9. Spin Torque Majority Gate

Transcription

1 eyond MOS computing 9. Spin Torque Majority Gate Dmitri Nikonov Thanks to George ourianoff 1

2 Outline Spin majority gate with in-pane magnetization Spin majority gate with perpendicular magnetization Magnetic adder 2

3 Micromagnetic Equations Landau-Lifshitz-Gilbert equation dm dm PJ M dt M M dt M et g M M p s 2 2 s ( ) g magnetic field/ enables MRAM wire td I 0 2 a 0 P Me s damping ~ 300nm 2 spin torque/ Enables STTRAM P I eff, torque 2 2 s M e a t Spin torque dominates switching for smaller nanomagnets 3

4 Elliptic Spin Torque Majority Gate (STMG) -V Iout A +V +V AND A Out MgO OR ofe GND Ta [Electric interface like STTRAM] 3 inputs and one output having their own fixed layers. Inputs exerts spin torques. ommon free layer switched according to the majority of inputs. D=free layer width, a = pillar width, t = free layer thickness 4

5 Elliptic Spin Torque Majority Gate (STMG) -V Iout A +V +V AND A Out MgO OR ofe GND Ta [Electric interface like STTRAM] 5 3 inputs and one output having their own fixed layers. ommon free layer switched according to the majority. Not separate nanomagnets with dipole interaction, stronger exchange interaction. a = pillar width, t = free layer thickness

6 Switching speed in-plane STMG 100% to 20% levels of MR Switching time Example of M projection (along the long axis) evolution. Switching speed for various polarities at nanopillars (p=v+, m=v-). No problem with vortices at a=12nm, t=2nm. 6

7 Polarities for Voltages ppp ppm A A Out Out pmp mpp A A Out Out 7

8 What is a vortex? Vortex closed magnetic flux. Minimizes demagnetization energy, higher exchange energy. Magnetization points out of plane in the middle a 2 e 3 2A M 0 2 D 2 e 3t 2 s 5nm 12nm exchange length A=exchange constant, not area a=vortex core radius (for circular disc, D~100nm, t~3nm) td 250nm e smaller td => uniform larger td => vortex of - shape 8

9 Dot thickness L, (nm) What is a Vortex 2R L Guslienko and Novosad, J. Appl. Phys. 96, 4451, (Permalloy) Vortex closed magnetic flux. Minimizes demagnetization energy, higher exchange energy. Magnetization points out of plane in the middle Dot Diameter 2R, (nm) Thin discs : uniform states. Thick and large discs : favor vortices. D = diameter of the disk We are here

10 Where is the oundary between regimes? 2 e 2A M 0 2 s 5nm exchange length reflects ratio of two energies A=exchange constant, not area a 3 2 R 2 e 12nm vortex core radius (for circular disc, 12t R=50, t=3) setting equal estimates for both energies td 250nm e smaller td => uniform larger td => vortex of -shape 10

11 When is vortex stable? STTRAM here Thin discs : uniform states. Thick and large discs : favor vortices. See Guslienko and Novosad, J. Appl. Phys. 96, 4451,

12 Patterns of magnetization in-plane Simulations with OOMMF (NIST) Switching from M pointing right to M pointing left. Vortices (circle) and anti-vortices (cross) appear and disappear. (ppp), I=4mA, a=24nm, t=2nm, at time intervals 0.2ns, left to right in rows. Example of undesirable switching [wider and thicker STMG]. Anti-vortex leaves at the edge. Vortex remains = not reaching MR value at output. (ppm), I=16mA, a=48nm, t=3nm. 12

13 Patterns of magnetization in-plane Simulations with OOMMF (NIST) Normal switching, without vortices. (ppm), I=4mA, a=24nm, t=2nm, at time intervals 0.2ns, left to right in rows. Example of undesirable switching. Vortex remains = not reaching MR value at output. (pmp), I=4mA, a=24nm, t=2nm, at time intervals 0.2ns, left to right in rows. 13

14 Regimes of Switching, a=20nm vort anti vort+anti anti vort vort+anti 14

15 Perpendicular Magnetization STMG +V +V -V Iout a a a a A a a Out a GND 7a 7a For materials like FePt, TboFe, etc. magnetic anisotropy favors out-of plane direction. Known to help decrease switching current in STTRAM ircuits formed by continuous magnetic wires, not broken down into nanomagnets. Switching is not limited by shape. Electrodes can be shifted to the periphery. 15

16 Patterns of magnetization perp. STMG Up Down Top and bottom arms promote switching, left arm resists. Domain walls propagate through arms, fight over the middle, propagate to the output arm. (pmp), I=0.05mA, a=20nm, t=2nm. Example of undesirable switching. Domain wall gets stuck in the middle of the cross, does not have enough energy to extend itself. (ppm), I=0.1mA, a=20nm, t=2nm. 16

17 Switching speed perp. STMG Much smaller current needed to switch. Stuck domain wall in ppm polarity. Still a wide range of parameters where switches in all polarities. 17 Good scaling with size, close to proportional to area. Higher current at 10nm due to shape anisotropy. Stuck domain wall more of a problem for larger sizes at higher current.

18 Gain in STMG Noise margin Varying the angle of magnetization of one of the inputs. Nonlinear characteristic required for logic to suppress noise, cascade stages. Similar to a MOS transfer characteristic, noise margin related to gain. 18

19 Stack of Layers and an Inverter u write u read AFM MgO Ru metal Well-known improvement on the layer design synthetic anti-ferromagnet layer (SAF) = 2 ferromagnet layers with Ru in between. Exchange interaction ensures that M are opposite. (+) higher stability vs. thermal fluctuations (+) smaller switching current. Here we use it to create an inverter by connecting the top and bottom layers. 19

20 One-it Full Adder A +V +V +V +V out Iout Sum -V Iout -V Inv Inv A +V GND 1 bit of a full adder requires 3 majority gates and 2 inverters. A very compact circuit. 20

21 Pattern of magnetization - adder Magnetization switching similar to the cross. Much less problem of stuck domain wall, perhaps due to less reflection from ends of wires. Very oscillatory, magnetization temporarily retreats to initial direction. Majority wins over the output in the end. 21

22 Switching speed - adder etter reliability of switching, at all values of current. Not much slower than 1 cross, limited not by distance, but by damping. Good scaling with size, proportional to current density. Saturation with current, limited not by strength of spin torque, but by damping (again). 22

23 omparison to MOS logic 28 transistors drivers A 3 STMGs 7 driver transistors Inv (+) Smaller area (-) Slower (+) Smaller power per gate (-) Smaller throughput per area (+) Non-volatile * MOS data from ITRS Inv A out Sum Sense amp Sense amp 23

24 Summary Spin majority gate with in-pane magnetization = elliptic shape. Problems with vortices Spin majority gate with perpendicular magnetization = cross shape. Problems with stuck domain walls Magnetic adder = efficient implementation with majority gates, compares favorably with low-power electronics 24