The Rock Magnetism of Fine Particles David J. Dunlop
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Physics of the Earth and Planetary Interiors, 26 (1981) 1—26 1 Elsevier Scientific Publishing Company, Amsterdam — Printed in The Netherlands The rock magnetism 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 rock magnetism 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 magnetization 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 magnetite 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 remanences. 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 remanence 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. saturation 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) hysteresis data for nearly spherical iron 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 Hematite 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 spin ~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 minerals. - 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.