Magnetization Dynamics and Coherent Spin Manipulation of a Propeller Gd(III) Complex with the Smallest Helicene Ligand

A homoleptic gadolinium(III) complex with the smallest helicene-type ligand, 1,10-phenanthroline-N,N′-dioxide (phendo) [Gd(phendo)4](NO3)3·xMeOH (phendo = 1,10-phenanthroline-N,N′-dioxide, MeOH = methanol), shows slow relaxation of the magnetization characteristic for Single Ion Magnets (SIM), despite negligible magnetic anisotropy, confirmed by ab initio calculations. Solid state dilution magnetic and EPR studies reveal that the magnetization dynamics of the [Gd(phendo)4]3+ cation is controlled mainly by a Raman process. Pulsed EPR experiments demonstrate long phase memory times (up to 2.7 μs at 5 K), enabling the detection of Rabi oscillations at 20 K, which confirms coherent control of its spin state.

S ingle molecule magnets (SMMs) enjoy renewed interest in the field of molecular magnetism 1,2 due to a rapid increase of the magnetization blocking temperatures approaching the boiling point of nitrogen 3−5 and their implementation as molecular qubits. Lanthanide complexes turned out to be much better candidates for high-temperature SMMs than the transition metals, 6 even though the latter can easily form highspin coordination clusters. 7 Rational tuning of the magnetic anisotropy by employing a proper ligand field was found to be the most efficient strategy toward higher spin reversal barriers in the design of SMMs based on single lanthanide ions (single ion magnets, SIMs). 8 High magnetic anisotropy is necessary for achieving high energy barriers for spin reversal, but not sufficient to get an excellent SMM because the spin−lattice (direct, Raman) relaxation processes or the quantum tunneling of magnetization (QTM) may significantly affect the blocking temperature. 9−12 In particular, Raman relaxation was recently found to be the limiting process below the blocking temperature of the record-breaking SIMs. 3,4,13 Single ion magnets displaying a wide magnetic hysteresis are potential candidates for data storage. 14 On the other hand, molecular nanomagnets with no magnetic hysteresis, but with sufficiently long quantum coherence times (T m ), are good candidates for spin qubits and quantum information processing. 15 This coherence time (called also phase memory time) determines the ability of a spin qubit to remain in the superposition of two states and to resist any uncontrolled interaction with its environment, thus, determining its utility in quantum technologies. 16 Lanthanide spin qubits are especially interesting, as they enable realization of multiple addressable qubits within a single molecule 17 or encoding an electron qubit using a nuclear qudit. 18 However, any potential application of lanthanide-based qubits is currently hindered by their coherence times, which are usually shorter by an order of magnitude as compared to 3d metal complexes. 19 Therefore, new studies in this area are required to overcome this drawback.
There are only several examples of slow magnetic relaxation for gadolinium(III) complexes. 20−26 The main reason is the magnetic isotropy of Gd III , which renders it unuseful for the design of SIMs. Due to the lack of an intrinsic magnetic anisotropy, any slow magnetic relaxation for Gd III complexes must stem from either (i) weak anisotropy 21 caused by orbital nondegeneracy of the ground term 8 S or (ii) low rate of the relaxation processes other than Orbach, which become dominant when the energy difference between all m J states of the Gd III ion is very small. Hence, Gd III -based SIMs give the perfect opportunity to study these processes. However, for the Gd III complexes studied so far, the slow magnetic relaxation is often attributed to the phonon bottleneck effect, and the spin− lattice relaxation was postulated to appear only under special circumstances, that is, in the presence of Gd−Pt bonds. 24 In this work we present a 4-fold propeller-shaped Gd III complex with the smallest helicene-type ligand N,N′dioxophenanthroline (phendo) 27 [Gd(phendo) 4 ](NO 3 ) 3 · xMeOH (1) with a slow relaxation of the magnetization governed by a Raman process and showing coherent spin dynamics. We demonstrate that the Raman relaxation process is intrinsic to the molecule in this case and depends weakly on temperature ∝T 3 as compared to T 5 or T 9 , postulated for Kramers ions. 28 Moreover, this Raman relaxation depends on the dilution of 1 in the solid state matrix. Both factors are crucial from the point of view of designing high-efficiency lanthanide-based molecular qubits, which is clearly highlighted in our case study.
The magnetic properties of the complex cation [Gd-(phendo) 4 ] 3+ were studied for the undiluted compound 1, for the methanolic solution (mass spectroscopy confirms the presence of this cation in methanol, as discussed in the SI), and for the three solid state diluted compounds prepared using its structural analog [Y(phendo) 4 ](NO 3 ) 3 ·xMeOH (2) as a diamagnetic matrix (2.73%, 0.47%, and 0.17% concentrations of Gd III ions). Magnetically diluted samples were tested using pulse EPR spectroscopy to show long phase memory time T m compared to other lanthanide-based qubits and fast Rabi oscillations at 20 K. (1) is obtained in the reaction of gadolinium(III) nitrate with 1,10phenanthroline-N,N′-dioxide (phendo) in methanol solution, which yields yellow plate-shaped crystals (see SI for details). Crystal structure of 1 was determined by single-crystal X-ray diffraction ( Table S2 in SI). 1 crystallizes in the centrosymmetric tetragonal space group I4/m. The Gd1 atom occupies a 4-fold rotation axis, and as a result, the asymmetric unit consists of only a quarter of the formula unit ( Figure S1). Two of the nitrate anions also occupy a special position of high symmetry (a 4-fold rotation axis and a mirror plane), which leads to a severe disorder, while the third one is placed on a mirror plane and is only slightly disordered (the presence of nitrate anions was confirmed by IR spectroscopy; see SI for details). Due to the high symmetry, it was impossible to find methanol molecules in the structural model, even if disorder was taken into account, and therefore, the SQUEEZE procedure was applied with the resulting voids of 921 Å 3 and 275 electrons at 117 K (1125 Å 3 and 251 electrons at RT). These values of electron density account for around 14 methanol molecules per unit cell, which leads to molecular volumes of 65.8 and 80.4 Å 3 per MeOH at 117 K and RT, respectively (consistent with the literature reports 29 ). The relatively large solvent accessible voids are responsible for the crystal breaking following the solvent loss at room temperature.
Gd III in 1 is coordinated by four neutral phendo ligands through the oxygen atoms of the N-oxide moieties. This constitutes the first example of a coordination complex involving this peculiar helical molecule, according to the CSD database search. Such a coordination environment of a Gd III ion results in a nearly perfect square antiprism geometry of its coordination sphere (Figure 1), as confirmed by SHAPE analysis (Table S3 in the SI). There are two relevant angles that define the distortion from an ideal square antiprism geometry: the twist angle φ and the compression/elongation angle θ. For the ideal geometry, these angles are 45°and 54.7°, respectively. 30 For [Gd(phendo) 4 ] 3+ , φ = 54.0°, θ 1 = 61.4°, and θ 2 = 60.1°at 117 K and φ = 54.5°, θ 1 = 61.2°and θ 2 = 60.3°at room temperature ( Figure 1).
The twist angle φ is crucial to determine the point group at the metal site, which is important for the appropriate description of the crystal field and resulting splitting of the m J states. As the twist angle φ differs from 45°, the symmetry of the gadolinium site changes from D 4d to D 4 with further inequivalence of the oxygen atoms O1 and O2 (Gd−O1 = 2.356(3), Gd−O2 = 2.349(3); values at 117 K), lowering the symmetry to C 4 . Due to the axial chirality of the ligand, the obtained complexes are also chiral and show a four-bladed propeller geometry, with the unit cell containing their racemic mixture: two Δ and two Λ enantiomers ( Figure 1). The lanthanide centers are quite well separated from each other, with the shortest Gd···Gd distance equal to 10.45 Å (along the c crystallographic direction). [Gd(phendo) 4 ] 3+ cations are separated by a nitrate ion along the 4-fold symmetry axis. Along the a direction, Gd···Gd distances equal a = 15.34 Å. Each Gd III ion has also four near neighbors in the ab-plane within 10.86 Å ( Figure S2).
Continuous Wave EPR and Ab Initio Calculations. In order to conduct detailed pulse EPR experiments and to study the spin dynamics of the complex cation [Gd(phendo) 4 ] 3+ , solid state dilution samples of 1 in the isostructural [Y(phendo) 4 ](NO 3 ) 3 ·xMeOH (2) were prepared with the intended Gd III molar fractions of 5%, 1%, and 0.3% (synthesis and characterization are described in the SI). The identity and purity of the solid state dilution samples were confirmed by powder X-ray diffraction ( Figure S4). The actual molar fractions of Gd III were determined with high accuracy by ICP-QMS analysis and are approximately 50% smaller than the intended ones (see SI for details), resulting in the following chemical formulas: Continuous wave EPR spectroscopy was employed in order to estimate the crystal field splitting in the studied [Gd-(phendo) 4 ] 3+ cation. Fast relaxation causes strong broadening of the EPR signal for the undiluted sample 1 ( Figure S11). Therefore, detailed studies in X-, K-, and Q-bands were performed for a powdered sample of 1Gd0.47% at 150 K ( Figure S12, black lines). In principle, seven Stevens crystal field parameters are required to describe an EPR spectrum of the . These crystal field parameters are not sufficient to completely describe the crystal field of [Gd III (phendo) 4 ] 3+ in 1, but allow the estimation of the total splitting of the ground m J states, which was found to be 0.12 cm −1 . 32 This value is at least an order of magnitude smaller compared to the thermal energy, even at the lowest temperature achievable in the magnetic measurements (1.8 K corresponds to 1.25 cm −1 ), hence, all m J states are assumed to be equally populated, even at 1.8 K.
Limiting the number of the CF parameters to three in the fitting of EPR data is fully supported by the results of the single-point ab initio calculations on the [Gd III (phendo) 4 ] 3+ cation performed using OpenMolcas 33 (see Tables S4 and S5 in the SI for details). The calculated terms agree with the assumption that B 2 0 , B 4 0 , and B 4 4 describe well the CF for [Gd III (phendo) 4 ] 3+ , as the total weight of these three parameters on the crystal field splitting amounts to about 99% (Table S4 in the SI). The calculated total splitting of the ground state is 0.48 cm −1 and confirms a very small magnetic anisotropy of the Gd III ion in 1.
Magnetic Properties. DC magnetic properties of 1 are typical for Gd III complexes and are discussed in the SI. Alternating current (AC) magnetic susceptibility measurements revealed an interesting dynamic behavior of 1. In the 1.8−3.5 K temperature range under an applied DC field of 0.3 T, the frequency dependence of the out-of phase (χ") magnetic susceptibility shows two maxima in the 0.4−1000 Hz range ( Figure S6c). This behavior is attributed to two relaxation processes, which were fitted using a generalized Debye model. However, it was impossible to obtain accurate τ values (τ, time of the spin−lattice relaxation of the magnetization) for the faster process, as the corresponding χ" maxima appear above 1000 Hz. On the other hand, the slower relaxation process, which shows weak temperature dependence, is assumed to result from dipole−dipole interactions between Gd III ions, leading to cooperative relaxation of larger units. Therefore, in order to study this complicated relaxation behavior of the [Gd(phendo) 4 ] 3+ cation itself, solid state diluted samples 1Gd2.73%, 1Gd0.47%, and 1Gd0.17% and the saturated solution of 1 in methanol (1sol; see the mass spectrometry results in the SI confirming the presence of [Gd III (phendo) 4 ] 3+ cations in the MeOH solution) were also studied by AC magnetic susceptibility measurements. The aforementioned slower relaxation process is significantly reduced for 1Gd2.73% and 1sol and vanishes completely for 1Gd0.47% and 1Gd0.17%, as depicted in Figures S6−S10 in the SI. This confirms the initial assumption that this slower relaxation process is related to dipole−dipole interactions. The τ values extracted from the magnetic field (H) dependencies of the AC magnetic susceptibility for the remaining faster process were fitted using the following equation: 1 where the first part accounts for the quantum tunneling of magnetization (QTM), 34 the second one is related to the direct relaxation process, 35 and the last one stands for thermally dependent but field-independent processes (Orbach and Raman). 36,37 The results obtained for all Gd III concentrations are presented in Figure 2 and summarized in Table 1.
Both QTM and direct relaxation become less important with increasing dilution, as expected for the consequent weakening of the dipole−dipole interactions between the unpaired electron spins of the Gd III centers. In order to minimize contributions from these processes, temperature dependencies of χ' and χ" were recorded under the optimal DC fields of 0.2 T for 1Gd2.73% and 0.35 T for 1Gd0.47%, 1Gd0.17%, and 1sol ( Figures S7−S10). The obtained magnetic relaxation times τ at different temperatures T were fitted using the following equation: 38 where C 0 corresponds to QTM, C 1 and n describe a Raman process, and C 2 and m correspond to the direct process. In principle, a direct process can be described with m = 1 for a typical spin−lattice relaxation and m = 2 for a spin−phonon bottleneck process. However, we assume that for diluted powder samples relaxation to the phonon bath is sufficiently fast and does not limit the energy transfer from a few Gd III ions in the lattice of the solid state diluted compounds. This assumption is in accord with the observation of a similar slow magnetic relaxation in a frozen solution of [Gd III (phendo) 4 ]-(NO 3 ) 3 ·xMeOH 1sol (c = 3(1) × 10 −3 mol/dm 3 ; note that, in the case of 1Gd0.17%, the molar concentration equals 2.2 × 10 −3 mol/dm 3 ). The control of the relaxation by spin−lattice processes rather than a spin−phonon bath is unusual for a Gd III compound, 20,22,26 but not unprecedented among magnetically isotropic systems. 39,40 Therefore, the τ −1 (T) was fitted assuming that m = 1 and C 0 and C 2 are fixed based on the results of the τ −1 (H) (eq 1), while C 1 and n are the only free parameters (except for 1sol, where C 0 was treated as a free parameter, as it was impossible to determine it from τ −1 (H) dependence). The Orbach process does not influence the The Journal of Physical Chemistry Letters pubs.acs.org/JPCL Letter magnetization dynamics due to the total splitting of the m J multiplet lower than 0.3 K, leading to an almost equal population of all m J states above 1.8 K. The fitting results are presented in Table 1 and Figure 3. The obtained n values approach n = 3 for both solid state dilutions as well as for 1sol, suggesting a two-phonon Raman-like relaxation process involving both optical and acoustic phonons. 41,42 The similar thermal dependence of τ for solid state diluted samples and a MeOH solution confirms that the studied slow magnetic relaxation is an intrinsic "molecular" property of the [Gd-(phendo) 4 ] 3+ cation and not the result of slow phonon exchange with the thermal bath (phonon bottleneck effect). Pulse EPR. In order to further confirm that the magnetization dynamics of 1 is controlled by the Raman-like process (τ −1 = CT 3 ) and not phonon-bottleneck (τ −1 = CT 2 ), we performed pulse EPR experiments (X-band; 9.24 GHz). All diluted samples show intense echo-detected signal which remains intense up to 30 K for 1Gd0.47% (Figure 4) and 1Gd0.17% ( Figure S13) and vanishes fast for 1Gd2.73%, ( Figure S14). In order to elucidate the spin−lattice relaxation times, inversion recovery sequence traces at 335 mT were fitted to the biexponential model to afford two time constants (Figures S15−S17). The longer one is assumed to be spin− lattice relaxation time, T 1 , and the shorter one is ascribed to the spectral diffusion, T 1,s . 43 This assumption is in accordance with the literature 44−49 and is additionally confirmed by the similarity of these T 1 values with τ obtained from AC magnetic susceptibility for the solid state diluted compounds. Note that both τ and T 1 represent the same physical quantity−the time of spin−lattice relaxation of magnetization. T 1,s , on the other hand, is found to be 5−10× shorter than T 1 (Tables S6−S8). The obtained T 1 values were fitted to eq 2, with the C 0 derived from the AC magnetic susceptibility measurements and m = 1. Results are presented in Figure S18 and Table 1 (C 1 ′ and n′). Both AC and EPR measurements yield similar n values, while C 2 (AC) and C 2 ′ (EPR) differ significantly because pulse EPR experiment probes the relaxation times of a discrete transition centered at 335 mT and the magnetic measurements determine the averaged relaxation time for all m J states. Moreover, the T 1 values obtained from EPR below 8 K are affected by the spectral diffusion which is much faster than spin-phonon relaxation at low temperatures. Nonetheless, both methods show that n = 3 Raman-like process is the fastest Wide distribution of relaxation times in the field dependence of the AC signal for 1sol (α approaching 0.36) does not enable a reliable fit to eq 1. b As no significant decrease of relaxation time is observed in the field dependence of the AC signal up to 0.7 T (Figure 2), the direct process is assumed to be negligible under H = 0.35 T. c Primed parameters are obtained from EPR data.  17%, and 1sol). Solid lines are the best fits to the eq 2 (see details in text and Table 1).  [Gd III (phendo) 4 ] 3+ is characterized by a nuclear spin-free coordination sphere, which limits the decoherence and is promising in terms of achieving long memory phase times. As the T 1 is sufficiently long not to limit the quantum coherence time (T m ), we tested the temperature-dependence of T m for the diluted gadolinium samples by recording the time decay of the Hahn echo ( Figures S19 and S20 and Tables S9−S11). For 1Gd2.73%, T m was found to be relatively short (around 150 ns in 5−10 K range), while for both 1Gd0.47% and 1Gd0.17%, the T m values exceed 2.5 μs at 5 K ( Figure 5). This value is surpassed by the atomic clock transitions in [Ho(W 5 O 18 ) 2 ] 9−50 or gadolinium-doped CaWO 4 crystal 51 and far from those obtained for record-breaking transition metal based qubits, 44,52,53 but remains higher than reported for other lanthanide-based molecular qubits 17,21,46,54 and is comparable with some obtained for transition metals such as 2.7 μs for VO(dpm) 2 42 and 2.4 μs for (Ph 4 P) 3 [Fe(CN) 6 ] 55 under identical conditions. Surprisingly, 1Gd0.47% shows systematically longer T m than the more diluted 1Gd0.17%. Taking into account blocking of QTM under applied magnetic field and small contribution of direct relaxation process ( Figure S22), the Raman process becomes a dominant magnetization relaxation mechanism in magnetically diluted 1. Therefore, optimization of this process becomes crucial for control of T 1 in similar assemblies, which is known to be a limiting factor for T m . 56 For the studied compounds Raman process coefficient C 1 is decreasing with gadolinium concentration in yttrium matrix, ranging from 2.73% to 0.17% (Table 1). This observation can be explained on the basis of diminishing number of gadolinium(III) spins interacting with phonons, while the latter should remain almost unchanged upon proceeding from 99.83% to 97.27% yttrium(III) in the crystal. However, the observed slowing of relaxation does not seem to depend linearly on concentration. Particularly, when the Raman process efficiency (Γ Raman = C 1 T 3 ) is divided by gadolinium(III) concentration to account for the probability of the relaxation of a single gadolinium(III) ion, the resulting efficiency of a single center relaxation seems to be increasing with dilution ( Figure S23). Possibly two-phonon relaxation mechanism may be favored by a diminishing of the direct process in 1Gd0.17%, increasing efficiency of spin interaction with high-energy phonons. However, this behavior, which may be contributing to the unexpected shortening of the T m in 1Gd0.17%, as compared to 1Gd0.47%, needs further studies for a wider series of concentrations that will be conducted in future.
The possibility to coherently manipulate the spin states in 1Gd0.47% and 1Gd0.17% was additionally probed by transient nutation experiments at 20 K. The resulting Rabi oscillations for 1Gd0.47% and 1Gd0.17% are presented in Figures 6 and S24, respectively. Their frequencies were derived from the fast Fourier transforms ( Figure 6, right panel) and are linearly dependent on B 1 , unlike the small feature at 15 MHz which is power-independent and coincides with the Larmor frequency of hydrogen nucleus ( Figures S25 and S26). Very fast Rabi oscillations (Ω R ≈ 100 MHz) are observed at the highest microwave power, which in principle could afford multiple Rabi oscillations given N ≈ Ω R T 2 > 50 at 20 K. However, much faster damping limits their number which is most likely caused by the inhomogeneity in the nutation frequency. 57 An enhanced decoherence demonstrated by shorter T m times for 1Gd0.17% is also observed in the nutation experiments, as number of Rabi oscillations that can be detected is smaller than in case of 1Gd0.47%, despite higher dilution of a former ( Figure S24).
We have extensively investigated the slow relaxation of the magnetization of the propeller-like gadolinium(III)-based single ion magnet in its [Gd III (phendo) 4 ](NO 3 ) 3 ·xMeOH salt and its solid state dilutions in the diamagnetic [Y III (phendo) 4 ](NO 3 ) 3 ·xMeOH matrix. The relaxation of the diluted compounds is driven dominantly by the Raman-like process with the relaxation time τ ∝ T −3 , which is unusual for Kramers ions. The observation of the slow relaxation of magnetization for both the frozen methanol solution of