Deterministic Control of Magnetization Dynamics in Reconfigurable Nanomagnetic Networks for Logic Applications Arabinda Haldar and Adekunle Olusola Adeyeye* Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore 117576, Singapore S Supporting Information *
ABSTRACT: Information processing based on nanomagnetic networks is an emerging area of spintronics, as the energy consumption and integration density of the current semiconductor technology are reaching their fundamental limits. Nanomagnetbased devices rely on manipulating the magnetic ground states for device operations. While the static behavior of nanomagnets has been explored, little information is available on their dynamic behavior. Here, we demonstrate an additional functionality based on their collective dynamic response and explore the concept utilizing networks of bistable rhomboid nanomagnets. The control of the magnetic ground states of the networks was achieved by the geometrical design of the nanomagnets instead of the conventional interelement dipolar coupling. Dynamic responses of both the ferromagnetic and antiferromagnetic ground states were monitored using broadband ferromagnetic resonance spectroscopy, the Brillouin light scattering technique, and direct magnetic force microscopy. Micromagnetic simulations and numerical calculations validate our experimental observations. This method would have potential implications for low-power magnonic devices based on reconfigurable microwave properties. KEYWORDS: nanomagnetic logic, nanomagnetic networks, magnetostatic interactions, magnetization dynamics, spintronics, ferromagnetic resonance spectroscopy, magnetic force microscopy promising for reconfigurable microwave applications,21 which can be operated in zero bias field, and the ground states can be switched by using simple field pulses.22 However, experimental evidence of this functionality is less known. One of the reasons that hinders this possibility is that a dipolar coupling driven AFM ground state requires a carefully adjusted field initialization process, and it is susceptible to structural imperfections. This approach is unreliable to obtain a uniform ground state over a large area. However, reconfigurable dynamic responses were demonstrated earlier by switching between ground magnetic states that were obtained through precise minor loop hysteresis23−25 or through hysteretic quasiuniform magnetization states.26 Note that these methods are slow in speed and involve a complex field initialization process, which may not be suitable for device integration. Therefore, it is of great interest to find alternatives that are not only capable of operating at zero bias field but also programmable in a fast and
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anomagnet-based memory and logic operations are of great technological interest due to their nonvolatility, ultrahigh density, unlimited endurance, and thermal robustness.1−3 They offer an appealing alternative over current CMOS technology, which is volatile and dissipates large power. They draw multiple research efforts, thereby resulting in remarkable progress in information processing based on spin waves,4−6 domain-wall motion-based devices,7−9 coupled vortices,10−12 binary nanomagnets (Ni80Fe20/Ni),13 and nanowires.14 Nanomagnetic logic has been realized using a magnetic quantum-dot cellular automata approach, and the operation of a majority logic gate was demonstrated in such systems.15−18 In this method, binary information is stored in bistable units, and the information is processed through dipolar-coupled chains leading to ferromagnetic (FM) and/or antiferromagnetic (AFM) ordering for appropriately structured arrays.19 The operation of nanomagnetic logic relies on appropriate magnetic ordering of the output magnet with respect to input (bias) magnets after a clocking field is applied.20 To date, most of the studies on such coupled chains have been focusing on their static behavior using magnetic force microscopy (MFM) and tuning them for different logic operations. Such architecture is © 2016 American Chemical Society
Received: December 14, 2015 Accepted: January 7, 2016 Published: January 7, 2016 1690
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Figure 1. (a) Demonstration of P-, Q-, and R-type nanomagnets for an initialization field, HI, of 2000 Oe → 0 along the x-axis showing the parameters used to define the geometry. (b) Energy landscape illustrating shift in energy minima and maxima in P-magnets as compared to Rmagnets. (c, d) Hysteresis loops in P- and R-magnets along geometrical short and long axes. (e) Simulated demagnetization field distributions at remanence due to a P-nanomagnet. (f) Line scans of the y-component of the stray field (HS‑y) at a distance of 50 (L1), 75 (L2), and 100 nm (L3) from the right edge of the nanomagnet. Simulated demagnetization field distributions for PQ, PQP, and PPQ networks at ferromagnetic (g) and antiferromagnetic (h) ground states. The gap (δ) between the coupled P- and Q-magnets is 50 nm.
combinations of such RNMs, which will enable advanced control on magnonic bands.22,24 A simple switching mechanism of the two ground magnetic states and its distinct dynamic responses are appealing for the development of magnetic logic gates and tunable RF/microwave devices that can be operated without the use of a bias magnetic field. This architecture is also promising for ultrahigh-density integration, as the dimensions of the networks are smaller compared to logic operations based on coupled vortices,28 nanowires,14 and domain-wall motionbased devices.7−9 In addition, one may use such nanomagnetic chains as a waveguide for spin-wave transport and manipulation. Such waveguides will not require a bias field, which is used in waveguides made from magnetic wires.29
simple manner. Moreover, robust designs are desired from a fabrication point of view, as mentioned earlier, so that they can be implemented in large-area patterns, which is particularly important for practical applications. Here, we propose and demonstrate a simple method to stabilize both the FM and AFM ground states over a large area using bistable nanomagnetic networks made from rhomboidshaped nanomagnets (RNMs), which addresses the abovementioned issues observed so far. Reconfigurable microwave properties have been demonstrated in these networks using ferromagnetic resonance (FMR) and Brillouin light scattering (BLS) spectroscopy. Instead of magnetic coupling induced anisotropy, we utilize shape-induced magnetic anisotropy from the RNM to achieve deterministic magnetic ground states. A RNM stabilizes into a unique magnetic ground state after being initialized along its geometrical short axis irrespective of its coupled neighbors in the network.27 Networks of two and three RNM networks were lithographically defined, and their magnetic ground states were directly imaged using MFM. By selectively placing the RNMs, unprecedented control of FM and AFM ground states of different types with distinct dynamics responses was obtained for the different networks. On the basis of the reconfigurable microwave properties, we propose the XOR logic operation using a network with two coupled RNMs. Micromagnetic simulations and numerical calculations were used to obtain insights in magnetization reversal mechanisms and magnetization dynamics. Reprogrammable magnetic ground states and microwave properties would have immediate implications for miniaturized microwave electronics.21 Our approach has several advantages over previous methods. Thanks to their geometry, RNM-based networks are suitable for obtaining arbitrary ground states over a very large area, which were elusive in dipolar-coupling-driven architecture. Periodic variation of magnetic properties in one, two, or all three spatial directions can now be achieved using
RESULTS AND DISCUSSION We utilize two types of rhomboid nanomagnets to construct the different magnetic ground states with a high degree of reliability. Figure 1a illustrates two RNMs, which are called Pand Q-type RNMs, along with a rectangular nanomagnet (Rtype) for reference. Note that the Q-magnet is a mirror image of the P-magnet. The dimensions of the RNMs were set to 300 nm × 130 nm × 25 nm (u × w × t), where u and w are the sides of the RNMs and t is the thickness. The angle of the slanted edge θ for the RNMs was 32°. Identical parameters were used for the R-magnet. For the coordinate system x-, y-, and z-axes were chosen to be along the short, long, and out-ofplane (thickness) directions of the nanomagnet, respectively. In order to investigate the magnetization reversal mechanisms, micromagnetic simulations were performed using the finite element based micromagnetic solver OOMMF, a public domain software.30 Simulated magnetization distributions in these stand-alone magnets are shown after initializing them with a field, HI, of 2000 Oe → 0 along the geometrical short axis (i.e., x-axis). At remanence magnetization always points upward (↑) in the P-magnets and downward (↓) in the Q1691
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Figure 2. (a) Schematics of the experimental setup showing the coplanar waveguides and the sample orientations on top of it. (b) Scanning electron micrographs of PQ, PQP, and PPQ networks, isolated PQ array, and reference R-magnet array. (c) Experimental MFM contrasts for all the samples mentioned above after initialization with HI: 2000 Oe → 0 along the short axis. Observed magnetization directions are shown as north pole and south pole. (d) Easy axis MOKE hysteresis loops for all the above-mentioned samples. The results are shown for δ = 100 nm for the coupled networks. (e) Simulated magnetic hysteresis loops for the PQ network (δ = 100 nm). Simulated spin configurations for the hard axis loop at field points (i to vi) are shown at the right.
magnets. In comparison, a multidomain magnetization with arbitrary net magnetization (↑ or ↓) was observed in Rmagnets. Figure 1b illustrates that unlike the R-magnets, the energy maximum (hard) and minimum (easy) of the RNMs do not lie along the geometrical short and long axis, respectively. We found a deviation (Δφ) of about 10° between the magnetic hard and geometrical short axis. As a consequence, a favorable magnetization direction at remanence occurs in the RNMs for field initialization along the geometrical short axis. The full magnetic hysteresis loops of P- and R-magnets were compared in Figure 1c and d for fields applied along the short and long axis, respectively. The RNMs tend to orient into well-defined ground states at a field Happ ≈ ±1000 Oe, while reducing the field applied along the x-axis (Figure 1c). On the other hand, a larger coercive field for the RNMs was observed for a field applied along the long axis (Figure 1d). Figure 1e shows the stray fields (HS) from a single P-type magnet. The regions of larger field strength are represented by darker contrasts in these images. The y-component of the stray fields (HS‑y) at a distance of 50 nm (L1), 75 nm (L2), and 100 nm (L3) from the right edge of the P-magnet is shown in Figure 1f. The maximum stray field (HS‑y) value at L3 is about 100 Oe, the direction of which depends on the magnetic orientation of the RNM. In order to manipulate the effective internal fields, we designed different physically separated but dipolar coupled networks by selectively choosing P- and Q-magnets according to the desired operation. Figure 1g,h show such networks, which consist of PQ, PQP, and PPQ magnets. The gap (δ)
between two neighboring nanomagnets was 50 nm. The FM ground states were obtained using HI (2000 Oe → 0) applied along the long axis (i.e., y-axis). On the other hand, HI (2000 Oe → 0) applied along the short axis results in down−up (↑↓), down−up−down (↑↓↑), and down−down−up (↑↑↓) magnetization orientations for PQ, PQP, and PPQ networks, respectively. For simplicity of discussion in what follows, we denote all the magnetization states obtained with HI along the short axis as an AFM state and a FM state for HI along the long axis. The stray field distributions in FM and AFM remanent configurations are also shown in Figure 1g,h. It should be noted that a nanomagnet in a network experiences different stray fields depending on the magnetic orientations of its coupled neighbors. This means that the effective field (Heff = Happ ± HS‑y; Happ refers to applied magnetic field) inside a nanomagnet in the network will be different, and this is pictorially indicated by yellow markers, which essentially indicate the direction of HS‑y as Happ = 0. It can be seen that the internal field increases in the AFM cases except for the PPQ network, where the stray field effect is almost canceled. On the other hand, the stray field direction is always in the opposite direction of magnetization in the FM ground states, leading to reduction of the internal fields. We have used this concept to control the microwave properties of the RNMs networks, as will be discussed in detail later. In order to experimentally validate the simulated results described in Figure 1, Permalloy (Ni80Fe20) RNMs with the above-mentioned dimensions were patterned using electron beam lithography on top of predefined coplanar waveguides (CPWs) made from a 200 nm thick, 20 μm wide Pt signal line 1692
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Figure 3. (a) Experimental and (b) simulated FMR absorptions spectra at remanence (Happ = 0) for PQ, PQP, and PPQ networks (δ = 50 nm), an isolated PQ array, and a reference R magnet array at AFM (red solid line) and FM (black dotted line) configurations. Prominent modes are denoted by black squares, red circles, and blue triangles. (c) Simulated spatial mode profiles for the prominent resonant peaks obtained in simulations for all the above-mentioned samples.
observations confirm that the stray fields from the nearest neighbor do not alter the magnetic orientations of individual nanomagnets in a network, and it is the shape anisotropy that defines the ground magnetic state. An MFM image for the rectangular nanomagnets shows the magnetizations mostly point upward with few nanomagnets in the multidomain ground states. To compare the experimental MFM contrasts from the samples, we have calculated the stray field (zcomponent) at a constant height, and the results are provided in Supporting Information Figure S2. These calculated results are in good agreement with the observed experimental MFM images. The collective magnetization reversal mechanism of the samples was studied using the magneto-optical Kerr effect (MOKE) setup in longitudinal MOKE configuration with an angle of incidence of 45° and a laser (635 nm) spot size of about 5 μm. The normalized easy axis hysteresis loops are shown in Figure 2d for all the samples (δ = 100 nm for the coupled networks). The coercive field (HC) values vary from 823 Oe for the PQ network and isolated PQ array to 860 Oe for PQP and PPQ networks. It can be seen that HC is larger in samples made from P- and Q-magnets as compared with HC = 602 Oe for the reference R-magnet. This is in agreement with the simulated results as shown in Figure 1d. We note that the values of the coercive field do not vary significantly with δ in the coupled networks (not shown). In order to investigate the reversal process when the field was applied along the short axis, we have used the micromagnetic method, and the results are shown in Figure 2e for PQ network (δ = 100 nm). An easy axis loop is shown for comparison. Magnetic configurations at different field locations are shown for a hard axis loop on the right side. At zero field, an AFM ground state (↓↑ or ↑↓) can be observed, as also confirmed with MFM measurements (Figure 2c). Next, the functionality of these networks based on reconfigurable magnetization dynamics is demonstrated using broadband FMR spectroscopy. In order to excite ferromagnetic
as shown in Figure 2a. Scanning electron microscopy (SEM) images of the coupled networks PQ, PQP, and PPQ for δ = 50 nm are shown in Figure 2b. Note that the coupled networks were also patterned for δ = 75 and 100 nm to investigate the effect of dipolar coupling (see Supporting Information Figure S1). Arrays of the networks were prepared to enhance the signal in the FMR absorption experiment, and the networks were decoupled by setting a large (>1.5 × u) distance between them. This implies that the FMR absorption will represent the response of a single network. In a real device, a single RNM network would be sufficient for operations with suitable detection techniques. For comparison, isolated arrays of PQmagnets and R-magnets were fabricated with identical dimensions, and the SEM images are also shown in Figure 2b. Note that the dimensions of the nanomagnets were chosen following extensive micromagnetic simulations to ensure a single domain ground magnetic state and pattern reliably on a large area. But the results are not limited to these dimensions and can be scaled down further. Some of the results on smaller dimensions will be discussed later in this report and in the Supporting Information. To investigate the ground states of the nanomagnets, we have used the MFM imaging technique in the conventional lift mode using a commercial CoCr-coated low-moment tip at a constant height (40 nm). Prior to MFM measurements shown in Figure 2c, the samples were initialized with HI: 2000 Oe → 0 along the short axis. PQ networks show sharp alternate bright and dark MFM contrasts in each network. This implies all the PQ networks have antiparallel magnetization: ↑↓. In the PQP network, an up−down−up (↑↓↑) magnetization state can be observed, whereas an up−up-down (↑↑↓) magnetization state was obtained in the PPQ network. It should be noted that similar MFM results are also obtained in the networks with δ = 75 and 100 nm (see Supporting Information Figure S2). P- and Q-magnets have ↑ and ↓ magnetization, respectively, in the isolated PQ array. Magnetic orientations are represented by north and south poles in the insets of Figure 2c. These 1693
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ACS Nano resonant modes, coplanar waveguides were used. FMR responses of the arrays were measured using a microwave vector network analyzer with the two ports connected to the CPW using ground−signal−ground (GSG)-type microwave probes. Rows of Figure 3a show the experimental FMR absorption spectra measured at zero field for all the samples (δ = 50 nm for the networks) at AFM and FM ground states obtained with HI: 2000 Oe → 0 applied along the x-axis (red solid line) and the y-axis (black dotted line), respectively. The results of isolated PQ- and R-magnet arrays are also shown for comparison. Three prominent resonant modes were observed for all the samples made from P- and Q-magnets in FM/AFM ground states, as denoted by black squares, red circles, and blue triangles, marked only in the spectra for hard axis initializations. A clear shift between the FM and the AFM spectra is observed in all the coupled networks. For instance in the PQ network, the modes at 5.14, 6.87, and 7.75 GHz in the FM state are shifted to 5.54, 7.19, and 7.98 GHz, respectively. Positive shifts (Δf) of the modes can also be observed in the other two coupled networks, although the magnitude of the shift is different for different networks. In the case of an isolated PQ array, no shift between FM/AFM FMR spectra is found. On the contrary, a single mode at 7.56 GHz is observed in the reference R-magnet array with no difference in the spectra for the two different field initializations. To identify the observed modes, we have carried out micromagnetic simulations using OOMMF, and the results are shown in Figure 3b. The five rows show the simulated FMR spectra for all the samples corresponding to experimental results in Figure 3a. All the major modes and the frequency shift between FM and AFM states are also observed in simulations for coupled networks. The slight difference between experimental and simulated spectra of the R-magnet is due to the difference in their ground magnetic state, which is multidomain in the simulation (Figure 1a) and mostly single domain in the experiment (Figure 2c). In order to obtain further insights into the modes, plots of simulated spatial mode profiles are shown in Figure 3c. Each row shows the spatial amplitude distributions of one sample for the modes denoted by colored symbols in Figure 3b. Modes, denoted by black squares, were found to be concentrated near the edges, and those denoted by red circles were located mainly at the center of the nanomagnets. From these surface profiles we identify the first as edge modes (EM) and the latter as center modes (CM). The modes marked with blue triangles have nodal lines near the edges of the nanomagnets. Note that these three types of modes were observed at remanence. Additional measurements were carried out to investigate the field dependence of these modes, and the results are provided in Supporting Information Figure S3. We found that the mode with highest frequency (denoted by blue triangles) appears only in the low-field regime (−600 Oe < Happ < 600 Oe), whereas the EM and CM persist over the full field cycle (−1400 Oe → 0 → 1400 Oe). For the analysis of the observed frequency shift, we concentrate on the center mode (f CM) for comparing the frequency shift between the FM and AFM states in the coupled networks (denoted by red circles). The frequency shift is defined as Δf CM = f CM(AFM) − f CM(FM). The experimental values of Δf CM are 320, 345, and 170 MHz for PQ, PQP, and PPQ networks, respectively. The variation of the frequency shift can be estimated using the Kittel formula:
fres =
γ (Heff + (Nz − Ny)My)(Heff + (Nx − Ny)My) 2π
where Nx, Ny, and Nz are the demagnetization factors along the x-, y-, and z-directions, respectively, and these factors obey the relation Nx + Ny + Nz = 4π. The variation in the effective fields inside the nanomagnets in different networks is pictorially depicted in Figure 1g and h. From our earlier discussions, Heff = Happ − HS‑y for the FM states of all the networks and Heff = Happ + HS‑y for the AFM states of PQ and PQP networks. Now to estimate Δf, we have calculated the demagnetization factors for an isolated rectangular magnet, for simplification, with u = 300 nm, w = 130 nm, and t = 25 nm according to the formulations derived by Aharoni.31 The calculated values are Nx = 0.683π, Ny = 0.286π, and Nz = 3.031π. Using these values in the Kittel formula, we have obtained a frequency shift Δf = 210 MHz for 50 Oe field variation, which is close to the value for the stray field estimated in Figure 1f. It should result in a frequency shift of 2 × Δf for PQ and PQP networks. On the other hand, as the stray field effect is nullified in the AFM state of the PPQ network, a frequency shift of Δf should be expected. This explains the variation of Δf CM in different networks. With this argument no frequency shift is expected in the absence of a stray field, and this is confirmed in the spectra for the decoupled arrays (isolated PQ and R). Note that the choice of center modes for analysis was based on their prominent intensities in the spectra. The edge modes with lower intensities also show similar shifts in frequencies to the center modes and the same explanation for frequency shifts holds for the edge modes. As magnetostatic interaction was found to play the key role in the dynamic responses, the effect of interelement gap, δ, has been systematically investigated. Figure 4a shows the
Figure 4. (a) Variation of experimental FMR absorption spectra for PQP network as a function of the interelement gap, δ, in the FM and AFM ground states. (b) Variation of Δf CM = f CM(AFM) − f CM(FM) with δ for the coupled networks PQ, PQP, and PPQ. Connecting lines between the symbols are a guide to the eye.
experimental FMR absorption spectra of the PQP network for δ = 50, 75, and 100 nm. Figure 4b shows the frequency shift of the center mode ( f CM) for all the coupled networks PQ, PQP, and PPQ as a function of δ. From the FMR spectra, it can be seen that the modes in the FM ground state are more sensitive to δ as compared to the modes in the AFM ground state. This may be attributed to the opposite stray field configurations in the FM and AFM states, as discussed earlier (Figure 1g and h). The frequency shift decreases with 1694
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ACS Nano increasing δ, and the results indicate that Δf can be tuned by varying δ, which is promising for practical applications. Next, we have experimentally demonstrated the XOR logic operation through distinct dynamic responses of the different ground magnetic states of the PQ network for δ = 50 nm, as shown in Figure 5. The ground states of the two constituting
CPW, as shown in Figure 6a. BLS measurements were performed by sweeping the excitation frequency in 100 MHz
Figure 6. (a) Experimental geometry for micro-BLS spectroscopy. Magnetization dynamics was measured from a single PQ network (δ = 50 nm) with a laser focused down to 250 nm. (b) BLS spectra at FM and AFM ground states as a function of excitation frequency.
steps from 4 to 10 GHz. The BLS spectra for the two ground magnetic states (FM and AFM) are shown in Figure 6b. FM (↓ ↓ and ↑↑) and AFM (↓↑ and ↑↓) ground states were obtained by applying HI along the long and short axis, respectively. We noticed that prominent resonant modes appear at 6.9 and 7.3 GHz for the FM and AFM states, respectively. This is in good agreement with the FMR spectra as shown for logic operation. A larger frequency shift is desirable for unambiguous identification of the modes in device operation. As we have shown before, Δf increases with increasing stray field contribution between FM and AFM states. In order to enhance the frequency shift, we have utilized this fact and fabricated a network of 10 RNMs for demonstration as shown in Figure 7a−c. Shown in Figure 7a is the SEM image of an array of 10 coupled alternate P- and Q-magnets (δ = 50 nm). The MFM image shows the AFM ground state after initialization (HI: 2000 Oe → 0) along the short axis (Figure 7b). Experimental
Figure 5. (a) Experimental absorption spectra for the PQ network (δ = 50 nm) at different ground states of the input magnets P and Q for the demonstration of XOR logic operation. (b) Truth table for the XOR gate where absorption at 7.2 GHz was used as an output.
RNMs (P and Q) were used as two logical inputs, where ↓ and ↑ magnetizations refer to logic input 0 and 1, respectively. FM (↓↓ and ↑↑) and AFM (↓↑ and ↑↓) ground states were obtained by applying HI along the long and short axis, respectively. We have used FMR to monitor the output of the device. We noticed a prominent resonant mode for the AFM states at 7.2 GHz in the FMR absorption spectra (Figure 5a), and it is defined as the logical output 1. In the FM states, however, the resonant modes appear at a different frequency, leading to no absorption at 7.2 GHz, thereby referring to logical output 0. The results obtained in this experiment represent an XOR logic operation as shown in Figure 5b. For practical implementations, the input magnetic states can be switched using electric/magnetic field pulses in a cross-point array structure, thereby acting as inputs. On the other hand, the FMR response can be read-out electrically using spin pumping32 and inverse spin-Hall effect.33,34 There are several benefits of this strategy. Because no bias field is required during the operation of the device, it dissipates less energy. The proposed logic device has smaller dimensions as compared to earlier demonstrations on logic operations based on vortices,28 nanowires,13 and domain walls,7−9 which implies much denser arrays. From the additional simulation results provided in Supporting Information Figure S4, switching between the FM and AFM states was obtained using a sub-nanosecond field pulse, which is promising for ultrafast operations.35 Since this is a first experimental proof of concept for the logic using a new strategy that utilizes bistable RNMs, several technical issues for practical implementation of real devices should be addressed in future works, which include on-chip reconfiguration of the inputs and readout mechanism, optimization of threshold frequency in a dense array, signal-to-noise ratio for electrical readout, delay time to synchronize different logic gates, and fanout operation. In order to assess the performance of a single network, we have carried out BLS measurements with a laser focused down to 250 nm, well known as micro-BLS.36 For demonstration, we have fabricated PQ networks (δ = 50 nm) on top of a shorted
Figure 7. (a) SEM micrograph of the networks of 10 nanomagnets with alternate P- and Q-magnets, denoted by 10PQ. (b) Experimental MFM image in the AFM ground state for the 10 PQ network. (c) Experimental and simulated FMR absorption spectra for the 10PQ network at FM and AFM ground states. (d) SEM image of downscaled PQP network with u × w × δ = 150 × 90 × 40 nm3, denoted by small PQP. (e) MFM image of the AFM ground state for the small-PQP network. (f) Experimental and simulated FMR absorption spectra at the FM and AFM ground state for the small-PQP network. 1695
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fabrication defects, and we showed uniform results in large-area arrays. The control of dynamic responses was achieved by manipulating the amplitude/direction of the magnetostatic interactions, and flexibility of tuning the dynamics has been emphasized by selectively placing the RNMs in a coupled network. Experimental results are validated using micromagnetic simulations and numerical analysis. Improvement of the operation of such devices was obtained by downscaling the dimensions and increasing the number of nanomagnets in a network. Operation of an XOR logic gate was experimentally demonstrated based on distinct dynamics of FM and AFM ground states. Ultrafast (subnanoseconds) switching of the different ground states was estimated using micromagnetic simulations. This approach offers several advantages, which include low power operation, ultrafast reconfiguration of the magnetization dynamics, and small device size. The implications of this work are not limited only to the proposed logic operation. The deterministic control over magnetic ground states and probing magnetization dynamics as an output will add extra functionalities in nanomagnetic network-based spintronic devices. As shown here, the ground state of an RNM is not affected by its coupled neighbor, which is an important attribute also for biasing operations and as a fixed layer in spin-valve devices. This method can also provide an unprecedented advantage for obtaining periodic magnetic properties in all three spatial directions over a large area deterministically. Tunabilities of the ground magnetic state as well as its dynamics in RNM networks are appealing for programmable logic and storage with larger integration density and low power operation. Moreover, RNM networks can be used as spin-wave waveguides that will not require a bias magnetic field for spin-wave transport. This may solve the requirement of the prohibitively large bias field used so far.29,37 Gating of spin-wave signals can be achieved by switching one of the magnets in the waveguide, which is promising for transistortype operation, as shown recently using nanowires.38 We believe that the results will facilitate the development of nanomagnetic network based information processing.
and simulated FMR absorption spectra for FM and AFM ground states are shown in Figure 7c. Two major modes are found from both experiment and simulation. We obtain the frequency shifts (Δf) of 1000 and 1200 MHz for the lower and higher frequency modes, respectively. These values are in good agreement with the simulated results, which are 1100 and 1300 MHz, respectively. The larger frequency shift is the outcome of the increase of the stray field due to more coupled neighbors. In order to assess the effect of the number (n) of nanomagnets in a network on Δf, additional simulations were carried out in downsized nanomagnetic networks by varying n (see Supporting Information Figure S5). We found that the value of the frequency shift increases with increasing n, and it is saturated above n = 15. In addition, these simulation results show that Δf has increased when the dimensions are downsized. For an experimental demonstration of this observation, an array of downscaled PQP networks was fabricated with u × w × δ = 150 × 90 × 40 nm3, hereafter denoted by small PQP, as shown in the SEM image in Figure 7d. The AFM ground state was stabilized in this array after initialization (HI: 2000 Oe → 0) along its geometrical short axis (Figure 7e). Shown in Figure 7f are the FMR absorption spectra that were acquired for FM and AFM ground states, and the results are compared with simulations. In a small PQP network, two prominent modes can be observed, and the value of Δf is 600 MHz, which is larger than Δf = 345 MHz obtained for a regular PQP network, although we also note that the line width of the resonant modes has increased slightly with size reduction. For unambiguous identification of the two distinct modes one should optimize the value of Δf, which can be achieved by increasing the number of nanomagnets in a network, as shown in Supporting Information Figure S5 or by using new materials with appropriate magnetic properties. In order to further assess the effect of dimensions on the dynamics, we have carried out simulations by varying the angle (θ) of the slanted edge of the RNM (see Supporting Information Figure S6) using the PQP network. The AFM ground state was obtained for θ as small as 10°, and a wide range of frequency tunability was found by varying θ. Another important parameter for optimization of performance and exploring new possibilities is the thickness of the RNMs. Simulation results provided in Supporting Information Figure S7 show the variation of coercive fields (easy axis), HC, as a function of thickness for a single P-magnet of two different sizes. HC has a maximum at 30 nm thickness for both the dimensions. Correct magnetic orientation was found for a thickness as high as 60 nm when initialized along the short axis. Thickness-dependent results indicate that it is possible to use such magnets in spin valve architecture by appropriately choosing the thickness for lower and higher coercive field values. One can also imagine creating an AFM lattice an inplane as well as in an out-of-plane direction with such nanomagnets. This may open up new opportunities for reconfigurable 2D and 3D microwave magnetic metamaterials.
METHODS Sample Fabrication. Oxidized Si substrates were spin-coated with PFI positive photoresist followed by optical lithography for patterning 20 μm wide coplanar waveguides with ground−signal−ground lines. After developing in AZ 300 MIF solution, a thin film stack of Cr (5 nm) and Pt (200 nm) was deposited using electron beam evaporation and sputtering technique, respectively. The bottom Cr layer was used for seeding. The CPWs were obtained by metal lift-off with acetone and ultrasonic agitation. Then the substrate was spin-coated with positive resist polymethyl methacrylate (PMMA) for patterning the nanomagnets on top of the CPWs using high-resolution electron beam lithography technique followed by developing in MIBK (methyl isobutyl ketone) and IPA (isopropyl alcohol) solution with MIBK:IPA = 1:3. Electron beam evaporation of a bilayer of Cr(5 nm)/ Ni80Fe20(25 nm) was carried out at 4.5 × 10−8 Torr base pressure and at 0.2 Å/s deposition rate. Magnetic nanostructures with sharp edges and gaps were obtained after metal lift-off with acetone and ultrasonic agitation. We have fabricated arrays of more than 3000 networks on the CPWs only to detect the dynamic response reliably. Brillouin Light Scattering Spectroscopy. Magnetization dynamic response was measured down to a single network by using the BLS technique, where a monochromatic laser (532 nm) beam was focused to ∼250 nm using a 100× microscope objective with large numerical aperture (0.75). The inelastically scattered laser beam from the sample was analyzed using a tandem Fabry−Perot interferometer (JRS Scientific Instruments). Stabilization of sample position was
CONCLUSIONS To summarize, we propose and experimentally demonstrate reconfigurable microwave properties by deterministically switching between two possible ground magnetic states, FM and AFM. Instead of magnetic coupling induced anisotropy, we utilize shape-induced magnetic anisotropy from rhomboidshaped nanomagnets to achieve deterministic magnetic ground states. This mechanism is less sensitive to uncontrollable 1696
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ACS Nano constantly monitored using a nanostage and a computer-controlled active stabilization routine. Micromagnetic Simulations. In order to visualize the magnetization reversal mechanism, micromagnetic simulations were carried out by solving the Landau Lifshitz Gilbert equation using threedimensional Object Oriented Micromagnetic Framework (OOMMF) software.30 Typical parameters for Permalloy were used: saturation magnetization, Ms = 800 emu/cm3, exchange constant, Aex = 13 × 10−7 erg/cm, magnetocrystalline anisotropy, K1 = 0. For simulations the samples were divided into three-dimensional arrays of cells of dimensions 5 × 5 × 5 nm3. The cell size is smaller than the exchange length (lex = 5.7 nm), which is defined as lex = √(A/2πMS2). For dynamic simulations, a damping constant α = 0.008 was used, and the data were plotted in the frequency domain by performing Fourier transforms. A larger α = 0.5 was used in quasi-static simulations for rapid convergence. The mask used for the simulations was derived from the scanning electron micrographs.
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ASSOCIATED CONTENT S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.5b07849. SEM and MFM images of coupled networks with δ > 50 nm, magnetic field dependence of microwave absorptions, simulated results for ultrafast switching, dependence of microwave responses on the number of nanomagnets in a network, geometry and thickness of the nanomagnets (PDF)
AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS This work was supported by the National Research Foundation, Prime Minister’s Office, Singapore, under its Competitive Research Programme (CRP Award No. NRF-CRP 10-201203), SMF-NUS New Horizon Awards, and Ministry of Education, Singapore AcRF Tier 2 (Grant No. R-263-000A19-112). A.O.A. is a member of the Singapore Spintronics Consortium (SG-SPIN). REFERENCES (1) Stamps, R. L.; Breitkreutz, S.; Åkerman, J.; Chumak, A. V.; Otani, Y.; Bauer, G. E. W.; Thiele, J.-U.; Bowen, M.; Majetich, S. A.; Kläui, M.; Prejbeanu, I. L.; Dieny, B.; Dempsey, N. M.; Hillebrands, B. The 2014 Magnetism Roadmap. J. Phys. D: Appl. Phys. 2014, 47, 333001. (2) Krawczyk, M.; Grundler, D. Review and Prospects of Magnonic Crystals and Devices with Reprogrammable Band Structure. J. Phys.: Condens. Matter 2014, 26, 123202. (3) Niemier, M. T.; Bernstein, G. H.; Csaba, G.; Dingler, A.; Hu, X. S.; Kurtz, S.; Liu, S.; Nahas, J.; Porod, W.; Siddiq, M.; Varga, E. Nanomagnet Logic: Progress toward System-Level Integration. J. Phys.: Condens. Matter 2011, 23, 493202. (4) Kostylev, M. P.; Serga, A. A.; Schneider, T.; Leven, B.; Hillebrands, B. Spin-Wave Logical Gates. Appl. Phys. Lett. 2005, 87, 153501. (5) Hertel, R.; Wulfhekel, W.; Kirschner, J. Domain-Wall Induced Phase Shifts in Spin Waves. Phys. Rev. Lett. 2004, 93, 257202. (6) Schneider, T.; Serga, A. A.; Leven, B.; Hillebrands, B.; Stamps, R. L.; Kostylev, M. P. Realization of Spin-Wave Logic Gates. Appl. Phys. Lett. 2008, 92, 022505. 1697
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