Experimental Clocking of Nanomagnets with Strain for Ultra Low Power Boolean Logic

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Nanomagnetic implementations of Boolean logic [1,2] have garnered attention because of their non-volatility and the potential for unprecedented energy-efficiency. Unfortunately, the large dissipative losses that take place when nanomagnets are
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  1   Experimental Clocking of Nanomagnets with Strain for Ultra Low Power Boolean Logic Noel D'Souza a , Mohammad Salehi Fashami a , Supriyo Bandyopadhyay b  and Jayasimha Atulasimha a,* a Department of Mechanical and Nuclear Engineering b Department of Electrical and Computer Engineering Virginia Commonwealth University, Richmond, VA 23284, USA Nanomagnetic implementations of Boolean logic 1,2  have garnered attention because of their non-volatility and the potential for unprecedented energy-efficiency. Unfortunately, the large dissipative losses that occur when nanomagnets are switched with a magnetic field 3  or spin-transfer-torque 4  inhibit the promised energy-efficiency. Recently, there have been experimental reports of utilizing the Spin Hall effect for switching magnets 5–7  , and theoretical proposals for strain induced switching of single-domain magnetostrictive nanomagnets 8–12 , that might reduce the dissipative losses significantly. Here, we experimentally demonstrate, for the first time, that strain-induced switching of single-domain magnetostrictive nanomagnets of lateral dimensions ~200 nm fabricated on a piezoelectric substrate can implement a nanomagnetic Boolean NOT gate and unidirectional bit information propagation in dipole-coupled nanomagnet chains. This portends ultra-low-energy logic processors and mobile electronics that may operate solely by harvesting energy from the environment without ever needing a battery. * Correspondence to be addressed to jatulasimha@vcu.edu  2   Nanomagnet-based logic switches 1,2 , in which logic bits 0 and 1 are encoded in two stable magnetization orientations along the easy (major) axis of a shape-anisotropic elliptical single-domainnanomagnet, and in which switching is accomplished by flipping the magnetization from one stable orientation to the other, have emerged as potential replacements for current complementary metal-oxide-semiconductor (CMOS) transistor switches because of superior energy-efficiency. In this letter, we demonstrate strain-induced switching of nanomagnets that could render nanomagnetic logic 2-3 orders of magnitude more energy-efficient than conventional transistor-based logic. A transistor dissipates at least ~10 4  kT of energy to switch in isolation 13  and 10 5  kT to switch in a circuit in a reasonable time of ~1 ns. In contrast, a magnetic binary switch may dissipate a mere ~10 2  kT of energy to switch in ~1 ns if implemented with an elliptical, two-phase composite multiferroic nanomagnet consisting of a single-domain magnetostrictive layer elastically coupled to an underlying piezoelectric layer 8–10 . When a tiny electrostatic potential is applied across the piezoelectric layer, it deforms and the resulting strain is transferred to the magnetostrictive layer, making its magnetization rotate by a large angle as shown in Fig. 1. Such rotations can be utilized to write bits in non-volatile memory 12,14,15 or implement Bennett-clocked logic gates in the fashion of magnetic quantum cellular automata 1,2,8,10 . So far, several experimental studies have been performed to demonstrate strain-induced magnetization switching 16–19 , but only in magnets that are either multi-domain 20 , or where strain moves domain walls to switch the magnetization (instead of rotating it) 21–23  or in single-domain nanomagnets where the coherent rotation is ~90º and not ~180 o24 . The experimental studies in this work demonstrate, for the first time, strain-induced 180 o  switching of  3   single-domain magnetostrictive nanomagnets on a piezoelectric substrate to realize a Boolean NOT logic gate and unidirectional propagation of logic bit information down a chain of nanomagnets. These are the key steps in the realization of strain-clocked nanomagnetic logic and information processing. Strain-induced switching of magnetization is demonstrated using magnetostrictive Co nanomagnets (nominal diameter ~200 nm) deposited on a (001) Pb(Mg 1/3 Nb 2/3 )O 3 –PbTiO 3  (PMN-PT) 70/30 substrate of dimensions 5  5  0.5 mm 3 . The experimental setup is described in Supplementary section A. At first, the substrate is poled with an 800 kV m -1  electric field and subsequently a linear strain-field characteristic is observed up to 400 kV m -1 . Next, the magnets are deposited on the poled substrate and their magnetizations “initialized” to the ‘down’ direction (  ) by applying a magnetic field of ~200 mT along the easy axis of the nanomagnets. Finally, an electric field of 400 kV m -1  is applied along the poling direction that generates a strain of ~400 ppm in PMN-PT which is mostly transferred to the ~12 nm thick nanomagnets and produces a stress of ~80 MPa therein (cobalt’s Young's Modulus ~200 GPa 25 ). The results of the material characterization of the cobalt thin-film (SEM, EDS, M-H curves, etc.) and the PMN-PT substrate (surface roughness, EDS) are shown in Supplementary Section B. The negligible effect of the thin CoO layer (< 2 nm over a period of several weeks) that develops on the Co nanomagnets owing to surface oxidation is also discussed in Supplementary section B(c). Three different cases are discussed below:  4   CASE I: Isolated nanomagnets (Fig. 1): We study an array of nanomagnets with inter-magnet spacing (~800 nm) large enough to disallow any significant dipole interaction between neighbours. They are all initially magnetized in the same (“down”) direction as shown in the left panel of Fig. 1a and the right panel indicates the direction in which we expect the magnetization to rotate when a tensile (+  ) or compressive (-  ) stress is applied. Figs. 1b and 1c show experimental MFM images of the nanomagnets prior to and after application of tensile stress. In Fig. 1b (magnet volume nominally 250×150×12 nm 3 ), the stress generated is not large enough to overcome the shape anisotropy of the magnets and make the magnetizations rotate. Thus, the pre-stress (Fig. 1b, left) and post-stress (Fig. 1b, right) magnetic states are identical. Fig. 1c (magnet volume nominally 200×175×12 nm 3 ) shows that nanomagnets with lower shape anisotropy do experience magnetization rotation. When stress is applied to these nanomagnets, their magnetizations orient themselves along the hard axis by rotating through ~90º. Upon removal of the stress, the magnetizations have equal probability of returning to their initial orientations or flipping to the opposite directions. Hence, one would expect 50% of the magnets will flip their magnetization orientation from "down" to "up" and the rest would flip back to the srcinal "down" state. However, owing to uncontrollable factors such as lithographic variances, surface roughness, stress concentration, etc., only a fraction of the magnets meet the correct condition (stress anisotropy greater than shape anisotropy to allow ~90º rotation), resulting in far fewer than 50% of the magnets flipping their magnetization orientations by 180º. The magnet dimensions are chosen to ensure that the shape anisotropy is high enough to allow good MFM  5   imaging and yet small enough to allow stress to rotate the magnetization (see supplementary section A). CASE II: Two dipole-coupled nanomagnets: Boolean NOT gate (Fig. 2): Consider two elliptical nanomagnets as shown in Fig. 2a that are spaced close enough to allow significant dipole coupling. Since the line joining their centres lie along the minor axes of the ellipses, the dipole coupling will favour anti-parallel ordering. Each nanomagnet encodes a logic bit in its magnetization orientation (say, the “up” orientation encodes bit 1 and “down” orientation bit 0). The magnetization orientation of the left and right magnets represents the input and output bit respectively. The anti-parallel ordering should make the output bit the logic complement of the input bit and make the magnet pair act as a NOT gate, but this is not automatic. Suppose that the right magnet’s orientation was initially “down” and an input bit (“0”) arrived to orient the left magnet’s orientation to the “down” state, thereby leaving both the magnets in the “down” state denoted by (  ) as in Fig. 2a(i). While the dipole coupling prefers the (  ) state, it is not strong enough (centre-centre distance ~300 nm) to make the right magnet’s (R) magnetization overcome its own shape anisotropy energy barrier and flip to assume the “up” orientation. To make it do so, we need to “clock” the magnetostrictive nanomagnets with stress. The left magnet is deliberately designed to be more shape anisotropic (~250×150×12 nm 3 ) than the right (~200×175×12 nm 3 ). Therefore, a global strain/stress that affects both nanomagnets will rotate only the right nanomagnet’s magnetization if the stress is strong enough to overcome the shape anisotropy of the right but not the left nanomagnet. This ensures unidirectionality in information propagation, i.e. the magnetization state of the left influences that of the right, but not vice versa.
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