Presentation is loading. Please wait.

Presentation is loading. Please wait.

Magnetic techniques for molecular and nanometric materials Dante Gatteschi & Roberta Sessoli February 2008.

Similar presentations


Presentation on theme: "Magnetic techniques for molecular and nanometric materials Dante Gatteschi & Roberta Sessoli February 2008."— Presentation transcript:

1 Magnetic techniques for molecular and nanometric materials Dante Gatteschi & Roberta Sessoli February 2008

2 Diapositive disponibili: ftp://lamm21.chim.unifi.it/pub/Corso_Gatteschi_Sessoli Per ogni problema scrivere a:

3 Molecular Magnetic Materials (nano) EPR (Gatteschi) Magnetic Techniques (Sessoli)

4 Molecular magnetic materials simple paramagnets: step 1 Interacting paramagnets: step 2 Size effects: step 3

5 Bulk 3D magnets

6 The first molecular ferromagnet Miller, Epstein et al. MolCrystLiqCryst 1985

7 The first room temperature molecular magnet Miller, Epstein et al. Science, 1991

8 Nitroxides T c = 0.6 K T C = 1.5 K

9 Fullerene T C = 16 K Alemand et al. Science 1991

10 p-NC-C 6 F 4 -CNSSN : a monomeric S-based radical

11 Single molecule magnets, SMM

12 The first single molecule magnet:Mn12-acetate S 4 ||z top view T. Lis Acta Cryst. 1980, B36, M S =-10 M S = 10 Easy axis of magnetization lateral view z Mn(AcO) 2 4H 2 O + KMnO 4 in 60% v/v AcOH/H 2 O [Mn 12 O 12 (OAc) 16 (H 2 O) 4 ]·2AcOH·4H 2 O Ground state S = 8 * * 3/2 = 10 M saturation = 2.S = 20  B Barrier 60 K

13 The library of molecular magnets: single chain magnets

14 More complex structures

15 Three different organizations 2: embedded in amorphous silica 3: LB film 4: SAM Bogani et al. Adv Mater in press

16 magnet paramagnet super paramagnet Reducing the size Classical physics Quantum mechanics ????????????

17 Paramagnet Inorganic radicals O2, NO.. Organic radicals Tyrosyl, nitroxides TM coordination compounds RE coordination compounds

18 Outline of the EPR section EPR in a nutshell: The principle of the experiment Basic EPR: the spin Hamiltonian HF experiments: Radicals and Biological systems Clusters

19 Outline of the EPR section 2 Spin interactions: The spin hamiltonian of pairs SH parameters of pairs The Mn12 testing ground: Epr Nmr

20 EPR Spectroscopy in a Nutshell It is like NMR but is limited to paramagnetic systems Invented by Zavoiski in Kazan in 1944 It needs a magnetic field and electromagnetic radiation Unlike NMR the field is scanned and the frequency is fixed

21 . General design of an EPR spectrometer Source klystron (conventional) FIR lasers ( > 240 GHz) Gunn diodes ( GHz) Carcinotron (very High power) Detector crystal diodes bolometers Schottky diodes Transmission line rectangular waveguides up to 150 GHz) corrugated waveguides. via space with refocusing devices oversized waveguides Magnet electromagnets (up to 1.5 Tesla) superconductive magnets (up to 17 Tesla) resistive magnets (30 Tesla) hybrid magnets (45 Tesla) pulsed magnets (hundreds of Tesla) Sample environment resonating structure temperature control multiple irradiation

22 . Most of the efforts for the development of EPR at high frequeny are aimed at the extention at millimeter and sub-millimeter waves of the general design of the conventional microwave bridge. The main problem along this path is the availability and/or the design and realization of devices (magic Tees, circulator, phase shifter etc.) able to carry on the function of the low-frequency analogoue. The microvave techniques are used in conventional EPR. The propagation of the radiation is made by using mono- modal metallic rectangular waveguides, metallic cavities and the other devices present in a typical microwave bridge. The microwave techniques can be successfully extended up to 150 GHz ca. Above this frequency waveguides become eccessively lossy (typical figure of merit 12 dB/m at 250 GHz) and the rectangular or cylindric cavities eccessively small.

23 EPR Spectroscopy in a Nutshell: Zeeman Term In a system with S= 1/2, when the static magnetic field is parallel to z, E(M)= Mgμ B H a transition is observed when g z  B H= hν= g e  B H 0 Similar expressions hold for x, and y. The g values and their anisotropy depend on the chemical environment, therefore they provide structural information

24 Zeeman Splitting

25 Some Useful Relations 1 GHz= x10 -2 cm -1 Res. Freq.BandRes. Field (GHz) g=2.00 9X Q W

26 Polycrystalline Powder EPR Spectra The EPR spectra of polycrystalline powders or frozen solutions provide the g x, g y, and g z values directly provided that the linewidth is smaller than the anisotropy

27 Polycrystalline Powder Spectra isotropic axial rhombic

28 The Spin Hamiltonian H =  B B.g.S+S.D.S+  k I k.A k.S ZeemanFine Hyperfine

29 Interazione iperfine e superiperfine Cu 2+ S=1/2 63 Cu I=3/2 69% 65 Cu I=3/2 31% 1- Termine di contatto: A xx =A yy =A zz =8  /3(g e g n  B  n )|  n (0)| 2 3- Pseudo- contatto : Interazione spin nucleare-momento orbitalico: è funzione dell’anisotropia di g Traccia non nulla, anisotropo 2- Termine dipolare: anisotropo, traccia nulla (A xx +A yy +A zz =0) 2nI+1 n=2, I=1 Informazioni sull’intorno di coordinazione

30 Il Cu 2+ nei prioni Determinazione dei diversi siti leganti e della stechiometria Determinazione del numero di azoti leganti per uno dei siti coordinanti Biochemistry , eq. 2 eq. 3 eq. 4 eq. 5 eq. 6 eq. Alta conc. Bassa conc. 5.3 eq. Cu 2+ Cu 2+ legato pH=4.00 pH=7.40 Cu 2+ libero Affinità per il Cu 2+ a pH>6 7 linee  min. 3 N leganti

31

32 Q-band of 6

33 6 in solution. RT, X-band

34 The spin hamiltonian and the parameters gA Cu /M Hz A N /MH z Q N /M Hz Euler angle/° x  = 35 y  = 14 z  = 0

35 High Frequency EPR: Why? increased resolution simpler spectra orientation effects spectra from integer spin systems with large zero field splitting sign of the zero field splitting different time scale

36 Enhanced Resolution The g tensor anisotropy of tyrosyl radicals present for instance in Photosystem II is completely resolved at high frequency. This provides important structural information, like their main orientation in the membranes.

37 Tyrosyl Radicals They are present in RNR and in Photosystem II RNR: ribonucleotide reductase catalyzes the reduction of ribonucleotide to deoxyribonucleotides

38 EPR of Tyrosyl rad. of S. typhymurium 250 GHz 9.45 GHz g x = g y = g z =2.0022

39 Tyrosyl Radical The g values are sensitive to the environment x y g x is the most sensitive, because of the interaction of the non-bonding oxygen orbitals Un et al. JACS 1999, 121, 5743

40 Resolution effect P700+ radical cation of PSI

41 Tyrosyl Radical in Different Environments N-ac-L-tyrL-tyr-HClRNRECPSII YD PSII YZ g x g y na g z na g iso Brustolon et al. J Phys Chem A 1999, 103, 9636

42 Tyrosyl Radical in Different Species Tyrosyl radical of RNR of different species E.coli mouse herpes typhimurium JACS 120, 5080, 1998

43 Orientation Effects in membranes

44 Il tensore g nei metalli di transizione

45 L’anisotropia del fattore g x 2 -y 2 xy xzyz z2z z x y Per un elettrone spaiato si ha: g i =g e +  gg e d n n=6-9 g // = g e + 8 /(Ed xy -Ed x 2 - y 2 ) g  = g e + 2 /(Ed yz - Ed x 2 - y 2 ) d x 2 -y 2 d z 2 d xy d xz,d yz Es: Cu 2+ elongato

46 d xy, d xz, d yz d x 2 -y 2,d z 2 d 1, 2 T 2g egeg t 2g Es: Ti 3+ d 2, 3 T 1g Es: V 3+ d 3, 4 A 1g Es: Cr 3+ d 5, 2 T 2g Es: Fe 3+ basso spin d 5, 6 A 1g Es: Fe 3+ alto spin d 6, 5 T 2g Es: Fe 2+ alto spin Stati fondamentali in campo ottaedrico -1

47 d 9, 2 E g Cu 2+ Stati fondamentali E g sono instabili rispetto alla distorsione Jahn-Teller e danno luogo a stati fondamentali orbitalmente non-degeneri Stati fondamentali in campo ottaedrico -2 d 8, 3 A 2g Es: Ni 2+ Es: Co 2+ d 7, 4 T 2g d 4, 5 E g Mn 3+ d x 2 -y 2 d z 2 d xy d xz,d yz elong. d z 2 d x 2 -y 2 d xz,d yz d xy comp. d z 2 d x 2 -y 2 d xz,d y z d xy comp. d x 2 -y 2 d z 2 d xy d xz,d yz elong.

48 Perturbative Approach = ±  /2S  g= 

49 Valori di g per coordinazione pseudo-ottaedrica Conf. elett. SStato fond.g x g y g z d 1 1/2 2 T 2g g e -2 /  1 g e -2 /  2 g e -8 /  3 d T 1g g e -9 /  g e -9 /  g e d 3 3/2 4 A 2g g e -8 /  1 g e -8 /  2 g e -8 /  3 d E g comp. g e -6 /  1 g e -6 /  2 g e elong.g e -2 /  1 g e -2 /  2 g e -8 /  3 d 5 HS5/2 6 A 1g g e g e g e d T 2g g e +2 /  1 g e +2 /  2 g e +2 /  3 d 7 3/2 4 T 2g O h 2(5-  )/32(5-  )/3 2(5-  )/3 elong. 0 02(3-  )/3 comp.442 d A 2g g e +8 /  1 g e +8 /  2 g e +8 /  3 d 9 1/2 2 E g elong.g e +2 /  1 g e +2 /  2 g e +8 /  3 comp. g e +6 /  1 g e +6 /  2 g e

50 g values for some ions

51 Spin hamiltonian for an individual spin H=  B B.g 1.S 1 + S 1.D 1.S 1 +  j S 1.A 1j.I j +.. Electronic Zeeman Electron- electron interaction (zero field splitting) Electron-nucleus interaction

52 Zero field splitting H= D[S 1z 2 -S 1 (S 1 +1)/3]+ E(S 1x 2 -S 1y 2 ) 0  E/D  1/3 diagonal Couples states differing in M by ±2

53 axial Completely rhombic

54 Origin of the zero field splitting For organic radicals: electron-electron dipolar interaction For transition metal and rare earth ions: spin- orbit interaction

55 Ligand field approximation = ±  /2S D 1 = 2 

56 A simpler treatment D=( /2)[g z -(g x +g y )/2]; E=( /4)[g x -g y ] For tetragonally elongated Ni(II): g x = g y = 2.25; g z = 2.24; =-315 cm -1 D= 1.57 cm -1

57 Higher order terms Higher order terms, which have their origin in higher order perturbations, are most coveniently described by Stevens operator equivalents: H=  n  k B n k O n k operator parameter n=0,±2,±4,..±2S; k=0,1…n

58 Advantages of the Stevens Operators They fully exploit the symmetry: easy calculations The number of the terms to be included are defined by symmetry For a C 4 quantization axis only the k= 0 and k= 4 terms must be included For C 2, k=0,2,4 The O n k operators couple states differing in M by ±k

59 Some examples of operators k=2O 2 0 =3S z 2 -S(S+1) O 2 2 =(S + 2 +S - 2 ) k=4O 4 0 =35S z 4 -30S(S+1)S z 2 +25S z 2 -6S(S+1)+3S 2 (S+1) 2 O 4 2 ={(7S z 2 -S(S+1)-5)(S + 2 +S - 2 )} S /2 O 4 3 ={S z (S + 3 +S - 3 )} S /2 O 4 4 =(S + 4 +S - 4 )/2{A,B} S =(AB+BA)/2 D=3B 2 0 ;E=B 2 2

60 Fine Structure When the Zeeman term is dominant each line is split into 2S equally spaced lines (fine structure) For an axial anisotropy the resonance fields are given by: H(M-M+1)=(g/g e )[H 0 +D’(M/2)(3cos 2  -1)] D’= D/(g e  B )

61 Nel limite di g  B H>>D e anisotropia uniassiale H // 2S linee separate da  H=2D/g  B H  2S linee separate da  H=D/g  B H(M  M+1)=(g e /g)[H 0 +(2M+1)/D’/2] D’=(3cos 2  -1)D/(g e  B )

62 (M=-3)=9D-3g  B H (M=-2)=4D-2g  B H (M=-1)=1D-1g  B H etc  E(-3,-2)=5D-g  B H  E(-2,-1)=3D-g  B H  E(-1,-0)=1D-g  B H campi di risonanza: H R (-3,-2)=(5D-h  )/g  B H R (-2,-1)=(3D-h  )/g  B H R (-1,-0)=(1D-h  )/g  B

63 H // HH T  2D/g  B D/g  B Per T  tutti i livelli sono equipopolati e l’intensità delle righe è proporzionale alla probabilità di transizione

64 Resonance fields for S states H(M  M+1)=(g e /g)[H 0 +(2M+1)/D’/2]; D’=(3cos 2  -1)D/(g e  B )

65 H // HH 2D/g  B D/g  B k B T<

66 HF-EPR Provides the Sign of D Negative D:±S lie lowest Easy axis type anisotropy At low T only the -S  -S+1 transition is observed

67 Quantitative LF Approach Bencini,A.; Ciofini,I.; Uytterhoeven, M.G. Inorg. Chim. Acta 1998, 274, 90 The energies of the LF levels are calculated using a full matrix diagonalization approach. The SH parameters, in principle to any order, are obtained by best fit of the calculated energies. Both classic crystal field and Angular Overlap parametrization can be used Ask him the program!

68 “EPR silent species” Ions with even numbers of unpaired electrons are EPR silent in a conventional X- or Q-band experiment due to large zero field splitting HF-EPR spectra of Mn(III), Fe(II), Ni(II), etc. become available

69 An example

70 Chromium(II) Manganese(III) x 2 -y 2 x 2 2 z 2 z 2 Compressed Elongated Jahn-Teller distortion

71 Chromium(II) Aquo Ion 329 GHz D=-2.20 cm -1 ; g= 1.98 Telser et al Inorg Chem 1998, 37, 5769

72 Manganese(III): SH Parameters Compressed: g z = 2.00; g x =1.97 D= 4.72 cm -1 B 2 0 = cm -1 B 4 0 = cm -1 B 4 4 = cm -1 Elongated: g z = 1.96; g x =1.99 D= cm -1 B 2 0 = cm -1 B 4 0 = cm -1 B 4 4 = cm -1 Dq=1600 cm -1

73 Vanadium(III) Alum 3 T 1g 3Ag3Ag OhOh S6S6

74 Vanadium(III) EPR D= cm -1 ; g z =1.9500; g xy = A z = , A xy = cm -1 Tregenna-Piggott et al Inorg Chem

75 Gadolinium Contrast Agents Contrast enhanced MRI is a very effective technique for detecting and characterizing lesions, for identifying patho- physiological abnormalities and for providing functional information. Usually contrast agents are slowly relaxing paramagnets. Gd 3+ is widely used because of its large spin Need for understanding the mechanism

76 Gadolinium Chelates DOTAP EOB-DTPA

77 Multifrequency Gd-DOTAP Spectra 9 GHz 94 GHz 249 GHz  H pp = 400 G  H pp = 25 G  H pp = 9 G The broadening effect is due to unresolved fine structure At high frequency Zeeman energy is much larger than zfs and the lines sharpen JACS 120, 1998m 5060

78 Gd-DOTAP in multilamellar aqueous dispersion

79 R. S. Drago: Physical methods for chemists (Saunders, 1992) J. S. Griffith: The theory of transition metal ions (Cambridge University Press, 1961) J. R. Pilbrow: EPR of transition metal ions (Clarendon Press, 1990) A. Abragam, B. Bleaney: EPR of transition ions (Dover, 1986) J. A. Weil, J. E. Wertz, J. R. Bolton: Electron Paramagnetic Resonance (Wiley, 1994) A. Bencini, D. Gatteschi: EPR of Exchange coupled systems (Springer Verlag, 1990) A. Bencini, D. Gatteschi: Electron Paramagnetic Resonance Spectroscopy, in Inorganic Electronic Structure and Spectroscopy, E.I. Solomon, A.B.P.Lever, Vol. I Wiley 1999 Riferimenti bibliografici

80 Libri: O. Kahn Molecular Magnetism VCH, Weinheim Review: A.-L. Barra, L.-C. Brunel, D. Gatteschi, L. Pardi, R. Sessoli, "High Frequency EPR Spectroscopy of Large Metal Ion Clusters. From Zero Field Splitting to Quantum Tunneling of the Magnetization" Acc. Chem. Res. 31, , D. Gatteschi, R. Sessoli “Quantum tunneling of magnetization and related phenomena in molecular materials” Angew. Chem. Int. Ed. 42, , D. Gatteschi, L. Pardi “High Frequency EPR Spectroscopy” in High Magnetic Fields, C. Berthier, L.P. Lévy, G. Martinez, Eds. Springer J. van Slageren et al. “Frequency-domain magnetic resonance spectroscopy of moleuclar magnetic materials” Phys. Chem. Chem. Phys. 5, , Riferimenti bibliografici

81 Programmi di simulazione Alcuni esempi: Sim (H. Weihe) (Inorg. Chem 32, 1993, 1216) Easyspin (S. Stoll) EPRNMR (J. A. Weil & M. J. Mombourquette) 3 - Convoluzione spettro (scelta di forme e larghezze di riga) 1 - Definizione del modello e dei parametri 2 - Calcolo delle probabilità di transizione per diverse orientazioni e campi


Download ppt "Magnetic techniques for molecular and nanometric materials Dante Gatteschi & Roberta Sessoli February 2008."

Similar presentations


Ads by Google