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Magnetic characteristics of ferromagnetic nanotube
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 310 (2007) 2445–2447 www.elsevier.com/locate/jmmm
Magnetic characteristics of ferromagnetic nanotube Jehyun Leea,b,, Dieter Suessb, Thomas Schreflc, Kyu Hwan Oha, Josef Fidlerb a
School of Materials Science and Engineering, Seoul National University, Seoul 151-742, Republic of Korea Institute of Solid State Physics, Vienna University of Technology, Wiedner HauptstraX e 8-10, 1140 Vienna, Austria c Department of Engineering Materials, University of Sheffield, Western Bank, Sheffield, UK
b
Available online 30 November 2006
Abstract Micromagnetic simulations are performed to study the magnetic and electromagnetic properties of a ferromagnetic tube. Hysteresis loops and possible equilibrium states are observed with external field applied perpendicular and parallel to the tube axis. We found an equilibrium state, which is composed of two oppositely directed vortices, with a domain wall between them. The anisotropic magnetoresistance (AMR) was estimated at every point of the hysteresis loops, in order to investigate its potentiality as an electric device in nano/micro device. As a result, we found that our system can be used as a magnetic sensor that behaves differently according to the magnetic field direction. r 2006 Elsevier B.V. All rights reserved. PACS: 75.60.C; 72.15.G; 75.60 Keywords: Ferromagnet nanotube; Magnetic domain; Anisotropic magnetoresistance; Micromagnetics
1. Introduction In recent years, nanosized magnetic structures such as dots, cylinders and wires were studied for fundamental and technological interest. A great deal of attention was focused on their magnetic behaviors and internal magnetic states because they are believed to have potential applications for magnetic memory, sensor and logical devices [1]. Ferromagnetic tubes are considered as a candidate for recording head, biomagnetic sensors and nanomedicine, and catalysts, because of its expected vortex magnetization state and floatibility in the liquid due to the empty inside [2–4]. Recently, Nielsch et al. [5] reported the electrochemical fabrication method and measured magnetic characteristics, and analytical study of the phase diagram of magnetic nanotube is reported by others [6]. They showed the experimental hysteresis loops and the theoretically expected equilibrium state. However, the transient Corresponding author. School of Materials Science and Engineering, Seoul National University, Seoul 151-742, Republic of Korea. Tel.: +82 2 880 8306. E-mail address: [email protected] (J. Lee).
0304-8853/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.10.1137
state and electromagnetic characters are not studied for the restriction of the calculation system. In this work, we introduced and performed micromagnetics simulation on a nanotube, focusing on its magnetic switching process and electromagnetic property, anisotropic magnetoresistance (AMR).
2. Micromagnetics simulation The numerical computer simulations were carried out using a three-dimensional hybrid finite element/boundary element micromagnetic code [7]. The effective field consists of exchange field, uni-directional crystalline anisotropy field, external field and magnetostatic field. A ferromagnetic tube finite element model is prepared, of height 1000 nm, inner diameter and outer diameter of 300 and 500 nm, respectively. Permalloy is assumed to the material, the parameters are as follows: saturation polarization J s ¼ 1:0 T, exchange constant A ¼ 13 pJ=m and the anisotropy constant K u ¼ 0. We applied an external field perpendicular (x-direction) and parallel to the tube axis (z-direction). The initial magnetization is randomly oriented.
ARTICLE IN PRESS 2446
J. Lee et al. / Journal of Magnetism and Magnetic Materials 310 (2007) 2445–2447
3. Results and discussion Equilibrium state is obtained by two ways. The first way is by minimizing the total magnetic energy from the randomly magnetized initial state. The second is finding a remanent state from the hysteresis curve with an external field applied parallel to the tube axis. These two methods conclude the same equilibrium states, which is shown in Fig. 1, and two oppositely directed vortices separated by a domain wall. The reason is believed to be the relatively short tube length compared to the diameters. The magnetostatic interference between the two tube bases prevents from rotating in the same direction during the magnetization process. The shape factors b ¼ rin =rout and g ¼ height=rout of our system are 0.6 and 4, respectively. From the analytic solutions, the energy of the vortex state is expected to be lower than that of the ferromagnet state [6], the micromagnetic results are shown in Fig. 2. Compared to the ferromagnet state the amount of the decreased magnetostatic energy is much higher than that of the increased exchange energy. During the magnetization process, the remanent magnetization (M/Ms) and coercivity when the field is applied parallel to tube direction are 0.64 and 0.038 T, and those with perpendicular field are 0.19 and 0.036 T, respectively. The shape of each hysteresis loop agrees well with the experimental results [5]. The magnetization process along the tube axis is triggered from the two tube bases, where is the local maxima of magnetostatic energy is located. A multi-vortex state is formed during the magnetization process perpendicular to the tube axis. Several numbers of vortices are formed on the tube surface, initiated at the inner surface. In order to test its potential as an electromagnetic device, we calculated the maximum deviation of the average angle y from the hysteresis loops. That maximum deviation gives us the maximum change of AMR according to the equation R¼ R0 þ DR cos2 y. The current direction is assumed parallel to the z-axis. We use the finite element mesh to intergrate cos2y numerically over the nanotube (Fig. 3). The cos2y varies from 0.044 to 1.0 (z-directional field) and from 0.55 to 0.0 (x-directional field). The equilibrium state shown in Fig. 1 gives 0.043 as an integrated cos2y over the sample. Assuming that DR in permalloy is approxi-
Fig. 1. Equilibrium state from random initial state. Curling domain wall (b) is located between the oppositely directed vortices (a) and (c).
Fig. 2. Magnetic energy comparison between the ferromagnet state (F state) and vortex state (V state). Each symbol indicates the total magnetic energy (square), exchange energy (circle) and magnetostatic energy (triangle).
Fig. 3. Hysteresis loops (empty circle) and integrated cos2y over the nanotube (filled circle) along the upper hysteresis curve, decreasing external field from 0.4 to 0.4 T. The current (black arrow) is applied along the tube axis, the external field (white arrow) is applied parallel (a) and perpendicular (b) to the tube axis.
ARTICLE IN PRESS J. Lee et al. / Journal of Magnetism and Magnetic Materials 310 (2007) 2445–2447
mately 5%, this values corresponds to maximum change in MR of 4.8%. 4. Conclusion The potential of ferromagnet nanotube as an effective magnetic sensor is studied using micromagnetic simulations. The AMR characteristics, which behave oppositely according to the field applying directions make it possible to be used as a biaxial sensor.
2447
References [1] R. Cowburn, M. Welland, Science 287 (2000) 1466. [2] S. Khizroev, M. Kryder, D. Litvinov, D. Thomson, Appl. Phys. Lett. 81 (2002) 2256. [3] A. Goldstein, M. Gelb, P. Yager, J. Control. Release 70 (2001) 125. [4] C.A. Haberzettl, Nanotechnology 13 (2002) R9. [5] K. Nielsch, F. Castano, S. Matthias, W. Lee, C. Ross, Eng. Mater. 7 (2005) 217. [6] J. Escrig, P. Landeros, D. Altbir, E.E. Vogel, P. Vargas, J. Magn. Magn. Mater. 308 (2007) 233. [7] J. Fidler, T. Schrefl, J. Phys. D 33 (2000) R135.
Journal of Magnetism and Magnetic Materials 310 (2007) 2445–2447 www.elsevier.com/locate/jmmm
Magnetic characteristics of ferromagnetic nanotube Jehyun Leea,b,, Dieter Suessb, Thomas Schreflc, Kyu Hwan Oha, Josef Fidlerb a
School of Materials Science and Engineering, Seoul National University, Seoul 151-742, Republic of Korea Institute of Solid State Physics, Vienna University of Technology, Wiedner HauptstraX e 8-10, 1140 Vienna, Austria c Department of Engineering Materials, University of Sheffield, Western Bank, Sheffield, UK
b
Available online 30 November 2006
Abstract Micromagnetic simulations are performed to study the magnetic and electromagnetic properties of a ferromagnetic tube. Hysteresis loops and possible equilibrium states are observed with external field applied perpendicular and parallel to the tube axis. We found an equilibrium state, which is composed of two oppositely directed vortices, with a domain wall between them. The anisotropic magnetoresistance (AMR) was estimated at every point of the hysteresis loops, in order to investigate its potentiality as an electric device in nano/micro device. As a result, we found that our system can be used as a magnetic sensor that behaves differently according to the magnetic field direction. r 2006 Elsevier B.V. All rights reserved. PACS: 75.60.C; 72.15.G; 75.60 Keywords: Ferromagnet nanotube; Magnetic domain; Anisotropic magnetoresistance; Micromagnetics
1. Introduction In recent years, nanosized magnetic structures such as dots, cylinders and wires were studied for fundamental and technological interest. A great deal of attention was focused on their magnetic behaviors and internal magnetic states because they are believed to have potential applications for magnetic memory, sensor and logical devices [1]. Ferromagnetic tubes are considered as a candidate for recording head, biomagnetic sensors and nanomedicine, and catalysts, because of its expected vortex magnetization state and floatibility in the liquid due to the empty inside [2–4]. Recently, Nielsch et al. [5] reported the electrochemical fabrication method and measured magnetic characteristics, and analytical study of the phase diagram of magnetic nanotube is reported by others [6]. They showed the experimental hysteresis loops and the theoretically expected equilibrium state. However, the transient Corresponding author. School of Materials Science and Engineering, Seoul National University, Seoul 151-742, Republic of Korea. Tel.: +82 2 880 8306. E-mail address: [email protected] (J. Lee).
0304-8853/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.10.1137
state and electromagnetic characters are not studied for the restriction of the calculation system. In this work, we introduced and performed micromagnetics simulation on a nanotube, focusing on its magnetic switching process and electromagnetic property, anisotropic magnetoresistance (AMR).
2. Micromagnetics simulation The numerical computer simulations were carried out using a three-dimensional hybrid finite element/boundary element micromagnetic code [7]. The effective field consists of exchange field, uni-directional crystalline anisotropy field, external field and magnetostatic field. A ferromagnetic tube finite element model is prepared, of height 1000 nm, inner diameter and outer diameter of 300 and 500 nm, respectively. Permalloy is assumed to the material, the parameters are as follows: saturation polarization J s ¼ 1:0 T, exchange constant A ¼ 13 pJ=m and the anisotropy constant K u ¼ 0. We applied an external field perpendicular (x-direction) and parallel to the tube axis (z-direction). The initial magnetization is randomly oriented.
ARTICLE IN PRESS 2446
J. Lee et al. / Journal of Magnetism and Magnetic Materials 310 (2007) 2445–2447
3. Results and discussion Equilibrium state is obtained by two ways. The first way is by minimizing the total magnetic energy from the randomly magnetized initial state. The second is finding a remanent state from the hysteresis curve with an external field applied parallel to the tube axis. These two methods conclude the same equilibrium states, which is shown in Fig. 1, and two oppositely directed vortices separated by a domain wall. The reason is believed to be the relatively short tube length compared to the diameters. The magnetostatic interference between the two tube bases prevents from rotating in the same direction during the magnetization process. The shape factors b ¼ rin =rout and g ¼ height=rout of our system are 0.6 and 4, respectively. From the analytic solutions, the energy of the vortex state is expected to be lower than that of the ferromagnet state [6], the micromagnetic results are shown in Fig. 2. Compared to the ferromagnet state the amount of the decreased magnetostatic energy is much higher than that of the increased exchange energy. During the magnetization process, the remanent magnetization (M/Ms) and coercivity when the field is applied parallel to tube direction are 0.64 and 0.038 T, and those with perpendicular field are 0.19 and 0.036 T, respectively. The shape of each hysteresis loop agrees well with the experimental results [5]. The magnetization process along the tube axis is triggered from the two tube bases, where is the local maxima of magnetostatic energy is located. A multi-vortex state is formed during the magnetization process perpendicular to the tube axis. Several numbers of vortices are formed on the tube surface, initiated at the inner surface. In order to test its potential as an electromagnetic device, we calculated the maximum deviation of the average angle y from the hysteresis loops. That maximum deviation gives us the maximum change of AMR according to the equation R¼ R0 þ DR cos2 y. The current direction is assumed parallel to the z-axis. We use the finite element mesh to intergrate cos2y numerically over the nanotube (Fig. 3). The cos2y varies from 0.044 to 1.0 (z-directional field) and from 0.55 to 0.0 (x-directional field). The equilibrium state shown in Fig. 1 gives 0.043 as an integrated cos2y over the sample. Assuming that DR in permalloy is approxi-
Fig. 1. Equilibrium state from random initial state. Curling domain wall (b) is located between the oppositely directed vortices (a) and (c).
Fig. 2. Magnetic energy comparison between the ferromagnet state (F state) and vortex state (V state). Each symbol indicates the total magnetic energy (square), exchange energy (circle) and magnetostatic energy (triangle).
Fig. 3. Hysteresis loops (empty circle) and integrated cos2y over the nanotube (filled circle) along the upper hysteresis curve, decreasing external field from 0.4 to 0.4 T. The current (black arrow) is applied along the tube axis, the external field (white arrow) is applied parallel (a) and perpendicular (b) to the tube axis.
ARTICLE IN PRESS J. Lee et al. / Journal of Magnetism and Magnetic Materials 310 (2007) 2445–2447
mately 5%, this values corresponds to maximum change in MR of 4.8%. 4. Conclusion The potential of ferromagnet nanotube as an effective magnetic sensor is studied using micromagnetic simulations. The AMR characteristics, which behave oppositely according to the field applying directions make it possible to be used as a biaxial sensor.
2447
References [1] R. Cowburn, M. Welland, Science 287 (2000) 1466. [2] S. Khizroev, M. Kryder, D. Litvinov, D. Thomson, Appl. Phys. Lett. 81 (2002) 2256. [3] A. Goldstein, M. Gelb, P. Yager, J. Control. Release 70 (2001) 125. [4] C.A. Haberzettl, Nanotechnology 13 (2002) R9. [5] K. Nielsch, F. Castano, S. Matthias, W. Lee, C. Ross, Eng. Mater. 7 (2005) 217. [6] J. Escrig, P. Landeros, D. Altbir, E.E. Vogel, P. Vargas, J. Magn. Magn. Mater. 308 (2007) 233. [7] J. Fidler, T. Schrefl, J. Phys. D 33 (2000) R135.