Voyage dans le nanomonde des aimants

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1 Voyage dans le nanomonde des aimants Wolfgang Wernsdorfer Laboratoire de Magnétisme Louis Néel C.N.R.S. - Grenoble S = 10 2 to 10 6 S = 1/2 to 30

2 Magnets nanoworld Mm 1 km 1 m 1 mm 1 mm 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 M / M S 0 M / M S 0 M / M S 0 Fe 8 1 K 0.7K 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 Fo µ B i.e. (2 nm) 3 of Co emu Josephson junctions A. Benoit, CRTBT, 1989

Beam Deposition regime HRTEL along a [110] direction fcc - structure, faceting blue:

7 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

8 Giant spin approximation 1000 atoms S 1000

9 Uniform rotation of magnetization: Stoner - Wohlfarth model (1949) single domain magnetic particle one degree of freedom: orientation q of magnetization M potential: E = K sin 2 q- m 0 M S H cos(q- j ) K = K m 0M S 2 (Nb - N a ) 2 E(!) 1 h = h 0 h > 0 H " # b h = 0 M 0! z T = 0 K a ! B B

10 Stoner - Wohlfarth switching field M 1 0 h sw = ( sin 2/3! + cos 2/3!) "3/2 h s w hard axis easy axis h Stoner - Wohlfarth astroid

11 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)

12 Lis, 1980 Single-molecule magnets (SMM) Giant spins Müller, 1993 Mn 12 S = 10 V 15 S = 1/2 Ni 12 S = 12 Mn 84 S 6 Fe 8 S = 10 Christou, 2004 Winpenny, 1999 Wiegart, 1984

13 Crystal of SMMs

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

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

16 Giant spin model Energy levels: Zeeman diagram 10 Energy H = 0 Energy (K) energy magnetic field quantum number M µ 0 H z (T) with S = 10, D = 0.27 K, E = 0.046K!

17 Tunneling probability at an avoided level crossing Landau-Zener model (1932) L. Landau, Phys. Z. Sowjetunion 2, 46 (1932); C. Zener, Proc. R. Soc. London, Ser. A 137, 696, (1932); E.C.G. Stückelberg, Helv. Phys. Acta 5, 369 (1932); S. Miyashita, J. Phys. Soc. Jpn. 64, 3207 (1995); V.V. Dobrovitski and A.K. Zvezdin, Euro. Phys. Lett. 38, 377 (1997); L. Gunther, Euro. Phys. Lett. 39, 1 (1997); G.Rose and P.C.E. Stamp, Low Temp. Phys. 113, 1153 (1999); M. Leuenberger and D. Loss, Phys. Rev. B 61, (2000); M. Thorwart, M. Grifoni, and P. Hänggi, Phys. Rev. Lett. 85, 860 (2000);

18 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! = "D S 2 z + E S 2 2 r ( 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)

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

20 Spin ground states of Mn based SMMs 25 Mn S 15 Mn Mn 4 Mn 12 5 Mn 2 Mn 9 Mn30 Mn 70 Mn number of Mn-ions

21 Anisotropy barriers of Mn based SMMs Mn 12 40!E (K) Mn 4 Mn 9 Mn 18 Mn Mn 2 Mn Mn Mn number of Mn-ions

22 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.

23 Development of molecular Spin-Electronics APS March Meeting 2004

orbitales le long de la molécule Magnétorésistance de

24 La spintronique moléculaire en marche Prédictions théoriques prometteuses DOS de Ni(001)/tricene/Ni(001) délocalisation des orbitales le long de la molécule Magnétorésistance de Ni(001)/tricene/Ni(001) en structure de vanne de spin Rocha et al., Nat. Mat. 4, 335, 2005.

Bonet, NANOFAB Evaporation sous angle Jonction par électromigration structure verticale Collaboration T.

25 Connexion électrique de molécules-aimants uniques 2 objectifs clés de nanofabrication Gap nanométrique 200 nm Liang et al., Nature, 417, 725 (2002). E. Bonet, NANOFAB Evaporation sous angle Jonction par électromigration structure verticale Collaboration T. Fournier, NANOFAB: plateforme de nanofabrication Monocouches moléculaires Vaporisation sous vide Auto-assemblage par la chimie des ligands Objectif du work package 3 du réseau QuEMolNa

26 Nanoworld Quantum world

Mesoscopic Physics 4 nm Mn 30 Mn 4 Mn 12 Mn 84 N 1 10 100 1000 Quantum world Classical world A. J.

27 Mesoscopic Physics 4 nm Mn 30 Mn 4 Mn 12 Mn 84 N Quantum world Classical world A. J.Tasiopoulos, A. Vinslava, W. Wernsdorfer, K. A.Abboud, and G. Christou, Angew. Chem. Int. Ed., 43, 2117 (2004)

28 Organizing Comitee: (Grenoble) -Vincent Bouchiat (CRTBT, CNRS) -Benjamin Grévin (SPrAM,CEA) -Stephan Roche (SPSMS, CEA) -Guy Royal (LEOPR, UJF)

29 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 K. Petukhov post-doc : GHz 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, P. Gandi, A. Sulpice, A. Benoit, CRTBT, CNRS, Grenoble L. Sorace, A.-L. Barra, LCMI - CNRS, Grenoble J. Villain, CEA, Grenoble D. Mailly, LPN, CNRS, Marcoussis V. Mosser, Schlumberger Industries, Montrouge M. Jamet, C. Raufast, V. Dupuis, P. Mélinon, A. Perez, DPM, CNRS, Lyon

30 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 P. Rey et D. Luneau, CEA, 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 Christou, 2004

Quantum dynamics in Single-Molecule Magnets

Quantum dynamics in Single-Molecule Magnets Wolfgang Wernsdorfer Laboratoire de Magnétisme Louis Néel C.N.R.S. - Grenoble S = 10 2 to 10 6 S = 1/2 to 30 permanent magnets macroscopic micron particles Magnetic