Single Electron Spin Resonance with Quantum Dots Using a Micro-magnet Induced Slanting Zeeman Field S. Tarucha Dep. of Appl. Phys. The Univ. of Tokyo ICORP (Int. Cooperative Research Project) - JST (Japan Science & Technology) Frontiers of Spintronics and Spin Coherent Phenomena in Semiconductors: A Symposium in Honor of E.I. Rashba 29 Feb. – 1 Mar, 2008 Harvard University Y. Tokura (NTT) M. Pioro-Ladriere T. Obata Y-S Shin S. Yoshida K. Hitachi ICORP Tokyo-U

Outline Micro-magnet technique for manipulating individual electron spins in quantum dots Spin rotation using a slanting Zeeman field and ac voltage Coexisting contributions from spin-orbit interaction and fluctuating hyperfine field Addressing two spins at different f ESR ’s Ability of making scalable qubits

Concept of Spin Qubit = ESR Static B z AC B x ESR Hamiltonian Qubit: a| >+b| > SLSL SRSR Loss and DiVincenzo PRA(1998) ac B DC B 0 ac I B ac induced by I ac flowing a coil I AC = 1 mA B ac ~ 1 mT  rotation: ~ 80 ns To address individual spins F. Koppens et al. Science 06 Straight forward, but problems of heating and designing for more qubits

From current drive to voltage drive for ESR Exchange control in a double quantum dot : Spin qubit with a basis of two-spin states J. Petta et al. Nature 05 (inter-dot coupling gate modulation) Exchange Vac z Electric dipole spin resonance (EDSR) via local interaction between electron spin and electric field V.N. Golovach et al. PRB 06 (Theory) K.C. Nowack et al. Science 07 Inhomogeneous hyperfine interaction E.A. Laird et al. PRL 07 Spin-orbit interaction Y. Tokura, ST, et al. PRL 06 M. Pioro-Ladriere, ST et al. APL 07 Electron oscillation in a slanting Zeeman field formed by a micro-magnet We proposed….

Electron Motion in a Slanting Magnetic Field Global dc B field and local ac E field  m x 1 nm = 1 mT ac B field

Slanting Field Induced by Ferromagnets Mater ial T C ( o C)  0 M S (T) b SL (T/  m) Fe Co Py Ni permanent magnets (5 mm x 0.5  m x 0.5  m) separated by 0.5  m gap y z x x = z = 0 Simulation results (Radia©+Mathematica): z y x x x ~1T/  m J.R.Goldman et al.,2000 J. Wrobel et al.,2004 Y. Yamamoto et al. Dy, Gd,….

Device Co 300 nm ESR V AC V AC = V 0 sin(2  ft) M Co 2DEG calixarene double-dot GaAs AlGaAs gate B0B0 dot 1dot 2 I dot Micro-magnet ESR gate b SL ~ 0.6 T/  m (saturation) 75 x (  m) B z (mT) 0 b SL 0 70 nm 80 nm 90 nm 300 nm M Co = 1.8 T Simulation M.Pioro-Ladriere, ST,.. APL 07

Formation of Double Quantum Dot VLVL VRVR (N L, N R ) = (0,0) (1,0) (0,1) (1,1) By adjusting two side gate voltage, A double quantum dot is formed. x z M Co 2DEG calixarene double-dot GaAs AlGaAs gate B0B0 70 nm dot 1dot 2 (0,1) (1,1) (0,0)(1,0) V g1 V g2 Stability diagram for double QD (2,0)

(1,0) ← (2,0) ← (1,1) ← (1,0) Ono, ST Science 02 Spin blockade (SB) region: Pauli exclusion principle → transport is blocked S D EZEZ E’ Z ECEC I dot (pA) 0 1 V SD = +1.4 mV, B 0 = 2 T V L (V) V R (V) (1,0) ( N 1,N 2 ) = (2,1) (1,1) SB LR I dot Two-electron double-dot is formed using appropriate gate bias. Stability diagram (high V SD ) (2,0) ESR Signal Detection using P-SB Koppens et al. Nature 06  I dot ESR on

13.6 GHz 14.1 GHz 14.9 GHz 15.5 GHz 16.1 GHz 16.7 GHz 17.3 GHz 17.9 GHz g = 0.41  B 0 =-65mT  B 0 = 0 mT g  B (B 0 +  B 0 )=hf ESR  B 0 = -65 mT for B 0 > 1 T 0 mT for B 0 0 …consistent with stray field Voltage Driven ESR using a Micro-magnet = 2.4 mT from f ESR fluctuations B AC ~ 1 mT

Static Zeeman field: B 0 +  B 0 Slanting Zeeman field: b SL 75 b SL ~ 0.6 T/  m (saturation) x (  m) B z (mT) 0 b SL 0 dot 1dot 2 B0B0 M 70 nm 80 nm 90 nm 300 nm M Co = 1.8 T B0B0 M x z dot 1dot 2 x (  m) B x –B 0 (mT) d ZZ -50 x1x1 x2x2  B 01  B 02 Effect of Magnetization of Ferromagnet → Shift of f ESR →Change of I ESR  B 0, b SL ∞ Magnetization of micro-magnet External B field Magnetization ~ 1 T Stray field of micro- magnet

B ESR = B Slant + B Hyper ± B SO ±: depending on crystal orientation Three contributions to I ESR coexist… They have different dependencies on B 0. ESR field generated by n-spin fluctuations  x ~ E AC B 0 -independent Spin-orbit  k ~ E AC ~B 0 Slantig Zeeman  x ~ E AC ~B 0 for B 0 < B s B 0 -independent for B 0 > B s Laird et al. PRL 07 Nowack et al. Science 07 B 0 dependence important

PAT: (1,1) triplet to (2,0) triplet From the power dependence and using the Bessel function We get E AC ~ 10  V/cm, large enough to drive the ESR. V L (V) V R (V) (1,0) (2,1) (1,1) I dot (pA) 0 10 V SD = +1.4 mV f = 25 GHz, -40 dBm  T(2,0) S(2,0) hf  Power (-dBm)  = 1  = 2  = 5 Power dependence of the T(1,1)-T(2,0) resonance. W. G. van der Wiel Rev. Mod. Phys. 75 (2003) T(1,1) Evaluation of High-frequency Electric Field E AC ….Using PAT 0.1  m E AC ESR V AC E0E0

Peak amplitude vs. external field B 0 < B S Magnetization region Increasing B 0, b SL Increasing I ESR Nuclei spin fluctuations + Hyperfine interaction = Effective nuclei slanting field b N SL ↓ Hyperfine driven ESR Laird et al, PRL2007 Contributions from Hyperfine Fields ~1.6 T Low B 0 field: B Slant,B Hyper >> B SO

SO Contributions from SO Effect Saturation point (E AC *) B AC ~ 1 mT. ESR field estimated from power dependence of I ESR (B 0 > 2T) B 0 =2.14 T B AC ~ B N /2 Nowack et al Science (2007) QD confinement energy Orbital spread b SL = 0.8 T/  m High B 0 field: B Slant, B SO >> B Hyper

RashbaDresselhaus SO Interaction Depending on Crystal Axis GaAs substrate [110] EBext [110] Our device

With micro-magnet, we can view the SO as an effective slanting field Our data suggests l SO > 0, i.e. l  < l   since E AC is along with b SL = 0.8 T/  m Delft work without micro-magnet: l SO =35  m K.C Nowack et al, Science (2007) l SO  > 

V ac  ESR RR With A 1 = 1.5 pA, A 2 = 9.5 pA, T 2 = 362 ns, Rabi = 0.8 MHz  R = 2  s f = 13.6 GHz Power = dBm Rabi Oscillations in Microwave Burst Exp.

Two Spins in a Displaced Ferro-magnet |  B 0 (Dot L)||  B 0 (Dot R)| > f ESR (Dot L)f ESR (Dot R)< Dot L Dot R  f > 1/T 2 * Address two spins at two different f ESR ’s If stray field from micro-magnet Then

Frequency vs. external field ( B 0 > B S )  Z = 13 ± 4 mT ZZ 13.71GHz hf = g  B B 1 hf = g  B B 2 ZZ d ~ 100 nm →  Z ~ 20 mT Expected Zeeman field profile x (  m) B0B0 M x z B x –B 0 (mT) d ZZ -50 dot 1dot 2 50 nm misalignment B 1 – B 0 B 2 – B 0 x1x1 x2x2 Addressing Two Spins at Different Frequencies Laird et al., PRL07 Two-spin address using Hyperfine+Micormagnet

f ESR1 f ESR2 f ESR3 B 0 +  B 1 +B2+B2 +B3+B3 Condition:  f ESR > 1/T 2 Addressing individual spins at different f ESR ’s Specific pattern of ferromagnets

z  B 0 (mT) b SL (T/  m) ~ 200 mT: 1.2 GHz b SL > 1 T/  m b SL x B0B  m thick Co (0.5  m W x 2  m L) Multiple Qubit Design Using Micro-magnets Strips separation d (  m) for d = 0.07 to 0.37  m For  f = 20 MHz ～ 1/T 2 ~60 qubits with  d ~ 5 nm d d Slanting field f ESR shift ~0.3  m

Conclusion Voltage-driven single spin resonance (EDSR) using a slanting Zeeman field Developed a spin resonance technique using a micro- magnet Distinguished contributions from SO interactions and fluctuating hyperfine field Demonstrated two-spin addressing at different f ESR ’s Proposed a way of implementing scalable qubits using a micromagnet technique Micro-magnet tech. … Ｇ ood for any normal materials