Dmitri
Mitcov
a,
Mikhail
Platunov‡
b,
Christian D.
Buch
a,
Anders
Reinholdt§
a,
Anders R.
Døssing
a,
Fabrice
Wilhelm
b,
Andrei
Rogalev
*b and
Stergios
Piligkos
*a
aDepartment of Chemistry, University of Copenhagen, Universitetsparken 5, DK-2100, Copenhagen, Denmark. E-mail: piligkos@chem.ku.dk
bESRF – The European Synchrotron, CS 40220, 38043 Grenoble Cedex 9, France. E-mail: rogalev@esrf.fr
First published on 30th July 2020
Magnetochiral dichroism (MΧD) originates in the coupling of local electric fields and magnetic moments in systems where a simultaneous break of space parity and time-reversal symmetries occurs. This magnetoelectric coupling, displayed by chiral magnetic materials, can be exploited to manipulate the magnetic moment of molecular materials at the single molecule level. We demonstrate herein the first experimental observation of X-ray magnetochiral dichroism in enantiopure chiral trigonal single crystals of a chiral mononuclear paramagnetic lanthanide coordination complex, namely, holmium oxydiacetate, at the Ho L3-edge. The observed magnetochiral effect is opposite for the two enantiomers and is rationalised on the basis of a multipolar expansion of the matter–radiation interaction. These results demonstrate that 4f–5d hybridization in chiral lanthanoid coordination complexes is at the origin of magnetochiral dichroism, an effect that could be exploited for addressing of their magnetic moment at the single molecule level.
MΧD can be harnessed by electromagnetic radiation from microwaves30 to hard X-rays,17,18,20 irrespective of its polarization and for a large variety of systems exhibiting simultaneous breaking of parity and time reversal symmetries. In diamagnetic or paramagnetic materials, time reversal can be broken by application of an external magnetic field resulting in occurrence of a field induced magnetic moment. The experimental manifestation of MΧD is the differential absorption of light with respect to the relative orientation of the wave vector of the incident light, k, and the applied external magnetic field, B, the effect being of opposite sign for enantiomers. In chiral magnetic materials, the observation of magnetochiral dichroism and birefringence is concomitant with natural circular dichroism (NCD) and birefringence and magneto-circular dichroism (MCD) and birefringence, associated with odd parity and a spontaneous or induced magnetization, respectively.14,31–33 Thus, the experimental difficulty lies in eliminating the effects of all other anisotropies which are typically larger than MΧD and therefore mask its weak response.
Ĥint = Ê1 + 1 + Ê2 + 2 + Ê3 + … | (1) |
The absorption cross-section, σ, is proportional to the square of the transition moment, 〈i|Ĥint|f〉, with |i〉 and |f〉 the initial and final states, respectively. We may write quantitatively:
σ ∝ σ0 + σ1 + σ2 | (2) |
(3) |
In the context of X-ray spectroscopy, magnetic dipole transitions (1) are very weak34 and can be neglected. On the contrary, ample experimental evidence demonstrates significant electric quadrupole contributions to hard X-ray absorption spectra.35 Thus, optical activity effects in the hard X-ray range arise from interference of electric dipole and electric quadrupole transitions as it has been experimentally demonstrated36–38 and theoretically confirmed.39 These interference contributions average to zero in randomly oriented samples (polycrystalline powders or liquids) and can only be detected on orientation ordered systems, e.g. single crystals. Furthermore, X-ray MΧD (XMΧD) was shown to be due to orbital toroidal currents in absorbing atoms,20,40 which are relevant to many phenomena, ranging from multiferroicity to superconductivity.
MΧD is, in general, a very weak effect with only very few examples reported to date. A prediction of MΧD was made by Groenewege31 in 1962 and was first observed in 1997 by Rikken and Raupach, in the visible luminescence spectra of a chiral Eu(III) complex.15 MΧD has since only been observed for a Ni(II) complex,16 two-dimensional chiral Cr(III)–Mn(II) ferrimagnets,21,22 for a diamagnetic molecular Zn(II) aggregate,23 for some diamagnetic organic compounds,24–26 in the photolysis of Cr(III) oxalates41,42 and in Bragg scattering.43 There are even fewer reports on observation of XMΧD. XMΧD was first observed in the Cr2O3 antiferromagnet17 and subsequently in the GaFeO3 ferrimagnet18 and more recently in Mn(II) and Co(II) molecule-based helices.20 The first attempt to observe XMΧD for molecular lanthanoid (Ln) complexes was performed on the 3d–4f coordination complex TbNi6.19 However, the validity of these results is not firmly established as the reported experimental XMΧD is too large for a paramagnetic system measured at room temperature and at relatively low magnetic field (1 T). We present herein the first example of unambiguous experimental observation of XMΧD for a mononuclear Ln complex, namely, Na5[Ho(ODA)3](BF4)2·6(H2O), (1), with ODA2− = oxydiacetate. Such mononuclear Ln-based complexes have been proposed as single-ion magnets44–48 displaying magnetic hysteresis at liquid nitrogen temperatures,49,50 electron-based qubits,51–54 coupled qubit–qudits55,56 and single molecule transistors.3–5,57–60
The crystal structures of Ln oxydiacetates have been previously described in detail.61 In 1, Ho(III) coordinates to three virtually planar tridentate ODAs to form the two enantiomers (Λ and Δ) of the nine-coordinate complex anion, [Ho(ODA)3]3− (Fig. 1A). The coordination geometry around Ho(III) is distorted face-centred trigonal prismatic (D3). 1 undergoes spontaneous resolution upon crystallisation. The crystal structures for 1Λ and 1Δ were refined in the trigonal R32 Sohncke space group with Flack parameters62,63 of 0.008(4) and 0.015(4), respectively (Table S1†).
In search of XMΧD of 1 we performed experiments at the L3 absorption edge of Ho exploiting the ESRF beamline ID12 dedicated to polarization dependent X-ray spectroscopy. At this edge, absorption of an incident X-ray photon promotes a 2p3/2 core electron into empty 5d or 6s valence states via the allowed electric dipole transitions (Δl = ±1) or to 6p or 4f states (Δl = 0,+2) via electric quadrupole transitions. Such quadrupolar 2p–4f transitions are easily distinguishable either in X-ray MCD (XMCD) or in resonant inelastic X-ray scattering spectra at the L3-edge64,65 of rare-earths, whereas their contribution at the L2-edge is more difficult to disentangle.66
We used left (L) or right (R) circularly polarised X-rays whose wave vector, k, was parallel (+) or antiparallel (−) to the external magnetic field, B. To identify two enantiomeric single crystals of 1 each displaying an optimal response, X-ray NCD (XNCD) spectra were recorded at room temperature on several crystals already characterised by X-ray crystallography, as crystals of macroscopically similar appearance do not yield the same XNCD intensity (Fig. S1†). This is because the penetration depth of X-rays at the L3-edge of rare-earths is typically of the order 10 microns, making the obtained response sensitive to the structural quality of this near-surface layer. The identified crystals were then inserted into an experimental station equipped with a 17 T superconducting magnet and a constant flow helium cryostat, where they were mounted on a cold finger oriented with the crystallographic, trigonal, c axis parallel to k and B (Fig. 1b and c).
For each enantiomerically pure crystal we acquired four distinct absorption spectra corresponding to different experimental configurations for the relative orientation of k and B and the polarization of X-rays, namely, L+, L−, R+, R−. From these, one can obtain the polarization averaged X-ray absorption spectrum (XAS) and the three dichroic contributions (XNCD, XMCD and XMΧD), allowed by the crystal symmetry, as:
XAS = [(L+) + (R+) + (L−) + (R−)]/4 | (4) |
XNCD = [{(L+) − (R+)} + {(L−) − (R−)}]/2 | (5) |
XMCD = [{(L+) − (R+)} − {(L−) − (R−)}]/2 | (6) |
XMΧD = [{(L+) + (R+)} − {(L−) + (R−)}]/2 | (7) |
The underlying physics of these three dichroisms is very different and the corresponding effective operators are very distinct: of purely electric charge nature for XNCD, of purely magnetic nature for XMCD, whereas magnetoelectric for XMΧD.40,67 The normalised XAS, XNCD, XMCD and XMΧD spectra of 1Λ and 1Δ are shown in Fig. 2. Note that the XAS and XMCD spectra should be strictly identical for two enantiomeric crystals, whereas the XNCD and XMΧD spectra should be of opposite sign. This is precisely what we observed experimentally. The XAS spectrum is dominated by the electric dipole allowed (Ê1·Ê1) transitions to localized 5d orbitals, giving rise to a very strong resonance at 8078 eV, the so-called “white-line”. Dipole allowed transitions to extended 6s states are much weaker and cannot be easily disentangled from the XAS spectrum. Electric quadrupole transitions (Ê2·Ê2) to strongly localized unoccupied 4f orbitals are also very weak and are barely noticeable in the XAS spectrum as a pre-edge feature at 8069 eV.68 The quadrupole contribution to the spectrum appears at about 9 eV below the “white-line” because of much stronger Coulomb interaction of the 4f electrons with the 2p3/2 hole.69
Fig. 2 Normalised X-ray dichroic traces recorded on 1Λ and 1Δ at the Ho L3-edge, at 2.7 K with an applied magnetic field of 4 T. (a) XAS (right scale) and XMCD (left scale). (b) XNCD and (c) XMΧD. |
The low temperature XNCD spectra are practically noise-free and have the same spectral shape and intensity as those measured at room temperature. This indicates that there is no symmetry change of the crystals in the studied temperature range. The intensity of the normalized XNCD is approaching 1%, which is significantly larger than previously reported values for XNCD at the L-edge of chiral Ln complexes.37,70 XNCD measures the mixing of electronic states with opposite parity in the ground state, which is at the origin of the non-linear optical properties of chiral systems. In the case of an L3 absorption edge, the selection rules for the Ê1·Ê2 interference term39 allow only transitions to the intra-atomic (d, p) and (d, f) hybridized states. The relatively weak XNCD intensities at photon energies corresponding to transitions to the 4f states (ca. 8069 eV) can reasonably be explained by their very strong localization and quasi-atomic character. As a result, they are only weakly hybridised with the 5d states and very little affected by the local chiral surroundings. The largest XNCD signal is observed at about 30 eV above the “white-line” and is extended over a very broad energy range of at least 70 eV. This indicates that extended intra-atomic states (6d, 6p, …) are strongly hybridized and strongly affected by the chiral ligand arrangement.
Contributions from quadrupole transitions are expected to be more pronounced in the XMCD spectra of Ho at the L3 edge because the 4f states have intrinsically magnetic character. For crystals that exhibit XNCD, the true artefact-free XMCD can be obtained only as a combination of four spectra measured independently, as given by eqn (6). The XMCD signal is obtained as the difference of two XNCD spectra measured with opposite directions of applied magnetic field. However, the microscopic origin of these two circular dichroisms is fundamentally different; only pure dipole transitions or absorption terms quadratic in k (see eqn (3)) contribute to XMCD. The XMCD intensity is about an order of magnitude larger than the XNCD one and contrary to XNCD the spectra are identical for both enantiomers. They consist of two main features: a large positive peak close to the XAS “white-line”, arising from dipole transitions to unoccupied 5d states and a well-defined negative peak about 8 eV lower in energy which is due to quadrupole transitions to unoccupied 4f states. This spectral shape is typical for Ho(III) ions66 and the assignment of the spectral features is in line with results of X-ray resonant magnetic scattering of Ho metal.71
The magnetic field dependence of the XMCD of 1 at 2.7 K (Fig. S2†) displays a rapid increase between 0 and 4 T, above which a more slow linear increase is observed, up to 17 T. Given that the XMΧD response is expected to be proportional to the sample's magnetisation,20 measurements were performed at applied magnetic fields of ±4 T to optimise between the field sweep waiting time for successive measurements and the sample's magnetization (about 80% of the maximum reachable value). This turns out to be very important because the measured XMΧD is at least two orders of magnitude weaker than the XMCD. XMΧD spectra were extracted from the same four experimental spectra according to eqn (7) where absorption of unpolarised X-rays was simulated by the sum of L and R spectra.
The same electric dipole-quadrupole interference terms (Ê1·Ê2) as for XNCD, but combined with the orbital toroidal current in the hybridised ground states, are responsible for XMΧD. Noisy but clearly observable XMΧD spectra of opposite sign for 1Λ and 1Δ were detected at the pre-edge (8069 eV) and the main (8078 eV) absorptions but not in the extended region. This indicates that the nonmagnetic empty extended states like 6p, or 6d do not contribute to XMΧD signal. On the contrary, the hybridised 4f–5d orbitals that contain a significant amount of orbital angular momentum give a sizeable contribution and carry a toroidal orbital moment. However, the fact that the XMΧD response depends on the same electric dipole-quadrupole interference terms (Ê1·Ê2) as for XNCD and on the orbital toroidal current of the hybridised states carrying the magnetic moment, responsible for XMCD, does not mean that the XMΧD response is simply the product of XMCD and XNCD. Even though the amplitude of the XMΧD response is in a first place indicating so, the sign of the XMΧD does not confirm this interpretation. It is true that the XMΧD spectral shape looks somewhat similar to the XNCD one and that the main features of the former have the same sign as these of the latter. However, these are not the same spectra. Furthermore, they are neither the product of the XNCD and XMCD responses. The XMCD signal changes sign around 8.072 keV. At the same energy the XNCD response also changes sign. Thus if the XMΧD response was defined by the product of the XMCD and XNCD responses, its sign should be conserved. However, it is experimentally observed that this is not the case since a clear sign change of the XMΧD response is observed around 8.072 keV. Furthermore, the XMΧD signal vanishes above 8.085 keV whereas the XNCD features are the most intense in this energy interval.
These findings confirm that X-ray spectroscopy is an excellent technique for the investigation of local chiral and magnetic properties in Ln-based coordination complexes, provided that the studied single crystals are of high enough enantiopurity to display strong XNCD, which is crucial for the observation of XNCD and XMΧD.
Footnotes |
† Electronic supplementary information (ESI) available: Details on the synthesis and crystallographic characterization of 1. CCDC 1899691 for 1Δ and 1899692 for 1Λ. For ESI and crystallographic data in CIF or other electronic format see DOI: 10.1039/d0sc02709j |
‡ Current address: Kirensky Institute of Physics, Federal Research Center KSC SB RAS, Akademgorodok 50, Bld. 38, 660036 Krasnoyarsk, Russia. |
§ Current address: Department of Chemistry, University of Pennsylvania, 231 South 34th Street, Philadelphia, PA 19014-6323. |
This journal is © The Royal Society of Chemistry 2020 |