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Constricted nanowire with stabilized magnetic domain wall
Author’s Accepted Manuscript Constricted nanowire with stabilized magnetic domain wall R. Sbiaa, M.Al Bahri
www.elsevier.com/locate/jmmm
PII: DOI: Reference:
S0304-8853(16)30237-2 http://dx.doi.org/10.1016/j.jmmm.2016.03.043 MAGMA61269
To appear in: Journal of Magnetism and Magnetic Materials Received date: 9 January 2016 Revised date: 27 February 2016 Accepted date: 11 March 2016 Cite this article as: R. Sbiaa and M.Al Bahri, Constricted nanowire with stabilized magnetic domain wall, Journal of Magnetism and Magnetic Materials, http://dx.doi.org/10.1016/j.jmmm.2016.03.043 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Constricted nanowire with stabilized magnetic domain wall
R. Sbiaa and M. Al Bahri Department of Physics, Sultan Qaboos University, P.O. Box 36, PC 123, Muscat, Oman
PACS 85.75.-d– Spintronics PACS 75.60.Ch– magnetic properties and materials PACS 75.76.+j– Spin transport (magnetoelectronics)
Abstract –Domain wall (DW)-based magnetic memory offers the possibility for
increasing the storage capacity. However, stability of DW remains the major drawback of this scheme. In this letter, we propose a stepped nanowire for pinning DW in a desirable position. From micromagnetic simulation, the proposed design applied to in-plane magnetic anisotropy materials shows that by adjusting the nanowire step size and its width it is possible to stabilize DW for a desirable current density range. In contrast, only a movement of DW could be seen for conventional nanowire. An extension to a multi-stepped nanowire could be used for multi-bit per cell magnetic memory.
1. Introduction Recently, magnetic nanowires that exhibit domain walls (DW), have been intensively investigated for high density magnetic memory and logic devices [18]. For the development of multi-bit per cell (MBPC) magnetic memory devices, it is crucial to control the position of DWs. It is different from the reversal of the magnetizations in magnetoresistive devices with more than one free layer [9,10]. Generally, the control of the DW position is possible by various forms of pinning schemes. Experimentally, creating artificial defects as constrictions are used to generate a potential that acts as a pinning site for DW [1116]. Designing pinning sites by lithography is challenging since this requires a high resolution lithography that is much better that making the nanowire itself. It is important to note that the size of the notch has to be much smaller than the width of the magnetic nanowire. Ion irradiation has been used to modify the magnetic properties of the exposed region which will act as a pinning site without heavy lithography process [17,18]. Nevertheless, the expansion of the irradiated area is always larger than the desired one, especially, for devices with only tens on nanometer in width. In this work, we
1
Fig. 1: (a) Schematic representations of a conventional nanowire and (b) a proposed stepped type nanowire where the step can be used for pinning the domain wall. The stepped nanowire can be made by shifting two parts in the y direction during the fabrication of the full device.
propose a new way for pinning DW in magnetic nanowire with adjustable size and position. The method is based on designing portions of the nanowire with the same size but with an off-set by a small distance in transverse direction as can be seen in Fig. 1. This off-set is conducted with a high precision during the lithography design.
2. Theoretical model Micromagnetic simulation was conducted to study the magnetic DW motions in the nanowire with the proposed scheme. Furthermore, this device could have larger number of pinning sites which leads to multi-bit per cell magnetic memory. The current-induced DW motion is investigated by numerically solving the LandauLifshiz-Gilbert equation (1)
using the public OOMMF code [19]. Here is the gyromagnetic ratio, is the damping constant fixed to 0.014 in this study and Heff is the effective magnetic field including the spin torque, exchange, demagnetizing and crystalline anisotropic fields. In the effective field, only the adiabatic spin torque term u (= JPμB/2eMs) is included 2
where J is the current density, P is the spin polarization of the current fixed to 0.6, μB is the Bohr magnetron, and e is the charge of the electron [20]. The length L and width w of the nanowire were varied while the thickness t was fixed to 3 nm. Fig. 1(a) shows a conventional type nanowire where the magnetization is aligned along the x-axis and the spin polarized current is flowing the in the x direction (length of the nanowire). The proposed scheme is represented in Fig. 1(b) where a step is created between two regions. This is much easier than forming a notch in a specific position. It can be made by defining two parts with an offset d in the y-direction as shown in Fig. 1(b). It is important to note that very high precision of the steps size can be realized using computer- aided-design (CAD) drawing prior to resist exposure.
3. Results and discussion An investigation of magnetization dynamics and domain wall movement in the two cases shown in Fig. 1 will be presented. The mesh size was fixed to 2nm × 2nm × 3nm. In this study, the magnetization was first initially aligned in the negative x direction and no external magnetic field was considered. The polarized electric current was flowing along the nanowire in the positive x direction. For the case of a conventional nanowire shown in Fig. 1 (a), DW was created and could be displaced by spin transfer torque effect from left to right without a possibility of stability. In Fig. 2, DW average velocity is plotted as a function of the current density J for different nanowire width values. An almost linear behavior was observed which is
Fig. 2: Domain wall velocity as a function of the polarized current for a conventional nanowire of length L of 200 nm and different width w. The magnetic properties of the nanowire are MS = 600 kA/m, Ku = 5.0104 J/m3 and A = 1.31011 J/m.
3
Fig. 3: Magnetization profile and domain wall position as a function of the time for a current density of 8.65×1011A/m2. (a) for t = 0.22 ns, (b) for t = 0.31 ns, (c) for t = 0.42 ns and (d) for t = 0.7 ns. The nanowire has a length L of 200 nm and width w of 40 nm. The magnetic properties are MS = 600 kA/m, Ku = 5104 J/m3 and A = 1.31011 J/m.
similar to what was reported by several groups [2123]. For the case of a very narrow nanowire (w = 20 nm), a slight deviation from the linear fit could be seen at low current density. The nanowire dimensions are shown in the insert of Fig. 2. In one dimension model and below the breakdown the average velocity can be analytically defined as:
and
= 2H + J
(2a)
= gPB/2eMs
(2b)
where g is the Landé factor and is the linearity coefficient which depends on the intrinsic properties of the material. In this set of calculation, the saturation magnetization, the magnetic anisotropy energy and the exchange stiffness were fixed to 600×103 A/m3, 5.0×104 J/m3 and 1.3×1011 J/m. From the dynamics of the DW, we observed a linear dependence of DW position with time leading to a constant velocity along the x direction of the nanowire. We selected the case of nanowire with dimension of 200 nm × 40 nm and recorded the magnetization profile in xy plane for different times. The current density was fixed to 8.65×1011A/m2. As our goal was to stabilize DW at certain position along the nanowire without using notches. For this reason, we varied the anisotropy energy Ku but DW could not be stabilized. In a second part of this work, we investigated DW dynamics in the design shown in Fig. 1(b). This scheme is easy to implement during the lithography process by designing 4
d = 5 nm
0.5
40 nm
1.0
200 nm
10 nm
mx
d
0.0 35 nm
-0.5
25 nm 15 nm
-1.0 0
1
2
3
4
5
t(ns) Fig. 4: Normalized x-component of nanowire magnetization as a function of time for different values of the off-set d. The length and width of the nanowire were fixed to 200 nm and 40 nm, respectively. The magnetic properties of the investigated material are MS = 600 kA/m, Ku = 1.0105 J/m3 and A = 1.31011 J/m.
intentionally creating an off-set in the CAD design before the laser or electron beam exposure. The length of the nanowire and its thickness were kept the same than in first part of this study. The dynamics of DW was investigated for a stepped nanowire as shown in Fig. 1(b) with different width w ranging from 20 to 60 nm. The values of Ms and A were the same as in Fig. 2 discussed earlier while Ku was fixed to 1.0×105 J/m3. The influence of the key parameter d on magnetization dynamics was investigated. Fig. 4 is a plot of the time dependence of the x component of the normalized magnetization for w = 40 nm. For small values of d (less than 10 nm), it was not possible to stabilize DW within the nanowire. The situation was similar to the conventional scheme shown in Fig. 1(a). However and as we were hoping to see, DW was blocked at the constricted region of the nanowire for d = 15 nm. It is important to note that the stability of DW occurs after small damped oscillations. The same behaviour was observed for w = 20 nm and 60 nm. It appears that the pinning DW requires a minimum value of d which itself depends on the nanowire width and the current density. In contrast to conventional type nanowire [Fig. 1(a)], DW could be pinned accurately at the stepped region. The pinning strength which depends on the parameters d, is related to the critical current density Jc which is the maximum current density to keep DW stability. Fig. 5 is a plot of Jc as a function of the parameter d for two values of w. Insert of Fig. 5 shows the geometry of the investigated device with a stabilized DW. For the same value of d, narrower device requires larger critical 5
Fig. 5: The critical current Jc versus the step size d for two different values of the nanowire width. The device geometry is shown in the insert and the magnetic properties are MS = 600 kA/m, Ku = 1.0105 J/m3 and A = 1.31011 J/m.
current to move DW from the stepped region. This is because the high pinning due to the remaining space wd. An almost linear dependence of Jc on d was observed for all cases. For real applications in the storage memory devices, it is important to move DW from one state to the other at relatively low current density.
4. Conclusion A new way for pinning accurately DW in magnetic nanowire was proposed. Micromagnetic simulation showed that by creating a stepped nanowire, it is possible to block (stabilize) DW precisely. The critical current for depinning DW showed a strong dependence on the nanowire step size, its width and the material properties. For instance, wider nanowire, requires smaller depinning current. The new device could be made in one step process during the fabrication of the nanowire by creating an off-set in the CAD file before the laser or electron beam exposure. Furthermore, this device could have more than one step leading to multi-bit per cell magnetic memory.
6
References [1] D. A. Allwood, G. Xiong, C. C. Faulkner, D. Atkinson, D. Petit and R. P. Cowburn, Science 309 1688 (2005). [2] S. S. P. Parkin, M. Hayashi, and L. Thomas, Science 320 190 (2008). [3] M. Yamanouchi et al., Science 317 1726 (2007). [4] M. Klaui M et al., J. Magn. Magn. Mater. 14 53 (2009). [5] R. Sbiaa and R. Chantrell, J. Appl. Phys. 117 053907 (2015). [6] L. Thomas et al., Science 315 1553 (2007). [7] O. Boulle et al., Phys. Rev. Lett. 101 216601 (2008). [8] S. J. Noh, R. P. Tan, B. S. Chun and Y. K. Kim, J. Magn. Magn. Mater. 322 3601 (2010). [9] R. Sbiaa, R. Law, S. Lua, E. L. Tan, T. Tahmasebi, C. C. Wang and S. N. Piramanayagam, Appl. Phys. Lett. 99 092506 (2011). [10] R. Sbiaa, J. Phys. D: Appl. Phys. 48 195001 (2015). [11] T. Koyama et al., Appl. Phys. Express 1 101303 (2008). [12] S. D. Kim, B. S. Chun and Y. K. Kim, J. Appl. Phys. 101 09F504 (2007). [13] S. H. Huang and C. H. Lai, Appl. Phys. Lett. 95 032505 (2009). [14] G. Malinowski, O. Boulle and M. Klaui, J. Phys. D. Appl. Phys. 44 384005 (2011). [15] S. J. Noh, Y. Miyamoto, M. Okuda, N. Hayashi and Y. K. Kim, J. Appl. Phys. 111 07D123 (2012). [16] H. Y. Yuan and X. R. Wang, Phys. Rev. B89 054423 (2014). [17] A. Vogel, S. Wintz, T. Gerhardt, L. Bocklage, T. Strache, M. Y. Im, P. Fischer, J. Fassbender, J. McCord and G. Meier, Appl. Phys. Lett. 98 202501 (2011). [18] M. A. Basith, S. McVitie, D. McGrouther and J. N. Chapman, Appl. Phys. Lett. 100 232402 (2012). [19] http://math.nist.gov/oommf/ [20] J. C. Slonczewski, J. Magn. Magn. Mater. 159 L1 (1996). [21] AV Khvalkovskiy, K. A. Zvezdin, Ya V. Gorbunov, V. Cros, J. Grollier, A. Fert and A. K. Zvezdin, Phys. Rev. Lett. 102 067206 (2009). [22] C. T. Boone, J. A. Katine, M. Carey, J. R. Childress, X. Cheng and I. N. Krivorotov, Phys. Rev. Lett. 104 097203 (2010). [23] R Lo Conte, E. Martinez, A. Hrabec, A. Lamperti T. Schulz, L. Nasri, L. Lazzarini, R. Mantovan, F. Maccherozzi, S. S. Dhesi, B. Ocker, C. H. Marrows, T. A. Moore and M. Klaui, Phys. Rev. B91 014433 (2015).
7
Highlights
A stepped nanowire is proposed to pin domain wall in desired position The new structure can be made by a simple off set of two single nanowires The critical current for moving domain wall from one state to the other could be tuned by adjusting the geometry of the device. The device could be used for multi-bit per cell memory by extending the steps in the device.
8
Keywords Domain wall memory; magnetic domain; magnetization reversal; micromagnetism
www.elsevier.com/locate/jmmm
PII: DOI: Reference:
S0304-8853(16)30237-2 http://dx.doi.org/10.1016/j.jmmm.2016.03.043 MAGMA61269
To appear in: Journal of Magnetism and Magnetic Materials Received date: 9 January 2016 Revised date: 27 February 2016 Accepted date: 11 March 2016 Cite this article as: R. Sbiaa and M.Al Bahri, Constricted nanowire with stabilized magnetic domain wall, Journal of Magnetism and Magnetic Materials, http://dx.doi.org/10.1016/j.jmmm.2016.03.043 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Constricted nanowire with stabilized magnetic domain wall
R. Sbiaa and M. Al Bahri Department of Physics, Sultan Qaboos University, P.O. Box 36, PC 123, Muscat, Oman
PACS 85.75.-d– Spintronics PACS 75.60.Ch– magnetic properties and materials PACS 75.76.+j– Spin transport (magnetoelectronics)
Abstract –Domain wall (DW)-based magnetic memory offers the possibility for
increasing the storage capacity. However, stability of DW remains the major drawback of this scheme. In this letter, we propose a stepped nanowire for pinning DW in a desirable position. From micromagnetic simulation, the proposed design applied to in-plane magnetic anisotropy materials shows that by adjusting the nanowire step size and its width it is possible to stabilize DW for a desirable current density range. In contrast, only a movement of DW could be seen for conventional nanowire. An extension to a multi-stepped nanowire could be used for multi-bit per cell magnetic memory.
1. Introduction Recently, magnetic nanowires that exhibit domain walls (DW), have been intensively investigated for high density magnetic memory and logic devices [18]. For the development of multi-bit per cell (MBPC) magnetic memory devices, it is crucial to control the position of DWs. It is different from the reversal of the magnetizations in magnetoresistive devices with more than one free layer [9,10]. Generally, the control of the DW position is possible by various forms of pinning schemes. Experimentally, creating artificial defects as constrictions are used to generate a potential that acts as a pinning site for DW [1116]. Designing pinning sites by lithography is challenging since this requires a high resolution lithography that is much better that making the nanowire itself. It is important to note that the size of the notch has to be much smaller than the width of the magnetic nanowire. Ion irradiation has been used to modify the magnetic properties of the exposed region which will act as a pinning site without heavy lithography process [17,18]. Nevertheless, the expansion of the irradiated area is always larger than the desired one, especially, for devices with only tens on nanometer in width. In this work, we
1
Fig. 1: (a) Schematic representations of a conventional nanowire and (b) a proposed stepped type nanowire where the step can be used for pinning the domain wall. The stepped nanowire can be made by shifting two parts in the y direction during the fabrication of the full device.
propose a new way for pinning DW in magnetic nanowire with adjustable size and position. The method is based on designing portions of the nanowire with the same size but with an off-set by a small distance in transverse direction as can be seen in Fig. 1. This off-set is conducted with a high precision during the lithography design.
2. Theoretical model Micromagnetic simulation was conducted to study the magnetic DW motions in the nanowire with the proposed scheme. Furthermore, this device could have larger number of pinning sites which leads to multi-bit per cell magnetic memory. The current-induced DW motion is investigated by numerically solving the LandauLifshiz-Gilbert equation (1)
using the public OOMMF code [19]. Here is the gyromagnetic ratio, is the damping constant fixed to 0.014 in this study and Heff is the effective magnetic field including the spin torque, exchange, demagnetizing and crystalline anisotropic fields. In the effective field, only the adiabatic spin torque term u (= JPμB/2eMs) is included 2
where J is the current density, P is the spin polarization of the current fixed to 0.6, μB is the Bohr magnetron, and e is the charge of the electron [20]. The length L and width w of the nanowire were varied while the thickness t was fixed to 3 nm. Fig. 1(a) shows a conventional type nanowire where the magnetization is aligned along the x-axis and the spin polarized current is flowing the in the x direction (length of the nanowire). The proposed scheme is represented in Fig. 1(b) where a step is created between two regions. This is much easier than forming a notch in a specific position. It can be made by defining two parts with an offset d in the y-direction as shown in Fig. 1(b). It is important to note that very high precision of the steps size can be realized using computer- aided-design (CAD) drawing prior to resist exposure.
3. Results and discussion An investigation of magnetization dynamics and domain wall movement in the two cases shown in Fig. 1 will be presented. The mesh size was fixed to 2nm × 2nm × 3nm. In this study, the magnetization was first initially aligned in the negative x direction and no external magnetic field was considered. The polarized electric current was flowing along the nanowire in the positive x direction. For the case of a conventional nanowire shown in Fig. 1 (a), DW was created and could be displaced by spin transfer torque effect from left to right without a possibility of stability. In Fig. 2, DW average velocity
Fig. 2: Domain wall velocity as a function of the polarized current for a conventional nanowire of length L of 200 nm and different width w. The magnetic properties of the nanowire are MS = 600 kA/m, Ku = 5.0104 J/m3 and A = 1.31011 J/m.
3
Fig. 3: Magnetization profile and domain wall position as a function of the time for a current density of 8.65×1011A/m2. (a) for t = 0.22 ns, (b) for t = 0.31 ns, (c) for t = 0.42 ns and (d) for t = 0.7 ns. The nanowire has a length L of 200 nm and width w of 40 nm. The magnetic properties are MS = 600 kA/m, Ku = 5104 J/m3 and A = 1.31011 J/m.
similar to what was reported by several groups [2123]. For the case of a very narrow nanowire (w = 20 nm), a slight deviation from the linear fit could be seen at low current density. The nanowire dimensions are shown in the insert of Fig. 2. In one dimension model and below the breakdown the average velocity can be analytically defined as:
and
(2a)
= gPB/2eMs
(2b)
where g is the Landé factor and is the linearity coefficient which depends on the intrinsic properties of the material. In this set of calculation, the saturation magnetization, the magnetic anisotropy energy and the exchange stiffness were fixed to 600×103 A/m3, 5.0×104 J/m3 and 1.3×1011 J/m. From the dynamics of the DW, we observed a linear dependence of DW position with time leading to a constant velocity along the x direction of the nanowire. We selected the case of nanowire with dimension of 200 nm × 40 nm and recorded the magnetization profile in xy plane for different times. The current density was fixed to 8.65×1011A/m2. As our goal was to stabilize DW at certain position along the nanowire without using notches. For this reason, we varied the anisotropy energy Ku but DW could not be stabilized. In a second part of this work, we investigated DW dynamics in the design shown in Fig. 1(b). This scheme is easy to implement during the lithography process by designing 4
d = 5 nm
0.5
40 nm
1.0
200 nm
10 nm
mx
d
0.0 35 nm
-0.5
25 nm 15 nm
-1.0 0
1
2
3
4
5
t(ns) Fig. 4: Normalized x-component of nanowire magnetization as a function of time for different values of the off-set d. The length and width of the nanowire were fixed to 200 nm and 40 nm, respectively. The magnetic properties of the investigated material are MS = 600 kA/m, Ku = 1.0105 J/m3 and A = 1.31011 J/m.
intentionally creating an off-set in the CAD design before the laser or electron beam exposure. The length of the nanowire and its thickness were kept the same than in first part of this study. The dynamics of DW was investigated for a stepped nanowire as shown in Fig. 1(b) with different width w ranging from 20 to 60 nm. The values of Ms and A were the same as in Fig. 2 discussed earlier while Ku was fixed to 1.0×105 J/m3. The influence of the key parameter d on magnetization dynamics was investigated. Fig. 4 is a plot of the time dependence of the x component of the normalized magnetization for w = 40 nm. For small values of d (less than 10 nm), it was not possible to stabilize DW within the nanowire. The situation was similar to the conventional scheme shown in Fig. 1(a). However and as we were hoping to see, DW was blocked at the constricted region of the nanowire for d = 15 nm. It is important to note that the stability of DW occurs after small damped oscillations. The same behaviour was observed for w = 20 nm and 60 nm. It appears that the pinning DW requires a minimum value of d which itself depends on the nanowire width and the current density. In contrast to conventional type nanowire [Fig. 1(a)], DW could be pinned accurately at the stepped region. The pinning strength which depends on the parameters d, is related to the critical current density Jc which is the maximum current density to keep DW stability. Fig. 5 is a plot of Jc as a function of the parameter d for two values of w. Insert of Fig. 5 shows the geometry of the investigated device with a stabilized DW. For the same value of d, narrower device requires larger critical 5
Fig. 5: The critical current Jc versus the step size d for two different values of the nanowire width. The device geometry is shown in the insert and the magnetic properties are MS = 600 kA/m, Ku = 1.0105 J/m3 and A = 1.31011 J/m.
current to move DW from the stepped region. This is because the high pinning due to the remaining space wd. An almost linear dependence of Jc on d was observed for all cases. For real applications in the storage memory devices, it is important to move DW from one state to the other at relatively low current density.
4. Conclusion A new way for pinning accurately DW in magnetic nanowire was proposed. Micromagnetic simulation showed that by creating a stepped nanowire, it is possible to block (stabilize) DW precisely. The critical current for depinning DW showed a strong dependence on the nanowire step size, its width and the material properties. For instance, wider nanowire, requires smaller depinning current. The new device could be made in one step process during the fabrication of the nanowire by creating an off-set in the CAD file before the laser or electron beam exposure. Furthermore, this device could have more than one step leading to multi-bit per cell magnetic memory.
6
References [1] D. A. Allwood, G. Xiong, C. C. Faulkner, D. Atkinson, D. Petit and R. P. Cowburn, Science 309 1688 (2005). [2] S. S. P. Parkin, M. Hayashi, and L. Thomas, Science 320 190 (2008). [3] M. Yamanouchi et al., Science 317 1726 (2007). [4] M. Klaui M et al., J. Magn. Magn. Mater. 14 53 (2009). [5] R. Sbiaa and R. Chantrell, J. Appl. Phys. 117 053907 (2015). [6] L. Thomas et al., Science 315 1553 (2007). [7] O. Boulle et al., Phys. Rev. Lett. 101 216601 (2008). [8] S. J. Noh, R. P. Tan, B. S. Chun and Y. K. Kim, J. Magn. Magn. Mater. 322 3601 (2010). [9] R. Sbiaa, R. Law, S. Lua, E. L. Tan, T. Tahmasebi, C. C. Wang and S. N. Piramanayagam, Appl. Phys. Lett. 99 092506 (2011). [10] R. Sbiaa, J. Phys. D: Appl. Phys. 48 195001 (2015). [11] T. Koyama et al., Appl. Phys. Express 1 101303 (2008). [12] S. D. Kim, B. S. Chun and Y. K. Kim, J. Appl. Phys. 101 09F504 (2007). [13] S. H. Huang and C. H. Lai, Appl. Phys. Lett. 95 032505 (2009). [14] G. Malinowski, O. Boulle and M. Klaui, J. Phys. D. Appl. Phys. 44 384005 (2011). [15] S. J. Noh, Y. Miyamoto, M. Okuda, N. Hayashi and Y. K. Kim, J. Appl. Phys. 111 07D123 (2012). [16] H. Y. Yuan and X. R. Wang, Phys. Rev. B89 054423 (2014). [17] A. Vogel, S. Wintz, T. Gerhardt, L. Bocklage, T. Strache, M. Y. Im, P. Fischer, J. Fassbender, J. McCord and G. Meier, Appl. Phys. Lett. 98 202501 (2011). [18] M. A. Basith, S. McVitie, D. McGrouther and J. N. Chapman, Appl. Phys. Lett. 100 232402 (2012). [19] http://math.nist.gov/oommf/ [20] J. C. Slonczewski, J. Magn. Magn. Mater. 159 L1 (1996). [21] AV Khvalkovskiy, K. A. Zvezdin, Ya V. Gorbunov, V. Cros, J. Grollier, A. Fert and A. K. Zvezdin, Phys. Rev. Lett. 102 067206 (2009). [22] C. T. Boone, J. A. Katine, M. Carey, J. R. Childress, X. Cheng and I. N. Krivorotov, Phys. Rev. Lett. 104 097203 (2010). [23] R Lo Conte, E. Martinez, A. Hrabec, A. Lamperti T. Schulz, L. Nasri, L. Lazzarini, R. Mantovan, F. Maccherozzi, S. S. Dhesi, B. Ocker, C. H. Marrows, T. A. Moore and M. Klaui, Phys. Rev. B91 014433 (2015).
7
Highlights
A stepped nanowire is proposed to pin domain wall in desired position The new structure can be made by a simple off set of two single nanowires The critical current for moving domain wall from one state to the other could be tuned by adjusting the geometry of the device. The device could be used for multi-bit per cell memory by extending the steps in the device.
8
Keywords Domain wall memory; magnetic domain; magnetization reversal; micromagnetism