Intermolecular interactions (dipolar and exchange)

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1 Intermolecular interactions (dipolar and exchange) SMM ideal Mn 2 ac Mn 4 (SB) spin chains, etc. MM...? doped Fe 6 Fe 5 Ga Fe 8 [Mn 4 ] 2 J/D

2 Mn 4 singlemolecule magnet Mn 4 O 3 (OSiMe 3 )(O 2 CMe) 3 (dbm) 3 Mn IV S = 3/2 Mn III S 2 = 2 S = 9/2

3 Mn 4 O 3 (OSiMe 3 )(O 2 CMe) 3 (dbm) 3 (SB) Symmetry space group: P6(3) Top view Side view

4 Dipolar coupling r B ( r ) = 4 3( r m r ) r ( r r ) r m r 5 2 z y B z 3cosθ r 3 2 x H Mn 4 (SB) mt

5 Intermolecular exchange coupling S 2 S Mn IV Mn III S S 2 S J' Mn IV Mn III J' S dipolar & exchange coupling S 2 S Mn IV Mn III S Mn4 (SB) 36 mt

6 Chainlike dipolar & exchange coupling Case Case 2 Case 3 J no reversed neighbors J J they have one reversed neighbor J J J J J it has two reversed neighbors

7 Hysteresis loops of a Mn 4 singlemolecule magnet Mn 4 O 3 (OSiMe 3 )(O 2 CMe) 3 (dbm) 3 Mn IV S = 3/2 Mn III S 2 = 2 S = 9/2

8 2 sqrt 3 Distribution of internal fields.4 K two one no reversed neighbor 4 36 mt 36 mt M in O µ H z (T)

9 Collective quantum phenomena Onebody tunnel transitions Twobody tunnel transitions JS 2.2 K S = 9/2

10 H i = D S 2 i,z H trans r i gµ B µ S i Two coupled SMM of S = 9/2 r H H = H H 2 J r S r S 2 (2S i ) energy states S i = 9/2 : energy states M i = S i, S i,, S i (2S )(2S 2 ) energy states S i = 9/2 : energy states M = S, S,, S M 2 = S 2, S 2,, S 2 D =.72 K ; E =.3 K ; J =. K E (K) 5 Energy (K) µ H z µ H z (T)

11 Zeeman diagram of two coupled SMM of S = 9/ Energy (K) (9/2,9/2) 6 (9/2,9/2) (9/2,9/2) (7/2,7/2) 2 3 (9/2,7/2) (9/2,3/2) (9/2,5/2) (9/2,7/2) µ H z (T)

12 Spinspin crossrelaxation the happy collaboration of two spins Examples: Transition 7 Initial state: (9/2,9/2) After tunneling: (7/2,9/2) Final state: (9/2,9/2) Transition 3 Initial state: (9/2,9/2) After tunneling: (7/2,7/2) Final state: (9/2,9/2)

13 M/M s.5.5 Hysteresis loop at 4 mk T/s.4 T/s.8 T/s.7 T/s.35 T/s.7 T/s.4 T/s µ H z (T) 3

14 Virtual phonon transitions H = H H 2 J r r S S 2 H i = D S 2 i,z H trans r i gµ B µ S i r H D =.72 K ; E =.3 K ; J =. K E (K) Energy (K) µ H z µ H z (T)

15 Parity of level crossing (9/2,9/2) M = 9 (K) 6 (9/2,9/2) (9/2,9/2) (7/2,9/2) total quantum number: M = m m2 M = H trans (T)

16 2 Spinspin crossrelaxation in Mn 2 ac E (K) µ H z (T)

17 Decoherence in magnetic mesoscopic systems Photons Conduction electrons Phonons Magnetic quantum system spin molecule nanoparticle chain Spin bath nuclear spins paramagnetic spins intermolecular interactions etc.

18 Interaction with photons (microwaves: to 5 GHz)

19 Quantum computing in molecular magnets Michael N. Leuenberger & Daniel Loss NATURE, 4, 79 (2) 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 5 with access times as short as. nanoseconds.

Energy (K).6.4.2.2 /2 S = /2 hω Absorption of microwaves.4.6 /2.6.4.2.2.4.6 µ H (T) V 5 S = /2.

20 Energy (K) /2 S = /2 hω Absorption of microwaves.4.6 / µ H (T) V 5 S = /2.5.4 K GHz. T/s M/M s.5 period: ms s. ms.5 ms ms 2 ms 3 ms µ H (T)

21 D =.5 K Energy (K) 2 /2 /2 Reducing intermolecular couplings Fe6 wheels: S = 3/2 3/2 5/2 5/ µ Hz (T) K M/M s T/s T/s T/s T/s T/s µ Hz (T) Doping with Ga Fe5Ga : S = 5/2

22 D =.5 K Energy (K) 2 /2 /2 Fe6 wheels: S = 3/2 3/ Reducing intermolecular couplings hω 5/2.4 5/2.2 µ Hz (T).2.4 M/M s K 8 db 6 db 5 db.4 T/s.8. T/s 2 GHz µ Hz (T) Doping with Ga Fe5Ga : S = 5/2

23 Photon assisted tunneling Absorption of circular polarized microwaves Energy M = hω tunneling H = 5 5 quantum number m Energy (K) M = hω hω M = ± µ H z (T) 7 8 9

24 Absorption of circular polarized microwaves (5 GHz).5 6 mk 5 GHz.7 T/s M/M s.5 P/P =.5.5 µ H z (T)

25 Absorption of circular polarized microwaves (95 GHz) M/M s mk 95 GHz.7 T/s P/P = µ H z (T)

26 Photon induced tunnel probability P EPR = P n ± P ± PEPR T S (K) n = n = (au) 6 7 n = n =... (au)

27 Perspectives concerning microwave experiments Quantum dynamic: spinecho like experiments

28 Conclusion Beginning: Mn 2 ac,5 M/M S, B L (T).5K.6K.9K 2.4K L. Thomas, B. Barbara, et al., Nature (996) R. Sessoli, D. Gatteschi, D. Hendrikson, G. Christou, et al. (993) M. Novak, C. Paulsen, B. Barbara, et al. (994) J. Friedman, M. Sarachik, et al., PRL (996) L. Thomas, B. Barbara et al., Nature (996)

29 Followed by: 3 systems Mn, Mn 2, Mn 3, Mn 4, [Mn 4 ] 2, Mn 5, Mn 6, Mn 7, Mn 8, Mn 9, Mn, Mn, Mn 2, Mn 3, Mn 6, Mn 8, Mn 2, Mn 24, Mn 26, Mn 3 Fe 2, Fe 3, Fe 4, Fe 5, Fe 6, Fe 7, Fe 8, Fe, Fe, Fe 3, Fe 7/9, Fe 9 Ni 4, Ni 5, Ni 6, Ni 8, Ni 2, Ni 2, Ni 24 Co 4, Co 6, Co Co 2 Gd 2, Co 2 Dy 2, Cr 2, CrNi 6, CrNi 2, CrCo 3, Fe Na 2, Fe 2 Ni 3, Mn 2 Dy 2, Mn 2 Nd 2, V 5, Ho,... S =, /2,, 3/2, 2, 5/2, 4, 9/2, 5,. 33/2

30 Size dependence? [Mn 3 O(OAc) 6 (py) 3 ]py Mn 4 O 3 (OSiMe 3 )(O 2 CMe) 3 (dbm) 3 (PPh 4 ) 2 [Mn 2 O 2 (O 2 CCH 2 Cl) 6 (H 2 O) 3 ] Mn 3 O 24 (OH) 8 (O 2 CCH 2 C(CH 3 ) 3 ) 32 (H 2 O) 2 (CH 3 NO 2 )

31 Mn 4 O 3 (O 2 CEt) 4 (dbm) 3 Control / origin of the magnetic anisotropy? S = 9/2 Mn 4 O 3 Cl(OAC) 3 (dbm) 3 Mn 4 O 3 (O 2 CPh) 4 (dbm) 3 Mn 4 O 3 (OSiMe 3 )(O 2 CMe) 3 (dbm) 3

Exchange biased Mn 4 M/M s.5.5.5 NA.4 K.5.5 µ H (T).4 K NA3.4 T/s.7 T/s.35 T/s.7 T/s.8 T/s.4 T/s.2 T/s M/M s M/M s.5.5 NA2 newrod.4 K.5.5 µ H (T) M/M s.5.35 T/s.7 T/s.8 T/s.4 T/s.2 T/s. T/s.5 T/s.3 T/s.

32 Exchange biased Mn 4 M/M s NA.4 K.5.5 µ H (T).4 K NA3.4 T/s.7 T/s.35 T/s.7 T/s.8 T/s.4 T/s.2 T/s M/M s M/M s.5.5 NA2 newrod.4 K.5.5 µ H (T) M/M s.5.35 T/s.7 T/s.8 T/s.4 T/s.2 T/s. T/s.5 T/s.3 T/s.5 NA.4 K.4 T/s.7 T/s.35 T/s.7 T/s.8 T/s.5.5 µ H (T) M/M s µ H (T) K NA2.4 T/s.7 T/s.35 T/s.7 T/s.8 T/s.4 T/s.35 T/s.7 T/s.8 T/s.4 T/s.5.5 µ H (T)

33 Rareearth ions: Ho 3 in Y.998 Ho.2 LiF 4 Effects of Strong Hyperfine Interactions, M/MS Ho 3 Tetragonal symmetry (Ho in S4) J = LS = 8; g J =5/4,5,,5, 2 mk 5 mk 5 mk H z (mt) / dm/dhz (/T) n= dh/dt > n=2 n= n= n= R. Giraud, W. Wernsdorfer, A.~M. Tkachuk, D. Mailly, and B. Barbara, Phys. Rev. Lett. 87, 5723 (2).

34 Slow dynamics in spinchains NC[Fe(III)(CN)Co(II)]NC A. R. Lescouezec, M. Julve, F. Lloret, Valencia University, Spain P. Herson, Y. Dromzée, M. Verdaguer Chimie Inorganique et Matériaux Moléculaires, CNRS, Paris.5 2. K H b M/M s µ H (T).7 T/s.35 T/s.7 T/s.8 T/s.4 T/s.2 T/s. T/s

35 Conclusion J. Villain: a school of physics & chemistry

36 Collaborations L. Thomas PhD 996: Mn 2 ac F. Lionti PhD 997: Mn 2 ac, Fe 7/9 I. Chiorescu PhD 2: Mn 2 ac, V 5 R. Giraud PhD 22: Ho 3 C. Thirion PhD 23: nanoparticles, GHz R. Tiron PhD 24: [Mn 4 ] 2, E. Bonet, W. Wernsdorfer, B. Barbara LLN, CNRS, Grenoble C. Paulsen, V. Villar, A. Sulpice, A. Benoit CRTBT, CNRS, Grenoble A.L. Barra, L. Sorace, LCMI CNRS, Grenoble D. Mailly LPN, CNRS, Marcoussis

37 Collaborations Concerning SMMs and spin chains C. Paulsen, A. Sulpice, V. Villar, T. Ohm, CRTBT CNRS A.L. Barra, L. Sorace, LCMI CNRS, Grenoble Group of G. Christou, Dept. of Chemistry, Florida Group of D. Hendrickson, Dept. of Chemistry, San Diego Group of D. Gatteschi et R. Sessoli, Univ. de Firenze, Italie Group of A. Cornia, Univ. de Modena, Italie Group of A. Müller, Univ. de Bielefeld, Germany Group of A. Powell, Univ. de Kahlsruhe, Germany Group of M. Verdaguer, Univ. P. et M. Curie, Paris Group of M. Julve, Univ. de Valence, Spain Group of R.E.P. Winpenny, Univ. de Manchester, UK Group of E. Coronado, Univ. de Valence, Spain Group of P. Rey et D. Luneau, CEA, Grenoble

38 Merci!

39 Mn 3 Giant spin approximation Example: Mn2ac Hilbert space: (2x2 ) 8 (2x3/2 ) 4 8 Mn 4 J J 2 J 4 J 3 J 25 K J 2 J 3 86 K J 4 < 43 K Energy(K) K S = D =.63 K S = 9 D' =.57 K quantum number M I. Tupitsyn (2)

40 One member of the Mn2 family easy axis z 58 y tilted JahnTeller axis [Mn 2 O 2 (O 2 CCH 2 Bu t ) 6 (H 2 O) 4 ] CH 2 Cl 2 CH 3 NO 2

41 Hysteresis loops M/M s K.6 K.7 K.5 K.4 K.8 T/s.3 K.2 K.5 K.9 K.8 K.7.4 K µ H z (T)

42 First attempt to find a model based on two spin multiplets: M/M s K.7 K.6 K even even odd odd odd odd.5 K.4 K.3 K.8 T/s.2 K Energy (K).5 K.9 K.8 K.7.4 K µ H z (T) even even even odd odd odd even even even even odd S= S= H z odd S = 9, D =.6 K S =, D =.5 K

43 MQT Strategy of single particle measurements Quasistatic measurements hysteresis loops H sw (θ,ϕ) magnetic anisotropy (forme, crystalline, surface) Dynamic measurements relaxation (T,H) P(T,H), H sw (T,dH/dt) activation volume damping factor "all" parameters are defined in the classical regime deviations for T > studying the crossover Tc and the escape rate QT as a function of external parameters: transverse fields, field directions, microwaves, etc.

44 Macroscopic Quantum Tunneling of magnetization.2 E( ) h > thermal activation Γ TA = Γ e E/k B T Γ QT = Γ ' e B.8 E k B T MQT.4 T K B 4*6/ 4 9 E k B T = E (θ, γ) k B T ε3/ 2 Sε 5/4 cotθ /6 K /3 ( cot θ2 ) K Crossover temperature: E k B T c = B T c = 9 4 *6 / 4 E k S ε/4 K K 2/ 3 ( cotθ ) cotθ / 6 Miguel and Chudnovsky, PRB (996) GwangHee Kim and Dae Sung Hwang, PRB (997)

easy axis Barium ferrite nanoparticle( nm) Macroscopic Quantum Tunneling of Magnetization of Single Ferrimagnetic Nanoparticles of Barium Ferrite ( nm) W.

45 easy axis Barium ferrite nanoparticle( nm) Macroscopic Quantum Tunneling of Magnetization of Single Ferrimagnetic Nanoparticles of Barium Ferrite ( nm) W.W. et al, PRL, 79, 44, (997) (45 ) T c (θ) µ H a ε /4 cotθ /6 ( cotθ 2/3 ) Tc(45 ) =.3 K T c ( )/T c T*(K) part. II.2 T(K) angle

46 Quantization of the magnetization Schematic view of the resonance fields of a giant spin S. The continuous red line is the classical switching fields of StonerWohlfarth. h z easy axis P(H) dh/dt H' H' The inset presents schematically a switching field histogram with H H H' H a 2S cos h x hard axis

47 Fe clusters ( 3 nm)

48 Fe clusters ( 3 nm) sample oxidation?!? surface spin frustration?!?

49 Comparison of Josephson and magnetic grain systems System Rf SQUID ring or currentbiased junction Single domain ferro or antiferromagnetic particle Macroscopic variable Control parameters q Form of potential near instability Trapped flux or Cooper pair phase External flux or Bias current I = I/Ic Critical current Ic dissipation Magnetization or Néel vector Applied magnetic field H = H/Hsw Magnetic anisotropy field Hsw Field directions or transverse fields dissipation q 2 q 3 q 2 q 3 or q 2 q 4 (depending on field direction) Number of particles involved in tunneling 5 23 electrons (SQUID) 8 magnetic moments

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