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The scaling of traditional complementary metal oxide semiconductor (CMOS) device is reaching its physical limit, and alternative emerging devices are being explored as possible CMOS substitutes. One of the most promising device technologies is nano-magnetic logic (NML), which is an energy-efficient computing paradigm. The inherent nonvolatility and low energy consumption make NML device possess wide application perspectives. The basic element of multiferroic NML is a sub-100 nm sized single domain magnet. Generally, the x-y plane determines the in-plane dimension, while the z direction indicates the thickness of nanomagnet. Classical binary logic states 0 and 1 are encoded in two stable magnetization orientations along the easy axis (major axis) of the elliptical nanomagnet, while the hard axis (minor axis) refers to null logic. In order to propagate logic bits between the neighbor nanomagnets, one requires a clock that periodically flips every magnet's magnetization along the hard axis simultaneously, and the dipole-dipole interaction between the neighbors will force the magnet into the correct orientation along the easy axis, and thus the logic bit propagates unidirectionally. In multiferroic NML, the majority gate is a basic element of nanomagnet logcal circuit. In this paper, the three-dimensional switching dynamic model of a multiferroic nanomagnetic majority gate is established, and its magnetization dynamics is simulated by solving the Landau-Lifshitz-Gilbert equation with considering the thermal fluctuation effects. The majority gate is implemented with dipole-coupled two-phase (magnetostrictive/piezoelectric) multiferroic elements and is simulated by using different strain clocks and changing the input. It is found that the majority gate works efficiently and correctly when receiving new input. It is also found that the optimal time interval of stress releasing between central nanomagnet and output nanomagnet is 0.1-0.2 ns. Removing stress earlier will reduce the success rate of the majority gate operation while the work frequency increases. The reason behind the phenomenon may be that removing stress earlier results in weak dipole-coupled interaction, which cannot overcome the shape anisotropy. These findings are beneficial to the design of multiferroic logic circuit.
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Keywords:
- multiferroic nanomagnet /
- majority gate /
- strain clock /
- magnetization dynamics
[1] Cowburn R P, Welland M E 2000 Science 287 1466
[2] Csaba G, Imre A, Bernstein G H, Porod W, Metlushko V 2002 IEEE Trans. Nanotechnol. 1 209
[3] Vacca M, Graziano M, Crescenzo L D, Chiolerio A, Lamberti A, Balma D, Canavese C, Celegato F, Enrico E, Tiberto P, Boarino L, Zamboni M 2014 IEEE Trans. Nanotechnol. 13 963
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[11] Zhang M L, Cai L, Yang X K, Qing T, Liu X Q, Feng C W, Wang S 2014 Acta Phys. Sin. 63 227503 (in Chinese) [张明亮, 蔡理, 杨晓阔, 秦涛, 刘小强, 冯朝文, 王森 2014 物理学报 63 227503]
[12] Bhowmik D, You L, Salahuddin S 2014 Nat. Nanotechnol. 9 59
[13] Ralph D C, Stiles M D 2008 J. Magn. Magn. Mater. 320 1190
[14] Fashami M S, Roy K, Atulasimha J, Bandyopadhyay S 2011 Nanotechnology 22 155201
[15] Souza N D, Fashami M S, Bandyopadhyay S, Atulasimha J 2016 Nano Lett. 16 1609
[16] Biswas A K, Ahmad H, Atulasimha J, Bandyopadhyay S 2017 Nano Lett. 17 3478
[17] Yilmaz Y, Mazumder P 2013 IEEE Trans. VLSI Syst. 21 1181
[18] Yang X K, Cai L, Kang Q, Bai P, Zhao X H, Feng C W, Zhang L S 2011 Acta Phys. Sin. 60 098503 (in Chinese) [杨晓阔, 蔡理, 康强, 柏鹏, 赵晓辉, 冯朝文, 张立森 2011 物理学报 60 098503]
[19] Chikazumi S 1964 Physics of Magnetism (New York: Wiley) p25
[20] Fidler J, Schrefl T 2000 J. Phys. D: Appl. Phys. 33 R135
[21] Brown W F 1963 Phys. Rev. 130 1677
[22] Fashami M S, Roy K, Atulasimha J, Bandyopadyay S 2011 Nanotechnology 22 309501
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[1] Cowburn R P, Welland M E 2000 Science 287 1466
[2] Csaba G, Imre A, Bernstein G H, Porod W, Metlushko V 2002 IEEE Trans. Nanotechnol. 1 209
[3] Vacca M, Graziano M, Crescenzo L D, Chiolerio A, Lamberti A, Balma D, Canavese C, Celegato F, Enrico E, Tiberto P, Boarino L, Zamboni M 2014 IEEE Trans. Nanotechnol. 13 963
[4] Imre A, Csaba G, Ji L, Orlov A, Bernstein G H, Porod W 2006 Science 311 205
[5] Niemier M T, Bernstein G H, Dingler A, Hu X S, Kurtz S, Liu S, Nahas J, Porod W, Siddiq M, Varga E 2011 J. Phys.: Condens. Matter 23 493202
[6] Yang X K, Zhang B, Cui H Q, Li W W, Wang S 2016 Acta Phys. Sin. 65 237502 (in Chinese) [杨晓阔, 张斌, 崔焕卿, 李伟伟, 王森 2016 物理学报 65 237502]
[7] Tiercelin N, Dusch Y, Klimov A, Giordano S, Preobrazhensky V, Pernod P 2011 Appl. Phys. Lett. 99 192507
[8] Atulasimha J, Bandyopadhyay S 2010 Appl. Phys. Lett. 97 173105
[9] Zhang N, Zhang B, Yang M Y, Cai K M, Sheng Y, Li Y C, Deng Y C, Wang K Y 2017 Acta Phys. Sin. 66 027501 (in Chinese) [张楠, 张保, 杨美音, 蔡凯明, 盛宇, 李予才, 邓永城, 王开友 2017 物理学报 66 027501]
[10] Alam M T, Kurtz S J, Siddiq M A J, Niemier M T, Bernstein G H, Hu X S, Porod W 2012 IEEE Trans. Nanotechnol. 11 273
[11] Zhang M L, Cai L, Yang X K, Qing T, Liu X Q, Feng C W, Wang S 2014 Acta Phys. Sin. 63 227503 (in Chinese) [张明亮, 蔡理, 杨晓阔, 秦涛, 刘小强, 冯朝文, 王森 2014 物理学报 63 227503]
[12] Bhowmik D, You L, Salahuddin S 2014 Nat. Nanotechnol. 9 59
[13] Ralph D C, Stiles M D 2008 J. Magn. Magn. Mater. 320 1190
[14] Fashami M S, Roy K, Atulasimha J, Bandyopadhyay S 2011 Nanotechnology 22 155201
[15] Souza N D, Fashami M S, Bandyopadhyay S, Atulasimha J 2016 Nano Lett. 16 1609
[16] Biswas A K, Ahmad H, Atulasimha J, Bandyopadhyay S 2017 Nano Lett. 17 3478
[17] Yilmaz Y, Mazumder P 2013 IEEE Trans. VLSI Syst. 21 1181
[18] Yang X K, Cai L, Kang Q, Bai P, Zhao X H, Feng C W, Zhang L S 2011 Acta Phys. Sin. 60 098503 (in Chinese) [杨晓阔, 蔡理, 康强, 柏鹏, 赵晓辉, 冯朝文, 张立森 2011 物理学报 60 098503]
[19] Chikazumi S 1964 Physics of Magnetism (New York: Wiley) p25
[20] Fidler J, Schrefl T 2000 J. Phys. D: Appl. Phys. 33 R135
[21] Brown W F 1963 Phys. Rev. 130 1677
[22] Fashami M S, Roy K, Atulasimha J, Bandyopadyay S 2011 Nanotechnology 22 309501
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