Cooperative Spin/Nanomagnetic Architectures: A Critical Evaluation

1. Cooperative Spin/Nanomagnetic Architectures:A Critical Evaluation Supriyo Bandyopadhyay Dept. of Electrical & Computer Engineering Virginia Commonwealth University Richmond, VA 23284, USA Quantum Device Laboratory

2. Why Spin At All? • Conventional electronics utilizes “charge” to store, process and communicate information. • Example: The MOSFET– when the channel is full of charge, the device is “on” and encodes logic bit 0. When the channel is depleted of charge, the device is “off” and encodes logic bit 1. • Switching from one bit to the other involves moving charges in or out of the channel, which causes a current (I) to flow with an associated power dissipation of IV or an energy dissipation of DQV, where DQ is the channel charge. • This dissipation is inevitable. Charge, being a scalar, only has magnitude and no direction. Therefore, different logic bits must be encoded in different amounts (or magnitude) of charge. Switching must involve changing the magnitude of the charge, which then invariably causes an energy dissipation of DQV . • This is a fundamental shortcoming of all “Charge Based Electronics”. Quantum Device Laboratory

3. Spin as a state vector to encode logic bits • Spin, unlike charge, is a pseudo vector with a fixed magnitude but variable polarization or “direction”. • Place a trapped or localized single electron in a dc magnetic field and the spin polarization becomes bistable: only polarizations parallel and anti-parallel to the field are eigenstates and are stable or metastable. • Encode logic bits in these two polarizations. • Switch by simply flipping the spin polarization, without physically moving the electron in space and causing a current flow. No DQV dissipation • Low energy paradigm 0 1 Global dc Magnetic Field Quantum Device Laboratory

4. Do SPINFETs and their cousins cause low energy dissipation as a result? • Absolutely not • SPINFETs do not utilize the vector nature of spin to reduce energy dissipation • It is still very similar to a MOSFET, except that current is modulated (transistor action realized) by changing spin polarization with a gate potential instead of changing carrier concentration in the channel • Information is still encoded in charge and current flows so that dissipation is not reduced at all • Comparison between SPINFETs and MOSFETs in APL, 85, 1433 (2004) • SPINEFT loses

5. Single Spin NAND gate – no transistor business Input1 Output Input2 • Nearest neighbor exchange coupling J • Inputs applied through local magnetic field; gmBBlocal>> J • J > gmBBglobal • Anti-ferromagnetic ordering in ground state Global field Quantum Device Laboratory

6. Spin wire • Nearest neighbor exchange coupling • Information replicated in alternate dots • Fan out • S. Bandyopadhyay, B. Das and A. E. Miller, Nanotechnology, 5, 113 (1994) Quantum Device Laboratory

7. The vexing issue of unidirectionality • Granular clocking • Need 3-phase clock • Propagates signal unidirectionally and allows pipelining of data • S. Bandyopadhyay, Superlattices and Microstructures, 37, 77 (2005) Quantum Device Laboratory

8. Rigorous quantum mechanical calculations of all the ground state configurations in the NAND gate, the gate error probability and energy dissipation can be found in H. Agarwal, S. Pramanik and S. Bandyopadhyay, New J. Phys., 10, 015001. Quantum Device Laboratory

9. The Good • Energy dissipated in switching a bit is kTln(1/p)… the Landauer Shannon limit! Here p is the bit error probability • With p = 10-9, the energy dissipated is 21 kT. Modern transistors dissipate 40,000-50,000 kT • Energy dissipated in the clock can be made arbitrarily small using adiabatic schemes • Very low power paradigm (very good) • Writing speed determined by t ~ h/(2gmBBlocal) = 0.7 psec with InSb q-dots if Blocal = 1 Tesla. Clock frequency is determined by how fast coupled spin system relaxes to ground state. About 1 nsec. Therefore, clock frequency is ~ 1 GHz. Quantum Device Laboratory

10. The Bad • Temperature of operation is determined by the requirement 2J =gmB Bglobal = kTln(1/p). With semiconductor quantum dots, J = 1 meV. Therefore, with p = 10-9, the temperature of operation is 1.1 K (very bad) • Room temperature operation requires J=0.3 eV. Maybe possible in molecules but certainly not in quantum dots • The global field required is 0.72 Tesla with InSb q-dots (not bad). Quantum Device Laboratory

11. What about spontaneous spin flips causing bit errors? … Assume 1 GHz clock. Then for p = 10-9, we need that the spin-flip time T1 should be 1 second! Quantum Device Laboratory

12. Search for materials withlong spin relaxation times • Organics have weak spin orbit interaction and hence could have long spin lifetimes…but would it be as long as 1 second above 1.1 K? Quantum Device Laboratory

13. Progress to date - experimental T2 time measured as 2 nsec at room temperature in Alq3 using ESR. At least 10 times larger than in inorganic materials. Possible phonon bottleneck effect. T1 time measured 1 second at 100 K. Largest reported in any system. Nature Nanotech., 2, 216 (2007). Quantum Device Laboratory

14. Conclusions regarding SSL • Very low power • Very low bit error probability • Synthesis difficult, but has been repeatedly demonstrated by many groups • Single spin reading and writing repeatedly demonstrated by many groups • Requires low temperature because we cannot make the exchange interaction very large • Best platform may be organic semiconductors because of the very long spin relaxation time

15. Other collective spin (or magnetic) approaches • Magnetic quantum cellular automata (originally Cowburn and Welland) • Spin wave based cellular non-linear networks (Khitun and Wang) Quantum Device Laboratory

16. Magnetic quantum cellular automata Shape anisotropy ensures that magnetization can point to the left (logic 0) or right (logic 1) • Apply a magnetic pulse (field pointing right) to set all dots to logic 1. • Apply an oscillating ac field whose negative phase represents logic 0 and positive phase logic 1. At the negative amplitude, the magnetization switches and points to left. DC component negative • If the initial magnetic pulse sets all dots to logic 0, then ac field has no effect • The magnetic pulse and the ac field are the two inputs. State of the dots is output. Realize the AND operation. Output Input 1 Input 2 Cowburn and Welland, Science, 287, 1466 (2000) Quantum Device Laboratory

17. Magnetic quantum cellular automata • This is a single gate, NOT a circuit or architecture. No information “propagates” here • Hence, no issue of unidirectional signal propagation from one gate to another Quantum Device Laboratory

18. Magnetic quantum cellular automata circuits(Scaled up version of SSL) • Csaba, Porod, Lugli, Csurgay, Int. J. Circuit Theory and Applications, 35, 281 (2007) • More of a circuit with signal propagation issues • Nanomagnetic dashes have shape anisotropy which makes magnetization bistable. Encode logic 0 and 1 1 0 Quantum Device Laboratory

19. Magnetic quantum cellular automata • Scaled up version of Single Spin Logic where the entire nanomagnet (consisting of about 10,000 spins) acts as a giant spin • Ground state is anti-ferromagnetic • Majority logic gate designed based on anti-ferromagnetic ordering Top view of majority logic gate Quantum Device Laboratory

20. Signal propagation • First apply a dc magnetic field to magnetize all dashes to the right • Then an input is applied to the leftmost dot • Next one flips, and then the next one, in a domino like fashion • Unidirectional propagation happens since there is an asymmetry between the state of the left neighbor and the state of the right, with the influence from left being stronger because of shape anisotropy that makes the vertical axis the easy axis of magnetization and the horizontal axis the hard axis Initializing clock Input applied Shift register Quantum Device Laboratory

21. The clock • Global clock, not granular… saves a lot of fabrication complexity • The price….. Non-pipelined architecture • The clock signal cannot reset all dash states until the final output has been produced • New input cannot be provided until the output has been produced Initializing clock Quantum Device Laboratory

22. What is a reasonable clock frequency? • The time to switch a nanomagnet is about 1 nsec • Therefore, the minimum clock period is N nsec, where N is the number of cells in a line • Claim is that nanomagnets can be produced with a density of at least 1010 cm-2, so that in a 10 cm2 chip, the longest line will have 3.16x105 cells • Therefore, the clock period is longer than 0.3 milliseconds • Clock frequency is limited to 3 kHz with this density… all because of non-pipelining Quantum Device Laboratory

23. Granular versus global clock • Magnetic quantum cellular automata can be operated with a granular clock (see Behin-Aein, Salahuddin and Datta, arXiv:0804.1389). This will increase speed since it will allow pipelining. However, the penalty is generating a local magnetic field around each clock. Harder than the scheme in SSL Quantum Device Laboratory

24. Other problems • In SSL, the nearest neighbor interaction is exchange which can be turned on or off by lowering or raising an electrostatic potential barrier between the neighboring cells. This requires a local electrostatic potential which can be applied via a simple gate pad. • In magnetic quantum cellular automata, the nearest neighbor interaction is dipole-dipole which cannot be turned on or off by lowering or raising an electrostatic potential barrier between neighboring cells. We need a local magnetic field to orient the magnetization of the selected nanomagnet. Much harder to generate a local magnetic field than to generate a local electric field. Quantum Device Laboratory

25. The Killer… Clock Synchronization for a Vector Clock • SSL uses a scalar clock … potential • MQCA uses a vector clock… magnetic field • The timing and direction of the field has to be synchronized across the entire chip. Possible, in principle, for granular clock, but very difficult. Impossible for global clock • Misalignment problem will cause many cells to not flip, leading to severe bit errors • The only reported experiment reports a failure rate of 25%! • A bit error probability of 25% cannot be handled. It has to remain on the order of 10-6 or less • This problem alone can make MQCA impractical

26. What about energy dissipation? • Energy dissipation to flip a nanomagnet with 104 spins is NOT 104 times the energy dissipated in flipping a single spin • Because of interactions between spins, it is much less. Salahuddin and Datta (APL, 90, 093503 (2007)) show that it is only about 35 times that of a single spin flip… Good news. • At room temperature, energy dissipated per bit flip is about 800 meV. Compare that with SSL where at 1.1 K, it was 2 meV. If MQCA were operated at 1.1 K, the energy dissipated per bit flip would have been ~ 4 meV. Thus, in terms of energy dissipation, MQCA is only slightly worse than SSL! Quantum Device Laboratory

27. The good, the bad and the ugly • Good • Low energy, ~35 kT to switch. Also room temperature operation • Bad • Slow, few kHz clock if globally clocked. Granular clocking is hard • Ugly • Error probability very high because of the misalignment problem (synchronization of a vector clock). Bit error probability in the only experiment reported (Science, 311, 205 (2006)) was about 25%. We need it to be 10-6 or less. Quantum Device Laboratory

28. The Spin Wave Bus: Another architecture with actual signal propagation • Information transmitted by spin waves without charge transfer. Hence no current flows. • Is it energy efficient as a result? Depends on the dissipation of spin waves that carry information • Supposedly reduces interconnect problem. But this requires selectively directing the wave which will require a waveguide • Phase logic: phase is a continuous variable which can degrade due to dephasing. How is signal restoration performed. Need a “phase-device” with non-linear characteristic Quantum Device Laboratory

29. Spin bus devices • Signal restoration at logic nodes requires a device with a non-linear characteristic for spin wave phase • Otherwise, use only for analog applications • Analogous to SAW devices Output Input Quantum Device Laboratory

30. Other issues • Spin waves decay because of magnon emission (scattering with phonons is a secondary issue, primary issue is emission of magnons which carry away energy). Some amplification is necessary. What is a “spin-wave-amplifier”? • There are no local interconnects, only global interconnects via a spin wave bus, but how is selective coupling to devices accomplished? What is the coupling efficiency? Quantum Device Laboratory

31. CONCLUSIONS • Single spin logic is low energy consuming, high speed (granular clock and pipelined) and high density. Fabrication challenging and low temperature operation • Magnetic quantum cellular automata can be operated at room temperature and low energy (not as low as SSL, but low). Cannot be “granular clocked”, at least not easily and hence non-pipelined and very slow. May be impractical because of large bit error probability • Spin wave bus may be low energy consuming but not as low as SSL or even MQCA. Room temperature operation possible. Probably reasonably fast. Not suitable for digital processing, may work well for analog processing Quantum Device Laboratory