Multi-bit magnetic memory using Fe 8 high spin molecules. Oren Shafir Magnetism Group, Physics Department

Multi-bit magnetic memory using Fe 8 high spin molecules Oren Shafir Magnetism Group, Physics Department

Outline Preface: memory unit Fe8 as a high spin molecule Quantum tunneling In Fe8 Experiments: Faraday force magnetometer μsr Discussion Summary

The memory of a memory unit Hysteresis loop 3

What do we mean by multi-bit memory? Single-bit Memory using the same measurement one can distinguish between two different preparation processes. Multi-bit Memory using the same measurement one can distinguish between more than two preparation processes. 4

Memory Unit Evolution 5 Atoms per bit 10 0 10 19 10 18 10 17 10 16 10 15 10 14 10 13 10 1 10 11 10 10 10 9 10 8 10 7 Magnetic cores Disk file Magnetic bubble Thin film Optical disk IBM QTM 10 6 10 5 10 4 10 3 1950 1960 1970 1980 year 1990 000 010 J. Harris and D. Awschalom, Physics World Jan.-1999

Outline Preface: memory unit Fe8 as a high spin molecule Quantum tunneling In Fe8 Experiments Faraday force magnetometer μsr Discussion Summary 6

Molecules as magnetic memory There are some properties that molecules must have if one wants to use them as magnetic memory: Existence of an hysteresis loop (energy barrier between two magnetization states) = the molecule can remember. Large interaction between the spins in the molecule (J) = the molecule acts as a single unit. Weak magnetic coupling between the molecules = every molecule behaves independently. 7

Fe8 Molecule [Fe 8 O (OH) 1 (C 6 H 15 N 3 ) 6 ]Br 7 (H O)Br8H O Iron Oxygen Nitrogen Carbon K. Wieghardt, K. Pohl, I. Jibril and G. Huttner, Angew. Chem. Int. Ed. Engl. 3 (1984), 77. Hydrogen The magnitude of magnetic interactions between the spins of the ions is between 0 to 170K. The magnetic interactions between the molecules are negligibly small. 8

Single crystal of Fe8 Single array of nanomagnets The magnetization is preferentially oriented parallel to an axis called the "easy axis. Easy axis Hard axis 9

The molecular spin in low temperatures S=10 (a) is parallel to the easy axis. (b) is perpendicular to the easy axis. M. Ueda & S. Maegawa, J. Phys. Soc. Jpn. 70 (001) This was confirmed by a polarized neutrondiffraction experiment. S 10 ( 5 ) ( 5 ) + 10 = 6 =

Hysteresis loop of Fe8 Temperature dependence 11 A. Caneschi et al. JMMM 00, 18 (1999) There is a temperature dependence above 0.4K. Equally separated steps can be seen at H m n 0. T The lower the temperature, the wider the hysteresis loop

Hysteresis loop of Fe8 sweeping rate dependence A. Caneschi et al. JMMM 00, 18 (1999) A. Caneschi et al. JMMM 00, 18 (1999) 1 Equally separated steps can be seen at H m n 0. T Fast sweeping rate wider hysteresis loop

Outline Preface: memory unit Fe8 as a high spin molecule Quantum tunneling In Fe8 Multi-bit memory Experiments: Faraday force magnetometer μsr Discussion Summary 13

The concept of tunnel splitting: S = 1 H = DS z + E( S x S y ) D = 0 E 0 0 0 E 0 D up 1 = 0 0 middle 0 = 1 0 down 0 = 0 1 Energy levels with E=0 Energy levels with E 0. 0 0 -D double degenerate -D+E -D-E Δ=E 14 1 cos(et) 1 cos( Δt) down exp( iht) up = = The spin will tunnel at a rate given by Δ from up to down.

The Hamiltonian of Fe8: S=10 Hamiltonian The main part of the spin Hamiltonian: H = DS gμ H z B z S z E ( S S ) x y D anisotropic constant (~0.7 K) E rhombic parameter (~0.046 K) The energy levels are: Energy( m) = Dm g μ B H z m where m is the quantum number of the level. The tunnel splitting between the two degenerated ground states: 15 8D Δ S, S = (S)! 8 [( S 1)! ] E D S

Experimental realization M s =S-1 M s =S M s =-S+1 M s =-S M s =S M s =-S a) In zero field the two wells are equally populated. b) An applied magnetic field selectively populates the right well. c) After removing the field the system returns to equilibrium (thermally). 16 Thermally assisted QT pure QT

The model and the hysteresis loop H = DSz + E( S x S y ) gμbs H Energy H nd ( n) = n 0.T. g μ m B No tunneling Landau Zener model M 17 H tunneling P m, m' = 1- exp - hgμ B πδ m, m' m m' dh/dt

Outline Preface: memory unit Fe8 as a high spin molecule Quantum tunneling In Fe8 Experiments: Faraday force magnetometer μsr Discussion Summary 18

Faraday force magnetometer Principle of measurement Measuring the varying capacitance. spatially varying magnetic field magnetic force The restoring force of the springs balances F. F = ( M ) B 19

Faraday force magnetometer The load cell Thermal link sample Phosphor- Bronze wire screwing Epoxy (Stycast) Brass The movable plate is suspended by four wires of phosphor bronze. Cu Thermal link Mixing chamber Coaxial wires Vaccum jacet C 0 C 1 1 0 = a M a Calibration constant z db dz z Superconducting solenoid magnet center line The load cell device, displaced from the center of a solenoid magnet in a dilution refrigerator.

Results - jumps in matching fields 15.4884 Capacitance [pf] 15.4883 15.488 15.4881-0.8-0.6-0.4-0. 0.0 0. 0.4 0.6 H [Tesla] The capacitance verses the magnetic field (dh/dt =0.15 T/min,T =40mK) The distance between steps is nearly constant 1 (the arrows are of equal length)

Sweep rate dependence Capacitance [a.u.] 3 1 0-1 - -3 0.4 0.15 0.1 0.03 dh z /dt [T/min] -1. -1.0-0.8-0.6-0.4-0. 0.0 H [Tesla] Capacitance in arbitrary units for various dh z /dt (at T=40mK). The vertical dotted lines are at the approximate matching fields H m n 0.1T.

Temperature dependence Capacitance (a.u.) 4 0 - T = 30mK T = 00mK T = 500mK T = 700mK T = 4.K -1. -1.0-0.8-0.6-0.4-0. 0.0 H [Tesla] Capacitance in a.u. for different temperatures (dh z /dt=0.15 [T/min]). The vertical dotted lines are at the approximate matching fields H m n 0.1T 3

Outline Preface: memory unit Fe8 as a high spin molecule Quantum tunneling In Fe8 Experiments: Faraday force magnetometer μsr Discussion Summary 4

Why measure Fe8 with μsr? We want to measure the magnetization of a few (or one) molecules We need a local probe Moreover, there is an ongoing effort to make Fe8 films μsr is applicable to films (while most techniques are not). 5

μsr Muon Spin Relaxation/Rotation High energy proton Carbon atom nucleus pion muon neutrino positron sample From the ISIS website (ISIS - pulsed neutron and muon source located at the UK) 6 Positron detector The muon provides information on the magnetic environment in its vicinity. ω μ = γ B μ

μsr experiment setup L R The beam direction easy axis of Fe8 applied field. Temperature : ~100mK (minimize activation effects). The initial polarization of the muons is 50 relative to z. 7

Asymmetry μsr Detected positrons time difference between the muon arrival at the sample and its decay Corrected asymmetry: R( t) L( t) A( t) = P ( t) R( t) + L( t) 8

The process - three step field cycle: process 1. A strong negative field of -T that is parallel to the z axis, polarizes the Fe8 molecules.1. The field is swept to an intermediate positive value H i, at a rate of 4 mt/s different process Energy. 3. The field is swept back to +50G at 9 the same rate same measurement m > 0 m < 0.3

Illustration of the double well potential in the field cycle Energy 30 m > 0 m < 0

Experiment results Asymmetry 0. 0.1 0.0-0.1-0. 0. 0.1 0.0-0.1-0. 0. 0.1 0.0-0.1-0. (a) (b) (c) Fe8 H i =0.1T H i =0.T H i =0.3T (d) (e) H i =0.1T H i =0.T H i =0.3T Holder 0 1 3 4 0 1 3 4 Time(msec) (f) There is a difference in amplitude. The solid lines are the fit to the function: A( t) = Asin( t) e ω μ = γ ω μ Reproducibility μ B λt. 31 Asymmetry Hematite

Analysis of the results ΔB = B Fe B Holder 8 = ω ( H ) ω ( H ) Fe 8 i γ μ Holder i ΔB [Gauss] 70 60 50 40 30 0 10 0.0 0.1 0. 0.3 0.4 0.5 0.6 0.7 H i [Tesla] The process: -T H i 50G Matching fields: H n = n.1kg. n = 0,1,... 3 (The solid line is a guide to the eye)

Two different setups Muon beam Several Fe8 single crystals were glued on a (a) Silver plate (b) small silver plate. Fe8 Fe8 In a different experiment the muons stopped in the silver plate 33

Analysis of the results muons hit the silver plate 0.6 44 Δω =ω full -ω empty [Mrad/sec] 0.4 0. 0.0-0. 30 15 0-15 ΔB [Gause] -1.0-0.8-0.6-0.4-0. 0.0 0. 0.4 0.6 0.8 Hi [T] 34 The resolution is worse, but a full hysteresis loop can be seen.

Outline Preface: memory unit Fe8 as a high spin molecule Quantum tunneling In Fe8 Experiments: Faraday force magnetometer μsr Discussion Summary 35

Comparison to the Landau-Zener model and to previous experiments P = 1- exp - hgμ B πδ m, m' m m' dh/dt 36 W. Wernsdorfer, R. Sessoli, Science 1999, 84, 133.

The probability to stay at m=-10 H=0 For example: kg < H i < 4kG P -10,10 1-p -10,10 H=kG Flip No Flip P -10,9 1-p -10,9 H=kG Flip No Flip P -10,9 1-p -10,9 The process: -T H i 50G Flip No Flip The probability not to tunnel - 37 (1-P -10,10 ) (1-P -10,9 )

Comparison to the Landau-Zener model 70 60 ΔB [Gauss] 50 40 30 0 10 0.0 0.1 0. 0.3 0.4 0.5 0.6 0.7 H i [Tesla] The agreement between theory and experiment is poor. 38

The same process for SmCo 4 3 1 SmCo -T H i 50G M [emu] 0-1 - -3-4 -5 0.0 0.1 0. 0.3 0.4 0.5 0.6 H i [T] ΔB [Gauss] 70 60 50 40 30 0 10 Fe8 39 0.0 0.1 0. 0.3 0.4 0.5 0.6 0.7 H i [Tesla]

Outline Preface: memory unit Fe8 as a high spin molecule Quantum tunneling In Fe8 Experiments: Faraday force magnetometer μsr Discussion Summary 40

Summary The qualitative result from the Faraday force magnetometer demonstrates again the quantum nature of the Fe8 crystals. Using the msr technique, which is also applicable to films, we observe quantum tunneling of the magnetization (QTM) in the Fe8 compound. We show that Fe8 can remember for at least 1/ hour which intermediate field was visited. Using Fe8, we can distinguish between at least six processes by performing the same measurement. 41 This warrants Fe8 molecules the candidacy for a multi-bit magnetic memory.

Acknowledgments: Dr. Y. Sheynin, Dr. M. Kapon, Prof. M. Kaftori - for sample preparation and characterization Prof. E. Polturak and Prof. M. Resnikov - for helping with the DR Technicians - Leonid Iomin, Mordehay Eilon, Shmuel Hoida for their help with the DR Prof. S. Maegawa, Dr. M. Ueda - for initial samples, Kyoto University, Japan Dr. A. Amato, C. Bains for μsr instrument support, PSI, Switzerland 4

Acknowledgments: My lab members: Shahar, Ariel, Meni, Oshri, Rinat, Eva, Lior and Amit Kanigel Special thank for Prof. Amit Keren. 43

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The exchange path ways connecting iron(iii) in Fe8 back J 1 = -147K J = -173K J 3 = -K J 4 = -50K 45

Blocking Temperature back At temperatures lower than the magnetic coupling J between ions inside the molecule, the spins of the ions are locked, and the molecules behave like non -interacting spins. 46 T [K] (a) parallel to the easy axis (b) perpendicular to the easy axis. M. Ueda & S. Maegawa, J. Phys. Soc. Jpn. 70 (001)

Hamiltonian of Fe8 back The effective spin Hamiltonian (without the Zeeman term): 47 D. Gatteschi and R. Sessoli, Angew. Chem. Int. Ed. 4, No. 3 (003), p. 68

What do we mean by multi-bit memory? Single-bit Memory using the same measurement one can distinguish between two different preparation processes. Multi-bit Memory using the same measurement one can distinguish between more than two preparation processes. μsr process 48

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

Zener time Δ /τ > 0 g tunnel μ B dh dt z Δ 0 τ tunnel = π Δ 0 Δ 0 h z Δ / π h > Δ0 0 g μ B dh dt z 50 P m, m' = 1- exp - hgμ B πδ m, m' m m' dh/dt dhz Δ 0 / hgμ B > 1 dt

Zener Time Mullen et al hα Δ >> 1 τ z Adiabatic limit: h / α hα Δ << 1 τ z sudden limit: Δ / α 51 α = lim de Δ 0 = dt g μ B dh z dt

Capacitance bridge magnetometer 3 terminal method C X N V NC N = VX C X = = CN VX V N N N X Basic bridge circuit of AH550A Capacitance Bridge 5 A capacitance bridge with transformer ratio arms.

Dilution refrigerator magnetometer Control unit Inner Vacuum chamber outer Vacuum chamber 53 Mixing chamber

Dilution refrigerator schematic view 54 magnetometer

Changes due to eddy currents Capacitance*100 [pf] 15.4904 15.4896 15.4888 15.4880 sweep rate 1.1 sweep rate 1 sweep rate 0.8 sweep rate 0.6 sweep rate 0.5 sweep rate 0.4 sweep rate 0.3 sweep rate 0. sweep rate 0.15 sweep rate 0.1 sweep rate 0.03 55 -.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5.0 H [T]

Pion decay π + μ + + ν μ Only left-handed neutrinos exist Pions have zero spin Pions at rest (p p = 0) Muons have a spin which is anti-parallel to their momentum μsr 56

Muon decay μsr The muon decays according to: μ e + + ν + + e ν μ The positron is usually energetic enough to travel a substantial distance before annihilating. 57 The violation of parity

Fe8 as hematite results 0.1 0.0-0.1 (a) Mask empty Asymmetry 0.1 0.0-0.1 (b) Fe 8 and mask 0.1 Ag and mask 0.0-0.1 (c) 0 1 3 4 5 6 Time Fe8 silver hematite mask The asymmetry of a hematite and glue mask (a) is very similar to mask and Fe8 (b), but different from mask and silver (c). Therefore, muons in Fe8 do not contribute to the asymmetry. 58

Comparison to the Landau-Zener model P = 1- exp - hgμ B πδ m, m' m m' dh/dt h = 7.638 10 1 [ K]/[ s] μ B = 0.67170099[ K]/[ T] dh / dt = 0.45[ T ]/[min] = 4.083 10 3 [ T ]/[ s] For Δ -10,10 =10-7 K P -10,10 = 0.0 For Δ -10,9 =3 10-7 K P -10,9 = 0.16 For Δ -10,8 =0 10-7 K P -10,8 = 0.99 59

Comparison to the Landau-Zener model Starting point - N -10 : N 10 = 1:0 H i (intermediate field) H i < ~0.T The probability not to tunnel 1-P -10,10 N -10 : N 10 0.9776 : 0.04 ~0.T < H i < ~0.44T (1-P -10,10 ) (1-P -10,9 ) 0.68 : 0.38 ~0.44T < H i < ~0.66T (1-P -10,10 ) (1-P -10,9 ) (1-P -10,8 ) 0 : 1 60 N -10 - the number of the molecules with spin up N 10 - the number of the molecules with spin down illustration

The simplest model double well potential Tunneling in a double well system: a) Non-coupling states. b) Coupling states giving rise to tunnel splitting, Δ. 61

The prediction The molecular approach to nanoscale magnetism A. Caneschi, D. Gatteschi, C. Sangregorio, R. Sessoli, L. Sorace, A. Cornia, M.A. Novak, C. Paulsen, W. Wernsdorfer Journal of Magnetism and Magnetic Materials Vo. 00 (1999) p. 18-01 (referred to the result in Mn1) These results also make Mn1ac more appealing for technological applications as it represents a multi- rather than a bi-stable single molecule memory unit. " 6

Summary The experimental work: Synthesizing Fe8 crystals Assembling a dilution refrigerator Fraday force magnetometer experiments (Design a load sensing variable capacitor; operating DR, SC magnet, capacitance bridge) μsr experiments 63

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