Investigation of slow magnetic relaxation in a series of 1D polymeric cyclobutane-1,1-dicarboxylates based on Ln^IIIV^IV₂ units (Ln^III = Tb, Dy, Ho, Er, Tm, Yb): rare examples of V^IV-4f single-molecule magnets

Abstract

The reactions of VOSO₄·3H₂O with Na₂(cbdc) (cbdc²⁻ – dianion of cyclobutane-1,1-dicarboxylic acid) and lanthanide(III) nitrates taken in a molar ratio of 1 : 2 : 1 were found to yield a series of isostructural heterometallic compounds [NaLn(VO)₂(cbdc)₄(H₂O)₁₀]_n (1_Ln, Ln = Tb, Dy, Ho, Er, Tm, Yb). These compounds are constructed from trinuclear anionic units [Ln(VO)₂(cbdc)₄(H₂O)₈]⁻ ({LnV₂}⁻) linked by Na⁺ ions into 1D polymeric chains. The crystal structures of 1_Dy and 1_Er were determined by single-crystal X-ray diffraction (XRD), and their isostructurality with 1_Tb, 1_Ho, 1_Tm, and 1_Yb was proved by powder X-ray diffraction (PXRD). According to alternating current (ac) magnetic susceptibility measurements, 1_Dy, 1_Er, and 1_Yb exhibited field-induced slow relaxation of magnetization. Compound 1_Er is the first representative of Er^III–V^IV single-molecule magnets. Measuring the temperature dependences of the phase memory time (T_m) for 1_Dy and 1_Yb using pulsed EPR spectroscopy allowed us to observe the phenomenon of phase relaxation enhancement (PRE) at temperatures below 30 K. In future, this phenomenon may contribute to the evaluation of relaxation times of the lanthanide ions.

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Introduction

Effective ways for the synthesis of heterometallic 3d–4f coordination compounds exhibiting properties of a bulk magnet at the molecular level are currently being developed.¹ While constructing such complex molecules, paramagnetic 3d-metal ions are used, which are often involved in spin–spin exchange interactions via a super-exchange mechanism through a diamagnetic bridging ligand.² Thus, the value of the exchange parameter affects the relaxation characteristics of a single-molecule magnet (SMM): strong exchange interactions enable reduction of the contribution of quantum tunneling of magnetization (QTM) to the relaxation of magnetization, increasing the value of the energy barrier for magnetization reversal, while the presence of weak and dipole–dipole interactions in the compound reduces the value of this parameter.³

Among all known SMMs based on heterometallic 3d–4f systems, the magnetic properties of Cu^II–Ln^III complexes are the most well-studied; the influence of the geometric characteristics of the molecule on the parameter of exchange interactions was shown for these compounds.⁴ Similar to Cu^II, the V^IV ion also has S = 1/2, however, the electronic structure of these ions is different: a single unpaired electron of V^IV is located on the d_xy orbital, but not on the d_x²−y² orbital, as in the case of Cu^II (Fig. S1†).⁵ In this regard, Cu^II–Ln^III and V^IV–Ln^III compounds cannot be expected to exhibit identical magnetic properties. In addition, the geometric features of the V^IVO²⁺ ion, i.e. the presence of an oxo group, exclude the formation of V^IV–Ln^III compounds similar in structure to their analogues containing the ions of Cu^II and other divalent 3d-metals. Despite ongoing studies of V^IV–Ln^III complexes, very few such compounds exhibiting SMM properties have been obtained so far.⁶ Therefore, the synthesis and detailed study of the magnetic properties of V^IV–Ln^III systems is an urgent task of modern coordination chemistry. The presence of a single unpaired d-electron also gives rise to the interest in V^IV compounds as potential candidates for molecular-based spin qubits⁷ and makes them convenient objects for the study by EPR spectroscopy.

On the other hand, it is of interest to study 3d–4f SMMs containing lanthanide ions rarely used for these purposes, for example, Er^III and Yb^III (see ref. 8) or non-Kramers lanthanide ions, Ho^III and Tm^III (see ref. 9 and 10), for which the coordination environment is of great importance to control the magnetic anisotropy. To date, 3d–4f SMMs with Ho^III, Er^III, Tm^III, and Yb^III ions still remain much less studied than their Tb^III and Dy^III-containing counterparts.

Polydentate ligands that combine chelation with a variety of bridging coordination modes enable the constructing stable anionic blocks with atoms of 3d-elements and binding them with 4f-metal ions in a polynuclear molecule or coordination polymer without the use of additional ligands. An additional factor in the design of 3d–4f compounds can be the alkali metal ions introduced at the synthesis stage, which are diamagnetic, but often play a structure-directing role in the formation of the structure in the crystal, and therefore can influence the molecular geometry of the complex and, in particular, the coordination environment of paramagnetic metal centers. The structure-directing role of alkali metal ions has been studied for coordination polymers of s-elements,¹¹ heteronuclear compounds of s-3d (see ref. 12) and s-4f metals.¹³ Very few such studies are known for heterometallic 3d–4f systems.¹⁴

In our previous studies, we investigated the influence of the ionic radii of M^I (M = Na, K, Rb, Cs) and Ln^III on the composition, structure, and magnetic properties of heterometallic compounds formed in the M^I–Ln^III–V^IV systems with anions of cyclobutane-1,1-dicarboxylic acid (H₂cbdc).^6a,c,15 According to X-ray diffraction studies, alkali metal ions in this series of compounds affect not only the crystal packing of the compound, but also the geometric characteristics of the Ln^III–V^IV molecular fragments that form it, and, as a consequence, the exhibited magnetic properties. For Na^I, the formation of 1D polymeric structures [NaLn(VO)₂(cbdc)₄(H₂O)₁₀]_n was found in the systems with diamagnetic rare-earth metal ions Y^III and Lu^III (see ref. 16), as well as with Gd^III (see ref. 15).

The present work is the logical continuation of our previous research, so it sets out to synthesize heterometallic Na^I–Ln^III–V^IV compounds with paramagnetic lanthanide ions from Tb^III to Yb^III having high magnetic anisotropy and to study the slow magnetic relaxation phenomenon in the resulting complexes.

Results and discussion

Synthesis

The reactions of aqueous oxovanadium(IV) nitrate (prepared via metathesis between VOSO₄·3H₂O and Ba(NO₃)₂ in water), Na₂(cbdc) and lanthanide(III) nitrates (Tb^III, Dy^III, Ho^III, Er^III, Tm^III, Yb^III) in a molar ratio of 1 : 2 : 1 yielded blue crystals of a series of heterometallic compounds [NaLn(VO)₂(cbdc)₄(H₂O)₁₀]_n (1_Ln). Barium nitrate was added to the reaction mixture to remove sulfate anions from the solution, because the presence of these anions causes the crystallization of Ln^III sulfates.

The description of crystal structures

According to PXRD data, all 1_Ln compounds are isostructural (Fig. S2 in ESI†). The crystal structures of 1_Dy and 1_Er were determined by single-crystal XRD. Compounds 1_Dy and 1_Er crystallize in monoclinic space group C2/c. The asymmetric units of 1_Dy and 1_Er contain one vanadium atom (V1), one lanthanide atom (Dy1 or Er1), and one sodium atom (Na1). In addition to the vanadyl oxo group, V1 atom coordinates two chelating cbdc²⁻ anions and one water molecule, thus forming mononuclear bis-chelate {VO(cbdc)₂(H₂O)}²⁻ moiety.

The geometry of vanadium coordination polyhedron is a distorted octahedron (VO₆) whose equatorial plane is formed by four carboxylate O atoms. The O atoms of the oxo group and water molecule occupy the axial positions and form the shortened (∼1.60 Å) and the elongated (∼2.30 Å) bonds with a metal center, respectively (Fig. 1 and Table 1). The V1 atom deviates from the equatorial plane by 0.371 Å (in 1_Dy) and 0.374 Å (in 1_Er) towards oxo group, giving rise to the increase of V=O/V–O(cbdc) bond angles and the decrease of V–O(cbdc)/V–O(H₂O) ones (Table 2).

Fig. 1 The fragment of the 1D polymeric chain of 1_Dy (cyclobutane moieties are omitted for clarity) [symmetry codes: (a) 1 − x, y, 0.5 − z; (b) −x, y, 0.5 − z; (c) −1 + x, y, z; (d) 1 + x, y, z].

Table 1 Selected bond lengths and the shortest interatomic distances (d, Å) in structures 1_Dy and 1_Er

Compound	1Dy (Ln = Dy)	1Er (Ln = Er)
Bond/distance	d
V=O	1.600(2)	1.602(4)
V–O(cbdc)	1.965(2)–2.024(2)	1.965(4)–2.024(4)
V–O(H2O)	2.299(2)	2.310(4)
Ln–O(cbdc)	2.361(2)	2.335(3)
Ln–O(H2O)	2.349(2)–2.384(2)	2.317(4)–2.372(4)
Na–O(cbdc)	2.536(2), 2.637(2)	2.530(4), 2.638(4)
Na–O(H2O)	2.411(2), 2.447(2)	2.413(4), 2.449(4)
Ln⋯V	5.719(1)	5.699(2)
V⋯V	6.245(1)	6.249(3)

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Table 2 Selected bond angles (ω, °) characterizing the coordination polyhedra of vanadium in complexes 1_Dy and 1_Er

Compound	1Dy	1Er
Angle	ω
V=O/V–O(cbdc)	100.00(10)–101.90(11)	99.98(18)–102.08(18)
V=O/V–O(H2O)	177.65(10)	177.91(18)
V–O(cbdc)/V–O(cbdc) (acute)	85.62(9)–90.12(8)	85.39(15)–90.24(15)
V–O(cbdc)/V–O(H2O) (acute)	76.84(8)–81.88(8)	76.76(14)–81.73(14)

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Each lanthanide atom binds to the two {VO(cbdc)₂(H₂O)}²⁻ moieties via the coordination of two unchelated carboxylate O atoms. In the resulting {LnV₂}⁻ trinuclear unit, the central lanthanide atom additionally coordinates six water molecules completing its polyhedron having the geometry of a triangular dodecahedron (TDD-8, the deviations from the ideal figure, CShM values are 0.630 and 0.640 for 1_Dy and 1_Er respectively) (see Table S1 in the ESI†).¹⁷ Selected bond angles in the coordination polyhedra of lanthanides in structures 1_Dy and 1_Er are given in Tables S2 and S3 in the ESI†.

The neighboring [Ln(VO)₂(cbdc)₄(H₂O)₈]⁻ units are linked into a 1D polymeric structure due to the coordination of Na atoms to the carboxylate O atoms involved in the chelation of vanadium (Fig. 1 and Table 1). Each Na atom coordinates two monodentate water molecules. The crystal structures of 1_Dy and 1_Er are additionally stabilized by the network of hydrogen bonds, whose formation involves all the coordinated water molecules, the carboxylate O atoms, and vanadyl oxo group (Tables S4 and S5 in the ESI†).

Magnetic properties

The magnetic properties of the series of isostructural compounds 1_Ln (Ln = Tb, Dy, Ho, Er, Tm, Yb) were studied by measuring the temperature dependences of molar magnetic susceptibility (χ) in the 2–300 K temperature range under 5000 Oe dc-magnetic field. For all compounds, the experimental χT values at 300 K are in satisfactory agreement with theoretical ones for two magnetically isolated V^IV ions and one Ln^III ion (Table 3). For Tb^III, Dy^III, Ho^III, Er^III, and Tm^III-containing compounds, the χT values at 300 K slightly exceed the theoretical ones, but generally fit into the range of acceptable deviations (about 10% from the corresponding theoretical χT value).

Table 3 The χT values for 1_Ln under 5000 Oe field

Compound	χT (theor.), cm^3 K mol^−1	χT (300 K), cm^3 K mol^−1	χT (2 K), cm^3 K mol^−1
1Tb (Tb^IIIV^IV2)	12.58	13.74	6.76
1Dy (Dy^IIIV^IV2)	14.93	15.06	8.49
1Ho (Ho^IIIV^IV2)	14.83	15.15	4.68
1Er (Er^IIIV^IV2)	12.24	12.53	6.58
1Tm (Tm^IIIV^IV2)	7.91	8.60	6.69
1Yb (Yb^IIIV^IV2)	3.33	3.37	2.24

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For 1_Dy, 1_Ho, 1_Er (Fig. 2), the χT values monotonously decrease in the range from 300 to 100 K and then gradually decrease with decreasing temperature. On cooling below 10 K, the χT values sharply drop and reach a minimum at 2 K.

Fig. 2 The experimental χT vs. T plots for compounds 1_Ln in the range of 2–300 K under 5000 Oe field.

For 1_Tb, a monotonous increase in the χT is observed in the range from 300 to 30 K, probably indicating the presence of weak ferromagnetic interactions. It should be noted that the field-induced orientation of polycrystals was excluded by using the mineral oil during the sample preparation (see Experimental part). With a further decrease in temperature, a sharp decrease in the χT value occurs, reaching a minimum at 2 K. For 1_Tm, the χT value remains virtually constant up to 16 K and then sharply decrease with a further decrease in temperature down to 2 K.

For 1_Yb, a monotonous decrease in the χT value is observed in the range from 300 to 2 K. Such a behavior of the compounds under study can be due to the possible presence of spin–spin antiferromagnetic interactions and/or the depopulation of the excited Stark sublevels.¹⁸ The M(H) and M(H/T) dependences for all obtained complexes were also measured at 2, 4, and 6 K (Fig. S3–S6 in the ESI†).

In order to study magnetization relaxation of the compounds, ac-magnetic susceptibility measurements were carried out. In the absence of a dc-magnetic field, the values of the out-of-phase component of dynamic magnetic susceptibility (χ″) were close to zero for all the compounds, which may be due to a strong contribution from quantum tunneling to the relaxation of magnetization. Application of an external dc-field enabled to significantly reduce this effect and observe the χ″ non-zero values for 1_Dy, 1_Er, 1_Tm, and 1_Yb (Fig. S7–S12 in the ESI†).

The highest relaxation times were achieved on applying the optimal fields of 1000 Oe for 1_Dy, 1_Er, 1_Tm, and 2500 Oe for 1_Yb (Fig. S13–S15†). To produce the τ vs. 1/T plots, the χ″(ν) isotherms were approximated by the generalized Debye model (Fig. S16–S19 in the ESI†). The plots of τ vs. 1/T thus obtained were approximated by the equations corresponding to different relaxation mechanisms and their combinations. In the high-temperature range, all the τ vs. 1/T dependences were approximated using only the Orbach relaxation mechanism (τ⁻¹ = τ₀⁻¹·exp{−Δ_eff/k_BT}) to estimate the value of the effective energy barrier (Fig. 3, 4 and 5).

Fig. 3 The τ vs. 1/T plots for 1_Dy under 1000 Oe field. Blue dashed lines represent the fittings of high-temperature ranges by the Orbach mechanism. Red solid lines represent the fittings in the whole temperature range by the sum of the Orbach and QTM relaxation mechanisms.

Fig. 4 The τ vs. 1/T plots for 1_Er under 1000 Oe field. Blue dotted line represents the fitting of a high-temperature range by the Orbach mechanism. Red solid line represents the fitting by the Raman relaxation mechanism.

Fig. 5 The τ vs. 1/T plots for 1_Yb under 2500 Oe field. Blue dotted line represents the fitting of a high-temperature range by the Orbach mechanism. Red solid line represents the fitting by the sum of the Raman and direct relaxation mechanisms.

According to the approximation of χ″ vs. ν dependencies by the generalized Debye model (Fig. S16†), there are at least two or even more relaxation processes for complex 1_Dy also confirmed by Cole–Cole plots (Fig. S20 in the ESI†). This may be due to the independent relaxation of Dy^III and V^IV ions¹⁹ and/or possible disorder of water molecules coordinated to Dy^III (see ref. 14c and 20). Unfortunately, we failed to obtain isostructural analogue of complex 1_Dy with diamagnetic d-metal ions (Zn^II, Cd^II), so it was impossible to evaluate the contribution of Dy^III ions to the magnetic relaxation dynamics of complex 1_Dy. Previously, the magnetic properties of isostructural complexes [NaLn(VO)₂(cbdc)₄(H₂O)₁₀]_n with diamagnetic rare-earth ions (Ln = Y^III, Lu^III) were studied.¹⁶ In both complexes, the presence of field-induced slow relaxation of magnetization was shown by ac-susceptibility measurements. This suggests the contribution of V^IV ions to the magnetic relaxation dynamics in the case of complex 1_Dy. Therefore, τ vs. 1/T plots for 1_Dy were built using both low-frequency (LF) and high-frequency (HF) maxima of χ″ vs. ν dependencies (Fig. 3). The good agreement between the experimental τ vs. 1/T plots and approximation equation can be achieved using parameters for the sum of the Orbach and QTM relaxation mechanisms (τ⁻¹ = τ⁻¹₀·exp{−Δ_eff/k_BT} + B) both for LF and HF (Table 4).

Table 4 The best-fit parameters of magnetization relaxation for 1_Dy

	Orbach		Orbach + QTM
	Δ eff/kB, K	τ 0, s	Δ eff/kB, K	τ 0, s	B, s^−1
LF	50.4 ± 0.2	2.70 × 10^−8 ± 8 × 10^−10	52 (fixed)	2.1 × 10^−8 ± 2 × 10^−9	560 ± 11
HF	26 ± 2	4 × 10^−7 ± 1 × 10^−7	39 ± 3	6 × 10^−8 ± 3 × 10^−8	9066 ± 294

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For 1_Yb, the best-fit of the experimental τ vs. 1/T dependence in the whole temperature range was achieved by the sum of the Raman and direct relaxation mechanisms according to the equation τ⁻¹ = C_RamanT^n_Raman + A_directTH⁴ (Fig. 5). For 1_Er, the corresponding fit was achieved with the use of only the Raman relaxation mechanism (τ⁻¹ = C_RamanT^n_Raman) (Fig. 4).

For 1_Tm, the χ″ values are less than the χ′ ones by more than 10 times (but χ′/χ″ ratio is close to 10), thus the presence of slow relaxation of magnetization is questionable in this case. All obtained magnetic relaxation data for 1_Tm is presented in the ESI (Fig. S21 and Table S6†).

The best-fit parameters for the approximations of τ vs. 1/T plots obtained for 1_Er and 1_Yb are given in Table 5.

Table 5 The best-fit parameters of magnetization relaxation for 1_Er and 1_Yb

Compound	Orbach		Raman + direct			Raman
	Δ eff/kB, K	τ 0, s	A direct, K^−1 Oe^−4 s^−1	C Raman, s^−1 K^−n_Raman	n_ Raman	C Raman, c^−1 K^−n_Raman	n_ Raman
1Er	19.2 ± 0.2	1.8 × 10^−8 ± 1 × 10^−9	—	—	—	41.0 ± 0.5	7 (fixed)
1Yb	44.8 ± 0.5	5.3 × 10^−8 ± 4 × 10^−9	1.20 × 10^−11 ± 2 × 10^−13	3.5 × 10^−2 ± 4 × 10^−3	7 (fixed)	—	—

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It is worth pointing out that for 1_Er, the value of n_Raman = 7 is lower than the expected value for the Kramers systems (n = 9), indicating the presence of a Raman process through spin-phonon relaxation.²¹

In addition, for all compounds, the calculations of alternative magnetic relaxation parameters were performed using MagSuite v.3.2 software.²² The results obtained are presented in Fig. S22–S24 and Tables S7–S9.†

The first V^IV–Dy^III SMM was described by K. Kotrle et al. (see ref. 6b), but the authors failed to determine possible relaxation mechanisms and estimate the effective energy barrier for this compound. The literature review showed that the value of Δ_eff/k_B calculated for 1_Dy is higher than those for the most known 3d-Dy^III SMMs with paramagnetic 3d-metal ions and a similar triangular dodecahedral DyO₈ coordination environment (Table 6).

Table 6 Parameters of slow magnetic relaxation of the reported 3d-Dy^III SMMs with paramagnetic 3d-metal ions and triangular dodecahedral DyO₈ coordination environment

Compound	Dy^IIIO8 coordination polyhedron	Δ eff/kB, K (Hdc, Oe)	τ 0, s	Ref.
^[1]bpy = 2,2′-bipyridine; ^[2]NO2-benz^− = 3-nitrobenzoate; ^[3]hfac^− = 1,1,1,5,5,5-hexafluoroacetylacetonate; ^[4]bpca^− = bis(2-pyridylcarbonyl)amine; ^[5]H2vanox = o-vanillinoxime; ^[6]Br-benz^− = 4-bromobenzoate; ^[7]HL = 6-chloro-2-pyridinol; ^[8]piv^− = trimethylacetate; ^[9]H2L = N,N′-dimethyl-N,N′-bis(2-hydroxy-3,5-dimethylbenzyl)ethylenediamine; ^[10]PhCO2^− = phenylacetate; ^[11]H2L = 6,6′-{(2-(dimethylamino)ethylazanediyl)-bis(methylene)}bis(2-methoxy-4-methylphenol); ^[12]H3L = N,N′-bis(3-methoxysalicylidene)-1,3-diamino-2-propanol; ^[13]OAc^− = acetate; ^[14]benz^− = benzoate; ^[15]H2L = (2-((2-hydroxy-3-methoxybenzylidene)amino)benzoic acid); ^[16]H2L = 2-{[(2-hydroxy-3-methoxybenzyl)imino]methyl}phenol; ^[17]H2L = 2-(benzothiazol-2-ylhydrazonomethyl)-6-methoxyphenol; ^[18]H3L = ligand formed from the in situ condensation reaction of 3-amino-1,2-propanediol with 2-hydroxy-1-naphthaldehyde; ^[19]phen = 1,10-phenanthroline; ^[20]mbenz^− = 3-methylbenzoate; ^[21]F-benz^− = 4-fluorobenzoate; ^[22]L = 1,3,5-Tris(2-di(2′-pyridyl)hydroxymethylphenyl)benzene; ^[23]OTf^− = trifluoromethanesulfonate; ^[24]4-^tBubenz = 4-tert-butylbenzoate; ^[25]tBudeaH2 = N-tert-butyldiethanolamine; ^[26]Cl-benz = 4-chlorobenzoate; ^[27]ipO^− = 2-hydroxyisophthalate; ^[28]HCO2^− = formate; ^[29]FcCO2^− = ferrocenecarboxylate; ^[30]teaH3 = triethanolamine; ^[31]MePh = toluene; ^[32]HL = 8-hydroxyquinoline. a TDD-8 = triangular dodecahedron.b BTPR-8 = bicapped trigonal prism.c SAPR-8 = square antiprism.d Rough estimation using ln(χ″/χ′) = ln(2πντ0) + Δeff/kBT equation.e Recalculated from cm^−1.
[Dy^III2Ni^II2(bpy^[1])2(NO2-benz^[2])10]	TDD-8^a	2.8 (0)	5.47 × 10^−6	23a
[{Dy^III(hfac^[3])3}2{Ni^II(bpca^[4])2}]·CHCl3	TDD-8	4.9 (1000)	1.3 × 10^−6	23b
[Fe^III6Dy^III3(OMe)9(vanox^[5])6(Br-benz^[6])6]	TDD-8	4.9 (1000)	5.2 × 10^−5	23c
[Dy^III2Co^II6(OH)4(L^[7])6(piv^[8])8(MeCN)2]·0.5CH2Cl2	TDD-8	7.7^d (1000)	5.7 × 10^−8	23d
[Co^II2(L^[9])2(PhCO2^[10])2Dy^III2(hfac)4]	TDD-8	8.8^d (0)	2.0 × 10^−7	23e
		7.8^d (1000)	3.9 × 10^−7
[{Dy^III(hfac)3}2{Fe^II(bpca)2}]·CHCl3	TDD-8	9.7 (1000)	8.7 × 10^−8	23b
[Ni^II3Dy^III3(O)(OH)3(L^[11])3(piv)3](ClO4)·8MeCN·3CH2Cl2·5.5H2O	TDD-8	∼10 (3000)	∼10^−6	23f
[Ni^II2Dy^III2(CO3)2(HL^[12])(EtOH)(OAc^[13])]·2EtOH	TDD-8	11.52 (1200)	5.01 × 10^−6	23g
[Fe^III6Dy^III3(OMe)9(vanox)6(benz^[14])6]	TDD-8	12.4 (2000)	8.0 × 10^−5	23h
[Co^II4Dy^III4(L^[15])4(piv)8(OH)4(MeOH)2] H2O·3MeOH	TDD-8	12.5 (0)	1.51 × 10^−6	23i
[Dy^III2Ni^II2Mn^III2(L^[16])4(OAc)2(OH)4(MeOH)2](NO3)2·2MeOH	TDD-8	13.0 (0)	2.8 × 10^−7	23j
[Dy^III2Ni^II4(L^[16])4(OAc)2(OH)4(MeOH)2]·4MeOH	TDD-8	13.4 (0)	3.4 × 10^−7	23j
[Dy^III2Ni^II2(OH)3(OAc)4(HL^[17])2(MeOH)3](ClO4)3 3MeOH	TDD-8 ↔ BTPR-8^b	7.6 (1200)	7.5 × 10^−6	23k
[Dy^III2Co^II8(OMe)2(L^[18])4(HL^[18])2(OAc)2(NO3)2(MeCN)2]·MeCN·H2O	TDD-8	14.89 (0)	1.68 × 10^−7	23l
[Dy^IIIFe^II(H2O)(phen^[19])(mbenz^[20])5]	TDD-8	17 (3000)	2.6 × 10^−9	23m
[Dy^IIINi^II(H2O)(phen)(mbenz)5]	TDD-8	20 (5000)	1.38 × 10^−8	23m
[Fe^III6Dy^III3(OMe)9(vanox)6(F-benz^[21])6]	TDD-8, TDD-8 ↔ SAPR-8^c	21.3 (1500)	4.1 × 10^−7	23c
[Dy^III2Ni^II2(bipy)2(mbenz)10]	TDD-8	25.9 (0)	1.16 × 10^−6	23a
[(L^[22])Dy^IIIMn^IV3O4(OAc)3(DMF)2](OTf^[23])	TDD-8	27 (0)	2.13 × 10^−8	23n
[Cr^III2Dy^III2(OMe)(OH)(4-^tBubenz^[24])4(^tBudea^[25])2(NO3)2]·MeOH·2Et2O	TDD-8 ↔ SAPR-8	31.3^e (0)	7.7 × 10^−8	23o
[Fe^III6Dy^III3(OMe)9(vanox)6(Cl-benz^[26])6]	TDD-8, TDD-8 ↔ SAPR-8	36.1 (2000)	3.4 × 10^−7	23c
[Dy^III2Ni^II2(bpy)2(benz)10]	TDD-8	39.9 (0)	1.80 × 10^−8	23a
[NaDy ^III (V ^IV O) 2 (cbdc) 4 (H 2 O) 10 ] n	TDD-8	LF: 50.4 (1000)	2.70 × 10 ^−8	This work
		HF: 26 (1000)	4 × 10 ^−7
[Dy^III2Cu^II6(ipO^[27])6(H2O)12]n	TDD-8	63.68 (2000)	3.77 × 10^−8	23p
[Mn^IV3Mn^III18Dy^IIIO20(OH)2(piv)20(HCO2^[28])4(NO3)3(H2O)7]·5MeNO2 H2O	TDD-8	74 (0)	2.0 × 10^−12	23q
[Dy^III2Cr^III2(OH)2(FcCO2^[29])4(NO3)2(Htea^[30])2]·2MePh^[31]·2THF	TDD-8	75 (0)	26 × 10^−9	23r
[Ni^II6Dy^III(L^[32])8(OAc)2(NO3)(OH)2(OMe)2]	TDD-8	122.73 (0)	7.64 × 10^−13	23s

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Considering the previously obtained magnetic data for potassium-containing analogues of 1_Dy and 1_Yb (see ref. 6a), it can be concluded that in V^IV–Ln^III systems with cbdc²⁻, the substitution of potassium by sodium ions giving rise to a significant change in the crystal structure and coordination environment of the lanthanide ion has a positive influence on their SMM behavior. For 1_Dy, the appearance of slow magnetic relaxation is observed compared to K^I–V^IV–Dy^III compound. One of the possible explanations for such differences in the magnetic behavior of two Dy-containing compounds may be the difference in Dy^III coordination polyhedra, which is a biaugmented trigonal prism (C_2v symmetry) in K^I–Dy^III–V^IV and a triangular dodecahedron (D_2d symmetry) in 1_Dy. Another factor influencing SMM behavior is supposed to be the longer Dy⋯V distances in 1_Dy (5.719 Å) compared to K^I–V^IV–Dy^III (4.627 Å), that allow weakening of dipole–dipole interactions between Dy^III and V^IV ions.

For 1_Yb, the increase in the Δ_eff/k_B value to 44.8 K occurs compared to the K^I–Yb^III–V^IV compound (Δ_eff/k_B = 26 K), although, in these compounds, the Yb^III coordination polyhedra have similar geometry (triangular dodecahedron) and the shortest Yb⋯V distances are also similar (5.684 Å in K^I–Yb^III–V^IV and ∼5.7 Å in 1_Yb). Thus, the possible influence of crystal packing and intermolecular interactions on SMM behavior can be assumed in this case.

The literature review showed that 3d-Er^III and 3d-Yb^III SMMs containing paramagnetic 3d-metal ions are quite rare (Tables 7 and 8). To date, compound 1_Er is the first representative of heterometallic V^IV–Er^III single-molecule magnets. The value of Δ_eff/k_B calculated for 1_Er is comparable with those for compounds with triangular dodecahedral ErO₈ coordination environment (Table 7). Among all reported heterometallic compounds of such type, 1_Yb displays the record value of Δ_eff/k_B (Table 8).

Table 7 The parameters of slow magnetic relaxation of the reported 3d-Er^III SMMs with paramagnetic 3d-metal ions

Compound	Er^III environment, coordination polyhedron	Δ eff/kB, K (Hdc, Oe)	τ 0, s	Ref.
^[1]2-PNO = 2-picoline-N-oxide; ^[2]piv^− = trimethylacetate; ^[3]2-ma = 2-methylalanine; ^[4]H2pmide = N-(2-pyridylmethyl)iminodiethanol; ^[5]p-Me-benz^− = 4-methylbenzoate; ^[6]o-tol = o-toluate; ^[7]H3L = (E)-2-(hydroxymethyl)-6-(((2-hydroxyphenyl)imino)methyl)-4-methylphenol; ^[8]H2L = N,N′-dimethyl-N,N′-bis(2-hydroxy-3-formyl-5-bromo-benzyl)ethylenediamine; ^[9]OAc^− = acetate; ^[10]H6L = 2,2′-(propane-1,3-diyldiimino)bis[2-(hydroxylmethyl)propane-1,3-diol]; ^[11]{HB(pz)3}^− = hydrotris(pyrazolyl)borate; ^[12]pyim = 2-(1H-imidazol-2-yl)pyridine; ^[13]Ph3PO = triphenylphosphineoxide; ^[14]HL = 3-methoxy-N-[2-(methylsulfanyl)phenyl]salicylaldimine. a PBPY-7 = pentagonal bipyramid.b SAPR-8 = square antiprism.c TDD-8 = triangular dodecahedron.d CSAPR-9 = capped square antiprism.e MFF-9 = muffin.f JBCSAPR-10 = bicapped square antiprism.g Recalculated from cm^−1.
{[Fe^IIIEr^III(CN)6(2-PNO^[1])5]·4H2O}n	ErN2O5, PBPY-7^a	43.55 (1000)	2.10 × 10^−9	24a
(Et3NH)2[Ni^II2Er^III2(OH)2(piv^[2])10]	ErO8, SAPR-8^b	18 (1000)	3.9 × 10^−6	3
[Cu^II8Er^III(OH)8(2-ma^[3])8Cl2](ClO4)·21H2O	ErO8, SAPR-8	22.9 (0)	4.74 × 10^−7	24b
		33 (1000)	9.48 × 10^−6
[Fe^III2Er^III2(OH)2(pmide^[4])2(p-Me-benz^[5])6]·2MeCN	ErN2O6, SAPR-8	16.51 (1000)	2.03 × 10^−7	24c
[Cr^IIIEr^III6(OH)8(o-tol^[6])12(NO3)(MeOH)5]·2MeOH	ErO8, TDD-8^c	4.5 (3000)	9.1 × 10^−8	24d
[NaEr ^III (V ^IV O) 2 (cbdc) 4 (H 2 O) 10 ] n	ErO 8 , TDD-8	19.2 (1000)	1.8 × 10 ^−8	This work
[Ni^II4Er^III(L^[7])2(HL^[7])2(MeCN)3Cl]·2H2O·2MeCN	ErO8, TDD-8	31.87^g (4000)	7.94 × 10^−11	24e
[Ni^IIEr^III(L^[8])(OAc^[9])(NO3)2(MeCN)]·MeCN	ErO9, CSAPR-9^d	11.91 (1000)	5.12 × 10^−8	24f
(NMe4)2[Cu^II3Er^III2(H3L^[10])2(NO3)7(MeOH)2](NO3)	ErO9, CSAPR-9	14.8 (0)	1.2 × 10^−7	24g
[Fe^IIIEr^III{HB(pz)3}^[11](CN)3(NO3)2(pyim^[12])(Ph3PO^[13])]2·2MeCN	ErN4O5, MFF-9^e	57.6^g (2500)	—	24h
[Ni^IIEr^III(L^[14])2(NO3)3]·0.5H2O	ErO10, JBCSAPR-10^f	12.1 (1000)	3.49 × 10^−7	24i

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Table 8 The parameters of slow magnetic relaxation of the reported 3d-Yb^III SMMs with paramagnetic 3d-metal ions

Compound	Yb^III environment, coordination polyhedron	Δ eff/kB, K (Hdc, Oe)	τ 0, s	Ref.
^[1]phen = 1,10-phenanthroline; ^[2]OTf^− = trifluoromethanesulfonate; ^[3]AcrCN = acrylonitrile; ^[4]PrCN = propionitrile; ^[5]MalCN = malononitrile; ^[6]piv^− = trimethylacetate; ^[7]H2butyrat = 3-aminobutyric hydroxamic acid; ^[8]2-ma = 2-methylalanine. a OC-6 = octahedron.b SAPR-8 = square antiprism.c TDD-8 = triangular dodecahedron.
{Yb^III(4-pyridone)4[Fe^II(phen^[1])2(CN)2]2}(OTf^[2])3·2MeCN	YbN2O4, OC-6^a	12.5/800	7.28 × 10^−6	25a
{Yb^III(4-pyridone)4[Fe^II(phen)2(CN)2]2}(OTf)3·2AcrCN^[3]	YbN2O4, OC-6	7.86/800	2.51 × 10^−5	25a
{Yb^III(4-pyridone)4[Fe^II(phen)2(CN)2]2}(OTf)3·2PrCN^[4]	YbN2O4, OC-6	10.28/800	1.46 × 10^−5	25a
{Yb^III(4-pyridone)4[Fe^II(phen)2(CN)2]2}(OTf)3·2MalCN^[5]·MeOH	YbN2O4, OC-6	4.83/800	5.82 × 10^−5	25a
[Na2Yb^III2Cu^II2(OH)2(piv^[6])10(EtOH)2]·EtOH	YbO8, SAPR-8^b	8.5/1000	2.1 × 10^−6	14c
[Yb^III{Cu^II4(butyrat^[7])4}2]Cl3·MeOH·26H2O	YbO8, SAPR-8	6.84/1000	1.04 × 10^−5	25b
[Yb^IIICu^II8(OH)8(2-ma^[8])8(Cl)2](ClO4)·21H2O	YbO8, SAPR-8	22.5/700	1.48 × 10^−8	24b
{[KYb(VO)2(cbdc)4(H2O)11]·2H2O}2	YbO8, TDD-8^c	23/2000	5.6 × 10^−7	6a
[NaYb(VO) 2 (cbdc) 4 (H 2 O) 10 ] n	YbO 8 , TDD-8	44.8/2500	5.3 × 10 ^−8	This work

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EPR spectroscopy of 1_Yb and 1_Dy

Continuous wave (CW) EPR spectra of 1_Yb and 1_Dy at room temperature are typical for oxovanadium(IV) complexes and display hyperfine structure of V^IV ion (Fig. 6). No signatures of Yb^III and Dy^III ions are observed at room temperature, but the spectrum is dominated by V^IV EPR signal. This signal can be simulated using typical²⁶g- and A-tensors (the latter refers to the hyperfine interaction tensors): g = [1.975 1.975 1.938], A = [185 185 520] MHz for 1_Dy, and g = [1.974 1.974 1.941], A = [164 164 521] MHz for 1_Yb. Reference compound 1_Y with diamagnetic rare-earth metal ion (Y^III) shows almost the same EPR signal of V^IV at room temperature and can be simulated using the very similar set of parameters g = [1.974 1.974 1.938], A = [184 184 518] MHz, which agrees well with previous data.¹⁶

Fig. 6 CW EPR spectra of 1_Dy, 1_Yb and 1_Y at 293 K and 10 K. Simulations are shown in red.

However, as the temperature lowers, EPR spectra of both 1_Yb and 1_Dy become broader, resulting in one line with unresolved structure at 10 K (Fig. 6). This trend is unusual as most relaxation processes become slower at low temperatures, leading to the narrowing of EPR lines. Remarkably, the EPR spectrum of reference compound 1_Y still shows a resolved hyperfine structure at 10 K; therefore, drastic broadening of EPR spectra in cases of 1_Yb and 1_Dy at 10 K should be assigned to the interactions between V^IV and Yb^III/Dy^III ions. Note that, in addition to V^IV signal, the 10 K spectrum of 1_Yb shows a small feature at ∼100 mT, that is tentatively assigned to the contribution of Yb^III.²⁷

These interactions are more clearly evident in pulse EPR. In order to complement ac-magnetic susceptibility data and shed light on faster processes on micro- and submicroseconds timescales, we performed measurements of phase memory time (T_m) for 1_Yb and 1_Dy at 10–60 K. Two-pulse (Hahn) echo was monitored as a function of interpulse delay, and stretched exponential analysis (, β = 2 ± 0.5) was then employed to obtain corresponding T_m values.

Fig. 7 shows the obtained T_m(T) dependences for 1_Yb, 1_Dy and the reference compound of molecular structure [KY(VO)₂(cbdc)₄(H₂O)₁₁]·2H₂O (M_Y)^6a,16 with diamagnetic rare-earth metal ion (see the ESI† for details and choice of M_Y). The T_m(T) dependence is observed to have a non-monotonous behavior for 1_Yb and 1_Dy: the relaxation accelerates leading to a decrease of T_m values, reaching minima at T ∼ 10–12 K. Moreover, reference compound M_Y with diamagnetic Y^III ion shows perfectly monotonous dependence without such peculiarity. Again, this means that the observed behavior for 1_Yb and 1_Dy owes to the interactions between V^IV and Yb^III/Dy^III. This also confirms that the V^IV–Yb^III and V^IV–Dy^III units are present when 1_Yb and 1_Dy are dissolved in water/glycerol, since otherwise their T_m(T) dependences would be similar to that of M_Y.

Fig. 7 T _m(T) dependences for 1_Yb, 1_Dy and the reference compound M_Y. Solid line guides the eye.

In fact, such phenomenon is generally known in literature and is called phase relaxation enhancement (PRE), i.e. an increase of the relaxation rate (decrease of T_m) induced by a partner spin coupled with observer spin by dipolar interaction.²⁸ In compounds 1_Yb and 1_Dy, we deal with the spins of two types – slow-relaxing S = 1/2 spins of V^IV, and much faster relaxing spins of Yb^III or Dy^III. If the spin of lanthanide ion relaxes (flips) much faster than that of vanadium, the dipolar interaction will be averaged and no effect on vanadium EPR should be observed.

This situation corresponds to CW EPR spectra of 1_Yb and 1_Dy at room temperature and to the T_m(T) dependences at T > 30 K. In another limit, if (hypothetically) lanthanide spin relaxed too slowly, there should be no PRE of the vanadium spin as well (this situation is not reached experimentally). However, at intermediate relaxation rate of the lanthanide spins the influence of such fluctuations on the T_m value of vanadium ion is anticipated, due to the dipolar coupling between these ions. At the same time, CW EPR spectrum should broaden due to the contribution of lanthanide.

Previous theoretical consideration of similar phenomena derived general expression for the electron spin echo decay of slow-relaxing spin in the presence of dipolarly-coupled fast-relaxing spin (see ref. 28a):

where R² = W² − A²(r)/4, and with θ₁₂ being the angle between ( for the target compounds) and . In particular, for R = 0, which corresponds to the maximum PRE effect (minimum at T_m(T) dependence), the phase relaxation is enhanced up to:

The eqn (2) qualitatively explains the behavior observed for 1_Yb and 1_Dy in Fig. 7. The analysis of experimental data allows one to potentially obtain the unique information on spin relaxation times of the lanthanide ions, which are hardly available otherwise being often too short to measure by EPR. However, quantification of this approach requires more work. For instance, eqn (2) should result in a decrease of T^eff_m down to ≈T^Ln₁, which can be estimated as ∼10 ns at PRE maximum ( and A(r) ∼ 200 MHz in point-dipole approximation based on the crystal structures). This short T_m values are not observed experimentally, meaning that more experimental factors should be theoretically taken into account to describe PRE in Ln^III–V^IV complexes. First, when 1_Yb and 1_Dy are dissolved for pulse EPR measurements, one should ensure that there is only one type of spin pairs (or spin triads) present in frozen solution, because if a part of the compound is fully dissolved and separate vanadium, and rare-earth blocks are present, the apparent T_m(T) will have two contributions which should be treated properly. Second, a distribution over parameters T^Ln₁ and g_z of the pairs (eqn (1)) should be significantly broad²⁹ and be treated accordingly. The other theoretical challenges are the proper introduction of an atom with strong spin–orbit coupling (relevant for all lanthanides) into the framework of the current PRE-theory and high sensitivity of T_m to the minor changes in the environment.²⁹ The optimization of the theory might be the topic of our future study. At the same time, the development of clear manifestations of PRE in 1_Yb and 1_Dy complexes potentially outlooks the use of such phenomena in complex characterization of relaxation times in molecular magnet candidates.

Conclusions

In the Na^I–Ln^III–V^IV system (Ln^III = Tb, Dy, Ho, Er, Tm, Yb) with cyclobutane-1,1-dicarboxylate anions (cbdc²⁻), the lanthanide ionic radius was found to have no impact on the structure of the resulting heterometallic compound. All six new Ln^III–V^IV compounds obtained have the same 1D polymeric structure formed by trinuclear anionic units [Ln(VO)₂(cbdc)₄(H₂O)₈]⁻ linked by Na⁺ ions.

According to ac-magnetic susceptibility measurements, the Dy^III-, Er^III-, and Yb^III-containing compounds showed field-induced slow relaxation of magnetization. Slow magnetic relaxation observed can be best described by the sum of the Orbach and Raman relaxation mechanisms for Dy^III–V^IV complex, the sum of Raman and direct relaxation mechanisms for Yb^III–V^IV complex, and only the Raman relaxation mechanism for Er^III–V^IV one.

For Dy^III–V^IV, two relaxation processes were suggested, which may result from the independent relaxation of Dy^III and V^IV centers and/or possible disorder of water molecules coordinated to Dy^III. For complexes with Tb^III, Ho^III, and Tm^III slow magnetic relaxation was not observed due to the possible appearance of weak intramolecular and/or dipole–dipole exchange interactions.

The Er^III-containing complex is the first representative of heterometallic Er^III–V^IV compounds exhibiting slow magnetic relaxation.

For Dy^III–V^IV and Yb^III–V^IV studied by EPR spectroscopy, the phenomenon of phase relaxation enhancement (PRE) was observed, which can be used for complex characterization of relaxation times in molecular magnet candidates.

Experimental

Materials and methods

New compounds were synthesized in air, using distilled water as the solvent. Starting reagents included VOSO₄·3H₂O (>99%), Ba(NO₃)₂ (>98%), cyclobutane-1,1-dicarboxylic acid (H₂cbdc, 99%, Acros Organics), NaOH (>99%), Tb(NO₃)₃·6H₂O (99.9%, Lanhit), Dy(NO₃)₃·5H₂O (99.9%, Lanhit), Ho(NO₃)₃·5H₂O (99.9%, Lanhit), Er(NO₃)₃·5H₂O (99.9%, Lanhit), Tm(NO₃)₃·5H₂O (99.9%, Lanhit), Yb(NO₃)₃·5H₂O (99.9%, Lanhit).

The infrared spectra of complexes 1_Ln were recorded in the frequency range of 4000–400 cm⁻¹ on a PerkinElmer Spectrum 65 Fourier transform infrared spectrometer equipped with a Quest ATR Accessory (Specac). Elemental analysis of the compounds synthesized was carried out on a EuroEA 3000 CHNS analyzer (EuroVector, S.p.A.).

The purity of compound samples was approved by powder X-ray diffraction. The patterns were measured on a Bruker D8 Advance diffractometer with a LynxEye detector in the Bragg–Brentano geometry, with the samples dispersed thinly on a zero-background Si sample holder, λ(CuKα) = 1.54060 Å, θ/θ scan with variable slits (beam length is 20 mm) in the 2θ-angle range from 5° to 50°, with a step size of 0.020°.

The magnetic properties of compounds 1_Ln were studied in the dc- and ac-modes on a Quantum Design PPMS-9 magnetometer in the temperature range of 2–300 K. Dc-magnetic fields with an intensity of 0–5000 Oe and ac-magnetic fields with intensity of 5 Oe, 3 Oe and 1 Oe within frequency ranges 10–100, 100–1000 and 1000–10 000 Hz, respectively, were applied using standard procedure.³⁰ All magnetic behavior studies were performed using ground polycrystalline samples, sealed in polyethylene bags and frozen in mineral oil to prevent the orientation of crystallites in a magnetic field. The paramagnetic component of the magnetic susceptibility (χ) was determined taking into account the diamagnetic contribution of the sample, evaluated from Pascal's constant, and the diamagnetic contributions of the mineral oil and the sample holder.

All EPR data were collected using Bruker Elexsys E580 spectrometer at X-band (9 GHz) at the Center of Collective Use “Mass spectrometric investigations” SB RAS. The spectrometer was equipped with helium flow cryostat and temperature control system (4–300 K). Continuous wave EPR spectra were obtained on polycrystalline powder samples under conditions avoiding microwave saturation and modulation broadening. Phase memory time was measured using two-pulse Hahn electron spin echo sequence for glassy water/glycerol (C ∼ 0.2 mM) solutions of target compounds. In all cases samples were placed into quartz sample tubes and studied. Simulations were performed using EasySpin.³¹

General synthesis procedure for [NaLn(VO)₂(cbdc)₄(H₂O)₁₀]_n (1_Ln, Ln = Tb, Dy, Ho, Er, Tm, Yb). A weighed sample of VOSO₄·3H₂O (0.100 g, 0.46 mmol) was dissolved in H₂O (15 mL), then Ba(NO₃)₂ (0.120 g, 0.46 mmol) was added, and the reaction mixture was stirred for 20 min at 40 °C. The solution of Na₂(cbdc) prepared by neutralization of H₂cbdc (0.133 g, 0.92 mmol) with NaOH (0.074 g, 1.84 mmol) in H₂O (10 mL) was added to the reaction mixture, and the stirring was continued. After 10 min Ln(NO₃)₃·xH₂O (m g, 0.46 mmol) was added. The reaction mixture was stirred for additional 10 min and allowed to stand for 1 hour, then BaSO₄ precipitate was removed by filtration. The resulting blue solution (25 mL) was allowed to evaporate slowly in air at 22 °C. X-ray quality blue crystals were obtained within 2 months. The crystals were separated from the mother liquor by filtration, washed with cold H₂O (t = 3 °C) and dried in air at 22 °C.

For 1_Tb: x = 6, m = 0.208. The yield was 0.113 g (46.3% based on VOSO₄·3H₂O). Anal. Calc for C₂₄H₄₄NaO₂₈TbV₂: C, 27.08; H, 4.17. Found: C, 27.01; H, 4.26%. IR (ATR), ν/cm⁻¹: 3642 w, 3348 br. m [ν(O–H)], 3234 m [ν(O–H)], 3000 w [ν(C–H)], 2957 w [ν(C–H)], 1634 m, 1582 s [ν_as(COO⁻)], 1555 s [ν_as(COO⁻)], 1443 m, 1431 m, 1391 s [ν_s(COO⁻)], 1349 s, 1254 m, 1242 m, 1229 m [ν(C–C)_cycle], 1195 w, 1162 w, 1122 m [γ(C(–C)₂)], 1061 w, 1012 w, 1000 w, 968 s [ν(V=O)], 952 s, 924 s, 875 w, 843 w, 807 w, 773 m, 762 m, 725 s [δ(COO⁻)], 647 s, 560 s, 533 s, 471 s, 444 s, 418 s.

For 1_Dy: x = 5, y = 0.202. The yield was 0.118 g (47.8% based on VOSO₄·3H₂O). Anal. Calc for C₂₄H₄₄DyNaO₂₈V₂: C, 26.99; H, 4.15. Found: C, 27.08; H, 4.20%. IR (ATR), ν/cm⁻¹: 3641 vw, 3351 br. m [ν(O–H)], 3229 m [ν(O–H)], 2999 w [ν(C–H)], 2956 w [ν(C–H)], 1631 m, 1581 vs [ν_as(COO⁻)], 1554 vs [ν_as(COO⁻)], 1443 m, 1431 m, 1390 s [ν_s(COO⁻)], 1348 s, 1254 m, 1242 m, 1229 m [ν(C–C)_cycle], 1196 w, 1161 w, 1122 m [γ(C(–C)₂)], 1061 w, 1012 w, 1000 w, 968 s [ν(V=O)], 952 s, 924 s, 874 w, 843 w, 807 w, 773 m, 762 m, 725 s [δ(COO⁻)], 649 vs, 604 s, 561 vs, 533 vs, 468 s, 450 vs, 440 vs, 415 s, 403 vs.

For 1_Ho: x = 5, y = 0.203. The yield was 0.126 g (51.2% based on VOSO₄·3H₂O). Anal. Calc for C₂₄H₄₄HoNaO₂₈V₂: C, 26.93; H, 4.14. Found: C, 26.90; H, 4.19%. IR (ATR), ν/cm⁻¹: 3641 vw, 3358 br. m [ν(O–H)], 3234 m [ν(O–H)], 3000 w [ν(C–H)], 2957 w [ν(C–H)], 1634 m, 1580 s [ν_as(COO⁻)], 1557 s [ν_as(COO⁻)], 1443 m, 1431 m, 1391 s [ν_s(COO⁻)], 1349 s, 1254 w, 1242 w, 1230 m [ν(C–C)_cycle], 1193 w, 1162 w, 1123 m [γ(C(–C)₂)], 1061 v.w, 1012 w, 1000 w, 968 s [ν(V=O)], 952 s, 924 m, 875 w, 843 w, 807 w, 773 m, 762 m, 725 s [δ(COO⁻)], 648 s, 561 s, 533 s, 470 s, 448 s, 438 s, 415 s, 403 vs.

For 1_Er: x = 5, y = 0.204. The yield was 0.113 g (45.8% based on VOSO₄·3H₂O). Anal. Calc for C₂₄H₄₄ErNaO₂₈V₂: C, 26.87; H, 4.13. Found: C, 26.79; H, 4.19%. IR (ATR), ν/cm⁻¹: 3641 vw, 3356 br. m [ν(O–H)], 3234 m [ν(O–H)], 3000 w [ν(C–H)], 2957 w [ν(C–H)], 1634 m, 1580 s [ν_as(COO⁻)], 1555 s [ν_as(COO⁻)], 1443 m, 1432 m, 1390 s [ν_s(COO⁻)], 1348 s, 1254 m, 1242 m, 1229 m [ν(C–C)_cycle], 1193 w, 1162 w, 1122 m [γ(C(–C)₂)], 1063 w, 1012 w, 1000 w, 968 s [ν(V=O)], 953 m, 924 m, 875 w, 843 w, 807 w, 773 m, 762 m, 725 m [δ(COO⁻)], 650 s, 595 s, 561 s, 532 s, 467 s, 446 s, 437 s, 420 s, 407 vs.

For 1_Tm: x = 5, y = 0.205. The yield was 0.077 g (31.2% based on VOSO₄·3H₂O). Anal. Calc for C₂₄H₄₄NaO₂₈TmV₂: C, 26.83; H, 4.13. Found: C, 26.94; H, 4.14%. IR (ATR), ν/cm⁻¹: 3639 vw, 3352 br. m [ν(O–H)], 3238 m [ν(O–H)], 3000 w [ν(C–H)], 2956 w [ν(C–H)], 1634 m, 1583 s [ν_as(COO⁻)], 1557 s [ν_as(COO⁻)], 1443 m, 1431 m, 1391 s [ν_s(COO⁻)], 1348 s, 1254 m, 1242 m, 1229 m [ν(C–C)_cycle], 1196 w, 1163 w, 1123 m [γ(C(–C)₂)], 1063 w, 1012 w, 1000 w, 968 s [ν(V=O)], 953 s, 924 m, 874 w, 843 w, 807 w, 773 m, 765 m, 725 s [δ(COO⁻)], 653 s, 595 s, 561 s, 533 s, 471 s, 448 s, 423 s.

For 1_Yb: x = 5, y = 0.207. The yield was 0.120 g (48.4% based on VOSO₄·3H₂O). Anal. Calc for C₂₄H₄₄NaO₂₈V₂Yb: C, 26.73; H, 4.11. Found: C, 26.67; H, 4.08%. IR (ATR), ν/cm⁻¹: 3639 vw, 3354 br. m [ν(O–H)], 3229 m [ν(O–H)], 3000 w [ν(C–H)], 2956 w [ν(C–H)], 1634 m, 1582 s [ν_as(COO⁻)], 1554 s [ν_as(COO⁻)], 1443 m, 1431 m, 1391 s [ν_s(COO⁻)], 1349 s, 1254 m, 1242 m, 1229 m [ν(C–C)_cycle], 1196 w, 1162 w, 1123 m [γ(C(–C)₂)], 1063 w, 1012 w, 1000 w, 968 s [ν(V=O)], 953 s, 924 m, 875 w, 843 w, 807 w, 773 m, 762 m, 726 s [δ(COO⁻)], 654 s, 561 s, 533 s, 466 s, 448 s, 440 s, 425 s, 416 s.

X-ray crystallography

The X-ray diffraction data sets for compounds 1_Dy and 1_Er were collected on a Bruker SMART APEX II diffractometer equipped with a CCD detector (Mo-K_α, λ = 0.71073 Å, graphite monochromator).³² A semiempirical absorption correction was applied using SADABS program.³³ The structures were solved by direct methods and refined by the full-matrix least squares with anisotropic displacement parameters for non-hydrogen atoms. The hydrogen atoms of the OH groups were determined from the difference Fourier maps; with other hydrogen atoms calculated geometrically and refined using a riding model. The calculations were performed with the SHELX-2014 program package³⁴via OLEX2 1.3 graphical user interface.³⁵ The crystallographic data for 1_Dy, 1_Er, and the structure refinement statistics are given in Table 9.

Table 9 Crystallographic parameters and structure refinement statistics for compounds 1_Dy and 1_Er

Parameter	1Dy	1Er
a R 1 = ∑||Fσ| − |Fc||/∑|Fo|. b wR2 = [∑w(Fo^2 − Fc^2)^2/∑w(Fo^2)^2]^1/2.
Empirical formula	C24H44DyNaO28V2	C24H44ErNaO28V2
Formula weight (g mol^−1)	1067.96	1072.72
T (K)	150
Crystal system	Monoclinic
Space group	C2/c
a (Å)	9.097(2)	9.088(4)
b (Å)	24.739(5)	24.681(11)
c (Å)	17.116(3)	17.098(8)
β (°)	104.682(7)	104.589(8)
V (Å^3)	3726.2(14)	3711(3)
Z	4	4
D calc (g cm^−3)	1.904	1.920
θ min –θ max (°)	2.97–33.14	2.46–31.83
μ (mm^−1)	2.59	2.85
No. of measured, independent and observed [I > 2σ(I)] reflections	7547, 3639, 3336	6910, 3159, 2796
R int	0.026	0.040
GOF	1.045	1.036
R 1 ^a, wR2 ^b (I > 2σ(I))	0.0259, 0.0548	0.0405, 0.0991
R 1 ^a, wR2 ^b (all data)	0.0298, 0.0567	0.0479, 0.1035
T min, Tmax	0.626, 0.747	0.456, 0.745
Δρmax, Δρmin (e Å^−3)	0.99, −1.01	1.98, −1.34

---

CCDC 2266768 and 2266772† contain the supplementary crystallographic data for 1_Dy and 1_Er.

Author contributions

Investigation, E. S. B., M. A. S., N. V. G., M. A. K., K. A. B., I. V. K.; formal analysis, E. S. B., M. A. S., N. V. G., M. A. K., K. A. B., I. V. K., M. V. F.; methodology, E. S. B., M. A. S., N. V. G., M. A. K., K. A. B., I. V. K., M. V. F., N. N. E.; visualization, E. S. B., K. A. B., I. V. K., M. V. F.; writing – original draft, E. S. B., M. A. S., K. A. B., N. N. E., M. A. K., I. V. K., M. V. F.; writing – review and editing, E. S. B., N. N. E., M. A. K., M. V. F., I. L. E.; supervision, conceptualization: E. S. B., M. A. K., M. V. F., I. L. E. All authors have read and agreed to the published version of the manuscript.

Data availability

The data supporting this article have been included as part of the ESI.†

Crystallographic data for 1_Dy and 1_Er have been deposited at the Cambridge Crystallographic Data Centre under CCDC 2266768 and 2266772† numbers and can be obtained from https://www.ccdc.cam.ac.uk/conts/retrieving.html.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the Ministry of Science and Higher Education of the Russian Federation as part of the State Assignment of the Kurnakov Institute of General and Inorganic Chemistry of the Russian Academy of Sciences.

Single-crystal and powder X-ray diffraction analyses, IR spectroscopy, CHN elemental analysis, and magnetic measurements were performed using the equipment of the JRC PMR IGIC RAS.

I. V. K. and M. V. F. thank Ministry of Science and Higher Education of the Russian Federation for access to EPR equipment. We thank Dr Maxim Yulikov (ETH-Zurich) for fruitful discussions on PRE.

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Footnote

† Electronic supplementary information (ESI) available: Orbital diagrams for Cu^II and V^IV ions; PXRD patterns for 1_Ln series; continuous shape measures (CShM) for LnO₈ coordination polyhedra in 1_Dy, 1_Er; tables of selected bond angles in structures 1_Dy, 1_Er; tables of hydrogen bond parameters in 1_Dy, 1_Er; the magnetization M(T) and M(H/T) dependences for 1_Ln, frequency dependences of the in-phase and out-of-phase parts of dynamic magnetic susceptibility for 1_Ln at T = 2 K under various dc-magnetic fields; frequency dependences of the in-phase and out-of-phase parts of dynamic magnetic susceptibility for 1_Dy, 1_Er, 1_Tm (under 1000 Oe dc-field), and 1_Yb (under 2500 Oe dc-field) at different temperatures; Cole–Cole plots for 1_Dy measured at 2–7.5 K; the τ vs. H plots for 1_Dy, 1_Er, 1_Yb at 2 K; the τ vs. 1/T plots and the best-fit parameters of magnetization relaxation for 1_Tm; the τ vs. 1/T plots for 1_Dy, 1_Er, 1_Yb processed using the MagSuite v.3.2 software and the best-fit parameters of magnetization relaxation calculated for 1_Dy, 1_Er, 1_Yb; CW EPR spectra of M_Y and 1_Y at 293 K and 10 K; IR spectra for 1_Dy in aqueous solution and crystalline state. CCDC 2266768 and 2266772. For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d4dt01779j

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