Origin (and control?) of the anisotropy in tetranuclear star shaped molecular nanomagnets

Transcription

1 Origin (and control?) of the anisotropy in tetranuclear star shaped molecular nanomagnets Lorenzo Sorace, Roberta Sessoli, Andrea Cornia Department of Chemistry & INSTM, University of Florence, Italy Department of Chemical and Geological Sciences, University of Modena, Italy Karlsruhe 11 October Workshop on magnetic anisotropy ECMM2013

2 Acknowledgments STM P. Totaro, M.E. Boulon, A.-L. Barra, K. C. M. Westrup, G. G. Nunes, A. Barison, J. F. Soares, D. SMM F. Back, M. Jackson, C. Paulsen Dept. of Chemistry U. Schiff, University of Florence, Sesto Fiorentino, Italy LNCMI-CNRS, Grenoble, France Departamento de Química, Universidade Federal do Paraná, Curitiba-PR, Brazil. Departamento de Química, Universidade Federal de Santa Maria, Camobi, RS, Brazil. Institut Néel CNRS & Université J. Fourier, Grenoble, France. 2

3 Magnetic Exchange in Molecular Materials H= S A. J. S B SMM STM J J J J J J J J J J xx xy xz yx yy yz zx zy zz H= J S A. S B + S A. D AB. S B + d AB. (S A xs B ) Isotropic (Heisenberg) J=1/3Tr(J) Anisotropic (traceless matrix) Antisymmetric (Dzyaloshinsky- Moriya)

4 Magnetic anisotropy of spin clusters Single Ion Dipolar & Exchange anisotropy

5 From the single spin to the pair 5

6 The Giant Spin Hamiltonian Why? Energy J >> k B T E ms Spin projection - m s S E -4 E 4 E -5 E 5 E -6 E 6 E -7 E 7 Hilbert space is (2S+1) instead of (2s i +1) Explains the major features of low temperature properties Does not depend on J (in first approximation) "up" E -8 E -9 E -10 E 8 E 9 E 10 "down"

7 Multispin and Giant Spin Hamiltonian H = Σ i,j J ij s i s j + Σ i s i D i s i + Σ i,j s i D ij s j + μ B Σ i s i g i B When J ij >>D, the total spin S is a good quantum number and the Giant Spin Hamiltonian describe the system properly: H = B S g s B + DS z 2 + E (S x 2 -S y2 )+ B nm O n m O n m = Stevens operators g S = Σ i c i g i D S = Σ i d i D i + Σ i,j d ij D ij Both magnitude and orientation of single ion tensors determine the global anisotropy Higher order terms in the GSH often arise as a consequence of departure from strong exchange limit

8 Why high order Spin Hamiltonian terms? The tunnel splitting according to perturbation theory Zeeman 2 th order =ħ T 4 th order 6 th order 8

9 The Giant Spin Hamiltonian What? H = B S g B + DS z 2 + E (S x 2 -S y2 )+ B nm O n m Quantum Properties of the SMM D, B n 0 height of the barrier (to be increased for applications) E, B n m coupling of M levels differing by 2 (E) or m (tunnelling,to be reduced for applications) Importance of understanding the origin of these anisotropy terms and finding a way to control to them Need for simple and easily tunable systems EPR (High Field/High Frequency) plays a key role

10 The propellers zoo V Cr Fe Ga Ga 4 Ga 3 Fe Ga 3 Cr Fe 4 Fe 3 Cr Fe 3 V

11 Fe4 Single-Molecule Magnets Antiferromagnetic coupling between central Fe(III) and external Fe(III) : J~15-20 cm -1 ground S=5 spin state D < 0 Exact or idealized C 3 axis Easy functionalization by replacement of methoxy groups with polyalkoxo ones: Fe 4 (CH 3 O) 6 (dpm) 6 + 2H 3 L Fe 4 (L) 2 (dpm) 6 + 6CH 3 OH Fe 4 (OMe) 6 (dpm) 6 Fe(III), S=5/2 C O... and many more J. Am. Chem. Soc. 1999, 121, 5302 Angew. Chem. Int.Ed. 2004, 43, 1136 J. Am. Chem. Soc. 2006, 128, 4742 Chem. Mater. 2008, 20, 2405

12 A library of functional groups By courtesy of A. Cornia

13 Magneto-structural correlations for Fe 4 family L. Gregoli et al. Chem. Eur. J. 2009, 15, 6456

14 Rotation of the anisotropy directions of peripheral Fe(III) y2 y2 y2 In GaFe(OMe) 2 (DBM) 6 D(Fe 2 )=+0.77 cm -1 Hard axis ~ perp to Z Intermediate axis ~ Fe1-Fe2 (Cornia et al. J. Mag. Res. 179, 2006, ) X Z Y z2 z2 z2 x2 On reducing, y 2 is tilted away from Z axis D S is less negative only varies 7.6 : D2 rotation has to be larger! JACS ,

15 The propellers zoo V Cr Fe Ga Ga 4 Ga 3 Fe Ga 3 Cr Fe 4 Fe 3 Cr Fe 3 V

16 Mixing metals in the propeller 283 GHz EPR Ga 3 Cr S=3/2 D Cr =0.470 cm -1 easy plane!! In collaboration with Dr. A.L. CNRS-GHML, Grenoble

17 Mixing metals in the propeller 230 GHz 190 GHz Two Fe III sites: D Cr 0.7 cm -1 E/D 0.1: easy plane!! In collaboration with Dr. A.L. CNRS-GHML, Grenoble

18 HF-EPR (230 GHz) of Fe 3 Cr derivative Fe 3 Cr, S=6 g=2 at 8.2 T D= cm -1 B 40 = cm -1 E=0.018 cm -1 g x =g y =2 ; g z =1.98 calc exp * * * * * * 20 K Fe 4 ; S=5 D=-0.42 cm -1 x x x 10 K 5 K B (T) Fe 3 Cr : Fe 4 = 84:16

19 SMM behavior from easy plane ions Easy Intermediate Hard Cr III, d 3 S = 6 D = cm -1 E 8 K ( E 15 K for Fe 4 ) Easy axis anisotropy results from spin noncollinearity P. Totaro et al. Dalton Trans, 2013, 42,

20 Fe 3 Cr(dpm) 6 (thme) 2, a trigonal SMM Cristallographically imposed trigonal symmetry: R-3c Pure Fe 3 Cr crystals Well-suited for single crystal EPR study S=6 + Trigonal anisotropy Determination of trigonal anisotropy Evaluate its effect on spin dynamics Evaluate its relation to microscopic parameters

21 W-band EPR of a single crystal of Fe 3 Cr (R-3c) Field direction Rotation 1 Easy-axis Hard plane 0.8 mm Field direction Rotation 2 Hard plane 0.8 mm Fe 3 Cr single crystals (~ 0.01*0.16*0.18 mm 3 )

22 Easy axis temperature dependence K 20 K 9 K * * * 6 K B (mt) Clear evidences of excited state population even at 6 K 12 transitions observed for S=6 and 10 transitions observed for S=5 at 40 K Evidence of the S=4 transitions in the 40 K spectrum Broadening of the high M S lines due to D-strain.

23 B res (mt) Axial anisotropy of ground and first excited states For S=6: g z =2.007 D= , B 40 < 5*10-7 cm -1 For S=5: g z =2.002 D = , B 40 <5*10-7 cm Only weak effects due to mixing M s S=6 B res = (g e /g) B 0 + [140*B 40 *M 3 S + 210*B 40 *M S2 +(2D-2330*B2330*B 40 )*M S +(D-855*B 40 )]/g S=5 B res = (g e /g) B 0 + [140*B 40 *M 3 S + 210*B 40 *M S2 +(2D-1660*B 40 )*M S +(D-865*B 40 )]/g

24 B res (mt) Trigonal anisotropy of Fe 3 Cr Cr III, d 3 S = / g = 2.019(1) D = (3) cm -1 B 4 0 = -1.98(2) x 10-7 cm -1 B 6 0 = 2.62(2) x 10-8 cm -1 B 4 3 = 5.0(2) x 10-4 cm -1 B 6 3 = 6.2(2) x 10-5 cm -1 B 6 6 = -6.0(1) x 10-7 cm -1

25 MSH simulation H MSH = Σ i,j J ij s i s j + Σ i s i D i s i + Σ i,j s i D ij s j + μ B Σ i s i g i B J ij and J ij : known from magnetic measurements g tensors: fixed by LF arguments D Cr : orientation defined by symmetry D Fe lying along C 2 symmetry axis

26 B res (mt) Fe3Cr hard plane: MSH simulation / Fe III and 1 Cr III : Hilbert space: 864x 864 Experimental behaviour reproduced very well Trigonal anisotropy arising from the non- collinearity of the D tensor of the peripheral Fe(III) Euler angles: b= = 85, = = 80

27 Giant Spin vs. Multi Spins The two models fit the EPR spectra but provide different tunnel splitting and Berry phase

28 High order transverse terms Ô 3 Ô Ô 3 6 Tunnel Splitting -6,6 Compensation field Bz(mT)

29 Increasing the spin of Fe 3 M propellers Fe Fe 4 3 a M robust propellers SMM V Fe III, d 5 S = 5 D = cm -1 E 15 K Cr III, d 3 S = 6 D = cm -1 E 8 K V III, d 2 S = 13/2 or 17/2 D?

30 Synthesis of Fe 3 V propeller Two steps synthesis 2 Li 3 (L et ) + [VCl 3 (thf) 3 ] Li 3 V(L Et ) 2 (vanadium core) + 3 LiCl Li 3 V(L Et ) [{Fe(dpm) 2 } 2 (μ-ome) 2 ] [Fe 3 V(L Et ) 2 (dpm) 6 ] + 3 LiOMe :( In contrast to Cr III, V III tends to get out from the propeller Successive recrystallizations yield enrichment of Fe 4 impurities in Fe 3 V.

31 Adding remnant Fe magnetization HF-EPR by chemical design 4 a robust of SMM Fe 3 V:Fe 4 95 GHz, T=20 K Fe 4, simulated 1d, simulated Fe 3 V, simulated H (KOe) D(Fe 4,S=5) = cm -1, g z =2.004 D(Fe 3 V,S=13/2) = cm -1, g z =2.043

32 Barrier (K) SPIN - D Fe Fe Fe 4 3 a M 3 M robust propellers propellers SMM r d n n

33 Adding Magnetization remnant Fe magnetization by chemical design 4 a robust dynamics SMM of Fe 3 V H dc =0 H dc = 1kOe E 21 K E 14 K Reduced tunneling in zero field for S=13/2

34 M ( B ) Adding remnant magnetization by chemical design Fe 4 a robust SMM Adding remnant magnetization by chemical design 10 H c (Fe 4 ) V 5 0 H c (Fe 3 V) o H (T) T= 90 mk T= 450 mk T= 900 mk Zero Field Tunneling is less efficient for S=13/2 In collaboration with Dr. Carley CNRS, Grenoble

35 Doubling Fe 4 a Trobust B by chemical SMM design Adding remnant magnetization by chemical design T B (Fe 3 V) Fe 3 V:Fe 4 V FC T B (Fe 4 ) ZFC Zero Field Tunneling is less efficient for S=13/2 In collaboration with Dr. Carley CNRS, Grenoble

36 Origin of magnetic anisotropy in Fe 3 V Knowing that D S =-0.31 cm -1 and g S =2.043 For V III g z ca. 1.7 and D V =-17cm -1!!! D d ( D D D ) d D S Fe Fe Fe Fe V V g c ( g g g ) c g S Fe Fe Fe Fe V V V(III) Cr(III) Fe(III) s 13/2 6 5 d Fe d M d Fe,Fe d Fe,M c Fe c M D dip /cm

37 V III : an orbitally degenerate d 2 ion A tribute to late Philip L. W. Tregenna-Piggott Villigen

38 V III : an orbitally degenerate d 2 ion D <0 only in rhombic symmetry!!

39 Origin of magnetic anisotropy in Fe 3 V V D d ( D D D ) d D d D d D S Fe Fe 1 Fe 2 Fe 3 V V Fe i, Fe j Fe i, Fe j Fe i, V Fe i, V j i i 1,3 Knowing the experimental D and d V = D V =-17 cm -1 The anisotropic exchange is tentatively given by : 2 ˆk g kk 2 L e J ˆ AB e g H 2 b exc e g b E A gz - ge - (2 ka) E For V III g z ca. 1.7!!!

40 What about the AS contribution? H AS = d 12 S 1 xs 2 V The polar vector d has to be oriented along the C 2 symmetry axis Fe-V d 12 No contribution to the axial anisotropy!

41 Concluding remarks Determination of the magnetic anisotropy of internal and external ions in the propeller structure. First spectrscopic determination of the trigonal transverse anisotropy in a model S=6 systems, and its origin Evaluation of its effect on tunnel splitting Exchange anisotropy contribution to the magnetic anisotropy can overcome the single-ion ones