The crystal structure of the Cu(II)-doped Zn-MOFs, i.e., Cu/Zn-MOF(5%), Cu/Zn-MOF(2%), and Cu/Zn-MOF(1%), was determined via powder X-ray diffraction (PXRD), which confirmed that they are isomorphous with pristine Zn-MOF (Fig. 2a). The presence of the doping Cu element was qualitatively confirmed by X-ray fluorescence (XRF) spectroscopy (Fig. 2b and S1). The Cu-Kα and Zn-Kα peaks were detected at 8.04 and 8.63 keV, respectively, and were accompanied by those of Cu-Kβ (8.90 keV) and Zn-Kβ (9.57 keV). Using the fundamental parameter method, the doped amount of Cu was estimated to be 5.2%, 2.2%, and 1.0% mol relative to Zn, which is consistent with each loading amount (5%, 2%, and 1%, respectively). Figure 3 shows the magnetization–field (M–H) curves of the Cu/Zn-MOFs. Almost saturation at a higher field region at 1.8 K can be observed (Fig. 3a), and the saturation magnetization is consistent with the loading amount. These curves are different from that of a pristine Cu-MOF having canted-spin antiferromagnetism with hysteresis (Fig. S2),37 suggesting that the Cu/Zn-MOFs are sufficient diluted to prevent three-dimensional magnetism. In contrast, Zn-MOF does not show any magnetization, which indicates that the magnetism is not due to impurities but to the doping Cu(II) sites. Furthermore, the complete active space self-consistent field (CASSCF) calculation using the program Orca afforded anisotropic g-factors in the S = 1/2 system, i.e., gx = 2.09, gy = 2.12, and gz = 2.52 (Table S1),38 which is almost consistent with those of electron spin resonance (ESR), i.e., gx = 2.065, gy = 2.120, and gz = 2.435 (vide infra). The temperature dependency of the M–H curves shown in Figs. 3b–3d matched well with those simulated using the PHI program,39 supporting that the magnetism stems from the doping Cu(II) sites.
Although the Cu/Zn-MOFs did not show any signals on alternating current (AC) susceptibility measurements in the absence of an applied field, such signals were observed under a magnetic field (Fig. S3 and Table S2). Figure 4 shows the imaginary part of the AC susceptibility (χ") of the Cu/Zn-doped MOFs under an applied field of 0.4 T. The real parts (χ') and the Cole–Cole plots are shown in Fig. S4. The χ" values obtained at various temperatures were fitted using the Debye relaxation equation (Eq. 1):40
$$\chi " = ({\chi }_{T}–{\chi }_{S})\frac{{\left(2\pi f\tau \right)}^{1-\alpha }\text{cos}(\pi \alpha /2)}{1+{2\left(2\pi f\tau \right)}^{1-\alpha }\text{sin}(\pi \alpha /2)+{\left(2\pi f\tau \right)}^{2-2\alpha }}$$
1
Here, χT, χS, f, τ, and α refer to the isothermal susceptibility, adiabatic susceptibility, AC frequency, relaxation time, and dispersion coefficient, respectively. The fitting parameters are summarized in Tables S3–S5. The peak of χ" shows a delay of spin reversal between the quantum states of MS = ± 1/2 and the relaxation time (τ) obtained by the Debye equation. The log-scale plots of τ and temperature were fitted using a combination of the direct process and the Raman process (Fig. 4d, equations 2–4):7
$${\tau }_{Direct}={AT}^{–1}$$
2
$${\tau }_{Raman}={CT}^{–m}$$
3
$${\tau }^{–1}={{\tau }_{Direct}}^{–1}+{{\tau }_{Raman}}^{–1}$$
4
Here, A and C are the coefficients of the direct and Raman processes, respectively, and m is the index of the Raman process. This spin-lattice relaxation is similar with that previously reported for [VIVO(dipivaloylmethanato)2] in the S = 1/2 system.7 As a general trend, dilution slows down the relaxation, i.e., τ (Cu/Zn-MOF(5%)) < τ (Cu/Zn-MOF(2%)) < τ (Cu/Zn-MOF(1%)), which can be explained by the weakening of the spin–spin interactions between Cu(II) centers. Particularly, Cu/Zn-MOF(1%) shows a τ of 15 ms at 1.8 K. The temperature dependency of these MOFs indicates the occurrence of a Raman process with m = 4.4–4.7 at a higher temperature (Table S6). Meanwhile, below ~ 2 K, the plots slightly deviate in the upper side from the theoretical curves, which suggests a slower relaxation induced by the phonon-bottleneck effect.
Figure 5 shows the results of X-band pulse-ESR spectroscopy measurements. Electron-spin relaxation was measured at the static magnetic field (328 mT) corresponding to the peak top of the Hahn-echo detected ESR spectrum (Fig. 5a). Spin-lattice (T1) and T2 relaxation times were determined by the inversion recovery method and Hahn-echo decay measurement, respectively. Both relaxation times were obtained by fitting using the following (stretched-)exponential equations (equations 5 and 6):20
$$I={I}_{0}+k\text{exp}\left[–{\left(\frac{{\tau }_{p}}{{T}_{1}}\right)}^{\beta }\right]$$
5
$$I={I}_{0}\text{exp}\left[–\left(\frac{2{\tau }_{p}}{{T}_{2}}\right)\right]$$
6
Here, I, I0, k, τp, and β refer to the echo intensity, initial echo intensity, pulse separation between the initial inversion p-pulse and the two-pulse sequence for the Hahn-echo detection, pulse separation between p/2-pulse and p-pulse in the two-pulse sequence, and stretch factor, respectively. The fitting parameters are summarized in Table S7–S10. The log-scale T1 plots are curved (Fig. 5b), suggesting the occurrence of multicomponent spin-lattice relaxation. This T1 multicomponent relaxation, which was determined using β, is consistent with the results of the AC susceptibility measurements showing the occurrence of direct and Raman processes (Fig. 4d). In contrast, the log-scale T2 plots lie on a straight line, suggesting a single spin–spin relaxation (Fig. 5c). T1 and T2 are at the microsecond and submicrosecond scales, respectively, and were measured below ~ 25 K. Cu/Zn-MOF(1%) shows longer T1 and T2 than Cu/Zn-MOF(2%) (Fig. 5d and 5e), which can be attributed to the weakening of spin–spin interactions in Cu/Zn-MOF(1%). This relaxation-extending effect is consistent with the results of the AC magnetic susceptibility measurements (Fig. 4). The longest T1 and T2 values of 13 µs and 0.41 µs, respectively, were obtained for Cu/Zn-MOF(1%) at 4 K. The T1 and T2 values of Cu/Zn-MOF(5%) could not be measured because the corresponding processes were too fast. Furthermore, Rabi oscillation was confirmed under different microwave powers using Cu/Zn-MOF(1%) at 10 K (Fig. 5f), indicating superposition of MS = ± 1/2 spin sublevels.as spin qubits.