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              <p>The magnitude of the orbital magnetic moment [1-9] and its role as a trigger of the Verwey transition [10-17] in the prototypical Mott insulator, magnetite, remain contentious. Using 1s2p resonant inelastic X-ray scattering magnetic linear angular distribution (RIXS-MLAD), we prove the existence of non-collinear orbital magnetic ordering and infer the presence of dynamical distortion creating a polaronic precursor for the metal to insulator transition. These conclusions are based on a subtle angular shift of the RIXS-MLAD spectral intensity as a function of the magnetic field orientation. Theoretical simulations show that these results are only consistent with non-collinear magnetic orbital ordering. To further support these claims we perform Fe K-edge X-ray magnetic circular dichroism (XMCD) in order to quantify the iron average orbital magnetic moment. Magnetite ([Fe 3+ ] A [Fe 3+ , Fe 2+ ] B O 4) is the most abundant iron bearing mineral on Earth and it finds many applications in areas such as palaeomagnetism, medicine, 16 data recording, and engineering [18]. Ever since Verwey's 17 pioneering work [19], an immense amount of research has 18 been dedicated to Fe 3 O 4 in view of its importance as a 19 reference for systems exhibiting the metal to insulator 20 transition [11, 20, 21]. In Fe 3 O 4 , the Verwey transition 21 occurs at T V ∼ 125 K and results in a spontaneous change 22 of both, the lattice symmetry and the electric conductiv-23 ity. Above T V Fe 3 O 4 has a cubic inverse spinel crystal 24 structure containing two different Fe sites. Fe 3+ ions re-25 side in tetrahedral (T d) interstices (the A sites) while 26 both Fe 2+ and Fe 3+ ions reside in octahedral (O h) inter-27 stices (the B sites). The A and B sublattices are anti-28 ferromagnetically coupled while the Fe ions in the same 29 sublattice are ferromagnetically coupled (Fig. 1a). 30 In ferromagnets and ferrimagnets, the spin and or-31 bital magnetic moments of the transition metal ions can 32 be directly quantified by applying the sum rules on the 33 L 2,3 XMCD signal [22]. In spite of the great success of 34 sum rules, the experimental and analysis procedures were 35 shown to be prone to huge uncertainties due to surface 36 effects [1]. Orbital magnetic moments as small as 0.01 µ B 37 [2] and as large as 0.33 µ B [3] were reported for Fe 3 O 4. 38 In addition, large orbital magnetic moment contributions 39 that are of equal absolute values but with antiparallel 40 coupling between the Fe A and B sublattices were also 41 suggested [4] (for a unit formula of Fe 3 O 4 : F e B µ L = 42 1 µ B and F e A µ L = −1 µ B). A summary of the orbital 43 and spin magnetic moments reported in literature using 44 various techniques is shown in Fig. S1. These large dis-45 crepancies regarding an essential quantity to many Mott 46 insulators [23] ask for a new approach. 47 In this work we employed a combination of Fe K-edge 48 XMCD and 1s2p RIXS-MLAD measurements to investi-49 gate the orbital magnetic moment of Fe in Fe 3 O 4. Exper-50 iments at the Fe K-edge (1s → 3d + 4p excitations) have 51 a probing depth of few µm and hence surface effects are 52 negligible offering a valuable advantage over L 2,3-edge 53 measurements. We quantified the average orbital mag-54 netic moment by performing K-edge XMCD. The accu-55 rately measured 1s2p RIXS-MLAD signal was used to 56 determine the average square orbital magnetic moment 57 which complements the average quantity obtained from 58 XMCD. A difference between the orbital magnetic mo-59 ment predicted by both experiments indicates compensa-60 tion: the orbital magnetic moments of the Fe ions must 61 be either antiparallel or non-collinear. 62 Guided by theoretical calculations, we show that the 63 only possibility to explain both of our experimental re-64 sults is the existence of a non-collinear magnetic orbital 65 ordering that can tilt the orbital magnetic moment as 66 large as 82 • away from the spin magnetic moment. We 67 proposed a model for this non-collinear orbital magnetic 68 ordering and inferred the presence of a dynamical distor-69 tion related to the X 3 phonon mode in the high tempera-70 ture phase. Our model imposes strong restrictions on the 71 candidate mechanisms for the Verwey transition [10, 24]. 72 We investigated highly stoichiometric (001), (110) and 73 (111) Fe 3 O 4 single crystals at room temperature. The av-74 erage orbital magnetic moment projected along the mag-75 netic field direction can be quantified by performing Fe K 76 pre-edge XMCD measurements [22]. Three main dichroic 77 features can be seen at E I = 7112.7 eV, E II = 7114 eV 78 and E III = 7115.1 eV with only significant angular de-79</p>
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