J. Geomag. Geoelectr., 39, 441-461,1987
Magnetic Remanence Coercivity of Rocks
Takesi NAGATAand Barbara J. CARLETON National Institute of Polar Research,ltabashi-ku, Tokyo, Japan
(ReceivedFebruary 24,1987; Revised May 15. 1987)
An anomalously large value of the ratio of remanence coercive force (HRc)to coercive force (Hc) (i.e. HRc/Hc) which is much beyond a range of HRc/Hc for a single phase magnetic mineral, is often found in natural rocks, particularly in extraterrestrial rocks. The observedlarge values of HRc/He are interpreted as mostly due to the coexistence of a high coercivity component (a) and a low coercivity component (b). In a binary system of high and low coercivity components, HRc is largely controlled by the high coercivity component and He largely by the low coercivity component in accordance with definitions of HRc and Hc, respectively. A simple model of such a magnetic binary systemfor purposes of estimatingthe magnetic coercivitiesof both components from the observedbulk values of HRc, He and IR/ Is is proposed, whereIR and Is respectivelydenote saturation remanenceand saturation magnetization. It is shown that the proposed model well approximates experimental data with an uncertainty of less than a factor of 2.
1. Introduction
The magnetic remanence coercive force (HRc) of magnetic (i.e. ferromagnetic and ferrimagnetic) materials is defined by ID(HRc)=0, where ID(H) denotes the DC demagnetization remanence acquired after saturation in one direction and the subsequent application of DC field of intensity H in the opposite direction. For a randomly oriented assemble of non-interacting uniaxial magnetic particles , the ratio of HRc to the coercive force (Hc) is theoretically given (WOHLFARTH, 1958, 1963) by
(1) As summarized by WOHLFARTH(1958, 1963), however, experimentally observed values of HRc/Hc of assemblies of single-domain (SD) particles dispersed in a non-magnetic matrix is always larger than 1.1, in the range of 1.3-2.0. The observed discrepancy of HRc/ Hc from the theoretical value is attributable partially to the magnetic interaction among magnetic particles and partially to the effect of considerably wide distribution of the anisotropy constant for individual particles. Hc and HRc of rock-forming minerals have been studied by WASILEWSKI (1973), DAY et al. (1977), DUNLOP(1981) and others. Their experimental results show that 1.1 447 448 T. NAGATA and B. 1. CARLETON particles, HRc/ Hc takes values intermediate between those of SD and MD particles, so that HRc/ Hc values for assemblies of magnetic grains of approximately the same composition and the same grain size diluted in non-magnetic matrix ranges between 1.1 and about 5 in general. However, observed values of HRc/ Hc for terrestrial and lunar rocks, as well as meteorites, which is a summary of magnetic hysteresis measurements of natural rocks obtained in the writers' laboratory, range widely from 1.3 to 102, as shown by the histograms of HRc/ Hc in Fig. 1, where HRc/ Hc>8 for 23% of terrestrial igneous rocks, while HRc/ Hc>8 for 76% of lunar rocks and 71% of chondritic meteorites. In some lunar rocks and chondrites, HRc/ He values exceed 30, amounting to more than 100 in extreme cases (e.g. NAGATA,1979). Fig. 1. Histograms of HRc/ Hc of terrestrial igneous rocks (Top), lunar rocks (Middle) and chondrites (Bottom). (HRc/ Hc values in logarithmic scale). N: number of measured rock samples. Magnetic Remanence Coercivity of Rocks 449 Special examples of anomalously large values of HRc/ Hc for some lunar rocks, in which ferromagnetic Fe-Ni metallic grains are mixed with superparamagnetically fine metallic grains, have already been qualitatively discussed (NAGATAet al., 1972; WASILEWSKI, 1973). It was noted in these studies that a superposition of the superparamagnetic magnetization on the ferromagnetization results in a much larger reduction of the He value than that of the HRc value. An experimental demonstration that a mixture of a high magnetic coercivity component and a low coercivity component can have an anomalously large value of HRC/He has been reported by DAY et al. (1977). Since it has been microscopically and magnetically confirmed that a number of natural rocks, having a large HRc value and a relatively small Hc value consist of both magnetically high coercive and low coercive components, it seems most likely that an observed large HRc/ Hc value for a rock indicates the co-existence of both high and low coercivity components together in the single rock piece. In the present study, the problem of magnetic coercivity of binary systems consisting of magnetically high and low coercivity components is more quantitatively examined. 2. Coercive Force (Hc) of a Binary System An example of experimental results for He and HRc measurements of a mixture of high coercivity SD particles and low coercivity MD particles of titanomagnetite obtained by DAY et al. (1977) is reproduced in Fig. 2(a). As shown in the figure, the SD particles are characterized by He=Hc(a)=1580 Oe and HRc=HRc(a)=2130 Oe so that HRc/ Hc=1.34, while the MD particles are characterized by Hc=Hc(b) =39 Oe and HRc-HRc(b)=148 Oe so that HRc(b)/Hc(b)=3.79. The mixing rate of SD particles within the total titanomagnetite is given by m, where all titanomagnetite grains are uniformly diluted in non-magnetic KBr powder to 1%. The Hc vs. m curve is an upward concave curve, in which He values are only several times as large as Hc(b)for m<0.5. The HRc vs. m curve is an upward convex curve, in which HRc values are nearly the same as HRc(a)for m?0.5 and larger than HRC(a)/3 for m>0.1. Thus, HRc/ Hc takes its maximum value (i.e. HRc/ Hc=30) around m=0.25. An approximate representation of He for a binary system consisting of high and low coercivity components has been discussed with respect to lunar rocks (NAGATAet al., 1972) and meteorites (NAGATAand FUNAKI,1982). In these previous works, the magnetization curve, I(H), in the course of magnetization from 0 to H after saturation magnetization in the opposite direction, is roughly approximated by (2) where IR denotes saturation remanence after saturated magnetization by H→+∞.IR and He for a binary system consisting of a high coercivity component (a), characterized by IR(a)and Hc(a), and a low coercivity component (b), characterized by 450 T. NAGATA and B. J. CARLETON Fig. 2. Hc(m) and HRc(m) of mixtures of high coercivity SD particles and low coercivity MD particles of titanomagnetite, 60Fe2TiO4"40Fe3O4.m: mixing rate of high coercivity component. (a) Experimental results, (DAY et al., 1977). (b) Theoretical results derived by the present model. Hc(1) for the case of I(H)' IR (1-H/Hc). Hc(2)for the case of I(H)=IR{1-(HcH+H2)/2(Hc)2}. IR(b)and Hc(b),in a mutual mixing rate m(a):m(b)=m:(1-m) are then given by (3) (4) where (5) The extreme case represented by (5) corresponds to a binary system composed of ferromagnetic particles (a) and superparamagnetic particles (b). Putting IR(a)/IR(b)=Y and Hc(a)/Hc(b)≡ η,、Hc/Hc(a)≡ ζis derived from(2),(3)and(4)as (b) Sinceη=40.5 and Y=11.0 in the case of example shown in Fig.2(a),the Hc vs. m curve in the present model is obtained from (6) and shown by curve Hc(1) in Fig. 2(b). Magnetic Remanence Coercivity of Rocks 451 As can be seen the general characteristics of the Hc vs. m curve given by (6) are in approximate agreement with the observed results. Since, however, in all magnetic hysteresis curves of terrestrial rocks, lunar rocks and meteorites measured in the writers' laboratory, it has been experimentally confirmed that (2*) is a better approximation than(2)for the measured l(H). Then,ζis derived from(2*) and(3)as (6*) Solving(6*)for a positive value ofζgives Hc/Hc(a)as a function of m,ηand Y. The Hc vs. m relation given by (6*) for the example shown in Fig. 2(a) is illustrated by Hc(2) curve in Fig. 2(b). The general characteristics of the Hc(2) vs. m curve based on the revised model are in reasonably good agreement with the observed results. Other experimental results of the He vs. m relation of a binary system (DAY et al., 1977) are reasonably well interpreted with the present revised model. 3. Remanence Coercive Force (HRC) According to the definition of HRc, HRc values for a high coercivity component (a) and a low coercivity component (b) are expressed in terms of the static remanent magnetization, Ir(H), which is acquired after magnetizing up to Hin a static magnetic field, as (7) respectively, where HRc(a)>HRc(b). HRc for a binary system of a mixture of (a) and (b) components with a mixing ratio of m to (1-m) is given by (8) 452 T. NAGATA and B. J. CARLETON Then, (7) and (8) lead to a relation, (9) For the purpose of evaluating HRc/ HRc(a)on the basis of (9), it is necessary to know functional forms of Ir(a)(H) and Ir(b)(H). Although exact functional forms of Ir(H) for individual magnetic grains are somewhat different from one another, their general characteristics must satisfy the following 3 conditions, i.e., A possible simple empirical formula of Ir(H) which can satisfy the three conditions and reasonably well fit the experimental data are (10) The empirical formula of Ir(H) can approximately represent the observed Ir(H) vs. H curves except for a weak field range from zero to about 30 Oe, where Ir(H) roughly follows Rayleigh's law. Putting (10) into (9), we get (11) because obviously HRc(a)≧HRc≧HRc(b). Putting HRc/HRc(a)≡ ζ*,IR(a)/IR(b)≡Y and HRc(a)/HRc(b)≡ η*,(11)is re-written as (12) Solving(12)for positive values gives ζ*≡(HRc/HRc(a))as a function of m with parametersη* and Y.Sinceη*=14.4 and Y=ll.0 in the case of the example in Fig. 2(a), the HRc vs. m curve in the present model is obtained from (12) and illustrated in Fig. 2(b). As shown in the figure, the calculated curve of HRc vs. m is upward convex and has closely similar characteristics to those of the experimental curve. 4. HRc/Hc of a Binary System Sinceζ ≡Hc/Hc(a)is subjected to 3 variables, m,ηand Y;the dependence ofζ upon these 3 variables will be separately examined by introducing a parameter,ξ, Magnetic Remanence Coercivity of Rocks 453 which is a function of only m and Y, namely, (13) which gives (14) Thenζ(m,η,Y) given by(6*)can be converted toζ(ξ,η)defined by (15) Solving(15)for positive value gives Hc/Hc(a)≡ ≡ζas a function ofξandη, as illustrated in Fig.3(a). A special characteristic ofζ(ξ,η), it will be noted,is thatζ ≡Hc/Hc(a)very gradually increases with an increase inξwithin a range ofξ ≦0.9 and then steeply increases to approach unity asξcontinue to increase toward 1.Equation(12)also is transformed to (16) Solving(16)for ..positivevalue gives ζ*≡HRc/HRc(a)as a function ofζandη*, as illustrated in Fig.3(b). As shoWn in Fig.3(b), theζ*(ξ,η)value approaches (16*) with an increase ofη*. Thusζ*value becomes practically independent ofη*for η*>10,and thereforeζ*is approximately represented by(16*). This characteristic feature ofdependence ofζ*(ξ,η*)onξandη*in Fig.3(b)forms a distinct contrast to the dependence ofζ(ξ,η)onξandηas shown in Fig.3(a). Since HRc/ Hc for a binary system consisting of a high coercivity component (a) and a low coercivity component (b) is given by (17) the HRc/Hc value can be estimated from ζ*(ξ,η*)/ζ(ξ,η)as a function ofξ, provided that HRc(a)/Hc(a)and an interrelation betweenη*andηare given or approximately assumed. As for a relationship between He and HRCof a single phase and single size component, experimental results that HRc/ Hc<2 for SD particles and HRc/ Hc=4-5 for MD particles are already mentioned. In the case of a binary system of a mixture of SD and MD particles,therefore, an approximate relation betweenη ≡He(a)/Hctb)and η*≡HRc(a)/HRc(b)may be represented by 454 T. NAGATA and B. J. CARLETON Fig.3.(a)ζ ≡Hc/Hc(a) ofabinary system as a function ofξandη ≡Hc(a)/Hc(b).(ηin logarithmic scale).(b) HRc/HRc(a)of a binary system as a function ofξandη*≡HRc(a)/HRc(b).(η*in logarithmic scale). (18) Figure 4 illustrates、HRc/He as a function ofξandη, whereη*=0.4ηand HRc(a)'Hc(a)=2 are assumeddfor an average condition of a binary system consisting of SD and MD particles. As clearly shown in the diagram, anomalously large values of HRc/Hc can occur forξ ≧05 and the maximum value of HRc/He increases nearly proportionally to an increase ofηwithin the range ofξapproximately from 0.7 to 0.8. An anomalously large value of HRc/ Hc is defined as HRc/ Hc>5 in the present study so that a case of HRc/ Hc>20 could be considered anomalous. In the standard model diagram of HRc/Hc magnitude dependent onξandηin Fig.4, the anomalously large value of HRc/Hc≧20 can take place for η≧30. Magnetic Remanence Coercivity of Rocks 455 Fig.4. HRc/He of a binary system as a function ofξandη, whereη*=0.4ηand HRc(a)/Hc(a)=2 are assumed.(ηandη*in logarithmic scale). 5. Correlation of IR with Hc and HRc As comprehensively reviewed and discussed by DUNLOP (1981, 1986), Hc, HRc and IR/ Is (IR normalized by saturation magnetization Is) of magnetite and titano- magnetite have mutual positive correlations, with all three magnetic hysteresis parameters increasing with a decrease of grain size down to the SD size. The two diagrams in the top line of Fig. 5 summarize, for example, observed correlations of IR/ Is with He and HRc in logarithmic scale for titanomagnetites of various grain sizes from SD particles to MD particles (DAY et al., 1977). As shown in the figures, the largest values of IR/Is approach 1 / 2, which is theoretically expected for an assembly of randomly oriented particles having the uniaxial magnetic anisotropy. The smallest values of IR/ Is are grouped around 2•~10-2, representing IR/Is values of MD particles larger than 102 ƒÊm in grain size. As pointed out by NEEL (1955), the relationship between IR/Is and Hc is largely controlled by the self- demagnetizing effect of MD particles themselves, IR/Is being related to He by an approximate expression such as (19) where N denotes the average demagnetizing factor of MD particles and Js is their 456 T. NAGATA and B. J. CARLETON Fig. 5. Correlations of IR/Ic with He (Top left) and HRc (Top right) of titanomagnetite, (DAY et al.,1977) and with Hc (Bottom left) and HRc (Bottom right) of Fe-Ni metallic grains in stony meteorites (NAGATA,1987). (Hc, HRc and IR/Is in logarithmic scale). saturation magnetization per unit volume, i.e..Ts=Is×(Density). Since N=3～4 and Js=300-480 emu/cm3 for magnetite and titanomagnetite grains in terrestrial rocks, the coefficient(NJs)-1 in(19)is estimated to be(05～1)×10-3 in order of magnitude. The observed relation between IR/ Is and He below Hc= 102 Oe in Fig. 5 is in approximate agreement with this estimate. Magnetic Remanence Coercivity of Rocks 457 The bottom two diagrams in Fig. 5 summarize observed correlations of IR/ Is with Hc and HRc in logarithmic scale for stony meteorites (NAGATA,1987). In the log (IRIIs)vs. log Hc diagram, IR/Is values range from about 1/2 to around 1 × 10-3, and He values from about 4×103 Oe to 5 Oe. The largest end magnitudes of IR/Is and He in this case are also in approximate agreement with respective values derived from the uniaxial anisotropy particle model. As far as the observed value, Hc=5-10 Oe, is accepted for the MD particle model,IR/Is=(2～3)×10-3 as obtained from(19)on the basis of this postulated value of Hc for meteoritic Fe-Ni metals(Js=(1.2～1.7)×103 emu/cm3)is in reasonably good agreement with the observed values of IR/ Is shown in Fig. 5. As discussed in the present study, however, a mixing of even a small amount of a high coercivity component results in an essential increase of HRc. The observed relatively large dispersion of IR/ Is vs. HRc plots may be due to the presence of the minor component of high coercivity in meteoritic metals. In the present discussions, therefore, the correlation diagrams of IR/ Is with Hc and HRc for meteoritic metals in Fig. 5 will be taken into consideration only for evaluating order of magnitude of the extreme values of IR/ Is, Hc and HRc, corresponding to their SD and MD states. b. Analysis of Observed Values of Hc, HRc and IR/ Is If it appears very likely that a high coercivity component (a) is a uniaxial anisotropy particle assembly such as SD particle assembly and a low coercivity component (b) is a MD particle assembly, and further saturation magnetization Is is approximately common in both components, (3) can be expressed by (3*) where IR(a)/Is=0.5 and IR(b)/Is takes an appropriate value for MD particles of the magnetic material concerned. Then, since Y≡IR(a)/IR(b)can be roughly estimated, m can be approximately estimated from the observed value of IR/Is by means of(3*). In a case where Yand m have been estimated as above,ζ(m,Y,η)andζ*(m,Y,η*) can be directly obtained by (b*) and (12), respectively. Examples of estimating the magnetic constitution of a rock from its observed values of Hc, HRc and IR/ Is in this manner are briefly demonstrated in the following, where more realistic assumptions expressed by HRc(a)/Hc(a)=1.5 and HRc(b)/Hc(b)=4 so that (18*) are adopted in the calculations. 458 T. NAGATA and B. J. CARLETON 6.1 Artificial rock containing titanomagnetites The magnetic hysteresis parameters of an artificially made rock containing titanomagnetite of m=0.25, shown in Fig. 2(a), are given by Hc=50 Oe, HRc=1,500 Oe and IR/Is=0.16. Since HRc/ Hc=30, this rock appears very likely to be composed of a high coercivity component of HRc(a)>1,500 Oe (whence Hc(a)> 1,000 Oe) and a low coercivity component of Hc(b)<50 Oe. As a thermomagnetic analysis of this rock indicates that Curie point is about 200°C which represents a Ti-rich titanomagnetite of about 60Fe2TiO4 40Fe3O4 in chemical composition, IR(b)/ Is of MD particles of the titanomagnetite is estimated to be about 0.04. From IR(a)/Is-0.5 and IR(b)/Is=0.04, Y=12.5 is obtained, and further m=0.26 is estimated by (3*) with IR/ Is=0.16. Then, by use of (6*), (12) and (18*), the value of ƒÅ needed to give HRc/ Hc= 30 is determined as ƒÅ=71.3. Results of a calculation for this rock on the basis of He=50 Oe, HRc=1,500 Oe, IR/ Is=0.16, IR(a)/ Is-0.5 and IR(b)/ Is-0.04 are summarized as m^=0.26,η=71.3,η*=26。7,ζ=0.039andζ*=0.784, and therefore,Hc(a)=1275 Oe, HRC(a)=1910 Oe, Hc(b)=18 Oe, HRc=72 Oe. On the other hand, the given experimental conditions to produce this artificial rock are m=0.25, Hc(a)=1580 Oe, HRc(a)=2130 Oe, Hc(b)=39 Oe, HRc(b)=148 Oe, IR(a)/Is=0.47, and IR(b)/Is=0.043, so that Y=10.9,η=40.5 andη*=14.4. As anticipated, Hc, HRc(a), HRc(b)and other parameters estimated from observed values of Hc, HRc and IR/ Is on the basis of the present model deviate within a factor of 2 from their respective true values, though the order of magnitude of each of the former are in agreement with those of the latter. As already pointed out in comparing Fig. 2(b) with Fig. 2(a), the present simple model does not exactly represent the experimental results, even if all boundary condition parameters in the present mathematical model, such as Hc(a),HRc(a), Hc(b), HRc(b), etc., are exactly given. In the present average SD-MD binary system model, HRc(a)/Hc(a)=1.5 and HRc(b)/Hc(b)=4 are generally assumed, instead of experimental values such as HRc(a)/Hc[a)=1.35 and HRc(b)/Hc(b)=3.79. It should be emphasized again that the present simple model of a magnetic binary system can separately evaluate the order of magnitude of magnetic coercivities of two constituting components from experimen- tally measured values of Hc, HRc and IR/Is of a whole bulk rock specimen. 6.2 Antarctic chondrites A large number of meteorites which have been collected from Antarctica include the chondrites having the anomalously large HRc/ Hc values. They are Yamato(Y)- 7301(H4), Y-74647 (H4-5), Y-74191 (L3), Y-74354 (L6), Y-74362 (L6) and others. The observed magnetic hysteresis parameters, Is, IR, Hc and HRc, and HRc/ Hc of the five Antarctic chondrites are given in Table 1(NAGATA and SUGIURA, 1976; NAGATA, 1979). Thermomagnetic analysis data show that the magnetic constituents in all the five chondrites are composed of a major component of kamacite and a minor component of plessite. The plessite phase in meteorites often contains fine single crystal grains of tetrataenite which have an anomalously large value of uniaxial magnetic anisotropy. (e.g. NAGATAand FUNAKI, 1982; NAGATAet al., 1986). The IR/ Is values of the Magnetic Remanence Coercivity of Rocks 459 Table 1. Observed magnetic hysteresis parameters of Antarctic chondrites. tetrataenite grains also are around 0.5 (e.g. NAGATA et al., 1987). Assuming that the major low coercivity component is composed of MD grains of kamacite and the minor high coercivity component is composed of uniaxially anisotropic grains of plessite, IR(a)/Is-0.5 and IR/Is=0.002-0.003 can be assumed. Taking IRc(b)/Is= 0.002 and IR(b)/Is=0.003 for Model (I) and Model (II), respectively, in the present analysis, Hc, HRc(a), Hc, HRc(b) and m for the five Antarctic chondrites are evaluated for Models (I) and (II) as given in Table 2. Although each estimated value of these magnetic hysteresis parameters may be associated with an uncertainty of a factor of 2, a general picture that the magnetic constituent of the chondrites is composed of (50m-200m)% of very fine particles of high coercivity having HRc(a) =(1- 3) •~ 103 Oe in major part of low coercivity grains having Hc=(5-20) Oe will be satisfactorily reliable. 7. Concluding Remarks It may have been qualitatively known that a magnetic material having a large value of HRc and a small value of Hc, say HRc/ Hc>20, is most likely to be composed Table 2. (Hc(a), HRc(a))for the high coercivity component and (Hc(b), HRc) for the low coercivity component and m of the Antarctic chondrites, obtained by the present binary system model analysis from the observed data given in Table 1. 460 T. NAGATA and B. J. CARLETON of a high coercivity component of HRc(a)>HRc and a small coercivity component of Hc(b) REFERENCES DAY, R., M. FULLER,and V. A. SCHMIDT,Hysteresis properties of titanomagneties; grain-size and composition dependence, Phys. Earth Planet. Inter., 13, 260-267,1977. DUNLOP,J. D., The rock magnetism of fine particles, Phys. Earth Planet. Inter., 26,1-26,1981. DUNLOP,J. D., Hysteresis properties of magnetite and their dependence on particle size: a test of pseude-single domain remanence models, J. Geophys. Res., 91, No. B9, 9569-9589,1986. NAGATA,T., Magnetic properties of Yamato-7301, -7305 and -7304 chondrites in comparison with their mineralogical and chemical compositions, Mem. Natl. Inst. Polar Res., Spec. Issue, 12,250-269, 1979. NAGATA,T., Magnetic properties of Antarctic meteorites, in Antarctic Meteorites, edited by National Institute of Polar Research, pp. 308-337, Kokin-Shoin, Tokyo, 1987 (in Japanese). NAGATA,T. and N. SUGIURA,Magnetic characteristics of some Yamato meteorites-Magnetic classifica- tion of stone meteorites, Mem. Natl. Inst. Polar Res., Spec. Issue, 10, 30-58,1976. NAGATA,T. and M. FUNAKI,Magnetic properties of tetrataenite-rich stony meteorites, Mem. Natl. Inst. Polar Res., Spec. Issue, 25, 222-250,1982. NAGATA,T., R. M. FISHER,and F. C. SCHWERER,Lunar rock magnetism, Moon, 4,160-186,1972. NAGATA,T., M. FUNAKI,and J. A. DANON,Magnetic properties of tetrataenite-rich meteorites (II), Mem. Natl. Inst. Polar Res., Spec. Issue, 41, 364-381,1986. NAGATA,T., J. A. DANON,and M. FUNAKI,Magnetic properties of Ni-rich iron meteorites, Mem. Natl. Inst. Polar Res., Spec. Issue, 46, 263-283,1987. NEEL, L., Some theoretical aspects of rock magnetism, Adv. Phys., 4,191-242,1955. WASILEWSKI,P. J., Magnetic hysteresis in natural minerals, Earth Planet. Sci. Lett., 20, 67-72,1973. WOHLFARTH,E. P., Relation between different modes of acquisition of the remanent magnetization of ferromagnetic particles, J. Appl. Phys., 29, 595-596, 1958. WOHLFARTH,E. P., Remanent magnetization materials, in Magnetism, Vol. III, edited by G. E. Rado and H. Suhl, pp. 351-393, Academic Press, New York, 1963.