A mixture of H₂BDC (23 mg, 0.137 mmol) and Dy(NO₃)₃·6H₂O (62.56 mg, 0.137 mmol) in 1.25 ml EtOH/DMF (V:V = 1:4) solution was sealed in a 15 ml Schlenk glass tube. To remove air, the Schlenk tube with reaction solution was purged and backfilled with argon gas three times, then heated in an oven at 100°C for 36 h. After the temperature was gradually reduced to room temperature, the colourless bulk crystals were obtained, and the yield was about 36% calculated based on Dy(III) ion. Anal. calcd. for C₁₄H₁₈DyN₃O₉: C, 31.44%; H, 3.39%; N,7.86%. Found: C, 31.52%; H, 3.45%; N, 7.79%.

The collected crystals of complex 1 were washed with ethanol, and dried in air. After then, the crystals were heated in an oven at 170°C for 24 h, complex 1a was obtained. Anal. calcd. for C₈H₄DyNO₇: C, 24.73%; H, 1.04%; N,3.60%. Found: C, 24.70%; H, 1.10%; N, 3.68%.

The colourless bulk crystals of complex 1@Y were obtained following the procedure described for complex 1 except that Dy(NO₃)₃·6H₂O was replaced by Dy(NO₃)₃·6H₂O and Y(NO₃)₃·6H₂O in a 1:10 M ratio. The accurate ratio of Dy/Y is 1:7.23 in the magnetically diluted complex 1@Y, which was determined by X-ray fluorescence spectrometry (Supplementary Figure S1). Elemental Anal. Calcd. for C₁₄H₁₈Dy_0.1215Y_0.8785N₃O₉: C, 35.76%; H, 3.86%; N, 8.94%. Found: C, 35.30%; H,3.89%; N, 8.63%.

The diffraction data for 1 were collected on a Bruker Smart CCD area-detector diffractometer using Mo-Kα radiation (λ = 0.71073 Å) in the ω-scan mode at 296 K. The diffraction data were treated using SAINT, and absorption corrections were applied by using SADABS. All the non-hydrogen atoms were located by Patterson’s method using the SHELXS program of the SHELXTL package and by subsequent Fourier syntheses (Sheldrick, 2008). The hydrogen atoms were determined theoretically and treated using a riding model. The hydrogen atoms were refined with isotropic thermal parameters. All non-hydrogen atoms were refined by full-matrix least-squares on F ² with anisotropic thermal parameters. All the calculations were performed by the SHELXTL-2014 program (Sheldrick, 2015). The details for the structural analyses of complex 1 are shown in Supplementary Table S1. The selected bond distances and angles for complex 1 are listed in Supplementary Table S2. The CCDC number of complex 1 is 2059079.

Infrared (IR) spectra were recorded as KBr pellets under vacuum condition. Complex 1a was immersed in DMF solvent for 3 days, it changed to complex 1-back. To study the stability of the framework and the loss of coordinated DMF molecules, the data at variable temperatures were collected for complex 1 and 1-back. The temperature-dependent IR spectra of complex 1 and 1-back were shown in Supplementary Figures S2, S3, respectively. The bands at 1,623 and 1,038 cm⁻¹ are assigned to the C=O stretching vibration (ν _CO) and the CH₃ rocking region (r _CH3) of DMF molecules, respectively (Freire and Alves, 2015; Ohashi and Takeshita, 2021). The peaks of 1,623 and 1,038 cm⁻¹ are disappeared when the temperature reached 175°C, which is due to the losing of DMF molecules. Except for some slight differences, such as a decomposed component of the ν _CO band at 1,686 cm⁻¹ (extremely small), the IR spectra of complex 1 and 1-back are almost the same (Supplementary Figure S4). The slight differences in IR spectra may be due to the perturbation of high temperature in the coordination environment. In addition, the temperature-dependent IR spectrum of complex 1-back is also consistent with that of complex 1. The results of IR spectra support that complex 1a can uptake DMF molecules and transform back to complex 1. The thermogravimetric analyses were performed in N₂ atmosphere at a heating rate of 10°C min⁻¹ from 30°C to 800°C for complex 1 and 1-back (Supplementary Figure S5). There is no weight loss before 140°C for complex 1 and 1-back. For complex 1, it reveals a weight loss of 27.31% between 140°C and 295°C, which corresponds to the loss of two coordination DMF molecules (27.33%). Then it shows a continued weight loss in the temperature range of 295–800°C, which is due to the collapse of the framework. For complex 1-back, there is a weight loss of 26.87% between 140°C and 295°C, which is slightly lower than the loss of two coordination DMF molecules (27.33%). A continued weight loss in the temperature range of 295–800°C is also due to the collapse of the framework. The results of thermogravimetric analysis for complex 1-back are consistent with those for complex 1. The recorded experimental PXRD pattern of 1 and 1@Y agree well with the simulated pattern from single-crystal X-ray diffraction data of 1, which confirms the phase purity for the microcrystal of 1 and 1@Y (Supplementary Figure S6). There are some slight differences between the experimental PXRD pattern of complex 1a and that of complex 1, which means that the framework of complex 1a is slightly deformed after high-temperature treatment.

The result of X-ray single-crystal diffraction indicates that complex 1 belongs to the monoclinic space group C2/c. There are one Dy(III) ion, one BDC²⁻ ligand, one nitrate ion and two DMF molecules in the asymmetric unit of 1. The Dy(III) ion is eight-coordinated, in which four BDC²⁻ ligands provide four oxygen atoms, one nitrate provides two oxygen atoms, and two DMF molecules provide two oxygen atoms for coordination. The Dy(III) center adopts a snub disphenoid (JSD-8) coordination geometry (Figure 1A), which was analyzed by the SHAPE 2.1 software, and the calculated results are listed in Supplementary Tables S3, S4 (Llunell et al., 2013). All bond lengths and bond angles are within the normal range. Each ligand BDC²⁻ catches four metal Dy(III) ions (Figure 1B). In this way, the adjacent Dy(III) ions are linked together, forming a one-dimensional chain along the c axis (Supplementary Figure S7). These chains are further bridged by the ligand BDC²⁻, giving rise to a three-dimensional network structure. Interestingly, there are no free solvent molecules in the three-dimensional channel because the coordinated DMF solvent molecules are filled into the pores (Figure 2). In order to realize the function of the magnetic switch, we studied the influence of the presence or absence of DMF molecules in the framework. After heating 24 h in an oven at 170°C, the coordinated DMF solvent molecules were removed. Not only the DMF molecules are absent in the pores, but also the number of coordination atoms around the Dy(III) center has changed. This means that the magnetic properties of complex 1a are different from those of complex 1. Complex 1a has been putted into DMF solvent for the purpose of proving the structural reversibility. Complex 1-back was obtained by putting complex 1a into DMF solvent for 3 days. As expected, the recorded experimental PXRD patterns of 1-back is consistent with the simulated pattern of complex 1. These results further indicate that complex 1 can transform to complex 1a by heating and then comeback to complex 1 by putting complex 1a into DMF solvent.

Variable temperature susceptibility measurements were carried out in a temperature range of 1.8–300 K under a DC field of 1.0 kOe. The plot of χ _M T versus T for a [Dy(BDC)(NO₃)(DMF)₂] unit is shown in Figure 3. The product χ _M T of complex 1 is 14.18 cm³ K mol⁻¹ at room temperature, which is in agreement with the theoretical value of 14.167 cm³ K mol⁻¹ for single Dy(III) ions (S = 5/2, L = 5, J = 15/2, g = 4/3). Upon cooling, the χ _M T value of complex 1 gradually decreases and reaches a minimum of 11.51 cm³ K mol⁻¹ at 25 K. This phenomenon could be ascribed to the depopulation of Stark sublevels of Dy(III) ion. As the temperature continues to decrease, the χ _M T value increases rapidly and reaches a maximum of 14.54 cm³ K mol⁻¹ at 1.8 K, which indicates the presence of ferromagnetic coupling between Dy(III) ions (Aulakh et al., 2015). For complex 1a, the value of χ _M T is 14.19 cm³ K mol⁻¹ at 300 K, which is closed to the theoretical value for one Dy(III) ion. Upon cooling, the χ _M T value decreases slowly in the high-temperature region, then decreases rapidly and reaches 9.19 cm³ K mol⁻¹ at 1.8 K, which is owing to the depopulation of Stark sublevels and/or the antiferromagnetic coupling between adjacent Dy(III) ions.

The field-dependence magnetizations of 1 and 1a were measured in the whole field (0–7 T) at the temperature from 1.8 to 10 K (Supplementary Figures S8, S9). For complex 1, the magnetization M reaches a saturated value (5.73 μ _B) at 7 T, which is larger than the observed value (5.23 μ _B) for one anisotropic Dy(III) ion (Tang et al., 2006). This phenomenon indicates that there is also a strong magnetic anisotropy in complex 1. Besides, the non-superposition of the M vs. H/T curves provides further evidence for the presence of strong magnetic anisotropy in this system (the inset of Supplementary Figure S8). For complex 1a, the value of M is still not saturated at 7 T.

The alternating current (AC) magnetic susceptibility of complexes 1, 1a and 1-back were measured to investigate their dynamic magnetic behaviour. For complex 1, the AC magnetic susceptibility measurements were done under a zero DC field and 1 kOe DC field. Obvious out-of-phase signals were observed in both cases, indicating that complex 1 exhibits SMM behaviour (Supplementary Figure S10). However, no out-of-phase signal was observed both under zero field and 1 kOe DC field, indicating that complex 1a does not show SMM behaviour (Supplementary Figure S11). Interestingly, complex 1-back exhibits an obvious out-of-phase signal (Supplementary Figure S12). The literatures demonstrate that subtle modification of solvent, auxiliary ligand, coordination environment and inter-molecular interaction have a significant impact on the magnetic dynamics of lanthanide single-molecule magnets (Zhang et al., 2016; Zhang et al., 2019; Kong et al., 2020). Compared with complex 1, the coordination environment may be slightly different in complex 1-back which has undergone the process of removing and absorbing DMF molecules, resulting in a difference of the magnetic relaxation (Figure 4). For complex 1, SMM behaviour disappears by removing the coordinated DMF molecules, and appears when recovering DMF molecules. In short, reversible switching of SMM behaviour is realized by desorption/adsorption of coordinated DMF molecules. In the whole tested DC field, only one relaxation process was observed for complex 1. In order to study the slow relaxation behaviour, both zero field and 1.0 kOe were chosen to test the dynamic magnetization due to the longest relaxation time (Supplementary Figures S13, S14). In the given fields and temperature ranges, the variable-frequency χ _M″ is shown in Figure 5 for 1. The Cole-Cole plots are fitted through the Debye model using CCFIT software (Guo et al., 2011). The extracted α values are listed in Supplementary Tables S5, S6. In zero DC field, the effective energy barrier is 37.01 (3) K with τ ₀ = 1.98 × 10^–7 s by fitting with the Arrhenius formula. The ln (τ) vs. T ⁻¹ curve indicates possible multiple slow relaxation processes, which is described in Eq. 1. The best resulting parameters are τ _QTM = 0 s, C = 143.95 K^−1.59 s⁻¹, n = 1.59, τ ₀ = 9.82 × 10^–8 s and U _eff = 43.02 K. However, in 1 kOe DC field, the ln(τ) vs. T ⁻¹ curve is replaced by a straight line, which indicates that it only has the Orbach process. The effective energy barrier U _eff is equal to 47.27 K with τ ₀ = 9.62 × 10^–8 s. It can be seen from Supplementary Table S7 that the quantum tunnelling effect (QTM) cannot be suppressed by antiferromagnetic coupling between neighbouring Dy(III) ions. However, ferromagnetic coupling between neighbouring Dy(III) ions may effectively suppress QTM. In this work, the QTM is also not observed, which proves the conclusion that the ferromagnetic interaction can suppress QTM. In order to further prove this conclusion, the alternating current (AC) magnetic susceptibility of diamagnetically diluted sample 1@Y was measurement under zero DC field (Supplementary Figure S15). In the low-temperature region, the peak values of the χ _M″ vs. ν curves does not move with increasing temperature, which indicates that there is an obvious QTM process in complex 1@Y. The Cole-Cole plots of 1@Y are fitted by the Debye model using CCFIT software (Supplementary Figure S16, Supplementary Table S8). The ln(τ) vs. T ⁻¹ curve indicates possible multiple slow relaxation processes, so the data are fitted using the Eq. 1 which includes QTM, Orbach and Raman processes (Supplementary Figure S17). The best resulting parameters are τ _QTM = 420.37 s, C = 3.32 K^−5.71 s⁻¹, n = 5.71, τ ₀ = 1.37 × 10^–8 s and U _eff = 41.00 K. The fitting result proves that there is a QTM process in complex 1@Y. These results further prove that the ferromagnetic interaction leads to the disappearance of the quantum tunneling process in complex 1. τ − 1 = τ Q T M − 1 + C T n + τ 0 − 1 ⁡ exp ( − U e f f k B T ) (1) ab initio calculations J d i p = − μ B 2 g 1 Z g 2 Z r 3 ( cos ⁡ θ − 3 ⁡ cos ⁡ φ 1 ⁡ cos ⁡ φ 2 ) (2)

To gain further insights into the magnetic coupling between neighbouring Dy(III) ions for complex 1, CASSCF calculations based on X-ray single-crystal structure were performed using MOLCAS 8.4 program (Aquilante et al., 2016) and SINGLE_ANISO programs (Chibotaru et al., 2008a; Chibotaru et al., 2008b; Ungur et al., 2009). A Dy(III) ion was randomly selected from complex 1, and the principal magnetic axe of this ground Dy(III) ion was calculated (Supplementary Figure S18). The calculated energy levels (cm⁻¹) and g (g _x , g _y , g _z ) tensors of the minimum KDs of the Dy (III) motif for complex 1 are shown in Supplementary Table S9. The calculated values of the correlative tensors in the ground state (m _J = ±15/2) are 0.002 (g _x ), 0.002 (g _y ) and 19.893 (g _z ), respectively. The results show a strong axial anisotropy in the ground state for complex 1, which leads to a slow magnetic relaxation behaviour in a zero field for complex 1. For complex 1, the m _J values of the ground states are mostly composed of ±15/2, and the predominant m _J values of the first excited states are ±13/2 (Supplementary Table S10). The calculated energy of the first excited states is 192.4 cm⁻¹. The value of the experimental energy barrier (47.27 K) is much smaller than the calculated value, suggesting that such a relaxation does not reach the first excited state due to fast under-barrier relaxation which is induced by anharmonic phonons (Lunghi et al., 2017; Kong et al., 2020) (Supplementary Figure S19; Supplementary Table S10). The principal magnetic axes of Dy(III) ions are parallel to each other based on the structure and symmetry of complex 1 (Supplementary Figure S20). According to Eq. 2, the calculated value of J _dip is 0.48 cm⁻¹. The calculation details are presented in the Supplementary Material. The small J _dip value proves that the magnetic interaction between neighboring Dy(III) ions is too weak to influence the intrinsic magnetic properties of complex 1.