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1 doi: /nature09478 Supplementary Figures and Legends Supplementary Figure 1. ORTEP plot of molecule 1 in phase I of Fe 4 C 5 viewed perpendicular (left) and parallel (right) to the idealized threefold axis. Colour code: black = C, yellow = S, red = O, green = Fe. Thermal ellipsoids are drawn at 50-% probability level. Supplementary Figure 2. DC magnetic properties of Fe 4 C 5, with best-fit calculated data drawn as a solid curve. WWW NATURE.COM/NATURE 1

2 " M (emu/mol) doi: /nature09478 Supplementary Figure 3. Isothermal M M vs. H/T measurements on Fe 4 C 5, along with best-fit calculated data drawn as solid curves 'M (emu/mol) T (K) ac frequency (Hz) Supplementary Figure 4. Frequency dependence of the imaginary (top) and real (bottom) components of the AC magnetic susceptibility of Fe 4 C 5 measured in zero static field and different temperatures (see colour scheme) WWW NATURE.COM/NATURE 2

3 (s) doi: /nature /T (K -1 ) Supplementary Figure 5. Temperature dependence of the relaxation time (black filled circles) and of the parameter describing the width of the distribution (blue squares). The red broken line represents the best fit using the Arrhenius law. Supplementary Figure 6. Frozen solution EPR spectra of Fe 4 C 5 at 95 GHz and two temperatures. Thin broken lines represent the simulated curves with parameters reported in the text. The asterisk indicates a spurious contribution arising from the cavity. WWW NATURE.COM/NATURE 3

4 counts doi: /nature diameter (nm) Supplementary Figure 7. (left) 2D representation of the STM image reported in Figure 1d. No filtering processes have been applied to this version of the image where single molecule features are clearly visible. (right) Statistical analysis obtained on a set of 6 independent images; the average size evaluated as the peak of a lognormal distribution (2.2 nm) agrees with the dimension of the Fe 4 C 5 molecules found by X-ray diffraction. Supplementary Figure 8. (left) XAS and XNLD of Fe 4 C 9 on Au. (right) XAS and XNLD of Fe 4 C 5 on Au. These spectra were obtained in identical experimental conditions. WWW NATURE.COM/NATURE 4

5 Supplementary Figure 9. Schematic view of the relative orientation of the polarization vectors and single ion cross sections used to simulate XNLD spectra. WWW NATURE.COM/NATURE 5

6 Supplementary Methods Synthesis and structural characterization. [Fe 4 (L) 2 (dpm) 6 ] (Fe 4 C 5 ) was prepared by reaction of the [Fe 4 (OMe) 6 (dpm) 6 ] precursor 30 with the functionalized ligand 7-(acetylthio)-2,2- bis(hydroxymethyl)heptan-1-ol (H 3 L). Elemental analysis calculated for C 88 H 152 Fe 4 O 20 S 2 : C 58.15, H 8.43, S 3.53 %; found: C 57.99, H 8.61, S 3.68 %. Crystallographic analysis showed that the crystalline material comprises at least three crystal phases with exactly the same chemical composition. Phase I is largely dominant in all preparations and grows as very thin plates; phase II and phase III are formed in minor amounts and give wellformed prisms. Unit cell parameters for the three forms are reported in Supplementary Table 1. All crystal forms contain the same Fe 4 molecular unit. In particular phase I contains four crystallographically independent Fe 4 molecules. The molecular structure of one of these is shown in Supplementary Figure 1. The structural parameters around the iron centres are very similar to those previously reported for this class of compounds. 14 More details of the crystal structure characterization are out of the scope of this Letter and are left for a more specialized publication. Bulk magnetic data. For DC and AC measurements we used a 9.28-mg microcrystalline sample of Fe 4 C 5 pressed in a pellet. DC data were recorded using a Quantum Design MPMS magnetometer at temperatures ranging from T = 1.9 to 300 K and in fields H = 1 koe (T < 30 K) or 10 koe (T > 30 K). Isothermal magnetization curves were recorded in fields up to 50 koe and at 1.9, 2.5 and 4.5 K. The M M /H ratio, where M M is the molar magnetization, was assumed to correspond to the static molar susceptibility M. Raw data were reduced using a molecular weight of and a diamagnetic correction (estimated from Pascal s constants) of emu/mol. The fitting of DC magnetic data was carried out using dedicated software, as described elsewhere. 31 M T vs. T data were fitted to a Heisenberg plus Zeeman Hamiltonian, assuming threefold symmetry for the cluster and using two different exchange-coupling constants to describe nearest-neighbour (J) and next-nearest-neighbour (J ) interactions with the J convention (Eq. S1). Ĥ Heis+Zee = J(Ŝ 1 Ŝ 2 +Ŝ 1 Ŝ 3 +Ŝ 1 Ŝ 4 ) + J (Ŝ 2 Ŝ 3 +Ŝ 3 Ŝ 4 +Ŝ 2 Ŝ 4 ) + μ B gŝ Ĥ (S1) (here, S 1 is the central spin vector and Ŝ is the total spin). A Curie-Weiss correction was introduced to reproduce the low-temperature drop of the M T product due to anisotropy effects. ( M T) = ( M T) T / (T - ) (S2) WWW NATURE.COM/NATURE 6

7 The best-fit parameters so obtained were g = (8), J = 16.74(4) cm -1, J = 0.05(2) cm -1 and = (4) K (Supplementary Figure 2). Isothermal M M vs. H data were fitted to a S = 5 giant-spin model, with axial zero-field splitting (Eq. S3), for which the D and the g parameters were refined to give g = 1.923(2) and D = (4) cm -1 (Supplementary Figure 3). Ĥ S=5 = μ B gŝ Ĥ + D[Ŝ z 2 - S(S+1)/3] (S3) The dynamics of the magnetization of a polycrystalline powder sample of Fe 4 C 5 was investigated by means of AC susceptibility measurements in zero static applied field performed with a homemade inductive set-up adapted to an Oxford Instruments MAGLAB2000 platform. In Supplementary Figure 4 the imaginary and real components of the susceptibility are reported as a function of the ac frequency for several temperatures. These curves were fitted with the Debye model, extended to take into account the distribution of the relaxation times according to: 1 1 (ω ) sin απ/ 2 χ'(ω) χ χ χ S T S 12 (ω) sin απ/ 2 (ω) 1 22 (S4) 1 (ω ) cos απ/ 2 χ "(ω) χ χ T S 12 (ω) sin απ/ 2 (ω) 1 22 The relaxation time,, and the width of the distribution, α, obtained with this procedure are reported in Supplementary Figure 5. A linear behaviour is observed in the Arrhenius plot, = 0 exp(u eff / k B T), thus allowing to extract the parameters: 0 = 0.061(2) s and U eff /k B = 14.8(1) K. The α parameter shows a gradual increase on lowering the temperature but its value remains relatively small despite the different crystallographically inequivalent molecules present in the dominant phase. EPR spectra. Spectra were recorded by using a Bruker Elexsys E600 CW spectrometer, operating at ca. 95 GHz, equipped with a 6 T split-coil superconducting magnet (Oxford Instruments). To avoid the complex convolution of signals coming from the different crystal phases and independent molecules in phase I, the EPR spectra were recorded on ca. 0.5 l of a frozen solution of Fe 4 C 5 in CH 2 Cl 2 :hexane 2:1 at 4 mm concentration (Supplementary Figure 6). Simulation of the spectra was performed by using a dedicated program based on full diagonalization of the Spin Hamiltonian matrix: 32 WWW NATURE.COM/NATURE 7

8 Ĥ EPR = μ B gŝ Ĥ + D[Ŝ z 2 - S(S+1)/3] + (E/2)(Ŝ Ŝ - 2 ) (S5) STM characterization. STM imaging was carried out on a NT-MDT Solver P47pro (NT-MDT, Zelenograd, Moscow, Russia; equipped with a custom built low-current head operated in air (Supplementary Figure 7). Tips were prepared by mechanical sharpening of Pt/Ir 90:10 wire. Simulation of XNLD spectra. In order to simulate the XNLD features observed in the monolayer of Fe 4 C 5 (Supplementary Figure 8) it was necessary to evaluate the absorption process occurring on each iron ion, considering its local anisotropy in both magnitude, sign and orientation with respect to the molecular reference frame. Finally, we needed to evaluate the effect of the preferential orientation of the molecules within the monolayer as obtained by DFT calculations. For each iron ion we define the cross-section for linear polarization parallel to the single ion anisotropy axis ( // ) and the cross-section for linear polarization perpendicular to the single ion anisotropy axis ( ). Following this approach and considering a single molecule of Fe 4 C 5 with its idealized threefold axis lying along the Au surface normal (Supplementary Figure 9) it is possible to attribute to the central ion an XNLD signal corresponding to XNLD Central = 1/2[ - // ] Central. On the other hand, for the peripheral ions, the anisotropy axis is perpendicular to the molecular axis and the XNLD signal for one ion is equal to XNLD Peripheral = -1/4[ - // ] Peripheral. The molecular XNLD signal is then evaluated as the weighted average of the contributions from one central ion and three peripheral ions: V - H = 1/4 ( Central + 3 Peripheral) = 1/8[ - // ] Central - 3/16[ - // ] Peripheral (S6) The final step of the calculation takes into account the distribution of orientations of the molecular axis, which is restrained to form an angle smaller than 35 with respect to the surface normal. The sample frame axes (X, Y, Z) are chosen so that Z is along the sample normal, X is horizontal and perpendicular to Z, and Y is vertical. In the experimental set-up, the propagation vector makes a angle with the Z axis so that the vertical and horizontal polarization vectors are given by V = (0,1,0) and H = (1/2,0,1/2). According to Brouder, 29 the general expression for dichroic crosssections with linear polarization is: ) = (cos( [ - // ] (S7) WWW NATURE.COM/NATURE 8

9 where is the angle between the polarization vector and the molecular axis. To evaluate the polarization vector and the molecular axis are given in the sample (X, Y, Z) reference frame by using standard polar coordinates, i. e. m = (sin()cos(), sin()sin(), cos()). For a molecule whose molecular axis forms an angle with the normal to Au surface, one gets V = [ ] Molecule ( V. m) 2 [ - // ] Molecule = [ ] Molecule (sin()sin() 2 [ - // ] Molecule and (S8) H = [ ] Molecule ( H. m) 2 [ - // ] Molecule = [ ] Molecule [sin()cos()/2 + cos()/2] 2 [ - // ] Molecule. The total XNLD signal for a collection of molecules whose axes lie within a cone of angle max is then simply given by: V - H ] Sample = = [ - // ] Molecule 0<<max 0<<2 {1/2 [sin()cos() + cos()] 2 (sin()sin()) 2 } sin(dd For max = 35 this results in: V - H ] Sample = /2 [ - // ] Molecule = {1/8[ - // ] Central - 3/16[ - // ] Peripheral } This final formula has been employed to reproduce the observed features in the Fe 4 C 5 monolayer. The different cross-sections ( and // for the central ion and for the peripheral ions) have been calculated within the Ligand Field Multiplet theory developed by T. Thole in the framework established by Cowan and Butler. 33 The distortion parameter D has been set in order to reproduce the splittings of the ground state sextuplet obtained by Tancini et al. from HF-EPR measurements (peripheral centers) 21 and calculated by Ribas et al. (central iron). 34 For all ions D has been set to 0. For the central ion, D = ev and the lowest lying level has longitudinal spin component m = ±5/2 with the m = ±3/2 and m = ±1/2 levels lying 0.28 mev and 0.43 mev respectively above in WWW NATURE.COM/NATURE 9

10 energy. These separations correspond to a zero-field splitting parameter D/k B = K. For the peripheral ions, D = ev and the lowest lying level is m = ±1/2 with the m = ±3/2 and m = ±5/2 levels lying 0.18 mev and 0.52 mev above the ground doublet, respectively. These separations correspond to a zero field splitting parameter of D/k B =1.05 K. WWW NATURE.COM/NATURE 10

11 Supplementary Tables Supplementary Table 1. Crystallographic data and refinement parameters for the three crystal phases of Fe 4 C 5. [a] Phase I Phase II Phase III Formula C 88 H 152 Fe 4 O 20 S 2 C 88 H 152 Fe 4 O 20 S 2 C 88 H 152 Fe 4 O 20 S 2 MW crystal system monoclinic monoclinic Monoclinic space group P2 C2/c P2 1 /n a / Å (6) (5) (4) b / Å (6) (3) (10) c / Å (10) (6) (5) / deg (14) (10) (9) V / Å (6) (4) (5) Z [a] all measurements carried out at 120(2) K using Mo-K radiation ( = Å). Supplementary Notes (30) S. Accorsi, A.-L. Barra, A. Caneschi, G. Chastanet, A. Cornia, A. C. Fabretti, D. Gatteschi, C. Mortalò, E. Olivieri, F. Parenti, P. Rosa, R. Sessoli, L. Sorace, W. Wernsdorfer, L. Zobbi, J. Am. Chem. Soc. 2006, 128, (31) A.-L. Barra, F. Bianchi, A. Caneschi, A. Cornia, D. Gatteschi, L. Gorini, L. Gregoli, M. Maffini, F. Parenti, R. Sessoli, L. Sorace, A. M. Talarico, Eur. J. Inorg. Chem. 2007, (32) C. J. H. Jacobsen, E. Pedersen, J. Villadsen, H. Weihe, Inorg. Chem.1993, 32, (33) B. T. Thole, G. van der Laan, J. C. Fuggle, G. A. Sawatzky, R. C. Karnatak and J. M. Esteva, Phys. Rev. B 1985, 32, (34) J. Ribas-Arino, T. Baruah, M. R. Pederson, J. Chem. Phys. 2005, 123, WWW NATURE.COM/NATURE 11