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Computation of switching fields of stacked magnetic hexagonal platelet particles
Journal of Magnetism and Magnetic Materials 114 (1992) 217-223 North-Holland
Computation of switching fields of stacked magnetic hexagonal platelet particles Y. Uesaka a, Y. Nakatani b and N. Hayashi b a Central Research Lab., Hitachi Ltd., Kokubunji, Tokyo 185, Japan b University of Electra-Communications,
Chofugaoka,
Chofu, Tokyo 182, Japan
Received 19 December 1991; in revised form 10 March 1992
Switching fields of magnetic hexagonal platelet particles, which were stacked to the easy axis directions, were investigated by computer simulation. The particles had the easy axes perpendicular to the hexagonal planes. The angular dependence of the switching fields became smaller when more particles were stacked and when the particles were stacked closer together. This result is considered as one of the reasons for the small angular dependence of the remanence coercivity of a longitudinally oriented barium ferrite medium. Absence of exchange interaction between adjacent layers in a particle also reduces the angular dependence of the switching field.
1. Introduction
Although computer simulation has revealed much about the switching mechanisms and switching fields (r-i,) of cubic, rectangular and hexagonal platelet particles, little is known about the switching mechanism and the switching field (II,) of several particles which are interacting with each other. Victora [l] investigated the angular dependence of ZYswfor stacked hexagonal particles and Spratt and the present authors [2] investigated the switching mechanisms and H,, of two interacting cubic particles. We used computer simulation to precisely investigate the H, of interacting hexagonal particles when magnetic fields were applied parallel or perpendicular to the easy axis directions. We investigated how the angular dependence of the switching mechanism and H, are affected by the number of the interacting particles and by the separation between them. The easy axes of hexagonal particles are perpendicular to the hexago-
nal planes and the particles can be stacked along the easy axis directions (fig. 1) We compared these simulation results with experimentally measured results. We have previously presented and published a preliminary report of part of this work [3].
2. Calculation
conditions
The calculation method reported previously 141. The material parameters tion were as follows: M, change stiffness constant A
to: Dr. Y. Uesaka, Central Research Hitachi Ltd., Kokubunji, Tokyo 185, Japan.
0304-8853/92/$0X00
Lab.,
used for the calcula= 300 emu/cm3, ex= 0.5 x 10e6 erg/cm,
z t
Correspondence
was similar to that
X
Fig. 1. Hexagonal platelet particles stacked in the z direction. There is no exchange interaction between the particles.
0 1992 - Elsevier Science Publishers B.V. All rights reserved
218
Y. Uesaka et pl. / Switching fields of stacked magnetic hexagonal platelet particles
damping constant (Y= 1.00, gyromagnetic ratio y = 1.76 X lo7 rad/(s Oejbdiameter (length of the longest diagonal) = 1000 A, height = 100 A. The height of each particle was divided into two layers and each edge of the hexagon was divided into three d@isions. For comparison, 100 A thick and 1000 A thick single particle case: were also simulated. The height of the 1000 A thick particle was divided into ten. The time step At used for all the simulations was 10 ps. In investigating the effect of the number of the stacked particles, the separation between adjacent particles was zero; that is, there was no exchange interaction between adjacent particles. To investigate the effect of the separation between two particles, this separation was varied from 0 to 150 A. The fields were applied on the particles with fully aligned magnetization in the the easy axis directions. To reduce computation time, when we applied a field in the --z direction (0 = O”,where 0 is the angle between the applied field and the --z direction), a small field, 0.001 Oe, was applied in the x direction (the direction of one of the edges of the hexagon) [51.
3. Results
21
3
1
5
7
Number of Particles Fig. 2. Effect of particle number on switching field H,. H,(O) is the H, at 0 = 0” and H,(90) is the H, at &J= 90”.
of Co-Ti-substituted barium ferrite particles [6,7]. This discrepancy will be discussed in section 4. 3.2. Switching mechanism and field with the field applied parallel to the hard axiS direction
When a uniform field H, is applied parallel to the hard axis direction of a spherical or spheroidal particle, the magnetization component along the H, direction changes linearly with the H,. It is interesting to see if this relationship holds for a
3.1. Switching field with the field applied parallel to the easy axis direction
The effect of the number of the stacked particles on the switching fields, H,,, is shown in fig. 2 for 0 = 0” (the field is applied parallel to the --z direction), Here, the separation between two adjacent particles is zero. H, increases with the number of stacked particles, and the rate of increase decreases as the number of particles becomes larger. The effect of separation between two interacting hexagonal particles on H, is shown in fig. 3, also for fields applied parallel to the -z direction. Hs,,, decreased by only slightly more than 1% when the separation was increased from 0 to 150 A. The H, values shown in figs. 2 and 3 are greater than 2000 Oe and are much larger than the coercivity, H,, or remanence coercivity, H,,
0
50
Separation
100
1
(A)
Fig. 3. Effect of particle separation between two particles on H,(O) is the H, at 0 = 0” and H,@O) is the H,, at 8=90”.
H,.
219
Y. Uesaka et al. / Switching fields of stacked magnetic hexagonal platelet particles
coherent rotation 90 30 60 Angle (degrees)
Hx (kOe) Fig. 4. Average magnetizations in the x and z directions when the field is applied in the x direction.
non-spherical or non-spheroidal particle such as a hexagonal particle. The average magnetizations in the hard axis direction (the x direction which is parallel to one of the edges of the hexagon; see fig. l), and in the easy axis direction (the z direction which is perpendicular to the hexagonal plane; see fig. 11, HX and a*, are shown in fig. 4, when the field is applied in the x direction. The height of the particle here is 1000 A, so we can ignore the shape anisotropy effect on I&,,. aX does not saturate even with an H, of 10 kOe, which is much higher than H, (Hk = 2 Ku/MS = 5 kOe, where K, is the uniaxial crystalline magnetic anisotropy constant). However, HZ abruptly falls to 0 at 4700 Oe, which is a little smaller value than H,. This means that, at that field, half the magnetic moments in the particle have negative z components and the rest have positive z components. The field at which fiZ abruptly falls to 0 for a non-spheroidal particle, is called I&,(90). Similar switching phenomena also occur in the stacked particles. The effect of the number of the stacked particles on I&(90) is shown in fig. 2, and the effect of the separation between two stacked particles is shown in fig. 3. The effect of the particle interaction on Z&,(90) is similar to the effect on H,(O). One might expect that I&(90) should reduce with increasing the number of the stacked platelets due to the negative
Fig. 5. Effect of the number of the stacked particles on the angular dependence of H,.
interaction between the magnetizations of the particles in the x direction. But the computational result is opposite to this expectation. The reason why I&,(90) increases with particle stacking can be explained as follows. The change in HZ is much larger than the change in aX at I&,(90). This could mean that H,(90) is more related to M, than to M,. On the other hand, the interaction between the magnetizations of the particles in the z direction is positive even when the field is applied to the x direction, though the
0
30
60
90
Angle (degrees) Fig. 6. Effect of separation between two particles on the angular dependence of H,. The angular dependence of H, of the single particle (height = 100 A) is also shown.
220
Y. Uesaka et-al. / Switching fields of stacked magnetic hexagonal platelet particles
3.3. Angular dependence of the switching field and switching mechanism
1.06 -0.017
Fig. 7. Distribution of magnetic moments in the transition region for a single particle with the fields applied at 0”, 15”, 45” and 90” in the transition regions (at Mz - 0).
interaction between the magnetizations of the particles in the x direction is negative. Therefore the Z&(90) increases with particle stacking.
The effect of the number of the stacked particles on the angular dependences of the H, is shown in fig. 5. 8 is the angle measured from the --z direction. The H, is the field when a, switches to a negative value or zero (ii?, switches to a negative value except at 8 = 900). The separation between adjacent particles is zero. The effect of the particle separation between the two interacting particles on the angular dependence of H, is shown in fig. 6. The vertical axes in figs. 5 and 6 are the H,_, normalized by the H,, at 0 = 0”. Increasing the number of interacting particles and decreasing the separation between them decreases the angular dependence of H,, except at 13= 90” (figs. 5 and 6). The angular dependence of the H,, of the 100 A thick single particle is similar to the angular dependence calculated from the analytically deParticle
I’. Vesaka et al. / Switching folds of stacked magnetic hexagonal platelet particles
rived coherent rotation mode. To reveal the reason for the similarity, we simulated the switching process at several 8 angles. The distribution of the magnetic moments in the transition regions are shown in fig. 7. At 8 = O”, the switching occurs in the crater mode. As the field is tilted from the easy axis direction to the hard axis direction, the switching mechanism changes from the crater to the coherent rotation mode. In the crater mode, no vortex structures are observed and the magnetic moments of the central part of the hexagon switch earlier than the magnetic moments at the edges [S]. The vortex structure is not observed in the coherent rotation mode, either. The resemblance between the coherent rotation and the crater modes is considered to cause the coincidence between the angular dependence obtained from the simulation and the dependence analytically derived from the coherent rotation mode. The distributions of the magnetic moments of four stacked particles at 8 = 0” are shown in fig. 8 and at 0 = 45 o in fig. 9. The switchings occur from edges of the hexagons of the top and bottom particles in both cases. It is not clear in this stage why the angular dependence of H,, of the stacked particles is smaller than that of the single particle.
4. Discussion The measured angular dependence of the iY, of a longitudinally oriented barium ferrite medium is shown in fig. 10. The H, here corresponds to H,,. The angular dependence of the H, is small, especially at small 0. This is similar to the angular dependence of H, for eight stacked particles shown in fig. 5, though, the angular dependence of H, at small 8 is smaller than that shown in fig. 5. In a longitudinally oriented barium ferrite medium, more than 10 particles are stacked in the easy axis directions (fig. 11). We therefore think that the stacking of the particles in the easy axis directions is one of the reasons for the small angular dependence of H, of the barium ferrite medium.
221
Angle (degrees) Fig. 10. Measured angular dependence nally oriented barium ferrite medium wt%).
of H, of a longitudi(packing fraction is 75
In Co-Ti-substituted barium ferrite, some of the Fe atoms are substituted by Co or Ti atoms. This substitution can diminish the exchange interaction between some layers. Consequently, we also investigated the angular dependence cf H,, for particles in which there were no exchange interactions between some of the adjacent xy layers (hexagon+ planes). The height of the particles were 200 A. The height was divided into 8 when the number of layers without exchange interaction was one or three, and divided into fourteen when the number was six. The result is shown in fig. 12. It is understood from the figure
Fig.
11. SEM
picture
of a longitudinally ferrite medium.
oriented
barium
222
Y. Uesaka et al. / Switching fields of stacked magnetic hexagonal platelet particles
the discrepancy between the H, at 8 = 0” derived by the simulation and the experimentally derived H, at 8 = 0”. However, H,, decreases with increasing number of non-exchange-interacting adjacent layers in a particle (fig. 13). This is another reason for us to believe that the adjacent layers with little or no exchange interaction affect magnetic properties of a Co-Ti-substituted barium ferrite medium.
5. Conclusion
0
30 60 Angle (degrees)
90
Fig. 12. Effect of the number of non-interacting adjacent layers (without exchange interaction) on the angular dependence of H,,.
that the angular dependence of H, becomes smaller as the number of adjacent layers without exchange interaction increases. We therefore conclude that these non-interacting adjacent layers are another reason for the small angular dependence of a longitudinally oriented barium ferrite medium. The H, of a barium ferrite medium and the H, at 13= 0” derived by simulation of a single hexagonal particle do not coincide with each other: the H, value at 8 = 0” is 995 Oe (fig. 10) but the H, at 6 = 0” is 2325 Oe (fig. 2). As the number of the stacked particles increases, H, increases (fig. 21, that is, the stacking increases
The H,, of stacked hexagonal particles were simulated. The Hsw at 8 = 0” increases with increasing number of stacked particles. When the field is applied to the hard axis direction (X direction), the average magnetization in that direction does not saturate even when a field twice the H, is applied. The average magnetization in the z direction, however, abruptly falls to 0 when the applied field is a little smaller than Hk. The angular dependence of H, decreases with increasing positive interaction (that is, with increasing numbers of stacked particles and with decreasing distance between adjacent particles). This is considered one of the reasons for the small angular dependence of H, of a longitudinally oriented barium ferrite medium. Adjacent layers in a particle without exchange interaction between them also decrease the angular dependence of H,,. The H, at 8 = 0” derived from the simulation was much larger than the H, derived experimentally. Increasing number of non-exchange-interacting adjacent layers decreases the H,, at 0 = 0”.
Acknowledgements
2-o[, Number of Separation Layers Fig. 13. Effect of the number of non-interacting adjacent layers (without exchange interaction) on H, at 0 = 0”.
The authors thank Dr. G.W. Spratt of Carnegie Mellon University for stimulating discussions and for measuring the magnetic properties of the longitudinally oriented barium ferrite medium. They, also thank Mr. N. Kodama at Hitachi Odawara Works for valuable discussions and taking SEM photographs of the medium. They are grateful to Dr. M. Katsumoto and Mr. H. Jnoue
Y. Uesaka et al. / Switching fields of stacked magnetic hexagonal platelet particles
at Hitachi Odawara Works for making the barium ferrite medium.
References [l] R. Victora, J. Appl. Phys. 63 (1988) 3423. [2] G.W. Spratt, Y. Uesaka, Y. Nakatani and N. Hayashi, IEEE Trans. Magn. MAG-27 (1991) 4790.
223
[3] Y. Uesaka, Y. Nakatani and N. Hayashi, Digests 15th Ann. Conf. on Magnetics in Japan (1991) 284. [4] Y. Nakatani, N. Hayashi and Y. Uesaka, Jpn. J. Appl. Phys. 30 (1991) 2503. [5] Y. Nakatani, Y. Uesaka and N. Hayashi, Jpn. J. Appl. Phys. 28 (1989) 2485. [6] D. Speliotis, IEEE Trans Magn. MAG-23 (1987) 3143. [7] G.W. Spratt, N. Kodama, H. Inoue, Y. Uesaka, and M. Katsumoto, IEEE Trans. Magn. MAG-27 (1991) 4660. [8] Y. Uesaka, Y. Nakatani and N. Hayashi, Jpn. J. Appl. Phys. 30 (1991) 2489.
Computation of switching fields of stacked magnetic hexagonal platelet particles Y. Uesaka a, Y. Nakatani b and N. Hayashi b a Central Research Lab., Hitachi Ltd., Kokubunji, Tokyo 185, Japan b University of Electra-Communications,
Chofugaoka,
Chofu, Tokyo 182, Japan
Received 19 December 1991; in revised form 10 March 1992
Switching fields of magnetic hexagonal platelet particles, which were stacked to the easy axis directions, were investigated by computer simulation. The particles had the easy axes perpendicular to the hexagonal planes. The angular dependence of the switching fields became smaller when more particles were stacked and when the particles were stacked closer together. This result is considered as one of the reasons for the small angular dependence of the remanence coercivity of a longitudinally oriented barium ferrite medium. Absence of exchange interaction between adjacent layers in a particle also reduces the angular dependence of the switching field.
1. Introduction
Although computer simulation has revealed much about the switching mechanisms and switching fields (r-i,) of cubic, rectangular and hexagonal platelet particles, little is known about the switching mechanism and the switching field (II,) of several particles which are interacting with each other. Victora [l] investigated the angular dependence of ZYswfor stacked hexagonal particles and Spratt and the present authors [2] investigated the switching mechanisms and H,, of two interacting cubic particles. We used computer simulation to precisely investigate the H, of interacting hexagonal particles when magnetic fields were applied parallel or perpendicular to the easy axis directions. We investigated how the angular dependence of the switching mechanism and H, are affected by the number of the interacting particles and by the separation between them. The easy axes of hexagonal particles are perpendicular to the hexago-
nal planes and the particles can be stacked along the easy axis directions (fig. 1) We compared these simulation results with experimentally measured results. We have previously presented and published a preliminary report of part of this work [3].
2. Calculation
conditions
The calculation method reported previously 141. The material parameters tion were as follows: M, change stiffness constant A
to: Dr. Y. Uesaka, Central Research Hitachi Ltd., Kokubunji, Tokyo 185, Japan.
0304-8853/92/$0X00
Lab.,
used for the calcula= 300 emu/cm3, ex= 0.5 x 10e6 erg/cm,
z t
Correspondence
was similar to that
X
Fig. 1. Hexagonal platelet particles stacked in the z direction. There is no exchange interaction between the particles.
0 1992 - Elsevier Science Publishers B.V. All rights reserved
218
Y. Uesaka et pl. / Switching fields of stacked magnetic hexagonal platelet particles
damping constant (Y= 1.00, gyromagnetic ratio y = 1.76 X lo7 rad/(s Oejbdiameter (length of the longest diagonal) = 1000 A, height = 100 A. The height of each particle was divided into two layers and each edge of the hexagon was divided into three d@isions. For comparison, 100 A thick and 1000 A thick single particle case: were also simulated. The height of the 1000 A thick particle was divided into ten. The time step At used for all the simulations was 10 ps. In investigating the effect of the number of the stacked particles, the separation between adjacent particles was zero; that is, there was no exchange interaction between adjacent particles. To investigate the effect of the separation between two particles, this separation was varied from 0 to 150 A. The fields were applied on the particles with fully aligned magnetization in the the easy axis directions. To reduce computation time, when we applied a field in the --z direction (0 = O”,where 0 is the angle between the applied field and the --z direction), a small field, 0.001 Oe, was applied in the x direction (the direction of one of the edges of the hexagon) [51.
3. Results
21
3
1
5
7
Number of Particles Fig. 2. Effect of particle number on switching field H,. H,(O) is the H, at 0 = 0” and H,(90) is the H, at &J= 90”.
of Co-Ti-substituted barium ferrite particles [6,7]. This discrepancy will be discussed in section 4. 3.2. Switching mechanism and field with the field applied parallel to the hard axiS direction
When a uniform field H, is applied parallel to the hard axis direction of a spherical or spheroidal particle, the magnetization component along the H, direction changes linearly with the H,. It is interesting to see if this relationship holds for a
3.1. Switching field with the field applied parallel to the easy axis direction
The effect of the number of the stacked particles on the switching fields, H,,, is shown in fig. 2 for 0 = 0” (the field is applied parallel to the --z direction), Here, the separation between two adjacent particles is zero. H, increases with the number of stacked particles, and the rate of increase decreases as the number of particles becomes larger. The effect of separation between two interacting hexagonal particles on H, is shown in fig. 3, also for fields applied parallel to the -z direction. Hs,,, decreased by only slightly more than 1% when the separation was increased from 0 to 150 A. The H, values shown in figs. 2 and 3 are greater than 2000 Oe and are much larger than the coercivity, H,, or remanence coercivity, H,,
0
50
Separation
100
1
(A)
Fig. 3. Effect of particle separation between two particles on H,(O) is the H, at 0 = 0” and H,@O) is the H,, at 8=90”.
H,.
219
Y. Uesaka et al. / Switching fields of stacked magnetic hexagonal platelet particles
coherent rotation 90 30 60 Angle (degrees)
Hx (kOe) Fig. 4. Average magnetizations in the x and z directions when the field is applied in the x direction.
non-spherical or non-spheroidal particle such as a hexagonal particle. The average magnetizations in the hard axis direction (the x direction which is parallel to one of the edges of the hexagon; see fig. l), and in the easy axis direction (the z direction which is perpendicular to the hexagonal plane; see fig. 11, HX and a*, are shown in fig. 4, when the field is applied in the x direction. The height of the particle here is 1000 A, so we can ignore the shape anisotropy effect on I&,,. aX does not saturate even with an H, of 10 kOe, which is much higher than H, (Hk = 2 Ku/MS = 5 kOe, where K, is the uniaxial crystalline magnetic anisotropy constant). However, HZ abruptly falls to 0 at 4700 Oe, which is a little smaller value than H,. This means that, at that field, half the magnetic moments in the particle have negative z components and the rest have positive z components. The field at which fiZ abruptly falls to 0 for a non-spheroidal particle, is called I&,(90). Similar switching phenomena also occur in the stacked particles. The effect of the number of the stacked particles on I&(90) is shown in fig. 2, and the effect of the separation between two stacked particles is shown in fig. 3. The effect of the particle interaction on Z&,(90) is similar to the effect on H,(O). One might expect that I&(90) should reduce with increasing the number of the stacked platelets due to the negative
Fig. 5. Effect of the number of the stacked particles on the angular dependence of H,.
interaction between the magnetizations of the particles in the x direction. But the computational result is opposite to this expectation. The reason why I&,(90) increases with particle stacking can be explained as follows. The change in HZ is much larger than the change in aX at I&,(90). This could mean that H,(90) is more related to M, than to M,. On the other hand, the interaction between the magnetizations of the particles in the z direction is positive even when the field is applied to the x direction, though the
0
30
60
90
Angle (degrees) Fig. 6. Effect of separation between two particles on the angular dependence of H,. The angular dependence of H, of the single particle (height = 100 A) is also shown.
220
Y. Uesaka et-al. / Switching fields of stacked magnetic hexagonal platelet particles
3.3. Angular dependence of the switching field and switching mechanism
1.06 -0.017
Fig. 7. Distribution of magnetic moments in the transition region for a single particle with the fields applied at 0”, 15”, 45” and 90” in the transition regions (at Mz - 0).
interaction between the magnetizations of the particles in the x direction is negative. Therefore the Z&(90) increases with particle stacking.
The effect of the number of the stacked particles on the angular dependences of the H, is shown in fig. 5. 8 is the angle measured from the --z direction. The H, is the field when a, switches to a negative value or zero (ii?, switches to a negative value except at 8 = 900). The separation between adjacent particles is zero. The effect of the particle separation between the two interacting particles on the angular dependence of H, is shown in fig. 6. The vertical axes in figs. 5 and 6 are the H,_, normalized by the H,, at 0 = 0”. Increasing the number of interacting particles and decreasing the separation between them decreases the angular dependence of H,, except at 13= 90” (figs. 5 and 6). The angular dependence of the H,, of the 100 A thick single particle is similar to the angular dependence calculated from the analytically deParticle
I’. Vesaka et al. / Switching folds of stacked magnetic hexagonal platelet particles
rived coherent rotation mode. To reveal the reason for the similarity, we simulated the switching process at several 8 angles. The distribution of the magnetic moments in the transition regions are shown in fig. 7. At 8 = O”, the switching occurs in the crater mode. As the field is tilted from the easy axis direction to the hard axis direction, the switching mechanism changes from the crater to the coherent rotation mode. In the crater mode, no vortex structures are observed and the magnetic moments of the central part of the hexagon switch earlier than the magnetic moments at the edges [S]. The vortex structure is not observed in the coherent rotation mode, either. The resemblance between the coherent rotation and the crater modes is considered to cause the coincidence between the angular dependence obtained from the simulation and the dependence analytically derived from the coherent rotation mode. The distributions of the magnetic moments of four stacked particles at 8 = 0” are shown in fig. 8 and at 0 = 45 o in fig. 9. The switchings occur from edges of the hexagons of the top and bottom particles in both cases. It is not clear in this stage why the angular dependence of H,, of the stacked particles is smaller than that of the single particle.
4. Discussion The measured angular dependence of the iY, of a longitudinally oriented barium ferrite medium is shown in fig. 10. The H, here corresponds to H,,. The angular dependence of the H, is small, especially at small 0. This is similar to the angular dependence of H, for eight stacked particles shown in fig. 5, though, the angular dependence of H, at small 8 is smaller than that shown in fig. 5. In a longitudinally oriented barium ferrite medium, more than 10 particles are stacked in the easy axis directions (fig. 11). We therefore think that the stacking of the particles in the easy axis directions is one of the reasons for the small angular dependence of H, of the barium ferrite medium.
221
Angle (degrees) Fig. 10. Measured angular dependence nally oriented barium ferrite medium wt%).
of H, of a longitudi(packing fraction is 75
In Co-Ti-substituted barium ferrite, some of the Fe atoms are substituted by Co or Ti atoms. This substitution can diminish the exchange interaction between some layers. Consequently, we also investigated the angular dependence cf H,, for particles in which there were no exchange interactions between some of the adjacent xy layers (hexagon+ planes). The height of the particles were 200 A. The height was divided into 8 when the number of layers without exchange interaction was one or three, and divided into fourteen when the number was six. The result is shown in fig. 12. It is understood from the figure
Fig.
11. SEM
picture
of a longitudinally ferrite medium.
oriented
barium
222
Y. Uesaka et al. / Switching fields of stacked magnetic hexagonal platelet particles
the discrepancy between the H, at 8 = 0” derived by the simulation and the experimentally derived H, at 8 = 0”. However, H,, decreases with increasing number of non-exchange-interacting adjacent layers in a particle (fig. 13). This is another reason for us to believe that the adjacent layers with little or no exchange interaction affect magnetic properties of a Co-Ti-substituted barium ferrite medium.
5. Conclusion
0
30 60 Angle (degrees)
90
Fig. 12. Effect of the number of non-interacting adjacent layers (without exchange interaction) on the angular dependence of H,,.
that the angular dependence of H, becomes smaller as the number of adjacent layers without exchange interaction increases. We therefore conclude that these non-interacting adjacent layers are another reason for the small angular dependence of a longitudinally oriented barium ferrite medium. The H, of a barium ferrite medium and the H, at 13= 0” derived by simulation of a single hexagonal particle do not coincide with each other: the H, value at 8 = 0” is 995 Oe (fig. 10) but the H, at 6 = 0” is 2325 Oe (fig. 2). As the number of the stacked particles increases, H, increases (fig. 21, that is, the stacking increases
The H,, of stacked hexagonal particles were simulated. The Hsw at 8 = 0” increases with increasing number of stacked particles. When the field is applied to the hard axis direction (X direction), the average magnetization in that direction does not saturate even when a field twice the H, is applied. The average magnetization in the z direction, however, abruptly falls to 0 when the applied field is a little smaller than Hk. The angular dependence of H, decreases with increasing positive interaction (that is, with increasing numbers of stacked particles and with decreasing distance between adjacent particles). This is considered one of the reasons for the small angular dependence of H, of a longitudinally oriented barium ferrite medium. Adjacent layers in a particle without exchange interaction between them also decrease the angular dependence of H,,. The H, at 8 = 0” derived from the simulation was much larger than the H, derived experimentally. Increasing number of non-exchange-interacting adjacent layers decreases the H,, at 0 = 0”.
Acknowledgements
2-o[, Number of Separation Layers Fig. 13. Effect of the number of non-interacting adjacent layers (without exchange interaction) on H, at 0 = 0”.
The authors thank Dr. G.W. Spratt of Carnegie Mellon University for stimulating discussions and for measuring the magnetic properties of the longitudinally oriented barium ferrite medium. They, also thank Mr. N. Kodama at Hitachi Odawara Works for valuable discussions and taking SEM photographs of the medium. They are grateful to Dr. M. Katsumoto and Mr. H. Jnoue
Y. Uesaka et al. / Switching fields of stacked magnetic hexagonal platelet particles
at Hitachi Odawara Works for making the barium ferrite medium.
References [l] R. Victora, J. Appl. Phys. 63 (1988) 3423. [2] G.W. Spratt, Y. Uesaka, Y. Nakatani and N. Hayashi, IEEE Trans. Magn. MAG-27 (1991) 4790.
223
[3] Y. Uesaka, Y. Nakatani and N. Hayashi, Digests 15th Ann. Conf. on Magnetics in Japan (1991) 284. [4] Y. Nakatani, N. Hayashi and Y. Uesaka, Jpn. J. Appl. Phys. 30 (1991) 2503. [5] Y. Nakatani, Y. Uesaka and N. Hayashi, Jpn. J. Appl. Phys. 28 (1989) 2485. [6] D. Speliotis, IEEE Trans Magn. MAG-23 (1987) 3143. [7] G.W. Spratt, N. Kodama, H. Inoue, Y. Uesaka, and M. Katsumoto, IEEE Trans. Magn. MAG-27 (1991) 4660. [8] Y. Uesaka, Y. Nakatani and N. Hayashi, Jpn. J. Appl. Phys. 30 (1991) 2489.