Axial dysprosium cyclopentadienyl-amide single-molecule magnets with hysteresis up to 92 kelvin

Abstract

Molecules showing magnetic memory effects at high temperatures could be used in high-density data storage devices. A magnetic hysteresis temperature (T_H) of 100 K has been achieved for a near-linear dysprosium bis(amide)-alkene single-molecule magnet (SMM), and a bent dysprosium cyclopentadienyl-amide SMM has shown T_H = 73 K. However, both these complexes exhibit fast magnetic relaxation at lower temperatures compared to dysprosium bis(cyclopentadienyl) SMMs. Here we report the synthesis of two highly axial dysprosium cyclopentadienyl-amide SMMs, [Dy{N(SiⁱPr₃)₂}(Cp^R)][Al{OC(CF₃)₃}₄] (1-Dy, Cp^R = Cp^ttt, C₅H₂^tBu₃−1,2,4; 2-Dy, Cp^R = Cpʹʹʹ, C₅H₂(SiMe₃)₃−1,2,4). We find T_H = 91 K for 1-Dy and 92 K for 2-Dy; ab initio calculations on 1-Dy show that magnetic relaxation is controlled by a combination of short dysprosium-ligand distances, a near-linear N–Dy–Cpʹʹʹ_centroid angle, and constrained vibrational modes. Together, this work demonstrates that dysprosium SMMs with large T_H values can be achieved with a judicious combination of π-aromatic and σ-donor ligands.

Molecules showing magnetic memory effects at high temperatures could be used in high-density data storage devices but often exhibit fast magnetic relaxation at lower temperatures. Here the authors report the synthesis of two highly axial dysprosium cyclopentadienyl-amide single molecule magnets with magnetic hysteresis temperatures of 91 K and 92 K.

Introduction

Magnetic memory effects have been observed in both lanthanide atoms^1,2 and molecules³, providing promising candidates for high-density data storage technologies⁴. Single-molecule magnets (SMMs) have been known for over thirty years⁵, and since 2011 lanthanide SMMs have provided the highest magnetic hysteresis temperatures (T_H, open hysteresis loops at zero-field for a magnetic field sweep rate of ca. 20 Oe/s)⁶. Lanthanide SMMs with carefully designed crystal field (CF) splitting have huge effective energy barriers to magnetic reversal (U_eff), which can deliver higher T_H and T_B (the temperature at which the magnetic relaxation rate is 100 s) values if magnetic relaxation mechanisms are sufficiently controlled^7–11. For dysprosium SMMs a linear geometry is most effective in stabilising magnetic states with the largest |m_J| projections, while destabilising those with the smallest |m_J| projections. Deviations from linearity or equatorial ligand coordination introduce transverse components in the CF that mix m_J states, diminishing U_eff, and to a greater extent T_H and T_B^4,12,13.

In 2017 the first dysprosocenium ([Dy(Cp^R)₂]⁺, Cp^R = C₅R₅) SMM [Dy(Cp^ttt)₂][B(C₆F₅)₄] (herein referred to as [Dy(Cp^ttt)₂]⁺, Cp^ttt = C₅H₂^tBu₃−1,2,4) was shown to have U_eff = 1780(13) K, T_H = 60 K and T_B = 53 K, due to a combination of a strong axial CF and rigid Cp^ttt ligands that substantially reduced two-phonon Raman relaxation^14–16. In the interim, analogous axial dysprosium complexes with two π-aromatic ligands have shown similar properties^12,13, with the leading example [Dy(Cp^iPr5)(Cp*)][B(C₆F₅)₄] (herein referred to as [Dy(Cp^iPr5)(Cp*)]⁺, Cp^iPr5 = C₅ⁱPr₅; Cp* = C₅Me₅) having U_eff = 2230(10) K, T_H = 80 K and T_B = 65 K, due to its large Cp^iPr5–Dy–Cp* angle (162.51(2)°^17,18). A related SMM, [Dy₂(Cp^iPr5)₂(μ-I)₃], has U_eff = 2345(12) K, T_H = 80 K and T_B = 72 K, but it sits in a slightly different class due to the strong exchange coupling arising from a 1 e^– Dy–Dy bond¹⁹. In 2025 the dysprosium bis(amide)-alkene SMM [Dy{N(SiⁱPr₃)[Si(ⁱPr)₂C(CH₃) = CHCH₃]}{N(SiⁱPr₃)(SiⁱPr₂Et)}][Al{OC(CF₃)₃}₄] (herein referred to as [Dy(amide)(amide-alkene)]⁺) set new record U_eff = 2652(16) K and T_H = 100 K as it shows N–Dy–N angles up to 165.3(8)° and Dy–N distances as short as 2.166(12) Å, but its T_B could not be extracted as at 2 K full relaxation takes less than 100 s; this was ascribed to the flexible bis-amide ligand environment promoting effective under-barrier relaxation processes²⁰. Also in 2025, the dysprosium cyclopentadienyl-amide SMM [Dy{N(SiⁱPr₃)₂}(Cp*)][Al{OC(CF₃)₃}₄] (herein referred to as [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺) was shown to have a high U_eff (2192(33) K), but its T_H is limited to 73 K and T_B was not defined; fast magnetic relaxation was attributed to both the presence of a flexible amide ligand and bent N–Dy–Cp*_centroid angle (ca. 152.5(2)°) giving excited states with mixed m_J contributions²¹.

As dysprosium bis(cyclopentadienyl) (e.g., [Dy(Cp^iPr5)(Cp*)]⁺¹⁷) and bis(amide) (e.g., [Dy(amide)(amide-alkene)]⁺²⁰) SMMs with respective Cp^R_centroid–Dy–Cp^R_centroid and N–Dy–N angles closest to linearity have provided the best SMMs of their class, we reasoned that improved performance could be obtained by targeting dysprosium cyclopentadienyl-amide SMMs that are less bent than [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺²¹. Coordinatively unsaturated lanthanide complexes tend to deviate from regular geometries due to their predominantly ionic, non-directional bonding regimes^22,23. We envisaged that high-performance dysprosium SMMs with near-linear N–Dy–Cp^R_centroid angles could be achieved by fine-tuning the steric complementarity of the two ligands.

Results and discussion

Synthesis

The lanthanide cyclopentadienyl-amide complexes, [Ln{N(SiⁱPr₃)₂}(Cp^R)][Al{OC(CF₃)₃}₄] (1-Ln, Ln = Y, Dy, Cp^R = Cp^ttt; 2-Ln, Ln = Y, Dy, Cp^R = Cpʹʹʹ, C₅H₂(SiMe₃)₃−1,2,4), were synthesised in 37–48% yields by hydride abstraction reactions of their corresponding precursors [Ln{N(SiⁱPr₃)₂}(Cp^R)(BH₄)] (3-Ln, Ln = Y, Dy, Cp^R = Cp^ttt; 4-Ln, Ln = Y, Dy, Cp^R = Cpʹʹʹ) with [CPh₃][Al{OC(CF₃)₃}₄]²⁴ in fluorobenzene at ambient temperature for 2 h, followed by recrystallisation from fluorobenzene solutions layered with n-hexane (Fig. 1a). Complexes 3-Ln and 4-Ln were themselves prepared by salt metathesis reactions of [Ln{N(SiⁱPr₃)₂}(µ-BH₄)₂]₄²⁵ with the respective KCp^R salt^26,27 in benzene at ambient temperature for 18 h, followed by extraction into n-hexane and filtration to remove the KBH₄ byproduct. Recrystallisation from saturated n-hexane solutions at –35 °C gave 3-Ln and 4-Ln in 62–83% crystalline yields.

Fig. 1. Synthesis of complexes 1-Ln, 2-Ln, 3-Ln and 4-Ln, and selected single crystal XRD data for the cations of 1-Dy, 2-Dy and [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺.

a Synthetic route to complexes 1-Ln, 2-Ln, 3-Ln and 4-Ln (Ln = Dy, Y). b Single crystal XRD structures (displacement ellipsoids set at 50%) of the cations of 1-Dy (Z′ = 2; 1-Dy^a and 1-Dy^b) and 2-Dy at 100 K, with hydrogen atoms omitted and key atoms labelled, together with top-down schematics of the cations of 1-Dy^a, 1-Dy^b and 2-Dy, illustrating the contrasting equatorial coordination environment (Dy = cyan, Si = orange, N = blue, C = grey, H = white). c Key metrics from single crystal XRD structures for 1-Dy^a, 1-Dy^b, 2-Dy and [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺²¹, the number in brackets represents 1 estimated standard deviation (esd).

Single crystal X-ray diffraction (XRD)

XRD data were collected on single crystals of 1-4-Ln (see Supplementary Information Figures S1–S10 and Tables S1–S4). The structures of 3-Ln and 4-Ln are similar to those of [Ln{N(SiⁱPr₃)₂}(Cp*)(BH₄)] (Ln = Y, Dy)²¹, though unusually we observe that 3-Dy and 3-Y are not isomorphic, crystallising in C2/c and P2₁/n space groups, respectively. In the solid-state the [Ln{N(SiⁱPr₃)₂}(Cp^R)]⁺ cations and [Al{OC(CF₃)₃}₄]^– anions of 1-Ln and 2-Ln are fully separated. The yttrium complexes 1-Y and 2-Y are isomorphic and isostructural with their respective dysprosium counterparts, so for brevity we focus our discussion on the cations of 1-Dy and 2-Dy (Fig. 1b). There are two unique cations in the monoclinic (P2₁/n) unit cell of 1-Dy with distinct geometries (1-Dy^a and 1-Dy^b), and one unique cation in the orthorhombic (Pna2₁) cell of 2-Dy. Key metrical parameters for all three cations, alongside the similar cation of [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺²¹, are collated in Fig. 1c (See Supplementary Information Table S1–S2 for further metrics of all complexes).

All the cations of 1-Dy^a, 1-Dy^b, 2-Dy and [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺²¹ have piano stool motifs with opposing {N(SiⁱPr₃)₂} and Cp^R ligands, flanked equatorially by isopropyl groups of the bis(silyl)amide ligands. The cation of 2-Dy has the greatest N–Dy–Cp^R_centroid angle (172.26(10)°), and [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺ the smallest (152.5(3)°)²¹. The two cations of 1-Dy show significantly different N–Dy–Cp^ttt_centroid angles between these extremes (1-Dy^a: 157.84(11)°; 1-Dy^b: 167.90(10)°). The Dy–N (2.204(3) Å) and Dy–Cp^R_centroid (2.332(2) Å) distances of 2-Dy are within error of the more linear cation of 1-Dy (1-Dy^b: Dy–N: 2.209(3) Å; Dy–Cp^R_centroid: 2.339(2) Å), and these are longer than the corresponding distances in [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺ (Dy–N: 2.192(3) Å; Dy–Cp^R_centroid: 2.314(14) Å)²¹; the Dy–Cp^ttt_centroid distance of the more bent cation of 1-Dy^a (2.345(2) Å) is statistically equivalent to the more linear cation, but it has a shorter Dy–N distance (2.185(3) Å).

The greater linearity of the cation of 2-Dy over both those of 1-Dy corresponds with a conformational difference in the bis(silyl)amide isopropyl groups (Fig. 1b). The cations of 1-Dy exhibit the same pincer-like motif as [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺²¹, with the two isopropyl groups straddling the dysprosium centre in a mirror-symmetric fashion. The resultant Dy···C distances of 1-Dy^a and 1-Dy^b between 2.815(5) and 3.209(5) Å engage in close electrostatic agostic-type interactions between methine C(1) and C(10) and methyl C(2) and C(11) C–H bonds to the Dy(III) ion, each in an η²-fashion. By contrast, in 2-Dy the two flanking isopropyl groups are orientated in opposing directions on opposite sides of the Dy(III) ion and show Dy···C distances in a narrower range (2.874(5)–3.072(5) Å). An additional proximal C(5) methyl group provides an extra η³-H–C–H electrostatic interaction, 3.045(4) Å distant, giving a more saturated equatorial environment. The corresponding C(5) methyl group in [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺²¹ and both cations of 1-Dy are found in similar vicinities, but remain remote from the dysprosium centres (Dy···C > 3.91 Å).

For both 1-Dy and 2-Dy the bulkier 1,2,4-substituted Cp^R ligands give more linear metal coordination geometries than seen in [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺²¹, which we attribute to the complementarity of the steric bulk of Cp^ttt and Cp′′′ to that of the bis(silyl)amide ligand. The C_ring–SiMe₃ bonds of 2-Dy (1.888(4)–1.892(4) Å) are longer than the C_ring–C^tBu bonds in 1-Dy^a and 1-Dy^b (1.524(7)–1.550(7) Å), which potentially enables the distinctive conformation of the {N{SiⁱPr₃)₂} isopropyl groups in the cation of 2-Dy. For all cations of 1-Dy and 2-Dy the combined ligand periphery fully encapsulates the dysprosium centre. This was quantified by the AtomAccess code²⁸, which uses the solid angle (SA) metric to assess the exposed surface area of a complexed ion (see Supplementary Information Figures S11–S13). A total 3.9% SA of the Dy(III) ion is visible in 2-Dy, with the largest potential binding site being only 1.6% SA. The two Dy(III) ions in 1-Dy have larger total SA (both 6.2%) and SA of the largest binding sites (both 2.8%), but these values are still lower than those seen for the relatively unencumbered [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺ (mean total SA: 10.0%, mean largest binding site SA: 6.6%)²¹.

Bulk characterisation data

Powder XRD data were collected on all complexes. Le Bail analysis²⁹ of the diffractograms obtained closely matched the single crystal XRD parameters and showed the absence of any other crystalline phase (see Supplementary Information Figures S14–S21). The ATR-IR spectra (see Supplementary Information Figures S22–S33) of 1-Ln, 2-Ln and 4-Ln exhibit superimposable absorption bands for each Y/Dy pair, while the 3-Ln pair show very similar spectra with slight deviations, especially at low frequency, consistent with our observation of the differing crystal phases exhibited by these two compounds. Absorptions corresponding to vibrational modes of the [Al{OC(CF₃)₃}₄]^– anions dominate the ATR-IR spectra of 1-Ln and 2-Ln, but strong electrostatic interactions of several methine and methyl groups of {N(SiⁱPr₃)₂} ligands with the coordinatively unsaturated Ln(III) cations is evidenced by the presence of lower-frequency C–H stretching modes between 2800 and 2580 cm⁻¹. The ATR-IR spectra of 3-Ln and 4-Ln exhibit characteristic resonances for κ³-BH₄ groups at ~2500 cm⁻¹ (terminal B–H) and between 2300–2100 cm^–1 (Ln-bound B–H)³⁰, alongside the distinctive agostic-type C–H stretch at ~ 2790 cm⁻¹ for all four complexes. Elemental analysis results obtained for 1-4-Ln are in not always in close agreement with the expected values, but this is consistent with standard issues associated with this form of analysis³¹, which is exacerbated by fluorine-rich compounds such as 1-Ln and 2-Ln³².

Solution characterisation data

Multinuclear NMR spectroscopy was performed on fluorobenzene solutions of 1-Ln and 2-Ln, and on d₆-benzene solutions of 3-Ln and 4-Ln (see Supplementary Information Figures S34–S63). The dysprosium complexes 3-Dy and 4-Dy exhibit paramagnetically broadened and shifted signals in their solution ¹H NMR spectra, while 1-Dy and 2-Dy appear entirely featureless between 200 and –200 ppm, save for solvent resonances. With all four dysprosium complexes the ¹¹B, ¹³C{¹H} and ²⁹Si NMR spectra obtained are similarly featureless apart from the ¹³C solvent resonances, consistent with our previous report of the Cp*-ligated analogues of these complexes²¹. A broad resonance for the [Al{OC(CF₃)₃}₄]^– counteranion is observed in the ¹⁹F NMR spectra at –94.8 ppm and –90.4 ppm for 1-Dy and 2-Dy, respectively, alongside a highly paramagnetically broadened and shifted fluorobenzene solvent resonance, at –110.9 and –108.8 ppm, respectively (cf. 113.1 ppm for unshifted fluorobenzene). Conversely, the ¹H, ¹³C{¹H}, ¹⁹F and ¹¹B NMR spectra of the yttrium analogues 1-4-Y are unambiguously assignable, in accord with the proposed structures, and are comparable to closely related complexes^20,21,25.

Magnetometry

Magnetic data were collected on microcrystalline samples of 1-Dy and 2-Dy using a superconducting quantum interference device (SQUID). The zero-field-cooled (ZFC) and field-cooled (FC) magnetic susceptibility data diverge at 30 K for 1-Dy and 40 K for 2-Dy (Fig. 2a and Supplementary Information Figures S64 and S74), which we attribute to the onset of magnetic blocking³³. We probed the magnetic reversal dynamics of 1-Dy and 2-Dy at low temperatures by DC waveform³⁴ and DC decay methods³⁵, and at higher temperatures under zero DC field by alternating current (AC) measurements (Fig. 2e and Supplementary Information Figures S65–S73 and S75–S85). The Arrhenius law [τ^–1 = 10^–Aexp(–U_eff/k_BT)] is followed for magnetisation reversal rates above 90 K for 1-Dy and 85 K for 2-Dy, with U_eff = 2466(35) K and A = –11.97(13) log₁₀(s) for 1-Dy, and U_eff = 2743(28) K and A = –12.9(1) log₁₀(s) for 2-Dy; this is in accord with Orbach relaxation proceeding by concatenated one-phonon transitions. The experimentally determined U_eff values of 1-Dy and 2-Dy are in good agreement with those predicted by SA-CASSCF-SO (see below), and are larger than those measured for [Dy(Cp^iPr5)(Cp*)]⁺ (2230(10) K)^17,18 and [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺ (2191(33) K)²¹, and similar to that for [Dy(amide)(amide-alkene)]⁺ (2652(16) K²⁰). The magnetisation reversal rates between 10 and 90 K for 1-Dy and between 12 and 85 K for 2-Dy have a power-law dependence (τ^–1 = 10^RTⁿ) that suggests relaxation by a two-phonon Raman scattering processes, with R = –8.2 (1) log₁₀(s^–1 K^–n) and n = 3.9(1) for 1-Dy and R = –4.73(15) log₁₀(s^–1 K^–n) and n = 2.66(8) for 2-Dy. Below 10 K (1-Dy) or 12 K (2-Dy) the rates become increasingly less dependent on temperature, which is associated with quantum tunnelling of the magnetisation (QTM; τ^–1 = 10^–Q), giving fitted rate constants of Q = 2.19(6) log₁₀(s) (1-Dy) and Q = 3.83(1) log₁₀(s) (2-Dy). Unlike [Dy(amide)(amide-alkene)]⁺²⁰ and [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺²¹, we were able to determine T_B of 7.2 K for 1-Dy and 39.5 K for 2-Dy; these values are both lower than those of [Dy(Cp^iPr5)(Cp*)]⁺ (65 K)¹⁷ and the current record 72 K for [Dy₂(Cp^iPr5)₂(μ-I)₃]¹⁹. Complexes 1-Dy and 2-Dy each show a second, much weaker signal, of a faster relaxation process below 20 K, which appear to have Raman-like temperature dependence (Figures S73 and S85); these could either be due to minor impurities or higher-order relaxation modes.

Fig. 2. Selected magnetic data for complexes 1-Dy, 2-Dy and [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺.

a Zero-field cooled and field cooled curves of 1-Dy (top) and 2-Dy (bottom) performed at 0.1 T. b M vs. H hysteresis loops at 22 Oe s⁻¹ for 1-Dy between 2 and 110 K (top) and 2-Dy between 2 and 95 K (bottom). c Enlargement of the closing 22 Oe s⁻¹ hysteresis loops for 1-Dy between 86 and 94 K (top) and 2-Dy between 90 and 95 K (bottom). d Coercive field (H_c) as a function of temperature for 1-Dy, 2-Dy and [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺²¹ as extracted from hysteresis measurements; closed hysteresis is determined to be H_c < 5 Oe (grey dashed line, field calibrated with a Pd standard). e Zero-field relaxation rates of the main relaxation processes in 1-Dy, 2-Dy and [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺²¹ fitted to Orbach, Raman and QTM contributions; for 1-Dy, U_eff = 2466(35) K, A = –11.97(13) log₁₀[s], R = –4.73(15) log₁₀[s^–1 K^–n], n = 2.66(8) and Q = 2.19(6) log₁₀[s]. Bars represent 1 esd of the distribution of rates; for 2-Dy, U_eff = 2743(28) K, A = –12.9(1) log₁₀[s], R = –8.2(2) log₁₀[s^–1 K^–n], n = 3^.9(1) and Q = 3.83(1) log₁₀[s]; for [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺²¹, U_eff = 2191(33) K, A = –11.8(1) log₁₀[s], R = –5.2(2) log₁₀[s^–1 K^–n], n = 3^.1(1) and Q = 1.06(4) log₁₀[s].

The variable temperature magnetic hysteresis properties of 1-Dy and 2-Dy were determined under DC fields at sweep rates of 22 Oe/s (Fig. 2b–d). The large zero-field steps at low temperatures are consistent with fast magnetisation reversal by QTM, as indicated in the AC data³³. At 2 K we find coercive fields (H_C) of 8.885(1) kOe for 1-Dy and 17.999(6) kOe for 2-Dy, which are similar to that for [Dy(amide)(amide-alkene)]⁺ (9.5 kOe at 2K²⁰), but greater than that of [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺ (2.8 kOe at 2 K²¹); these are all far lower than [Dy₂(Cp^iPr5)₂(μ-I)₃], which shows H_C > 140 kOe below 60 K due to strong intramolecular exchange coupling¹⁹. We find that, as for [Dy(amide)(amide-alkene)]⁺²⁰ and [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺²¹, H_C decreases relatively slowly with temperature (ca. 2 kOe K^–1) for 1-Dy and 2-Dy over a wide temperature range (Fig. 2d). Comparison of the magnetic reversal rates of 1-Dy and 2-Dy with [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺²¹ (Fig. 2e) shows that this is because they all only switch from Raman to Orbach regimes at high temperatures³⁶, which is itself a consequence of the large U_eff barriers. However, while H_C drops to <5 Oe at 73 K to define T_H for [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺²¹, H_C is still > 50 Oe for 1-Dy and 2-Dy at this temperature, with soft high-temperature magnetic hysteresis profiles comparable to [Dy(amide)(amide-alkene)]⁺²⁰. Above 80 K, H_C starts to decrease more rapidly with temperature for 1-Dy and 2-Dy, with T_H = 91 K for the former and T_H = 92 K for the latter complex (c.f. T_H = 80 K for [Dy(Cp^iPr5)(Cp*)]⁺¹⁷ and 100 K for [Dy(amide)(amide-alkene)]⁺²⁰).

Static electronic structure calculations

We used OpenMolcas³⁷ to perform state-average complete active space self-consistent field spin-orbit (SA-CASSCF-SO) calculations on the cations of 1-Dy and 2-Dy, with no optimisation of experimentally-determined atomic coordinates (see Supplementary Information Tables S8–S10). We find that the ground ⁶H_15/2 multiplets are split by 2865 K for 1-Dy^a, 2798 K for 1-Dy^b, and 2845 K for 2-Dy. These cations all have ground Kramers doublets (KD) with Ising-like anisotropy (g_z > 19.995, g_x and g_y < 10^–4), which correspond to m_J = ±15/2 functions when quantised along their main magnetic anisotropy axes. The first excited states lie at 878 (1-Dy^a) and 842 K (1-Dy^b) and 894 K (2-Dy) above the ground state, with excited states showing collinear magnetic anisotropy until the fifth KD for 1-Dy^a (2395 K) and 1-Dy^b (2367 K), and the sixth KD for 2-Dy (2631 K), which is the barrier over which one-phonon magnetic reversal is expected to proceed (Fig. 3)³⁸. These values are greater than those calculated for the related dysprosium cyclopentadienyl-amide complex [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺ (CF splitting = 2642 K, first excited state = 770 K, fifth KD = 2220 K²¹), and the low-lying excited states of 1-Dy^a, 1-Dy^b and 2-Dy show more pure m_J compositions as expected from their nearer-to-linear Cp^R_centroid–Dy–N angles. The overall CF splitting for 1-Dy^a, 1-Dy^b and 2-Dy are all smaller than that calculated for the major component of the dysprosium bis(amide)-alkene complex [Dy(amide)(amide-alkene)]⁺ (3001 K²⁰), which was predicted to relax via the fifth KD (2585 K), which we attribute due to the greater electrostatic potential of two charge-dense σ-donor ligands interacting with the Dy(III) ion rather than one σ- and one π-donor here³⁹. However, the first excited state of [Dy(amide)(amide-alkene)]⁺ (841 K²⁰) is lower-lying than predicted for 1-Dy^a, 1-Dy^b and 2-Dy, and its excited states are less pure, thus we anticipate that under-barrier magnetic relaxation processes should be suppressed in 1-Dy and 2-Dy by comparison.

Fig. 3. Calculated electronic structure of the two cations of complex 1-Dy (1-Dy^a and 1-Dy^b) and the cation of 2-Dy.

Atomic coordinates are from single crystal XRD data, and crystal field states are from SA-CASSCF-SO wavefunction. Dark blue: cation of 1-Dy^a with N–Dy–Cp^ttt_centroid = 157.84(11)°; cyan: cation of 1-Dy^b with N–Dy–Cp^ttt_centroid = 167.9(1)°; red: cation of 2-Dy with N–Dy–Cp′′′_centroid = 172.26(10)°.

Spin dynamics calculations

We performed ab initio spin dynamics calculations using our recently developed methods^40–42 on 2-Dy and a model of 1-Dy derived from the packing of 2-Dy, as the large unit cell of 1-Dy precludes calculations on this structure (see methodology). In this method, periodic density-functional theory (DFT) calculations are performed to obtain an optimised geometry and phonons. The optimised geometries of 2-Dy and [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺²¹ are in excellent agreement with those determined by single crystal XRD; key bond lengths (Dy–N, Dy–Cp^R_centroid) are within 0.03 Å of the crystal structure geometry, and the N–Dy–Cp^R_centroid angles are within 3°. Our model of 1-Dy using the surrogate packing of 2-Dy is in good agreement with cation 1-Dy^a, predicting a 159° N–Dy–Cp^R_centroid angle (Supplementary Information Table S11). The low energy phonon density of states ( < 200 cm^-1) that is responsible for driving Raman relaxation is very similar for all three systems, and similar to that previously determined for [Dy(amide)(amide-alkene)]⁺²⁰, but distinct from [Dy(Cp^ttt)₂]⁺⁴³ (Supplementary Information Figures S86–S89).

Multiconfigurational SA-CASSCF-SO calculations allow us to simulate the electronic structure of the SMM and, with the calculated phonons, determine spin-phonon coupling⁴⁴. This spin-phonon coupling is then used to simulate the spin-dynamics at zero field via the Raman and Orbach mechanisms using our existing methodologies⁴² and established theory⁴¹. We find excellent agreement between the calculated and experimental magnetic reversal rates in the one-phonon Orbach region, however we underpredict the two-phonon Raman rates for all three systems (Fig. 4a); note that we do not simulate QTM processes. The discrepancy is worst for 1-Dy, possibly due to our use of a model which uses the packing of 2-Dy. Nevertheless, we accurately simulate the relative ordering of the three systems; the calculated Raman reversal rates for 2-Dy at 40 K are around fifty times slower than those of [Dy(amide)(amide-alkene)]⁺²⁰ and [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺²¹, and are ca. ten times slower than those of [Dy(Cp^ttt)₂]⁺⁴³.

Fig. 4. Temperature dependence of experimental and calculated magnetic relaxation rates and coercive fields of complexes 1-Dy, 2-Dy and [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺.

a Experimental (points) and calculated (lines) magnetic relaxation rates, τ⁻¹, vs. temperature of 1-Dy (blue), 2-Dy (red) and [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺²¹ (green). b Experimental (points) and calculated (lines) coercive field, H_C, vs. temperature of 1-Dy (blue), 2-Dy (red) and [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺²¹ (green).

We have previously used the one-phonon spectral density (phonon DOS weighted by spin-phonon coupling strength; Supplementary Information Figure S90) to explain Raman relaxation in terms of spin-phonon coupling as a function of phonon energy. However, this metric does not explain the relative behaviour of the present systems: all three Cp^R-amide complexes have similar spectral densities, but Raman rates differ by orders of magnitude. Furthermore, the spectral density of [Dy(Cp^ttt)₂]⁺ is smaller than the other four amide-containing complexes, but the calculated Raman relaxation rate is faster than for 1-Dy and 2-Dy (Supplementary Information Figure S91). Finally, the spectral density of [Dy(amide)(amide-alkene)]⁺²⁰ is larger than [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺²¹, and yet their Raman rates are very similar. These apparent discrepancies arise because the one-phonon spectral density includes all spin-phonon coupling matrix elements equally, including those that do not contribute to Raman relaxation. In the two-phonon Raman scattering mechanism, only spin-phonon coupling matrix elements that couple the initial and final states (viz. the ground state doublet) to the intermediate “virtual state” state c (in these complexes, this is the set of the other states in the ⁶H_15/2 manifold) contribute. Thus, the traditional one-phonon spectral density is not a very helpful metric for explaining differences in Raman relaxation rates.

One way to rectify this would be to compare a “truncated spectral density” only including the relevant matrix elements (Supplementary Information Figure S92). However, this is very similar for all amide-containing systems, with [Dy(Cp^ttt)₂]⁺ being distinctly smaller. This suggests that the strength of the spin-phonon coupling which drives Raman relaxation is similar between all four amide-containing complexes. To go one step further, we have recently derived a “Raman spectral density”⁴², which is the temperature-independent part of the Raman rate equation. The temperature-dependent rate integrand is then the Raman spectral density multiplied by the Bose-Einstein phonon occupation factors (Supplementary Information Equation S1 and S1). Across the five systems being compared here, both the Raman spectral density and the rate integrand (at 40 K) are consistent with the calculated Raman relaxation rate, varying by orders of magnitude between the systems (Supplementary Information Figure S93). While all five systems have highly pure $∣m_J=\pm \frac{15}{2}⟩$ ground state doublets ( > 99%), we see good correlation with the Raman rate and the impurity of this ground state doublet (i.e., $∣m_J\ne \pm \frac{15}{2}⟩$ character, which itself correlates with the N–Dy–Cp^R_cent angles, Fig. 1c) for the four amide systems, while [Dy(Cp^ttt)₂]⁺⁴³ does not follow this trend (Supplementary Information Figure S94). This suggests that in 2-Dy, suppression of the Raman rate is due to the highly pure $∣m_J=\pm \frac{15}{2}⟩$ ground state doublet, despite the presence of the amide ligand, which induces strong spin-phonon coupling.

To understand the differing contribution of the Cpʹʹʹ and amide ligands, spin-phonon calculations were performed using localized phonon modes of 2-Dy obtained from partial Hessian vibrational analysis (PHVA)⁴⁵, where phonon modes are localized to the ligands of 2-Dy. The PHVA phonon DOS of the amide ligand is similar to that of Cpʹʹʹ, but the one-phonon and Raman spectral densities are much larger for the former (Supplementary Information Figures S95–S97). This differing PHVA Raman spectral density confirms the role of the amide ligand in inducing strong spin-phonon coupling, but the similarity of the PHVA DOS suggests that it is the charge density that is more responsible for the strong spin-phonon coupling, rather than its increased flexibility compared to Cpʹʹʹ.

As SMMs are superparamagnets with no magnetic phase transitions, their magnetic hysteresis properties are determined by the underlying molecular spin dynamics⁴⁶. Simulations of the magnetic hysteresis for 1-Dy, 2-Dy and [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺²¹ (summarised for ease of visualisation as coercive field versus temperature, Fig. 4b), which necessitates calculations of the relaxation rates as a function of magnetic field and orientation^20,42, overpredict the coercive field in all cases due to our underprediction of the zero-field rates. This is different to our previous results for [Dy(amide)(amide-alkene)]⁺²⁰ and [Dy(Cp^ttt)₂]⁺⁴³ where we underpredicted the coercive field. This indicates that we do not have a systematic deviation in our methodology, but rather something that is system dependent, and likely arising from the use of DFT for optimisation and calculation of phonon modes, as well as possibly from the omission of dynamic correlation in our spin-phonon coupling calculations with SA-CASSCF-SO. Nonetheless, again we predict the correct experimental ordering and find very good qualitative agreement with the experimental trends.

To conclude, we have shown that judiciously selected π-aromatic and σ-donor ligands can be combined to provide highly axial lanthanide complexes, and in the case of dysprosium analogues this has delivered huge magnetic remanence temperatures. To achieve improved dysprosium SMMs in future, the simplest approach is still to increase CF splitting by reduced metal-ligand bond distances, increased ligand charge densities, and increased inter-ligand angles^7–11. However, our ab initio calculations herein show the intrinsic dichotomy of this approach, in that the use of charge-dense amides is itself a cause of stronger spin-phonon coupling, that may lead to faster Raman relaxation, rather than the flexibility of the ligand itself. However, the present complexes 1-Dy and 2-Dy show that this can be mitigated by increasing the linearity of the complex which increases the purity of the ground state doublet and suppresses Raman relaxation rates. We note that complexes such as [Dy(C₄R₄)₂]^{– 47}, [Dy(Cp^R)(C₄R₄)]⁴⁸ and [Dy(Cp^R)(OAr)][B(C₆F₅)₄] (Ar = aryl)⁴⁹ have all been targeted¹². Here we have highlighted how ligand steric complementarity has to be of prime consideration for controlling the lanthanide coordination sphere to deliver more linear complex geometries that effectively suppress under-barrier magnetic relaxation mechanisms.

Methods

Synthesis and characterisation

All manipulations were conducted under argon with the strict exclusion of oxygen and water by using Schlenk line and glove box techniques. Glassware was flame-dried under vacuum prior to use. Argon was passed through a column of activated 3 Å molecular sieves and Cu catalyst prior to use. Isolated compounds were dried in vacuo on a Schlenk line to the point at which the flask could maintain a constant static pressure less than 5 × 10^-3 mbar. C₆H₆ and C₆D₆ were purchased anhydrous, degassed, and stored under argon over a K mirror or activated 3 Å molecular sieves, respectively. n-Hexane was refluxed over molten potassium for 3 days, distilled, and stored under argon over a potassium mirror. C₆H₅F was refluxed over CaH₂ for 3 days, distilled, and stored under argon over activated 3 Å molecular sieves. [Ln{N(SiⁱPr₃)₂}(BH₄)₂]²⁵, KCp^ttt26, KCp′′′²⁷ and [CPh₃][Al{OC(CF₃)₃}₄]²⁴ were prepared according to literature procedures.

NMR spectra were recorded at 298 K on a Bruker AVIII HD 400 MHz or 500 MHz spectrometer. Chemical shifts are reported in ppm and coupling constants in Hz. ¹H and ¹³C{¹H}_DEPTQ NMR spectra recorded in C₆D₆ are referenced to the solvent signal⁵⁰. NMR spectra recorded in C₆H₅F were locked to an internal sealed capillary of C₆D₆, with ¹H NMR spectra referenced using the highest intensity peak of the lower frequency fluorobenzene multiplet (δ_H 6.86) and ¹³C{¹H}_DEPTQ spectra referenced to C₆D₆. ¹¹B/¹¹B{¹H} (H₃BO₃/D₂O), ¹⁹F (C₇H₅F₃/CDCl₃) and ²⁹Si{¹H}_DEPT90 (SiMe₄) NMR spectra were referenced to external standards. The C(CF₃)₃ carbon resonances of the [Al{OC(CF₃)₃}₄]^– anion was not observed in the ¹³C{¹H} NMR spectra of 1-Y or 2-Y, likely due to quadrupolar broadening by the 100% abundant I = ⁵/₂ ²⁷Al nuclei and coupling to multiple 100% abundant I = ¹/₂ ¹⁹F nuclei.

Single crystal XRD data were collected on either a Rigaku XtalLAB Synergy-S diffractometer (1-Ln, 2-Ln, 3-Ln) or a Rigaku FR-X diffractometer (4-Ln), both equipped with a HyPix 6000HE photon counting pixel array detector and a mirror-monochromated Cu Kα X-ray source (λ = 1.5418 Å). Intensities were integrated from data recorded on 0.5° frames by ω rotation. Cell parameters were refined from the observed positions of all strong reflections in each data set. A Gaussian grid face-indexed with a beam profile was applied for all structures, with crystal faces determined directly on the mounted crystal using CrysAlisPro⁵¹. The structures were solved using SHELXT⁵²; the datasets were refined by full-matrix least-squares on all unique F² values⁵³. Anisotropic displacement parameters were used for all non-hydrogen atoms with constrained riding hydrogen geometries, with the exception of borohydride H atoms, which were located in the difference map and refined isotropically; U_iso(H) was set at 1.2 (1.5 for methyl groups) times U_eq of the parent atom. Crystallographic disorder in the [Al{OC(CF₃)₃}₄]^– anions of 1-Ln were modelled by treating each of the three disordered perfluoroalkoxy groups present in each structure as an equivalent residue, which were then allowed to freely refine over two positions, converging at a final ratio of 0.66: 0.34 for 1-Dy and 0.77: 0.23 for 1-Y. To aid the refinement of 1-Y, one Al···F distance was restrained to be over 3.1 Å, and two disordered O and two disordered C atoms were allowed to occupy the same space. Similarity thermal restraints were applied to the disordered anion, and enhanced rigid bond restraints were used on all atoms. The datasets for 2-Ln, 3-Ln and 4-Ln did not exhibit any significant disorder, though 2-Y was refined a two-component inversion twin. For 3-Ln and 4-Ln the B–H bonds were restrained to be approximately 1.15 Å, and the H···H distances were restrained to be approximately equal. The largest features in the final difference syntheses were close to heavy atoms and were of no chemical significance. CrysAlisPro⁵¹ was used for control and integration, and SHELX^52,53 was employed through OLEX2⁵⁴ for structure solution and refinement. ORTEP-3⁵⁵ and POV-Ray⁵⁶ were used for molecular graphics.

Powder XRD data were collected at 100 K using a Rigaku FR-X rotating anode single crystal X-ray diffractometer with a HyPix 6000HE photon counting pixel array detector and a mirror-monochromated Cu Kα X-ray source (λ = 1.5418 Å). Samples of crystalline material finely ground and mixed into a paste with minimal Fomblin were mounted on glass filaments⁵⁷. Data were collected between 3 and 120 °θ with a detector distance of 150 mm and a beam divergence of 1.5 mRad using CrysAlisPro⁵¹. For data processing, the instrument was calibrated using silver behenate as standard, then the data were reduced and integrated using CrysAlisPro⁵¹. Le Bail profile analysis was performed using Profex 5.5.0 using default refinement and convergence limits⁵⁸. ATR-IR spectra were recorded as microcrystalline powders using a Agilent Cary FT-IR spectrometer with a diamond-ATR module within an argon-filled glovebox at ambient temperature. Elemental analysis (C, H, N) samples were prepared in an argon-filled glovebox at the Microanalytical service, Department of Chemistry, the University of Manchester³².

General procedure for the synthesis of 1-Ln and 2-Ln

A solution of 3-Ln or 4-Ln (0.2 mmol) in C₆H₅F (2 mL) and a solution of [CPh₃][Al{OC(CF₃)₃}₄] (242.0 mg, 0.2 mmol) in C₆H₅F (2 mL) were combined with gentle agitation and left to stand for 2 h at ambient temperature. The volatiles were removed in vacuo, and the residues triturated with excess n-hexane (3 × 2 mL) to remove the majority of the concomitantly formed HCPh₃. The resulting solid was redissolved in C₆H₅F (1 mL), filtered, and layered with n-hexane (ca. 5 mL), which upon diffusion at –35 °C gave the title complexes as crystalline solids. The supernatants were decanted and the crystals dried in vacuo. No attempt was made to collect any subsequent crop.

[Dy{N(SiⁱPr₃)₂}(Cp^ttt)][Al{OC(CF₃)₃}₄] (1-Dy)

Yield: 163.2 mg, 0.0965 mmol, 48%, pale yellow crystals. Anal. Calcd for C₅₁H₇₁AlDyF₃₆NO₄Si₂ (1691.73 g mol^-1) C, 36.21; H, 4.23; N, 0.83. Found: C, 35.42; H, 3.82; N, 0.76. ¹⁹F NMR (376.40 MHz, C₆H₅F): δ 94.78 (s, OC(CF₃)₃). FTIR (ATR, microcrystalline): ṽ (cm^–1) = 2964 (w), 2873 (w), 2785 (w), 2793 (w), 2594 (w), 1466 (w), 1349 (m), 1295 (s), 1275 (s), 1238 (s), 1211 (s), 1162 (s), 1067 (w), 1002 (m), 968 (s), 880 (m), 831 (m), 755 (w), 726 (s), 710 (s), 668 (m).

[Y{N(SiⁱPr₃)₂}(Cp^ttt)][Al{OC(CF₃)₃}₄] (1-Y)

Yield: 120.1 mg, 0.0742 mmol, 37%, colourless crystals. Anal. Calcd for C₅₁H₇₁AlF₃₆NO₄Si₂Y (1618.13 g mol^-1) C, 37.86; H, 4.42; N, 0.87. Found: C, 37.97; H, 4.24; N, 0.82. ¹H NMR (400.07 MHz, C₆H₅F): δ 6.37 (s, 2H, 3,5-CH), 1.12 (s, 18H, 1,2-CCMe₃), 0.97 (s, 9H, 4-CCMe₃), 0.87 (d, ³J_HH = 7.5 Hz, 18H, CH(CH₃)₂), 0.55 (sept, ³J_HH = 7.3 Hz, 6H, CH(CH₃)₂). ¹³C{¹H}_DEPTQ NMR (100.60 MHz, C₆H₅F): δ 146.39 (s, 4-CCMe₃), 145.22 (s, 1,2-CCMe₃), 121.99 (q, ¹J_FC = 292 Hz, OC(CF₃)₃), 117.94 (s, 3,5-CH), 34.71 (s, 1,2-CCMe₃), 33.43 (s, 4-CCMe₃), 32.64 (s, 1,2-CCMe₃), 30.78 (s, 4-CCMe₃), 18.48 (s, CH(CH₃)₂), 15.32 (s, CH(CH₃)₂). ¹⁹F NMR (376.40 MHz, C₆H₅F): δ 75.08 (s, OC(CF₃)₃).). ²⁹Si{¹H}_DEPT90 NMR (79.48 MHz, C₆H₅F): δ –4.86 (s). FTIR (ATR, microcrystalline): ṽ (cm^–1) = 2964 (w), 2873 (w), 2785 (w), 2793 (w), 2594 (w), 1466 (w), 1349 (m), 1295 (s), 1275 (s), 1238 (s), 1211 (s), 1162 (s), 1067 (w), 1002 (m), 968 (s), 880 (m), 831 (m), 755 (w), 726 (s), 710 (s), 668 (m).

[Dy{N(SiⁱPr₃)₂}(Cp′′′)][Al{OC(CF₃)₃}₄] (2-Dy)

Yield: 129.8 mg, 0.0746 mmol, 37%, pale yellow crystals. Anal. Calcd for C₄₈H₇₁AlDyF₃₆NO₄Si₅ (1739.95 g mol^-1) C, 33.13; H, 4.11; N, 0.81. Found: C, 32.94; H, 3.91; N, 0.70. ¹⁹F NMR (376.40 MHz, C₆H₅F): δ 90.40 (s, OC(CF₃)₃). FTIR (ATR, microcrystalline): ṽ (cm^–1) = 2956 (w), 2874 (w), 2792 (w), 2737 (w), 2591 (w), 1462 (w), 1351 (m), 1296 (s), 1274 (s), 1237 (s), 1210 (s) 1165 (s), 1087 (m), 1024 (m), 1002 (m), 970 (s), 932 (m), 871 (m), 827 (m), 755 (m), 726 (s), 708 (m), 666 (m).

[Y{N(SiⁱPr₃)₂}(Cp′′′)][Al{OC(CF₃)₃}₄] (2-Y)

Yield: 144.0 mg, 0.0864 mmol, 43%, pale yellow crystals. Anal. Calcd for C₄₈H₇₁AlF₃₆NO₄Si₅Y (1666.35 g mol^-1) C, 34.60; H, 4.29; N, 0.84. Found: C, 35.10; H, 4.21; N, 0.78. ¹H NMR (400.07 MHz, C₆H₅F): δ 7.42 (s, 2H, 3,5-CH), 1.05 (d, ³J_HH = 7.2 Hz, 36H, CH(CH₃)₂), 0.77 (sept, ³J_HH = 7.4 Hz, 6H, CH(CH₃)₂), 0.28 (s, 18H, 1,2-CSiMe₃), 0.21 (s, 9H, 4-CSiMe₃). ¹³C{¹H}_DEPTQ NMR (100.60 MHz, C₆H₅F): δ 145.26 (s, 1,2-CSiMe₃), 140.60 (s, 3,5-CH), 140.28 (s, 4-CSiMe₃), 121.99 (q, ¹J_FC = 292 Hz, OC(CF₃)₃), 18.76 (s, CH(CH₃)₂), 14.48 (s, CH(CH₃)₂), 0.72 (s, 1,2-CSiMe₃), -0.77 (s, 4-CSiMe₃). ¹⁹F NMR (376.40 MHz, C₆H₅F): δ 75.20 (s, OC(CF₃)₃). ²⁹Si{¹H}_DEPT90 NMR (79.48 MHz, C₆H₅F): δ –4.85 (s, N(SiⁱPr₃)₂), –7.54 (s, 4-SiMe₃), –7.73 (s, 1,2-SiMe₃). FTIR (ATR, microcrystalline): ṽ (cm^–1) = 2956 (w), 2874 (w), 2792 (w), 2737 (w), 2591 (w), 1462 (w), 1351 (m), 1296 (s), 1274 (s), 1237 (s), 1210 (s) 1165 (s), 1087 (m), 1024 (m), 1002 (m), 970 (s), 932 (m), 871 (m), 827 (m), 755 (m), 726 (s), 708 (m), 666 (m).

General procedure for the preparation of borohydrides 3-Ln and 4-Ln

A mixture of [Ln{N(SiⁱPr₃)₂}(BH₄)₂]₄ (Ln = Dy: 260.4 mg; Ln = Y, 223.6 mg; 0.5 mmol) and KCp^ttt (136.3 mg, 0.5 mmol) or KCp′′′ (160.4 mg, 0.5 mmol) were suspended in C₆H₆ (10 mL) and stirred at ambient temperature for 18 h. The crude reaction mixture was evaporated to dryness in vacuo and the product extracted into n-hexane (3 × 10 mL), and the solution then concentrated to ca. 5 mL. Storage at –35 °C gave crystalline material, which was triturated with cold (–35 °C) n-hexane (2 × 1 mL) and dried thoroughly in vacuo. An additional crop was obtained on storage of the n-hexane triturate at –35 °C.

[Dy{N(SiⁱPr₃)₂}(Cp^ttt)(BH₄)] (3-Dy)

Yield: 232.0 mg, 0.314 mmol, 62%, colourless crystals. Anal. Calcd for C₃₅H₇₅BDyNSi₂ (739.47 g mol^-1) C, 56.85; H, 10.22; N, 1.89. Found: C, 56.14; H, 10.40; N, 1.98. ¹H NMR (400.07 MHz, C₆D₆): δ 87.5 (broad, FWHM ~ 7,000 Hz), 23.0, 18.0, 17.5, 17.1, 16.0, 3.01 (broad, FWHM ~ 28,000 Hz), –33.25 (broad, FWHM ~ 12,000 Hz). FTIR (ATR, microcrystalline): ṽ (cm^–1) = 2946 (s), 2864 (s), 2699 (m), 2487 (m), 2200 (w), 2132 (w), 1468 (s), 1386 (w), 1363 (m), 1234 (m), 994 (s), 972 (s), 956 (s), 942 (s), 879 (s), 826 (s), 692 (s).

[Y{N(SiⁱPr₃)₂}(Cp^ttt)(BH₄)] (3-Y)

Yield: 277.3 mg, 0.416 mmol, 83%, colourless crystals. Anal. Calcd for C₃₅H₇₅BNSi₂Y (665.88 g mol^-1) C, 63.13; H, 11.35; N, 2.10. Found: C, 62.72; H, 11.48; N, 2.16. ¹H{¹¹B} NMR (400.07 MHz, C₆D₆): δ 6.29 (s, 2H, 3,5-CH), 1.50 (s, 18H 1,2-CCMe₃), 1.35 (d, ¹J_YH = 13.3 Hz, 4H, BH₄), 1.32 (d, ³J_HH = 7.3 Hz, 18H, CH(CH₃)₂), 1.28 (d, ³J_HH = 7.3 Hz, 18H, CH(CH₃)₂), 1.26 (s, 9H, 4-CCMe₃), 0.90 (sept, ³J_HH = 7.3 Hz, 6H, CH(CH₃)₂). The BH₄ resonance in the ¹¹B-coupled ¹H spectrum is a very broad quartet of doublets, obscured by the ⁱPr and ^tBu resonances. ¹¹B NMR (128.36 MHz, C₆D₆): δ –19.34 (pent, ¹J_BH = 83.3 Hz, BH₄). ¹³C{¹H}_DEPTQ NMR (100.60 MHz, C₆D₆): δ 140.86 (d, ¹J_YC = 0.6 Hz, 1,2-CCMe₃), 139.42 (d, ¹J_YC = 2.2 Hz, 4-CCMe₃), 113.35 (d, ¹J_YC = 0.9 Hz, 3,5-CH), 34.83 (s, 1,2-CCMe₃), 34.30 (s, 1,2-CCMe₃), 33.99 (s, 4-CCMe₃) 32.27 (s, 4-CCMe₃), 21.18 (s, CH(CH₃)₂), 20.38 (s, CH(CH₃)₂), 18.13 (s, CH(CH₃)₂). ²⁹Si{¹H}_DEPT90 NMR (79.48 MHz, C₆D₆): δ − 3.99 (s, N(SiⁱPr₃)₂). FTIR (ATR, microcrystalline): ṽ (cm^–1) = 2951 (s), 2865 (s), 2694 (m), 2487 (m), 2202 (w), 2129 (m), 1458 (s), 1393 (m) 1361 (m), 1238 (s), 1169 (m), 1001 (m), 930 (s), 874 (s), 834 (m), 720(s), 678 (m).

[Dy{N(SiⁱPr₃)₂}(Cp′′′)(BH₄)] (4-Dy)

Yield: 276.9 mg, 0.352 mmol, 70%, colourless crystals. Anal. Calcd for C₃₂H₇₅BDyNSi₅ (787.69 g mol^-1) C, 48.79; H, 9.60; N, 1.78. Found: C, 48.41; H, 9.76; N, 1.86. ¹H NMR (400.07 MHz, C₆D₆): δ 84.1 (broad, FWHM ~ 7,500 Hz), 19.5, 14.1, 13.9, 13.5, 12.4, 4.5 (broad, FWHM ~ 29,000 Hz), –36.7 (broad, FWHM ~ 14,000 Hz). FTIR (ATR, microcrystalline): ṽ (cm^–1) = 2946 (s), 2865 (s), 2689 (m), 2494 (m), 2265 (w), 2216 (w), 2139 (w), 1461 (m), 1391 (w), 1244 (s), 1194 (m), 1143 (w), 1087 (s), 994 (s), 933(s), 881 (m), 853 (s), 826 (s), 751 (s), 722 (s), 687 (s).

[Y{N(SiⁱPr₃)₂}(Cp′′′)(BH₄)] (4-Y)

Yield: 235.9 mg, 0.330 mmol, 66%, colourless crystals. Anal. Calcd for C₃₂H₇₅BNSi₅Y (714.10 g mol^-1) C, 53.82; H, 10.59; N, 1.96. Found: C, 52.71; H, 10.96; N, 2.10. ¹H{¹¹B} NMR (400.07 MHz, C₆D₆): δ 6.97 (s, 2H, 3,5-CH), 1.27 (d, ³J_HH = 7.4 Hz, 18H, CH(CH₃)₂), 1.26 (d, ³J_HH = 7.4 Hz, 18H, CH(CH₃)₂), 1.16 (d, ¹J_YH = 13.2 Hz, 4H, BH₄), 0.94 (sept, ³J_HH = 7.4 Hz, 6H, CH(CH₃)₂), 0.45 (s, 18H, 1,2-SiMe₃), 0.25 (s, 9H, 4-SiMe₃). The BH₄ resonance in the ¹¹B-coupled ¹H spectrum is a very broad quartet of doublets, obscured by the ⁱPr resonances. ¹¹B NMR (128.36 MHz, C₆D₆): δ –19.04 (pent, ¹J_BH = 85.2 Hz, BH₄). ¹³C{¹H}_DEPTQ NMR (100.60 MHz, C₆D₆): δ 139.09 (d, ¹J_YC = 0.9 Hz, 1,2-CSiMe₃), 135.35 (s, 3,5-CH), 130.22 (d, ¹J_YC = 2.8 Hz, 4-CSiMe₃), 21.01 (s, CH(CH₃)₂), 20.24 (s, CH(CH₃)₂), 17.29 (s, CH(CH₃)₂), 1.97 (s, 1,2-CSiMe₃), 0.87 (s, 4-CSiMe₃). ²⁹Si{¹H}_DEPT90 NMR (79.48 MHz, C₆D₆): δ –3.81 (s, N(SiⁱPr₃)₂), –8.13 (s, 4-SiMe₃), –8.44 (s, 1,2-SiMe₃). FTIR (ATR, microcrystalline): ṽ (cm^–1) = 2946 (s), 2865 (s), 2689 (m), 2494 (m), 2265 (w), 2216 (w), 2139 (w), 1461 (m), 1391 (w), 1244 (s), 1194 (m), 1143 (w), 1087 (s), 994 (s), 933(s), 881 (m), 853 (s), 826 (s), 751 (s), 722 (s), 687 (s).

Magnetometry

Magnetic measurements were performed on a Quantum Design MPMS3 superconducting quantum interference device (SQUID) magnetometer. Crystalline samples of 1-Dy (27.7 mg) and 2-Dy (24.2 mg) were ground to a microcrystalline powder and placed into a borosilicate NMR tube along with eicosane (22.8 mg and 24.1 mg respectively). The eicosane was melted by gentle heating and dispersed throughout the sample to immobilise the crystallites. After cooling, the tube was placed under vacuum (ca. 5 × 10^-3mbar) and flame-sealed to give an ampoule with a length of ca. 3 cm. The ampoule was mounted in the centre of a drinking straw using friction by wrapping it with Kapton tape, and the straw was fixed to the end of the sample rod. The measurements were corrected for the diamagnetism of the straw, borosilicate tube and eicosane using calibrated blanks, for the shape of the sample using Quantum Design Geometry Simulator (correction factor 1.006 for 1-Dy and 1.033 for 2-Dy), and for the intrinsic diamagnetism of the sample, which was estimated as the molecular weight multiplied by ‒0.5 $\times$ 10^–6 cm³ K mol^–1.

Zero-field cooled / field cooled (ZFC/FC) magnetic susceptibility was measured under a 0.1 T field at 0.5 K min^–1 between 1.8 and 300 K. Equilibrium susceptibility measurements were performed using vibrating sample magnetometry (VSM) mode with 5 mm vibrational amplitude and 2 s averaging time. Hysteresis measurements were performed between ± 7 T at low temperature, and ± 3 T at higher temperatures on the approach to T_H, using VSM mode with a 5 mm vibration amplitude and 2 s averaging time. All field-swept measurements were performed in continuous sweep mode with a sweep rate of 22 Oe s^–1 across the entire field range. The field was corrected using a Pd reference sample measured under the same conditions and interpolated using B-spline fitting functions²⁸.

DC decay measurements of 2-Dy were performed at temperatures between 2 and 21 K. The sample was initially saturated at 7 T before being the field was swept to 22 Oe (calibrated with a standard palladium sample to give an actual field of 0 Oe)³⁵ at 700 Oe/s. The moment was measured throughout the whole process using VSM mode with 5 mm amplitude and averaging time of 2 s. The data was fitted to a stretched exponential function $M\left(t\right)=M_{\mathrm{eq}}+\left(M_0-M_{\mathrm{eq}}\right)\exp \left[-{\left(\frac{t}{{\tau }^{*}}\right)}^{\beta }\right]$. During the fitting process, M_eq was fixed to zero and M₀ fixed to the first stable point at target field.

Alternating current (AC) susceptibility measurements were recorded at temperatures between 2 and 130 K (1-Dy), and 2 and 142 K (2-Dy), using 8 frequencies per decade between 0.1 and 1000 Hz with a 5 Oe oscillating field. Due to instrumental limitations, 750 and 1000 Hz frequencies were measured with a 2 Oe oscillating field. Averages were performed for 2 s or for 10 cycles, whichever was longer.

Waveform measurements³⁴ were performed to obtain low frequency in-phase and out-of-phase susceptibilities between 2 and 70 K (1-Dy), and 24 and 90 K (2-Dy). The magnet was reset before the sample was cooled in zero field and the moment measured as a function of time as a square wave dc field was applied. The magnitude of the field was ± 8 Oe, the sweep rate 700 Oe s^–1, with frequencies in the range 100 μHz to 100 mHz. Measurements were performed using VSM mode with a vibrational amplitude of 0.5 mm and averaging time of 0.5 s. A fixed range of 1 V was used to avoid unevenly spaced datapoints due to autoranging delays. In- and out-of-phase susceptibilities were extracted from the Fourier transform of the magnetic field and sample moment using CC-FIT2^18,35.

Susceptibilities extracted from analysis of waveform data and AC measurements were fitted to a Generalised Debye model $\chi \left(\omega \right)={\chi }_S+\left({\chi }_T-{\chi }_S\right)\frac{1}{1+{\left(i\omega \tau \right)}^{1-\alpha }}$ or a Double Generalised Debye model$\chi \left(\omega \right)={\chi }_{total}+\frac{\Delta {\chi }_1}{1+{\left(i\omega {\tau }_1\right)}^{1-{\alpha }_1}}+\frac{\Delta {\chi }_2}{1+{\left(i\omega {\tau }_2\right)}^{1-{\alpha }_2}}$ in CC-FIT2 to extract relaxation rates and distributions^18,35 (Tables S5 and S6). Here, ${\tau }^{-1}$ is the relaxation rate, $\omega$ is the angular frequency of the oscillating field, $\alpha$ parameterizes the width of the distribution¹⁸, ${\chi }_T$ and ${\chi }_S$ are the isothermal and adiabatic susceptibilities, ${\chi }_{total}={\chi }_{1S}+{\chi }_{2S}$, $\Delta {\chi }_1={\chi }_{1T}-{\chi }_{1S}$ and $\Delta {\chi }_2={\chi }_{2T}-{\chi }_{2S}$.

Computational

CASSCF-SO calculations were performed with OpenMolcas 24.06³⁷ on the cationic components of 1-Dy (including both cation geometries) and 2-Dy at the crystal structure geometries. To represent the crystalline environment, a single cation was embedded in a spherical point charge cluster of unit cells with a radius of approximately 40 Å. These point charges are CHELPG charges obtained from gas-phase DFT calculations of each anionic and cationic component. The spherical cluster was surrounded by a spherical conductor which screens unphysical surface charges, to reproduce the Madelung potential⁴⁰. The second order Douglas-Kroll-Hess Hamiltonian was used⁵⁹, and ANO-RCC basis sets of varying quality: VTZP contractions on Dy, VDZP on coordinated N and C, and VDZ elsewhere⁶⁰. The resolution of the identity approximation was used with the Cholesky ‘atomic compact’ auxiliary basis set⁶¹. State averaged CASSCF calculations were performed with 21 sextet, 224 quartet, and 490 doublet states. Of these, the lowest 21, 128 and 130 states were mixed with spin-orbit coupling.

To calculate the spin-phonon coupling, we followed our established methodology^40–44,62. First, periodic DFT geometry optimizations were performed using VASP^63–66 on 2-Dy (version 6.4.3), [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺²¹, and a model of 1-Dy (version 6.6.0). The large unit cell of 1-Dy precludes performing periodic DFT calculations on it. Instead, we used the optimized geometry of 2-Dy, substituting Cp”‘ for Cp^ttt and optimised this geometry. The PBE functional was used⁶⁷, with a plane wave basis set with an energy cutoff of 900 eV (determined by convergence testing) and PAW pseudopotentials including 4f-in-core pseudopotential on Dy^68,69. The electronic structure was sampled at the Γ point. The D3 dispersion correction was used⁷⁰. Atomic positions and cell parameters were optimized, fixing the cell volume to experiment (2-Dy), and half that of experiment (1-Dy model, accounting for the different packing between 1-Dy our model). Phonons were calculated by finite displacements using Phonopy⁷¹.

CASSCF calculations were performed following the same methodology as the calculations at the crystal structure geometry, other than only the high-spin 18 sextet roots (i.e., ⁶H + ⁶F) were calculated. The electronic structure is very similar to that calculated at the crystal structure geometries (Supplementary Information Tables S12-S14). The spin-phonon coupling for each phonon was calculated using our linear vibronic coupling method^44,63.

Magnetic relaxation rates were calculated at the optimized DFT geometry using Tau2⁴². In addition to rate calculations on 1-Dy, 2-Dy and [Dy{N(SiⁱPr₃)₂}(Cp*)]⁺²¹, we additionally calculated the relaxation rates of [Dy(amide)(amide-alkene)]⁺²⁰ and [Dy(Cp^ttt)₂]⁺⁴³, based on the spin-phonon calculations in our previous studies but using our updated methodology in Tau2. A 2 Oe field was applied along the principal axis. One phonon (Orbach and direct, equation 3 of ref. ⁴²) and Raman-I (equation 15 of ref. ⁴²) rates were calculated. An anti-Lorentzian lineshape was used, with fixed full-width at half-maximum (FWHM) linewidths between 1-100 cm⁻¹. For Raman rates, the phonon lineshape is restricted to the equivalent of 2 standard deviations of the full lineshape and modes whose phonon energy plus the phonon linewidth is less than the first excited Kramers doublet are included in the Raman rate calculation. In Tau2, Raman rates are evaluated via calculation of a temperature-independent “Raman spectral density” (equations 11−14 of ref. ⁴²); this is evaluated on an even-spaced grid of phonon energies with a resolution of FWHM / 10. For one phonon rates, all modes are included. Phonons were sampled on Γ centred q-meshes from 1×1×1 to 3×3×3. While our calculated phonons have no imaginary modes at the Γ point, meshes other than 1×1×1 have small ( < 10i cm⁻¹) imaginary modes. Their effect is negligible since (consistent with our previous studies^20,43) rates calculated on the 1×1×1 mesh are indistinguishable from others, whether imaginary modes are removed or set to their absolute value (Figure S98). Rates showed little dependence on FWHM (Figure S99–S101), so for consistency with our previous studies we chose a FWHM of 10 cm^−120,43. Raman rates were calculated between the ground state doublet, including 16 spin-orbit states (the ⁶H_15/2 level) in the sum over c states. For one-phonon rates, transitions within the ⁶H_15/2 level were included. Hysteresis simulation followed the methodology we developed for [Dy(amide)(amide-alkene)]⁺²⁰. Rates were calculated on a mesh of temperatures (1–120 K), field orientations (50 on a Fibonacci hemisphere) and field magnitudes (2 Oe, and 0.05-7 T every 0.05 T, slightly finer than our previous study).

In the partial Hessian vibronic analysis (PHVA) of 2-Dy, atoms outside the localized region were assigned near-infinite mass (10⁹ a.u.), driving modes with these atoms towards zero energy, and resulting in periodic phonons localized modes in the region of interest. This results in a large spike at near zero energy in the PHVA phonon DOS (Supplementary Information Figure S95a). When calculating the spin-phonon coupling, contributions from the point charge region were excluded. This PHVA analysis was performed on three regions: the Cpʹʹʹ ligand, the amide ligand (in both cases excluding the central Dy) and the whole [Dy{N(SiⁱPr₃)₂}(Cpʹʹʹ)]⁺ cation, in addition to a calculation using non-localized phonons but only including spin-phonon coupling of the point charge region.

DFT geometry optimizations and vibrational analyses were performed on 3-Y, 4-Y, the cations of 1-Y and 2-Y, and separately the [Al{OC(CF₃)₃}₄]^– anion, for the purposes of assigning the experimental IR spectra (Figures S24, S27, S30 and S33)⁷². Calculations were performed in the Orca 5.0 software package⁷³, at the PBE0^74,75-D4^76,77 / def2-TZVP⁷⁸ level (including the default effective core potential for yttrium⁷⁹). The default Orca 5.0 integration grids, convergence method, and convergence thresholds (for both SCF and geometry iterations) were used throughout. The SCF energy calculations were expedited through employment of the RIJCOSX approximation⁸⁰ (and associated def2/J auxiliary basis set⁸¹) and DIIS convergence acceleration⁸². Geometry-optimized structures were verified as minima on the potential energy surface through the absence of imaginary vibrational modes.

Author contributions

Conceptualisation: J.E.-K., D.P.M. Methodology: J.E.-K., B.E.A., W.J.A.B., J.R., S.C.C., J.B., N.F.C., D.P.M. Investigation: J.E.-K., B.E.A., W.J.A.B., J.R., S.C.C., J.B. Visualisation: J.E.-K., B.E.A., W.J.A.B., S.C.C., N.F.C., D.P.M. Funding acquisition: N.F.C., D.P.M. Project administration: N.F.C., D.P.M. Supervision: N.F.C., D.P.M. Writing – original draft: J.E.-K., N.F.C., D.P.M. Writing – review & editing: J.E.-K., N.F.C., D.P.M.

Peer review

Peer review information

Nature Communications thanks the anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Funding

European Research Council grant StG-851504 (W.J.B., N.F.C.). European Research Council grant CoG-816268 (S.C.C., J.B., D.P.M.). Leverhulme Trust grant RPG-2013−16 (J.E.K., N.F.C., D.P.M.). UK Engineering and Physical Sciences Research Council EP/R002605X/1, EP/P001386/1, EP/S033181/1 and EP/T011289/1. Australian Research Council Discovery Project DP260102523 (B.A. and N.F.C.). Computational resources were provided by the National Computational Infrastructure with funding from the Australian Government.

Data availability

Research data generated in this study have been deposited on FigShare at https://figshare.com/doi/10.48420/32567592. A preprint of this article was deposited on ChemRxiv⁸³. All data are available from the corresponding authors upon request. Source Data are provided with this manuscript. Crystallographic data for the structures reported in this Article have been deposited at the Cambridge Crystallographic Data Centre, under deposition numbers CCDC 2558778 (1-Dy), 2558779 (1-Y), 2558780 (2-Dy), 2558781 (2-Y), 2558782 (3-Dy), 2558783 (3-Y), 2558784 (4-Dy) and 2558785 (4-Y). Copies of the data can be obtained free of charge via https://www.ccdc.cam.ac.uk/structures/. Source data are provided with this paper.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at https://doi.org/10.1038/s41467-026-77104-z.