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 2013- Workshop on magnetic anisotropy ECMM2013
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
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)
Magnetic anisotropy of spin clusters Single Ion Dipolar & Exchange anisotropy
From the single spin to the pair 5
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) 10-20 instead of (2s i +1) 10 4 10 8 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"
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
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
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
The propellers zoo V Cr Fe Ga Ga 4 Ga 3 Fe Ga 3 Cr Fe 4 Fe 3 Cr Fe 3 V
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
A library of functional groups By courtesy of A. Cornia
Magneto-structural correlations for Fe 4 family L. Gregoli et al. Chem. Eur. J. 2009, 15, 6456
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, 29-37 ) 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 2006 128, 4742-4755
The propellers zoo V Cr Fe Ga Ga 4 Ga 3 Fe Ga 3 Cr Fe 4 Fe 3 Cr Fe 3 V
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. Barra @ CNRS-GHML, Grenoble
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. Barra @ CNRS-GHML, Grenoble
HF-EPR (230 GHz) of Fe 3 Cr derivative Fe 3 Cr, S=6 g=2 at 8.2 T D=-0.179 cm -1 B 40 =1.6 10-6 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 0 2 4 6 8 10 12 B (T) Fe 3 Cr : Fe 4 = 84:16
SMM behavior from easy plane ions Easy Intermediate Hard Cr III, d 3 S = 6 D = -0.18 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, 4416-4426
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
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 )
Easy axis temperature dependence -1 0-6 -5-5 -4-4 -3-2 -1-3 -2 0 1 1 2 2 3 3 4 4 5 5 6 40 K 20 K 9 K * * * 6 K 1000 2000 3000 4000 5000 6000 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.
B res (mt) Axial anisotropy of ground and first excited states 5000 4000 For S=6: g z =2.007 D= -0.1845, B 40 < 5*10-7 cm -1 For S=5: g z =2.002 D = - 0.155, B 40 <5*10-7 cm -1 3000 2000 1000 Only weak effects due to mixing -6-5 -4-3 -2-1 0 1 2 3 4 5 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
B res (mt) Trigonal anisotropy of Fe 3 Cr Cr III, d 3 S = 6 3600 3400 3200 3000 0 20 40 60 80 100 120 140 160 180 / 1 2 0 1-1 0-2 -1 g = 2.019(1) D = - 0.1855(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
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
B res (mt) Fe3Cr hard plane: MSH simulation 3500 3400 3300 3200 3100 3000 0 20 40 60 80 100 120 140 160 180 / 1 2 0 1-1 0-2 -1 3 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
Giant Spin vs. Multi Spins The two models fit the EPR spectra but provide different tunnel splitting and Berry phase
High order transverse terms Ô 3 Ô 6 4 6 Ô 3 6 Tunnel Splitting -6,6 Compensation field Bz(mT)
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 = -0.45 cm -1 E 15 K Cr III, d 3 S = 6 D = -0.18 cm -1 E 8 K V III, d 2 S = 13/2 or 17/2 D?
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 ) 2 + 1.5 [{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.
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 0 10 20 30 40 50 60 H (KOe) D(Fe 4,S=5) = -0.43 cm -1, g z =2.004 D(Fe 3 V,S=13/2) = -0.31 cm -1, g z =2.043
Barrier (K) SPIN - D Fe Fe Fe 4 3 a M 3 M robust propellers propellers SMM 7 6 5 4 20 15 10 0.4 0.3 0.2 0.1 0.0 r 2 3 4 5 d n n
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
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) -5-10 -2-1 0 1 2 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 Paulsen @ CNRS, Grenoble
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 Paulsen @ CNRS, Grenoble
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 1 2 3 S Fe Fe Fe Fe V V g c ( g g g ) c g 1 2 3 S Fe Fe Fe Fe V V V(III) Cr(III) Fe(III) s 13/2 6 5 d Fe 0.121429 0.138776 0.186813 d M 0.008333 0.028571 0.128205 d Fe,Fe 0.151786 0.173469 0.233517 d Fe,M -0.047222-0.080952-0.181624 c Fe 0.37778 0.40476 0.47222 c M -0.13333-0.21429-0.41667 D dip /cm -1-0.005-0.0132-0.0365
V III : an orbitally degenerate d 2 ion A tribute to late Philip L. W. Tregenna-Piggott Villigen 20-2-2010
V III : an orbitally degenerate d 2 ion D <0 only in rhombic symmetry!!
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 =0.00833 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!!!
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!
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