Order—disorder transformation and reverse thermo-remanent magnetism in the FeTiO3Fe2O3 system

J. Phys.

Chem. Solids

Pergamon Press 1963. Vol. 24, pp. 517-528.

ORDER-DISORDER THERMO-REMANENT

Printed in Great Britain.

TRANSFORMATION AND REVERSE MAGNETISM IN THE FeTiO,-Fe,O, SYSTEM YOSl-llKAZU ISHIKAWA*

The Institute for Solid State Physics, University of Tokyo and

YASUHIKO Geophysical (Received

SYONO

Institute, University

19 July

of Tokyo, Japan

1962; revised 23 November

1962)

Abstract-The order-disorder transformation and the reverse thermo-remanent magnetization (reverse T.R.M.) have been investigated in detail in synthesized solid solutions of xFeTiOs-(1 -x) FesOs with x around 0.5. It has been confirmed that the reverse T.R.M. is closely related to the order-disorder transformation which exists in this system; the reverse T.R.M. is observed only in a state of metastable equilibrium, and not in specimens either completely ordered or completely disordered. The reverse T.R.M. is found to be the result of antiparallel superexchange interaction between the magnetic moments of the ordered phase and the moments of an Fe-rich metastable phase which is created around the ordered structure in the process of the development of order. The detailed kinetic process of the development of order in this system has also been elucidated. The origin of the metastable phase has been investigated in detail and a model which can consistently explain the experimental results on the reverse T.R.M. is presented. 1. INTRODUCTION

REVERSE thermo-remanent magnetism (reverse T.R.M.) is the phenomenon whereby a specimen is cooled through the Curie point in a magnetic field and the remanent magnetization is in a direction opposite to that of the field originally applied. This self-reversal phenomenon of remanent magnetization was first discovered by the NAGATA group(l) in certain minerals extracted from Haruna rocks and it attracted great attention throughout the world in the fields of rock magnetism and paleomagnetism. Until this time, the existence of rocks which have the natural remanent magnetization direction nearly in the opposite direction to the earth’s present magnetic field had been believed uniquely to be due to the reversal of the geomagnetic field in the past. The most extensive investigation of this phe* Present address : Laboratoire de Physique du M&al, Institut Grenoble, France. B

d’l?lectrostatique et Fourier, B.P. 319,

nomenon has been carried out by UYEDA.@)It has been found that the reverse T.R.M. is an intrinsic property of the solid solution of FeTiOs and Fez03 (xFeTiOa--( 1 - x)FezOs), which constitute the ferromagnetic minerals of the rock. Furthermore, he has found that the reverse T.R.M. is observed only in the specimen with x around 0.5, whose magnetic properties are sensitive to heat treatment.@) The effect of heat treatment was examined in detail by one of the authors and specimens in this range of composition have been found to show the order-disorder transformation of the atomic arrangement of titanium and iron ions.(s) The disordered specimen is parasitic ferromagnetic with the crystal symmetry RkZ’, while the ordered one is ferrimagnetic with the crystal symmetry R3. The reverse T.R.M. is, therefore, expected to be closely related to the order-disorder transformation of this system. On the basis of his experimental results, UYEDA proposed a tentative explanation that the reverse 517

YOSHIKXZU

5 18

ISHIKXWA

T.R.lLI. is the result of antiparallel coupling between the magnetic moments of ordered and disordered phases coexisting in a specimen.@) Magnetic interaction was expected to be the superexchange interaction. Uyeda’s model of the exchange coupling of two phases was supported by MEIKLEJOHN and CARTER(~) who observed a slight shift of the hysteresis loop of 0.6 FeTiOs0.4 Fez03 at 300°K after cooling in a magnetic field through the Curie point.(‘n Uyeda’s model is, however, too simple to explain the complex features of the reverse T.R.M. of this system. He had to assume in his model that the disordered region has a Curie point higher than that of the ordered region, in order to produce the reverse T.R.M. This assumption contradicts the experimental results that the disordered phase has a Curie point 20-30°K lower than that of the ordered phase, if the compositions are the same. Furthermore, both Uyeda and Meiklejohn noticed in their experiments that the characteristics of the reverse T.R.M. were different sample by sample, even if the composition of the samples were the same. This made their results very complicated, and the detailed mechanism of this phenomenon has remained uncertain. We have suggested in the previous paper(s) that this phenomenon may be closely related to a metastable phase which is created on the boundary of the ordered phase, so that a careful study of this phenomenon might make clear not only the mechanism of the reverse T.R.M., but also the kinetic process of the order-disorder transformation of this system. In this paper, we describe the results of our experiments carried out to find the relation between order-disorder transformation process and the reverse T.R.M. A model is proposed which explains consistently the various features of the reverse T.R.M. of this system. Some information about the kinetic process of the order-disorder transformation in this oxide system which has been elucidated by this investigation is also presented. The results on the reverse T.R.M. have already been reported briefly.(s) 2. EXPERIMENTAL

RESULTS

1. Kinetic process of order-disorder

Specimen with most prominent

transformation ?c around 0.5, which show the order-disorder transformation,

and

YASUHIRO

SYONO

were used in our experiments. They were prepared by the same method as previous reported(s) and were shown by X-ray analysis to be single phase. The compositions were determined by an X-ray method which give results in good agreement with chemical analysis.(s) Each specimen was sealed carefully into an evacuated silica tube in order to avoid oxidation or reduction during heat treatment at high temperature, and all measurements were carried out with the specimen still sealed. The long range order parameter S(T)

THoC FIG. 1. Magnetization

at r~c~rn temperature ing temperature.

vs. quench-

of the specimen at a temperature T was determined by quenching the specimen from this temperature and measuring the magnetization in a magnetic field of 8500 Oe at room temperature, which has been shown to be approximately proportional to the long range order parameter S.(s) The temperature dependence of the equilibrium value of S(T), obtained by keeping the specimens for a long time at the temperature T, is shown in Fig. 1. The number of each curve in the figure indicates mole percentage of ilmenite in the specimen. It should be noted that the maximum values of magnetization at room temperature of the specimen with .X = 0.48 and 0.465, which were annealed for more than 3 days at low temperatures

ORDER-DISORDER

TRANSFORMATION

AND REVERSE

THERMO-REMANENT

MAGNETISM

519

In Fig. 2(a) (b) and (c), the isothermal variations of the long range order parameter (magnetization at room temperature) measured at various temperatures are presented for three different compositions. These results were obtained by annealing the disordered specimen at a temperature TH for a certain time interval t, and quenching it to

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FIG. 3. Temperature dependence of slopes of logarithmic increase of long-range order, obtained from Fig. 2 for three compositions.

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,

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100

(cl FIG. 2. Isothermal time variations of long-range order (magnetization at room temperature) for various temperatures (a) 56 mole per cent FeTiOa (b) 51 mole per cent FeTiOs. (c) 48 mole per cent FeTiOs.

are fairly small compared with those of x = 0.51 and O-56. This suggests that the perfect order cannot be established in the former specimens.

room temperature. The ordinate of these figures are normalized to MO, the magnetization at room temperature of complete ordered 56 mole per cent FeTiOs. This approximate normalization may be permitted, because a decrease of the concentration of ilmenite in the specimen reduces the magnetic moment at 0°K while it raises the Curie point, so that the room temperature magnetizations of these three specimens are expected to remain nearly constant in the completely ordered state. These figures show that the isothermal variation of the long range order parameter, S(T) is proportional to the logarithm of the annealing time over a wide time range.. The initial stage of the ordering process (t 5 5 min) cannot be detected

520

YOSHIKAZU

ISHIKAWA

by our method. The slopes A of the time variation curves obtained from Fig. 2(a), (b) and (c) are plotted in Fig. 3 as a function of temperature. From this figure, we find that A is approximately proportional to exp( -E/H’) and is almost independent of the composition. The isothermal change of long range order S in this system is, therefore, expressed by the following relation, as long as the specimen is in a state far from equilibrium. S(T) = A0 exp( -E/AT)

and

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-1

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7OO’C 100

annealing time 209

-

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where E,‘obtained from Fig. 3 is 0.33 eV. This relation indicates that the velocity of development of order is strongly temperature dependent and an appreciable increase of order can hardly be expected at temperatures below 500°C. Accordingly the ordered structure can never be developed in a specimen with x less than 0.40, because they have the order-disorder transformation temperature less than 500°C. 2. The reverse T.R.M.

of the specimen in the course of development of order

The thermo-remanent magnetization of the specimen in various stages of order was produced by the following procedure. A specimen was annealed at a temperature TH (a SOO’C) for a certain time t, quenched to room temperature to detect the state of order, reheated to 45O”C, and finally cooled to room temperature with a magnetic field of 100 Oe applied only from 450°C down to some temperature Ta. The thermo-remanent magnetization at room temperature thus produced was measured by an ordinary ballistic method. The Curie point of the ferrimagnetic phase responsible for T.R.M. in the specimen was determined by measuring the temperature at which the thermo-remanent magnetization disappeared. After a series of magnetic annealing from 450°C to various temperatures Ta, the specimen was reheated to TH and annealed at this temperature for a further long time. One of the advantages of this system is such that a repetition of the magnetic annealing between 450°C and room temperature does not disturb the arrangements of ions as was discussed in the previous section. In Fig. 4(a), the thermo-remanent magnetization measured at room temperature for the 56 mole per cent FeTiOs is plotted against Ta. Each

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FIG. 4. (a) Thermo-remanent magnetizations of 56 mole per cent FeTiOs annealed at 700°C for various times. Abscissa is the temperature down to which a magnetic field was applied during cooling. (b) Isothermal changes of long-range order (upper curve) and maximum reverse T.R.M. at 700°C in 56 mole per cent FeTiOa.

ORDER-DISORDER

TRANS~UR~AT~~~AN~

REVERSE THERETO-REMA~E~T

curve corresponds to the results obtained for a different annealing time at TH = 700°C. The Curie point of the thermo-remanent magnetization Tet determined by the method described above, is also indicated in the figure. No appreciable change of the Curie point was observed in the process of development of order at 700°C. From these figures we find that, for a specimen in the early stages of development of order, the reverse T.R.M. was found to be produced even if the magnetic field was apphed only down to a temperature appreciably above the Curie point of the induced thermo-remanent magnetization. Since the T.R.M. is knawn to be produced if the magnetic field is applied down to below the Curie point of the phase,@” this fact suggests that another phase (or phases) exist with a range of Curie temperature higher than that of the thermo-remanent magnetization, which is presumably that of the ordered phase. This unknown phase is designated hereafter as the x-phase. As the Curie point of the disordered phase is lower than that of the ordered phase of the same composition, the x-phase must be an Fe-rich region as compared with both the ordered and disordered phases. If the magnetic moment of the x-phase is fairly small compared with that of the ordered phase, the anti-parallel coupling between the magnetic mament of the ordered phase and that of the x-phase, which was locked in the direction of the field applied during the magnetic annealing process, results in the self reversal of the remanent magnetization. Fig. 4(a) also shows that the Curie points of the x-phase, which are distributed over a range of temperature, change with the development of order. When the specimen was cooled to a temperature far below the Curie point of the ordered phase, a normal T.R.M. was superimposed on the reverse T.R.M. This effect was more pronounced if the specimen is annealed for a long time. The maximum values of the reverse T.R.M. obtained from Fig. 4(a) are plotted in Fig. 4(b) as a function of the annealing time at 700°C. The upper curve in the figure indicates the long range order parameter developed by the annealing process, while the lower curve is the maximum reverse T.R.M. of the specimen. The striking result is that the reverse T.R.M. exists only in the intermediate state, and is not found in either the fully ordered state or in the disordered state. These facts indicate

MAGNETISM

521

FIG. 5. hothermal

changes of long-range order (upper and maximum reverse TAM. at 700°C in 51 mole per cent FeTiOs. (Cf. Fig. 4b).

curve)

cIearIy that the x-phase which is responsible for the reverse T.R.M. is o&y a metastabie phase: that is, it is created in the process of the formation of order and tends to disappear if the crystal reaches equilibrium. SimiIar experiments were carried out for specimens with .z = 031 and the results are presented in Figs. 5 and 6. The result obtained by annealing the specimens at 7tlO”C is almost the same aa that Nr $J& 0 O -1

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annealing

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6. Thermo-remanent magnetization of 53 mole per cent FeTiOs annealed at 600°C for various times (Cf. Fig. 4a). FIG.

YOSHIKXZU

522

ISHIKAWA

Mi emu

4

i

2

ll\ 0

i 100

TC

00

400

T,‘C

-I t

FIG. 7. Thermo-remanent magnetization of 51 mole per cent FeTiOa furnace-cooled from 1000°C. Abscissa is the temperature down to which a magnetic field was applied during cooling.

of x = O-56, but in this case, the reverse T.R.M. (the metastable phase) does not disappear completely, even after annealing for more than 100 hr at 7OO”C, as shown in Fig. 5. When the specimen was annealed at 600°C however, the characteristics of magnetic annealing were found to be fairly different from those at 700°C. As shown in Fig. 6, the Curie points of metastable phase still

and

YASUHIKO

SYONO

increase after annealing for more than 65 hr, indicating that the difference in composition between the metastable phase and matrix increases with prolonged annealing. Furthermore, in this case, the maximum reverse T.R.M. is always produced when the magnetic field is applied down to room temperature during cooling from 450°C. These figures indicate that the metastable phase created in the annealing process at 600°C has the same characteristics as that created only in the early stage of annealing at 700°C (t N 6 min). In a later Section we shall discuss in more detail such a difference in the kinetic process with temperature and composition. We have thus found that the characteristics of the reverse T.R.M. were quite different, even if the long range order is the same. The most prominent case was found for the specimen with x = 0.56 which was cooled with the furnace from 1000°C. After this heat treatment, the magnetization at room temperature is about 85 per cent of that of the perfectly ordered specimen, indicating that the long range order is fairly well developed in the specimen. The characteristics of the magnetic annealing of this specimen, however, are quite different from the previous cases, as shown in Fig. 7, which was obtained by the same method as described previously. The Curie points of the

Mr emy 9

1.0

100

H(Oe1

120

-1.0

-2.0 FIG. 8. Field dependence of the thermo-remanent magnetization. Magnetic field was applied only down to a temperature above the Curie point for the reverse T.R.M.

ORDER-DISORDER

TRANSFORMATION

AND REVERSE

metastable phase are distributed over a range of 200°C above the Curie points of the ordered phase. This is an indication that a considerable amount of metastable phase with compositions quite different from the matrix still exists in combination with the ordered phase as a result of such furnace-cooling. 3. Magnetic properties ofx-phase It is difficult to measure the magnetic properties of the metastable x-phase by any direct means, because the x-phase always exists in combination with the strong ferrimagnetic ordered phase. Therefore the magnetic properties of the x-phase were estimated from the reverse T.R.M., which indicates indirectly their magnetic properties. In Fig. 8 the field dependence of the reverse T.R.M. is shown, together with the field dependence of the normal T.R.M. for both the ordered phase (x = 0.56) and the disordered phase (x = 0.51). The reverse T.R.M. was produced in the specimen with x = O-56, which was previously furnacecooled from lOOO”C, by applying a magnetic field H from 450°C down to a temperature just above the Curie point of the ordered phase, so as not to produce the normal T.R.M. The field dependence of the reverse T.R.M. obtained by this procedure is presumably that of the pure x-phase. This figure shows that the characteristics of the x-phase are quite similar to those of the disordered phase, that is, in the case of both the disordered phase and the x-phase, a magnetic field of 10 Oe is sufficient to produce the saturated thermoremanent magnetization, while for the ferrimagnetic ordered phase, more than 100 Oe is necessary to saturate the T.R.M. The field dependence of the disordered state is a characteristic of the parasitic ferromagnet;@) that is, in this case, the demagnetizing field, which prevents the saturation of the remanent magnetization, is very small The x-phase has, therefore, the very weak magnetic moment and is presumably in the disordered state. In Fig. 9, the field dependence of the reverse T.R.M. for a specimen with x = 0.56, annealed at 700°C is shown for various annealing times. The reverse T.R.M. was produced by the same method as described above for each annealing time. The field dependence of the reverse T.R.M. thus obtained is found to be almost the same

THERMO-REMANENT

MAGNETISh%

523

throughout the ordering process; that is, even for the specimen annealed for only 10 min at 7OO”C, the reverse T.R.M. was saturated by a weak field. This fact indicates that the x-phase is not present in regions as small as one or two atomic layers thick on the boundary of the ordered phase even in the early stage of ordering. If the x-phase region were fairly small, it would behave as superparamagnetic particles at high temperature and it should become very difficult to saturate the magnetic moment of the x-phase, which, in turn, should result in hard saturation of the reverse T.R.M. 80

I @iii i Mr

-

120

H(Oe) :

60hr

=

20min

3.5hr

x =0.56 700°C

annealing

t

time

FIG. 9. Field dependence of the reverse T.R.M. of 56 mole ner . cent FeTiOs annealed for different times at 700°C. Magnetic field was applied only down to a temperature above the Curie point.

4. Magnetic interaction between the ordered phase and the x-phase In order to estimate the order of magnitude of magnetic coupling between the magnetic moments of the order phase and the x-phase, we have measured the hysteresis of the remanent magnetization produced at room temperature. In Figs. 10 and 11, the results obtained for specimens with x = 0.465 and x = 0.51 are shown. They are annealed at 600°C for 2 hr and 20 min respectively beforehand, and the reverse T.R.M. was produced by applying a magnetic field of 100 Oe from 450°C down to room temperature. A magnetic field was then applied at room temperature in the direction opposite to the reverse T.R.RI., and the remanent magnetization was measured by the ballistic method. Each point in the figure corresponds to the remanent magnetization obtained after applying the magnetic field indicated on the abscissa. As Fig. 10 shows, more than 14,000 Oe is

521

YOSHIKAZU

ISHIKAWA

and

YASUHIKO

SYONO

Mr emu/g

-

H

-0.10

-30000

-20000

I00,00 $------------‘----------~:-----‘-~------’,3 20000

H (Oe)

30000

I x = 0.465 ‘H FIG. 10. Remanence

hysteresis of 46.5 mole per cent FeTiOs with reverse T.R.M.

necessary to destroy the reverse T.R.M. of the specimen in which x = 0.465. On the other hand, the remanent magnetization produced in the opposite direction to the reverse T.R.M. at room temperature by a field strength of 30,000 Oe can be easily destroyed by a field of 1000 Oe applied

in the direction of the reverse T.R.M. Such an asymmetric hysteresis suggests that the magnetic moments of the x-phase, which were fixed in the direction of the applied field during magnetic annealing, do not change their directions even if an external field as strong as 30,000 Oe is applied

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I 10000

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20000

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in the opposite direction. This situation is schematically illustrated in the figure. In the case of x = 0.51, we have also an asymmetric hysteresis as shown in Fig. 11, although the remanence coercivity is reduced to 3400 Oe. In the case of x = 0.56, a remanence coercivity of 760 Oe was obtained for the specimen annealing 600°C for 20 min. Such a decrease in remanence coercivity is not due to decrease in the strength of magnetic coupling but due to increase in the normal remanence magnetization produced from the part which does not couple with the metastable x-phase. The remanent hysteresis was also measured for both a completely ordered specimen (x = O-56) and a disordered specimen (x = 0.51). The remanent coercivities are found to be 200 Oe and 3000 Oe respectively, indicating that the coercive force is fairly small even for the disordered specimen. Accordingly the asymmetry hysteresis observed in a magnetic field of 30,000 Oe is the most clear evidence that the magnetic moments of the ordered phase and x-phase are coupled through a superexchange interaction. DISCUSSION 1. Discussion of reverse T.R.M.

6OOT

2Omin

anneal

FIG. 11. Remanence hysteresis of 5lrmole FeTiOs with reverse T.R.M.

per cent

We have suggested that the reverse T.R.M. is the result of anti-parallel coupling between the magnetic moments of the ordered phase and an

ORDER-DISORDERTRANSFORMATION

AND REVERSE THERMO-REMANENT

Fe-rich rnetastable phase. Moreover the x-phase must be atomically in antiphase with respect to the ordered phase in order that the resultant magnetic moments of the two phases can be aligned antiparallel through a superexchange interaction. The possibility of the existence of such a metastable phase was examined by following graphically the development of the ordered phase in the disordered matrix. Fig. 12(a) is a two dimensional representation of disordered 0.5 FeTiOs0.5 FesOs. The positions of Ti ions, indicated by black circles in the figure, were chosen by means of a table of random digits. An ordered phase was developed in the disordered matrix by rearranging the metal ions as shown by the arrows in the figure. Here we assume that diffusion of ions takes place more easily within the same layer than between the layers. Figure 12(b) indicates schematically the ordered phase thus produced, on the boundary of which we find the Fe-rich metastable regions. These regions may correspond to the “X-phase” although their boundaries cannot be clearly determined. As the Ti ions rejected from the Fe layers in the ordered phase are displaced to the same layers in the metastable phase, the x-phase is always in antiphase to the ordered phase. Therefore a superexchange interaction acting between the neighbouring layers can align the resultant magnetic moments of the two phases antiparallel. Of course, Ti-rich metastable regions are also created on the boundary. However, they do not affect the reverse T.R.M., because the Curie point of this phase is lower than that of the ordered phase. Thus, the graphical study shows that our antiphase-contact two-phase model is fairly promising, and we believe that the phenomenon of the reverse T.R.M. of the Haruna type is satisfactory explained by our model. The assumption of the preferential diffusion of Ti ions within the C-plane, which is essential for our model, is hoped to be examined experimentally in near future. 2. ~is~~sion

of the khetic process of orderimg

In this Section we summarize the results concerning with the kinetic process of order-disorder transformation in the ilmenite-hematite system, which was elucidated by the investigation of the reverse T.R.M. The various features of the reverse T.R,NI. observed in the ordering process,

MAGNETISM

525

whieh were presented in Figs. 4, 5 and 6, are also explained on the basis of the kinetic process. (1) When a disordered specimen is annealed at a temperature T below the order-disorder transformation temperature, long range order is developed in the disordered matrix. The isothermal change of the long range order parameter S’{Z’) is approximately expressed by the following relation, so long as the specimen is in a state far from equilibrium, S( Z’,t) = AO exp( - E/kT) log t where E is found to be about O-3 eV and is independent of the concent~tion of Ti ions in the crystal. Similar logarithmic time dependence has been observed in the case of the magnetic after effect in Alnico V(s) and other material@’ and has been interpreted by N&EL@~) and by STREETand WOOLEY(~)as a relaxation phenomenon where the relaxation times are distributed over a wide range of time. It is possible that the relaxation times or the activation energies of diffusion of Ti ions by which the ordered structure is developed in the ilmenite-hematite system are distributed over a wide range, because they may depend on various configurations of surrounding ions and vacancies.(ls) According to a simple calculation based on the assumption of a square-type distribution function of the relaxation times, the slope A of the logarithmic curve is proportional to the absolute temperature 3= This relation is actually observed for Alnico V(s) and FesO4.(1r) The kinetic process of ordering in this system is, however, apparently quite different from such a simple case. (2) In the early stage of the ordering process, a metastable phase with a concentration of Ti ions different from both the ordered and disordered phase is created on the boundary. The difference in concentration between the metastable phase and the ordered phase first increases and then decreases again with further annealing. The composition of the ordered phase remains almost unaltered throughout the whole process of the development of order. The metastable phase does not disappear even after the long-range order attains its equilibrium value, and further annealing is necessary in order to remove the metastable phase. (3) The ordered phase is developed by diffusion

526

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and

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of Ti ions, which is expected to take place preferentially within the C-plane. The metastable phase created on the boundary by this diffusion antiphase to the process is always atomically ordered phase. The reverse T.R.M. of this system is the result of antiparallel coupling of the spins of the ordered phase and of the metastable phase, through a superexchange interaction. (4) If the annealing temperature is fairly low (T < 6OO”C), only small size ordered regions are developed, always in contact with metastable regions. The ordered region is presumably magnetically single domain, so that the reverse T.R.M.

of disordered 50 mole per cent FeTiOs.

is produced even if the magnetic field is applied down to room temperature as really observed in Fig. 8(a). On the other hand, if the specimen is annealed at a high temperature (T > 7OO”C), the ordered regions grow in size rather than number. Therefore, if the specimen is annealed at 700°C for a long time, most of the ordered regions are too large in size to be affected by the metastable phase on the boundary and the normal T.R.M. is produced if the magnetic field is applied down to below the Curie point of the ordered phase which was shown in the last two figures of Fig. 4(a).

OR lER-DISORDER

TRANSFORMATION

AND REVERSE THERMO-REMANENT

MAGNETISM

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(b) FIG. 12. (b) Ordered phase and x-phase developed in the disordered matrix. The boundary of x-phase, which is presumably not definite in the actual crystal, is shown schematically in the figure.

In the intermediate stage of ordering, however, we found that the normal T.R.M. was produced if the magnetic field was applied down to almost 100°C below Tc(cf. the third and the fourth curve of Fig. 4a). We may expect that, in this stage of ordering, the ordered phase has reached a size such that it remains magnetically single domain (or almost single domain) near the Curie point, but becomes multidomain at low temperatures. A similar situation was first suggested by &THENAU(14) in order to explain the fact that the coercive force of barium-ferrite has a maximum at a temperature below the Curie point. When the multidomain structure becomes stable at low

temperature and the coercive force becomes less than the applied field, some of magnetic moments, which were directed in the direction opposite to the applied field by the negative coupling field just below the Curie point of the ordered phase may change their direction to that of the applied field by domain wall motion and a normal T.R.M. is produced. (5) If the concentration of Ti ions in the specimen is decreased, the tendency that the ordered phase grown in size is decreased. It becomes, therefore, difficult to remove the metastable phase for the specimen with low concentration of Ti ions, as is indicated in Fig. 5.

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Acknowledgements-The authors wish to express their thanks to Professors S. CHIKAZUMI, T. NAGATA and S. AKIMOTO for valuable discussion and advice. Their thanks are also due to Dr. C. D. GRAHAM, Jr. for reading and criticizing the manuscript, and to Mr. H. HA~HIURAfor his preparation of specimens. This research was partly supported by a research grant of the Ministry of Education. REFERENCES I. NAGATAT., UYEDA S. and AKIMOTO S., J. Geomugn. Geoelect., Kyoto 4, 22 (1952). 2. UYEDA S., Japanese J. Geophys. 2, 1 (1958). 3. ISHIKAWAY., J. phys. Sot. Japan 13, 828 (1958). 4. MEIKLEJOHNW. H. and CARTER R. E., J. appl. Pkys. 30, 2020 (1959).

and

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SYONO

5. ISHIKAWA Y. and SYONO Y., J. phys. Sot. Japan 17S, BI, 714 (1962). 6. ISHIKAWAY. and AKIMOTO S.,._.T. _phvs. Sac. _.Jaapun _ _ 12, 1083 (1957). 7. NAGATA T., Rock magnetism. Revised edition by MARUZENp. 147 (1961). 8. SYONO Y. and NAGATA T., J. Geomagn. Geoelect. Kyoto (in press). 9. STREETR. and WOOLEY J. C., Proc. phys. Sot. Lond. A62, 562 (1949). 10. BARBIERJ. C., Ann. Phys. Puris 9, 84 (1954). II. SHIMIZU Y., J. Geomagn. Geoelect. Kyoto 11, 125 (1960). 12. NOEL L., J. Phys. Radium 11,49 1950); 12, 339 (51). 13. IDA S. and INOUET., J. phys. Sot. Japan. lfS, BI 281 (1962). 14. RATHENAUG. W., Rev. mod. Phys. 25, 297 (1953).