Investigating the influence of nuclear fluctuations on magnetic quantum tunneling. Oren Shafir, Amit Keren Magnetism Group, Physics Department

Transcription

1 Investigating te influence of nuclear fluctuations on magnetic quantum tunneling Oren Safir, Amit Keren Magnetism Group, Pysics Department

2 Fe8 Molecule Single Molecule Magnet [Fe 8 O (OH) 1 (C 6 H 15 N 3 ) 6 ] 8+ Iron Oxygen Nitrogen Carbon K. Wiegardt, K. Pol, I. Jibril and G. Huttner, Angew. Cem. Int. Ed. Engl. 3 (1984), 77. Hydrogen Te magnitude of magnetic interactions between te spins of te ions is between 0 to 170K. Te magnetic interactions between te molecules are negligibly small (~0.05K).

3 Single crystal of Fe8 Single crystal of Fe8 (array of nanomagnets) Te magnetization is preferentially oriented parallel to an axis called te "easy axis. (Syntesized in te Tecnion.) Easy axis 3 Hard axis

4 Te molecular spin in low temperatures S=10 3 = + S Fe 5 M. Ueda & S. Maegawa, J. Pys. Soc. Jpn. 70 (001) (a) is parallel to te easy axis. (b) is perpendicular to te easy axis. 4 S = ( 5 ) ( 5 ) = (Tis was confirmed by a polarized neutron-diffraction experiment)

5 Hysteresis loop of Fe8 W. Wernsdorfer et al. J. Appl. Pys. 87 (000), 5481 A. Canesci et al. JMMM 00, 18 (1999) Tere is a temperature dependence above 0.4K. Equally separated steps can be seen at H m n 0. T. Te ysteresis sape depends on te field sweeping rate. 5

6 Te Hamiltonian of Fe8: S=10 Te main part of te spin Hamiltonian: Hamiltonian ZFS H = DS gμ H z B z S z E ( S S ) x y D anisotropic constant (~0.7 K) E rombic parameter (~0.046 K) Te energy levels (E=0) are: Energy( m) = Dm g μ B were m is te quantum number of te level. E is responsible for te tunnel splitting. H z m D Hm ( ) = m 0. mt [ ] gμ B 6

7 Te concept of tunnel splitting: S = 1 H D 0 = DSz + E( Sx S y) = E 0 E D up 1 = 0 0 middle 0 = 1 0 down 0 = 0 1 Energy levels wit E=0 0 Energy levels wit E D double degenerate -(D-E) -(D+E) Δ=E 7 1 cos( Et) 1 cos( Δt) down exp( iht) up = = Te spin will tunnel at a rate given by Δ from up to down.

8 Energy levels and tunnel splitting in Fe8 Energy [K] Energy Energy levels Fe8 levels E= H [T]

9 Te model and te ysteresis loop Landau Zener model P m, m' = 1- exp - gμ B πδ m, m' m m' dh/dt No tunneling 9 M H tunneling

10 Te model and te ysteresis loop Energy 10

11 Δ teory and experiment Cudnovsky and Garanin: (PRB (001)) 8D Δ S, S = 8 [( S 1)! ] (S)! E D S Δ 10 10, K Tis is only an approximate solution, because even very small iger-order transverse couplings can make an important contribution to Δ k. Wernsdorfer et al (J. Appl. Pys. 87 (000), 5481) ave measured Δ 10 for many different sweeping rates using te Landau-Zener model. Teir experiment sowed tat Δ 10 ~10-7 K. exp teory 11

12 Evidence for te Role of Nuclei in QTM Hole digging 30 ΔT - Te time needed to relax 0.5% of te saturation magnetization T = 40mK M ini = 0 H = 0.04 T 1 R. Sessoli et. al. JMMM 6 (001)

13 Evidence for te Role of Nuclei in QTM Hole digging 30 13

14 Researc Goals In tis researc we try to observe te effect of te nuclear spins on te QTM in Fe8 by examining te influence of RF (radio frequency) on its ysteresis loop. By giving a comb of RF pulses we warm te nuclei of te H atoms (more ten 100 atoms in every molecule) and look at te effect on te magnetization curve. 14

15 Faraday force magnetometer Te load cell Termal link Termometer RF coil Movable plate Kel-f Pospor- Bronze wire Epoxy Brass Fixed plate Screwing Copper Measuring te varying capacitance. spatially varying magnetic field magnetic force Te sample is glued wit GE-Varnis to kel-f (witout protons) as a termal link to avoid metallic parts near te coil.

16 Faraday force magnetometer inside te DR DR 48 C C = a M z db dz z Termal link Mixing camber Coaxial wires Vaccum jacet a Calibration constant center line Superconducting solenoid magnet Superconducting Gradient coils 16 Te load cell device, displaced from te center of a solenoid magnet in a dilution refrigerator.

17 Magnetization measurements T/min, field cool from 4.K, no gradients Cap [nf] H [T] Because te sample is off-center, te gradient is a function of H. 17

18 Field sweep rate dependance T/min 0.5 T/min 0.1 T/min 5.3 Cap [nf] H [T] base temperature, 1 [T]/[min]=16.66 [mt]/[sec] 18

19 Temperature dependance Temp 630mK Temp 50mK Temp 130mK Cap [a.u.] H [T] 19 Te temperature of te sample is iger ten te resistor (mesearment wile cooling, sweep rate 0.5T/min)

20 NMR Spectrometer back 0

21 NMR - T measurement 1

22 NMR data of Fe8 - T Ueda T Amp [a.u] base Temp, 0.99T, 1.71MHz Equation: y = A1*exp(-x/t1) + y0 Ci^/DoF = R^ = y ± A ± t ± Temp 5K Equation: y = A1*exp(-x/t1) + y0 Time [uses] 15 Ci^/DoF = R^= Amp 10 y ± A ±.6899 t ± Time [micro sec]

23 T NMR Hig Temp pure crystals in NMR system (witout G-Varnis) 14 Eco Intencity [a.u] Temp = 90K Eco Intencity [a.u] Temp=90K τ [μsec] τ [μsec] te line is a fit to te function: y = A 1 *exp(-x/t ) + y 0 T (90K)=0± [μsec] and T (90K)=13.8±0.13 [μsec]. 3

24 T - Temperature dependence Ueda T 4 18 T [msec] Temp [K] 4

25 NMR - T1 measurement 5

26 NMR data of Fe8 - T1 Ueda T T1 measerement 140mK, 0.99T Amp [a.u] Equation: y = y0 + A1*exp(-x/t1) Ci^/DoF = R^= y ± A ± t ± Time [sec] 6

27 NMR data of Fe8 - Pulse lengt Ueda T Amp [A.U.] Pulse widt [usec] Amp1 Amp Amp3 Amp4 Amp MHz, no gradients, 140mK Δ H < 40G H [T] ω= γh pulse = ± 0.5μ H = 10± 30G 1 Δ H < H 1 Te RF excites all te visible protons 7

28 Measuring wit RF We saw tat we can saturate te nuclei (we give a comb of pulses until te eco is gone). For tecnical reasons we can detect NMR signal only above ~0.3T (1MHz). Trying to transmit near or between te jumps cause termally assisted QTM. T1 is in te order of 100 sec. Terefore we decided to transmit at 0.3T (wen te jumps are expected at negative field) and sweep te field wit a rate of 0.5 T/min and see if it is effecting te jumps eigt. 8

29 Measuring wit RF Cap [pf] Temp [K] H [T] T RF Time [sec] 9

30 Measuring wit RF wit stop 0.3T (no RF) wit stop 0.3T (no RF) wit stop 0.3T (no RF) wit stop 0.3T (wit RF) wit stop 0.3T (wit RF) Cap [pf] H [T] 30 We don t see any effect of te RF radiation.

31 Conclusions - NMR We are convinced tat te jumps come from te sample, but we are not sure wy tey are irreproducible. We are confidant at te NMR T1 and T measurements. We don t see any effect of te RF radiation. But 31

32 Jumps and Temperature Temp [K] Temp [K] Cap [nf] Cap [nf] H H [T] [T] 3 sweep rate 0.1T/min

33 Jumps and Temperature dc/dh Derivative of te capacitance TEMP Temp [K] H [T] From positive to negative magnetic field 33 (sweep rate 0.1T/min)

34 Jumps and Temperature Load cell Same measurement wit fixed capacitance (no moving parts) T/min Temp [K] Cap [pf] H [T] 34 sweep rate 0.T/min

35 New setup for te Faraday force magnetometer Termal link Termometer RF coil Movable plate Kel-f Pospor- Bronze wire Epoxy Brass Fixed plate Screwing Copper Te termometer and te sample are connected to te DR separately.

36 Jumps and Temperature Load cell Same measurement witout close termal link between te sample and te termometer. sweep rate = 0.1 [T]/[min], Indipendent termometer 0.17 Temp [K] Cap [nf] H [T] 36

37 Super-radiance 37

38 Jumps and Temperature A jump in te Capacitance is always followed by a jump in te temperature. Te temperature jumps are not caused by te mecanical movement of te load cell We believe tat te cause of te eat burst is superradiance (wic as been seen in similar molecular magnet). 38

39 39 End

40 Te excange patways connecting iron(iii) in Fe8 back J 1 = -147K J = -173K J 3 = -K J 4 = -50K 40 C. Delfs, et al. Inorg. Cem. 3, 3099 (1993).

41 Blocking Temperature back At temperatures lower tan te magnetic coupling J between ions inside te molecule, te spins of te ions are locked, and te molecules beave like non -interacting spins. 41 T [K] (a) parallel to te easy axis (b) perpendicular to te easy axis. M. Ueda & S. Maegawa, J. Pys. Soc. Jpn. 70 (001)

42 Zero field splitting back Te large S ground state as S+1 spin microstates, wic correspond to te M S states in te absence of transverse anisotropy. Tese can be split up in zero field by spin-orbit coupling or magnetodipolar interactions if S>½. Tis is called zero-field splitting. Magnetodipolar interactions are usually small (10-1 cm -1 ) Spin-orbit coupling can mix orbital angular momentum of te electronically excited state into te ground state. 4

43 Zero field splitting back Te zero-field splitting can be described by a term in te spin Hamiltonian: Here D is a 3 x 3 matrix: We can rewrite te spin Hamiltonian term as: were: Te D term canges te energies of te M S states. Te E terms mixes te M S states (wit ΔM S =), i.e. te pure M S states are no longer te energy eigenstates of te system. 43

44 Hamiltonian of Fe8 back N l 1 n n H = γ Sz α n( S+ + S ) n= 1 Te effective spin Hamiltonian (witout te Zeeman term): 44 D. Gattesci and R. Sessoli, Angew. Cem. Int. Ed. 4, No. 3 (003), p. 68

45 Experimental realization back M s =S-1 M s =S M s =-S+1 M s =-S M s =S M s =-S a) In zero field te two wells are equally populated. b) An applied magnetic field selectively populates te rigt well. c) After removing te field te system can returns to equilibrium (termally) if T is ig enoug. 45 Termally assisted QT pure QT

46 46 Te eigenvectors and eigenvalues of H 0 are: Te spin will tunnel at a rate given by: ( ) /4 / / /4 B z B x z B x x z z B x B z D g g DS g S S g D g μ μ μ μ μ = + = + H Δ 0 =gμ B x known as tunnel splitting Te concept of tunnel splitting: S=1/ ( ) + + = t g e z x B z x x t i cos 1 1 μ H z x B g + = Δ μ 4 / 1 1 1, 4 / z x B as z x B s g D E g D E + = + + = μ μ

47 47 Te eigenvectors and eigenvalues of H 0 are: Te spin will tunnel at a rate given by: ( ) B z B x z B x x z z B x B z D g g DS g S S g D g μ μ μ μ μ = + = + H Δ 0 =gμ B x known as tunnel splitting Te concept of tunnel splitting: S=1/ 4 / 1 1 1, 4 / z x B as z x B s g D E g D E + = + + = μ μ z x B g + = Δ μ ( ) + + = t g e z x B z x x t i cos 1 1 μ H

48 Zener time Δ /τ > 0 g tunnel μ B d dt z Δ 0 τ tunnel = π Δ 0 Δ 0 z Δ / π > Δ0 0 g μ B d dt z 48 P m, m' = 1- exp - gμ B πδ m, m' m m' dh/dt dz Δ 0 / gμ B > 1 dt

49 Zener Time Mullen et al α Δ >> 1 τ z Adiabatic limit: / α α Δ << 1 τ z sudden limit: Δ / α 49 α = lim de Δ 0 = dt g μ B d z dt

50 Hole digging Wernsdorfer et al., Pys. Rev Letters, 84 (000), 965 Starting from M init applying a small field H dig for a time t dig A field H is applied to measure te sort time square root relaxation rate Γ sqrt (H, H dig, t dig ) 50 P(H z ) te normalized distribution of molecules wic are in resonance at H z back

51 back Hole digging Wernsdorfer et al., Pys. Rev Letters, 84 (000), 965 μ 0 H dig =14 mt As a result a very sarp ole is dug into te rater broad distribution of Γ sqrt Γ ole = Γ sqrt (H, H dig, t dig =0)- Γ sqrt (H, H dig, t dig ) Te ole line widt σ is close to te yperfine level broadening 51

52 Te nuclear effect on te QT - yperfine interactions Prokof ev and Stamp (Pys. Rev. Lett. 1998, 80, 5794) Te dynamic nuclear field cange te energy levels. Consequently, tunneling will start before and will end after matcing conditions. Te effective tunnel rate at te matcing field: Δ Δ eff T E -S =E S +gsμ B H+ξ dip E S 5

53 Researc Goals In tis researc we try to observe te effect of te nuclear spins on te QTM in Fe8 by examining te influence of RF (radio frequency) on its ysteresis loop. By giving a comb of RF pulses we warm te nuclei of te H atoms (more ten 100 atoms in every molecule) and look at te effect on te magnetization curve. eff ( ) ( ) T T T ( ) ( ) Δ Δ Δ T 0 Δ T T 0 eff 53

54 Capacitance bridge magnetometer 3 terminal metod C X N V NC N = VX C X = = CN VX V N N N X Basic bridge circuit of AH550A Capacitance Bridge 54 A capacitance bridge wit transformer ratio arms.

55 Dilution refrigerator scematic view 55 magnetometer

56 NMR data of Fe8 - Ueda et. al NMR Data M. Ueda, PD tesis, Kyoto University, 001 M. Ueda, S. Maegawa, S. Kitagawa, Pys. Rev. B. 66 (001)

57 Results - jumps in matcing fields grad=0 ; Rate=0.3T/min 6.10 grad=0 ; Rate=0.1T/min Capacitance [pf] Capacitance [pf] H [T] H [T] Te capacitance verses te magnetic field (dh/dt = 5, 1.6 mt/sec, T =100mK) Sampling Rate: 1/1.7 Hz 57

58 Wit and witout gradient coils T/min, base temp Cap [a.u] witout grad wit grad -7.A H [T] Te Gradient Coils give 100 Gauss/Cm (1 T/m) 58 Because te sample is off-center, te gradient is a function of H.

59 Temperature and sweep rate T/min 0. T/m 0.5 T/m 0.7 T/min 0.8 Temp [K] H [T] Te sample rate is similar to all runs 59

60

61 Ponons 61