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Interaction effects in high density magnetic particulate media
ARTICLE IN PRESS
Physica B 343 (2004) 48–52
Interaction effects in high density magnetic particulate media Mihai Cerchez*, Laurentiu Stoleriu, Alexandru Stancu Faculty of Physics, ‘‘Alexandru Ioan Cuza’’ University, 11 Blvd Copou, Iasi 6600, Romania
Abstract The paper presents a micromagnetic study of the particulate high density recording media. The main difference in the behavior of such a system is the appearance of magnetic clusters which lead to a different behavior of the system. New hypotheses for interpreting such systems are presented. r 2003 Elsevier B.V. All rights reserved. PACS: 75.50.Ss; 75.50.Tt; 75.60.Ej Keywords: Micromagnetism; Preisach model; Clusters
1. Introduction
2. The magnetic system
The interactions in magnetic recording media are one of the important factors of limitations especially due to media noise and they may be due to exchange coupling or to the magnetic fields created by the magnetic moment of the magnetic particles in the system. Generally, one may consider the particulate magnetic media as a statistical ensemble of particles, described by a coercive and an interaction field distribution which shifts during the magnetization processes with an amount proportional to the magnetic moment of the sample. We have shown [1] that, for strongly correlated systems, with only magnetostatic interactions, one may obtain a completely different behavior of the statistics of the systems, which could lead to misinterpreting the magnetic characterization parameters.
We simulated particulate systems with different packing fractions and orientations of easy axes, magnetostatic interparticle interactions, the dynamics of the magnetic moment of particles described by the Landau–Lifshitz–Gilbert equation, and we produced several magnetization processes. During the magnetization processes, we recorded the interaction field of each particle for each value of the applied field and studied the evolution of the interaction field distribution. For low values of the packing fraction (0.2), one obtains a typical symmetrical distribution of interaction which, during the magnetization process, has a parabolic variation of the variance, and shifts with a quantity proportional to the magnetic moment of the system [2,3]. As the packing fraction gets higher, the parameters obtained seem to loose their significance. This is because instead of a moving distribution with variable variance, the interaction field distribution changes from a one-peak distribution
*Corresponding author. Tel.: +40-32-201175; fax: +40-32201205. E-mail address: [email protected] (M. Cerchez).
0921-4526/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2003.08.043
ARTICLE IN PRESS M. Cerchez et al. / Physica B 343 (2004) 48–52
at saturation, to a two-peak distribution and back to one peak at negative saturation. This behavior is due to the strong interactions which lead to clusters (Fig. 1) that act like separate entities within the particulate system, similar to magnetic domains in bulk materials. If one saturates the system in one direction and applies an increasing field in the opposite direction, at the beginning one obtains nucleation clusters which become larger as the field increases, like the moving walls of the magnetic domains of a bulk material. Due to this behavior, one can call this clusters ‘‘superferromagnetic domains’’ in the extended sense of the term used in Ref. [4]. In the case of our systems, the magnetic moments of the particles inside the superferromagnetic domain are not perfectly aligned as to provide saturation, but nevertheless, the general behavior is similar. During the magnetization process, the presence of the superferromagnetic domains that switch from one direction to the other, gives rise to practically two peaks in the interaction field distribution. In the paper we study the formation and characterization of superferromagnetic domains in high density media.
Fig. 1. The system configuration for an intermediary value of the magnetic moment. The degree of grey gives the direction of the magnetic moment of the particle.
49
3. Simulations and discussions We generated a particulate system simulating a recording media consisting of 1400 particles having easy axes orientations within an angle of 25 with respect to a preferential orientation, in the plane of the sample. The particles are randomly distributed in a thin layer (3 average diameters thick) with an initial packing fraction of 0.42. Uniaxial anisotropies of particles were considered, with a normal distribution of anisotropy fields having a mean value of 3000 Oe and a standard deviation of 100 Oe. We also considered a normal distribution of particle diameters with a mean value of 20 nm and a standard deviation of 2 nm. Magnetostatic interactions between particles are taken into account. Each particle interacts with a number of neighbors which are determined as the particles which produce a certain minimum field. In-plane periodic boundary-free conditions were used. To create samples with variable packing fractions we expand the system by multiplying the coordinates of each particle by a certain coefficient. We also created systems with different dispersions of the orientation of particles’ easy axes for a sample with given positions of the particles. Thus, we created samples which offer the possibility to study the statistical parameters of the system for various packing fractions and degrees of orientation of the easy axes. In Fig. 2a and b, we present the interaction field distribution corresponding to a number of magnetic states of the system during the magnetic hysteresis loop (MHL) process. The magnetic field is applied along the symmetry axis of the system. Fig. 2a is for the high-packing fraction sample (PF=0.42) and oriented easy axes of particles within 25 . Fig. 2b represents the same states for a equivalent system of the same packing fraction but with random orientations of the easy axes of the particles. In Fig. 2a, one may observe that the shape of the interaction field distribution changes during the MHL process from a one-peak distribution to a two-peak distribution and respects the symmetry of the MHL process. The weight of the peaks change during the magnetization process but their position remains the same as in the beginning of
ARTICLE IN PRESS M. Cerchez et al. / Physica B 343 (2004) 48–52
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0.18 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 -4000 -3000 -2000 -1000
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Fig. 2. The evolution of the interaction field distribution in different magnetic states of the particulate system in two cases: an oriented sample (a) and a random oriented sample (b).
the process. This observation is important because, although one may observe a significant mean field contribution, the position of the peaks seem to be not sensitive to this. In Fig. 2b one may notice that this effect is almost negligible and that the interaction field distribution acts in the ‘‘traditional’’ moving way. We interpret this behavior in terms of the contributions of the magnetic clusters in the media which interact with each other rather than individual particles. Thus one obtains a statistical distribution of clusters without a noticeable effect from the mean field distribution. The behavior is similar to that of the ferromagnetic domains in the sense that, due to large interactions within the cluster, all particles corresponding to one cluster are oriented in the same direction. The behavior of
the border between clusters is similar to the domain wall movement as particles from one cluster switch to the direction of the particles in the neighboring cluster. In order to establish the rules which govern this behavior of high packing oriented particle ensemble we performed an analysis of the change in the area of each of the peaks of the interaction field distribution with respect to the magnetic moment of the sample. The important observation is that the area of each peak varies in a linear manner with magnetic moment of the sample. This leads to an interesting possibility of developing a Preisach model with a two peaks distribution and a new interpretation of the ‘‘linear moving’’, this time as the dependence of the area of the peaks against the magnetic moment (Fig. 3).
ARTICLE IN PRESS M. Cerchez et al. / Physica B 343 (2004) 48–52
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0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 -4000
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Fig. 2 (continued).
Fig. 3. The dependence of the area of the peaks of the interaction field distribution on the magnetic moment of the sample.
4. Conclusion We studied a magnetic particulate system with high packing and good orientations of the easy
axes of the particles, yielding strong magnetic interactions, both statistical and mean field. We observed the forming of magnetic clusters and a ‘‘domain’’-like behavior of the clusters.
ARTICLE IN PRESS 52
M. Cerchez et al. / Physica B 343 (2004) 48–52
We established a new rule of behavior for this kind of systems and a new understanding of the ‘‘moving’’ for a new type of Preisach model. Acknowledgements This work has been partially supported by the Romanian CERES and CNCSIS grants A and AT.
References [1] M. Cerchez, L. Stoleriu, A. Stancu, P.R. Bissell, Limits of the Preisach model for strongly correlated particulate systems, DP-09, Intermag 2003, Boston. [2] A. Stancu, L. Stoleriu, M. Cerchez, J. Appl. Phys. 89 (11) (2001) 7260. [3] M. Pardavi-Horvath, E. Della Torre, F. Vajda, G. Vertesy, IEEE Trans. Magn. 29 (1993) 3793. [4] S. Morup, P.H. Christensen, B.S. Clausen, J. Magn. Magn. Mater. 68 (2) (1987) 160.
Physica B 343 (2004) 48–52
Interaction effects in high density magnetic particulate media Mihai Cerchez*, Laurentiu Stoleriu, Alexandru Stancu Faculty of Physics, ‘‘Alexandru Ioan Cuza’’ University, 11 Blvd Copou, Iasi 6600, Romania
Abstract The paper presents a micromagnetic study of the particulate high density recording media. The main difference in the behavior of such a system is the appearance of magnetic clusters which lead to a different behavior of the system. New hypotheses for interpreting such systems are presented. r 2003 Elsevier B.V. All rights reserved. PACS: 75.50.Ss; 75.50.Tt; 75.60.Ej Keywords: Micromagnetism; Preisach model; Clusters
1. Introduction
2. The magnetic system
The interactions in magnetic recording media are one of the important factors of limitations especially due to media noise and they may be due to exchange coupling or to the magnetic fields created by the magnetic moment of the magnetic particles in the system. Generally, one may consider the particulate magnetic media as a statistical ensemble of particles, described by a coercive and an interaction field distribution which shifts during the magnetization processes with an amount proportional to the magnetic moment of the sample. We have shown [1] that, for strongly correlated systems, with only magnetostatic interactions, one may obtain a completely different behavior of the statistics of the systems, which could lead to misinterpreting the magnetic characterization parameters.
We simulated particulate systems with different packing fractions and orientations of easy axes, magnetostatic interparticle interactions, the dynamics of the magnetic moment of particles described by the Landau–Lifshitz–Gilbert equation, and we produced several magnetization processes. During the magnetization processes, we recorded the interaction field of each particle for each value of the applied field and studied the evolution of the interaction field distribution. For low values of the packing fraction (0.2), one obtains a typical symmetrical distribution of interaction which, during the magnetization process, has a parabolic variation of the variance, and shifts with a quantity proportional to the magnetic moment of the system [2,3]. As the packing fraction gets higher, the parameters obtained seem to loose their significance. This is because instead of a moving distribution with variable variance, the interaction field distribution changes from a one-peak distribution
*Corresponding author. Tel.: +40-32-201175; fax: +40-32201205. E-mail address: [email protected] (M. Cerchez).
0921-4526/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2003.08.043
ARTICLE IN PRESS M. Cerchez et al. / Physica B 343 (2004) 48–52
at saturation, to a two-peak distribution and back to one peak at negative saturation. This behavior is due to the strong interactions which lead to clusters (Fig. 1) that act like separate entities within the particulate system, similar to magnetic domains in bulk materials. If one saturates the system in one direction and applies an increasing field in the opposite direction, at the beginning one obtains nucleation clusters which become larger as the field increases, like the moving walls of the magnetic domains of a bulk material. Due to this behavior, one can call this clusters ‘‘superferromagnetic domains’’ in the extended sense of the term used in Ref. [4]. In the case of our systems, the magnetic moments of the particles inside the superferromagnetic domain are not perfectly aligned as to provide saturation, but nevertheless, the general behavior is similar. During the magnetization process, the presence of the superferromagnetic domains that switch from one direction to the other, gives rise to practically two peaks in the interaction field distribution. In the paper we study the formation and characterization of superferromagnetic domains in high density media.
Fig. 1. The system configuration for an intermediary value of the magnetic moment. The degree of grey gives the direction of the magnetic moment of the particle.
49
3. Simulations and discussions We generated a particulate system simulating a recording media consisting of 1400 particles having easy axes orientations within an angle of 25 with respect to a preferential orientation, in the plane of the sample. The particles are randomly distributed in a thin layer (3 average diameters thick) with an initial packing fraction of 0.42. Uniaxial anisotropies of particles were considered, with a normal distribution of anisotropy fields having a mean value of 3000 Oe and a standard deviation of 100 Oe. We also considered a normal distribution of particle diameters with a mean value of 20 nm and a standard deviation of 2 nm. Magnetostatic interactions between particles are taken into account. Each particle interacts with a number of neighbors which are determined as the particles which produce a certain minimum field. In-plane periodic boundary-free conditions were used. To create samples with variable packing fractions we expand the system by multiplying the coordinates of each particle by a certain coefficient. We also created systems with different dispersions of the orientation of particles’ easy axes for a sample with given positions of the particles. Thus, we created samples which offer the possibility to study the statistical parameters of the system for various packing fractions and degrees of orientation of the easy axes. In Fig. 2a and b, we present the interaction field distribution corresponding to a number of magnetic states of the system during the magnetic hysteresis loop (MHL) process. The magnetic field is applied along the symmetry axis of the system. Fig. 2a is for the high-packing fraction sample (PF=0.42) and oriented easy axes of particles within 25 . Fig. 2b represents the same states for a equivalent system of the same packing fraction but with random orientations of the easy axes of the particles. In Fig. 2a, one may observe that the shape of the interaction field distribution changes during the MHL process from a one-peak distribution to a two-peak distribution and respects the symmetry of the MHL process. The weight of the peaks change during the magnetization process but their position remains the same as in the beginning of
ARTICLE IN PRESS M. Cerchez et al. / Physica B 343 (2004) 48–52
50
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0.18 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 -4000 -3000 -2000 -1000
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Fig. 2. The evolution of the interaction field distribution in different magnetic states of the particulate system in two cases: an oriented sample (a) and a random oriented sample (b).
the process. This observation is important because, although one may observe a significant mean field contribution, the position of the peaks seem to be not sensitive to this. In Fig. 2b one may notice that this effect is almost negligible and that the interaction field distribution acts in the ‘‘traditional’’ moving way. We interpret this behavior in terms of the contributions of the magnetic clusters in the media which interact with each other rather than individual particles. Thus one obtains a statistical distribution of clusters without a noticeable effect from the mean field distribution. The behavior is similar to that of the ferromagnetic domains in the sense that, due to large interactions within the cluster, all particles corresponding to one cluster are oriented in the same direction. The behavior of
the border between clusters is similar to the domain wall movement as particles from one cluster switch to the direction of the particles in the neighboring cluster. In order to establish the rules which govern this behavior of high packing oriented particle ensemble we performed an analysis of the change in the area of each of the peaks of the interaction field distribution with respect to the magnetic moment of the sample. The important observation is that the area of each peak varies in a linear manner with magnetic moment of the sample. This leads to an interesting possibility of developing a Preisach model with a two peaks distribution and a new interpretation of the ‘‘linear moving’’, this time as the dependence of the area of the peaks against the magnetic moment (Fig. 3).
ARTICLE IN PRESS M. Cerchez et al. / Physica B 343 (2004) 48–52
51
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Fig. 2 (continued).
Fig. 3. The dependence of the area of the peaks of the interaction field distribution on the magnetic moment of the sample.
4. Conclusion We studied a magnetic particulate system with high packing and good orientations of the easy
axes of the particles, yielding strong magnetic interactions, both statistical and mean field. We observed the forming of magnetic clusters and a ‘‘domain’’-like behavior of the clusters.
ARTICLE IN PRESS 52
M. Cerchez et al. / Physica B 343 (2004) 48–52
We established a new rule of behavior for this kind of systems and a new understanding of the ‘‘moving’’ for a new type of Preisach model. Acknowledgements This work has been partially supported by the Romanian CERES and CNCSIS grants A and AT.
References [1] M. Cerchez, L. Stoleriu, A. Stancu, P.R. Bissell, Limits of the Preisach model for strongly correlated particulate systems, DP-09, Intermag 2003, Boston. [2] A. Stancu, L. Stoleriu, M. Cerchez, J. Appl. Phys. 89 (11) (2001) 7260. [3] M. Pardavi-Horvath, E. Della Torre, F. Vajda, G. Vertesy, IEEE Trans. Magn. 29 (1993) 3793. [4] S. Morup, P.H. Christensen, B.S. Clausen, J. Magn. Magn. Mater. 68 (2) (1987) 160.