# Magneto-Chiral Dichroism of Chiral Lanthanide Complexes in the Context of Richardson's Theory of Optical Activity

Langit Cahya Adi, Oliver Willis, Alessio Gabbani, Geert Rikken, Lorenzo Di Bari, Cyrille Train, Francesco Pineider, Francesco Zinna, Matteo Atzori

<figure><img src="image_1.png" /></figure>

## ► To cite this version:

Langit Cahya Adi, Oliver Willis, Alessio Gabbani, Geert Rikken, Lorenzo Di Bari, et al., Magneto-Chiral Dichroism of Chiral Lanthanide Complexes in the Context of Richardson's Theory of Optical Activity. Angewandte Chemie International Edition, 2024, 10.1002/anie.202412521. [http://dx.doi.org/10.1002/anie.202412521](http://dx.doi.org/10.1002/anie.202412521)

HAL Id: hal-04830376

https://hal.science/hal-04830376v1

Submitted on 11 Dec 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_2.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Magneto-Chiral Dichroism of Chiral Lanthanide Complexes in the Context of Richardson's Theory of Optical Activity

Langit Cahya Adi,[a] Oliver G. Willis,[b] Alessio Gabbani,[b,c] Geert L. J. A. Rikken,[a] Lorenzo Di Bari,[b] Cyrille Train,[a] Francesco Pineider,[b,c] Francesco Zinna,[*b] and Matteo Atzori*[a]

[a] Dr. Langit Cahya Adi, Prof. Cyrille Train, Dr. Geert Rikken, Dr. Matteo Atzori
Laboratoire National des Champs Magnétiques Intenses, CNRS, Univ. Grenoble Alpes, INSA Toulouse, Univ. Toulouse Paul Sabatier, EMFL
F-38042 Grenoble, France
Email: matteo.atzori@lncmi.cnrs.fr

[b] Dr. Olivier G. Willis, Dr. Alessio Gabbani, Prof. Lorenzo Di Bari, Prof. Francesco Pineider, Dr. Francesco Zinna
Dipartimento di Chimica e Chimica Industriale, Università di Pisa
I-56124 Pisa, Italy
Email: francesco.zinna@unipi.it

[c] Dr. Alessio Gabbani, Prof. Francesco Pineider
Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze
I-50019 Sesto Fiorentino (FI), Italy

Supporting information for this article is given via a link at the end of the document.

**Abstract:** Here we report on the Magneto-Chiral Dichroism (MChD) detected through visible and near-infrared light absorption of two enantiomeric pairs of Er"" and Tm"" chiral complexes featuring a propeller-like molecular structure. The magnetic properties show typical features of isolated paramagnetic ions associated with $^{4}_{15/2}$ and $^{3}$H$_{6}$ ground state terms. MChD spectroscopy shows high $g_{MChD}$ dissymmetry factors of ca. 0.12 T$^{-1}$ and 0.05 T$^{-1}$ ($T = 4.0$ K and **B** = 1.0 T) for Er"" and Tm"", respectively, associated with the magnetic-dipole allowed $^{4}_{13/2} \leftarrow \^{4}_{15/2}$ and $^{3}$H$_{5} \leftarrow \^{3}$H$_{6}$ transitions. MChD signals of the two complexes were detected up to room temperature and under magnetic fields up to 5.0 T. For the first time, the MChD results reported here are discussed in the context of the Richardson theory of lanthanide optical activity and provide clear indications on the strongest MChD-active electronic transitions of lanthanide complexes.

## Introduction

The chiroptical activity of molecular systems in both light absorption and emission enables several technological applications in fields ranging from chiral photonics to optoelectronics.[1,2] Chiral molecules can be used to prepare chiral organic light-emitting diodes (OLEDs), light polarization sensitive phototransistors and spin filtering devices, to cite a few.[3-10] A thorough understanding of the chiroptical activity of the molecular components is therefore essential to design and prepare efficient molecular materials for the above-mentioned applications.

Characteristic chiroptical properties shown by chiral molecular systems are Natural Circular Dichroism (NCD) and Birefringence (NCB), which represent a differential absorption and refraction of left- and right-circularly polarized light, respectively.[11,12] Other, at first sight similar properties are Magnetic Circular Dichroism (MCD) and Magnetic Circular Birefringence (MCB) that correspond to a differential absorption and refraction of circularly polarized light propagating parallel to a magnetic field **B**.[13,14]

A less investigated magneto-optical property shown uniquely by chiral systems is Magneto-Chiral Anisotropy (MChA). MChA refers to the ability of chiral magnetized systems to differentially absorb, emit or refract unpolarized light when the light wavevector **k** is parallel to **B**.[15-19] The resulting optical phenomena are referred as Magneto-Chiral Dichroism (MChD) and Magneto-Chiral Birefringence (MChB).[11,15,20,21] Analogous to NCD, MChD provides spectral responses equal in magnitude but opposite in sign for two enantiomers, and as in MCD, the signal intensity is intrinsically correlated to the system's magnetization, but does not require polarized light to be observed.[22-24]

After the first demonstration of MChA in emission on an Eu"" chiral complex,[16] lanthanide f-f transitions have been proven to be suitable for the observation of strong MChD activity also through light absorption,[25-31] with among the strongest $g_{MChD}$ dissymmetry factors (*vide infra*) reported to date.[26,30,32]

Most lanthanide complexes are paramagnetic systems, characterized by intrinsically large spin-orbit couplings. Some Ln"" ions feature electronic transitions allowed by magnetic-dipole selection rules in the vis-NIR range.[33-35] The key-role of magnetic-dipole allowed transitions to observe strong MChD responses and large $g_{MChD}$ dissymmetry factors was anticipated by the seminal theoretical studies on magneto-chiral effects by both Wagnière[20] and Barron and Vrbancich[15] and it has been recently experimentally demonstrated by some of us.[32]

The strong MChD activity of magnetic-dipole allowed transitions stems from the fact that MChA depends on magnetic (**m**) and electric (**μ**) transition dipole moments as the **μm**"" product.[20] The two **m** terms have different origins. **m**' is associated with the magnetic-dipole moment tensors of the electronic transitions and **m**" to the external magnetic field **B**. It is instructive to recall here that NCD depends on the **μm**' product, while MCD on the **μμm**"" product.[20]

These considerations point out that strong MChD signals should be observed for the electronic transitions that are characterized by a strong natural optical activity (NCD-active).[36] On the other hand, the shape of the signals, their temperature and
magnetic field dependence are determined by the interaction with **B** as for MCD. This latter aspect is at the basis of the microscopic MChD molecular theory developed by Barron and Vrbancich. [15] Barron and Vrbancich first described the molecular properties tensors associated to MChD in the frame of a semi-classical formalism, and then, they developed a quantum mechanical description of the phenomenon, by deriving magneto-chiral analogous of the Faraday A-, **B**- and C-terms to describe the origin, the shape and the temperature dependence of MChD signals.[15] Their characteristics are indeed very similar to those for the Faraday effect. The magneto-chiral A-terms originate in the Zeeman splitting of the ground state induced by the magnetic field, they are temperature independent and have a dispersive lineshape. The **B**-terms originate in a mixing of ground and/or excited states by the magnetic field, they are temperature independent and have an absorptive lineshape. The C-terms involve the change of Boltzmann population of the ground state split by the magnetic field, and their intensity and shape are temperature dependent.[15] This theory has been recently validated by experimental studies[26,37] and theoretical calculations.[37]

In contrast, selection rules that define the relative intensity of MChD activity for *d-d* and *f-f* electronic transitions have never been clearly defined.

In 1980, Richardson derived for the first time the selection rules that govern the relative intensity of the chiroptical properties (NCD and Circularly Polarized Luminescence, CPL) associated with the *f-f* electronic transitions of Ln<sup>III</sup> chiral complexes.[38] The theory is based on the calculation of the electric- and magnetic-dipole transition moments vectors and the rotatory strength. This allowed to derive the selection rules based on the *S*, *L*, *J* quantum numbers (Table S1). Then, the perturbations induced by spin-orbit coupling were considered at the first order and 4f-electron/crystal field interactions was treated at the second order. These are necessary to produce non-vanishing magnetic-dipole and electric-dipole transitions moments for various types of transitions (Table S2). Finally, the transitions were categorized as a function of the electric-dipole strength *E*, the rotatory strength *R* and the dissymmetry factor *D*. Those associated with the *I* and *II* categories have the highest relative electric-dipole and rotatory strength and the highest dissymmetry factor, while those with *III* and *IV* exhibit the weakest values (Table S3).[38]

Richardson's analysis, although limited to term-to-term transitions and not considering the point symmetry at the lanthanide center induced by the crystal/ligand field, allowed one to identify the most CD- and CPL-active lanthanide transitions and those associated with the highest dissymmetry factors.[38]

The aim of this work is to probe the relevance of Richardson's theory of lanthanide optical activity for MChD. We have selected homoleptic chiral lanthanide complexes of Er<sup>III</sup> and Tm<sup>III</sup> with BINOL chiral ligands (BINOL = 1,1'-bi-2-naphtholate)[39] for three reasons. First, their mononuclear homoleptic homometallic nature makes them model systems to experimentally investigate *f-f* electronic transitions without adding structural and spectral complexity as in the case of heterometallic 3d-4f chiral clusters;[28,32] second, Er<sup>III</sup> and Tm<sup>III</sup> feature a multitude of absorptions bands related to *f-f* electronic transitions with

different character, a magnetic-dipole allowed one (⁴I₁₃/₂ ← ⁴I₁₅/₂ and ³H₅ ← ³H₆, for Er<sup>III</sup> and Tm<sup>III</sup>, respectively) and several electric-dipole induced transitions; third, their magnetic-dipole allowed transitions were classified by Richardson as E-I, R-I and D-II, and therefore promising to observe strong chiroptical activity as it has been experimentally observed recently with room-temperature NCD measurements,[40] while the other transitions belong to lower Richardson's categories and are associated with a weaker chiroptical activity and lower dissymmetry factors.[38]

Based on these considerations, if the Richardson's theory for optical activity also holds for MChD, one should observe strong MChD signals for the ⁴I₁₃/₂ ← ⁴I₁₅/₂ and ³H₅ ← ³H₆ transitions, and much weaker MChD responses and *g*<sub>MChD</sub> values for the others.

## Results and Discussion

The enantiopure Ln<sup>III</sup>(X)-BINOL chiral complexes formulated as [TMG-H]<sub>3</sub>[Ln(R/S-BINOL)<sub>3</sub>] (Ln<sup>III</sup> = Er<sup>III</sup> (Er), Tm<sup>III</sup> (Tm)) (TMG-H = tetramethyl guanidinium; BINOL = 1,1'-bi-2-naphtholate) described by Walsh and coworkers were selected for this study. They were synthesized following the reported procedures.[39] Slow vapor diffusion of heptane into a dichloromethane solution provides moisture inert cubic crystals suitable for MChD measurements. Er and Tm are isostructural complexes that crystalize in the I₂₃ chiral cubic space group with one crystallographically independent molecule in the unit cell (Z = 8). The molecular structure shows a Ln<sup>III</sup> ion hexacoordinated by the six oxygen donors of the three binaphtholate ligands in a distorted octahedral tris-chelated coordination geometry (D<sub>3</sub> point group symmetry). Three tetramethyl guanidinium cations stabilized the negative charge and the low coordination number coordination geometry of the Ln<sup>III</sup> ion with directional bifurcated hydrogen-bonds pointing towards two different binaphtholate ligands (Figure 1).[39] The *S* and *R* chirality of the ligands induces a *A* and *Δ* chirality centered on the Ln<sup>III</sup> ion, respectively, resulting in a propeller-like chiral molecular complex (Figure 1).[26,41]

<figure><img src="image_3.png" /><figcaption>**Figure 1.** Molecular structures of complexes Er and Tm [ref. 39] where the coordination geometry and the chiral configuration of the Ln<sup>III</sup> ion, the hydrogen-bonds between the cation and the anionic ligands and the propeller-like overall structure are highlighted.</figcaption></figure>

NCD and MCD spectra were recorded in solution at room temperature, the latter measured under an applied magnetic field of **B** = 1.4 T (Figure S1). The NCD properties of complexes Er
and **Tm** were already reported[40] and hence, here we briefly recall the main salient features. **Er** shows the strongest NCD activity for the ⁴I₁₃/₂ ← ⁴I₁₅/₂ transition manifold falling between 1430 and 1600 nm and **Tm** for the ³H₅ ← ³H₆ manifold centered at ca. 1210 nm. While the NCD response of **Er** is composed by at least three strong contributions of similar intensity associated with the crystal field splitting of the first excited state (vide infra), 2 shows one main contribution at 1208 nm. The calculated gNCD dissymmetry factors (equation S1) are ca. +0.26/-0.15, -0.34/+0.40 and +0.40/-0.32 at 1514, 1524 and 1539 nm for the Er-(R) and Er-(S) respectively and +0.38 and -0.31 for Tm-(S) and Tm-(R). These values, although they are not the highest reported to date for the same transitions,[40] are particularly high, in agreement with the Richardson's theory of lanthanide optical activity. Such values indicates that *m'* is significant with respect to μ (*m'* ≈ 0.1μ).

The MCD spectra show signals associated with the above-mentioned transitions that have a similar shape, although they are more fine-structured than the NCD bands, probably as a consequence of the Zeeman splitting of both ground and excited states. The gMCD values (equation S2) are of the order of 10⁻² T⁻¹ at room temperature. The complexes being paramagnetic, much higher values for gMCD can be expected at low temperatures.

The magnetic properties of compounds Er and Tm were investigated by magnetic susceptibility measurements on microcrystalline powdered samples of Er-(R) and Tm-(S) (Figures S2 and S3). The room-temperature molar magnetic susceptibility times the temperature, χM T, assumes values of 11.82 and 6.85 cm³ K mol⁻¹ for Er-(R) and Tm-(S), respectively, that are consistent with the expected values (11.48 cm³ K mol⁻¹ and 7.15 cm³ K mol⁻¹) for one isolated Erill (J = 15/2, gJ = 6/5) and Tmill (J = 6, gJ = 7/6) ion.[42,43] As the temperature is decreased from 300 K to 100 K, the χM T values show a gradual linear decrease, while upon further lowering of the temperature, they decrease down to 5.09 and 0.84 cm³ mol⁻¹ K at 2.0 K, for Er-(R) and Tm-(S) respectively, as expected by the thermal depopulation of Stark levels in lanthanide complexes.[44] At T = 2.0 K, the magnetization saturates at ca. 4.5 and 2.0 μB Er-(R) and Tm-(S) respectively, in

agreement with typical values observed for isolated Erill (M₅ = 4.7 μB) and Tmill (M₅ = 2.5-3.5 μB) centers[45,46] without strong magnetic anisotropy and with micro-crystallites randomly oriented with respect to the external magnetic field.[43]

Absorption spectra were recorded on single crystals of Er-(R) and Tm-(R) with vis-NIR unpolarized light propagating along the *a* cubic axis. The thermal variations (4.0-290 K) of the absorption spectra in the regions of interest (430-1000 nm and 1400-1600 nm for Er and 620-850 nm and 1100-1300 nm for Tm) are reported in Figures S4 and S5. Multiple sharp absorption peaks associated with the *f-f* electronic transitions involving the ⁴I₁₅/₂ ground state and the spectroscopic levels deriving from the ⁴I, ⁴F, ⁴S, and ²H spectroscopic terms of the Erill ion are observed for Er (Figure S4) and the ³H₆ ground state and the spectroscopic levels ³H₄ and ³F₃ of the Tmill ion for Tm (Figure S5). The assignment of the absorptions manifolds is reported in Table 1.

The investigated electronic transitions provide complex absorptions manifolds as a result of the crystal field splitting of the excited states *J* levels in up to *J*+1 *M*<sub>*J*</sub> states, given that ±*M*<sub>*J*</sub> forms Kramers doublets. Focusing on the manifolds associated with the ⁴I₁₃/₂ ← ⁴I₁₅/₂ and ³H₅ ← ³H₆ magnetic dipole-allowed |Δ*J* = 1| transitions of Er and Tm respectively, the low temperature absorption spectrum (T = 4.0 K) of Er indeed shows several peaks associated with the possible transitions between the lowest energy sublevel of the ⁴I₁₅/₂ ground multiplet, which is the only one thermally populated at 4.0 K, and the seven Kramers doublets of the first excited state (Figure S4b). The position and the relative intensity of the various contributions is dictated by the ligand field splitting and the symmetry of the Erill coordination geometry. The absorption coefficients and the fine-structure of the ⁴I₁₃/₂ ← ⁴I₁₅/₂ manifold are in agreement with previous findings.[32] The same considerations are valid for the low temperature NIR absorption spectrum of Tm in spite the fact that a lower number of transitions between sublevels is observed. Tm shows three main peaks, two of them associated with much higher absorption coefficients than that of the Erill ⁴I₁₃/₂ ← ⁴I₁₅/₂ manifold, in which several transitions of similar energy are probably convoluted (Figure S5b).[40]

<table><caption>**Table 1.** Assignment of the Erill and Tmill absorption peaks, transition properties, Richardson's classification [38] and gMCHD values (T = 4.0 K and B = 1.0 T).</caption><thead><tr><th>Compound</th><th>λ (nm)</th><th>Electronic transition</th><th>Transition properties</th><th>Richardson classification</th><th>g<sub>MCHD</sub> (T<sup>-1</sup>), λ (nm)</th></tr></thead><tbody><tr><td>Er</td><td>475-495</td><td>⁴F<sub>7/2</sub> ← ⁴I<sub>15/2</sub></td><td>ΔJ = 4, ΔL = 3, ΔS = 0</td><td>E-I, R-II, D-III</td><td>0.001(1), 450.2</td></tr><tr><td>Er</td><td>505-530</td><td>²H<sub>11/2</sub> ← ⁴I<sub>15/2</sub></td><td>ΔJ = 2, ΔL = 1, ΔS = 1</td><td>E-III, R-III, D-II</td><td>0.001(1), 522.6</td></tr><tr><td>Er</td><td>540-560</td><td>⁴S<sub>3/2</sub> ← ⁴I<sub>15/2</sub></td><td>ΔJ = 6, ΔL = 6, ΔS = 0</td><td>E-I, R-II, D-III</td><td>0.004(1), 546.3</td></tr><tr><td>Er</td><td>640-670</td><td>⁴F<sub>9/2</sub> ← ⁴I<sub>15/2</sub></td><td>ΔJ = 3, ΔL = 3, ΔS = 0</td><td>E-III, R-III, D-II</td><td>0.03(1), 658.0</td></tr><tr><td>Er</td><td>780-820</td><td>⁴I<sub>9/2</sub> ← ⁴I<sub>15/2</sub></td><td>ΔJ = 3, ΔL = 0, ΔS = 0</td><td>E-III, R-III, D-II</td><td>0.03(1), 800.1</td></tr><tr><td>Er</td><td>960-1000</td><td>⁴I<sub>11/2</sub> ← ⁴I<sub>15/2</sub></td><td>ΔJ = 2, ΔL = 0, ΔS = 0</td><td>E-I, R-II, D-III</td><td>0.03(1), 967.2</td></tr><tr><td>Er</td><td>1450-1550</td><td>⁴I<sub>13/2</sub> ← ⁴I<sub>15/2</sub></td><td>ΔJ = 1, ΔL = 0, ΔS = 0</td><td>E-I, R-I, D-II</td><td>0.12(1), 1514.6</td></tr><tr><td>Tm</td><td>650-700</td><td>³F<sub>3</sub> ← ³H<sub>6</sub></td><td>ΔJ = 3, ΔL = 2, ΔS = 0</td><td>E-III, R-III, D-II</td><td>0.005(1), 685.3</td></tr><tr><td>Tm</td><td>760-805</td><td>³H<sub>4</sub> ← ³H<sub>6</sub></td><td>ΔJ = 2, ΔL = 0, ΔS = 0</td><td>E-I, R-II, D-III</td><td>0.002(1), 794.7</td></tr><tr><td>Tm</td><td>1130-1230</td><td>³H<sub>5</sub> ← ³H<sub>6</sub></td><td>ΔJ = 1, ΔL = 0, ΔS = 0</td><td>E-I, R-I, D-II</td><td>0.047(1), 1213.5</td></tr></tbody></table>
MChD measurements were performed at $T = 4.0$ K with an alternating magnetic field **B** within the 0.0–2.0 T range applied along the light wavevector **k**. Figure 2 shows the **B** dependence of the MChD spectra for Er-(R) and Tm-(S) along the a cubic axis.

MChD signals of opposite sign for the two enantiomers of Er and Tm are observed for each electronic transition detected in absorption (Figure 2 and 3). For Er, the most intense contribution is associated with the $^4I_{13/2} \leftarrow ^4I_{15/2}$ magnetic-dipole allowed transition manifold with three intense contributions at ca. 1533, 1514 and 1505 nm and two less intense contributions at ca. 1528 and 1470 nm (Figure 2). The three electric-dipole induced transitions involving the $^4I_{11/2}$, $^4I_{9/2}$, $^4F_{9/2}$ terms provide weaker $\Delta A_{MChD}$ signals with similar intensity, while those associated with the $^4S_{3/2}$, $^2H_{11/2}$, $^4F_{7/2}$ terms, although still detectable, are close to the detection limit of our experimental setup (Figure 2). For 2, the most intense contribution is associated with the $^3H_5 \leftarrow ^3H_6$ magnetic-dipole allowed transition manifold with one intense contribution at ca. 1213 nm, while the two electric-dipole induced transitions involving the $^3H_4$ and $^3F_3$ terms provide MChD signals with $\Delta A_{MChD}$ a factor ca. 70 and ca. 20 less intense (Figure 3). Interestingly, although the absorption spectrum shows an intense absorption peak at ca. 1190 nm (Figure S5b), only the transition between the lowest energy sublevel of the ground state and the

lowest energy sublevel of the first excited state at ca. 1213 nm provides a strong MChD signal (Figure 3), in agreement with the chiroptical response observed with NCD and MCD spectroscopies (Figure S1).[40]

At 4.0 K, as the magnetic field magnitude increases, the MChD intensity increases following the Brillouin functions of the Erill ion. This is explicitly shown in Figure 2b and 3b for the $\Delta A_{MChD}$ signal associated with the $^4I_{13/2} \leftarrow ^4I_{15/2}$ and $^3H_5 \leftarrow ^3H_6$ manifolds. For both Er and Tm shows that higher $\Delta A_{MChD}$ values can be obtained if **B** is increased further as M does not reach saturation at 2.0 T. We have thus extended our MChD investigations to magnetic fields up to ±5.0 T by taking advantage of the resistive magnets of the LNCMI-CNRS French high magnetic field facility. As expected, between 2.0 and 5.0 T, $\Delta A_{MChD}$ increases further for both Er and Tm, reaching almost saturation at 5.0 T (Figures 2b-3b, and S6-S7). It is interesting to note that in contrast to the low magnetic field regime (0.0-2.0 T), where a clear increase of the MChD intensity at the $\lambda_{max}$ of the signal is observed, above 3.0 T, for both Er and Tm, the overall area of the MChD signal associated with the manifold allows reproducing the Brillouin function, while the contribution at a fixed wavelength ($\lambda_{max}$) saturates, underestimating the total MChD contribution.

<figure><img src="image_4.png" /><figcaption>**Figure 2.** (a) Magnetic field dependence of $\Delta A_{MChD}$ for Er-(R) (blue) and Er-(S) (red) at $T = 4.0$ K. Insets show the details of the most intense MChD signals and the spectroscopic terms associated with the electronic transitions. (b) Magnetic field dependence of $\Delta A_{MChD}$ (integrated area of the MChD signal in the 1450-1550 nm range) compared to the calculated magnetization curve based on the Brillouin function assuming $J = 15/2$, $g_J = 6/5$. The MChD spectra in the 0-5 T range are reported in Figure S6.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>**Figure 3.** (a) Magnetic field dependence of $\Delta A_{MChD}$ for Tm-(R) (blue) and Tm-(S) (red) at $T = 4.0$ K. Insets show the details of the most intense MChD signals and the spectroscopic terms associated with the electronic transitions. (b) Magnetic field dependence of $\Delta A_{MChD}$ (integrated area of the MChD signal in the 1150-1250 nm range) compared to the calculated magnetization curve based on the Brillouin function assuming $J = 6$, $g_J = 7/6$. The MChD spectra in the 0-5 T range are reported in Figure S7.</figcaption></figure>

The analysis of the MChD and absorption spectra ($T = 4.0$ K, $B = 1.0$ T) permits to determine the $g_{MChD}$ dissymmetry factors (equation S3) for the observed transitions (Table 1). It can be clearly seen that for Er the $^{4}\text{I}_{13/2} \leftarrow \^{4}\text{I}_{15/2}$ magnetic-dipole allowed transition, with a strong $\Delta A_{MChD}$ response at $\lambda = 1514.6$ nm and a relative low absorption coefficient for the same fine-structured absorption, provides a $g_{MChD}$ of $0.12(1) \text{ T}^{-1}$. It is instructive to compare this value with that recently reported for the same transition in a chiral $\{\text{Er}_5\text{Ni}_6\}$ metal cluster ($0.24 \text{ T}^{-1}$).[32] In that case, the MChD signal associated with the $^{4}\text{I}_{13/2}$ multiplet provided a single strong signal at 1516.2 nm and several much weaker contributions in the 1450-1550 nm range. In this case, instead, at least three signals of similar MChD intensity are observed due to the given ligand field splitting, reducing the $g_{MChD}$ estimated at a given wavelength.[47]

For Tm, the $^{3}\text{H}_5 \leftarrow \^{3}\text{H}_6$ magnetic-dipole allowed transition, with a strong $\Delta A_{MChD}$ response of ca. $0.75 \text{ cm}^{-1}$ at $\lambda = 1213.5$ nm and an absorption coefficient of ca. $16 \text{ cm}^{-1}$ provides a $g_{MChD}$ of ca. $0.047(1) \text{ T}^{-1}$. Such a value, which represents the first ever reported for Tm$^{III}$, it is relatively strong and not reduced by multiple MChD signals associated with the same multiplet as for the signal described above for Er. Its lower value when compared to that of the Er$^{III}$ electronic transition having the same magnetic-dipole character and the same Richardson classification can be ascribed to the reduced magnetic moment and the lower magnetic anisotropy of the Tm$^{III}$ ion with respect to the Er$^{III}$.[44]

MChD temperature dependence studies within the 4.0-290 K range were performed with an alternating magnetic field of $B = \pm 1.0$ T. Figure 4 shows the $T$ dependence of the MChD spectra for Er-(R) and Er-(S) along the a cubic axis, while that of Tm-(R)

and Tm-(S) is presented in Figure 5. Focusing on the most intense MChD signal of Er, the effect of increasing the temperature from 4.0 K up to ca. 50 K, induces a MChD signal intensity decrease that follows the temperature dependence of the material's magnetization (Figure 4b). In this temperature range, although the overall fine-structure of the MChD signal is rather complex, it can be clearly seen that the MChD signals shapes are mostly of absorption type, indicating that a MChD C term mechanism dominates.[15,26] As the temperature increases further, the spectra shape change, becoming of dispersive-type lineshape, indicating the dominance of a T-independent MChD A term. The complexity of the overall MChD signal associated with the $^{4}\text{I}_{13/2} \leftarrow \^{4}\text{I}_{15/2}$ manifold is considered responsible for the deviation of the MChD intensity with respect to the expected $T$ dependence of the magnetization of Er in the 50-290 K temperature range (Figure 4b). Similar considerations apply to Tm, with the exception that the simpler MChD signal profile associated with the $^{3}\text{H}_5 \leftarrow \^{3}\text{H}_6$ manifold shows a clear change from the dominance of a temperature dependent MChD C term in the low temperature regime (ca. 4.0-50 K) to a temperature independent MChD A term in the high temperature regime (50-290 K) following the material magnetization (Figure 5b).[26,30]

As a consequence of their high $\Delta A_{MChD}$, both complexes show detectable MChD signals at room temperature associated with their respective magnetic-dipole allowed transitions. The $g_{MChD}$ values at $T = 290$ K assume values of ca. $0.013(1) \text{ T}^{-1}(\lambda = 1514.6$ nm) and $0.003(1) \text{ T}^{-1}(\lambda = 1213.5$ nm) for Er and Tm respectively, that are one order of magnitude lower than those observed at $T = 4.0$ K. This is consistent with previous findings.[30,32]
<figure><img src="image_6.png" /><figcaption>**Figure 4.** (a) Temperature dependence of $\Delta A_{MChD}$ for Er-(R) (blue) and Er-(S) (red) at $B = 1.0$ T. Insets show the details of the most intense MChD signals and the spectroscopic terms associated with the electronic transitions. (b) Temperature dependence of $\Delta A_{MChD}$ ($\lambda = 1514.6$ nm) compared to magnetization data.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Figure 5.** (a) Temperature dependence of $\Delta A_{MChD}$ for Tm-(R) (blue) and Tm-(S) (red) at $B = 1.0$ T. Insets show the details of the most intense MChD signals and the spectroscopic terms associated with the electronic transitions. (b) Temperature dependence of $\Delta A_{MChD}$ ($\lambda = 1213.5$ nm) compared to magnetization data.</figcaption></figure>

Overall, these findings show that the relative intensity and the $g_{MChD}$ dissymmetry factors of the investigated f-f electronic transitions follows the Richardson classification of lanthanide optical activity,[38] while the temperature and magnetic field dependence of each MChD signal follows the Barron-Vrbancich theory.[15] This is further corroborated by the MChD studied reported on other lanthanide complexes. The MChD of mononuclear Yb$^{III}$ complexes, featuring a unique $^{2}$F$_{5/2}$ ← $^{2}$F$_{7/2}$ magnetic-dipole allowed transition classified by Richardson as E-I, R-I, D-II, the same as the $^{4}$I$_{13/2}$ ← $^{4}$I$_{15/2}$ for Er$^{III}$ and the $^{3}$H$_{5}$ ← $^{3}$H$_{6}$ for Tm$^{III}$, has shown strong $\Delta A_{MChD}$ responses detectable up to room temperature and among the highest $g_{MChD}$ values.[26,30] On

the contrary, the MChD studies on Dy$^{III}$ ions, that does not have any f-f electronic transition falling in the first classes of the Richardson classification, have indeed shown $g_{MChD}$ one order of magnitude lower than the E-I, R-I, D-II, transitions of Er$^{III}$, Yb$^{III}$ and Tm$^{III}$, and MChD signals that cannot be easily detected up to room temperature.[27,28]

## Conclusion

In conclusion, we investigated the MChD properties of Er$^{III}$ and Tm$^{III}$ mononuclear chiral complexes that have shown remarkable chiroptical activity (NCD) in the NIR range. The main MChD
signals were observed for the same transitions that were identified by Richardson as favorable for the observation of a high NCD-activity, thus characterized by a magnetic-dipole allowed character, high rotatory strength and relatively high dissymmetry factors in the frame of a spin-orbit coupling and crystal field perturbative approach. Such transitions provide $g_{MChD}$ that are one or two orders of magnitude higher than those that do not satisfy the $ΔJ = 0, ±1, ΔS = 0$ and $ΔL = 0$ selection rules and that are classified as weakly NCD responsive. Therefore, Richardson's theory of optical activity can be considered a good basis to identify MChD-active electronic transitions and guide further studies on MChD through light absorption and emission in lanthanide complexes.

These results also call for unprecedented computational studies on the MChD of chiral lanthanide complexes to identify the selection rules that apply between the ground state and excited state manifolds sublevels induced by the crystal field splitting. Indeed, while Richardson's theory allows for the identification of the most promising MChD-active electronic transitions, it does not provide a fine analysis of the different contributions within the involved electronic states. A thorough understanding of the selection rules between spectroscopic terms sublevels associated with symmetry elements of the coordination geometry is expected to guide a fine-tuning the MChD properties of chiral lanthanide complexes by a rational chemical design.

## Acknowledgements

The French National Research Agency (ANR) is acknowledged for financial support through MaChiNaCo (ANR-19-CE09-0018), Switch-MChD (ANR-23-CE07-0003), and PRINCIPE (ANR-23-CE07-0015) projects. This project has received financial support from the CNRS through the MITI interdisciplinary programs through its exploratory research program. We acknowledge the support of the LNCMI-CNRS, member of the European Magnetic Field Laboratory (EMFL). O.G.W is grateful for the financial support received from the European Commission Research Executive Agency, Horizon 2020 Research and Innovation Programme under the Marie Skłodowska-Curie grant agreement No. 859752-HEL4CHIROLÉD-H2020-MSCA-ITN-2019.

**Keywords:** Chirality • Lanthanides • Magneto-Chiral Dichroism • Chiroptical Activity • High Magnetic Fields

## References:

[1] J. Crassous, M. J. Fuchter, D. E. Freedman, N. A. Kotov, J. Moon, M. C. Beard, S. Feldmann, *Nat. Rev. Mater.* **2023**, *8*, 365–371.

[2] H. Kuang, C. Xu, Z. Tang, *Adv. Mater.* **2020**, *32*, 2005110.

[3] J. R. Brandt, F. Salerno, M. J. Fuchter, *Nat. Rev. Chem.* **2017**, *1*, 0045.

[4] Y. Yang, R. C. da Costa, D. Smilgies, A. J. Campbell, M. J. Fuchter, *Adv. Mater.* **2013**, *25*, 2624–2628.

[5] F. Zinna, U. Giovanella, L. Di Bari, *Adv. Mater.* **2015**, *27*, 1791–1795.

[6] O. G. Willis, F. Zinna, L. Di Bari, *Angew. Chem. Int. Ed.* **2023**, *135*, DOI 10.1002/ange.202302358.

[7] S. Ohkoshi, S. Takano, K. Imoto, M. Yoshikiyo, A. Namai, H. Tokoro, *Nat. Photon.* **2014**, *8*, 65–71.

[8] B. L. Feringa, *Acc Chem Res* **2001**, *34*, 504–513.

[9] R. Jankowski, M. Wyczesany, S. Chorazy, *Chem. Commun.* **2023**, *59*, 5961–5986.

[10] J. J. Zakrzewski, M. Liberka, J. Wang, S. Chorazy, S. Ohkoshi, *Chem. Rev.* **2024**, *124*, 5930–6050.

[11] L. D. Barron, *Molecular Light Scattering and Optical Activity*, Cambridge University Press, **2004**.

[12] L. D. Barron, *Chem. Soc. Rev* **1986**, *15*, 189.

[13] P. J. Stephens, *J. Chem. Phys.* **1970**, *52*, 3489.

[14] J. Mack, M. J. Stillman, N. Kobayashi, *Coord. Chem. Rev.* **2007**, *251*, 429–453.

[15] L. D. Barron, J. Vrbancich, *Mol. Phys.* **1984**, *51*, 715–730.

[16] G. L. J. A. Rikken, E. Raupach, *Nature* **1997**, *390*, 493–494.

[17] G. L. J. A. Rikken, *Magneto-Chiral Dichroism and Birefringence, in Comprehensive Chiroptical Spectroscopy Vol. 1*, Wiley-VCH Verlag GmbH & Co., **2012**.

[18] M. Atzori, G. L. J. A. Rikken, C. Train, *Chem. Eur. J.* **2020**, *26*, 9784–9791.

[19] M. Atzori, C. Train, E. A. Hillard, N. Avarvari, G. L. J. A. Rikken, *Chirality* **2021**, *33*, 844–857.

[20] G. H. Wagnière, *Chem. Phys.* **1999**, *245*, 165–173.

[21] G. Wagnière, A. Meier, *Chem. Phys. Lett.* **1982**, *93*, 78–81.

[22] C. Train, R. Gheorghe, V. Krstic, L.-M. Chamoreau, N. S. Ovanesyan, G. L. J. A. Rikken, M. Gruselle, M. Verdaguier, *Nat. Mater.* **2008**, *7*, 729–734.

[23] M. Atzori, I. Breslavetz, K. Paillot, K. Inoue, G. L. J. A. Rikken, C. Train, *J. Am. Chem. Soc.* **2019**, *141*, 20022–20025.

[24] M. Atzori, I. Breslavetz, K. Paillot, G. L. J. A. Rikken, C. Train, *J. Mater. Chem. C* **2022**, *10*, 13939–13945.

[25] F. Pointillart, M. Atzori, C. Train, *Inorg. Chem. Front.* **2024**, *11*, 1313–1321.

[26] M. Atzori, K. Dhbaibi, H. Douib, M. Grasser, V. Dorcet, I. Breslavetz, K. Paillot, O. Cador, G. L. J. A. Rikken, B. Le Guennic, J. Crassous, F. Pointillart, C. Train, *J. Am. Chem. Soc.* **2021**, *143*, 2671–2675.

[27] M. S. Raju, K. Dhbaibi, M. Grasser, V. Dorcet, I. Breslavetz, K. Paillot, N. Vanthuyne, O. Cador, G. L. J. A. Rikken, B. Le Guennic, J. Crassous, F. Pointillart, C. Train, M. Atzori, *Inorg. Chem.* **2023**, *62*, 17583–17587.

[28] X. Wang, S.-Q. Wang, J.-N. Chen, J.-H. Jia, C. Wang, K. Paillot, I. Breslavetz, L.-S. Long, L. Zheng, G. L. J. A. Rikken, C. Train, X.-J. Kong, M. Atzori, *J. Am. Chem. Soc.* **2022**, *144*, 8837–8847.

[29] K. Taniguchi, M. Nishio, S. Kishiue, P.-J. Huang, S. Kimura, H. Miyasaka, *Phys. Rev. Mater.* **2019**, *3*, 45202.

[30] K. Dhbaibi, M. Grasser, H. Douib, V. Dorcet, O. Cador, N. Vanthuyne, F. Riobé, O. Maury, S. Guy, A. Bensalah-Ledoux, B. Baguenard, G. L. J. A. Rikken, C. Train, B. Le Guennic, M. Atzori, F. Pointillart, J. Crassous, *Angew. Chem. Int. Ed.* **2023**, *135*, DOI 10.1002/ange.202215558.
[31] M. S. Raju, K. Paillot, I. Breslavetz, G. Novitchi, G. L. J. A. Rikken, C. Train, M. Atzori, *J Am Chem Soc* **2024**, *146*, 23616–23624.

[32] C.-Y. Li, L. C. Adi, K. Paillot, I. Breslavetz, L.-S. Long, L.-S. Zheng, G. L. J. A. Rikken, C. Train, X.-J. Kong, M. Atzori, *J. Am. Chem. Soc.* **2024**, *146*, 16389–16393.

[33] J.-C. G. Bünzli, *Coord. Chem. Rev.* **2015**, 293–294, 19–47.

[34] J.-C. G. Bünzli, *Acc. Chem. Res.* **2006**, *39*, 53–61.

[35] J.-C. G. Bünzli, S. V. Eliseeva, *Chem. Sci.* **2013**, *4*, 1939.

[36] G. L. J. A. Rikken, E. Raupach, *Phys. Rev. E* **1998**, *58*, 5081–5084.

[37] M. Atzori, H. Ludowieg, M. Cortijo, I. Breslavetz, K. Paillot, P. Rosa, C. Train, J. Autschbach, E. A. Hillard, G. L. J. A. Rikken, *Sci. Adv.* **2021**, 7, eabg2859–eabg2859.

[38] F. S. Richardson, *Inorg. Chem.* **1980**, *19*, 2806–2812.

[39] J. R. Robinson, X. Fan, J. Yadav, P. J. Carroll, A. J. Wooten, M. A. Pericàs, E. J. Schelter, P. J. Walsh, *J. Am. Chem. Soc.* **2014**, *136*, 8034–8041.

[40] O. G. Willis, F. Zinna, G. Pescitelli, C. Micheletti, L. Di Bari, *Dalton Trans.* **2022**, *51*, 518–523.

[41] J. Crassous, *Chem. Commun.* **2012**, *48*, 9684.

[42] L. Sorace, C. Benelli, D. Gatteschi, *Chem. Soc. Rev.* **2011**, *40*, 3092.

[43] M. Briganti, E. Lucaccini, L. Chelazzi, S. Ciattini, L. Sorace, R. Sessoli, F. Totti, M. Perfetti, *J. Am. Chem. Soc.* **2021**, *143*, 8108–8115.

[44] L. Sorace, D. Gatteschi, in *Lanthanides and Actinides in Molecular Magnetism*, Wiley, **2015**, pp. 1–26.

[45] Y. Meng, Y. Qiao, Y. Zhang, S. Jiang, Z. Meng, B. Wang, Z. Wang, S. Gao, *Chem. Eur. J.* **2016**, *22*, 4704–4708.

[46] K. L. M. Harriman, I. Korobkov, M. Murugesu, *Organometallics* **2017**, *36*, 4515–4518.

[47] A. Sickinger, B. Baguenard, A. Bensalah-Ledoux, Y. Guyot, L. Guy, F. Pointillart, O. Cador, M. Grasser, B. Le Guennic, F. Riobé, O. Maury, S. Guy, *J. Mater. Chem. C Mater* **2024**, *12*, 4253–4260.
Entry for the Table of Contents

<figure><img src="image_8.png" /></figure>

Here we report on the Magneto-Chiral Dichroism of two pairs of Er'''' and Tm'''' chiral complexes investigated through visible and near-infrared light absorption in a wide temperature (4-290 K) and magnetic field (0-5 T) range. The results are presented and discussed in the frame of the Richardson's theory of lanthanides optical activity originally developed to identify the most promising chiroptical transitions for lanthanide-based systems.

<figure><img src="image_9.png" /></figure>