Quantum dynamics in Single-Molecule Magnets - towards molecular spintronics

Transcription

1 Quantum dynamics in Single-Molecule Magnets - towards molecular spintronics Wolfgang Wernsdorfer Institut Néel CNRS - Grenoble S = 10 2 to 10 6 S = 1/2 to 30

2 Magnets nanoworld Mm 1 km 1 m 1 mm 1 µm 1 nm

3 permanent magnets macroscopic micron particles Magnetic structures nanoparticles clusters atomic molecular clusters atoms S = multi - domains single - domains spins 1 mm 20 nm 3 nm 1 nm

4 Magnetization reversal in magnetic structures permanent magnets macroscopic micron particles nanoparticles clusters atomic molecular clusters atoms S = multi - domains nucleation, propagation and annihilation of domain walls single - domains uniform rotation, curling, etc. spins quantum tunneling, interference, coherence 1 S 1 S 1 S Fe 8 0.7K M/M -1 M/M -1 M/M 1K 0.1K µ 0 H(mT) µ 0 H(mT) µ 0 H(T)

5 Magnetization reversal in magnetic structures permanent magnets macroscopic micron particles nanoparticles clusters atomic molecular clusters atoms S = multi - domains nucleation, propagation and annihilation of domain walls single - domains uniform rotation, curling, etc. spins quantum tunneling, interference, coherence Classical magnetism Micromagnetics Landau Lifshitz Gilbert equation Quantum magnetism Schrödinger equation Operator formalism Path intergrals ab-initio calulations etc.

6 Micro-SQUID magnetometry particle stray field B 1 µm fabricated by electron beam lithography (D. Mailly, LPN, Marcoussis - Paris) sensitivity : 10-4 Φo µ B i.e. (2 nm) 3 of Co Josephson junctions A. Benoit, CRTBT, emu

7 Roadmap of the micro-squid technique 1 S(µ B ) Quantum limit of a SQUID 0 3 nm? information storage Years

8 nano-squid G1 SWNT Gnd G2 500 nm J.-P. Cleuziou, W. Wernsdorfer, V. Bouchiat, Th. Ondarçuhu, M. Monthioux, Nature Nanotechnology, 1, 53 (2006)

9 Cobalt cluster of 3 nm V. Dupuis, A. Perez, LPMCN, Lyon: LASER vaporization and inert gas condensation source Low Energy Cluster Beam Deposition regime HRTEL along a [110] direction fcc - structure, faceting blue: 1289-atoms truncated octahedron grey: added atomes, total of 1388 atomes Ideal case: truncated octagedron with 1289 or 2406 atoms for diameters of 3.1 or 3.8 nm

10 Giant spin approximation 1000 atoms S 1000

11 Uniform rotation of magnetization: Stoner - Wohlfarth model (1949) single domain magnetic particle one degree of freedom: orientation θ of magnetization M potential: E=K sin 2 θ µ 0 M S H cos(θ ϕ) K=K µ 0M S 2 (Nb N a ) 2 E(θ) 1 h = h 0 h > 0 H ψ ϕ b h = 0 M 0 θ z T = 0 K a θ B B

12 Stoner - Wohlfarth switching field M 1 0 h sw = ( sin 2/3 θ+cos 2/3 θ) 3/2 h sw hard axis easy axis h Stoner - Wohlfarth astroid

13 Temperature dependence of the switching fields of a 3 nm Co cluster µ 0 H z (T) K 1 K 2 K 4 K 8 K 0.04 K T B - 14 K t 1 s µ 0 H y (T) => in agreement with the Néel Brown theory PRL 86, 4676 (2001)

14 Finding the anisotropy from 3D switching field measurements E 0 = m 2 z + 0.4m 2 x 0.1[ m 2 x m 2 y + m 2 x m 2 z + m 2 2 y m ] z PRL 86, 4676 (2001)

15 Switching of magnetization by non-linear resonance studied in single nanoparticles Energy H Magnetization angle H Dynamical astroid C. Thirion, W. Wernsdorfer, D. Mailly Nature Mat.2, 524 (2003)

16 Magnetization reversal via precession Measurement Simulation 0.15 t = 10 ns static 4.4 GHz 3.2 GHz 2.4 GHz µ 0 H z (T) µ 0 H x (T) C. Thirion, W. Wernsdorfer, D. Mailly, Nature Mat.2, 524 (2003)

17 Lis, 1980 Single-molecule magnets (SMM) Giant spins Mn 12 S = 10 Tb J = 6 Ni 12 S = 12 QuickTime et un décompresseur Animation sont requis pour visualiser cette image. Mn 84 S 6 Fe 8 S = 10 Christou, 2004 Winpenny, 1999 Wiegart, 1984

18 Crystal of SMMs QuickTime et un décompresseur Animation sont requis pour visualiser cette image.

19 Micro-SQUID array crystal B crystalsize> fewµm to emu temperature K field < 1.4 T and < 20 T/s rotation of field transverse field several SQUIDs at different positions 50 µm

20 Micro-magnetometry µ-hall Effect µ-squid B sample B sample 1 µm Hall bars 1 to 10 µm Jospheson Junctions Based on Lorentz Force Measures magnetic field V H = αi ne M Large applied in-plane magnetic fields (>20 T) Broad temperature range Single magnetic particles Ultimate sensitivity ~10 2 µ B Based on flux quantization Measures magnetic flux Applied fields below the upper critical field (~1 T) Low temperature (below T c ) Single magnetic particles Ultimate sensitivity ~1 µ B

21 Giant spin approximation (Fe 8 ) S = 10 Fe III : s = 5/2

22 Giant spin model Spin Hamiltonian: Η= DS 2 z + E S 2 r ( 2 x S y )+ gµ B S H r (2S + 1) energy states: M = -S, -S+1,, S magnetic anisotropy Zeeman energy Energy levels: Zeeman diagram 10 Energy H = 0 Energy (K) quantum number M µ 0 H z (T) with S = 10, D = 0.27 K, E = 0.046K

23 Tunneling probability at an avoided level crossing Landau-Zener model (1932) S, m' > S, m > energy ² 1 - P 1 P P =1 exp c 2 dh /dt S, m > magnetic field S, m' > c = π 2h gµ B m m' µ 0

24 M/M S mk v=140 mt/s v=70 mt/s v=14 mt/s v=2.8 mt/s µ 0 H(T) Application of Landau-Zener tunneling Fe 8 S = Energy (K) µ 0 H z (T) 10 Η= DS 2 z + E S 2 r 2 ( x S y )+ gµ B S H r with S = 10, D = 0.27 K, E = 0.046K A.-L. Barra et al. EPL (1996)

25 Magnetization reversal in magnetic structures permanent magnets macroscopic micron particles nanoparticles clusters atomic molecular clusters atoms S = multi - domains single - domains spins Tunneling splitting ~ E D ~ H x D S 2S E << D Tunneling probability P =1 exp c 2 dh /dt 2 Η= DS z + E ( 2 Sx 2 r Sy )+ gµ B S H r

26 easy axis Barium ferrite nanoparticle(10 nm) Macroscopic Quantum Tunneling of Magnetization of Single Ferrimagnetic Nanoparticles of Barium Ferrite (10 nm) W.W. et al, PRL, 79, 4014, (1997) T c (θ) µ 0 H a ε 1/4 cot θ 1/ 6 ( 1 + cot θ 2/3 ) 1 T c ( θ)/t c (45 ) Tc(45 ) = 0.31 K angle θ

27 Temperature dependence Spin Hamiltonian: Η= DS 2 z + E S 2 2 r ( x S y )+ gµ B S H r (2S + 1) energy states: M = -S, -S+1,, S Spin-phonon coupling : M = ±1, ±2 Energy E thermally assisted tunneling Anisotropy barrier E Anisotropy constant D S 2 Spin quantum number M

28 Spin ground states of Mn based SMMs S Mn 4 Mn 2 Mn 9 Mn 19 Mn 25 Mn 18 Mn 12 Mn 30 Mn 84 Mn number of Mn-ions

29 Anisotropy barriers of Mn based SMMs Mn 6 60 Mn 12 E (K) 40 Mn 5 Mn 9 20 Mn 4 Mn 18 Mn 70 0 Mn 2 Mn 30 Mn 25 Mn number of Mn-ions

30 Quantum Tunneling of Magnetization in Lanthanide Single-Molecule Magnets Bis(phthalocyaninato)terbium Naoto Ishikawa, Department of Applied Chemistry, Chuo University, Tokyo 0.5 nm E (K) 600 K 1.5 nm N.Ishikawa, et al., J.Phys.Chem. A 106, 9543 (2002) J. Am.Chem.Soc. 125, 8694 (2003) Inorg.Chem. 42, 2440 (2003) J.Phys.Chem. A 107, 9543 (2003) J. Phys.Chem.B 108, (2004) H (T)

31 Quantum Tunneling of Magnetization in Lanthanide Single-Molecule Magnets Bis(phthalocyaninato)terbium Naoto Ishikawa, Department of Applied Chemistry, Chuo University, Tokyo T/s 2% Tb M/M s 0 E (K) 600 K K 2.0 K 7 K µ 0 H (T) H (T) N. Ishikawa, M. Sugita, W. Wernsdorfer, Angew. Chem. Int. Ed. 44,2 (2005) N. Ishikawa, M. Sugita, W. Wernsdorfer, J. Am. Chem. Soc. 127, 3650 (2005)

32 Exchange-biased quantum tunnelling in a supramolecular dimer of single-molecule magnets QuickTime et un décompresseur Animation sont requis pour visualiser cette image. 9/2-9/2 J J -9/2 9/2 W. Wernsdorfer, N. Aliaga-Alcalde, D. N. Hendrickson & G. Christou Nature 416, 406 (2002)

33 Premières mesures micro-squid sur une molécules aimants photo-commutables MoCu6 (coll. V. Marvaud, M. Verdaguer et al.) Transfert d électron photo-induit Mo IV hν Cu II Mo V Cu I S=1/2 isolés T/s S=3 2 M/N µ B h 10 h 0.04 K 1 K 4 K 0.04 K 1 K 4 K µ 0 H (T)

34 Premières mesures micro-squid sur les analogues photo-magnétiques du bleu de Prusse (coll. A. Bleuzen, M. Verdaguer et al.) Fe Co Rb C N Aimant moléculaire photo-commutable Rb I Co III [Fe II (CN) 6 ] Co III (LS) + Fe II hν (LS) Co II (HS) + Fe III (LS) S= 0 S= 0 S= 3/2 S= 1/ K A50 M/M s irradiation with white light µ 0 H (T) En cours : mesure d une seule nanoparticule photo-commutable 0 min 1 min 5 min 20 min 30 min 70 min 100 min 3 h 4 h 12 h

35 Quantum computing in molecular magnets Michael N. Leuenberger & Daniel Loss NATURE, 410, 791 (2001) implementation of Grover's algorithm storage unit of a dynamic random access memory device. fast electron spin resonance pulses can be used to decode and read out stored numbers of up to 10 5 with access times as short as 0.1 nanoseconds.

36 MCEUEN group (Cornell)

37 Molecular spintronics Nicolas Roch Franck Balestro Edgar Bonet Vincent Bouchiat Wolfgang Wernsdorfer V gate

38 Molecular spintronics : first devices.. Molecular transistor : Cornell Delft Harvard QuickTime et un décompresseur TIFF (LZW) sont requis pour visionner cette image. Liang et al., Nature 417, Ferromagnetic electrodes : Park et al., Nature 417, H. Heersche et al., PRL 96, (2006) QuickTime et un décompresseur TIFF (LZW) sont requis pour visionner cette image. Harvard, Cornell, Berkeley, Cornell Pasupathy et al., Science 306, M.-H. Jo et al., Nano Lett., 6, 2014 (2006)

39 Cecile Delacour Clemens Winkelmann Lapo Bogani Laetitia Marty Romain Maurand Vincent Bouchiat Wolfgang Wernsdorfer Molecular spintronics V gate

40 Single-walled carbon nanotube junction S G SWNT D

41 Magnetic flux coupling: nano-squid G1 SWNT Gnd G2 500 nm J.-P. Cleuziou, W. Wernsdorfer, V. Bouchiat, Th. Ondarçuhu, M. Monthioux, Nature Nanotechnology, 1, 53 (2006)

42 Magnetization switching of single molecules micro-squid versus nano-squid (CNT-SQUID) Optimising the flux coupling factor 50 nm stray field particle nanoparticle junction 20 nm 1000 nm substrate micro-bridge Josephson junctions stray field molecule S QuickTime and a TIFF (Uncompressed) decompressor are needed to see this picture. carbon nanotube junction S 0.6 nm molecule 1 nm nanotube substrate

43 Carbon nanotube SQUID fabrication G1 Gnd G2 SWNT 500 nm single-walled CNTs: Rice University. dispersed in water by sonication using sodium dodecyl sulphate (SDS) surfactant. n-doped silicon substrate with 350 nm thick thermally grown SiO 2 => backgate functionalized => monolayer of aminopropyltriethoxysilane substrate was dipped in the dispersion of CNTs and withdrawn (combing technique) thoroughly washed in distilled water nanotube location with AFM aligned e-beam lithography metal electrodes: 3 nm Pd + 50 nm Al R 30 kω and no significant gate effect at 300 K fabricated about 100 CNT-SQUIDs and 300 CNT-superconducting transistors using singlewalled CNTs, ropes of CNTs, and multi-walled CNTs: 30 % worked J.-P. Cleuziou, CEMES-CNRS, Toulouse, France F. Carcenac, RTB-LAAS, Toulouse, France

44 Combing technique substrate was dipped in the dispersion of CNTs and withdrawn Competition between: Nanotube adsorption on silanized surface Capillary alignment S. Gerdes, T. Ondarcuhu, S. Cholet, C. Joachim, Europhys. Lett. 48, 292 (1999).

45 CNT 2.0µm Ropes Individual SWNT diameter 0.8 nm deposition Combing technique S. Gerdes, T. Ondarcuhu, S. Cholet, C. Joachim, Europhys. Lett. 48, 292 (1999).

46 Nanotube E-beam lithography PMMA e-beam SiO 2 Si n++ (a) Nanotube deposition (combing) (b) Resist deposit (c) Insolation with e-beam Al (50 nm) Pd (3 nm) gate (d) Development (e) Metal evaporation (f) Lift-off

47 G1 CNT Carbon nanotube SQUID V BG G2 500 nm I On On V G1 II Off On V G1 III Off Off V G1 V G2 V G2 V G2

48 V ( µv) Case I on-on CNT-SQUID characteristics 0 Φ 0 /4 Φ 0 /2 I ( na) I (na) µ 0 H z (mt) Case III off-off V ( µv) I (pa) I (pa) µ 0 H z (mt)

49 Preliminary estimation of the flux sensitivity of CNT-SQUIDs CNT-SQUID characteristics I sw histogram na/φ N = I (na) Count Φ/ Φ I (na) Flux sensitivity: [3.5 pa]/([3 na/φ 0 ]*sqrt[10000]) 10-5 Φ 0 when averaging I sw during 1 s at a rate of 10 khz.

50 Estimation of magnetic flux variation for Mn12 with S = 10 stray field molecule S QuickTime and a TIFF (Uncompressed) decompressor are needed to see this picture. carbon nanotube junction S 0.6 nm molecule 1 nm nanotube substrate The total magnetic flux Φ of a uniformly magnetized sphere, R = 0.5 nm. 1 2 Φ = µ0 m R Φ = 1.1 x 10-4 Φ0 for Mn12 with S = 10 Flux sensitivity for the CNT-SQUIDs: 10-5 Φ0 when averaging Isw during 1 s at a rate of 10 khz further improvement, Irfan Siddiqi, Berkeley

51 Conclusion - SMMs nice quantum systems (tunneling, interference, coherence, etc.) increasing the anisotropy barrier (S, D) interconnecting of SMMs (switchable) Molecular spintronics V gate V gate

52 Collaborations (Physics) L. Thomas PhD 1996: Mn 12 -ac F. Lionti PhD 1997: Mn 12 -ac, Fe 17/19 I. Chiorescu PhD 2000: Mn 12 -ac, V 15 R. Giraud PhD 2002: Ho 3+ C. Thirion PhD 2003: nanoparticles, GHz R. Tiron PhD 2004: [Mn 4 ] 2 S. Bahr PhD started 2005: GHz K. Petukhov post-doc : GHz F. Balestro, E. Bonet, W. Wernsdorfer, B. Barbara, LLN, CNRS, Grenoble T. Ohm PhD 1998: Fe 8 V. Villar PhD 2001: Fe 8, chaines E. Lhotel PhD 2004: chaines V. Bouchiat, C. Paulsen, A. Benoit, CRTBT, CNRS, Grenoble L. Sorace, post-doc 2003: GHz A.-L. Barra, LCMI - CNRS, Grenoble J. Villain, CEA, Grenoble D. Mailly, LPN, CNRS, Marcoussis

53 Winpenny, 2003 Collaborations (Chemistry) Group of G. Christou, Dept. of Chemistry, Florida Group of R. Sessoli, D. Gatteschi, Univ. de Firenze, Italie Group of A. Cornia, Univ. de Modena, Italie Group of R.E.P. Winpenny, Univ. de Manchester, UK Group of E. Brechin, Univ. de Manchester, UK Group of T. Mallah, Orsay Group of V. Marvaud, Univ. P. et M. Curie, Paris Group of A. Müller, Univ. de Bielefeld, Germany Group of A. Powell, Univ. de Kahlsruhe, Germany Group of D. Hendrickson, Dept. of Chemistry, San Diego Group of E. Coronado, Univ. de Valence, Spain Group of D. Luneau, Univ. of Lyon, France Group of G. Royal, Univ. J. Fourier, Grenoble Group of R. Clerac & C. Coulon, Univ. Bordeaux, Pessac Group of H. Miyasaka, Tokyo Metropolitan Uni. Group of M. Verdaguer, Univ. P. et M. Curie, Paris Group of M. Julve, Univ. de Valence, Spain SMMs SCMs Mn 84 QuickTime et un décompresseur Animation sont requis pour visualiser cette image. Christou, 2004

54 Acknowledgement G1 SWNT Gnd J.-P. Cleuziou, CEMES-CNRS, Toulouse G2 500 nm F. Carcenac, RTB-LAAS, Toulouse, France J.-P. Cleuziou, W. Wernsdorfer, V. Bouchiat, Th. Ondarçuhu, M. Monthioux, Nature Nanotechnology, 1, 53 (2006)