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Collective Effects Kang L. Wang Raytheon Distinguished Professor of Physical Electronics Device research Laboratory Center on Functional Engineered NanoArchitectonics -- FENA (www.fena.org) Western Institute of Nanoelectronics – WIN (www.win-nano.org) California NanoSystems Institute – CNSI (www.cnsi.ucla.edu) University of California - Los Angeles E-mail: [email protected]) WIN Outline Introduction Interaction in the space and the Order Parameter Collective effects and state variables Variability issues of spintronics versus nanoelectronics Examples: Spin wave bus MQCA SPIN FET Molecules and atoms WIN Summary 2 Charge State Variable (RT) Conventional Electronics employs indept electron entity and Coulomb interaction C 1/r WIN As the size of the devices goes down, the Coulomb (electrostatic) Capacitance energy arises. Leading to the increase of the energy per one electron and thus to high variability as quantum fluctuations become important E e /C Vdd 2 u-nm r Order Parameter The solution: To switch to interactions other than Coulomb 3 Corrections for Coulomb Energy Whatever the new interaction will be it is going to the some part of the ELECTRODYNAMIC interaction: ElectroDynamic Interaction = Coulomb + Corrections Many-body or Quantum Single electron level dynamic static (relativistic v/c) (multipole, short-ranged 1/r n,n>2) Too weak to work with Dynamic: of relativistic origin including spins, magnetic, multiferroics WIN E> KT Effective interactions in many-electron collective variables Static: Multi-pole, short ranged ~ 1/rn, n>2 Ferroelectric Big Molecules (collective variables) 4 Many-electron collective variables for information processing Examples of the order parameters and collective variables Ferromagnetic r Ferroelectric e M Magnetization order parameter e r D Collective variable representing the state of many-electron system (e.g., position) r M r D Dipole moment order parameter (bose-condensation of plasmons) Molecules WIN Miltiferroic Both previous order parameters These we can call a first level collective variables, they are actually fields r r inr space r M(x),D(x) Excitations of these can be called a second level collective variables 5 Excitations of the order parameters as the second level collective variables Domain walls in ferromagnets (1 wall) WIN Fixed layer on Goldstone excitations of the order parameter: for example spin waves: off on oxide layer Free layer (no wall) Fixed layer off oxide layer Free layer MTJ memory unit can be view as a domain-wall trap Topological excitations of the order parameters: for example ferromagnetic vortices Is it possible to use Ferroelectric or even MultiFerroic , Domain walls, Topological excitations, Goldstones? Are they advantageous in any way ? 6 Variability: Electronics vs Spintronics Electronics WIN Spintronics The Same Principle for elemental Electrics and Spintronics circuit units (FET and spin-FET) 7 Variability Issues Electronics Spintronics V /V C / C CN 1/ 3 a Total range spin vector = 2S+1 q/6 2.4 10 20 N 1/ 3 a Farads ( bulk N a ) 1 / 1/(2S 1) 2 where bulk is the Bohr magneton per atom, and for Ni is 0.33 V / V N 1 stair 6 1/ 3 eV Na 2.8 / S / S Na Thermal fluctuations give Gaussians: 8 WIN 6 TN 1/ 3 (eV ) Na 2.8 TS (eV ) Na 8 Variability Charge Spin N a N 1/ C (6 eV / To ) 3 ~ 10 or a linear length of 77 nm 7 N a S 2.8 eV / To ~ 10 or a linear size of 1.6 nm • High enough energy • Collective particles Room Temperature. Quantum fluctuations of the projection of the Spin WIN 2 Ovchinnikov and Wang, APL 2008 10 Spintronics for low power – Spin as a state variable E kBT ln r For Single Spin e B 2me 1 E exp( ) r k BT E g B B For N Spins E 2.B 2N B B 11 WIN E=2 B B = 1.157×10-4 eV at 1 T) Bmin155 Tesla – Not practical! E NkBT ln 2 if independently Single electron or collective variables should be used to satisfy thermal stability and power dissipation requirements E ~ kBT ln r if collectively E ~ kBT ln r per variable Datta, APL 90, 093503(2007) 11 Summary Comparison of Electronic, Spin and Optical State Computing Independent electrons Lower bound (Impractical Limit) Mechanism Energy Size Electronic 3kBT 1 nm Practical limit ~3-5 nm Spin 70kBT 7 nm Practical limit >20 nm Optical 3600kBT 20 nm Practical limit >90 nm WIN Victor Zhirnov 12 Summary Comparison of Electronic, Spin and Optical State Computing Correlated electrons Mechanism Lower bound (Impractical Limit) Energy Size Electronic 3kBT 1 nm Practical limit~20~70 nm Spin 3kBT 2 nm Practical limit ~2~7 nm Optical 3600kBT 20 nm Practical limit >90 nm WIN 13 Spin Logic Devices Phase modulation/Amplification/ Superposition Spin Waves Magnetic Cellular Automata I3 output I1 I2 Sugahara- Tanaka Spin FET 3-terminal RAP Spin Valves/Spin Torque WIN Paralle l AntiParalle l 0 14 Spin Wave Bus -- Spin-Based Logic Device and transfer of information (Phasetronics) Three terminal device (three MOS with a common ferromagnetic film) Two inputs – One output The input is provided by a Source -Drain current pulse ISD WIN The output is the inductive voltage between two nearest source ( or drain) contacts VSS 15 Experiment – Spin wave Propagation Signal/Pulse Generator Oscilloscope 50 GHz circulator 100 nm NiFe ACPS line ACPS line Z X 50 m Y SiO2 Magnetic Film Time resolved inductive voltage measured WIN 2 m nm Quartz or Semiconductor Substrate 16 Experimental Data – SW transport in CoFe film Phase shift (Degree) Amplitude changes (dB) 6.0 6.0 5.5 5.5 5.0 5.0 Frequency (GHz) 3dB 4.0 2dB 3.5 1dB 3.0 0dB -1dB 2.5 -2dB 2.0 -3dB 1.5 -4dB Frequnecy (GHz) 4dB 4.5 4.5 45Deg 4.0 35Deg 25Deg 3.5 15Deg 3.0 5Deg 2.5 -5Deg -15Deg 2.0 -25Deg 1.5 -35Deg 1.0 1.0 0.5 0.5 0 0 50 100 150 200 250 300 50 100 150 200 250 300 External magnetic field (Oe) External magnetic field (Oe) Prominent modulation by weak (10 50 Gauss) magnetic field M. Bao, J-Y Lee, A Khitun, K. L Wang, D. W. Lee and S. Wang, 3-D mapping of spin wave propagation in CoFe thin film, (2007). WIN 17 General Concept and Some Results 6.0 5.5 5.0 4dB 4.5 Frequency (GHz) Experimental data on amplitude and phase modulation for the structure with 100nm CoFe film in the frequency range (0.5 6 GHz) and magnetic field range (0 350G) Prominent power (8dB/20G) and phase modulation ( 60Deg/10G) in the specific frequency regions Amplitude changes (dB) 3dB 4.0 2dB 3.5 1dB 3.0 0dB -1dB 2.5 -2dB 2.0 -3dB 1.5 -4dB 1.0 0.5 0 50 100 150 200 250 External magnetic field (Oe) “AND”, “OR”, “NOT” gates Maj WIN 18 300 Prototype Three-Terminal Device Logic state - spin wave phase Spin wave interferometer Phase control by the direction of current in the excitation loop Only two phases 0 and detection Input 1 Input 2 Out-of-Phase In Phase: Amplification Out of Phase: Cancellation Output Voltage (mV) In-Phase 12 In-phase Out of phase Frequency = 3GHz 10 8 6 4 2 0 0 100 200 300 400 500 600 700 800 Magnetic Field (Oe) WIN A. Khitun, M. Bao, Y. Wu, J-Y Kim, A. Hong, A. Jacob, K. Galatsis, and K. L. Wang, Logic Devices with Spin Wave Buses – an Approach to Scalable Magneto-Electric Circuitry, Proceeding of MRS, (in press), 2008 19 Mitigating eddy current losses in nanoscale devices CoFe; 100 nm Ferrite (Fe3O4) Insulating film 2, 4, or 8 m 100 "Insulator" 10 25 Eddy current losses 20 1 Frequency, GHz 30 35 30 0.0 0.5 Fig. (1) 1.0 1.5 2.0 0.1 k, waves/micron 2 m 10 25 4 m 1 20 15 15 Dispersion 0.0 Wide film 8 m 0.5 1.0 1.5 2.0 k, waves/micron Decay length, microns 100 Dispersion Decay length, microns Frequency, GHz 35 0.1 Fig. (2) CoFe; 100 nm 0.1 T WIN Continuous metallic Eddy current losses severely damp spin waves in a metallic film. Continuous metallic Eddy current loss can be reduced by laminations. Jim Allen – UCSB 20 Prototype Device by Kostylev et al: Logic state - spin wave amplitude Spin wave interferometer Phase modulation by magnetic field Gradual phase shift control up to 2.5 I, A WIN Interferometer output signal amplitude, dB / 2D Graph 2 f0 -5 -10 U -15 -20 -25 -30 =0.8 =0 -35 Umin -40 7.095 7.100 7.105 7.110 7.115 7.120 Spin wave frequency, GHz Kostylev, M.P., et al., Spin-wave logical gates. APL, 2005. 87(15): p. 153501-1-3. 21 7.125 Follow-up work by T. Schneider et al. The same device structure as for the prototype (Kostylev et al.) Logic state - spin wave amplitude Phase modulation by magnetic field (Input current 1200mA XNOR, NAND logic gates demonstrated WIN T. Schneider, A.A. Serga, B. Leven, B. Hillebrands, R.L. Stamps and M.P. Kostylev, Realization of spin-wave logic gates, APL, 92, 0022505, 2008 22 Speed of Operation Internal delay time = propagation distance/group velocity Propagation distance: ~ (submicron) Group velocity: gr= d/dk (~ 107 cm/s ) Experimental Data: Delay time ~ 10-100 ps 100nm CoFe film, RT Propagation distance: 2 Group velocity: ~105 m/s or 107cm/s Current device: 1 ns Ultimate limit: <10 ps 12 Oscilloscope Output (mV) The fundamental limit for device operation speed – limited spin wave group velocity. operation speed by the scaling down the signal propagation distance (submicron) 15 9 6 3 0 -3 -6 -9 -12 -15 0.0 WIN Subtracted H=0 from H=50 Oe 0.5 1.0 1.5 Time (ns) 23 2.0 Numerical modeling: Multifunctional MagnetoElectric Cell Landau-Lifshitz-Gilbert formalism dm m H eff m H eff dt 1 2 m - the unit magnetization vector Ms - the saturation magnetization - the gyro-magnetic ratio - the phenomenological Gilbert coefficient M V 2 A 2 2K H eff 2 m (m e )e H pulse Ms Ms A - the exchange constant K - the uniaxial anisotropy constant e - the unit vector along with the uniaxial direction Hpulse - the pulse field Sang-Koog Kim, Sung-Chul Shin, and Kwangsoo No Seoul National University, IEEE TRANSACTIONS ON MAGNETICS, VOL. 40, NO. 4, JULY 2004 WIN 24 Spin Wave Modulation by Electric Field R. Ramesh (Berkeley) Modulation via the exchange bias coupling in FM/MF structure S. Wang (Stanford) K. Wang (UCLA) Work Integrated by Ajey P. Jacob (Intel) WIN 25 Magnetic Nanofabric: Spin Wave multibit processor ACPS Line (input f1,f2,f3,…fn) Silicon Oxide Modulator fn ME Cell ACPS Line (output f1,f2,f3,…fn) fn Silicon Oxide Piezoelectric Ferromagnetic Film Silicon Substrate Input WIN Output Equivalent circuit (f1,f2,f3,…fn) VC (f1) VC (f2) (f1,f2,f3,…fn) VC (fn) … 26 Magnetic Nanofabrics:- Spin Wave device’s building blocks- A. Khitun, M. Bao and K. L. Wang (UCLA) Basic Element /Symbol Structure Schematics H ext Voltage Input Converter Voltage-to-Spin Wave Insulator (e.g. SiO2) Ferromagnetic Film (e.g. CoFe) Spin Wave Output Semiconductor Substrate (e.g. Si) Inductive Voltage Output t = - Spin Wave-to- Voltage Insulator (e.g. SiO2) (a) Spin Waves Input (1) (2) Semiconductor Substrate (e.g. Si) 1 m Splitter/Combiner Output A 50 nm Input Output B Input A Output (b) Input B Conducting Wire Spin Wave Modulator Im Hm Insulator Ferromagnetic Film Semiconductor Substrate (c) VG Magnetoelectric Cell (ME) (e.g. Piezoelectric-Piezomagnetic) Metal gate Ferroelectric (e.g. PZT) Ferromagnetic Film (e.g. CoFe, NiFe) (d) PAGE 5/ WIN 27 Silicon Substrate 27 SW Logic Efficiency Estimates Energy per bit Energy to excite spin wave a) External magnetic field (e.g. coil) b) Internal excitation (e.g. spin torque) Number of functions without restoration (amplification) a) Physical Parameter Estimated Range Spin wave energy 1kT – 100kT E SW 0 MH extVSW (Hext ~ 100Oe, VSW: 0.1um2 - 0.01um2) Energy to create a magnetic field 102kT – 104kT Eloop I Z ext 2 ext M Ms 2 2h Z ext 2 Spin wave coherence length /wavelength L/ (M/M ~0.01, ~107 rad/s/Oe, Z~50Ohm, ~ 10-12s) h: 1um – 10nm Ref.1 100-1000 (L ~ 50um@RT) : 100nm-10nm 102kT-105kT Signal restoration energy Electromagnetic coupling f CV 2 Ediss Eii ij H jj Q 2 - magnetoelectric coupling range from 10 to 1000 mV/(cm Oe) Ref.2 Signal propagation speed Spin wave group velocity 106 cm/s - 107cm/s Time delay vg k (function of film thickness) Propagation length/Spin wave velocity 0.05ns-1ns d / vg d range from 1um to 100nm Scaling factor and Defect Tolerance Spin wavelength Operation frequency Spin wave frequency 10nm - 100nm (insensitive to defects with size << ) 1GHz - 200GHz (NiFe, CoFe) Ref.3,4 (depends on the material structure) 1) Khitun A., Nikonov D.E., Bao M., Galatsis K., and Wang K.L., Feasibility study of logic circuits with spin wave bus. Nanotechnology 18, p. 465202, 2007. 2) Eerenstein, W., N.D. Mathur, and J.F. Scott, Multiferroic and magnetoelectric materials. Nature, 2006. 442(17): p. 759-65. 3) Covington, M., T.M. Crawford, and G.J. Parker, Time-resolved measurement of propagating spin waves in ferromagnetic thin films. Physical Review Letters, 002. 89(23): p. 2372021-4. 4) Vasiliev S.V., Kruglyak V.V.,Sokolovskii M.L., and Kuchko A.N., Spin wave interferometer employing a local nonuniformity of the effective magnetic field, JOURNAL 28 OF APPLIED PHYSICS 101, p. 113919 (2007). WIN Spin Wave Logic Devices Experimentally demonstrated devices: M.P. Kostylev, A.A. Serga, T. Schneider, B. Leven, B. Hillebrands, Spin-wave logical gates. APL, 87(15): p. 153501-1-3, 2005. T. Schneider, A.A. Serga, B. Leven, B. Hillebrands, R.L. Stamps and M.P. Kostylev, Realization of spin-wave logic gates, APL, 92, 0022505, 2008 A. Khitun, M. Bao, Y. Wu, J-Y Kim, A. Hong, A. Jacob, K. Galatsis, and K. L. Wang, Logic Devices with Spin Wave Buses – an Approach to Scalable Magneto-Electric Circuitry, Proceeding of MRS, (in press), 2008 Ferromagnetic resonance controlled by electric field: A.A. Semenov, S.F. Karmanenko, V.E. Demidov, B.A. Kalinikos, S. Grinivasan, A.N. Slavin, J.V. Mantese, Ferrite-ferroelectric layered structures for electrically and magnetically tunable microwave resonators. APL 88, 033503, 2006. Spin wave modulation using multiferroics: None WIN 29 Magnetic Logic - Cellular Automata NAND gates form the building blocks for circuits inside your computer WIN 30 Logic Gates using MQCA = Current state-of-the-art: the majority logic gate. Imre et al, Science 311, 205 (2006) WIN 31 Instability of bits 0° is unstable Energy (normalized) vs. θ WIN 32 Vertical Lines The TheProblem Solution– –stray Add fields stabilizing causebits vertical to leftbits andtoright flip first WIN 33 The B-gate (NAND function) 00 WIN 10 01 11 D. Carlton, UCB 34 these gates can be linked together to do logic... = WIN D. Carlton, UCB 35 Nano magnet Switching speed Direct observation of spin transfer switching by x-ray microscopy. c a c b b a) 0 ns • 20 nm CoPt free layer • 5 nm Cu as a tunneling layer • Fe as Fixed layer b) 0.15 ns d) 8.6 ns e) 9.0 ns f) 9.6 ns g) 12.0 ns h) 12.2 ns i) 13.2 ns Y. Acremann et al., PRL 96, 217202/1-4 (2006) WIN dd f ee gg h i f 0.6 h c) ns i Joachim Stöhr – SLAC with Yves Acremann 36 Spin FET Field Effect in DMS Confirmed Al Al2O3 MnGe on n-type Ge substrate 2 Field-Effect Moment (10-5emu) MnGe Ge Al 1 0 -3V -6V -12V -30V 0V 30V -1 -2 -3000 -2000 -1000 0 1000 2000 3000 Field (Oe) Schematic Spin gain FET structure with a MnGe/SiGe quantum well. WIN 37 Transistor with Memory JingJing Chen and KL Wang et al., App. Phys. Letts. 90, 012501 2007 37 Molecular Building Blocks Physical Molecular Change Molecular Motion store WIN Rotational Conformation 2 2m 1 ~ exp (a Eb ) Ptun MEMORY applications Phase Change tsw L L m v 2 Eb LOGIC applications 38 Molecular Rotation - metallacarboranes Metal carborane molecules “electronic switching” Atomic Scale: 90 rotation Cu(II) Cu(I) Tetrahedral Rotor “ON” Square planar “OFF” Stator -3 Current density (A/cm2) 1.0x10 -4 5.0x10-4 Cu(I)(dmp)(phen-Si)PF6 Cu(I)(dmp)(bisp-Si)PF6 0.0 -4 -5.0x10-4 5.2eV LUMO -3 -1.0x10-3 -3 -1.5x10-3 -10 4.6eV 4.1eV EF -5 0 Voltage (V) 5 10 Ec Metal I-V characteristics • Negative differential resistance due to tunneling through molecular rotor WIN • Hysteresis due to rotation EF Ev HOMO P+ Si 39 Acknowledgments V Zhirnov and R Cavin A Jacob, J Allen, A Khitun, I Ovchinnikov, M Bao H Ohno, Tanaka, and K Ando All the FENA, WIN & CNSI participants All students, postdoctoral fellows, Faculty and visitors as well as collaborators around the world Support: DARPA, SRC, NSF, Marco, NERC, ARO, AFOSR, ONR, and many industrial companies 40 WIN 40