b of a given size, unlike the idealized perfect crystals T kT dear to theoreticians, have a range of possible VJSHK HI 2 domain structures. Despite this fact, extrapolating = f~exp — 2kT ~ — ~ (1) average observed domain structure in the manner of Fig. 3 gives an estimate of d 0 for titanomagne- In (1), f~~ lO’°s~,E,, is the energy barrier to be tite that agrees remarkably well with theory (cf. crossed to achieve thermal equilibrium, k is Boltz- Fig. 12(a), results of Moskowitz, 1980). mann’s constant and V is particle volume. The final expression assumes H parallel to the easy 2.2. Magnetic hallmarks oftransitions axis of uniaxial particles, but quasi-analytic or numerical expressions are readily obtained for Figure4 expands on Fig. I by adding H~data other orientations and anisotropies (Stoner and for many of the minerals listed in Table I. [For H~ Wohlfarth, 1948; Johnson and Brown, 1959; L.D.

05 005 10005 l~m i0~m lOO~&m 1111111 I I IIII1I~ I 1111111 1111111 I IIIIIIJ I Hevnc/,~e 300K Iron 77K Thaivç.~eii~,x 04, (BonerJee,/97/,

-~ (2~4~Q/)fl/953 3()C~/((~y/977) Chevo//,er 8 Mcthieu. /943) • Luborsky, /96/)

II000_ -1000 Mojnet/te,77K ~ 0~’- ~ ICC 7 (Dun)op,/973b) ‘\ - 00

I I \ (o~’rneo~&d) ° / 300K(Porry,/965) “ Magnetliefurrovieo/&1 / 390K(Gottschoik,/935) +1~ 0 I I I 111111 III 1,111111 I I jitiji I I 1111111 I I 1111111 I (3 ocA iocoA I~m 1C~m l00~m Particle diameter, d Fig. 4. Coercive force as a function of particle size. Dashed lines indicate the SD—MD transitions in iron and magnetite. Based on Luborsky (1961, fig. 2) with added data for hematite, magnetite and titanomagnetite. S 5 Schutts, pers. comm., 1979). Relaxation to (Néel, 1955; Stacey, 1963) equilibrium (“unblocking”) is substantially corn- j ~ H, /N (5) plete in a time t ~ IT. Thus the coercive force or “unblocking field” is the value of H necessary to (N is demagnetizing factor) as for MD grains with make IT ~ t, yielding (Bean and Livingston, 1959; well-developed domain structure and to take into K.neller and Wohlfarth, 1966; Dunlop and West, account the special importance of surface pinning 1969) and rotation processes in very small MD grains by ______substituting SD values of H~.H~= 500 Oe is a H~(V,T, t) = H T2HKkT1n(fot) realistic figure for SD magnetite with moderate K — shape anisotropy [see Fig.3 ~11(a),0.25J SD curve]. It implies ~rS ~ 125 emu cm 5 in magnetite = HK — Hq(V, T, t) (2) just above d0, whereas ~rs = 0.5J~just below d0. The expected discontinuity in J~remains substan- Hq is the “fluctuation field” or “viscosity field” tial even though continuity in H~has been re- (Néel, 1950, 1955): [Equations analogoi~sto (1) quired. and (2) apply to activation in MD The observed hallmarks of the SD—MD transi- particles (Street and Woolley, 1949; Nêel, 1950; tion, however, are similar d —n dependences of Dunlop, l973a; Gaunt, 1977)]. both H~and J~over very broad MD size ranges, The criterion for SP behaviour is that H~ 0 at with a smooth transition to SD values at d0 in room temperature T0. Thus 3 (3) kettedboth cases.in ironTheandSD—MDhematitetransition(Figs. I isandwell4),bracjust- d, = cV3[2kToln(fot)/JHK]” barely covered by the magnetite data, and not where 1 ~ C ~ 6/ir depending on particle shape. reached at all by the titanomagnetite data. The

Equation 2 then simplifies to (Kneller and Lubor- value of n in the d “ law is about 1 for iron, sky, 1963) titanomagnetite and unannealed magnetite, about H~(d,T 0) = HK(TO)[l — ~/d~/d~] (4) 0.65 for hematite and 0.4—0.5 for annealed mag- netite. Internal stress seems to play a controlling which fits the data for iron and hematite in Fig. 4 role (Lowrie and Fuller, 1969), higher n values reasonably well, characterizing moremagnetostrictive materials and Saturation remanence j,~is a more sensitive unannealed crushed particles. Theoretical interpre- indicator than H~of the SP— SD transition. Except tations of the d — ~dependence of H~(e.g., Stacey, at d= d,, where it increases abruptly from 0 to 1963; Stacey and Wise, 1967; McIntyre, 1970) ~J~,J~has no size dependence in SD particles, have difficulty in explaining values of n ~ 0.5. For an experimental demonstration of the sharp- ness of remanencechanges at the SP threshold, see 2.3. Transitional domain structures and pseudo-SD Banerjee’s (1971) data for hematite. Quasi-SP be- magnetization haviour, which blurs the transition if magneto- static interactions are strong, is absent in weakly The various minerals considered in Fig. 4 have magnetic hematite. similar patterns of magnetic behaviour, although At the SD—MD transition, one would antic- their absolute transition sizes vary widely. The ipate a less extreme but otherwise similar discon- logarithmic scale brings the SD range of each tinuity in J~.An SD particle isalways magnetized into prominence. It tends to conceal the to saturation but once recognizable domain struc- fact that the SD range encompasses a minute ture develops, remanent states of lower magnetiza- fraction of the size spectrum of most naturally tion become available and are strongly favoured occurring minerals (Evans, 1977). In fact, both by self-demagnetization. A conservative approach Nèel (1955) and Stacey (1963) dismissed SD par- that is likely to overestimate rather than under- tides as being a rarity in nature. estimate the saturation remanence is to assume In the intervening twenty years, a gradual reas- 6 sessment has been taking place. The range of tides become SD, a domain wall whose volume Vp., exhibited by paleomagnetic rema- is sufficiently small should have a single polariza- nences extends well beyond the plausible limits for tion or sense of spin rotation and a permanent pinned domain walls, and frequently the intensi- moment (2/ii~)V~J,(Stacey and Banerjee, 1974). ties of weak-field remanence appear incompatible For convenience, such walls will be called “SD with self-demagnetization in MD particles. The walls”, although the single wall domain is not a parallel evidence for continuity of strong-field re- region of parallel spins. Subdivision of walls by manences and coercive forces across the SD—MD Bloch lines is the norm in iron, but SD walls are boundary was discussed in the last section. The energetically possible in less strongly magnetic SD affinities of small MD particles seem estab- minerals, magnetite for example (Dunlop, l977b). lished beyond reasonable doubt. The y-component of applied field (parallel to Where opinions differ sharply is on the mecha- the main domains) produces wall displacement nism of this pseudo-SD effect. Some workers (e.g., without affecting the internal structure of the wall Schmidt, 1973) argue that two-domain (2 D) par- or its moment. The z-component of field (parallel tides possess an intrinsically strong and stable to the moment of one of the wall domains in Fig. 5 remanence that, in effect, bridges the gap between and perpendicular to the main domains) exerts no SD and larger MD particle properties. Others (e.g., pressure on the wall but does change the structure Dunlop et al., 1974; Banerjee, 1977) argue for the of the wall: one of the wall domains enlarges at presence of identifiable additional moments with the expense of the other via Bloch line displace- stronger pinning than (and some degree of inde- ment. If the wall is SD, it must instead respond by pendence from) domain wall displacements. The some rotation process, coherent or incoherent. The two points of view can be reconciled if the addi- independence of wall displacement (MD) and wall tional moments are an intrinsic feature of the moment processes is discussed in detail by Dunlop domain wall itself (Stacey and Banerjee, 1974). (l977b). Moskowitz and Banerjee (1979) argue for Figure 5(b) illustrates the rotation of spins surface moments, appealing to the d 1 variation across the Bloch line in passing between the front of the surface/volume ratio of a particle. How- and back wall domains. Spin 5 rotates, in the ever, in magnetite at least, TRM goes as d “, plane of the Bloch line, .through successive posi- where n = 0.6—0.7 (Day, 1977; see also Fig. 14), tions a, b, . . . ,g into the corresponding spin 5’ in and ~rs and H~have even weaker dependences. the rear domain. Spin 4 rotates, again about an These dependences are more obviously compatible axis OP perpendicular to the plane of the Bloch with the domain wall volume/particle volume line, into 4’. Even spin 1 undergoes, in principle, ratio, since wall area/particle volume goes as d —‘ the same set of rotations about its own axis, and in addition both the number of walls (or nowhere breaking exchange coupling with the equivalently, wall spacing) and wall thickness neighbouring main domain.

slowly increase with increasing d. Notice that at each position a, b, c, ... within The model of Fig. 5, an outgrowth of Dunlop’s the Bloch line, the angles between 5a and 4a, (1977b) “psark” model, illustrates how a 2 D par- between 4a and 3a, etc. (or between Sb and 4b, 4b tide can have both MD and SD behaviour. The and 3b,...) are the same as the angles between 5 180°domain wall is subdivided by a Bloch line and 4, 4 and 3, etc., or between 5’ and 4’, 4’ and 3’, (Shtrikman and Treves, 1960) into two wall do- etc., within the wall domains themselves. This fact mains in which the spins rotate (in the plane of the is easily verified in the seccind part of Fig. 5(b), wall) clockwise and counterclockwise, respectively, where spin 4 is seen to rotate through a cone in passing from left to right between the main making a constant angle with the x—z plane, which domains, contains the successive positions of spin 5. The particle pictured has no net moment, ex- If the spin cones are now imagined to represent dept the very small uncompensated moment of the successiye temporal states of all the spins in an Bloch line. However, just as sufficiently fine par- originally SD wall, instead of the successive spatial 7 >~ 4~. . ~ k~ 15~ ~. ->~ \: I / a’ ~ ~/j~>>1~ ~ 7~~J~<1~

Ha L~P 1 ~:j/

Fig. 5. (a) A cut-awayview of a 1800 Bloch wall in a 2 D particle. Progressiverotationof spins across the wall is represented by spins 1—9 and l’—9’. These lines of spins have opposite polarizations or senses of rotation, characteristic of the two wall domains. Large open arrows are schematicrepresentations of mutually orthogonal net magnetic momenri of main domains, wall domains and Bloch line (arrows not to scale). (b) Progressiverotationof various spins in (a) across the Bloch line is represented by spins a—g. Rotation in each case is about an axis OP perpendicular to the plane of the Bloch line, forming cones of spins. positions of individual spins in the Bloch line, the MD (self-demagnetization-linlited) displacement of angles between all neighbouring spins are seen to walls or Bloch lines from a zero- or near-zero remain constant throughout the rotation. This pro- magnetization state, and SD-like rotation of per- cess is coherent rotation of an SD wall. Incoherent manent wall moments with little or no change in processes are also possible. They amount to pas- overall intensity of magnetization. Other transi- sage of a virtual Bioch line across an SD wall, tional structures have been proposed; circular spin transforming it into an SD wall of opposite polari- structure (Morrish and Yu, 1955) and stable curled zation and moment. state (Dunlop, I973c) are examples. They are anal- Thus the SD—MD transition may be bridged by ogous to broad walls without recognizable main 2 D structures with a combination of responses: domains and their field response can be modelled 8 by extending the approach of Fig. 5. presence is difficult to prove or disprove through An entirely different explanation of the particle magnetic measurements because they cannot be size dependence of .J~,has been advanced by decoupled from the main domains and from wall Halgedahi and Fuller (1980), based on their ob- displacements. servation that 40% of x = 0.6 titanomagnetite par- The attractive feature of transitional domain tides 5—15 ,.tm in size (well above d0 ~ 0.6 hum, structures in particles just above critical SD size is Table I) fail to nucleate a domain wall following the predicted mutual independence of their MD saturation. Since the probability that a particle and SD-like responses. In the nucleation model of contains a defect or surface irregularity strong Halgedahl and Fuller (1980), MD and SD-like enough to nucleate a wall decreases in smaller responses are exhibited by physically distinct MD particles, the size dependence OUrs is explained in and metastable SD particles. In this section, hys- a natural way by the varying proportions of MD teresis properties are examined for evidence of this and metastable SD particles. The size dependence anticipated dual response. The evidence from ther- of H~(Fig. 4) is not obviously accounted for, un- mal properties has been reviewed elsewhere less nucleation fields are themselves size depen- (Dunlop, I 977b). dent. It also remains to be seen whether particles Saturation remanence due to pinned displaced remain in a metastable SD state following TRM walls or Bloch lines is limited by self- acquisition. demagnetization to a value ~ H~/N (eq. 5). This MD relation is plotted as 4the1T/3.dashedThe datalines forin Fig. 6, with N taken to be 3. Isothennal magnetic properties 1.5—120 ~zmmagnetites (Parry, 1965) agree rea- sonably well with MD theory, but the 0.22 ~tm 3.1. Hysteresis and transitional domain structures particles, whose structure is inferred to be 2 D (Dunlop, 1973c), have a decided enhancement of In 3 D and larger particles, SD wall moments remanence over and above that allowed by the tend to mutually cancel and other pseudo-SD internal . An alternative inter- mechanisms, e.g., surface moments, “dislocation- pretation is that N < 4~r/3,since the domains line moments” (Verhoogen, 1959), come into themselves are not equidimensional (Merrill, 1977). prominence (see e.g., Parry, 1981). While these Then a match can be produced between experi- undoubtedly enhance both the remanence and the ment and MD theory for the fine particles but not average of small MD particles, their for the coarser ones. Initial susceptibility x 0 due to MD processes is also limited by self-demagnetization: Mogneti/e I

d~O.22~,.m • d~/.5-/2O#m Xo = 1 +N (6) 40 ‘~u~00,/98/al (Par,~y,/9651 Xj A the limiting value 1/N being attained when the 30 /~‘ intrinsic susceptibility x1 >> l/N~0.25 emu 3 0e ‘. SD susceptibility is (Stoner and ~ ~ 20 ~ cm / -• ~ Wohlfarth, 1948; Dunlop, 1969)

.~ ~- I = 0.349J~/HR (7) 0 20 40 60 80 $00 CO 20 40 60 80 00 (HR is remanent coercive force), and can be either Coercive force, Hc (0~’) greater or less than 0.25 emu cm3 Oe — Fig. 6. Measurements of saturation remanence and coercive Dunlop (1974, fig. 1) foundx > 0.25 emu cm3 force for 0.22 ~m (at various temperatures) and — 0 1.5—120 urn magnetites at room temperature, compared with Oe for the 0.10 and 0.22 ism magnetites fea- the predictions ofMD theory (dashed lines; eq. 5 of the text). tured in Fig. 7. This observation is still compatible Redrawn from Parry (I96~)md Dunlop (1981a). with eq. 6 if N is somewhat less than 4ir/3 because 9

Magnetite Shcherbakov, 1978; Moskowitz and Banerjee, 20L 1979). At the 2 D—3 D transition, we might expect d~O./O#m I a discontinuity in magnetic properties. The only // hint of such a discontinuity is the pseudo-SD .5 / threshold near 0.2 ~tmproposed by Levi and Mer- rill (1978) on the basis of the Lowrie—Fuller test (Section 3.2). There is no striking evidence for .0 ~ MD discontinuous size dependences of either H~(Fig. 4) or TRM (Fig. 14). On the other hand, there is a 0.5 total lack of data in the crucial 0.25—I ~smregion.

~ c I I I 3.2. Diagnosing domain structure ~a 0 200 400 600 .5 d 0. 22#m • Whereas the last section concerned the induc- tive use of isothermal magnetic properties in learn- ‘SD ing more about hypothesized. domain structures, •— .0 z~*__t.~_~MD the present section considers their deductive usein — — diagnosing the presence in rocks of particles with well-established structures (SP, SD and MD). This 0.5 is a subject of enduring practical interest (e.g., Deutsch et al., 1981; Murthy et al., 1981; C 0 200 400 600 Radhakrishnamurty et al., 1981; Senanayake and

Temperature , T ~C~i McElhinny, 1981; Wasilewski, 1981; all this issue). The temperature dependence of initial suscept- Fig. 7. Measured initial susceptibility as a function of tempera- ibility Xo has been widely used (in the manner of tare for small MD magnetites, compared with the predictions Fig. 7) to discrimihate SP from MD behaviour of SD and MD theories (eqs. 7 and6, respectively, of the text). (see, e.g., Deutsch et al., 1981; Radhakrishnamurty After Dunlop (1981a). et al., 1981; both this issue). The interpretations are not unambiguous (Senanayake and Mc- of either slight particle elongation or subdivision Elhinny, 1981, this issue). into 2 D structure. However, the temperature de- A simple alternative test is the value of Xo’ at a pendence of Xo in Fig. 7 favours an SD-like sus- single temperature, normalized to saturation mag- ceptibility (eq. 7) rather than an MD one (eq. 6). netization J~to remove the effect of concentration. Of course,3 Oe ‘ifinx1fineis considerablySD particlesless[itsthanvalue0.25in bulkemu mineral(In practice,properties,wholex rock values rather than the cm 3 Oe’ (Stacey, rock and mineral ratios0 andare J~thearesame.)usedFrombut wholeeqs. 6 magnetite1963)], thenistheabouttemperatureI emu dependencecm of x 1 ~‘~11 and 7, Xo/J is ~ (Ni) ~‘for MD particles and compromise the dimple decomposition into SD 0.349 (HR) ‘for SD particles below their block- and MD functions imagined in Fig. 7. Further- ing temperature TB. In either case, for magnetite more if N depends on domain structure (Merrill, at room temperature, Xo /J~~ 0.7 X io~ Oe —‘ 1977) which is in turn temperature dependent (e.g., (H~= 500 Oe for SD magnet te assumed). Butler and Banerjee, 1975a,b; Soffel, 1977b), the For SP particles (i.e., SD particles at T~TB) MD susceptibility is no longer temperature in- Xo/~~ V.15/ICT (8) variant. The permanent moments of transitional domain (Bean and Livingston, 1959). SP behaviour of wall structures are important in a limited size range, moments, MD particles, etc. is also described by extending, in equidimensional magnetite, from d0 (8) if V is interpreted to be V.,,, Barkhausenjump (0.05—0.06 ~m) to 0.2—0.3 ~sm(Dunlop, l977b; volume, etc. For magnetite with d d8 = 0.03 ,.sm 11

‘.0 Ala

x~0-0.6

0.06 4:14 (DoySyn!he~Fce, 0/,~d0n0m0gnetI!eS./977) 0.8 (Ow’/op, /9730~~ 0.4 TV 04

Ipso’ MO

-~ 0.2 ~ ~o ~4~’06~V

0.1 200 400 600

— ~. (a)1.0 A//erna/i,g fi~/d(oe peck)

Co 5 Magne/ite (a) (Johnson ci 0/1975)

~ 1 osc~°inmis,~e,~cks -~ 0.25 Ce IIIII~III ~I Ii (O~c~~a A~as’,/98/) 0l \ 0.5// CeCe 2000 o.\\ IRM Leg 37 gob(ros (I) \ 020~ ~00 Ce

ICe ARM —~, S.’ ~ .I I

—~ 0.0o 00 ‘ 200 ‘ 300 400

(b) 4/ternahng field, /1(Oe peak) ~. ( Fig. II. (a) AF demagnetization c~es of weak-field TRM of Leg 37 .4 ~ ~ Leg30 gcô~~C C SD. small MD and large MD particles of magnetite, illustrating seflzed ~ 1Hff ~ (•), ~ the progressive change towards soft exponential and subex- 9~0S C.) ponential curves with increasing particle size. After Dunlop - Leg 45 se,*ized (I 973c). (b) A semi-logarithmic plot of AF demagnetization ~(,h~s (+) curves for fine and coarse magnetites. On either side of the dashed line (corresponding to an exponential curve on a linear ______scale) relative stabilities of weak-field and strong-field rema- C, I 15 ao 25 3~O nences are reversed. after et (b) /4’Wc Redrawn Johnson al. (1975).

Fig. 10. Domain-structure diagnosis using both .J~/J~and HR/HC. Values of J 1~/J,corresponding to SD—PSD (pseudo- Bailey and Dunlop (1975) believe the test is an SD) and PSD—MD transitions are indicated by lines superim- indirect expression of the very different shapes of posed on the data for synthetic titanomagnetites in (a). Differ- the AF demagnetization curves of large MD par- ent rock types in (b) have different relations between the two diagnostic parameters. After Day Ct al. (1977) and Dunlop and tides on one hand and small MD and SD particles Pr~vot(1981). on the other (Fig. 11(a)). In an MD particle, the 12 observed AF coercivities (H~)0are reduced from DSDP bosc//s, intrinsic values (I~)~by the internal demagnetiz- Legs 37 8 45 ing field NJr of the remanence in question 0.8 - (Bailey, /980) (R~)0=(i~0)1—N./~ (9) The stronger the remanence, the more the intrinsic

(SectionAF demagnetization8) can producecutvea similaris shiftedeffect.)toAnlowerex- 0.6 - increcsL ~ coercivities. (In SD particles, interaction fields ponential curve (suitably renormalized) is in- oxidation variant under such shifts along the J~-axis.Sub- / “MD-type” and “SD-type” Lowrie— Fuller char- exponential and super-exponential curves generate 0.4 acteristics respectively. That these shapes of curves correspond to different domain structures is for- tunate but fortuitous. Figure 11(b) shows data for magnetite by John- 0.2 son Ct al. (1975) 4hat support this theoretical model. Therespondsdashedtolinean onexponentialthis semi-logarithmicAF demagnetizationplot cor- 1f curve on a linear plot. The SD-type Lowrie— Fuller 100 200 I I I , T~.(°C) I~ I I I (b) 0 0.4 0.6 0.8 1.0 t’/tloskow//z, /980,~ Oxidation parameter , z (approximate)

10 - Ti/anomcqhemi~e, bFig.tionspredicts12.in (a)x~~0.6aCalculatedchangetitanomaghemite,fromSP—SD,MD toSD—2afterSD behaviourDMoskowitzand 2 D—3in(1980).micron-sizeD transiLine -

for the process proposed in (a): in DSDP basalts with vaiying — — — —‘- — — — - b degreestitanomagnetiteof low-temperatureupon low-temperatureoxidation, J~/J,oxidation.rises (b)steadilyEvidencewith J.6.I0 Curie temperature, which is a measure of oxidation. After ~J Bailey (1980). 2D characteristics (stability decreasing with increasing intensity of remanence) correspond to super- exponential (convex up) curves, and the MD-type

curves. o.~~ ~ - o.~ characteristics correspond to sub-exponential

4. Chemical remanence (CRM) SR C I I’ Domain str~icturecalculations are relevant to 0 0.2 0.4 0.6 0.8 .0 the properties of CRM. Figure 12(a) shows transi- (a) Oxidation parameter, z tion sizes in x 0.6 titanomagnetite as a function 13

of low-temperature oxidation, as calculated by .~ Magnet//c Moskowitz (1980). The SD—2 D transition is pre- “~ ~ /98/) dicted to occur about 0.5 ~sm in unoxidized . titanomagnetite, in agreement with Soffel’s (1971) 0.15 experimental estimate (Fig. 3). All the transition sizes tend to increase with maghemitization. .!~ 0 I I’ Butler (1973) suggested that oxidizing SD / °/ C~ titanomagnetite in submarine basalts (following a b line like a in Fig. 12(a)) could result in unstable 0.05. SD behaviour. More important, perhaps, is the . oxidation behaviour of somewhat larger particles, ~ I I I’ which fora broad range of starting sizes in the 2 D C 10 00 and >2 D regions can eventually (following a line P0,/ic/c d,ome/er,d (#m) like b) acquire a CRM of SD stability. Fig. 13. Particle-size dependence of normalized DRM intensity There is a good deal of experimental evidence for artificially sedimented magnetites. Redrawn after Amerigian that this latter process, or something like it, does (1981). occur in submarine rocks. Figure 12(b), after Bai- ley (1980), shows a clear progression from MD to to remove the size dependence of 4,, a size depen- SD values of 4, /4 with increasing oxidation. Curie dence intrinsic to the DRM alignment process temperatures > 450°C cannot be produced by persists. At large sizes, alignment efficiency drops low - temperature oxidation of an x = 0.6 because of mechanical settling effects. Of more titanomagnetite and are irrelevant to the trend. interest in a fine-particle context is the decrease in Except for Johnson and Merrill’s (1972, 1974) submicron magnetites, where thermal fluctuations work on maghemitization of magnetite, there has perturb perfect alignment of the moments of set- been little recent systematic laboratory study of tling particles. CRM.. The burning practical question is whether Both these effects have long been predicted CRM is field-controlled or coupled to pre-existing theoretically (Collinson, 1965; King and Rees, remanence in the parent mineral. Exchange con- 1966; Stacey, 1972). Amerigian’s results represent trol seems to be the rule, to judge by Porath’s the first convincing verification of these predict- (1968) work on inversion of maghemite to hema- ions. tite, Wilson and Smith’s (1968) study of high- Barton et al. (1980) have investigated in detail temperature oxidation of titanomagnetite, Marshall the time and field dependences of DRM intensity and Cox’s (1971) work on low-temperature oxida- in redeposited muds containing micron- and sub- tion of titanomagnetite, and numerous studies (e.g., micron-size particles. The field dependence predic- Evans and Wayman, 1977) of the inversion of ted by Stacey’s (1972) thermal fluctuation model is titanomagheniite. The key may well be Johnson followed in the case of dilute slurries, but not in and•Merrill’s (1972, 1974) observation that in the concentrated slurries, where additional gravita- maghemitization of magnetite, exchange-coupled tional and frictional torques become important. CRM results if parent and daughter are SD size but field control holds in MD particles. 6. Therinoremanence (TRM)

5. Detrital remanence (DRM) 6.1. Intensity of TRM

There is a great need for careful, systematic The particle size dependence of TRM in mag- study of the field and particle-size dependence of netite is shown in Fig. 14, which is an extension of DRM. Figure 13 shows important recent work by Day’s (1977) fig. 8 to incorporate data by Levi Amerigian (1981). After normalization of the data (1974) on large single crystals. There is a remarka- 14

iocx~ I~m lO~m ICO~m mm 10mm I 111111) I I 111111 I 1111111 I I 1111111 I I 1111111 I

II- ~l0 Mognetite £ Roquel (/954) ° Porry (/965) \ ~ Robins (/972) I 0 Dun/op (1973c)

I - • RohmonLevi eto/.(/974)(/973) - I

- 0.1

0,01 - 001 I I I I 1111111 I 11111111 I I 1111111 I I I’liII I000~ I~m I0~m I00~&m mm 10mm Particle diameter ,o’ Fig. 14. Particle-size dependence of I Oe TRM in magnetite, between d’0.05 ~m (dashed line at left) and 5 mm. Most of the submicron data fall well above the average d 06 line through the other data and barely within the dispersion limits (shaded area) suggested by the spread in the larger-particledata. Based on Day (1977, fig. 8) with the addition of data by Levi (1974).

to — —z — ————-c-: ble continuity in the size dependence: a single / 0.2~ — — — — — — — power law holds, to a first approximation, over

f // ~I6~L~— five decades of d, or 15 decades of V. The threshold 08: / / for pseudo-SD moments around 15—20 ~tm sug- Ill gested by Parry’s (1965) data is not supported by ‘‘ subsequent measurements (Rahman et al., 1973; I, / Levi, 1974). On the other hand, there does appear l / ii, to be a threshold in the titanomagnetite data (Day, I I C ~ 0076 1977, fig. 9). Uncertainty about the existence of an

I // 0. — — .— — upper limit fpr significant pseudo-SD effects in ~ 041’ / — — MD particles makes the relation of the Lowrie— / — Fuller test (Section 3.2) to domain structure transi-

~02 ///// — tions tenuous.

fl/f-/ / /..- ..‘ ——— — — — — thenetitesDunlop’s1—250lie ,~mwell(l973c)data.aboveWhetherdatathe forbest-fittingthis0.076—0.22“excess”line~tmTRMthroughmagis - /—. ————— o ,~ —,~ significant and indicates a source of pseudo-SD 20 40 60 do moments umque to 2 D particles remains to be App//ed , H(oe) seen. Fig. 15. Measured TRM induction (points andsolid curves) of SD and small MD magnetite particles, compared with SD A long-standing puzzle has been the field de- theory (dashed curves; eq. 10 of the text). Particle sizes are pendence of TRM in SD and nearly SD particles. indicated. After Dunlop (1975). Néel’s (1949) theory of aligned uniaxial particles 15 in an axial field predicts range of temperatures bracketting TB. An exact I VJ,(T~)H (10) expression is given by Dodson and McClelland- ~TRM =4~tanh( kTB ) yieldsBrownan(1980).implicitSettingequation~r~t*forwhenT~ T T~in (1) The theoretical dashed curves in Fig. 15 graph this TB function for various values of V. All the measured F( T8 )F’( TB) curves have a steep initial slope but saturate slowly, as though a broad range of particle sizes were — JSOHKO V 1 — HI 12 (12) present. Averaging over random particle orienta- — 2k log( fot*) HK( TB) j tions changes the theoretical curves in this general I. way (Stacey and Banerjee,, 1974). Reformulating where J~~4(7~), HKO HK(To), F~J,/J,0, F’ the problem at the outset using the Stoner— HK /HKO. TB is thus a function of particle size, Wohlfarth (1948) theory, before angular averaging, time or cooling rate, and applied field. Analogous results in excellent fits to the data (L.D. Schutts, expressions can be written for blocking of wall V.A. Schmidt, pers. comm., 1979). Particle interac- moments, domain wall displacements, etc. tions, which were formerly invoked (Dunlop and The size dependence of TB has been examined West, 1969) to produce a fit, must play a minor by Dunlop (l973c) and Clauter and Schmidt (1981, role. this issue). A perennial difficultyin trying to match The lack of any very marked particle-size de- theory to experiment is the spread of particle sizes pendence in the data is strong evidence for rotata- in any test sample, leading to a spectrum (albeit ble SD or SD-like moments of similar volume narrow in well-prepared samples) of TB values. (e.g., V~for wall moments) in 2 D magnetites. The Within this limitation, the data appear to confirm theoretical curves, which assume the entire particle eq. 12. Certainly the finest particles have the lowest volume is activated for SD, 2 D and > 2 D par- blocking temperatures. tides alike, are strongly size-dependent. Day’s Everitt (1961, 1962) was probably the first to (1977, fig..6) data confirm the lack of a strong size examine the field dependence of blocking temper- dependence in 1—140 ~smtitanomagnetites; TRM- ature. He showed, as (12) predicts and Sugiura field characteristics in this size range are well (1980) and Clauter and Schmidt (1981, this issue) explained by MD theory (Nêel, 1955; see also have since confirmed, that the blocking tempera- Dunlop and Waddington, 1975, Tucker and O’Reilly, I 980a,b). _____ .0 6.2. Blocking temperatures 0.8 The blocking temperature spectrum of TRM, b.I~ ______and particularly the mutual independence of dif- j o.~ ferent TB fractions of TRM, is of fundamental ~

importanceterminationt~, a characteristic(Thellieras thecoolingbasisand Thellier,oftime,paleointensitygiven1959).by At(York,TB,de- ~)~ 0.20.4 ~ Magnet//c ~ the relaxation time ‘r of an SD particle is of order ..~ (Sugiupo /98 l978a) 2kT~ IdT ~ ______= ______V4( TB)HK( TB) ~ (11) °0 200Tam~etature,71°C)400 600 A similar expression is given by Stacey and Fig. 16. Continuous cumulative partial TRM spectra measured during cooling of SD magnetite (points and solid curves) Banerjee (1974). Equation 11 supposes that .1, and compared with theoretical stepwise spectra for three values of HK do not change significantly over a narrow applied field. AfterSugiura (1980). 16 ture spectrum shifts to lower temperatures as H hemites. Wohlfarth (1980) has successfully used a increases. “Unbiocking” temperatures during zero- similar approach to test the field dependence of field cooling are therefore always higher than the ordering temperature of a number of spin blocking temperatures observed during in-field glasses (Wohlfarth, 1977, 1979). cooling (e.g., Dunlop and West, 1969). A formerly neglected question which is cur- Figure 16 reproduces the results of Sugiura rently being actively pursued is the dependence of (1980). By assuming a single value of V and subdi- (weak-field) blocking temperature on rate of cool- viding the HK spectrum into II fractions, he ob- ing (York, I 978a,b; Dodson and McClelland- tamed a close match of theoretical (eq. 12) and Brown, 1980; Halgedahl et al., 1980). This is a experimental TB spectra. question of practical significance to paleomagne- An alternative approach, which circumvents the tists studying slowly cooled orogens (Pullaiah et problem of dispersion of V and HK, is “fluctua- al., 1975). Figure 17 (calculations by Dunlop, based tion analysis” (Dunlop, J 976), in which H~(T) on eqs. 11 and 12) illustrates theoretical predict- data are compared to eq. 2. Since it is immaterial ions of TB and the width of the 5—95% blocking whether a particle is unblocked by increasing T at interval (York, I 978a) for SD magnetite with vari- fixed H until T = TB or by increasing H at fixed T ous values of the product VHKO. [The curves are until H = H~,H~(T) data give information equiva- not materially altered in the MD case, since f~~ lent to TB( Hj data. Dunlop (1976) and Dunlop lOb s_1 (Gaunt, 1977) for both MD wall displace- and Bina (1977) find excellent agreement with ments and SD rotations.] TB is sharp and time- eq. 2 using SD and 2 D magnetites and mag- insensitive for high TB values (larger SD particles)

Mognelite

IGc 1150 50 250 350 450 550 I I I I I I I I I I I 111111 I I 111111111 I I I I I I I I I I .“~T”T Go

lOMo lOMa \\\ \\\ \\\ \\\ \\\ \\\ \\\\ \\\ ~ ‘° \\\ \\\ \\\ IOo

. rn \\\ \\\ \\\ \\\ \\\ \\\ \~ im \\\ \\\ \\\ \\\ \\\ \\\ \~

~Ih

I ~ ~ I~\~ , I. lOs 50 150 250 ‘ 350 450 \\550 S/ockinq ~ ~bAxkinq tempercttiv 7~ (DC) Fig. 17. Theoretical relation between cooling rate and blocking temperature (weak fields assumed) for SD magnetite, calculated from eqs. II and 12 of the text. Each set of curves describes an ensemble with a single value of VHKO. The upper and lower curves of each set correspond to 5 and 95% blocking or unblocking (relaxation) of remanence. 17 but blocking occurs over as much as a 300 C range 50 Hematite ./ and is sensitive to cooling rate for low TB values (Dun/~,a S/ithnq,

(ultrafine, nearly SP particles). -~ /977) ./ There is some indirect confirmation of these predictions based on geological evidence (Dunlop / and Buchan, 1977) but detailed testing on a / laboratory time scale is just beginning. /•. It is worth mentioning that both Dodson and 7. • QO7-O/5~am

McClelland-Brown (1980) and Halgedahi et al. .~ so ,i~ £ / • 38-59,,un (1980) predict that TRM intensities, as well as .~ 7 blocking temperatures, are cooling-rate dependent. The predicted effect on intensity seems to have been documentedin recent very rapid Thellier-type ‘~ zo S io paleointensity determinations on archeological mi- £ crosamples (Fox and Aitken, 1980). •

7. Viscous magnetization changes 0 5 Any ferromagnetic particle near its blocking I temperature exhibits magnetization relaxation on a j normal time scale. The spread of 5 and 95% curves 0 I I 0 along the time axis in Fig. 17 gives an indication Thne in hours (logarithm/c scale) of the time scale for viscous changes in particle Fig. 18. Acquisition of VRM by of various particle ensembles of a single size. Viscous effects are sizes in a field of SOc. The left-hand scale corresponds to the normally small at room temperature because only 0.07—0.15 ~m data and the right-hand scale to the other data. AfterDunlop and Stirhng (1977). a small part of the TB spectrum lies near T0 (i.e., is nearly SP). Rocks that have prominent SP frac- tions, such as some submarine rocks, red beds and Only those SD particles that are very near SP lunar and breccias (Section 3.2), are of size are significantly viscous at T0. Consequently course likely to be viscous, viscous magnetization should be strongly size de- It can be shown (e.g., Dunlop, 1973a) that if the pendent. This is clearly the case for SD hematites distributionf(V, II~~)of SD particle volumes and (Fig. 18). In fact, Dunlop and Stirling (1977) at- microscopic coercive forces is reasonably uniform tribute the viscosity of the coarser samples to over the range of VHKO affected by viscous changes contamination by finer particles. at T0 The viscosity coefficient of SD and transitional

dJ . magnetites (Fig. 19) goes as d —n with n = 1—1.5, a d log = s (13) TRMmuch (Figs.stronger4 andsize 14).dependenceThere is thana suggestionH~,~rs ofor a constant called the viscosity coefficient. A log t relatively high magnetic viscosity in the 5—15 ~im dependence of viscous changes is very frequently range, presumably originating in thermally observed experimentally (e.g., Fig. 18). However, activated wall motion (Gaunt and Mylvaganam, significant departures from log t behavior have 1979). However, the trend of increasing S with been reported for lunar rocks (Gose et al., 1972), increasing particlesize contradicts the observations achondrites (Nagata, 1981, this issue), submarine of Zhilyaeva and Mimbaev (1965) over the same basalts (Dunlop and Hale, 1977; Lowne and Kent, size range and is suspect. 1978), and fine - particle magnetites (Dunlop, Viscously acquired isothermal remanence 198 lb), and are a basic prediction of some theories (VRM) represents paleomagnetic noise. VRM is (Walton, 1980). normally thought of as “soft” or easily erased by 18

4 0.1 I 10 100 I 11111111 11111111) .4

I~

.11 ~IIiI~iil11IiI —— — — Magnetite \ II..,.., I 0.4 0’ 0.1 I 10 I00 Particle diameter, d cam) Fig. 19. Observed particle-size dependence of the viscosity coefficient for acquisition of induced magnetization in magnetite. After Dunlop (1981b).

AF demagnetization. Unfortunately ihis is not al- 8. Magnetostatic particle interactions ways so (Fig. 20). Starting from eq. 2, Dunlop and Stirling (1977), show that the maximum AF coer- The concentration of magnetic minerals in rocks civity exhibited by VRM acquired in time t is is usually <1% and quite frequently <<1% by volume. The particles are far from being uniformly ln( f0t0) (14) dispersed, however. Primary oxides, magnetite, in = HK[1 — ln( fe’) J particular, are commonly concentrated as inclu- where t0 is a time characteristic of the AF demag- sions in silicate hosts (Evans and Wayman, 1970; netizing process. All other factors being equal, Murthy et al., 1981, this issue) or in clusters in the minerals with high intrinsic coercivity HK (iron groundmass (Newberry et al., 1980). Secondary and hematite, for instance) will have the hardest oxides are concentrated in fractures and cleavage VRM values, planes. Deuterically oxidized titanomagnetites consist of interacting magnetite-like regions sep- arated by ilmenite lamellae (Larson et al., 1969). Even nominally homogeneous grains, when ex- 4. Red limestone amined by transmission microscopy, are

O’Reilly, 1976; J.C. Briden, pers. comm., 1980). Interacting SP particles behave collectively as SD particles (Radhakrishnamurty et al., 1973). Collective behaviour of SD particles (“interaction

‘~‘ domains”)often subdividedare alsoby observedmicrolamellae(Craik(Mansonand Isaac,and 5hr 1960). Magnetostatic interaction increases d0 (Morrish and Watt, 1957) but decreases d5 (Clauter and Schmidt, 1981), thereby broadening the SD

~ OQ ~500~o I I I I I 500I sizetiesTheofrange.SDeffectandofPSDinteractionsparticles hason hystereticbeen knownproperfor a-

4/,Wnat,ng field, M~’i’Oeifl?Si~ long time. Initial susceptibility increases (KOster, Fig. 20. Measured AF demagnetization of VRM acquired by a 1970; Davis, 1980), coercive force decreases (Davis hematite-bearing sedimentary rock in various times I of cx- and Evans, 1976; Corradi and Wohlfarth, 1978; posure to a 5 Oe field. After Biquand and Prévot (1971). Schmidbauer and Veitch, 1980) or remains con- 19

0.:__0.:__0.:

E C I /1111111 2000~ I / I 111111 C 2000 / Field, H (Oe) / F,e/d, H (Oe) Field, H (Oe)

/ Mognetile, p: 40% Mognet/te - i/men/Fe Magnet/Fe - ulvospinel -0.5 -0.5 mntergrowth -0.5

Fig. 21. Observed hysieresis loops for three samples containing interacting magnetite particles or regions of particles. The intrinsic loops that would be measured in the absence of particle interaction can be determined by replotting thedata, using an inclinedI axis, shown in each case as a dash-dot line. Intrinsic values of.Jrs/Js are close to 0.5 in each case. Redrawn after Davis and Evans (1976). stant (Davis, 1980) with increasing concentration can be produced by strong magnetostatic interac- or packing factor. tion. Veitch and Stephenson (1978) and Veitch Figure 21 illustrates hysteresis loops measured (1980) have measured TRM acquisition in two- by Davis and Evans (1976) for a p = 40% by component “macroparticles” that simulate the volume dispersion of synthetic SD-size magnetite same microscopic situation. - particles ~nd for natural magnetite—ilmenite and The intrinsic AF coercivity (H~)1of a rema- magnetite— ulvOspinel exsolution intergrowths with nence J~is depressed, in exact analogy with eq. 9, comparable magnetite packing factors. The aver- by the mean interaction field — NpJ~ age internal field H, is related to external field H0 ~ = (~‘~ — N .j ~16 as plotted by “ C /~ ~. C/, P r H. = H — N J ~l5~ If magnetic particles were umformly dispersed in 1 0 ‘ ‘ rocks, p would be 1% or less and (H~)~~ (He),. where N is the demagnetizing factor of either the Segregation and clustering of magnetic particles sample or the grains containing intergrowths. If results in interaction fields which are locally much the observed hysteresis loop is represented by J = greater than the average [“local fields” or the 1(H0), then solving with eq. 15 [i.e., replotting “fluctuating” internal field of N~el(1954)]. Signifi- J =f(H0) with respect to an inclined J axis of cant reductions in coercivity resulting from inter- slope (Np)~] yields the intrinsic hysteresis loop actions are inferred by Dunlop and West (1969) J =f’(H1). The appropriate inclined axes needed for TRM, ARM (anhysteretic remanence) and to “unshear” the loops are indicated in Fig. 21. saturation remanence, and by Dankers (1981) for Intrinsic values of J~/J~are all close to 0.5, dem- saturation remanence, and are directly shown by onstrating that the magnetite particles or inter- Schmidbauer and Veitch (1980) for ARM and growth regions are SD and have uniaxial ani- saturation remanence (see also Cisowski, 1981, this sotropy. issue). As the ultimate in magnetostatic interaction, Of greatest practical impact is the predicted Stavn and Moi-rish (1979) have calculated theoreti- effect of interactions on the intensities of ARM cal hysteresis loops for two-component SI? par- and TRM (Dunlop and West, 1969; Jaep, 1969, tides, one entirely enclosing the other. Wasp- 1971; Shcherbakov and Shcherbakova, 1977). Since waisted, and re-entrant hysteresis curves, shifts discrepancies between theoretical and experimen- along J or H axes, indeed all the features normally tal TRM field dependences in SD particles (Sec- associated with exchange interaction of two phases, tion 6.1, Fig. 15) seem to be accounted for by 20

MCgnellle pursued as vigorously as it was then. It is hearten-

08 (Am/op ci 0/. /9751 ~ ing to see that Professor Nagata does not regard ARM p-25~IO~~~ the subject as laid to rest and is himself a con- ~ 02 ~ tributor to this volume in his honour. ~ /“L~007~—~ Fine particles have always been the focus of 0.4 / / I ~ ~ / /1 C42%~’’~’ rock magnetic theories and experiments. Indeed, ~ / / ii~r.~ ~, /7 ,~..._ the success of demands some 0.2 ( / 20’C 2.3% source of ultrafine particle behaviour, whether as- ~ / ie,-octmoo ( ocoo~’s sociated with visible opaques (Parry, 1981, this ~ nu 0 2030 issue) or with finer submicroscopic phases (Murthy 0/red field, H (Oci et al., 1981, this issue). We have an excellent Fig. 22. The effect of particle interaction on ARM induction in first-order understanding of domain structure and magnetite. Interactions arechanged by changing either temper- its relation to strong-field isothermal properties ature or concentration. The TRM induction curve compares (Sections 2.1, 2.2 and 3.2). These questions are poorly with the ARM induction curve measured at 538°C,the mean blocking temperature. Redrawn after Dunlop et al. (1975) relevant to magnetic recording and permanent and Sugiura (1979). magnet technology and have been studied exhaus- tively (Wohlfarth, 1978). But the habits and habi- tat of fine particles in rocks are more elusive. random particle orientations, the role formerly Domain observations on micron-size natural ascribed to interactions (Dunlop and West, 1969) particles (Soffel, l977a,b, 1981, this issue; Halge- is now questionable. Furthermore, Sugiura (1979) dahl and Fuller, 1981, this issue) emphasize the finds only a weak dependence of TRM on con- comparative simplicity of domain patterns result- centration in dilute magnetite dispersions. ing from strong fields and the subtlety of There is no question, however, of the control- weak-field remanence and thermally nucleated ling role played by particle interaction in ARM structures. Displacements of simple plane walls acquisition (e.g., Dunlop et al., 1975; Sugiura, seem largely irrelevant to weak-field processes; the 1979; Schmidbauer and Veitch, 1980; Cisowski, hardest remanence resides in irregular regions 1981, this issue). Figure 22 compares ARM induc- pinned by irregularities and defects, often at the tion curves measured in independent studies. In particle surface, and defies theoretical modelling. one case, interactions were weakened by measur- Pinning is even stronger in submicron particles: ing ARM at high temperatures, in the other by the H~—d relation is continuous throughout the diluting the dispersions. Notice that the TRM MD range in all common magnetic minerals. curve in the left-hand graph does not resemble the What is surprising is the similar continuity~of ARM curve measured at the average blocking remanences, strong-field and weak-field alike. temperature, 538°C.The divergence is particularly Bending of pinned walls should permit efficient severe in weak fields; ARM analog methods of “screening” of remanence under the influence of paleointensity determination (e.g., Banerjee and self-demagnetization in MD grains of all sizes, Mellema, 1974) are therefore dubious. The coerciv- with a discontinuous increase to unscreened values ity spectrum of ARM, on the other hand, is a near in SD particles. SD-like moments of walls them- replica of the TRM coercivity spectrum (Dunlop selves (Section 2.3) are therefore of interest as a et al., 1973; Levi and Merrill, 1976). potential “remanence bridge” across the SD—MD transition, although experimental evidence for their existence (Section 3.1) is equivocal. Here we might 9. Summary and future directions learn a great deal on the theoretical side from the extensive recent literature on domain wall struc- Although it is now almost 30 years since the tures in thin films of interest in magnetic bubble first edition of Nagata’s classic “Rock Magnetism” technology (e.g., Hubert, 1975; MacNeal and appeared in 1953, rock magnetism today is being Humphrey, 1979). 21

A very general “remanence bridge” mechanism, and usually a small fraction at that, of any popula- demonstrated experimentally for x = 0.6 tion of magnetic particles is viscous under given titanomagnetite by Halgedahi and Fuller (1980), is experimental conditions. To compare theory and the persistence of a metastable SD state in par- experiment, one needs to know at least broadly, tides larger than critical SD size following satura- the granulometry of the sample. It is the detailed tion, due to the difficulty of nucleating a domain magnetization relaxation phenomenon itself that is wall. If a similar SD state tends to persist in revealed in viscous changes. In TRM experiments, particles carrying weak-field TRM, it must be the the details of the blocking range are cavalierly principal cause of enhanced PSD remanence. The ignored, even though it is clear (e.g., Fig. 17) that comparatively high coercivity of PSD particles is the notion of a single blocking temperature is a not explained by this model. The reverse fields gross oversimplification. Perhaps magnetic viscos- applied in the courseof AF demagnetization should ity deserves re-examination as a means of probing aid in nucleating a domain wall, whose pinning the “fine structure” of the TRM blocking process! will then govern coercivity. Many questions about viscous magnetization re- “Diagnostic” tests of domain structure (Section main unsettled. The relative importance of nearly- 3.2) are not all of equal value. HR/H~is less well SP and moderately large MD particles (Deutsch et understood and less definitive than J,~/J~.Suscept- al., 1981, this issue; see also Fig. 9) is an example. ibility is the best test of SP behavior. The Lowrie— Another is the importance of “hard” VRM as a Fuller (1971) test may respond to differences be- noise contributor in hematite- and iron-bearing tween the coercivity spectra of coarse and fine MD rocks. particles, and only very indirectly to domain struc- The issue of interaction fields in rocks ture. If so, the spectral shapes themselves possess (Section 8), after lying largely dormant for a de- more direct diagnostic value. cade, has lately revived. This is an intriguing area The current lack of fundamental studies of of research, where competing theoretical formula- DRM and CRM (Sections 4 and 5) is unfortunate tions may be diametrically opposed (e.g., Davis, in view of the effort being directed toward paleo- 1980) and intuition frequently fails. The recent secular variation records in lake sediments (Lund experimental evidence’shows very clearly that re- and Banerjee, 1979) and paleomagnetic studies of manences, both weak-field and strong-field, and thermally and chemically remagnetized metamor- coercivities are significantly weakened by the mean phic rocks (van der Voo, 1979). Barton et al.’s interaction field arising from a magnetic con- (1980) and Amerigian’s (1981) studies of the field, centration of a few percent by volume or by local time and particle size dependences of DRM are interaction,fields of similar magnitude in particle encouraging first steps towards codifying the ex- clusters. Even VRM may be interaction dependent perimental characteristics of DRM. (Creer et al., 1970). Of particular interest is the TRM (Section 6) retains its central position in experimental d~monstrátion by Clauter ,and rock magnetism and its fascination. Recent studies Schmidt (1981, this issue) of collective behaviour of how the spectrum of partial TRM’s changes of interacting SP particles. The oft-cited ARM— with particle size, applied field, and interactions TRM analogy is called into question by Levi and (Sugiura, 1980; Clauter and Schmidt, 1981) are Merrill’s (1976) observation of wide variations in very important. Still more measurements are ARM/TRM ratios, including values > 1, and needed, particularly measurements made at high Sugiura’s (1980) evidence of very different con- temperature with the aim of following the TRM centration dependences of ARM and TRM. If growth process. Much recent theorizing has been ARM and TRM are analogous interaction- devoted to the effect of time or cooling rate on controlled processes (Jaep, 1971), one occurring at blocking temperatu,res (Section 6.2). This ~key 7~and the other at TB, these results are inexpli- question must soon be tested experimentally. cable. Viscous magnetization (Section 7) is experimen- Stress effects have not figured at all in this brief tally and theoretically difficult. Only a fraction, survey. In view of the difficulties we have in 22 interpreting the inter-relation of scalars (tempera- References ture, time) and vectors (field, magnetization), ad- ding a tensor quantity to the system can only be Amerigian, C., 1981. Particle size dependence of detrital regarded as opening up a new dimension of com- nent magnetization: implications for the role of Brownian motion. Geophys. J. R. Astron. Soc. (in press). plexity! Nevertheless, this field is of practical Bailey, ME., 1975. The magnetic properties of pseudo-single significance, it is active (e.g., Cisowski et al., 1973; domain grains. M.Sc. thesis, University of Toronto. Pozzi, 1973; Kean et al., 1976; Hodych, 1977; Bailey, M.E., 1980. Magnetic properties of deep-ocean basalts. Wasilewski, 1977; Martin et al., 1978) and real Ph.D. thesis, University of Toronto. progress is being made in codifying and interpre- Bailey,pseudo-singleM.E. anddomainDunlop,magnetiteD.J., 1975.andPreisacha rationaleanalysisfor theof ting the phenomena (e.g., Pozz.i, 1973, 1979). “Lowrie— Fuller” test. EOS, 56: 975 (abstract). Predicting directions of future research is al- Bando, Y., Kiyama, M., Yamamoto, N., Takada, T., Shinjo, T. most as uncertain a business as political forecast- and Takaki, H., 1965. Magnetic properties of a-Fe 203 fine ing. We do seem to be on the threshold of looking particles. J. Phys. Soc. Jpn., 20: 2086. beyond the crude SP— SD—MD classification into Baneijee, S.K., 1971. New grain size limits for palaeomagnetic stability in hematite. Nature (London) Phys. Sci., 232: the realm of the structure, perhaps even the fine 15—16. structure, of small MD particles. It is here that the Banerjee, S.K., 1977. On the origin of stable remanence in key to understanding the stable remanence of rocks pseudo- grains. J. Geomagn. Geoelectr., 29: must lie. On the theoretical side, Moskowitz and 3 19—329. Banerjee (1979) and Shcherbakov (1978) have ex- Banerjee, S.K. and Mellema, J.P., 1974. A new method for the determinationof paleointensity from the A.R.M. properties tended domain structure calculations to predict of rocks. Earth Planet. Sci. Lett., 23: 177—184. 2 D—3 D, 3 D—4 D, etc. transitions, and models Barton, C.E., McElhinny, M.W. and Edwards, D.J., 1980. for the internal structure of 180°Bloch walls and Laboratory studies of depositional DRM. Geophys. J. R. transitional (SD— 2 D) particles are amenable to Astron. Soc., 61: 355— 377. Bean, C.P. and Livingston, J.D., 1959. . J. experimental testing. Urgently needed are domain AppI. Phys., 30: 120S— l29S. structure observations at high temperature, and on Biquand, D. and Prévot, M., 1971. A.f. demagnetization of submicron particles, and magnetic measurements viscous remanent magnetization in rocks. Z. Geophys., 37: in the data gap between 0.25 and I ~.tmin mag- 471-485. netite. As usual, the experimental difficulties out- Brecher, A. and Cutrera, M., 1976. A scanning electron micro- weigh the theoretical ones. This is not entirely to scope (SEM) study of the structure of iron meteorites and their synthetic analogs. J. Geomagn. be regretted, for experiments directed at proving Geoelectr., 28: 31—45. or disproving contentious predictions are likely to Butler, R.F., 1973. Stable single domain to superparalnagnetic be the most rewarding ones. transition during Jow-temperature oxidation of oceanic basalts. J. Geophys. Res., 78: 6868—6876. Butler, R.F. and Banerjee, S.K., 1975a. Single-domain grain-size Acknowledgements limits for metallic iron. J. Geophys. Res., 80: 252—259. Butler, R.F. and Banei~ee,S.K., l975b. Theoretical single- For discussions in recent years on one or more domain grain-size range in magnetite and titanomagnetite. of the topics of this review, I would like to thank J. Geophys. Res., 80: 4049—4058. Monika Bailey, Subir Banerjee, Neal Bertram, Bob Chevallier. R. and Mathieu, S., 1943. Propriètès magnétiques Butler, Ernst Deutsch, Ted Evans, Michael Fuller, des poudres d’hèmatite—influence des dimensions des Paul Gaunt, Chris Hale, Susan Halgedahl, Ted grains. Ann. Phys., 18: 258—288. Cisowski, S., 1981. Interacting vs. non-interacting single do- Irving, Shaul Levi, Ron Merrill, Bruce Moskowitz, main behaviour in natural and synthetic samples. Phys. Minoru Ozima, Michel Prêvot, Larry Schutts, Earth Planet. inter., 26: 56—62. Valera Shcherbakov, Frank Stacey, Peter Wohl- Cisowski, C.S., Fuller, M., Rose, M~F.and Wasilewski, P.J.. farth and Derek York. They are in no way to 1973. Magnetic effects of explosive shocking of lunar soil. blame for my ideas and opinions, however.’ The Geochim. Cosmochim. Acta, 37 (Suppl. 4): 3003-3017. Clauter, D. and Schmidt, V.A., 1981. Shifts in the blocking rock magnetism research of the Toronto group is temperature spectra for magnetite powders as a function of supported by the Natural Sciences and Engineer- grain size and applied field. Phys. Earth Planet. Inter., 26: ing Research Council Canada. 81-92. 23

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&— ‘°~ The ratio HR /H 444~~’8SO-MO OSOP kilrusive rocks 0 of remanent to ordinary I .~‘594ebl ~ Am/qo 8 Presvt, /980 coercive force (sometimes called T or RH) has I ~ilx4,,4,~&e ~P~C~8 ~ -J IV O6w,w~ diagnostic value (e.g., Dunlop, 1969; Wasilewski, P50-MO • L~v30 q4bMs~ 0 • gsrqss~,,, 1973, 1981, this issue; Day et al., 1976, 1977). For a LeO 37 ~ p,~l,ie,

8 I ~ V I SD particles, 1.1 HR/HC ~ 2 (Stoner and - I + L~4d,~n*,8, Wohlfarth, 1948; Gaunt, 1960). “True” MD par- &iVV•+i I a ,, +1 6 I aa_ SlatL.V I tides showing no pseudo-SD effects (d~ 15 ,~tmin I a~a •aL~a.I I a~i::1 magnetite) have HR~ ~ 4 (Rahman et al., 1973). ~:~. ~ Very high values (HR /H0 > 10) often indicate the 2 I ~ 1 •:.a :•.• :•~ :• ~ 2~ ~ presencepractical ofexamplea largeofSPthisfraction.classificationFigurescheme.9 shows a C’ __~~ ~.i t•~...l~+++ •• ~ ~•. ,•. ..r.I++ The ratio ~rs /J~(sometimes called R ~)is defini- 0 0.2 04 I.•08 0.0 lO~12 1c~o~edfèrrsnogoe//c susceph~//,ty,k,~m/4 tive. If Jrs/J~ ~ 0.5, SD particles are indicated. Fig. 8. Histogram of initial susceptibility (total susceptibility According to eq. 5, J~/J5~ HC/NJS for MD wall less paramagnetic susceptibility), ktm (mXo of the text), nor- displacements limited by self-demagnetization. malized to .15 for drilled submarine intrusive rocks. Very high Realistic MD values are Jrs/J~ ~ 0.02 for iron, susceptibilities indicate SP material. After Dunlop and Prèvot ~ 0.05 for magnetite and ~ 0.1 for x 0.6 (1981). titanomagnetite. As Fig. 10 illustrates, there is no lack of intermediate ~rS/J~values, in both rocks at room temperature, x0/J5 ~ 300 X 10 ~ Oe —‘. and synthetic particle dispersions. These inter- While this is an upper limit, it is clear that SP mediate values are evidence of pseudo-SD rema- particles can be one or two orders of magnitude nence in quite large particles and not just in 2 D more susceptible than stable SD or MD particles, and transitional particles. [SeeOldfield et al. (1981, this issue) for an applica-. Figure 10(a) suggests the existence of a- single, tion of high SP susceptibili~es.]Significant SP universal J~/J~vs. HR /j~~function, but Fig. 10(b) fractions are found in some classes of ocean-floor demonstrates that nature as usual abhors simplic- rocks (e.g., Fig. 8), sediments (Creer, 1961) and ity. Each rock type examined by Dunlop and lunar rocks (Nagata and Carleton, 1970; Gose et Prévot (1981) showed an inverse relationship be- al., 1972; see also Fig. 9). tween these ratios, but there was no universal function. The magnetic mineral in all the rocks was nearly pure magnetite. 1 One of the most fashionable tests of domain structure is the comparison of AF (alternating- 600 o BoscH HR//IC: ~ . field) demagnetization characteristicsof weak-field A 0/or/fe and strong-field remanences (Lowne and Fuller, + Lunor rocks ~ 400 4 o 1971). This test has been shown to discriminate, in magnetite at least, between MD particles with I :040 pseudo-SD effects (d~ 15 ~tm)and larger, “true” MD particles (Bailey, 1975), rather than between 200 SD and small MD particles. The test is also valua- A ble in detecting co-existing populations of fine and A /0 coarse particles (Dunlop et al., 1973; Murthy et A + A 5P al., 1981, this issue). L200 400 600 800 Precisely why the test works, remains something Rernonent coercive force, HR (Oei of a mystery. Schmidt (1976) came to the para- Fig. 9. A domain-structure classification scheme based on the doxical conclusion that, theoretically, the observed value of HR/HC, applied to some terrestrial and lunar rocks. Lowrie— Fuller characteristics of SD and MD par- AfterWasilewski (1973). tides should be interchanged.