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Quadrupolar interaction in metal particulate recording media
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Journal of Magnetism and Magnetic Materials 231 (2001) 347–354
Quadrupolar interaction in metal particulate recording media Yasuo Tateno* Recording Media Company, Sony Corporation, 3-4-1 Sakuragi, Tagajo-shi, Miyagi-ken 985-0842, Japan Received 1 September 2000; received in revised form 9 January 2001
Abstract Interparticle interactions in metal particulate recording media were studied by experiments. A new analysis method to evaluate the magnetic interactions in the media is considered. In the present paper, differences between the normalized DC demagnetization remanence and isothermal remanent magnetization curves are interpreted as a deviation of the magnetic switching field, that is the magnetic interaction field, dH. The parameter dH is confirmed to be useful in evaluating quantitatively the interparticle interaction in the media. The magnetic anisotropy constant derived from the interparticle interaction can be obtained from the angular dependence of the magnetic interaction field, dH. As a result, it is found that quadrupolar interactions play a remarkably important role in the origin of the magnetic anisotropy in metal particulate media. The magnetic anisotropy energy derived from the interparticle interaction is useful in discussing the thermal stability of the media’s recorded pattern. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Metal particles; Remanence curve; Quadrupolar interaction; Magnetic anisotropy; Thermal stability
1. Introduction Usually, interparticle interactions in the recording media have been investigated by means of Henkel plot and dM plot methods [1,2]. It is well known that metal particulate media (MP tape), which use acicular metal particles, have negative (demagnetizing-like) interactions in the direction of the particle’s orientation [3,4]. Also it has been reported that other acicular particulate media, such as g-Fe2O3, Co-modified g-Fe2O3 and CrO2, show negative interactions [5,6]. However, Baferrite particulate media, which consist of fine hexagonal platelet particles, display the positive (magnetizing-like) interactions in the easy axis *Tel.: +81-22-367-2629; fax: +81-22-367-2725. E-mail address: [email protected] (Y. Tateno).
direction [7,8]. The polarity of the interparticle interactions in particulate media is considered to be associated with the particle shape. However, the origin of the negative interaction in metal particulate media has not been understood clearly. The purpose of this study is to make clear the cause of the negative interactions along the easy axis direction in the metal particulate media. The usual method to evaluate the magnetic interaction in the media is comparing two kinds of remanence curves, DC demagnetization remanence (DCD) and isothermal remanent magnetization (IRM) curves [9]. Due to the magnetic interaction fields in the media, normalized DCD and IRM curves are not always consistent [1]. Usually, the discrepancy between the remanence curves is interpreted as a deviation of the remanent magnetization, dM [2].
0304-8853/01/$ - see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 1 ) 0 0 1 5 7 - 3
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In this paper, a new analysis method is considered from a different point of view. The difference between the remanence curves is interpreted as a deviation of the magnetic switching field. Such deviation is the magnetic interaction field, dH, which is newly defined in the present study. General characteristics of the interparticle interactions in the media are revealed with the angular dependence of the interaction field, dH, from which the magnetic anisotropy constant can also be obtained. The magnetic anisotropy energy derived from the interparticle interaction is useful in discussing the thermal stability of the media’s recorded pattern.
netizing field is equal to 4pM sin2y. The magnetic layer of MP tape is assumed to be a thin film in this case. The basis of this assumption is that the magnetic interactions derived from the static fields are long-range interaction. In the present study, only the applied field direction components of the remanent magnetization and the interaction field are considered. This is an approximation in order to carry out the experiments systematically. To investigate the angular dependence of the interaction fields is useful for reducing the systematic error derived from the simple assumption.
3. Theory 2. Experiments The measured sample is commercially available 8 mm MP tape, which consists of acicular particles whose average length and aspect ratio are 0.18 mm and 9.0, respectively. DCD and IRM curves were measured using a vibrating sample magnetometer (VSM) in several directions in the plane which is normal to the media plane and along a head scanning direction. Measurement angles were y=08, 308, 608 and 908 between the applied field direction and the media plane. The angular dependence of the remanence curves is assumed to be symmetrical about the direction along the media plane (y=08). AC demagnetizing fields for IRM curve measurements were applied in the direction along a hard magnetization axis of the media, in which the media exhibit broad switching field distribution. In this case, AC demagnetized states are independent of the switching field distribution in each measurement direction. According to the Preisach hysteresis model studies, it is pointed out that the AC demagnetized states affect the interparticle interactions in the media [10,11]. In this study, the AC demagnetized states by AC fields along the hard axis are assumed to be approximately equivalent to a thermally demagnetized states in the Preisach plane [11]. In each measurement, the demagnetizing field was compensated at each measurement point based on the simple assumption that the demag-
Magnetic interactions in the media are usually evaluated by the Henkel plot and the dM plot methods [1,2]. In these methods, the remanent magnetization, M, is regarded as a function of the magnetic field, H. Then DCD and IRM curves, which are normalized to saturation remanence, are represented as MDCD ðHÞ and MIRM ðHÞ, respectively. MDCD ðHÞ varies from +1.0 to 1.0, and MIRM ðHÞ varies from 0 to +1.0 with increasing magnetic field, H. The modified function, [1MDCD(H)]/2, which varies from 0 to +1.0, can be compared directly with MIRM ðHÞ. When magnetic interactions are absent in the media, the relation between MDCD ðHÞ and MIRM ðHÞ is expressed by Wohlfarth as follows [12]: MDCD ðHÞ ¼ 122 MIRM ðHÞ:
ð1Þ
This relation means that the function [1MDCD(H)]/2 is completely consistent with MIRM ðHÞ. On the other hand, when magnetic interactions are present in the media, the relation between MDCD ðHÞ and MIRM ðHÞ is expressed by Kelly et al. as follows [2]: MDCD ðHÞ ¼ 122 MIRM ðHÞ þ dMðHÞ:
ð2Þ
This relation means that the discrepancy between the functions, [1MDCD(H)]/2 and MIRM ðHÞ, is defined as dMðHÞ=2. The dM plot method, however, fails when the remanence curve shows overhang, which is found often in perpendicular media [13], because the
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Y. Tateno / Journal of Magnetism and Magnetic Materials 231 (2001) 347–354
remanence curves have negative dM/dH; in other words, the relation between the remanence curve and the magnetic field is not a one-to-one correspondence. It is pointed out in a later section that the remanence curves of the metal particulate media show these overhangs in some cases. As is well known, the Preisach hysteresis model is also a useful tool for describing the magnetic interactions in the media [14–16]. However, the same problem as the dM plots lies in the Preisach model. The negative dM/dH is a cause of trouble not only in the dM plots but also in the Preisach model [17]. Future subjects seem to lie in this region, though it is outside the scope of the present paper. In this paper, a new analysis method is considered from a different point of view. The difference between the remanence curves is interpreted as a deviation of the magnetic switching field, that is the interaction field, dH [18]. The usual parameter to represent the magnetic switching field in the media is the remanence coercivity. Therefore, it is reasonable to express the interaction field, dH, as the difference between two kinds of remanence coercivities, Hr and Ha , which are obtained from the DCD and IRM curves, respectively. In this paper, dH is defined as dH ¼ Hr 2Ha . Hr is independent of the interaction field because it is obtained at the normalized magnetization, MDCD ¼ 0, while Ha is affected by the interaction field because it is obtained at MIRM ¼ 0:5 [9]. Then, the magnetic interaction in the media can be evaluated by the parameter dH. In this method, the remanence curve is regarded as a function of the normalized remanent magnetization, M, which varies from 0 to +1.0. DCD and IRM curves are represented as HDCD ðMÞ and HIRM ðMÞ, respectively. The relations between HDCD ðMÞ, HIRM ðMÞ and dH are expressed phenomenologically as follows based on the assumption that the magnetic interaction field is proportional to the normalized remanent magnetization, M [18–20]. HDCD ðMÞ ¼ H0 ðMÞ22ð2M21Þ dH;
ð3Þ
HIRM ðMÞ ¼ H0 ðMÞ22M dH;
ð4Þ
dH ¼ Hr 2Ha :
ð5Þ
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H0 ðMÞ is an intrinsic remanence curve, which is hypothetical remanence curve obtained after compensating for the interaction field correspond to the value of M from 0 to +1.0. In this method, the relation between the remanence curve and the remanent magnetization is one-to-one correspondence even when the remanence curve shows overhang. The magnetic anisotropy constant can be obtained from the angular dependence of the interaction field, dHðyÞ. The angular dependence of magnetic anisotropy energy, EðyÞ, which corresponds to the saturation magnetization, MS , is expressed as follows using an interaction field factor, NInt: ðyÞ, which is defined in this paper as dHðyÞ divided by the remanent magnetization, MðyÞ, at each measurement point. NInt: ðyÞ ¼ dHðyÞ=4pMðyÞ;
ð6Þ
EðyÞ ¼ 22pMS2 NInt: ðyÞ:
ð7Þ
The interaction field factor, NInt: ðyÞ, which is different than the conventional one which was introduced by Corradi and Wohlfarth [21], is rather equivalent to the mean interaction field factor, a, introduced by Atherton and Beattie on the basis of the mean field theory [19] . The newly defined interaction field factor, NInt: ðyÞ, is useful in estimating the interaction field at any magnetization value. As a result, the magnetic anisotropy energy which can be compared with that obtained from the torque measurement method can be obtained from the angular dependence of the interaction field, dHðyÞ, which is obtained from the minor loop magnetization process. In general, the thermal stability of the magnetization in the media is associated with the magnetic anisotropy energy of each magnetic particle in the media. The interparticle interactions also play an important role on this point. Therefore, the magnetic anisotropy energy derived from the interparticle interaction should be useful in discussing the thermal stability of the media’s recorded pattern [22].
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Fig. 2. Angular dependence of the remanence coercivities, Hr and Ha .
Fig. 1. Angular dependence of the remanence curves, DCD and IRM curves (y=08, 308, 608, 908).
4. Results and discussion Normalized DCD and IRM curves in each direction are shown in Fig. 1. In all of the measurement directions, the DCD and IRM curves are not consistent. In the cases of y ¼ 08 and 908, the switching fields of the IRM curves are larger than those of the DCD curves because of the negative (demagnetizing-like) interactions, as is well known. On the contrary, in the cases of y ¼ 308 and 608, the switching fields of the IRM curves
are smaller than those of the DCD curves, and the IRM curves exhibit overhangs because of the positive (magnetizing-like) interactions. It is to be noted that the remanence curve occasionally shows an overhang even in a longitudinal media. This fact is revealed with the study of the angular dependence of the remanence curves. The angular dependence of Hr and Ha is shown in Fig. 2. Hr has a minimum at y ¼ 08, which is the intrinsic easy magnetization axis direction obtained from the torque measurement method. The angular dependence of Ha is considerably different from that of Hr . Ha at y ¼ 08 is larger than Hr in that direction because of the negative interaction, and Ha at y ¼ 308 and 608 are smaller than Hr in those directions because of the positive interaction. As a result, Ha has a minimum at y ¼ 308. These results imply that the direction of the easy axis in the minor loop magnetization process is not always the same as that in the major loop magnetization process because of the interparticle interaction in the media. The angular dependence of the interaction field, dH, is shown in Fig. 3. dH at y ¼ 308 and 608 are positive, +140 and +210 Oe, respectively. dH at y ¼ 08 and 908 are negative, –100 and –220 Oe, respectively. Apparently, the angular dependence of the interaction field, dH, includes not only sin 2y component but also sin 4y component.
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Fig. 3. Angular dependence of the interaction field, dHðyÞ.
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Fig. 4. Angular dependence of the interaction field factor, NInt.(y). (empirical fitting by the Legendre polynominal).
equation of the curve is as follows: In the case of metal particulate media, which is a typical perfectly isolated particles system, the magnetic interaction fields in the media are derived from the dipole–dipole interactions. If the arrangement of the particles in the media has a cubic symmetry, the dipole–dipole interactions would cancel each other. However, the arrangement of the oriented acicular particles does not seem to exhibit the cubic symmetry in the media. Therefore, MP tape would show the magnetic anisotropy derived from the interparticle interactions. In the case of the dipole–dipole interactions, the angular dependence of the interaction field can be expressed by a Legendre polynominal [23]. Judging from the experimental data shown in Fig. 3, not only the second term, P2 ðcos yÞ, but also the fourth term, P4 ðcos yÞ, are necessary to express the angular dependence of the interaction field in the media. P2 ðcos yÞ and P4 ðcos yÞ are defined as follows: P2 ðcos yÞ ¼ ð1=2Þð3 cos2 y21Þ;
ð8Þ
P4 ðcos yÞ ¼ ð1=8Þð35 cos4 y230 cos2 y þ 3Þ:
ð9Þ
Fig. 4 shows the angular dependence of the interaction field factor, NInt: ðyÞ, and the best fitting curve by the Legendre polynominal. The empirical
NInt: ðyÞ ¼ þ0:05 þ 0:19 P2 ðcos yÞ20:33 P4 ðcos yÞ: ð10Þ The second term, P2 ðcos yÞ, and the fourth term, P4 ðcos yÞ, represent the components of dipolar interactions and quadrupolar interactions, respectively. The positive sign of the second term is a result of the contribution of end-to-end particle pairs in the media. The negative sign of the fourth term is derived from the contribution of adjacent particle pairs. The most important fact shown by the empirical equation (10) is that the contribution of the fourth term is evidently larger than that of the second term. The best fitting curve shown in Fig. 4 has a maximum at nearly y ¼ 458 because of the negative quadrupolar interactions in the media. Consequently, the metal particulate media exhibit negative interactions in the intrinsic easy axis direction (y ¼ 08). The quadrupolar interactions play a remarkably important role in the metal particulate media. This result is related to the fact that MP tape consist of the oriented acicular particles [24]. Therefore, these results are obviously different from those of a perpendicularly oriented Ba-ferrite particulate media, which consist of platelet particles [25]. The fact that the easy axis of the interparticle interaction in the metal particulate media exists at nearly y ¼ 458 seems to be significant in the
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recording process. Because the magnetization process nearby the transition region is regarded as that of the minor loop, the magnetization nearby the transition region in the media’s recorded pattern is supposed to be inclined along the easy axis of the interparticle interaction. This tendency seems to be especially notable in the case of high density recording. In order to obtain the magnetic anisotropy constant derived from the interparticle interaction, Eq. (10) is converted as follows: NInt: ðyÞ ¼ 20:09 þ 1:37 sin2 y21:44 sin4 y:
ð11Þ
In general, the angular dependence of the magnetic anisotropy energy, EðyÞ, is expressed as follows: EðyÞ ¼ Const:þKu1 sin2 y þ Ku2 sin4 y:
ð12Þ
If the saturation magnetization of MP tape is 239 emu/cm3, then the magnetic anisotropy constants, Ku1 and Ku2 , are obtained from Eqs. (7), (11) and (12) as follows: Ku1 ¼ 20:49 106 erg=cm3 ;
ð13Þ
Ku2 ¼ þ0:52 106 erg=cm3 :
ð14Þ
The difference of the magnetic energy between y ¼ 08 and 458 is estimated to be 0.12 106 erg/cm3, which is an energy barrier between metastable states, y ¼ 458 and 458. Also the difference of the magnetic energy between y ¼ 458 and 908 is estimated to be 0.15 106 erg/cm3, which corresponds to the energy barrier between y ¼ 458 and 1358. Generally, the thermal stability of the recorded pattern of the media is evaluated by an activation volume. The equilibrium relation between the magnetic anisotropy energy, Ku , and the activation volume, Va , is expressed as follows: Ku Va ¼ kB T;
ð15Þ
where kB is a Boltzmann’s constant and T is an absolute temperature. The magnetic anisotropy energy derived from the interparticle interaction of the media, 0.12 106 erg/cm3, is equivalent to the activation volume of 345 nm3 (3.45 10–19 cm3) at T=300 K. If the marginal volume for practical use is assumed to be 100 times the critical value [26,27], the minimum volume of the stable media’s
Fig. 5. DCD and IRM curves after being compensated for the interaction field (y=608).
recorded pattern is equal to the volume of a cube 32.4 nm on a side and is much smaller than that of the particle in the media. Therefore, the media’s recorded pattern will always be stabilized by the interparticle interaction at near room temperature when the remanent magnetization is along the easy axis of the interparticle interaction. The activation volume derived from the magnetic interaction field is much smaller than those which are obtained from a magnetic viscosity measurement [28–33]. A further consideration is necessary concerning the relation between two kinds of the activation volumes, in other words, the relation between the magnetic interaction field and a fluctuation field. The new analysis method to evaluate the interparticle interaction in the media described in this paper is based on the assumption that the interaction field is proportional to the remanent
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magnetization, M. It is important to confirm whether the assumption is reasonable or not in order to conclude the study. Fig. 5 shows the normalized DCD and IRM curves at y ¼ 608 with those which are compensated for the interaction field. The interaction field compensation is carried out based on relations (3) and (4). Although the DCD and IRM curves before the correction are clearly different from each other, the overhangs of the curves disappear after the compensation and the corrected DCD and IRM curves are much more consistent with each other. These results support that the assumption mentioned above is quite reasonable. As shown in Fig. 5, the interaction fields compensation process in the DCD and IRM curves described above is the process contrary to the linearization of the Henkel plots [20]. Hypothetical fields to correct the DCD and IRM curves, which can be obtained through a trial-anderror method in the linearization of the Henkel plots, is equivalent to the interaction field, dH, which is obtained directly from the DCD and IRM curves. The new analysis method to evaluate the interparticle interaction in the media introduced in this study has been also applied to the perpendicularly oriented Ba-ferrite particulate media, the metal evaporated tape (ME tape) and Co–O perpendicular media, and reasonable results are obtained [25,34,35]. The quadrupolar interactions also play important role in these media. The signs of the fourth terms of the Legendre polynominal obtained from the empirical equations, however, are different in each media and seem to be associated with the shape of the particle and the morphology of the magnetic layer of the media. Numerical simulation of micromagnetics is a useful tool to visualize the interparticle interactions and the thermally activated magnetic reversal in the media [36–40]. The results of the present study point out that the quadrupolar interactions must be considered to obtain further information on the magnetic behavior of the recording media. However, the quadrupolar interactions in the media have been hardly regarded as important. Future subjects appear to lie in this region.
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5. Summary 1. The magnetic interaction field, dH, which is defined as the difference of two kinds of remanence coercivities, Hr and Ha , is confirmed to be useful to evaluate the interparticle interaction in the media. 2. The interaction field factor, NInt: ðhÞ, which is defined as dH divided by the remanent magnetization, M, is introduced. The angular dependence of the interaction field factor, NInt: ðhÞ, of the media is represented well by a Legendre polynominal which includes the second and fourth terms. 3. The quadrupolar interactions play a remarkably important role in the metal particulate media. The negative quadrupolar interaction is the reason why the metal particulate media displays negative interactions in the intrinsic easy axis direction (h ¼ 08). 4. The magnetic anisotropy constant derived from the interparticle interaction is obtained from the angular dependence of the interaction field, dH. The magnetic anisotropy constants, Ku1 and Ku2 , are 0.49 106 and +0.52 106 erg/cm3, respectively. 5. The energy barrier derived from the interparticle interaction is estimated to be 0.12 106 erg/ cm3, which corresponds to the activation volume of 345 nm3 at room temperature. Acknowledgements The author would like to acknowledge the continuing guidance and encouragement of Prof. T.Miyazaki of Tohoku University. Thanks are due to my many colleagues with whom I have discussed this problem. The comments of Dr. A. Lane of the University of Alabama also helped to clarify the article. And the thorough and helpful comments of the reviewers on preliminary versions of the article are gratefully acknowledged. References [1] O. Henkel, Phys. Stat. Sol. 7 (1964) 919. [2] P.E. Kelly, K. O’Grady, P.I. Mayo, R.W. Chantrell, IEEE Trans. Magn. 25 (1989) 3881.
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[3] P.R. Bissell, A. Lyberatos, J. Magn. Magn. Mater. 95 (1991) 27. [4] D.E. Speliotis, W. Lynch, J. Appl. Phys. 65 (1991) 4496. [5] G.W.D. Spratt, P.R. Bissell, R.W. Chantrell, J. Magn. Magn. Mater. 75 (1988) 309. [6] E. Schwab, R.J. Veitch, IEEE Trans. Magn. 25 (1989) 3632. [7] P.I. Mayo, A. Bradbury, R.W. Chantrell, P.E. Kelly, H.E. Jones, P.R. Bissell, IEEE Trans. Magn. 26 (1990) 228. [8] D.E. Speliotis, IEEE Trans. Magn. 26 (1990) 1891. [9] K. O’Grady, IEEE Trans. Magn. 26 (1990) 1870. [10] F. Vajda, E. Della Torre, J. Appl. Phys. 75 (1994) 5689. [11] P.D. Mitchler, E. Dan Dahlberg, E. Engle, R.M. Roshko, IEEE Trans. Magn. 31 (1995) 2499. [12] E.P. Wohlfarth, J. Appl. Phys. 29 (1958) 595. [13] K. Ouchi, N. Honda, IEEE Trans. Magn. 36 (2000) 16. [14] E. Della Torre, IEEE Trans. Audio Electroacoust. 14 (1966) 86. [15] F. Vajda, E. Della Torre, IEEE Trans. Magn. 27 (1991) 4757. [16] V. Basso, G. Bertotti, IEEE Trans. Magn. 30 (1994) 64. [17] E. Della Torre, J. Appl. Phys. 36 (1965) 518. [18] R.J. Veitch, IEEE Trans. Magn. 26 (1990) 1876. [19] D.L. Atherton, J.R. Beattie, IEEE Trans. Magn. 26 (1990) 3059. [20] X. He, C. Alexander Jr., M.R. Parker, IEEE Trans. Magn. 28 (1992) 2683. [21] A.R. Corradi, E.P. Wohlfarth, IEEE Trans. Magn. 14 (1978) 861. [22] R.W. Chantrell, J. Magn. Magn. Mater. 95 (1991) 365.
[23] S. Chikazumi, Physics of Ferromagnetism, 2nd Edition, Oxford, New York, 1997, 266pp. [24] H.N. Bertram, C. Seberino, J. Magn. Magn. Mater. 193 (1999) 388. [25] Y. Tateno, Proceedings of ICF-8, to be published. [26] P.-L. Lu, S.H. Charap, IEEE Trans. Magn. 30 (1994) 4230. [27] Y. Hosoe, I. Tamai, K. Takahashi, T. Yamamoto, T. Kanbe, Y. Yajima, IEEE Trans. Magn. 33 (1997) 3028. [28] E.P. Wohlfarth, J. Phys. F 14 (1984) L155. [29] H. Nishio, J. Magn. Soc. Japan 13 (Suppl. S1) (1989) 697. [30] K. Song, M.R. Parker, J.W. Harrell, J. Magn. Magn. Mater. 120 (1993) 180. [31] A.M. De Witte, M. El-Hilo, K. O’Grady, R.W. Chantrell, J. Magn. Magn. Mater. 120 (1993) 184. [32] G. Bottoni, D. Candolfo, A. Cecchetti, IEEE Trans. Magn. 29 (1993) 2643. [33] R.J. Veitch, H.J. Richter, P. Poganiuch, H. Jakusch, E. Schwab, IEEE Trans. Magn. 30 (1994) 4074. [34] Y.Tateno, J. Magn. Soc. Japan, to be published. [35] Y.Tateno, K.Iwasaki, Proceedings of PMRC-2000, to be published. [36] H.N. Bertram, IEEE Trans. Magn. 22 (1986) 460. [37] E.D. Boerner, H.N. Bertram, IEEE Trans. Magn. 33 (1997) 3052. [38] C. Seberino, H.N. Bertram, IEEE Trans. Magn. 33 (1997) 3055. [39] R.W. Chantrell, J. Hannay, J. Magn. Soc. Japan 21 (Suppl. S2) (1997) 283. [40] B. Yang, D.R. Fredkin, IEEE Trans. Magn. 34 (1998) 3842.
Journal of Magnetism and Magnetic Materials 231 (2001) 347–354
Quadrupolar interaction in metal particulate recording media Yasuo Tateno* Recording Media Company, Sony Corporation, 3-4-1 Sakuragi, Tagajo-shi, Miyagi-ken 985-0842, Japan Received 1 September 2000; received in revised form 9 January 2001
Abstract Interparticle interactions in metal particulate recording media were studied by experiments. A new analysis method to evaluate the magnetic interactions in the media is considered. In the present paper, differences between the normalized DC demagnetization remanence and isothermal remanent magnetization curves are interpreted as a deviation of the magnetic switching field, that is the magnetic interaction field, dH. The parameter dH is confirmed to be useful in evaluating quantitatively the interparticle interaction in the media. The magnetic anisotropy constant derived from the interparticle interaction can be obtained from the angular dependence of the magnetic interaction field, dH. As a result, it is found that quadrupolar interactions play a remarkably important role in the origin of the magnetic anisotropy in metal particulate media. The magnetic anisotropy energy derived from the interparticle interaction is useful in discussing the thermal stability of the media’s recorded pattern. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Metal particles; Remanence curve; Quadrupolar interaction; Magnetic anisotropy; Thermal stability
1. Introduction Usually, interparticle interactions in the recording media have been investigated by means of Henkel plot and dM plot methods [1,2]. It is well known that metal particulate media (MP tape), which use acicular metal particles, have negative (demagnetizing-like) interactions in the direction of the particle’s orientation [3,4]. Also it has been reported that other acicular particulate media, such as g-Fe2O3, Co-modified g-Fe2O3 and CrO2, show negative interactions [5,6]. However, Baferrite particulate media, which consist of fine hexagonal platelet particles, display the positive (magnetizing-like) interactions in the easy axis *Tel.: +81-22-367-2629; fax: +81-22-367-2725. E-mail address: [email protected] (Y. Tateno).
direction [7,8]. The polarity of the interparticle interactions in particulate media is considered to be associated with the particle shape. However, the origin of the negative interaction in metal particulate media has not been understood clearly. The purpose of this study is to make clear the cause of the negative interactions along the easy axis direction in the metal particulate media. The usual method to evaluate the magnetic interaction in the media is comparing two kinds of remanence curves, DC demagnetization remanence (DCD) and isothermal remanent magnetization (IRM) curves [9]. Due to the magnetic interaction fields in the media, normalized DCD and IRM curves are not always consistent [1]. Usually, the discrepancy between the remanence curves is interpreted as a deviation of the remanent magnetization, dM [2].
0304-8853/01/$ - see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 1 ) 0 0 1 5 7 - 3
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Y. Tateno / Journal of Magnetism and Magnetic Materials 231 (2001) 347–354
In this paper, a new analysis method is considered from a different point of view. The difference between the remanence curves is interpreted as a deviation of the magnetic switching field. Such deviation is the magnetic interaction field, dH, which is newly defined in the present study. General characteristics of the interparticle interactions in the media are revealed with the angular dependence of the interaction field, dH, from which the magnetic anisotropy constant can also be obtained. The magnetic anisotropy energy derived from the interparticle interaction is useful in discussing the thermal stability of the media’s recorded pattern.
netizing field is equal to 4pM sin2y. The magnetic layer of MP tape is assumed to be a thin film in this case. The basis of this assumption is that the magnetic interactions derived from the static fields are long-range interaction. In the present study, only the applied field direction components of the remanent magnetization and the interaction field are considered. This is an approximation in order to carry out the experiments systematically. To investigate the angular dependence of the interaction fields is useful for reducing the systematic error derived from the simple assumption.
3. Theory 2. Experiments The measured sample is commercially available 8 mm MP tape, which consists of acicular particles whose average length and aspect ratio are 0.18 mm and 9.0, respectively. DCD and IRM curves were measured using a vibrating sample magnetometer (VSM) in several directions in the plane which is normal to the media plane and along a head scanning direction. Measurement angles were y=08, 308, 608 and 908 between the applied field direction and the media plane. The angular dependence of the remanence curves is assumed to be symmetrical about the direction along the media plane (y=08). AC demagnetizing fields for IRM curve measurements were applied in the direction along a hard magnetization axis of the media, in which the media exhibit broad switching field distribution. In this case, AC demagnetized states are independent of the switching field distribution in each measurement direction. According to the Preisach hysteresis model studies, it is pointed out that the AC demagnetized states affect the interparticle interactions in the media [10,11]. In this study, the AC demagnetized states by AC fields along the hard axis are assumed to be approximately equivalent to a thermally demagnetized states in the Preisach plane [11]. In each measurement, the demagnetizing field was compensated at each measurement point based on the simple assumption that the demag-
Magnetic interactions in the media are usually evaluated by the Henkel plot and the dM plot methods [1,2]. In these methods, the remanent magnetization, M, is regarded as a function of the magnetic field, H. Then DCD and IRM curves, which are normalized to saturation remanence, are represented as MDCD ðHÞ and MIRM ðHÞ, respectively. MDCD ðHÞ varies from +1.0 to 1.0, and MIRM ðHÞ varies from 0 to +1.0 with increasing magnetic field, H. The modified function, [1MDCD(H)]/2, which varies from 0 to +1.0, can be compared directly with MIRM ðHÞ. When magnetic interactions are absent in the media, the relation between MDCD ðHÞ and MIRM ðHÞ is expressed by Wohlfarth as follows [12]: MDCD ðHÞ ¼ 122 MIRM ðHÞ:
ð1Þ
This relation means that the function [1MDCD(H)]/2 is completely consistent with MIRM ðHÞ. On the other hand, when magnetic interactions are present in the media, the relation between MDCD ðHÞ and MIRM ðHÞ is expressed by Kelly et al. as follows [2]: MDCD ðHÞ ¼ 122 MIRM ðHÞ þ dMðHÞ:
ð2Þ
This relation means that the discrepancy between the functions, [1MDCD(H)]/2 and MIRM ðHÞ, is defined as dMðHÞ=2. The dM plot method, however, fails when the remanence curve shows overhang, which is found often in perpendicular media [13], because the
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remanence curves have negative dM/dH; in other words, the relation between the remanence curve and the magnetic field is not a one-to-one correspondence. It is pointed out in a later section that the remanence curves of the metal particulate media show these overhangs in some cases. As is well known, the Preisach hysteresis model is also a useful tool for describing the magnetic interactions in the media [14–16]. However, the same problem as the dM plots lies in the Preisach model. The negative dM/dH is a cause of trouble not only in the dM plots but also in the Preisach model [17]. Future subjects seem to lie in this region, though it is outside the scope of the present paper. In this paper, a new analysis method is considered from a different point of view. The difference between the remanence curves is interpreted as a deviation of the magnetic switching field, that is the interaction field, dH [18]. The usual parameter to represent the magnetic switching field in the media is the remanence coercivity. Therefore, it is reasonable to express the interaction field, dH, as the difference between two kinds of remanence coercivities, Hr and Ha , which are obtained from the DCD and IRM curves, respectively. In this paper, dH is defined as dH ¼ Hr 2Ha . Hr is independent of the interaction field because it is obtained at the normalized magnetization, MDCD ¼ 0, while Ha is affected by the interaction field because it is obtained at MIRM ¼ 0:5 [9]. Then, the magnetic interaction in the media can be evaluated by the parameter dH. In this method, the remanence curve is regarded as a function of the normalized remanent magnetization, M, which varies from 0 to +1.0. DCD and IRM curves are represented as HDCD ðMÞ and HIRM ðMÞ, respectively. The relations between HDCD ðMÞ, HIRM ðMÞ and dH are expressed phenomenologically as follows based on the assumption that the magnetic interaction field is proportional to the normalized remanent magnetization, M [18–20]. HDCD ðMÞ ¼ H0 ðMÞ22ð2M21Þ dH;
ð3Þ
HIRM ðMÞ ¼ H0 ðMÞ22M dH;
ð4Þ
dH ¼ Hr 2Ha :
ð5Þ
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H0 ðMÞ is an intrinsic remanence curve, which is hypothetical remanence curve obtained after compensating for the interaction field correspond to the value of M from 0 to +1.0. In this method, the relation between the remanence curve and the remanent magnetization is one-to-one correspondence even when the remanence curve shows overhang. The magnetic anisotropy constant can be obtained from the angular dependence of the interaction field, dHðyÞ. The angular dependence of magnetic anisotropy energy, EðyÞ, which corresponds to the saturation magnetization, MS , is expressed as follows using an interaction field factor, NInt: ðyÞ, which is defined in this paper as dHðyÞ divided by the remanent magnetization, MðyÞ, at each measurement point. NInt: ðyÞ ¼ dHðyÞ=4pMðyÞ;
ð6Þ
EðyÞ ¼ 22pMS2 NInt: ðyÞ:
ð7Þ
The interaction field factor, NInt: ðyÞ, which is different than the conventional one which was introduced by Corradi and Wohlfarth [21], is rather equivalent to the mean interaction field factor, a, introduced by Atherton and Beattie on the basis of the mean field theory [19] . The newly defined interaction field factor, NInt: ðyÞ, is useful in estimating the interaction field at any magnetization value. As a result, the magnetic anisotropy energy which can be compared with that obtained from the torque measurement method can be obtained from the angular dependence of the interaction field, dHðyÞ, which is obtained from the minor loop magnetization process. In general, the thermal stability of the magnetization in the media is associated with the magnetic anisotropy energy of each magnetic particle in the media. The interparticle interactions also play an important role on this point. Therefore, the magnetic anisotropy energy derived from the interparticle interaction should be useful in discussing the thermal stability of the media’s recorded pattern [22].
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Fig. 2. Angular dependence of the remanence coercivities, Hr and Ha .
Fig. 1. Angular dependence of the remanence curves, DCD and IRM curves (y=08, 308, 608, 908).
4. Results and discussion Normalized DCD and IRM curves in each direction are shown in Fig. 1. In all of the measurement directions, the DCD and IRM curves are not consistent. In the cases of y ¼ 08 and 908, the switching fields of the IRM curves are larger than those of the DCD curves because of the negative (demagnetizing-like) interactions, as is well known. On the contrary, in the cases of y ¼ 308 and 608, the switching fields of the IRM curves
are smaller than those of the DCD curves, and the IRM curves exhibit overhangs because of the positive (magnetizing-like) interactions. It is to be noted that the remanence curve occasionally shows an overhang even in a longitudinal media. This fact is revealed with the study of the angular dependence of the remanence curves. The angular dependence of Hr and Ha is shown in Fig. 2. Hr has a minimum at y ¼ 08, which is the intrinsic easy magnetization axis direction obtained from the torque measurement method. The angular dependence of Ha is considerably different from that of Hr . Ha at y ¼ 08 is larger than Hr in that direction because of the negative interaction, and Ha at y ¼ 308 and 608 are smaller than Hr in those directions because of the positive interaction. As a result, Ha has a minimum at y ¼ 308. These results imply that the direction of the easy axis in the minor loop magnetization process is not always the same as that in the major loop magnetization process because of the interparticle interaction in the media. The angular dependence of the interaction field, dH, is shown in Fig. 3. dH at y ¼ 308 and 608 are positive, +140 and +210 Oe, respectively. dH at y ¼ 08 and 908 are negative, –100 and –220 Oe, respectively. Apparently, the angular dependence of the interaction field, dH, includes not only sin 2y component but also sin 4y component.
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Fig. 3. Angular dependence of the interaction field, dHðyÞ.
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Fig. 4. Angular dependence of the interaction field factor, NInt.(y). (empirical fitting by the Legendre polynominal).
equation of the curve is as follows: In the case of metal particulate media, which is a typical perfectly isolated particles system, the magnetic interaction fields in the media are derived from the dipole–dipole interactions. If the arrangement of the particles in the media has a cubic symmetry, the dipole–dipole interactions would cancel each other. However, the arrangement of the oriented acicular particles does not seem to exhibit the cubic symmetry in the media. Therefore, MP tape would show the magnetic anisotropy derived from the interparticle interactions. In the case of the dipole–dipole interactions, the angular dependence of the interaction field can be expressed by a Legendre polynominal [23]. Judging from the experimental data shown in Fig. 3, not only the second term, P2 ðcos yÞ, but also the fourth term, P4 ðcos yÞ, are necessary to express the angular dependence of the interaction field in the media. P2 ðcos yÞ and P4 ðcos yÞ are defined as follows: P2 ðcos yÞ ¼ ð1=2Þð3 cos2 y21Þ;
ð8Þ
P4 ðcos yÞ ¼ ð1=8Þð35 cos4 y230 cos2 y þ 3Þ:
ð9Þ
Fig. 4 shows the angular dependence of the interaction field factor, NInt: ðyÞ, and the best fitting curve by the Legendre polynominal. The empirical
NInt: ðyÞ ¼ þ0:05 þ 0:19 P2 ðcos yÞ20:33 P4 ðcos yÞ: ð10Þ The second term, P2 ðcos yÞ, and the fourth term, P4 ðcos yÞ, represent the components of dipolar interactions and quadrupolar interactions, respectively. The positive sign of the second term is a result of the contribution of end-to-end particle pairs in the media. The negative sign of the fourth term is derived from the contribution of adjacent particle pairs. The most important fact shown by the empirical equation (10) is that the contribution of the fourth term is evidently larger than that of the second term. The best fitting curve shown in Fig. 4 has a maximum at nearly y ¼ 458 because of the negative quadrupolar interactions in the media. Consequently, the metal particulate media exhibit negative interactions in the intrinsic easy axis direction (y ¼ 08). The quadrupolar interactions play a remarkably important role in the metal particulate media. This result is related to the fact that MP tape consist of the oriented acicular particles [24]. Therefore, these results are obviously different from those of a perpendicularly oriented Ba-ferrite particulate media, which consist of platelet particles [25]. The fact that the easy axis of the interparticle interaction in the metal particulate media exists at nearly y ¼ 458 seems to be significant in the
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recording process. Because the magnetization process nearby the transition region is regarded as that of the minor loop, the magnetization nearby the transition region in the media’s recorded pattern is supposed to be inclined along the easy axis of the interparticle interaction. This tendency seems to be especially notable in the case of high density recording. In order to obtain the magnetic anisotropy constant derived from the interparticle interaction, Eq. (10) is converted as follows: NInt: ðyÞ ¼ 20:09 þ 1:37 sin2 y21:44 sin4 y:
ð11Þ
In general, the angular dependence of the magnetic anisotropy energy, EðyÞ, is expressed as follows: EðyÞ ¼ Const:þKu1 sin2 y þ Ku2 sin4 y:
ð12Þ
If the saturation magnetization of MP tape is 239 emu/cm3, then the magnetic anisotropy constants, Ku1 and Ku2 , are obtained from Eqs. (7), (11) and (12) as follows: Ku1 ¼ 20:49 106 erg=cm3 ;
ð13Þ
Ku2 ¼ þ0:52 106 erg=cm3 :
ð14Þ
The difference of the magnetic energy between y ¼ 08 and 458 is estimated to be 0.12 106 erg/cm3, which is an energy barrier between metastable states, y ¼ 458 and 458. Also the difference of the magnetic energy between y ¼ 458 and 908 is estimated to be 0.15 106 erg/cm3, which corresponds to the energy barrier between y ¼ 458 and 1358. Generally, the thermal stability of the recorded pattern of the media is evaluated by an activation volume. The equilibrium relation between the magnetic anisotropy energy, Ku , and the activation volume, Va , is expressed as follows: Ku Va ¼ kB T;
ð15Þ
where kB is a Boltzmann’s constant and T is an absolute temperature. The magnetic anisotropy energy derived from the interparticle interaction of the media, 0.12 106 erg/cm3, is equivalent to the activation volume of 345 nm3 (3.45 10–19 cm3) at T=300 K. If the marginal volume for practical use is assumed to be 100 times the critical value [26,27], the minimum volume of the stable media’s
Fig. 5. DCD and IRM curves after being compensated for the interaction field (y=608).
recorded pattern is equal to the volume of a cube 32.4 nm on a side and is much smaller than that of the particle in the media. Therefore, the media’s recorded pattern will always be stabilized by the interparticle interaction at near room temperature when the remanent magnetization is along the easy axis of the interparticle interaction. The activation volume derived from the magnetic interaction field is much smaller than those which are obtained from a magnetic viscosity measurement [28–33]. A further consideration is necessary concerning the relation between two kinds of the activation volumes, in other words, the relation between the magnetic interaction field and a fluctuation field. The new analysis method to evaluate the interparticle interaction in the media described in this paper is based on the assumption that the interaction field is proportional to the remanent
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magnetization, M. It is important to confirm whether the assumption is reasonable or not in order to conclude the study. Fig. 5 shows the normalized DCD and IRM curves at y ¼ 608 with those which are compensated for the interaction field. The interaction field compensation is carried out based on relations (3) and (4). Although the DCD and IRM curves before the correction are clearly different from each other, the overhangs of the curves disappear after the compensation and the corrected DCD and IRM curves are much more consistent with each other. These results support that the assumption mentioned above is quite reasonable. As shown in Fig. 5, the interaction fields compensation process in the DCD and IRM curves described above is the process contrary to the linearization of the Henkel plots [20]. Hypothetical fields to correct the DCD and IRM curves, which can be obtained through a trial-anderror method in the linearization of the Henkel plots, is equivalent to the interaction field, dH, which is obtained directly from the DCD and IRM curves. The new analysis method to evaluate the interparticle interaction in the media introduced in this study has been also applied to the perpendicularly oriented Ba-ferrite particulate media, the metal evaporated tape (ME tape) and Co–O perpendicular media, and reasonable results are obtained [25,34,35]. The quadrupolar interactions also play important role in these media. The signs of the fourth terms of the Legendre polynominal obtained from the empirical equations, however, are different in each media and seem to be associated with the shape of the particle and the morphology of the magnetic layer of the media. Numerical simulation of micromagnetics is a useful tool to visualize the interparticle interactions and the thermally activated magnetic reversal in the media [36–40]. The results of the present study point out that the quadrupolar interactions must be considered to obtain further information on the magnetic behavior of the recording media. However, the quadrupolar interactions in the media have been hardly regarded as important. Future subjects appear to lie in this region.
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5. Summary 1. The magnetic interaction field, dH, which is defined as the difference of two kinds of remanence coercivities, Hr and Ha , is confirmed to be useful to evaluate the interparticle interaction in the media. 2. The interaction field factor, NInt: ðhÞ, which is defined as dH divided by the remanent magnetization, M, is introduced. The angular dependence of the interaction field factor, NInt: ðhÞ, of the media is represented well by a Legendre polynominal which includes the second and fourth terms. 3. The quadrupolar interactions play a remarkably important role in the metal particulate media. The negative quadrupolar interaction is the reason why the metal particulate media displays negative interactions in the intrinsic easy axis direction (h ¼ 08). 4. The magnetic anisotropy constant derived from the interparticle interaction is obtained from the angular dependence of the interaction field, dH. The magnetic anisotropy constants, Ku1 and Ku2 , are 0.49 106 and +0.52 106 erg/cm3, respectively. 5. The energy barrier derived from the interparticle interaction is estimated to be 0.12 106 erg/ cm3, which corresponds to the activation volume of 345 nm3 at room temperature. Acknowledgements The author would like to acknowledge the continuing guidance and encouragement of Prof. T.Miyazaki of Tohoku University. Thanks are due to my many colleagues with whom I have discussed this problem. The comments of Dr. A. Lane of the University of Alabama also helped to clarify the article. And the thorough and helpful comments of the reviewers on preliminary versions of the article are gratefully acknowledged. References [1] O. Henkel, Phys. Stat. Sol. 7 (1964) 919. [2] P.E. Kelly, K. O’Grady, P.I. Mayo, R.W. Chantrell, IEEE Trans. Magn. 25 (1989) 3881.
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