A nanomagnets majority logic gate based on heterogeneous multiferroic structure global strain clock

Dou Shu-Qing; Yang Xiao-Kuo; Xia Yong-Shun; Yuan Jia-Hui; Cui Huan-Qing; Wei Bo; Bai Xin; Feng Chao-Wen

doi:10.7498/aps.72.20230866

Abstract

In the post-Moore era, nanomagnetic logic circuits have shown great potential to replace complementary metal oxide semiconductor (CMOS) circuits. A majority logic gate, as the core of a nanomagnetic logic circuit, is equivalent to the inverter in the CMOS circuit. A nanomagnetic logic majority gate generally has four nanomagnets arranged in a “T” shape. The nanomagnets in the three corners of the “T” (I₁, I₂, I₃) are the three inputs, and the middle nanomagnet is the output (O).This paper proposes a nanomagnet majority logic gate based on the global strain clock of heterogeneous multiferroic structure, by utilizing the difference in response to the same strain between positive magnetostrictive coefficient material (Terfenol-D) and negative magnetostrictive coefficient material (Ni). From bottom to top, the device is mainly composed of a silicon substrate, a piezoelectric layer, and four elliptical cylindrical nanomagnets. PMN-PT is used as the piezoelectric layer’s material, and three Ni-based nanomagnets (I₁, I₂, and I₃) are utilized as input, while Terfenol-D is used as the material for the output nanomagnet (O).Besides, a two-step calculation mode of “high-stress start-low-stress calculation” is designed, that is, the O is first switched to the “Null” with a stress of –30 MPa, and then the stress decreases to –15 MPa, so that the O can realize majority calculation under the coupling of I₁, I₂, and I₃. The micromagnetic simulation software MuMax3 is adopted to simulate the performance of the device. The results reveal that the device can successfully perform continuous majority calculation through any three-terminal input combination. By using the two-step calculation mode, the calculation accuracy of the device can reach 100%, its cycle of continuous calculation is 2.75 ns, and the cycle energy consumption is about 64 aJ. It is found that the change of energy potential well, caused by the change of stress anisotropy energy and dipole coupling energy, is the main reason that determines the magnetization dynamic behavior of the device. Therefore, the results of this paper can provide important guidance for designing nanomagnetic logic circuits.

Keywords:

Authors and contacts

1.
Fundamentals Department, Air Force Engineering University, Xi’an 710051, China
2.
College of Artificial Intelligence, Chongqing Technology and Business University, Chongqing 400067, China

Corresponding author: Yang Xiao-Kuo, yangxk0123@163.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 62274183) and the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2022JQ-073).

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References

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[3]	Gypens P, Leliaert J, Van Waeyenberge B 2018 Phys. Rev. Appl. 9 034004 Google Scholar
[4]	Gonelli M, Fin S, Carlotti G, Dey H, Csaba G, Porod W, Bernstein G H, Bisero D 2018 J. Magn. Magn. Mater. 460 432 Google Scholar
[5]	Imre A, Csaba G, Ji L, Orlov A, Bernstein G, Porod W 2006 Science 311 205 Google Scholar
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[9]	Gu Z, Nowakowski M E, Carlton D B, Storz R, Im M Y, Hong J, Chao W, Lambson B, Bennett P, Alam M T, Marcus M A, Doran A, Young A, Scholl A, Fischer P, Bokor J 2015 Nat. Commun. 6 6466 Google Scholar
[10]	杨晓阔, 张斌, 崔焕卿, 李伟伟, 王森 2016 65 237502 Google Scholar Yang X K, Zhang B, Cui H Q, Li W W, Wang S 2016 Acta Phys. Sin. 65 237502 Google Scholar
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[13]	Alam M T, Kurtz S J, Siddiq M A J, Niemier M T, Bernstein G H, Hu X S, Porod W 2011 IEEE Trans. Nanotechnol. 11 273 Google Scholar
[14]	张明亮, 蔡理, 杨晓阔, 秦涛, 刘小强, 冯朝文, 王森 2014 63 227503 Google Scholar Zhang M L, Cai L, Yang X K, Qin T, Liu X Q, Feng C W, Wang S 2014 Acta Phys. Sin. 63 227503 Google Scholar
[15]	Bhowmik D, You L, Salahuddin S 2014 Nat. Nanotechnol. 9 59 Google Scholar
[16]	Suh D I, Bae G Y, Oh H S, Park W 2015 J. Appl. Phys. 117 17D714 Google Scholar
[17]	Sengupta A, Choday S H, Kim Y, Roy K 2015 Appl. Phys. Lett. 106 143701 Google Scholar
[18]	Ostwal V, Debashis P, Faria R, Chen Z H, Appenzeller J 2018 Sci. Rep. 8 16689 Google Scholar
[19]	Liu M, Zou Q, Ma C R, Collins G, Mi S B, Jia C L, Guo H M, Gao H J, Chen C L 2014 ACS Appl. Mater. Interfaces 6 8526 Google Scholar
[20]	Cui H Q, Cai L, Yang X K, Wang S, Feng C W, Xu L, Zhang M L 2017 J. Phys. D:Appl. Phys. 50 285001 Google Scholar
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[26]	Chen Y B, Yang X K, Wei B, Cui H Q, Song M X 2020 IEEE Access 8 77802 Google Scholar
[27]	Zhang J, Lee W K, Tu R, Rhee D, Zhao R, Wang X, Liu X, Hu X, Zhang X, Odom T, Yan M 2021 Nano Lett. 21 5430 Google Scholar
[28]	Chen A T, Piao H G, Zhang C H, Ma X P, Algaidi H, Ma Y C, Li Y, Zheng D X, Qiu Z D, Zhang X X 2023 Mater. Horiz. DOI: 10.1039/d3mh00378
[29]	Khojah R, Xiao Z, Panduranga M K, Bogumil M, Wang Y, Goiriena-Goikoetxea M, Chopdekar R V, Bokor J, Carman G P, Candler R N, Di Carlo D 2021 Adv. Mater. 33 2006651 Google Scholar
[30]	Huang B, Zhu W, Hua L, Wang J, Guo Y 2022 Curr. Appl. Phys. 41 139 Google Scholar
[31]	Jin T L, Hao L, Cao J W, Liu M F, Dang H G, Wang Y, Wu D P, Bai J M, Wei F L 2014 Appl. Phys. Express 7 043002 Google Scholar
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[33]	Roy K, Bandyopadhyay S, Atulasimha J 2011 Phys. Rev. B 83 224412 Google Scholar
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[35]	Chen Y B, Wei B, Yang X K, Liu J H, Li J, Cui H Q, Li C, Song M X 2020 J. Magn. Magn. Mater. 514 167216 Google Scholar
[36]	Beleggia M, Graef M D, Millev Y T, Goode D A, Rowlands G 2005 J. Phys. D: Appl. Phys. 38 3333 Google Scholar
[37]	Vacca M, Graziano M, Crescenzo L D, Chiolerio A, Lamberti A, Balma D, Canavese G, Celegato F, Enrico E, Tiberto P, Boarino L, Zamboni M 2014 IEEE Trans. Nanotechnol. 13 963 Google Scholar
[38]	Fidler J, Schrefl T 2000 J. Phys. D:Appl. Phys. 33 R135 Google Scholar
[39]	Boechler G P, Whitney J M, Lent C S, Orlov A O, Snider G L 2010 Appl. Phys. Lett. 97 103502 Google Scholar

Cited By

图 1 椭圆柱体纳磁体布尔逻辑编码方式

Figure 1. Cylindrical elliptical nanomagnet logic coding for Booleans.

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图 2 NMLC组件　(a)择多逻辑门 (b) 铁磁耦合互连线; (c) 反铁磁耦合互连线

Figure 2. NMLC Components: (a) Majority gate; (b) ferromagnetic coupling interconnect wire; (c) anti-ferromagnetic coupling interconnect wire.

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图 3 异质多铁结构全局应变时钟纳磁体择多逻辑门　(a) 立体结构; (b) 俯视图

Figure 3. Nanomagnets majority gate based on global strain clock of heterogeneous multiferroic structure: (a) Stereo structure; (b) top view.

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图 4 应变时钟作用示意图

Figure 4. Schematic diagram of strain clock.

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图 5 异质多铁择多门连续工作磁化动态过程　(a) 初始态000, 输入依次为“101”, “000”, “111”和“001”时的磁化动态曲线; (b) 第3周期, 即“0000”条件下输入“111”择多计算详细磁化动态过程; (c)—(n) 异质多铁择多门中纳磁体磁化状态

Figure 5. Magnetization dynamic process of the majority gate continuously work: (a) The dynamics of the magnetization curve when the initial state is “000” and the input is “101”, “000”, “111”, “001” in sequence; (b) the detailed magnetization dynamic process calculated at the third cycle, i.e., at input “111” under “0000” conditions; (c)–(n) magnetization states of nanomagnets in the majority gate.

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图 6 纳磁体能量势垒方向及其能量势阱方向　(a) 能量势阱附近的单侧波动; (b) 跨越短轴的双侧波动; (c) 施加极性相反的电压时或者撤去电压后, 磁矩进动的方向

Figure 6. Nanomagnet’s energy potential well direction and its energy barrier direction: (a) Unilateral fluctuations near the energy potential well; (b) bilateral fluctuations across the short axis; (c) the direction of the magnetic moment progresses when a voltage of opposite polarity is applied or when the voltage is removed.

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图 7 异质多铁择多门所有择多计算情形下, O的磁矩的动态变化. 0—0.5 ns, 施加–30 MPa应力; 0.5—3 ns, 施加–15 MPa应力. “000-0”代表初始状态为: I₁I₂I₃ = 000, O = 0时O的磁矩的动态变化曲线

Figure 7. Dynamic variation of the magnetic moment of O for all calculation cases of the logic gate. 0–0.5 ns, –30 MPa stress applied; 0.5–3 ns, –15 MPa stress applied. “000-0” represents the dynamic variation of the magnetic moment of O when the initial state is: I₁I₂I₃ = 000 and O = 0.

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图 8 信息传出逻辑门的所有情形下, O和T_O的磁矩的动态变化. 全局应变时钟: 0—0.5 ns, 施加–30 MPa应力; 0.5—1.5 ns, 施加–15 MPa应力; 1.5—2.5 ns, 施加250 MPa应力. T_O控制时钟: 0—2.5 ns, 施加300 MPa应力. “000-0”代表初始状态为: I₁I₂I₃ = 000且O = 0时, O的磁矩的动态曲线; “0000-0”代表初始状态为: I₁I₂I₃O = 0000且T_O= 0时, T_O的磁矩的动态曲线

Figure 8. Dynamic variation of the magnetic moments of O and T_O for all cases of information passing out of the logic gate. Global strain clock: 0–0.5 ns, –30 MPa stress applied; 0.5–1.5 ns, –15 MPa stress applied; 1.5–2.5 ns, 250 MPa stress applied. T_O control clock: 0–2.5 ns, 300 MPa stress applied. “000-0” represents the dynamic curve of the magnetic moment of O when the initial state is: I₁I₂I₃ = 000 and O = 0; “0000-0” represents the dynamic curve of the magnetic moment of T_O when the initial state is: I₁I₂I₃O = 0000 and T_O= 0.

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图 9 异质多铁择多门连续计算时的能量演化　(a) 全局应变时钟; (b)—(f) I₁, I₂, I₃, O及T_O的能量密度; (g) T_O 控制时钟

Figure 9. Energy evolution during continuous computation of the logic gate: (a) Global strain clock; (b)–(f) energy density of I₁, I₂, I₃, O and T_O; (g) control the clock of T_O.

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图 10 纳磁体磁矩偏转90°　(a)—(c) 一致的单畴态偏转; (a), (d)—(g), (c) 非一致的“C”形态偏转

Figure 10. Nanomagnet magnetic moment switching 90°: (a)–(c) Uniform single-domain Switching; (a), (d)–(g), (c) non-uniform “C” form Switching.

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表 1 器件尺寸及布局参数

Table 1. Parameters of the device size and layout.

名称	尺寸/nm	名称	尺寸/nm
所有纳磁体长轴 a	120	I₂与O间距 l₁	80
所有纳磁体厚度 h	10	I₁, I₃与O间距 l₂	120
O的短轴 b₁	90	T_O与O间距 l₃	50
其余纳磁体短轴 b₂	80	T₁, T₂, T₃分别与I₂, I₂, I₃ 水平间距 l₄	20
压电层长度 l_y	700	T₁, T₂, T₃分别与I₂, I₂, I₃ 垂直中心距 l₅	80
压电层宽度 l_x	265	压电层厚度 l_z	100

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表 2 纳磁体材料参数

Table 2. Material parameters of nanomagnets.

	Terfenol-D	Ni
杨氏模量 Y/10¹⁰ Pa	8	21.4
磁致伸缩系数 λ_S/10^–4	+6	–0.2
吉尔伯特阻尼系数 α	0.1	0.045
饱和磁化强度 M_S/(10⁵ A·m^–1)	8	4.85
交换作用常数 A/(10^–11 J·m^–1)	0.9	1.05

DownLoad: CSV

表 3 应变时钟参数

Table 3. Strain clock parameters.

时钟参数	数值/MPa	时钟参数	数值/ns
σ₊	250	t₁	1.25
σ_H–	–30	t₂	1.75
σ_L–	–15	t₃	2.75
$ \sigma_{T_{O} } $	300	t₄	3

DownLoad: CSV

map

[1]	DeBenedictis, P E 2017 Computer 50 72 Google Scholar
[2]	Liu S L, Hu X S, Nahas J J, Niemier M T, Porod W, Bernstein G H 2011 IEEE Trans. Nanotechnol. 10 757 Google Scholar
[3]	Gypens P, Leliaert J, Van Waeyenberge B 2018 Phys. Rev. Appl. 9 034004 Google Scholar
[4]	Gonelli M, Fin S, Carlotti G, Dey H, Csaba G, Porod W, Bernstein G H, Bisero D 2018 J. Magn. Magn. Mater. 460 432 Google Scholar
[5]	Imre A, Csaba G, Ji L, Orlov A, Bernstein G, Porod W 2006 Science 311 205 Google Scholar
[6]	Orlov A, Imre A, Csaba G, Ji L, Porod W, Bernstein G 2008 J. Nanoelectron. Optoelectron. 3 55 Google Scholar
[7]	刘嘉豪, 杨晓阔, 危波, 李成, 张明亮, 李闯, 董丹娜 2019 68 017501 Google Scholar Liu J H, Yang X K, Wei B, Li C, Zhang M L, Li C, Dong D N 2019 Acta Phys. Sin. 68 017501 Google Scholar
[8]	Carlton D B, Lambson B, Scholl A, Young A T, Dhuey S D, Ashby P D, Tuchfeld E, Bokor J 2011 IEEE Trans. Nanotechnol. 10 1401 Google Scholar
[9]	Gu Z, Nowakowski M E, Carlton D B, Storz R, Im M Y, Hong J, Chao W, Lambson B, Bennett P, Alam M T, Marcus M A, Doran A, Young A, Scholl A, Fischer P, Bokor J 2015 Nat. Commun. 6 6466 Google Scholar
[10]	杨晓阔, 张斌, 崔焕卿, 李伟伟, 王森 2016 65 237502 Google Scholar Yang X K, Zhang B, Cui H Q, Li W W, Wang S 2016 Acta Phys. Sin. 65 237502 Google Scholar
[11]	Atulasimha J, Bandyopadhyay S 2010 Appl. Phys. Lett. 97 173105 Google Scholar
[12]	张楠, 张保, 杨美音, 蔡凯明, 盛宇, 李予才, 邓永城, 王开友 2017 66 027501 Google Scholar 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 Google Scholar
[13]	Alam M T, Kurtz S J, Siddiq M A J, Niemier M T, Bernstein G H, Hu X S, Porod W 2011 IEEE Trans. Nanotechnol. 11 273 Google Scholar
[14]	张明亮, 蔡理, 杨晓阔, 秦涛, 刘小强, 冯朝文, 王森 2014 63 227503 Google Scholar Zhang M L, Cai L, Yang X K, Qin T, Liu X Q, Feng C W, Wang S 2014 Acta Phys. Sin. 63 227503 Google Scholar
[15]	Bhowmik D, You L, Salahuddin S 2014 Nat. Nanotechnol. 9 59 Google Scholar
[16]	Suh D I, Bae G Y, Oh H S, Park W 2015 J. Appl. Phys. 117 17D714 Google Scholar
[17]	Sengupta A, Choday S H, Kim Y, Roy K 2015 Appl. Phys. Lett. 106 143701 Google Scholar
[18]	Ostwal V, Debashis P, Faria R, Chen Z H, Appenzeller J 2018 Sci. Rep. 8 16689 Google Scholar
[19]	Liu M, Zou Q, Ma C R, Collins G, Mi S B, Jia C L, Guo H M, Gao H J, Chen C L 2014 ACS Appl. Mater. Interfaces 6 8526 Google Scholar
[20]	Cui H Q, Cai L, Yang X K, Wang S, Feng C W, Xu L, Zhang M L 2017 J. Phys. D:Appl. Phys. 50 285001 Google Scholar
[21]	Yuan J H, Yang X K, Wei B, Chen Y B, Cui H Q, Liu J H, Dou S Q, Song M X, Fei L 2023 Phys. Rev. Appl. 19 014003 Google Scholar
[22]	Bandyopadhyay S, Atulasimha J, Barman A 2021 Appl. Phys. Rev. 8 041323 Google Scholar
[23]	危波, 蔡理, 杨晓阔, 李成 2017 66 217501 Google Scholar Wei B, Cai L, Yang X K, Li C 2017 Acta Phys. Sin. 66 217501 Google Scholar
[24]	Yilmaz Y, Mazumder P 2013 IEEE Trans. Very Large Scale Integr. VLSI Syst. 21 1181 Google Scholar
[25]	D’Souza N, Salehi Fashami M, Bandyopadhyay S, Atulasimha J 2016 Nano Lett. 16 1069 Google Scholar
[26]	Chen Y B, Yang X K, Wei B, Cui H Q, Song M X 2020 IEEE Access 8 77802 Google Scholar
[27]	Zhang J, Lee W K, Tu R, Rhee D, Zhao R, Wang X, Liu X, Hu X, Zhang X, Odom T, Yan M 2021 Nano Lett. 21 5430 Google Scholar
[28]	Chen A T, Piao H G, Zhang C H, Ma X P, Algaidi H, Ma Y C, Li Y, Zheng D X, Qiu Z D, Zhang X X 2023 Mater. Horiz. DOI: 10.1039/d3mh00378
[29]	Khojah R, Xiao Z, Panduranga M K, Bogumil M, Wang Y, Goiriena-Goikoetxea M, Chopdekar R V, Bokor J, Carman G P, Candler R N, Di Carlo D 2021 Adv. Mater. 33 2006651 Google Scholar
[30]	Huang B, Zhu W, Hua L, Wang J, Guo Y 2022 Curr. Appl. Phys. 41 139 Google Scholar
[31]	Jin T L, Hao L, Cao J W, Liu M F, Dang H G, Wang Y, Wu D P, Bai J M, Wei F L 2014 Appl. Phys. Express 7 043002 Google Scholar
[32]	Pathak P, Mallick D 2022 IEEE Trans. Magn. 58 3401406 Google Scholar
[33]	Roy K, Bandyopadhyay S, Atulasimha J 2011 Phys. Rev. B 83 224412 Google Scholar
[34]	Bhattacharya D, Al-Rashid M M, D'Souza N, Bandyopadhyay S, Atulasimha J 2017 Nanotechnology 28 015202 Google Scholar
[35]	Chen Y B, Wei B, Yang X K, Liu J H, Li J, Cui H Q, Li C, Song M X 2020 J. Magn. Magn. Mater. 514 167216 Google Scholar
[36]	Beleggia M, Graef M D, Millev Y T, Goode D A, Rowlands G 2005 J. Phys. D: Appl. Phys. 38 3333 Google Scholar
[37]	Vacca M, Graziano M, Crescenzo L D, Chiolerio A, Lamberti A, Balma D, Canavese G, Celegato F, Enrico E, Tiberto P, Boarino L, Zamboni M 2014 IEEE Trans. Nanotechnol. 13 963 Google Scholar
[38]	Fidler J, Schrefl T 2000 J. Phys. D:Appl. Phys. 33 R135 Google Scholar
[39]	Boechler G P, Whitney J M, Lent C S, Orlov A O, Snider G L 2010 Appl. Phys. Lett. 97 103502 Google Scholar

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Vol. 72, Issue 15 - 2023-08-05

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