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Magneto-optical Kerr effect in (titano)magnetite, pyrrhotite and hematite
36
Physics of the Earth and Planetary Interiors, 65 (1990) 36—42 Elsevier Science Publishers B.V., Amsterdam
Magneto-optical Kerr effect in (titano) magnetite, pyrrhotite and hematite E. Appel, V. Hoffmann and H.C. Soffel Institut für Ailgemeine und Angewandle Geophysik, Universität MOnchen, Theresienstrasse 41, W-8000 MOnchen 2 (FR. G.) (Received November 27, 1989; revision accepted April 9, 1990)
ABSTRACT Appel, E., Hoffmann, V. and Soffel, H.C., 1990. Magneto-optical Kerr effect in (titano)magnetite, pyrrhotite and hematite. Phys. Earth Planet. Inter., 65: 36—42. The successful application of the magneto-optical Kerr effect in rock magnetism is demonstrated. Domain structures of the most frequently occurring ferromagnetic minerals in rocks—(titano)magnetite, pyrrhotite and hematite—are shown. Surprisingly, the method works with hematite, where the Bitter pattern technique is not appropriate. Skin depths and sublattice interactions are discussed to explain the effect.
1. Introduction Domain observations are of fundamental importance for the analysis of the micromagnetic structure and for the understanding of macroscopic magnetic properties. In the past, domain observations in rock magnetism mostly used the Bitter pattern technique and an optical microscope. Successful experiments with the Bitter technique were carried out on (titano)magnetite(s) and pyrrhotite. Gustard (1967) and Gallon (1968) reported Bitter structures on hematite; however, efforts to reproduce such experiments usually fail. Moskowitz et al. (e.g. 1988) and Soffel et al. (1990) observed dried Bitter patterns on (titano)magnetite with the scanning electron microscope. Smith (1980) applied the Lorentz electron microscope to domain observations on magnetite. Important results of domain observations in rock magnetism are the determination of the critical grain size for single-domain—multi-domain transitions (Soffel, 1971, 1977), the stress control of domain structures in titanomagnetites (Appel and Soffel, 1984, 1985), detection of nucleation processes (Halgedahl and Fuller, 1980), tempera0031-9201/90/$03.50
© 1990
—
Elsevier Science Publishers B.V.
ture-induced domain pattern changes (Metcalf and Fuller, 1987; Heider et a!., 1988) and external stress-induced domain pattern changes (Appel and Soffel, 1985). Halgedahi (1987) gave a review of research activities. Although the Bitter pattern technique was very successful in rock magnetic studies, it is limited to observations of stray fields along domain walls. The direction of the magnetization vector within the domains cannot be detected. Hoffmann et a!. (1987) reported the first application of the magneto-optical Kerr technique to titanomagnetites. Observations with the Kerr technique show domains directly, and the magnetization direction within domains can be analysed qualitatively by grey-scale variations and even quantitatively in certain cases (Rave et al., 1987). In this paper we report the progress in the use of the magneto-optical Kerr technique for other natural magnetic minerals by showing Kerr images of (titano)magnetite, pyrrhotite and hematite. The aim of the study is to demonstrate the successful application of the technique. Interpretations of domain structures are given only very briefly for this reason.
37
MAGNETO-OPTICAL KERR EFFECT IN ROCK MAGNETISM angle vs.~ plane of
2. Magneto-optical Kerr effect and technique of observation The physical principles of the magneto-optical Kerr effect are only fully explained in terms of quantum mechanics (spin—orbit interaction of electron moments; e.g. Argyres, 1955). A non quantum mechanical overview has been given, for example, by Kranz and Hubert (1963). For a qualitative approach it is sufficient to consider the Lorentz force on conduction electrons in the magnetic field of the magnetic domain moments. A linear polarized light beam is reflected from the surface of a magnetic material (Fig. 1). The electrons near the surface are forced to oscillate parallel to the electric field (E-vector). Because of the Lorentz force a Kerr component K (K parallel to E x B) originates, and consequently the plane of electron oscillation is rotated. Hence, the polarization plane of the reflected light beam is different from that of the incident beam E. Different orientations of B within neighbouring domains result in different rotations of the polarization plane, which can be detected by an appropriate analyser orientation in terms of grey-scale contrasts. Graduation of the grey scale from black to white refers to graduation of the domain magnetization from zero to 1800 (further details are given by Hoffmann et a!., 1990).
-_________
M
~
_____________________________
Fig. 1. Physical principles of the Kerr effect (for explanations see text). E and N are the electric field vectors of the incident light beam and of the normally reflected light beam respectively. K is the electric field vector of the reflected light beam which originated from the domain magnetization. Two domains with antiparallel homogeneous magnetizations (arrows) are indicated by black and white.
The Kerr amplitude K is proportional to the spontaneous magnetization M~.Kerr contrasts are M~.The application of the K2 and therefore magneto-optical Kerr effect to materials with low M~,such as ferrimagnetic minerals, requires special sample preparation and image-processing techniques. First, an extremely smooth and stress-free surface has to be prepared by polishing with amorphous Si0 2 solution (Hoffmann et a!., 1987). Kerr contrasts are enhanced by the use of a —
—
Fig. 2. Kerr image of a natural magnetite crystal. The surface is slightly inclined to a (110) plane.
38
E. APPEL ET AL.
digital image-processing system (Schmidt et a!., 1985). The observed surface is recorded in a saturated stage (reference image without magnetic contrasts). The reference image is subtracted from the subsequent!y observed Kerr image. The result is a high-contrast difference image showing the magnetic domains in terms of different grey scales. Electronic noise is reduced by averaging difference images of the same domain structure,
with magnetite and hence Kerr contrasts are expected to be distinctly weaker. Despite the low M~ the Kerr technique still works. However, more accurate adjustments of the polarizer, analyser, compensator and the rectangular aperture, as well as a higher number of averaging cycles, are required. Figure 3 shows domain structures on a synthetic Al- and Mg-doped titanomagnetite with uniaxial domain shape. Bent domain boundaries indicate stress dominance (Appe! and Soffe!, 1984, 1985). Grey-scale variations within the domains point to locally varying magnetization directions, which are probably also stress induced (Appel and Soffel, 1985).
3. Observations of magnetic domains with the magneto-optical Kerr effect 3.1. Magnetite and titanomagnetites
Naturally occurring titanomagnetites generally show much more complicated domain patterns
Magnetite, Fe304, has the highest spontaneous magnetization of all naturally occurring minerals (480 kA m~). As expected, Kerr contrasts are well pronounced (Hoffmann, 1988). Figure 2 shows a natural single crystal of magnetite. Christmas-tree-shaped domain patterns (Stephan, 1955) indicate that the surface is slightly inclined to a (110) plane. Classical 180, 71 and 1090 domain walls represent two easy directions of magnetization within the observed surface. Titanomagnetites, Fe3 ~Ti~O4, are most frequently found in compositions around x 0.6 in basalts. M~is about five times lower compared
than their synthetic equivalents. This is already known from Bitter pattern studies (Appel and Soffe!, 1984, 1985). Figure 4 shows a Kerr image of a natural titanomagnetite in a basalt. Kerr contrasts are rather distinct in some parts of the grain but the domain structure is very cornplicated. There are areas with almost parallel domains, areas with good contrast but chaotic domain shape and large areas with grey-scale variations but without any recognizable domains. Our Kerr observations confirm the statement that internal stress in naturally occurring titanomagnetites is high and varies strongly in amount and
—
=
.1~
~
~
-:.
~t.
Fig. 3. Kerr image of a synthetic titanomagnetite Fe2 ,8Ti052A1015Mg0 204.
39
MAGNETO-OPTICAL KERR EFFECT IN ROCK MAGNETISM
~
J~.. •
~
~ .r~
~
~ .:
‘~:
~
~
~
N
-
—1 Fig. 4. Kerr image of a natural titanomagnetite in a basalt (Curie temperature 242°C).
directions within short distances (Appe! and Soffel, 1984).
iaxial crystalline anisotropy and from Bitter pattern studies (Soffel, 1981). 3.3. Hematite
3.2. Pyrrhotite Pyrrhotite, Fe7S8, has a spontaneous magneti1). zation similar toare titanomagnetites (— 100 rn Kerr contrasts well pronounced. ThekAdomain shape shown in Fig. 5 represents a typical uniaxia! domain structure, as it is expected from the un-
Fig. 5. Kerr image of a natural pyrrhotite.
Hematite, a-Fe03, is antiferromagnetic with a small spontaneous (M~ M~ 2 kA mresidual 1) as a result of spin magnetization canting. The small value should not permit domain observations with the Kerr technique because of too weak contrasts. Surprisingly, this is not the case. Williams et al. —
40
EAPPELETAL.
(1958) have observed domains in a-Fe203 by using the Faraday effect. We found that Kerr contrasts are even more pronounced than in magnetite and for some samples they are detectable without image processing. The explanation of why the method works with wealdy magnetic hematite is hard to give in terms of M~.The skin depth d of an electromagnetic field is proportional to (aitw) —1/2 (where a is conductivity, p~ is permeability and w is frequency). The permeability ~.t 1 + k(SI uthts) (where k is susceptibility) of magnetite is of the =
order of 10 for crystalline anisotropy controlled spin rotations corresponding to the formula k
4K
= —
__i!
4K
—
_~~a
(K3 and K2 are crystalline anisotropy constants; Syono, 1965). Experimental results for conductivities of magnetite and hematite vary over a broad range. Mean values for magnetite (a iO~—io~ ~2’ m~ Landolt-Börnstein, 1982) and hematite (a 65—285 ~ m~ Lando!t-Börnstein, 1982) =
=
I
Fig. 6. Kerr images of a synthetic hematite particle. Upper, zero field: lower, applied field of
—
0.1 T parallel to the surface.
41
MAGNETO-OPTICAL KERR EFFECT IN ROCK MAGNETISM
result in a ratio of skin depths for hematite and magnetite with dFe2O3/dFe3O4 ranging from about six to 40 (in consideration of ji values and constant frequency). This is far too low to equalize the low ratio of M~values for hematite to magnetite (— 1/60 000). An alternative explanation of strong Kerr contrasts in hematite could be that Kerr rotations depend on the sublattice magnetization (one sublattice interacting more than the other) rather than on the resulting spin-canting moment. Figure 6 shows a synthetic hematite particle in zero field (left side) and with an annlied field of
—
0.1 T (right side). Three major domains and one
(right side) or two (left side) smaller ones are shown. Different grey scales mean different magnetization direction. The domain shape is cornpletely different from that observed in other magnetic minerals. This is certainly a consequence of the negligible stray field energy (small Ms). Figure 7 shows two different isothermal remanence (‘saturation’ field 0.15 T) states in naturally occurring hematite. Complete domain reorganization is obvious from grey-scale changes. Even a single-domain particle (arrow in Fig. 7) is remagnetized.
5’
Fig. 7. Kerr images of natural hematite. Two opposite isothermal remanence stages are shown. A single-domain particle is marked by the arrow.
42
4. Conclusions Domain observations with the magneto-optical Kerr effect were successfully carried out on the most frequently occurring magnetic minerals in rocks; magnetite, titanomagnetite (x — 0.6), pyrrhotite and hematite. The applicability of the Kerr method to hematite is of special importance because the Bitter pattern technique fails in this case. New possibilities arise with Kerr observations. Variations of the magnetization direction within domains can be analysed qualitatively and possibly quantitatively (Hoffmann et a!., 1990). There is no limitation of the Kerr technique at higher temperature. Hence heating experiments, which are basically important in understanding thermoremanent magnetization acquisition in multidomain particles, may be possible up to the Curie temperature of magnetite or hematite, Acknowledgements The experimental work was carried out at the Institut für Werkstoffwissenschaften VI at the University of Erlangen. We thank Prof. Hubert, R. Schafer and W. Rave for their help and for stimulating discussions. The work was financially supported by the Deutsche Forschungsgemeinschaft (DFG).
References Appel, E. and Soffel, H.C., 1984. Model for the domain state of Ti-rich titanomagnetites. Geophys. Res. Lett., 11: 189— 192. Appel, E. and Soffel, H.C., 1985. Domain state of Ti-rich titanomagnetites deduced from domain structure observations and susceptibility measurements. J. Geophys., 56: 121—132. Argyres, P.N., 1955. Theory of the Faraday and Kerr effects in ferromagnetics. Phys. Rev., 97(2): 334—345. Gallon, T.C., 1968. The ferromagnetic domain structure of haematite. Proc. R. Soc. London Ser. A, 303: 525—529. Gustard, B., 1967. The ferromagnetic domain structure in haematite. Proc. R. Soc. London Ser. A, 297: 269—274. Halgedahl, S., 1987. Domain pattern observations in rock magnetism: progress and problems. Phys. Earth Planet, Inter., 46: 127—163. Halgedahl, S. and Fuller, M., 1980. Magnetic domain observa-
E. APPEL ET AL.
tions of nucleation processes in fine particles of intermediate titanomagnetite. Nature, 288: 70—72.
Heider, F., Halgedahl, S.L. and Dunlop, D.J., 1988. Temperature dependence of magnetic domains in magnetite crystals. Geophys. Res. Lett., 15: 499—502.
Hoffmann, V., 1988. Sichtbarmachung der magnetischen Bereichsstrukturen synthetischer und naturlicher Titanomagnetite mit dem magnetooptischen Kerr-Effekt. Ph.D. Thesis, FB Geowiss., University of Munich. Hoffmann, V., Schafer, R., Appel, E., Hubert, A. and Soffel, H.C., 1987. First domain observations with the magnetooptical Kerr effect on Ti-ferrites in rocks and their synthetic equivalents. J. Magn. Magn. Mat., 71: 90—94. Hoffmann, V., Appel, E. and Soffel, H.C., 1990. Quantitative magneto-optical
Kerr effect on titanomagnetites.
Phys.
Earth Planet. Inter., 65: 28—35. Kranz, J. and Hubert, A., 1963. Die Moglichkeiten der KerrTechnik zur Beobachtung magnetischer Bereiche. Z. Angew. Phys., 15: 220—232. Landolt-Börnstein, 1982. Physical Properties of Rocks. Vol. ib, pp. 243244. Metcalf, M. and Fuller, M., 1987. Domain observations of titanomagnetites during hysteresis at elevated temperature and thermal cycling. Phys. Earth Planet. Inter., 46: 120—126. Moskowitz, B.M., Halgedahl, S. and Lawson, C.A., 1988. Magnetic domains on unpolished and polished surfaces of titanium-rich titanomagnetite. J. Geophys. Res., 93 (B4): 3372—3386. Rave, W., Schafer, R. and Hubert A., 1987. Quantitative observation of magnetic domains with the magneto-optical Kerr effect. J. Magn. Magn. Mat., 65: 7—14. Schmidt, F., Rave, W. and Hubert A., 1985. Enhancement of magneto-optical domain observation by digital image processing. IEEE Trans. Magn., 21: 1956—1958. Smith, P.P.K., 1980. The application of Lorentz electron microscopy to the study of rock magnetism. Inst. Phys. Conf. Ser., 52: 125—128. Soffel, H.C., 1971. The single domain—multidomain transition in natural intermediate titanomagnetites. Z. Geophys., 37: 45 1—470. Soffel, H.C., 1977. Pseudo-single domain effects and single domain—multidomain transition in natural pyrrhotite deduced from domain structure observations. J. Geophys., 42: 351—359. Soffel, H.C., 1981. Domain structure of natural fine-grained pyrrhotite in a rock matrix (diabase). Phys. Earth Planet. Inter., 26: 98—106. Soffel, H.C., Aumuller, C., Hoffmann, V. and Appel, E., 1990. Three-dimensional domain observations of magnetite and titanomagnetites using the dried colloid SEM method. Phys.
Earth Planet. Inter., 65: 43—53. Stephan, W., 1955. Bitterstreifen auf Nickel. Exp. Tech. Phys., 1: 1—13. Syono, Y., 1965. Magnetocrystalline arlisotropy and magnetostriction of Fe 304—Fe2TiO4-series with special application to rock magnetism. Jap. J. Geophys., 4: 71—143. Williams, H.J., Sherwood, R.C. and Remeika, J.P., 1958. Magnetic domains in a-Fe203. J. Appl. Phys., 29: 1772—1773.
Physics of the Earth and Planetary Interiors, 65 (1990) 36—42 Elsevier Science Publishers B.V., Amsterdam
Magneto-optical Kerr effect in (titano) magnetite, pyrrhotite and hematite E. Appel, V. Hoffmann and H.C. Soffel Institut für Ailgemeine und Angewandle Geophysik, Universität MOnchen, Theresienstrasse 41, W-8000 MOnchen 2 (FR. G.) (Received November 27, 1989; revision accepted April 9, 1990)
ABSTRACT Appel, E., Hoffmann, V. and Soffel, H.C., 1990. Magneto-optical Kerr effect in (titano)magnetite, pyrrhotite and hematite. Phys. Earth Planet. Inter., 65: 36—42. The successful application of the magneto-optical Kerr effect in rock magnetism is demonstrated. Domain structures of the most frequently occurring ferromagnetic minerals in rocks—(titano)magnetite, pyrrhotite and hematite—are shown. Surprisingly, the method works with hematite, where the Bitter pattern technique is not appropriate. Skin depths and sublattice interactions are discussed to explain the effect.
1. Introduction Domain observations are of fundamental importance for the analysis of the micromagnetic structure and for the understanding of macroscopic magnetic properties. In the past, domain observations in rock magnetism mostly used the Bitter pattern technique and an optical microscope. Successful experiments with the Bitter technique were carried out on (titano)magnetite(s) and pyrrhotite. Gustard (1967) and Gallon (1968) reported Bitter structures on hematite; however, efforts to reproduce such experiments usually fail. Moskowitz et al. (e.g. 1988) and Soffel et al. (1990) observed dried Bitter patterns on (titano)magnetite with the scanning electron microscope. Smith (1980) applied the Lorentz electron microscope to domain observations on magnetite. Important results of domain observations in rock magnetism are the determination of the critical grain size for single-domain—multi-domain transitions (Soffel, 1971, 1977), the stress control of domain structures in titanomagnetites (Appel and Soffel, 1984, 1985), detection of nucleation processes (Halgedahl and Fuller, 1980), tempera0031-9201/90/$03.50
© 1990
—
Elsevier Science Publishers B.V.
ture-induced domain pattern changes (Metcalf and Fuller, 1987; Heider et a!., 1988) and external stress-induced domain pattern changes (Appel and Soffel, 1985). Halgedahi (1987) gave a review of research activities. Although the Bitter pattern technique was very successful in rock magnetic studies, it is limited to observations of stray fields along domain walls. The direction of the magnetization vector within the domains cannot be detected. Hoffmann et a!. (1987) reported the first application of the magneto-optical Kerr technique to titanomagnetites. Observations with the Kerr technique show domains directly, and the magnetization direction within domains can be analysed qualitatively by grey-scale variations and even quantitatively in certain cases (Rave et al., 1987). In this paper we report the progress in the use of the magneto-optical Kerr technique for other natural magnetic minerals by showing Kerr images of (titano)magnetite, pyrrhotite and hematite. The aim of the study is to demonstrate the successful application of the technique. Interpretations of domain structures are given only very briefly for this reason.
37
MAGNETO-OPTICAL KERR EFFECT IN ROCK MAGNETISM angle vs.~ plane of
2. Magneto-optical Kerr effect and technique of observation The physical principles of the magneto-optical Kerr effect are only fully explained in terms of quantum mechanics (spin—orbit interaction of electron moments; e.g. Argyres, 1955). A non quantum mechanical overview has been given, for example, by Kranz and Hubert (1963). For a qualitative approach it is sufficient to consider the Lorentz force on conduction electrons in the magnetic field of the magnetic domain moments. A linear polarized light beam is reflected from the surface of a magnetic material (Fig. 1). The electrons near the surface are forced to oscillate parallel to the electric field (E-vector). Because of the Lorentz force a Kerr component K (K parallel to E x B) originates, and consequently the plane of electron oscillation is rotated. Hence, the polarization plane of the reflected light beam is different from that of the incident beam E. Different orientations of B within neighbouring domains result in different rotations of the polarization plane, which can be detected by an appropriate analyser orientation in terms of grey-scale contrasts. Graduation of the grey scale from black to white refers to graduation of the domain magnetization from zero to 1800 (further details are given by Hoffmann et a!., 1990).
-_________
M
~
_____________________________
Fig. 1. Physical principles of the Kerr effect (for explanations see text). E and N are the electric field vectors of the incident light beam and of the normally reflected light beam respectively. K is the electric field vector of the reflected light beam which originated from the domain magnetization. Two domains with antiparallel homogeneous magnetizations (arrows) are indicated by black and white.
The Kerr amplitude K is proportional to the spontaneous magnetization M~.Kerr contrasts are M~.The application of the K2 and therefore magneto-optical Kerr effect to materials with low M~,such as ferrimagnetic minerals, requires special sample preparation and image-processing techniques. First, an extremely smooth and stress-free surface has to be prepared by polishing with amorphous Si0 2 solution (Hoffmann et a!., 1987). Kerr contrasts are enhanced by the use of a —
—
Fig. 2. Kerr image of a natural magnetite crystal. The surface is slightly inclined to a (110) plane.
38
E. APPEL ET AL.
digital image-processing system (Schmidt et a!., 1985). The observed surface is recorded in a saturated stage (reference image without magnetic contrasts). The reference image is subtracted from the subsequent!y observed Kerr image. The result is a high-contrast difference image showing the magnetic domains in terms of different grey scales. Electronic noise is reduced by averaging difference images of the same domain structure,
with magnetite and hence Kerr contrasts are expected to be distinctly weaker. Despite the low M~ the Kerr technique still works. However, more accurate adjustments of the polarizer, analyser, compensator and the rectangular aperture, as well as a higher number of averaging cycles, are required. Figure 3 shows domain structures on a synthetic Al- and Mg-doped titanomagnetite with uniaxial domain shape. Bent domain boundaries indicate stress dominance (Appe! and Soffe!, 1984, 1985). Grey-scale variations within the domains point to locally varying magnetization directions, which are probably also stress induced (Appel and Soffel, 1985).
3. Observations of magnetic domains with the magneto-optical Kerr effect 3.1. Magnetite and titanomagnetites
Naturally occurring titanomagnetites generally show much more complicated domain patterns
Magnetite, Fe304, has the highest spontaneous magnetization of all naturally occurring minerals (480 kA m~). As expected, Kerr contrasts are well pronounced (Hoffmann, 1988). Figure 2 shows a natural single crystal of magnetite. Christmas-tree-shaped domain patterns (Stephan, 1955) indicate that the surface is slightly inclined to a (110) plane. Classical 180, 71 and 1090 domain walls represent two easy directions of magnetization within the observed surface. Titanomagnetites, Fe3 ~Ti~O4, are most frequently found in compositions around x 0.6 in basalts. M~is about five times lower compared
than their synthetic equivalents. This is already known from Bitter pattern studies (Appel and Soffe!, 1984, 1985). Figure 4 shows a Kerr image of a natural titanomagnetite in a basalt. Kerr contrasts are rather distinct in some parts of the grain but the domain structure is very cornplicated. There are areas with almost parallel domains, areas with good contrast but chaotic domain shape and large areas with grey-scale variations but without any recognizable domains. Our Kerr observations confirm the statement that internal stress in naturally occurring titanomagnetites is high and varies strongly in amount and
—
=
.1~
~
~
-:.
~t.
Fig. 3. Kerr image of a synthetic titanomagnetite Fe2 ,8Ti052A1015Mg0 204.
39
MAGNETO-OPTICAL KERR EFFECT IN ROCK MAGNETISM
~
J~.. •
~
~ .r~
~
~ .:
‘~:
~
~
~
N
-
—1 Fig. 4. Kerr image of a natural titanomagnetite in a basalt (Curie temperature 242°C).
directions within short distances (Appe! and Soffel, 1984).
iaxial crystalline anisotropy and from Bitter pattern studies (Soffel, 1981). 3.3. Hematite
3.2. Pyrrhotite Pyrrhotite, Fe7S8, has a spontaneous magneti1). zation similar toare titanomagnetites (— 100 rn Kerr contrasts well pronounced. ThekAdomain shape shown in Fig. 5 represents a typical uniaxia! domain structure, as it is expected from the un-
Fig. 5. Kerr image of a natural pyrrhotite.
Hematite, a-Fe03, is antiferromagnetic with a small spontaneous (M~ M~ 2 kA mresidual 1) as a result of spin magnetization canting. The small value should not permit domain observations with the Kerr technique because of too weak contrasts. Surprisingly, this is not the case. Williams et al. —
40
EAPPELETAL.
(1958) have observed domains in a-Fe203 by using the Faraday effect. We found that Kerr contrasts are even more pronounced than in magnetite and for some samples they are detectable without image processing. The explanation of why the method works with wealdy magnetic hematite is hard to give in terms of M~.The skin depth d of an electromagnetic field is proportional to (aitw) —1/2 (where a is conductivity, p~ is permeability and w is frequency). The permeability ~.t 1 + k(SI uthts) (where k is susceptibility) of magnetite is of the =
order of 10 for crystalline anisotropy controlled spin rotations corresponding to the formula k
4K
= —
__i!
4K
—
_~~a
(K3 and K2 are crystalline anisotropy constants; Syono, 1965). Experimental results for conductivities of magnetite and hematite vary over a broad range. Mean values for magnetite (a iO~—io~ ~2’ m~ Landolt-Börnstein, 1982) and hematite (a 65—285 ~ m~ Lando!t-Börnstein, 1982) =
=
I
Fig. 6. Kerr images of a synthetic hematite particle. Upper, zero field: lower, applied field of
—
0.1 T parallel to the surface.
41
MAGNETO-OPTICAL KERR EFFECT IN ROCK MAGNETISM
result in a ratio of skin depths for hematite and magnetite with dFe2O3/dFe3O4 ranging from about six to 40 (in consideration of ji values and constant frequency). This is far too low to equalize the low ratio of M~values for hematite to magnetite (— 1/60 000). An alternative explanation of strong Kerr contrasts in hematite could be that Kerr rotations depend on the sublattice magnetization (one sublattice interacting more than the other) rather than on the resulting spin-canting moment. Figure 6 shows a synthetic hematite particle in zero field (left side) and with an annlied field of
—
0.1 T (right side). Three major domains and one
(right side) or two (left side) smaller ones are shown. Different grey scales mean different magnetization direction. The domain shape is cornpletely different from that observed in other magnetic minerals. This is certainly a consequence of the negligible stray field energy (small Ms). Figure 7 shows two different isothermal remanence (‘saturation’ field 0.15 T) states in naturally occurring hematite. Complete domain reorganization is obvious from grey-scale changes. Even a single-domain particle (arrow in Fig. 7) is remagnetized.
5’
Fig. 7. Kerr images of natural hematite. Two opposite isothermal remanence stages are shown. A single-domain particle is marked by the arrow.
42
4. Conclusions Domain observations with the magneto-optical Kerr effect were successfully carried out on the most frequently occurring magnetic minerals in rocks; magnetite, titanomagnetite (x — 0.6), pyrrhotite and hematite. The applicability of the Kerr method to hematite is of special importance because the Bitter pattern technique fails in this case. New possibilities arise with Kerr observations. Variations of the magnetization direction within domains can be analysed qualitatively and possibly quantitatively (Hoffmann et a!., 1990). There is no limitation of the Kerr technique at higher temperature. Hence heating experiments, which are basically important in understanding thermoremanent magnetization acquisition in multidomain particles, may be possible up to the Curie temperature of magnetite or hematite, Acknowledgements The experimental work was carried out at the Institut für Werkstoffwissenschaften VI at the University of Erlangen. We thank Prof. Hubert, R. Schafer and W. Rave for their help and for stimulating discussions. The work was financially supported by the Deutsche Forschungsgemeinschaft (DFG).
References Appel, E. and Soffel, H.C., 1984. Model for the domain state of Ti-rich titanomagnetites. Geophys. Res. Lett., 11: 189— 192. Appel, E. and Soffel, H.C., 1985. Domain state of Ti-rich titanomagnetites deduced from domain structure observations and susceptibility measurements. J. Geophys., 56: 121—132. Argyres, P.N., 1955. Theory of the Faraday and Kerr effects in ferromagnetics. Phys. Rev., 97(2): 334—345. Gallon, T.C., 1968. The ferromagnetic domain structure of haematite. Proc. R. Soc. London Ser. A, 303: 525—529. Gustard, B., 1967. The ferromagnetic domain structure in haematite. Proc. R. Soc. London Ser. A, 297: 269—274. Halgedahl, S., 1987. Domain pattern observations in rock magnetism: progress and problems. Phys. Earth Planet, Inter., 46: 127—163. Halgedahl, S. and Fuller, M., 1980. Magnetic domain observa-
E. APPEL ET AL.
tions of nucleation processes in fine particles of intermediate titanomagnetite. Nature, 288: 70—72.
Heider, F., Halgedahl, S.L. and Dunlop, D.J., 1988. Temperature dependence of magnetic domains in magnetite crystals. Geophys. Res. Lett., 15: 499—502.
Hoffmann, V., 1988. Sichtbarmachung der magnetischen Bereichsstrukturen synthetischer und naturlicher Titanomagnetite mit dem magnetooptischen Kerr-Effekt. Ph.D. Thesis, FB Geowiss., University of Munich. Hoffmann, V., Schafer, R., Appel, E., Hubert, A. and Soffel, H.C., 1987. First domain observations with the magnetooptical Kerr effect on Ti-ferrites in rocks and their synthetic equivalents. J. Magn. Magn. Mat., 71: 90—94. Hoffmann, V., Appel, E. and Soffel, H.C., 1990. Quantitative magneto-optical
Kerr effect on titanomagnetites.
Phys.
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