Introduction

Directed by requirements of miniaturization and multi-tasking for devices and sensors, molecular materials are investigated because they can incorporate several functionalities in a single phase.¹ They can co-exist,² or interplay giving the switching of one property by the other or even generating new physical cross-effects.³ For instance, the coupling between magnetism and photosensitivity of the material can result in light-induced ferrimagnetism⁴ or photoswitching of second-harmonic light when the system is chiral.^3c Other products of magneto-optical coupling include magneto-chiral dichroism, optically addressable qubits, and magnetoluminescence.^{5, 6, 7} Aiming at high-density data storage, an enormous scientific interest is given to single-molecule magnets (SMMs), which exhibit a magnetic memory effect at the molecular level.⁸ The design strategy for high-performance SMMs is based on the use of lanthanide ions (Ln³⁺) of an oblate-type character of the highest m_J state's electron density, in an axially strengthened ligand field.⁹ As a result, the Dy³⁺-based SMMs raised the magnetic blocking to ca. 80 K,¹⁰ making SMM-based memory devices achievable.¹¹ Some Ln³⁺-based SMMs offer intriguing optical features due to the emission from f–f electronic transitions.¹² Luminescent SMMs were studied for magneto-optical correlations,¹³ e.g., the spectroscopic determination of ligand-field states,¹⁴ control over emission by a magnetic field,¹⁵ and field sensing by the optical signal.¹⁶ One of the emerging routes is optical thermometry using SMMs, aiming at a non-invasive read-out of temperature through the emission of a magnetic center.^{1f, 2b, 16, 17} Since the effect of slow magnetic relaxation is T-dependent, insight into the working temperature is of primary importance for future SMM-based devices.¹⁸ The idea is to construct a single-phase material that will exhibit both the SMM and thermometric effects (Scheme 1). It will have vast advantages over the system of two bonded materials showing these properties separately as the composite will have a slower response and an additional noise in SMM features can appear. Such issues are solved for SMM-based optical thermometers which give a fast sensing response and the undisturbed SMM features. To accomplish such an idea, the working T-range between magnetic and optical effects must overlap. Among the known SMMs showing optical thermometry, only one example meets this criterion but within a narrow range of 5–10 K while the other report shows the ca. 10 K overlap between the moderate optical thermometry and the SMM features generated by the strong field of 3.6 T.^{17b, 19} The difficulty of finding T-overlap can be attributed to the limited working regime for most SMMs;^9c thus, optical thermometry has to operate at cryogenic temperatures. This happens for some Ln^III complexes but these examples -did not show the distinct SMM effect.¹³ Thus, the simultaneous design of magnetic anisotropy, as well as thermometry at cryogenic temperatures, is the key to achieving high-performance SMM-based optical thermometers.

In recent years we and others employed cyanido complexes of d-block metal ions for bimetallic d-f systems working as luminescent SMMs.^{2b, 20, 21-23} Using this strategy, optical thermometry was found in the vis or NIR region;^{2b, 21, 22} however, no overlap with SMM behavior was identified due to moderate magnetic anisotropy. We also demonstrated that magnetic anisotropy of Dy^III centers can be enhanced by the post-synthetic dehydration of a three-dimensional (3D) Dy^III−[Co^III(CN)₆]³⁻ framework.²³ To get large magnetic anisotropy for an SMM-based luminescent system, we decided to study an analogous framework built of Tb³⁺ ions. These 4 f metal centers show green emission due to f–f electronic transitions.²⁴ They are non-Kramer's magnetic centers but of large magnetic anisotropy when embedded in a crystal field of high symmetry. This was identified for complexes built with phthalocyaninato ligands (D_4d symmetry),^{1g, 8b, 25} and recently for arachno-carboranyl ligands (D_6h symmetry).²⁶ The Tb^III-analog of the 3D hydrated Dy^III−[Co^III(CN)₆]³⁻ network was shown to give moderate magnetic anisotropy;²⁷ but its dehydration toward the D_3h symmetry and their emission was not presented. Here, we report structures, magnetic and optical properties of the 3D coordination network, [Tb^III(H₂O)₂][Co^III(CN)₆] ⋅ 2.7H₂O (1), and its dehydrated phase, Tb^III[Co^III(CN)₆] (2) (Figure 1). The latter shows the conjunction of SMM behavior and optical thermometry, with a wide T-overlap of their working ranges. These effects are enriched by the magnetic dilution as shown in the [Tb_0.026Y_0.974(H₂O)₂][Co(CN)₆] ⋅ 2.7H₂O (1 md) and Tb_0.026Y_0.974[Co(CN)₆] (2 md) phases.

Results and Discussion

The initial system, 1, was obtained from an aqueous solution of Tb^III(NO₃)₃ and K₃[Co^III(CN)₆], while 2 was prepared by the thermal dehydration of 1 (see SI). The single-crystal X-ray diffraction (SC-XRD) studies revealed a single-crystal-to-single-crystal manner of transition between 1 and 2 (Figures 1 and S1, Tables S1–S4). This happens due to the stability of the coordination skeleton built of rigid octahedral [Co^III(CN)₆]³⁻ units and Tb³⁺ ions. All the CN⁻ ligands serve as molecular bridges between the Tb^III and Co^III centers, as depicted by SC-XRD and IR spectra (Figure S2). The inorganic Tb[Co(CN)₆] network is stable up to ca. 570 K, as shown by TGA (Figure S3). The hydrated 1 crystallizes in an orthorhombic Cmcm space group. Per the formula unit, it contains a single [Co(CN)₆]³⁻ ion, two aqua ligands coordinated to the Tb^III center, as well as two water molecules of crystallization (Figure 1a). The resulting Tb^III complex has a coordination number of eight, constituted by two O-atoms and six N-atoms from CN^– molecular bridges. The geometry for the {Tb^IIIO₂N₆} unit is close to a square antiprism (SAPR-8); however, the first coordination sphere can be also described as a bicapped trigonal prism (BTPR-8) (Table S3). The removal of all water molecules leads to the dehydrated phase of 2, of a hexagonal P6₃/mmc space group. The geometry of the {Co^IIIC₆} unit remains unchanged but the Tb^III coordination sphere transforms into a trigonal prism (TPR-6), consisting of six N-atoms of cyanido ligands (Table S4). The transformation between 1 and 2 is reversible as shown by the powder X-ray diffraction (P-XRD) patterns (Figure S4).

The modification of the Tb^III coordination sphere between 1 and 2 phases was studied as the source of the changes in its magnetic anisotropy. The magnetic characteristics were gathered for 1 and 2, and their Y^III-diluted samples, 1 md and 2 md (see the SI, Figure 2, Table 1, and Figures S5–S19). The direct-current (dc) experiments indicate that the magnetic susceptibility-temperature product at 300 K, χ_MT, are 11.38 (1) and 11.43 cm³mol⁻¹K (2) which are close to the expected ones for a free Tb³⁺ ion (11.82 cm³mol⁻¹ K). Upon cooling, the χ_MT decreases due to the thermal depopulation of the excited m_J levels of the ⁷F₆ ground multiplet. Field-dependent magnetization at 2 K for 1 and 2 saturates at 4.38 and 4.54 μ_B, respectively, as typical for uncoupled Tb^III centers with the m_J=6 ground level (Figure S5).^25b-26 The magnetic isolation given by bulky [Co^III(CN)₆]³⁻ linkages offers a prerequisite for the SMM effect of Tb³⁺ ions. However, under the H_dc of 0 Oe, the out-of-phase magnetic susceptibility (χ_M”) for 1 at 2 K is negligible (Figure S6). The application of the dc field can quench QTM and induce the appearance of the χ_M” maxima but this is not the case, indicating fast under-barrier relaxation in 1 (Figure S7). We found that it can be decelerated by magnetic dilution. The diluted sample, 1 md, reveals a field-induced χ_M”(ν) maximum below 1500 Hz at 2 K. Under the optimal 2 kOe, both in-phase χ_M’(ν) and out-of-phase χ_M”(ν) curves were plotted in the 2–8.5 K T range, and the relaxation time, τ, at each temperature, was fitted using the generalized Debye model (Figures 2a, S8, and S9). The obtained τ values with ones extracted from the H-dependent experiment, result in the τ(H, T) relationship described by the equation (1a):

(1a)

where the four terms represent relaxation pathways of Orbach, Raman, QTM, and Direct types. To better understand the nature of the Raman mechanism the second term can be represented by the sum of the contributions originating from the crucial phonon modes (equation 1b:²⁸

(1b)

Taking the latter into account the T dependence of relaxation time for 1 md was fitted using QTM and Direct parameters extracted from the H variable experiment and Raman relaxation described by two vibrational modes of 28(2) and 340(17) cm⁻¹. The Orbach pathway was not found for this phase (Figures 2a, S8, and S9). The best-fit parameters are collected in Table 1. 2 reveals the χ_M” signal in the high-frequency regime under a zero external dc field (Figures 2b, S10, and S11). Although the χ_M” maxima are lying above the detection limit of 1500 Hz, this onset of dc-field-free slow magnetic relaxation suggests the improved SMM effect after dehydration. More precise studies of 2 were performed with an applied dc field. To find an optimal H_dc, the ac dependences were analyzed in the 0–9 kOe range at 15 K (Figure S12). Upon elevating the dc field, the τ values increase as evidenced by the continuous shift of the χ_M”(ν) maxima. However, above 3 kOe magnetic relaxation slows down to a much smaller extent (Figure S12). Thus, we chose H_dc=3 kOe, under which the T-variable data were collected in the 2–42 K range (Figures 2b and S13). The relaxation times were then extracted and their combination with the ones extracted from the H_dc-variable experiment (Figure S12) gave all parameters of the magnetic relaxation (Table 1). Due to the presence of weak interactions affecting the relaxation time at the lowest temperatures, the Raman contribution was fitted with the term depicted in eq. 1a. The resulting fit shows that the QTM effect dominates at the lowest T, further, the Raman contribution with the power n of 4.79(6) plays an essential role, while the highest T-range above 30 K is governed by Orbach relaxation (Figures 2b, S12, and S13). The thermal energy barrier of 594(18) cm⁻¹ (854(26) K) is comparable with the largest ones for Tb^III SMMs ^[8b,26] and matches the theoretical value (Tables S7 and S9).

Prompted by the value of ΔE unveiled under the external dc field, we decided to obtain a more pronounced SMM behavior using the dilution effect. The 2 md-Tb_xY_1–xCo (x=0.01–0.11) samples were prepared (see the SI, and Figure S14). The ac data revealed that the Tb^III concentration at the 10 % level is proper to induce the SMM behavior with χ_M”(ν) maxima lying below 1500 Hz (Figure S15). Further decrease of the Tb^III amount slows down the relaxation giving the magnetic hysteresis loop. It is the most visible for 2 md-Tb_0.01Y_0.99Co. For this system, the blocking temperature is 5 K, however, the M(H) butterfly shape appears due to the QTM effect (Figure 3a). The dilution reveals an evident deceleration effect, which is pronounced for the τ values at lower T (Figure S15d). This improvement can be ascribed to the quenching of dipolar Tb−Tb interactions. A similar trend, but for the weaker SMM, was also found for 1 and 1 md.

For full ac characterization, the 2 md-Tb_0.026Y_0.974Co system, named 2 md, was selected (Figures 2c and S16–S19). The zero-dc-field curves for 2 md were used to extract the set of τ values up to 30 K (Figure 2c). The ln(τ) vs. T⁻¹ plot shows linear dependence of Arrhenius type above 17 K, giving the energy barrier of 52.1(7) cm⁻¹. This value is too small for the expected Orbach relaxation, suggesting that the dc-field-free relaxation is governed by the Raman process. In the lower T regime, the QTM still plays a pivotal role. After the application of the dc field, the QTM is quenched, the Raman is modified, and the Orbach appears to be well visible for the high-T range above 35 K. All three T dependencies under different H_dc values were fitted simultaneously with the Orbach parameters (τ₀, ΔE) and two vibrational frequencies (ω₁, ω₂) shared. The Orbach relaxation is described by the energy barrier of 596(8) cm⁻¹ (859(12) K), close to found for 2 (Table 1). This proves that the Orbach process is due to the generated Tb^III complexes of 2. On the other hand, the crucial vibrational modes were identified as 306(3) and 729(31) cm⁻¹, with C_i parameters being H-dependent. The ac magnetism was also used to check the reversibility of the dehydration (Figures S20 and S21).

The conclusions from the ac magnetic measurements are supported by the ab initio calculations performed for Tb^III centers of 1 and 2 (Figures 3 and S22, Tables S5–S10), and the emission spectra at various T (Figures 3 and S23–S27). The calculations provided the energy positions of the excited m_J levels for the Orbach relaxation; in 1, the relaxation can occur through the first excited pair at ca. 100 cm⁻¹ while, in 2, the Orbach process is likely to occur through the third one, at ca. 580 cm⁻¹ above the ground level (see Supporting Information for details). The magnetic axes for the ground states were calculated (Figures 1b and S22). In 1, it nearly goes through the walls of two triangular arrangements of CN⁻ ligands with a deviation towards aqua ligands. In 2, the anisotropy axis goes ideally perpendicular to the triangular walls of the trigonal prismatic polyhedron along the 3-fold rotation axis. The validity of the calculations is confirmed by the good reproduction of the dc data, especially for 2 (Figure S5). The T-variable emission spectra, in the range of the ⁵D₄→⁷F₆ electronic transition, were gathered down to 3.5 K for 1, 2, 1 md, and 2 md. For this transition in 2 md at 3.5 K only three maxima are observed (Figure 3b). They correlate with the calculated energies of the ground pseudo-doublet, the first excited one, and those of higher energy. A similar case was found for 2, while for 1 and 1 md the comparison between the calculations and the low-T spectra needed the analysis of the hot bands. We calculated the energy splitting for the emissive ⁵D₄ multiplet (Table S10). It helped us in the assignment of transitions which enables the magneto-optical correlations (Figures S23–S26).

The optical properties of 1 were first studied using UV-vis-NIR absorption spectra. An intense absorption band below 380 nm is due to d–d electronic transitions of Co^III embedded in a strong crystal field (Figure S28). In the next step, the emission properties of 1, 2, 1 md, and 2 md were studied (Figures 4, 5, and S29–S44, Tables S11–S26). The presence of [Co(CN)₆]³⁻ ions, which at least partially transfer the excitation energy to the Tb^III centers, induces the green 4 f metal-centered luminescence at 300 K for 1 and 2 (Figures 4, S29, and S30).²⁷ For 1, the UV irradiation of the 240–370 nm band (Figure S29) induces Tb³⁺ emission peaks at 490, 540, 582, 619, and 640 nm (Figure 4a). Such a pattern is related to f–f electronic transitions of the ⁵D₄→⁷F₆, ⁷F₅, ⁷F₄, ⁷F_3, and ⁷F₂ origin, respectively. Within each emissive band, several sharp components can be identified reflecting the crystal field splitting. Moreover, in the 500–750 nm range, an additional band at ca. 610 nm appears which is attributed to red emissive [Co(CN)₆]³⁻ ions (³T_1g→¹A_1g transition, Figure S32).^{20, 29} It was found strong for the Y^III-based analog of 3 (Figure S31). In 1, the residual Co^III-centred emission with the Tb^III-related peaks produces a yellowish-green emission at 300 K (Figures S33 and S44). 2 exhibits a series of Tb^III bands but shows modified energy-splitting patterns (Figures 4a and S35). The intensity of the d–d band is weaker when compared with 1 (Figure S32). Moreover, 2 shows ca. 6.8 and ca. 5.3 times stronger intensities of the ⁵D₄→⁷F₆ and ⁵D₄→⁷F₅ emissive peaks, respectively (Figure 4a). The increase of Tb^III-centered emission is supported by the lifetime measurements, which reveal the increased value in 2 (Figure 4b). With the higher contribution of Tb^III emission, 2 at 300 K shows green emission without a yellow hue (Figures S35 and S44). The re-hydrated 1′ reveals an identical emission to the one for 1 (Figure S32).

Both 1 and 2 were tested in the 300–3.5 K range for optical thermometry (Figures 5, and S33–S44, and Tables S11–S26). For 1, upon cooling, the intensity of Tb^III emissive lines increases faster than the Co^III emission suggesting the enhanced efficiency of the sensitization process combined with the reduction of the quenching effect by O−H oscillators. As a result, down from 230 K the emission color shifts to green (Figures S33 and S44). Below 90 K, the increase of Tb³⁺ emission slows down and further slightly decreases due to the thermal depopulation of the hot transitions (Figures 5a, S23, S33, and S34). For 2 similar trends are observed. By lowering the temperature, the Tb^III emission increases, and a set of gradually depopulating hot bands is found (Figures 5a, S25, S35, and S36). To assign the specific peaks to hot and cold electronic transitions, we analyzed the spectra using the calculated energy splitting both for the ground and excited multiplets of Tb^III centers (Figures S23–S27). 1 and 1 md show a large overlap between emissive bands which stays in agreement with the small splitting both for the ground and emissive multiplets (Figures S23 and S24). On the contrary, 2 and 2 md exhibit the large energy splitting for the ground Tb^III multiplet providing good separation of the cold emission bands. Thus, the hot bands are distinguished much easier, especially since the splitting for the emissive multiplet is smaller (Figures 5a, S26, and S27). The other, lower-energy bands behave similarly for 1, and in the whole T range the emission of the ⁵D₄→⁷F₅ origin dominates (Figure S33). Then, the emission color shifts from yellowish-green to a deeper green due to the red emission of the Co^III origin which becomes marginal at low T. On the contrary, 2 exhibits an unusual cooling-induced change in the emission color. On cooling from 300 to 200 K, it behaves similarly as 1 shifting the emission from yellowish-green to green, but, at lower T, the emission shifts toward the white color (Figures S35 and S44). This is related to the change in the ratio between the main emission components corresponding to the ⁵D₄→⁷F₆ and ⁵D₄→⁷F₅ transitions (Figure S35). The intensity of the ⁵D₄→⁷F₅ band in comparison to the ⁵D₄→⁷F₆ one is usually stronger. Both these transitions are of a dominant electron-dipole character, thus, they are sensitive to the local environment; however, they belong to different selection rules, ΔJ=±2 and ΔJ=±1, respectively. It results in distinguishable sensitivity to, e.g., the local structure and the Tb^III-ligand bond covalency.³⁰ The ⁵D₄→⁷F₅ band is strongly dependent on the asymmetry of the ligand field, so it appears that the high-symmetry Tb^III centers in 2 provide a rare example of weakening the ⁵D₄→⁷F₅ band in comparison to the ⁵D₄→⁷F₆ band.

We found that the thermal variation of Tb³⁺-based emission peaks provides the route to the thermometry effect (Figures 5 and S33–S36). As the measure of the intensity, we used the integrated areas for the peaks ( , Figures S34 and S36, Tables S12, S14, S20, and S22). Similar characteristics can be obtained with the emission intensities at the maximum ( , Figures S33 and S35, Tables S11, S13, S19, and S21). Both 1 and 2 offer many combinations of peaks suitable for the thermometric parameters, Δ= / , among which one is assigned to the hot band, while the second is the cold band. Thus, we explore the cooling-induced enhancement of the cold bands and the disappearance of the hot bands. As the energy splitting of the emissive multiplet is small, the lowest-lying excited levels are still populated below 50 K, and the thermometry appears in the 10–100 K range. All four f–f bands of the ⁵D₄→⁷F_6,5,4,3 origin for 1 and 2 can be employed for the thermometry (Figures 5 and S33–S36); however, the highest-energy ⁵D₄→⁷F₆ band of 2 is particularly good as the hot bands are easily distinguished. The Δ(T) relationship is given by a Mott–Seitz model, equation 2:^{18, 24}

(2)

where Δ₀ is the thermometric parameter at T=0 K, α_i and α₂ are the ratios between non-radiative and radiative rates, and ΔE₁ and ΔE₂ are the activation energies for the non-radiative channels. The best-fit ΔE₁/k_B, ΔE₂/k_B values lie in the ranges of 110–180 and 30–40 K, respectively, for 1, and 130–230 and 39–45 K, respectively, for 2 (Tables S11–S14). To evaluate the performance of Δ(T) curves, parameters of relative thermal sensitivity, S_r=|∂Δ/∂T|/T, and T uncertainty, δT=(δΔ/Δ)/S_r were examined, taking into account the criteria of good performance thermometry, S_r>1% K⁻¹ and δT<1 K.^{18, 24} Such analysis revealed that selected Δ parameters provide good performance in the characteristic λ ranges (Figures 5c and S33–S36), working for the low T region up to 113 K (Tables S19–S22). 1 and 2 offer a readout in four different visible-light sub-ranges of the emission spectra related to ⁵D₄→⁷F_J transitions. Furthermore, using the integrated areas, the best performances were found for the Δ(T) curves obtained for the ⁵D₄→⁷F₆ transition, which, for 1, provides the maximal S_r of 5.49 % K⁻¹ at 13.6 K for the Δ parameter defined as / , and, for 2, gives the high maximal S_r of 5.28 % K⁻¹ at 15.9 K with the Δ parameter defined as / . More importantly, for 2 in the wide 6–42 K range, the high-performance regime for most of Δ(T) curves overlaps with the SMM (Figures 2 and 5c). The T-dependent emission of 1 md and 2 md was also examined (Figures 5 and S37–S44). They exhibit similar Tb^III emission as 1 and 2. However, at 300 K, the emission originating from Co^III is dominant (Figures S37, S38, and S44). Upon cooling, emission intensities of both origins increase, yet for the Tb^III faster. In 1 md/2 md, the thermometry based on the ⁵D₄→⁷F_5,4,3 transitions is disabled due to the broad Co^III emission but the emission of the ⁵D₄→⁷F₆ transition can be used for thermometry (Figures 5 and S39–S43, Tables S15–S18 and S23–S26). The analyses for 1 md revealed a good thermometric performance in the 8–78 K range with the max. S_r of 2.58 % K⁻¹ at 18.3 K using Δ= / . The ⁵D₄→⁷F₆ transition of 2 md offers two parameters, Δ= / and Δ= / , showing working T-ranges of 6–96 K and 10–110 K, respectively (Figures 5, Tables S13 and S17). The max. S_r values are enhanced, reaching 5.44 % K⁻¹ at 14.7 K for the first range. 1 md and 2 md serve also as higher-T optical thermometers employing the intensity ratio between Tb^III and Co^III emissions (Figures 5, S39, and S40, Tables S15–S18 and S23–S26). Thus, the obtained set of compounds explores two types of optical thermometry, the single-center one working on the hot and cold f-f electronic transitions, and the dual-center one relying on the thermally coupled d–d and f–f emissive states (Figure S45).

Conclusion

We report a 3D Tb^III−Co^III network showing a reversible dehydration-induced phase transformation that gives trigonal prismatic Tb^III complexes bearing six cyanido ligands. These Tb^III complexes combine high symmetry and the axial alignment of charged ligands, two prerequisites for high-performance Tb^III SMMs, rarely accessible within the coordination chemistry. As a result, they exhibit large magnetic anisotropy with a thermal energy barrier of 594(18) cm⁻¹, comparable with the best Tb^III SMMs.^{8b, 25, 26} Moreover, the obtained SMMs exhibit optical thermometry which works at the cryogenic T-range, thus overlapping with the region of the SMM phenomenon.

We prove that the high-symmetry Tb^III complexes with the axial alignment of charged ligands are great candidates for the generation of luminescent SMMs whose temperature operating ranges for both physical properties overlap, which realizes the idea of the SMM-based optical thermometer for the future application in magnetic nanodevices with optically self-monitored temperature. The high-performance SMM behavior for Tb^III, as the product of high local symmetry and the axial arrangement of ligands, follows the well-defined, yet rarely realized, strategy for strong magnetic anisotropy. On the contrary, we show that such specific Tb^III complexes reveal efficient optical thermometry below 100 K. It uses the strong thermal variation of hot emission bands from the higher-lying m_J states within the emissive ⁵D₄ multiplet to the series of m_J levels of the ground ⁷F₆ multiplet. We found two key features of the obtained complexes that result in the optical thermometry of desired characteristics. First, the large energy splitting for the ground multiplet provides a good separation of the emission components related to cold electronic transitions, thus the hot bands, showing strong T-dependence, can be employed in the thermometer's construction. Second, the large energy splitting is observed for the ground multiplet, but for the emissive multiplet is much smaller. As a result, the higher-lying energy states of the emissive multiplet are populated even below 100 K enabling the observation of the hot emission bands disappearing down to low T. The high symmetry may contribute to this effect as it is expected to induce not only the pure bottom m_J state of the ground but also the emissive multiplet decreasing the related emission in comparison to that from the hot bands. These features are critical for optical thermometry overlapping with the SMM property in the broad range of 40 K. As the emission of Tb^III centers always occurs from the same types of energy multiplets, it is expected that Tb^III centers in a high symmetry environment with the axially aligned negatively charged ligands will give efficient low-T optical thermometry accompanied by the SMM effect.

Conflict of interest

The authors declare no conflict of interest.