Large orbital magnetic moment measured in the [TpFeIII(CN)3]− precursor of photomagnetic molecular Prussian Blue Analogues Supplementary Information Sadaf Fatima Jafri1 , Evangelia S. Koumousi2,3,4,5 , Philippe Sainctavit1,6 , Amélie Juhin1 , Vivien Schuler1 , Oana Bunau1 , Dmitri Mitcov4,5 , Pierre Dechambenoit4,5 , Corine Mathonière2,3 , Rodolphe Clérac4,5 , Edwige Otero6 , Philippe Ohresser6 , Christophe Cartier dit Moulin7,8 , and Marie-Anne Arrio∗1 1 Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, UMR7590, CNRS, UPMC, IRD, MNHN, 75252 Paris Cedex 05, France 2 CNRS, ICMCB, UPR 9048, F-33600, Pessac, France 3 Univ. Bordeaux, ICMCB, UPR 9048, F-33600, Pessac, France 4 CNRS, CRPP, UPR 8641, F-33600, Pessac, France 5 Univ. Bordeaux, CRPP, UPR 8641, F-33600, Pessac, France 6 Synchrotron SOLEIL, L’Orme des Merisiers Saint-Aubin, France 7 CNRS, UMR 8232, Institut Parisien de Chimie Moléculaire, F-75005, Paris, France 8 Sorbonne Universités, UPMC Univ Paris 06, UMR 8232, IPCM, F-75005, Paris, France July 4, 2016 S1 Crystallographic data of the FeTp complex Single crystal of (N(C4 H9 )4 )[(Tp)FeIII (CN)3 ]·3H2 O (FeTp) was mounted in CargilleTM NHV immersion oil on a 50 mm MicroMountsTM rod at 120 K. The crystallographic data were collected with Bruker APEX II Quasar diffractometers, housed at the Institut de Chimie de la Matière Condensée de Bordeaux, and equipped with a graphite monochromator centered on the MoKα path. The program SAINT was used to integrate the data, which was thereafter corrected for absorption using SADABS [1]. The structure was solved by direct methods and refined by a full-matrix least-squares method on F2 using SHELXL2013 [2]. All non-hydrogen atoms were refined anisotropically. Hydrogen atoms were assigned to ideal positions and refined isotropically using suitable riding models. Reflections were merged by SHELXL according to the crystal class for the calculation of statistics and refinement. Figures 1 and SI-1 were generated using CrystalMaker R (CrystalMaker Software Ltd, www.crystalmaker.com). ∗ Marie-Anne.Arrio@impmc.upmc.fr 1 Figure S1: Projection view of the crystal structure of FeTp at 120 K showing the packing of the anionic complexes, the [N(C4 H9 )4 ]+ cations and the lattice water molecules in the (ac) plane. All the hydrogen atoms are omited for clarity. Fe, N, C, O and B atoms are indicated in orange, light blue, grey, red and pink, respectively. The light blue dotted lines are indicating the H-bonding between the cyanide groups and the lattice water molecules. 2 Compound (N(C4 H9 )4 )[(Tp)FeIII (CN)3 ]·3H2 O F W / g mol−1 643.94 Crystal color orange Crystal system triclinic Space group P1̄ Temperature / K 120 a / Å 11.1956(4) b / Å 11.2191(4) c / Å 15.9740(6) α/ ◦ 87.2840(10) β/ ◦ 76.7360(10) γ/ ◦ 60.8650(10) 3 V / Å 1700.91(11) Z 2 R1 (I > 2σ(I)) 0.0630 wR2 (all data) 0.1801 Rint 0.0277 a b a CCDC 1451192 P P P P b R1 = ||F0 | − |Fc ||/ |F0 | , wR2 = [ (F02 − Fc2 )2 / (F02 )2 ]1/2 Table S1: Crystallographic data of FeTp. 3 S2 Magnetic data of the FeTp complex Magnetic susceptibility measurements were performed on a Quantum Design SQUID magnetometer MPMS-XL housed at the Centre de Recherche Paul Pascal (Pessac) at temperatures between 1.85 and 300 K and dc magnetic fields ranging from -7 to 7 T. Microcrystalline powder of FeTp (13.24 mg) introduced in sealed polyethylene bag, which was containing 10.88 mg of paraton oil. Prior to the experiments, the field-dependent magnetization was measured at 100 K in order to detect the presence of any bulk ferromagnetic impurities. In fact, paramagnetic or diamagnetic materials should exhibit a perfectly linear dependence of the magnetization that extrapolates to zero at zero dc field. The sample appeared to be free of any significant ferromagnetic impurities. The magnetic data were corrected for the sample holder, paratone oil and the intrinsic diamagnetic contributions. Figure S2: (top) The χT versus T curve at 0.1 T, (bottom right) reduced magnetization curve (M versus B/T ) for FeTp at different temperatures and (bottom left) magnetization versus field B. χ is defined as the molar magnetic susceptibility and equal to M/B, M being the magnetization and B the dc applied magnetic field. 4 S3 Experimental XAS : raw data and background subtraction Figure S3: Experimental XAS spectrum (blue line), XAS spectrum before the edge set to zero (black line), XAS spectrum after subtraction (green line) of the arctangent functions (dashed red line) for sample FeTp at 2 K. The baseline function (bl(E) with E the photon energy in eV) is a linear combination of two arctangent function to fit the absorption step edge at L3 (711.4 eV) and L2 (723.7 eV) edges:   π 2 π 1 1 1 bl(E) = { arctan(E − 711.4) + arctan(E − 723.7) }+{ } ∗ 0.044 π 2 3 π 2 3 After subtraction of the baseline, the XAS spectrum is normalized to 1 at peak c of the L3 edge i.e is divided by the absorption value at the energy of peak c. The XMCD spectrum is divided by the same value. S4 Parameters used for Ligand Field Multiplet calculations and Lz , Sz , Tz expectation values The parameters used for Figure 3 are given in Table S2 10Dq Dσ Dτ κ ∆i ∆f Veg Vt2g B C3v with MLCT 2.8 0.07 0.12 0.7 3.0 3.4 -0.8 1.8 6.5 C3v no MLCT 2.8 0.07 0.12 0.7 - - - - 6.5 Oh with MLCT 2.8 0 0 0.7 3.0 3.4 -0.8 1.8 6.5 Oh no MLCT 2.8 0 0 0.7 - - - - 6.5 Table S2: Parameters used in the Ligand Field Multiplet simulations. All the calculations were made with ζ3d = 0.059 eV, ζ2p = 8.199 eV (atomic values). κ is dimensionless, B is expressed in Tesla. The other parameters are given in eV (1 eV = 11605 K). 5 The Lz , Sz , Tz expectation values for the four previous set of parameters are given in Table S3. hLz i hSz i hTz i C3v with MLCT -1.2361 -0.4882 -0.1146 C3v no MLCT -1.3941 -0.5012 -0.0924 Oh with MLCT -0.7754 -0.1704 -0.0594 Oh no MLCT -0.8521 -0.1786 -0.0523 Table S3: Expectation values for Lz , Sz , Tz for the set of parameters given in Table S2. S5 S5.1 Origin of the failure of the spin sum rule Influence of spectral resolution Instead of applying the sum rules to the convoluted calculated spectra, it can be applied to the calculated discrete transitions before applying any broadening function. By doing so, we discard the possible weight transfer between L3 and L2 edges induced by spectral broadening. With this approach, one obtains hSzeff i = −0.634, which is indeed quite similar to the value obtained by the sum rule applied to the convoluted theoretical spectra. The deviation is still equal to 29% compared to the LFM value hSzeff,LFM i = −0.889, so that the failure of the spin sum rule cannot fully be attributed to the spectral broadening. Figure S4: Unconvoluted transition intensities (sticks : |hf |ε̂ · ~r|ii|2 ) for the XMCD spectrum calculated at T = 0 K using the parameters listed in Table 1 (main text). Insert : zoom of the region between L3 and L2 edges S5.2 Influence of cutoff energy between L3 and L2 edges Another important aspect for the application of the spin sum rule is the choice of the cutoff energy that separates the XMCD signal into its contribution to the L3 edge and to the L2 edge. The value chosen here was 716.8 eV, although this choice is not straightforward because there are many transitions with non-zero amplitudes close to this energy (i.e., 1000 times smaller than the largest transitions, see Figure S4). If the cutoff energy is varied between 715.8 and 717.8 eV, one finds that the effective spin hSzeff i changes by ≈ 1%. Hence, we can conclude that the cutoff energy cannot be the cause for the failure of the spin sum rule. S5.3 Influence of temperature The calculation for hLz i, hSz i and hTz i have been performed at 0 K. For finite temperatures, we first calculated the thermal average values for hLz i, hSz i and hTz i which are given by the Boltzmann distribution 6 at temperature T. For hLz i it reads hLz i(T ) = Pn Ei −Eo i=0 hi|Lz |iiexp[−( kT )] Pn Ei −Eo i=0 exp[−( kT )] (1) where i is the index running on the initial states, Ei is the energy of the initial state i and the Boltzmann constant k = 8.617 × 10−5 eV.K−1 . For hSz i and hTz i, similar formula are applied. The values obtained from the calculations at 0 K, 2 K and 4 K are reported in Table S4. Whatever the temperature, the orbit sum rule is obeyed whereas the spin sum rule is not. LFM calculations Sum rules: calculated Spectra Sum rules: calculated sticks 0K 2K 4K 0K 2K 4K 0K 2K 4K hLz i -1.2361 -1.2359 -1.2216 -1.2358 -1.2357 -1.2225 -1.2363 -1.2362 -1.2230 hSz i -0.4882 -0.4881 -0.4825 -0.2135 -0.2136 -0.2117 -0.2319 -0.2318 -0.2295 hSzeff i -0.8894 -0.8893 -0.8791 -0.6149 -0.6149 -0.6083 -0.6331 -0.6330 -0.6261 Table S4: Ground state average values of Lz , Sz and Szeff extracted from multiplet calculations and spin sum rules (on calculated spectra and sticks of calculated spectra) at 0 K, 2 K and 4 K for the atomic value of 2p spin-orbit coupling ζ2p = 8.199 eV. S6 S6.1 Angular dependence of the orbit and spin magnetic moments and average values Angular dependence [ijk] α(◦ ) hSz i hSz i (0) × cos (α) hLz i hLz i (0) × cos (α) hTz i [001] 0 -0.4882 -0.4882 -1.2361 -1.2361 -0.1146 [001] 90 -0.0060 0.0 -0.0636 0.0 -0.0989 [001] 90 -0.0060 0.0 -0.0636 0.0 -0.0989 [110] 90 -0.0060 0.0 -0.0636 0.0 -0.0989 [011] 45 -0.3476 -0.3452 -0.8758 -0.8740 -0.0827 [101] 45 -0.3476 -0.3452 -0.8758 -0.8740 -0.0827 [111] 54.7 -0.2850 -0.2821 -0.7163 -0.7143 -0.0689 Table S5: hSz i, hLz i and hTz i values calculated in the LFM model for different orientations of the external magnetic field relative to the C3 axis of the molecule. The C3 axis is along the [001] axis of the molecule and α is the angle between C3 axis and the z axis that is the direction of the x-ray propagation vector k (i.e. the direction of B in the present XMCD experiments). hSz i (0) and hLz i (0) are the values of hSz i and hLz i at α = 0. S6.2 Average values From LFM calculations, we obtained hLz i(α) ≈ cos(α) × hLz i(0). In the present case, α is obviously the acute angle between the C3 axis and the B direction so that 0 6 α 6 π2 (this is equivalent to say that, for a paramagnetic ion, the magnetization is never antiparallel to the external magnetic field). Then the k propagation vector only maps the half sphere along the [001] direction of the C3 axis. The average value of a f (α, φ) function (α, φ are the angular spherical coordinates) on the half sphere is given by: Z α=π/2 Z φ=2π 1 faverage = sin(α)f (α, φ)dαdφ (2) 2π α=0 φ=0 7 If f (α, φ) = hLz i(α) = cos(α).hLz i(0) then hLz iaverage = = = 1 2π Z π/2 0 Z 1 hLz i(0) 2π 1 hLz i(0) 2 2π sin(α)hLz i(α)dαdφ (3) 0 Z 0 π/2 Z 2π cos(α) sin(α)dαdφ (4) 0 (5) Similarly one obtains: hSz iaverage = 12 hSz i(0). If the C3 axis are uniformly distributed in a cone of half angle at maximum of Θ then the angular average for the orbital magnetic moment yields hLz iaverage = 21 [1+cos(Θ)hLz i(0)] and a similar expression for the spin magnetic moment. From the ratio between the measured and the calculated magnetic moments, one deduces that Θ = 65˚. References [1] G. M. Sheldrick, SADABS, version 2.03, Bruker Analytical X-Ray Systems, Madison, WI, 2000. [2] G. M. Sheldrick, Acta Cryst., A64, 112, 2008. 8