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Polarization ‘crossover’ of field induced magnetic anisotropy in ferromagnetic amorphous alloys
Journal of Magnetism and Magnetic North-Holland. Amsterdam
Materials
81
59 (1986) 81-85
POLARIZATION ‘CROSSOVER’ OF FIELD INDUCED IN FERROMAGNETIC AMORPHOUS ALLOYS P.D. HODSON Department Received
ANISOTROPY
and J.E. EVETTS
of Metallurgy and Materials Science, Unioersity of Cambridge,
1 October
MAGNETIC
Pembroke Street, Cambridge,
CB-7 3QZ. UK
1985
,hB,Z during polarization ‘crossover’ are reported. Field induced magnetic anisotropy data for amorphous Co,,Fe,Mo,Si They were calculated from the magnetization energies of 12 mm diameter disk specimens cut from melt-spun ribbon. The magnitude of the anisotropy change produced and the kinetics of the change are in excellent agreement with a recent activation energy spectra model for structural polarization phenomena in amorphous metals. It is also shown that polarization ‘crossover’ can occur for any arbitrary anisotropy reorientation angle. It is expected that all other anisotropic properties of an amorphous alloy will display similar polarization ‘crossover’ phenomena.
1. Introduction Evetts and Hodson [l] presented an extension to anisotropic polarization phenomena of the Gibbs et al. activation energy spectra model for isotropic structural relaxation [2]. The amorphous structure was assumed to be initially isotropic and to change as a result of changing population densities over the energy levels of a distribution of isolated or weakly coupled Two Level Systems (TLS). The application of a polarizing ‘force’, X will alter an isotropic collection of previously equivalent equilibrated TLS in a manner that depends on the orientation angle of each TLS, $, to X. During isothermal annealing under the influence of such a polarizing force, any anisotropic property changes taking place will result from the anisotropic repopulation of individual TLS towards new local equilibria. The number density of atomic ‘processes’ available for relaxation (TLS in their upper energy state), q,(E),,,,,,, will be a function of +. Partial activation energy spectra [l] exist for every angle of TLS and will be repopulated differently as the Characteristic Annealing Function [2] sweeps across the spectrum of available atomic rearrangement processes linearly with In t in the usual way. Fig. 1 shows two of these partial spectra, for + = 0 and + = n/2. A con0304-8853/86/$03.50 Q Elsevier Science Publishers (North-Holland Physics Publishing Division)
WMBER DENSITY OF WAILABLE PROCESSES
E Fig. 1. Schematic partial processes with activation to a ‘ force’ X,
spectra of number density of available energy E for TLS at angles 0 and n/2
tinuum of partial spectra for all other angles will lie between these two extremes. One prediction to come from this model which is particularly easily tested is the detailed form of polarization ‘crossover’. This was first briefly reported by Egami [3] who described unpublished qualitative results of Flander, subsequently published in ref. [4]. The present paper reports field induced magnetic anisotropy crossover data for Co,,Fe,Mo? B.V.
82
P. D. Hodson, J. E. Eoetts / Polarization
Si,,B,2 (Vacuumschmelze GmbH ‘Vitrovac’ which support the predictions of ref. [l].
6025)
‘crossover
in amorphous crlloys
NUMBER DENSITY OF AVAILABLE PROCESSES
2. Theory Consider the effect of the application of a polarizing ‘force’ upon the development of an anisotropy. Suppose X is applied at q, to isotropic stabilized material for time t, to t, (fig. 2) and followed by annealing at the same temperature with the same magnitude of ‘force’, now at an angle of 71/2 to its previous direction until the induced anisotropy reaches zero, at t = t,. In the experiments described below, the ‘force’ was a magnetic field sufficient to saturate the specimen, and the anisotropy produced was magnetic anisotropy. It is important to emphasise that predictions can be made using fig. 1 about the rates of anisotropy evolution, irrespective of more detailed knowledge about the material. The rate of change of the number density of available atomic rearrangement processes, shown in fig. 3 (and thus of the anisotropy change, for approximately energy independent coupling constants, c(E)) should be twice as great with In t during the second step as during the first step. Fig. 3 shows the spectrum of out-of-equilibrium processes after these two anneals for just two partial spectra at 8 = 0 and 8 = n/2. The perpendicular anisotropies induced
EC
Ei
E
Fig. 3. Schematic activation energy spectra at the point of polarization ‘crossover’. The anisotropy corresponding to the low energy (dotted) processes cancels out that of the high energy (hatched) processes. to produce isotropy.
during each step (the hatched and dotted areas in fig. 3) now cancel each other out, leaving the material apparently isotropic in its magnetization energies (K sin’p + K sin2( p - a/2) = K, which is clearly isotropic). By subsequently annealing this ‘isotropic’ material in an isotropic rotating magnetic field at T,, an anisotropy should reappear in the original direction as the atomic rearrangement processes corresponding to the dotted area are regenerated and this low energy part of the spectrum becomes isotropic again. When the centre of the characteristic annealing function reaches the crossover point energy, EC, at time t,, only the
AK
AK
II ’
‘s \
A ./
c7
J t1
2
ln
t
Fig. 2. Schematic anisotropic property changes, showing In t kinetics that are twice as fast during annealing in stage II with the “force” reoriented by q/2.
Fig. 4. Schematic polarization ‘crossover’ property changes. An anisotropy develops from t, to t3 in a seemingly isotropic material under isotropic conditions.
P. D. Hodson, J. E. Evetts /
Polarization‘ ‘crossover’ in amorphous alloys
hatched q,(E) will remain, giving an anisotropy of half the previous maximum in its original direction (fig. 4). Beyond this point the anisotropy will fall again until it reaches zero when the annealing function reaches the isotropic q,(E) line again at Ei. The deviations from ‘In t kinetics’ at low energies are a consequence of the finite ‘breadth’ of the activation energy spectrum [5], while those at high energies result from the finite width of the characteristic annealing function (- kT) [6] and may thus cover up to one decade of time. It is important to note the hitherto unstated fact that polarization ‘crossover’ can occur for any reorientation angle, and that the detailed description given above for 90” is simply a special case of a more general phenomenon. For example, it would be possible to anneal in a field at 0” followed by annealing at 45” until the resultant easy axis lay along 22.5’ (only in the case of 90” reorientation can isotropy be achieved). By then annealing along this 22.5” direction, the net anisotropy should exhibit ‘crossover’ by reorientating towards 0” moving back towards again, before eventually 22.5”. Indeed, polarization ‘crossover’ would be exhibited by annealing in a field at whatever angle the resultant direction might be terminated at, during the 45” field annealing. 3. Experimental method Co,,Fe,Mo,Si,,B,, was chosen for the experimental investigation of field induced magnetic anisotropy because its saturation magnetostriction is less than 3 X lo-’ [7], making it insensitive to the stresses involved in specimen preparation. Such multicomponent cobalt-based glasses also have particularly large field induced anisotropies (e.g. up to 160 Jm-’ in Co,,,,Fe,,,Mo,B,,Si, [4]), making them easy to study. Disks of 12.5 mm diameter were cut from meltspun material supplied by Vacuumschmelze GmbH (‘Vitrovac’ 6025) using ceramic scissors to minimise the disturbance of their magnetic state. The diameter of a disk was uniform to < 2%. The, use of spark erosion was tried, but only reduced the error to 1% and led to unacceptable embrittlement even at the lowest cutting rates used. All the specimens used were first given a
83
stabilisation preanneal to remove their as-cast anisotropies (of about 40 JmP3) by annealing for 3600 s at 603 K in a rotating field of 2300 Am-‘, which was enough to overcome the demagnetizing field and saturate a specimen in an in-plane direction. These rotating fields were produced by two orthogonal sets of Helmholtz coils placed outside the non-inductively wound furnace, and driven at 50 Hz at n/2 out of phase with each other. This frequency is higher than that generally deemed necessary to prevent magnetic aftereffects in domain walls [8,9]. Annealing of carefully aligned specimens in static fields was carried out using a solenoid wound on the outside of the same furnace. All heat treatments after the initial stabilization anneal were carried out at 493 K. It should be noted that the form of the activation spectrum for as received material might already be such as to produce polarization crossover during this initial stabilisation anneal in the rotating field. This would make interpretation of subsequent behaviour very difficult. In order to eliminate this possibility, the anisotropy of each material was monitored during stabilisation. The isotropic state remained in all cases after it was attained, indicating polarization crossover effects could be discounted. The magnetic anisotropy energy density of each disk, K,, was calculated by measuring the disk’s magnetization energies at various angles to some arbitrary direction (actually that of melt-spinning). The anisotropy was assumed to be uniaxial and in-plane, magnetization energies at angles 8 being given by El = K, + K,sin2(8
- /?),
where p is the angle of the easy from 0”. By measuring the in-plane magnetization energies at 0 = O”, 45”, and 90”, the isotropic (K,) and anisotropic (K,) energy terms could be calculated, as could the easy axis direction, p. Typical experimental errors were 10 JmP3 in K, and K, and 15’ in j3. 4. Results and discussion
90’
Fig. 5 shows polarization reorientation of field
‘crossover’ data for a annealing angles. For
84
P. D. Hodson, J. E. Euetts / Polarization
‘crossouer’ in amorphous alloys
0.20-
P
0.150.100.05 -100
’
In t
Fig. 5. Field induced anisotropy changes for C0,,Fe,Mo2Si,hB,2 at 493 K, showing polarization ‘crossover’. Annealing times are expressed in seconds.
easy directions of magnetization near the 0 = 0” direction K, is classified as negative; for easy directions near 8 = 90” it is classified as positive [lo]. In region I of fig. 5 an easy axis can be seen to develop along the field direction at a rate approximately linear with In t, indicating a broad activation energy spectrum [2]. After 1.23 X lo4 s the field direction during annealing was changed to 8 = 90” (region II). The anisotropy, remaining close to 8 = O”, now decayed towards zero, again approximately linearly with In t after the expected initial transient. The rate of decrease with In t was twice as great as the rise, as predicted in fig. 2. After 5.4 X lo3 s K, reached approximately zero and the specimen displayed isotropic magnetization energies. During subsequent rotational field annealing (region III) K, increased from zero with its previous initial 8 = 0” easy direction and then decayed again towards zero. The maximum, of around half its previous value. occurred at
6
7
Fig. 7. The change in Co,,Fe,Mo,Si,,B,,, plotted ‘crossover’ for a reorientation
8
9
10
magnetic easy direction in as sin2/3, during polarization angle of 45’.
approximately 3.6 x 103s. It was expected to occur at = 5.4 X lo3 s, the time for K, to reach zero in region II, but the possible experimental error in K, could account for this. Fig. 6 shows the effect of annealing at 8 = 90” (region II) beyond the point where K, becomes zero and starts to increase in magnitude again, now with a t9 = 90’ easy direction. After the same time as the previous step (1.23 x 104s) the field direction was returned to 6’= 0’ for another 5.4 x 103s until K, was again zero (region III). When followed by rotational field annealing (region IV) this led to the growth and decay of an anisotropy with a 8 = 90” easy direction this time. The maximum occurred after about 5.4 x 103. Fig. 7 shows the variation of the easy direction during annealing in a field at 22.5”, after a stabilizing preanneal and anneals first at 0’ and then at 45’ until the net easy direction first became 22.5”. The data are actually presented in the form of sin’j3, rather than /?, as this is the form in which they are calculated and reduces scatter. During rotational field annealing the easy direction clearly moves towards 0” again, as predicted, reaching about 5” after 4000 s.
5. Conclusions
Fig. 6. Polarization Co,,Fe,Mo,Si,,B,,
‘crossover’ of field induced at 493 K after a three-stage
anisotropy anneal.
in
The field induced magnetic anisotropy data presented here for Co,,Fe,Mo,Si,,B,, demonstrate good agreement with the predictions of (1) in terms of the directions, rates of evolution, maxima and times for maxima during rotational field
P. D. Hodson, J. E. Evetts / Polarization
annealing (fig. 2). In addition, polarization ‘crossover’ has been demonstrated and explained for arbitrary reorientation angles of magnetic anisotropy. It is emphasised that such ‘crossover’ phenomena are a general feature of all anisotropy polarization phenomena in amorphous materials; these data simply provide evidence from magnetic anisotropy induced by field annealing. Similar results have been obtained for strain anneal induced magnetic anisotropy [ 111.
1. Acknowledgements The authors would like to thank Telcon Metals Ltd. of Manor Royal, Crawley, UK and the S.E.R.C., for whose support they are indebted, Dr. H.-R. Hilzinger, of Vacuumschmelze GmbH for the supply of material, and Professor D. Hull for the provision of Laboratory facilities.
‘crossover’ in amorphous alloys
85
References [l] J.E. Evetts and P.D. Hodson, Proc. 5th Intern. Conf. on
[2] [3] [4] [5] [6] [7] [8]
[9] [lo] [ll]
Rapidly Quenched Metals, eds. S. Steeb and H. Warlimont (North-Holland, Amsterdam, 1985) p. 671. M.R.J. Gibbs, J.E. Evetts and J.A. Leake, J. Mater. Sci. 18 (1983) 278. T. Egami, IEEE Trans. Magn. MAG-17 (1981) 2600. P.J. Flanders, T. Egami and C.D. Graham, Jr. IEEE Trans. Magn. MAG-19 (1983) 1904. H. Kronmtiller, Phys. Stat. Sol. (b) 127 (1985) 531. J.A. Leake, M.R.J. Gibbs, S. Vryenhoef and J.E. Evetts, J. Non-Cryst. Solids 61-62 (1984) 787. Vacuumschmelze GmbH data sheet. K.-Y. Ho, Q. Wang and T.-L. Sun, Proc. 5th Intern. Conf. on Rapidly Quenched Metals, eds. S. Steeb and H. Warhmont (North-Holland, Amsterdam, 1985) p. 1267. 0. Kohmoto, H. Fujishima and T. Ojima, IEEE Trans. Magn. MAG-16 (1980) 440. O.V. Nielsen, A. Hemando, V. Madurga and J.M. Gonzalez, J. Magn. Magn. Mat. 46 (1985) 341. P.D. Hodson, PhD thesis, University of Cambridge (1986).
Materials
81
59 (1986) 81-85
POLARIZATION ‘CROSSOVER’ OF FIELD INDUCED IN FERROMAGNETIC AMORPHOUS ALLOYS P.D. HODSON Department Received
ANISOTROPY
and J.E. EVETTS
of Metallurgy and Materials Science, Unioersity of Cambridge,
1 October
MAGNETIC
Pembroke Street, Cambridge,
CB-7 3QZ. UK
1985
,hB,Z during polarization ‘crossover’ are reported. Field induced magnetic anisotropy data for amorphous Co,,Fe,Mo,Si They were calculated from the magnetization energies of 12 mm diameter disk specimens cut from melt-spun ribbon. The magnitude of the anisotropy change produced and the kinetics of the change are in excellent agreement with a recent activation energy spectra model for structural polarization phenomena in amorphous metals. It is also shown that polarization ‘crossover’ can occur for any arbitrary anisotropy reorientation angle. It is expected that all other anisotropic properties of an amorphous alloy will display similar polarization ‘crossover’ phenomena.
1. Introduction Evetts and Hodson [l] presented an extension to anisotropic polarization phenomena of the Gibbs et al. activation energy spectra model for isotropic structural relaxation [2]. The amorphous structure was assumed to be initially isotropic and to change as a result of changing population densities over the energy levels of a distribution of isolated or weakly coupled Two Level Systems (TLS). The application of a polarizing ‘force’, X will alter an isotropic collection of previously equivalent equilibrated TLS in a manner that depends on the orientation angle of each TLS, $, to X. During isothermal annealing under the influence of such a polarizing force, any anisotropic property changes taking place will result from the anisotropic repopulation of individual TLS towards new local equilibria. The number density of atomic ‘processes’ available for relaxation (TLS in their upper energy state), q,(E),,,,,,, will be a function of +. Partial activation energy spectra [l] exist for every angle of TLS and will be repopulated differently as the Characteristic Annealing Function [2] sweeps across the spectrum of available atomic rearrangement processes linearly with In t in the usual way. Fig. 1 shows two of these partial spectra, for + = 0 and + = n/2. A con0304-8853/86/$03.50 Q Elsevier Science Publishers (North-Holland Physics Publishing Division)
WMBER DENSITY OF WAILABLE PROCESSES
E Fig. 1. Schematic partial processes with activation to a ‘ force’ X,
spectra of number density of available energy E for TLS at angles 0 and n/2
tinuum of partial spectra for all other angles will lie between these two extremes. One prediction to come from this model which is particularly easily tested is the detailed form of polarization ‘crossover’. This was first briefly reported by Egami [3] who described unpublished qualitative results of Flander, subsequently published in ref. [4]. The present paper reports field induced magnetic anisotropy crossover data for Co,,Fe,Mo? B.V.
82
P. D. Hodson, J. E. Eoetts / Polarization
Si,,B,2 (Vacuumschmelze GmbH ‘Vitrovac’ which support the predictions of ref. [l].
6025)
‘crossover
in amorphous crlloys
NUMBER DENSITY OF AVAILABLE PROCESSES
2. Theory Consider the effect of the application of a polarizing ‘force’ upon the development of an anisotropy. Suppose X is applied at q, to isotropic stabilized material for time t, to t, (fig. 2) and followed by annealing at the same temperature with the same magnitude of ‘force’, now at an angle of 71/2 to its previous direction until the induced anisotropy reaches zero, at t = t,. In the experiments described below, the ‘force’ was a magnetic field sufficient to saturate the specimen, and the anisotropy produced was magnetic anisotropy. It is important to emphasise that predictions can be made using fig. 1 about the rates of anisotropy evolution, irrespective of more detailed knowledge about the material. The rate of change of the number density of available atomic rearrangement processes, shown in fig. 3 (and thus of the anisotropy change, for approximately energy independent coupling constants, c(E)) should be twice as great with In t during the second step as during the first step. Fig. 3 shows the spectrum of out-of-equilibrium processes after these two anneals for just two partial spectra at 8 = 0 and 8 = n/2. The perpendicular anisotropies induced
EC
Ei
E
Fig. 3. Schematic activation energy spectra at the point of polarization ‘crossover’. The anisotropy corresponding to the low energy (dotted) processes cancels out that of the high energy (hatched) processes. to produce isotropy.
during each step (the hatched and dotted areas in fig. 3) now cancel each other out, leaving the material apparently isotropic in its magnetization energies (K sin’p + K sin2( p - a/2) = K, which is clearly isotropic). By subsequently annealing this ‘isotropic’ material in an isotropic rotating magnetic field at T,, an anisotropy should reappear in the original direction as the atomic rearrangement processes corresponding to the dotted area are regenerated and this low energy part of the spectrum becomes isotropic again. When the centre of the characteristic annealing function reaches the crossover point energy, EC, at time t,, only the
AK
AK
II ’
‘s \
A ./
c7
J t1
2
ln
t
Fig. 2. Schematic anisotropic property changes, showing In t kinetics that are twice as fast during annealing in stage II with the “force” reoriented by q/2.
Fig. 4. Schematic polarization ‘crossover’ property changes. An anisotropy develops from t, to t3 in a seemingly isotropic material under isotropic conditions.
P. D. Hodson, J. E. Evetts /
Polarization‘ ‘crossover’ in amorphous alloys
hatched q,(E) will remain, giving an anisotropy of half the previous maximum in its original direction (fig. 4). Beyond this point the anisotropy will fall again until it reaches zero when the annealing function reaches the isotropic q,(E) line again at Ei. The deviations from ‘In t kinetics’ at low energies are a consequence of the finite ‘breadth’ of the activation energy spectrum [5], while those at high energies result from the finite width of the characteristic annealing function (- kT) [6] and may thus cover up to one decade of time. It is important to note the hitherto unstated fact that polarization ‘crossover’ can occur for any reorientation angle, and that the detailed description given above for 90” is simply a special case of a more general phenomenon. For example, it would be possible to anneal in a field at 0” followed by annealing at 45” until the resultant easy axis lay along 22.5’ (only in the case of 90” reorientation can isotropy be achieved). By then annealing along this 22.5” direction, the net anisotropy should exhibit ‘crossover’ by reorientating towards 0” moving back towards again, before eventually 22.5”. Indeed, polarization ‘crossover’ would be exhibited by annealing in a field at whatever angle the resultant direction might be terminated at, during the 45” field annealing. 3. Experimental method Co,,Fe,Mo,Si,,B,, was chosen for the experimental investigation of field induced magnetic anisotropy because its saturation magnetostriction is less than 3 X lo-’ [7], making it insensitive to the stresses involved in specimen preparation. Such multicomponent cobalt-based glasses also have particularly large field induced anisotropies (e.g. up to 160 Jm-’ in Co,,,,Fe,,,Mo,B,,Si, [4]), making them easy to study. Disks of 12.5 mm diameter were cut from meltspun material supplied by Vacuumschmelze GmbH (‘Vitrovac’ 6025) using ceramic scissors to minimise the disturbance of their magnetic state. The diameter of a disk was uniform to < 2%. The, use of spark erosion was tried, but only reduced the error to 1% and led to unacceptable embrittlement even at the lowest cutting rates used. All the specimens used were first given a
83
stabilisation preanneal to remove their as-cast anisotropies (of about 40 JmP3) by annealing for 3600 s at 603 K in a rotating field of 2300 Am-‘, which was enough to overcome the demagnetizing field and saturate a specimen in an in-plane direction. These rotating fields were produced by two orthogonal sets of Helmholtz coils placed outside the non-inductively wound furnace, and driven at 50 Hz at n/2 out of phase with each other. This frequency is higher than that generally deemed necessary to prevent magnetic aftereffects in domain walls [8,9]. Annealing of carefully aligned specimens in static fields was carried out using a solenoid wound on the outside of the same furnace. All heat treatments after the initial stabilization anneal were carried out at 493 K. It should be noted that the form of the activation spectrum for as received material might already be such as to produce polarization crossover during this initial stabilisation anneal in the rotating field. This would make interpretation of subsequent behaviour very difficult. In order to eliminate this possibility, the anisotropy of each material was monitored during stabilisation. The isotropic state remained in all cases after it was attained, indicating polarization crossover effects could be discounted. The magnetic anisotropy energy density of each disk, K,, was calculated by measuring the disk’s magnetization energies at various angles to some arbitrary direction (actually that of melt-spinning). The anisotropy was assumed to be uniaxial and in-plane, magnetization energies at angles 8 being given by El = K, + K,sin2(8
- /?),
where p is the angle of the easy from 0”. By measuring the in-plane magnetization energies at 0 = O”, 45”, and 90”, the isotropic (K,) and anisotropic (K,) energy terms could be calculated, as could the easy axis direction, p. Typical experimental errors were 10 JmP3 in K, and K, and 15’ in j3. 4. Results and discussion
90’
Fig. 5 shows polarization reorientation of field
‘crossover’ data for a annealing angles. For
84
P. D. Hodson, J. E. Euetts / Polarization
‘crossouer’ in amorphous alloys
0.20-
P
0.150.100.05 -100
’
In t
Fig. 5. Field induced anisotropy changes for C0,,Fe,Mo2Si,hB,2 at 493 K, showing polarization ‘crossover’. Annealing times are expressed in seconds.
easy directions of magnetization near the 0 = 0” direction K, is classified as negative; for easy directions near 8 = 90” it is classified as positive [lo]. In region I of fig. 5 an easy axis can be seen to develop along the field direction at a rate approximately linear with In t, indicating a broad activation energy spectrum [2]. After 1.23 X lo4 s the field direction during annealing was changed to 8 = 90” (region II). The anisotropy, remaining close to 8 = O”, now decayed towards zero, again approximately linearly with In t after the expected initial transient. The rate of decrease with In t was twice as great as the rise, as predicted in fig. 2. After 5.4 X lo3 s K, reached approximately zero and the specimen displayed isotropic magnetization energies. During subsequent rotational field annealing (region III) K, increased from zero with its previous initial 8 = 0” easy direction and then decayed again towards zero. The maximum, of around half its previous value. occurred at
6
7
Fig. 7. The change in Co,,Fe,Mo,Si,,B,,, plotted ‘crossover’ for a reorientation
8
9
10
magnetic easy direction in as sin2/3, during polarization angle of 45’.
approximately 3.6 x 103s. It was expected to occur at = 5.4 X lo3 s, the time for K, to reach zero in region II, but the possible experimental error in K, could account for this. Fig. 6 shows the effect of annealing at 8 = 90” (region II) beyond the point where K, becomes zero and starts to increase in magnitude again, now with a t9 = 90’ easy direction. After the same time as the previous step (1.23 x 104s) the field direction was returned to 6’= 0’ for another 5.4 x 103s until K, was again zero (region III). When followed by rotational field annealing (region IV) this led to the growth and decay of an anisotropy with a 8 = 90” easy direction this time. The maximum occurred after about 5.4 x 103. Fig. 7 shows the variation of the easy direction during annealing in a field at 22.5”, after a stabilizing preanneal and anneals first at 0’ and then at 45’ until the net easy direction first became 22.5”. The data are actually presented in the form of sin’j3, rather than /?, as this is the form in which they are calculated and reduces scatter. During rotational field annealing the easy direction clearly moves towards 0” again, as predicted, reaching about 5” after 4000 s.
5. Conclusions
Fig. 6. Polarization Co,,Fe,Mo,Si,,B,,
‘crossover’ of field induced at 493 K after a three-stage
anisotropy anneal.
in
The field induced magnetic anisotropy data presented here for Co,,Fe,Mo,Si,,B,, demonstrate good agreement with the predictions of (1) in terms of the directions, rates of evolution, maxima and times for maxima during rotational field
P. D. Hodson, J. E. Evetts / Polarization
annealing (fig. 2). In addition, polarization ‘crossover’ has been demonstrated and explained for arbitrary reorientation angles of magnetic anisotropy. It is emphasised that such ‘crossover’ phenomena are a general feature of all anisotropy polarization phenomena in amorphous materials; these data simply provide evidence from magnetic anisotropy induced by field annealing. Similar results have been obtained for strain anneal induced magnetic anisotropy [ 111.
1. Acknowledgements The authors would like to thank Telcon Metals Ltd. of Manor Royal, Crawley, UK and the S.E.R.C., for whose support they are indebted, Dr. H.-R. Hilzinger, of Vacuumschmelze GmbH for the supply of material, and Professor D. Hull for the provision of Laboratory facilities.
‘crossover’ in amorphous alloys
85
References [l] J.E. Evetts and P.D. Hodson, Proc. 5th Intern. Conf. on
[2] [3] [4] [5] [6] [7] [8]
[9] [lo] [ll]
Rapidly Quenched Metals, eds. S. Steeb and H. Warlimont (North-Holland, Amsterdam, 1985) p. 671. M.R.J. Gibbs, J.E. Evetts and J.A. Leake, J. Mater. Sci. 18 (1983) 278. T. Egami, IEEE Trans. Magn. MAG-17 (1981) 2600. P.J. Flanders, T. Egami and C.D. Graham, Jr. IEEE Trans. Magn. MAG-19 (1983) 1904. H. Kronmtiller, Phys. Stat. Sol. (b) 127 (1985) 531. J.A. Leake, M.R.J. Gibbs, S. Vryenhoef and J.E. Evetts, J. Non-Cryst. Solids 61-62 (1984) 787. Vacuumschmelze GmbH data sheet. K.-Y. Ho, Q. Wang and T.-L. Sun, Proc. 5th Intern. Conf. on Rapidly Quenched Metals, eds. S. Steeb and H. Warhmont (North-Holland, Amsterdam, 1985) p. 1267. 0. Kohmoto, H. Fujishima and T. Ojima, IEEE Trans. Magn. MAG-16 (1980) 440. O.V. Nielsen, A. Hemando, V. Madurga and J.M. Gonzalez, J. Magn. Magn. Mat. 46 (1985) 341. P.D. Hodson, PhD thesis, University of Cambridge (1986).