Joint Project between Japan and Korea M. Jeong, M. Song, S. Lee (KAIST, Korea) +KBSI T. Ueno, M. Matsubara (Kyoto University, Japan)+Fukui Univ.

Transcription

1 Joint Project between Japan and Korea M. Jeong, M. Song, S. Lee (KAIST, Korea) +KBSI T. Ueno, M. Matsubara (Kyoto University, Japan)+Fukui Univ. +Vasiliev(Turku)

2 31 P NMR at low temperatures ( down to 40 mk) and at a high field (7 T) (Samples are P-doped normal Si with 4 % 29 Si) (Insulator) n c = 4 x (Metal) 6.5x x x x x No NMR ESR (Fujii s Talk) DNP NMR No NMR 2 Phonon Echoes NMR 1 Three-bath model at high fields and low T New T 2 mechanism below 1 K

3 S18 (1.8x10 19 /cc) and S56 (5.6x10 19 /cc): Metallic samples: Strongly-correlated electron system 1) T 1 Measurements Magnetization Recoveries after 180 pulse for S 18 and S 56 S S

4 Analysis of two-step-decay processes by three-bath model We found two-step decay processes at low temperature below about 1 K under high fields (7 T) Nuclear Zeeman Bath T 1 (Korringa) T 1 (fast) Conduction Electron Bath R K : Magnetic Kapitza Resistance? T 1 (slow) 3 He- 4 He Mixture Bath C Z /C E ~ ( µ N H /k B T ) 2 /(T /T F )" (H 2 /T 3 ) C Z ~ C E at T = 50 mk for B = 7 T

5 for T 1 (fast) and for T 1 (slow) "M "t = # M # M(T e) T 1 = M # M(T e) $ /T e (1) Zeeman and electric baths decay together : Energy Conservation between Zeeman and Electric bath: (M " M(0))# H = 1 2 $ (T e2 " T e 2 (0)) (2) T = T N = T e (3) (C N + C ele ) "T "t = 1 R K (T # T He#bath ) (4)

6 Characteristic Behavior of Three-Bath Model (M 0 -M(t))/M 0 10 For the case that T 1_Korriga << T 1_E ath 1 T 1 ~ " C $ E # C E +C z % ' T 1 & Korringa 0.1 b ~ C Z C E +C Z " T 1 ~ C E +C z $ # C E % ' T 1_ ele & time

7 T 1 = K/T bath T 1 = K/T e T 1 (slow) may be determined by Kapitza resistance between conduction electron and 3 He- 4 He bath

8 2) T 2 measurement First observation of T 2 below 1 K.

9 NMR spectrum for S18 and S56 S18 S56 Knight shift of 31 P-NMR from Lamor frequency Inhomogeneous broadening of 1/T 2 * ~ 10 6 sec -1

10 1/T 2 = (1/T 2 ) dip + (1/T 2 ) excess 1) (1/T 2 ) dip is determined by the rigid lattice for 4 % 29 Si- 31 P dipole. (1/T 2 ) dip is independent of T and n. 2) We found (1/T 2 ) excess. (1/T 2 ) excess = # M 2, $ % M 2 " c, T < 0.6 K T > 0.6 K " c = " 0 (T /T F ) #m, m = 4 ~ 5 1) depends on the concentration n. M 2 Thus fluctuating fields responsible for T 2 is either the dipole interaction between P-P or the RKKY. 2) τ c T strongly depends on T and dipole between 31 P- 3 1P is too small. Thus electrons have to be involved.

11 Motional Narrowing (from Slichter s book) (motional narrowing) (Rigid lattice) 1/T 1 ~ M 2 τ c / (1+(ωτ c ) 2 ) 1/T 2 ~ M 2 τ c, where M 2 is the 2nd moment of the fluctuation field. But if τ c > 1/ 2, then 1/T 2 2 (Rigid Lattice)

12 Temperature-dependence of τ (T) n=3 n=4 n=5 τ (T) ~ (a / v F ) (T / T F ) 4~5

13 H RKKY = # A(R kl )I k $ I l, I 1 x + I 2 x, I 1 I 2 k"l [ ] = 0 1) Non-identical spins due to inhomogeneous broadening Truncation of the RKKY H RKKY = # A(R kl )I z k I l z, I 1 x + I 2 x, I 1 2 z I z k"l [ ] " 0 /T 2, where (I 1+ I 2+ + I 1- I 2- )-terms are cancelled in phase factor by inhomogeneous broadening and only (I z1 I z2 ) - term is left. 2) Low density of conduction electrons (E F ~100 K) large RKKY 1/T 2 = M 2 = A(R kl ) 2 ~ (hyperfine) 2 /E F ~ (120MHz) 2 /(10 4 GHz) ~ 1ms "1 for Rigid Lattice case

14 Motional Narrowing formula for T 2 1 T 2 = where Re " # 0 [ I x,h RKKY (o)][ I x,h RKKY (t)] dt "" k#l k ' l ' h 2 Tr{I x 2 } H RKKY = # A(R kl )I z k I l z, I 1 x + I 2 x, I 1 2 z I z Assuming k"l A(R kl (0))A(R k ' l ' (t)} = " A(R kl )e $ih m t / h A(R k ' l ' )e ih m t = A(R kl ) " k#l k ' l ' [ ] " 0 " kl 2 %kk ',ll ' e $t /& c (T ) 1/T 2 = M 2 " c (T ), where M 2 = 1 9 # k A(R k,l ) 2

15 J. Phys.:Conf. Ser. 150, (2008) The set-up for phonon echoes is the same as NMR (120 MHz), where the sample is immersed in liquid 3 He- 4 He mixtures. We measured three samples; (L-P) : Low-doped Si (n = 6x10 17 ) in powder form, Echoes (L-B ) : Low-doped Si (n = 6x10 17 ) in plate(bar) with thickness of 0.1 mm, No Echo (H-P) : High-doped Si (n = 6x10 19 ) in powder form metallic sample NMR 1) Why were Phonon echoes observed for powder sample? D / Sound velocity ~10 µm/ 10 km/s~1/100 MHZ Phonon

16 at 2τ = 150 µs NMR(120 MHz)

17 3) Temperature-dependence of echo intensity No echo is observed above T λ Echo Intensity vs. T at 2τ = 150 µsec

18 Low-doped Si (n = 6x10 17 ) in powder form, immersed in 3 He- 4 He mixtures (n ~ n c = 4 x10 18 /cc) Dynamical Polarization Phonon Echoes in Piezoelectric materials 1) Echoes is formed by non-linear terms of elastic constant F = 1/2 C 2 S 2 +(1/6 c 3 S 3 )+1/24C 4 S 4 S " 2# S + 2 $0 (1" %S 2 )S = f (t) E(2" ) # (T 2 /2)$E 1 E 2 2 (1% e %2" /T 2 )e %2" /T 2 where " = 2 T 2 and # = c 4 /2c 2 Coupling with rf-field (E-field) determine E 1 and E 2. Piezoelectric βe 1 E 2 2 is a fitting parameter for an experiment

19 "2#S Drag force of sphere with radius a, moving with velocity, due to elastic collision of quasi particles in 3 He- 4 He mixture in Knudsen regime F drag = " 2#S, # = 2/T 2, 2 = A" v n n T 2 a" ρ n = ρ n (4) +ρ n (3) S

20 Why P-doped Si near n c has piezoelectricity. P-clusters exist for n < n c (see ESR (c and d)). M. Chiba and A. Hirai, J. Phys. Soc. Jpn., 33, 730 (1972) n c = 4 x /cc Note that cluster (2P, 3P and 4P) signals can be observed even for n << n c.

21 Thank you for your attention

22

23

24

25 T 1 measurement for sample for S 56 Recovery of magnetization after 180 pulse below 1K New features in T 1 b S 56 at T=140 mk at 7 T and low temperatures Above T = 1 K, the recovery is a single-exponential decay. Below 1 K, the magnetization is decayed in two steps. M 0 " M(t) = (a " b) # e " T 1 ( fast ) + b # e M 0 t t " T1 ( slowt )

26 Hamiltonian to describe the entangled state of nuclear spin Q-bits H en = µ B B" z # g n µ n BI z + A" $ I + (dipole) (Zeeman) (Hyperfine) H e#e = &(% i # µ)n i" + & t ij' c + i" c j" + U& n i( n i) i" (Hubbard Model) i T 2 in metallic sample reflects nuclear spin dynamics in the entangled states (ensemble average)

27 Phonon Echo signal by dynamical polarization echoes

28 3. ESR in insulator sample (n = 6.5 x /cm 3 ) f o = 80 GHz (~3 T), ω m = 330 Hz,

29 Temperature-dependence of ESR signals

30 Numerical Solution for Bloch Equation h(" '," res ) = 1 2# exp & $ ("' $" res ) 2 ) ( + ' 2% 2 * ω δω ω ω M "#IN ($%) = % m 2& ' 2& /% m 0 M " (t,$%)cos% m t dt M " IN (# $# res ) = & % $% M "$IN (#'$#)h(#',# res )d#'

31

32 Numerical Simulation of Bloch Equation (T 1 unknown) dm z dt dm x dt = "B 1 M y # M z # M 0 T 1 = #"b z M y # M x T 2 dm y dt = "b z M x # "B 1 M z # M y T 2 b z = $% " + B m cos% m t Passage conditions 2 " A = #B 1, B m $ m " R = B m B 1 $ m T 1, " F = $ m T 1, Adiabatic passage Rapid Passage Fast passage h("," res ) = 1 2# exp & $ (" $" res) 2 ) ( + ' 2% 2 * σ/γ= ω m /2π=330 T 2 = T 1 for T 1 <10-4 s T 2 =1x10-4 s for T 1 >10-4 s

33 M x (t) M z (t) M y (t) M x-in M y-in M x-ot M x_in M y_in M x_outt

34 T 1 - Dependence of Intensity for various passage conditions

35 T 1 (T) at B = 3T First observation of T 1 at high fields T 1 (T=0.1 K) is expected to be 10 sec at B = 3 T.

36 Dynamic Nuclear Polarization of 31 P (DNP)? "I I + + I # =10% =10 3 $ µ NH 2k B T T = 6.9 K, H = 3 T "# "# "# E + E - Tx (H,T) ~ H 2 "#