The possible use of spin rather than charge as a state variable in devices for processing and storing information has been widely discussed1,2, because it could allow low-power operation and might also have applications in quantum computing. However, spin-based experiments and proposals for logic applications typically use spin only as an internal variable, the terminal quantities for each individual logic gate still being charge-based3,4,5,6,7,8. This requires repeated spin-to-charge conversion, using extra hardware that offsets any possible advantage. Here we propose a spintronic device that uses spin at every stage of its operation. Input and output information are represented by the magnetization of nanomagnets that communicate through spin-coherent channels. Based on simulations with an experimentally benchmarked model, we argue that the device is both feasible and shows the five essential characteristics9,10 for logic applications: concatenability, nonlinearity, feedback elimination, gain and a complete set of Boolean operations.
Our proposal has certain features in common with previous work. For example, as in a previous proposal for spin-based logic4, it uses non-local spin signals11,12. However, whereas ref. 4 requires sophisticated circuitry to amplify these signals and create the Amperian magnetic fields to switch nanomagnets, our proposal uses the non-local spin signal to directly switch a nanomagnet, which constitutes the input to the next stage. Other related examples include the magnetic quantum cellular automata (MQCA) architecture13,14,15 and domain wall logic16, which use magnetic representation of information and do not require spin-to-charge conversion. In all these cases, however, information is communicated through Amperian magnetic fields generated by current-carrying wires. In contrast, our use of spin currents should allow communication signals to be selectively routed between specific input and output magnets (logic bits) that need not be nearest neighbours. In short, we are presenting a vision for an all-spin logic using nanomagnets as digital spin capacitors to store information and spin currents to communicate (Fig. 1a), with versatility comparable to that of standard charge-based architectures that use charge capacitors to store information and charge currents to communicate (Fig. 1b). It also has the potential for low-power operation17,18 that can enable continued downscaling.
The basic concept underlying the all-spin logic device (ASLD) is illustrated in Fig. 1a. The bistable nanomagnets can be switched between their stable states representing binary data (right- or left-magnetized in Fig. 1a) if enough torque is exerted on them. Information stored in the magnetization direction of an input magnet is used to generate a spin current that can be routed along a spin-coherent channel to a desired location, where it determines the final state of the output magnet based on the spin–torque phenomenon19,20,21,22. Overall, what is achieved is the switching of an output magnet in accordance with the information provided by the input magnet using energy provided by Vsupply. Both the information and the energy are conveyed through the channel spin current. Later, we will describe an alternative scheme (Fig. 2) in which the energy is delivered directly from Vsupply to the output magnet, and only the information is conveyed by the channel spin current. This could be an advantage, but at the expense of a more complicated clocking scheme. Interestingly, the COPY operation described above can be changed to a NOT operation simply by changing the polarity of the voltage applied to the input. A negative voltage injects majority spins (that is, spins parallel to the magnetization of the input magnet), the presence of which turns the output magnet parallel to the input magnet, but a positive voltage extracts majority spins, the absence of which turns the output anti-parallel to the input.
Although these properties have been experimentally demonstrated23,24, there is an additional property that we believe should be true but has not been experimentally established to our knowledge. Typically, the input magnet is ‘fixed’ and not switched easily, but the output magnet is ‘free’ to be switched. For logic applications we would like input and output magnets to be identical because the output of one stage needs to function as the input to the next. However, we would like the switching action to be non-reciprocal, directed from the input to the output and not the other way around (no feedback). We believe that this can be accomplished by designing each magnet to have an input side with a tunnelling interface that enhances spin injection in semiconductors25,26,27,28,29,30/metals31 and an output side with a low-resistance interface that suppresses back-injection of spins. The version in Fig. 2 uses smaller spin signals in the channel, which should also reduce the effect of feedback. Both these approaches, however, are yet to be demonstrated experimentally.
Based on what has just been described, four of the five essential characteristics for logic applications should be ensured if the present device is implemented. ‘Concatenability’ is ensured, because both input and output are in the same form, namely magnetization direction. ‘Nonlinearity’ comes naturally through the bistability of the input and output magnets (see the energy landscape of a magnet in Fig. 2b), which provides digitization of information from a weak analogue spin signal to definitive binary states, automatically correcting any error in magnetization direction. As such, one could view the magnets as ‘digital spin capacitors’ analogous to charge capacitors. ‘Feedback elimination’ requires that inputs determine the state of the corresponding outputs, and not vice versa. As mentioned above we propose two possible approaches to ensure this. ‘Gain’ suggests that the energy needed to switch the output must not come from the input, but from an independent source, namely the power supply. In our scheme the input magnet provides the information to switch the output magnet, but the switching energy comes from the voltage sources (Vsupply) attached to the magnets. This feature is essential to maintain the signal level during logic processes over a long concatenated chain of gates. The fifth essential characteristic, namely a complete set of Boolean logic gates, will be discussed later (Fig. 3).
The conducting channel that transmits information from the input to the output magnet can be viewed as an ‘interconnect’, and in principle could be a metal or a semiconductor. The non-local spin–torque phenomenon on which this proposal is based has so far been demonstrated only in all-metal structures23,24. Semiconductors exhibit longer spin coherence lengths32,33,34,35. However spin injection from a ferromagnetic contact into a semiconductor has been a serious problem25, and although there have been significant advances in spin injection into semiconductors26,27,28,29,30, especially graphene36,37, the injection efficiency is still low. This in turn means that more current has to be driven into the semiconducting channel from an input magnet to create a large enough spin accumulation that can switch the corresponding output magnet. We will now describe an alternative scheme that could operate with lower spin accumulation levels in the channel, which hereafter will be called transfer signal.
Consider Fig. 2b which shows the energy landscape of a magnet. Previously, the role of the transfer signal in the channel was to switch the output magnet between its stable states A and C, which involves overcoming the energy barrier between them. If, instead, the magnetization of the output magnet was put in its high energy state (state B in Fig. 2b), then all the transfer signal has to do is to tilt it towards state A or C. However, the transfer signal still has to overcome thermal fluctuations at state B, which may tilt the magnet the wrong way. After that, the internal field of the magnet itself will drive its magnetization to one of the energy minima, thereby digitizing the information. It should be mentioned that the basic idea of first putting a magnet in a high energy (‘neutral’) state and using a weaker field to tip it towards one of its stable states was first discussed by Bennett38 to our knowledge, and similar ideas have been presented by several authors in different contexts39,40. More recently, this switching scheme has been experimentally demonstrated in the context of MQCA devices14.
In the proposed all-spin switch, the magnetization of the output magnet (data bit) is put along its high-energy state by applying Vsupply to a magnet permanently fixed in the direction illustrated in Fig. 2a. This process accumulates spins in the direction of the fixed magnet in the spacer region (which can be made of copper) on top of the output magnet. This in turn exerts a non-local spin–torque on the output magnet, driving it to its neutral state (state B). To our knowledge, using spin–torque to put the magnetization of a magnet in its neutral state has been discussed for the first time in this paper and it is not obvious that this can indeed be done. We have performed extensive simulations using an experimentally benchmarked model based on the Landau–Lifshitz–Gilbert (LLG) equation to assess the feasibility of this procedure. Our simulations first suggest that it is possible to neutralize the magnet along state B using spin–torque. Second, by appropriate magnet design, the same amount of spin–torque that can switch the magnetization can also put it in its neutral state. (Details are described in Supplementary Sections S3 and S4. Note also that Supplementary Section S1.A discusses how the magnet alignments depicted in Fig. 2a can possibly be achieved in practice.)
Figure 2c shows an example of switching the output magnet and Fig. 2d illustrates such a switching event using two pulses (which are depicted in Fig. 2e) providing two spin–torques: one is large, exerted by the application of Vsupply, and the other is small, exerted by application of Vbias, which sends the transfer signal from the input magnet through the channel to the output magnet. The deviation of the plateau in Fig. 2c from the neutral state mz = 0 (where mz ≡ cos θ) is due to the bias spin–torque. This deviation, in practice, has to be larger than thermal fluctuations for the switching to be deterministic. (The effect of thermal fluctuations is discussed in Supplementary Section S5.) Our simulations show that even in the presence of thermal fluctuations and some other non-idealities such as misalignments in the magnet directions (Supplementary Sections S6 and S7), the transfer signal in the channel has to exert a torque on the output magnet that is only a tenth of what is needed to switch it. This is because the transfer signal only provides the bias needed to tip the magnet in the desired direction (A or C). The bulk of the switching energy comes from Vsupply, which places the output magnet in its neutral state B.
The spin–torque exerted by Vsupply has to overcome two main internal fields of the output magnet to put its magnetization at B. One field is the so-called uniaxial field, which is in the plane of the thin-film magnet and gives it its two stable states (representing binary bits) as in Fig. 2b. The other is the out-of-plane demagnetizing field, which keeps the magnetization in the plane. It is known experimentally41,42 that reducing this field22 results in lower switching voltages/currents in the case of flipping a magnet between its two stable states A and C. Our simulations (Supplementary Section S4) show that in the presence of this field, it is even harder to put the magnet along state B, but if this field is absent, the amount of torque necessary to do so would be significantly less (Supplementary Fig. S3b, inset).
We have already discussed four of the five essential characteristics for general-purpose digital logic circuits. We will now consider essential characteristic (5), namely a minimal set of Boolean logic operations from which all other logic functions can be constructed. A complete minimal set is composed of a basic binary operator like logical AND or logical OR and the unary operator NOT. AND and OR gates can be combined with NOT to make NAND and NOR gates. Here, as an example, we describe how the aforementioned logic gates could be composed of several all-spin switches. However, it might prove beneficial to use the all-spin switch concept presented in this paper to construct functional gates such as full-adder, multiplier, and so on by alternative designs bypassing the brute force use of NAND/NOR gates.
Figure 3a shows two gates (A and B). Each gate is a two-input, one-output gate with a middle fixed input. The send mode in gate A refers to the application of Vbias to the input structures (as in Fig. 2a) such that they send the transfer signal to the output. The receive mode in gate A refers to Vsupply applied to the output structure (as in Fig. 2a), neutralizing its magnetization and thus making it ready to receive information. The idle mode for which no voltage is applied is described in the caption of Fig. 3. The final state of the output is determined by the superposition of spin currents (rule of majority) injected from inputs into the channel. As such the gate can function as an AND/OR gate. Flipping the direction of the middle fixed input magnet toggles the functionality between OR ↔ AND. This input is only ‘fixed’ as long as the gate functions as an AND or as an OR gate. This fixed input has to be switched if reconfiguration is desired. However, this requires extra connections, which inevitably add to the complexity of the circuitry. As described earlier, the polarity of Vbias applied to the input determines whether the transfer signal in the channel is a COPY or a NOT of the input. If Vbias > 0 is applied to all the inputs, then gate A acts as a NAND/NOR instead of AND/OR. Transfer of information in a long concatenated chain of gates can be achieved by properly clocking (Fig. 3b) the gates as described in the caption of Fig. 3. This clocking could be made simpler if the permanently fixed magnets on top of the structures were shared by many data bits. Owing to space limitations, only the logic gates of Fig. 2a are described here, but the device in Fig. 1a could also be used to construct similar logic gates. The signal would then travel by clocking Vsupply (see Fig. 1a) applied to the inputs as in a shift register43.
Recent experimental work has shown reversible magnetization switching using non-local spin currents23,24, where the path for charge current and spin current are separate. What has not been demonstrated experimentally is the switching of a magnet with two separate pulses where one provides the gain (see vertical structure in Fig. 2a) and the other provides the bias (see the lateral channel in Fig. 2a). The required voltage levels could vary widely from tens of millivolts to volts depending on the materials and interfaces used, while the pulsewidths should be on the scale of the switching time for the nanomagnets used, generally being a few nanoseconds if switched with spin–torque.
The possible advantage of our proposed ASLD over CMOS arises from the potential for extremely low switching energies (that is, the energy dissipated throughout switching). The self-correcting feature provided by magnets should make it possible to reduce the switching energy to being several kBTroom per magnet rather than several kBTroom per spin 17,18. However, at this time this remains to be experimentally demonstrated. The dissipation in existing spin–torque devices (see for example refs 44 and 45) is far in excess of the theoretical minimum, and more work is needed to bring real devices closer to the ideal limit. (See Supplementary Section S8 for some possible approaches.) The same applies to switching times, which are typically several nanoseconds44 in present-day devices, but could be reduced to several picoseconds by appropriate magnet design46 (see Supplementary Section S8 for some possible approaches), so as to be competitive with CMOS.
We end the paper by noting that although the current proposal is strictly for digital logic applications, principles similar to this could potentially find use in artificial neural networks and spin-based solid-state quantum computing. For example the spin accumulation in the channel underneath a given output magnet (Fig. 3a) could provide a ‘weighted average’ of different inputs that makes it switch (‘fire’) when it exceeds a threshold. Alternatively, the magnets on top of the channel could possibly serve as an input–output interface for spin-based quantum computing in the channel where the magnets can initialize the system through spin currents and store the output information of a given computation with high stability.
The authors would like to give thanks to M. Lundstrom for input throughout the course of this work. B.B. is grateful to Abu-Naser Zainuddin for joint development of the model for the stochastic LLG equation. B.B. would also like to thank his colleagues K. Camsari, X. Fong, C. Augustine and L. Siddiqui for scientific interactions and discussions. This work also benefited from discussions with D. Nikonov, G. Bourianoff, J. Bokor and A. Seabaugh. This work was supported by the Nanoelectronics Research Initiative (NRI).
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Nature Physics (2018)