Field-Induced Single-Ion Magnet Phenomenon in Hexabromo- and Hexaiodorhenate(IV) Complexes

Two mononuclear ReIV complexes of general formula (PPh4)2[ReX6] [PPh4 = tetraphenylphosphonium cation, X = Br (1) and I (2)] have been prepared and structurally and magnetically characterised. Both compounds crystallise in the triclinic system with space group Pı̄. Their structures are made up of hexahalorhenate(IV), [ReX6]2−, anions, and bulky PPh4 cations. Each ReIV ion in 1 and 2 is six-coordinate and bonded to six halide ions in a quasi regular octahedral geometry. In their crystal packing, the [ReX6]2− anions are well separated from each other through the organic cations, generating alternated anionic and cationic layers, and no intermolecular Re−X···X−Re interactions are present. Variable-temperature dc magnetic susceptibility measurements performed on microcrystalline samples of 1 and 2 show a very similar magnetic behaviour, which is typical of noninteracting mononuclear ReIV complexes with S = 3/2. Ac magnetic susceptibility measurements reveal the slow relaxation of the magnetisation in the presence of external dc fields for 1 and 2, hence indicating the occurrence of the field-induced single-ion magnet (SIM) phenomenon in these hexabromoand hexaiodorhenate(IV) complexes.


Introduction
The last decade has witnessed a rapid advance in the development of mononuclear Single-Molecule Magnets (SMMs), the so-called Single-Ion Magnets (SIMs), which are mainly discrete molecules that are based on one paramagnetic and highly anisotropic ion belonging mainly to the d-block or f-block metals and displaying slow relaxation of the magnetisation [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. These nanosized magnetic systems are often considered to be promising candidates for future technological applications, such as high-density information storage or quantum computing at the molecular level, among others [15,16].
Herein, we report the preparation, crystal structures, and magnetic properties of two mononuclear Re IV complexes of general formula (PPh 4 ) 2 [ReX 6 ] [PPh 4 + = tetraphenylphosphonium cation, X = Br (1) and I (2)], moreover studying the effect of the halide ligand and the crystal packing on the magnetisation relaxation dynamics.
In the crystal packing of 1 and 2, the [ReX 6 ] 2− anions are well separated from each other through the bulky PPh 4 + cations, which generate alternated anionic and cationic layers, respectively ( Figure 2a,b). The shortest Re···Re separation is ca. 10.43 (1) and 10.85 Å (2). The shortest X···X distance is approximately 6.52 and 5.93 Å for 1 and 2, respectively. It is worth pointing out that the [ReBr 6 ] 2− anions are arranged in a very similar way in 1, that is, with all of the anionic units orientated in the same direction, whereas the [ReI 6 ] 2− anions display different orientations in the crystal of 2 ( Figure 2).
on the magnetisation relaxation dynamics.
(a) (b) A field dependence of the molar magnetisation (M) plot for 1 and 2 at 2.0 K is given in the respective insets of Figure 3a(1),b(2). In all the cases, the M values display a continuous increase with the applied magnetic field, the higher M values being 1.57 (1) and 1.53 µB (2) at 5.0 T, which are in agreement with those of similar mononuclear Re IV complexes that were reported in the literature [18,[27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. Given that no significant intermolecular interactions are observed in the crystal structures of 1 and 2, as indicated in the structure description, the shortest intermolecular Re-X···X-Re distances are covering the range of 5.93-6.52 Å, we have performed the treatment of the experimental data of the χMT versus T plots through the anisotropic Hamiltonian of Equation (1) (where Ŝz is the easy-axis spin operator, H is the applied field, β is the Bohr magneton, g is the Landé factor, and D is the ZFS for the Re IV ion).
By assuming that g|| = g⊥ = g for the two complexes, we have fitted the experimental magnetic susceptibility data of the compounds 1 and 2, affording the following parameters: The solid red line, indicating the fit in Figure 3a(1),b(2), matches quite well the experimental curves in both cases. The g and D values that are computed for 1 and 2 are in agreement with those calculated for previously reported mononuclear Re IV complexes [18,[27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. The |D| value that is obtained for 2 is somewhat greater than that of the complex 1.

Ac Magnetic Susceptibility
Alternating current (ac) magnetic susceptibility measurements were performed on microcrystalline samples of 1 and 2 in the temperature range of 2-7 K and in a 3.5 G ac field oscillating at different frequencies. In both cases, no out-of-phase ac signals (χ″M) are observed at A field dependence of the molar magnetisation (M) plot for 1 and 2 at 2.0 K is given in the respective insets of Figure 3a(1),b(2). In all the cases, the M values display a continuous increase with the applied magnetic field, the higher M values being 1.57 (1) and 1.53 µ B (2) at 5.0 T, which are in agreement with those of similar mononuclear Re IV complexes that were reported in the literature [18,[27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. Given that no significant intermolecular interactions are observed in the crystal structures of 1 and 2, as indicated in the structure description, the shortest intermolecular Re-X···X-Re distances are covering the range of 5.93-6.52 Å, we have performed the treatment of the experimental data of the χ M T versus T plots through the anisotropic Hamiltonian of Equation (1) (whereŜ z is the easy-axis spin operator, H is the applied field, β is the Bohr magneton, g is the Landé factor, and D is the ZFS for the Re IV ion).

Ac Magnetic Susceptibility
Alternating current (ac) magnetic susceptibility measurements were performed on microcrystalline samples of 1 and 2 in the temperature range of 2-7 K and in a 3.5 G ac field oscillating at different frequencies. In both cases, no out-of-phase ac signals (χ" M ) are observed at H dc = 0 G. However, out-of-phase ac signals, with observable χ" M maxima, take place at low temperatures in 1 and 2 when an external dc magnetic field (H dc = 1000 and 5000 G) is applied (Figures 4 and 5). This magnetic behaviour would indicate that the two studied systems (1 and 2) exhibit slow relaxation of the magnetisation and, therefore, single-ion magnet (SIM) phenomenon . Nevertheless, the relaxation dynamics that the two compounds exhibit is not equally affected by the external dc magnetic fields. While the H dc = 5000 G seems to be optimal for compound 1 (with the presence of more χ" M maxima that shift towards higher frequencies), this magnetic field results in being less useful for studying the magnetic relaxation in 2, where a decrease of the number of χ" M maxima in the χ" M versus ν plot occurs (Figures 4 and 5). In both 1 and 2, the intensity of the χ" M peaks increases with increasing the external dc magnetic field.
The insets in Figures 4 and 5 show the ln(τ) versus 1/T plot for complexes 1 and 2, respectively. In the high-temperature region, the experimental data that were obtained from the frequency-dependent χ" M peaks draw a straight line pretty much in both cases along the ranges of ca. 0.25-0.35 K −1 for 1 ca. 0.35-0.50 K −1 for 2. Consequently, these experimental data were fitted to the Arrhenius equation (τ = τ o exp(U eff /k B T), where τ o is the preexponential factor, τ is the relaxation time, U eff is the anisotropy (effective) energy barrier to the magnetisation reorientation, and k B is the Boltzmann constant) by considering that the magnetisation relaxation only involves an Orbach process [12]. In this way, we can evaluate the U eff and τ o parameters in this region for 1 and 2 and compare their values with those previously reported. These fits are indicated as dashed lines in the insets of Figures 4 and 5, and Table 2 provides the U eff and τ o values thus obtained for 1 and 2.
Magnetochemistry 2020, 6, x FOR PEER REVIEW 5 of 11 Hdc = 0 G. However, out-of-phase ac signals, with observable χ″M maxima, take place at low temperatures in 1 and 2 when an external dc magnetic field (Hdc = 1000 and 5000 G) is applied (  Figure 4; Figure 5). This magnetic behaviour would indicate that the two studied systems (1 and 2) exhibit slow relaxation of the magnetisation and, therefore, single-ion magnet (SIM) phenomenon . Nevertheless, the relaxation dynamics that the two compounds exhibit is not equally affected by the external dc magnetic fields. While the Hdc = 5000 G seems to be optimal for compound 1 (with the presence of more χ″M maxima that shift towards higher frequencies), this magnetic field results in being less useful for studying the magnetic relaxation in 2, where a decrease of the number of χ″M maxima in the χ″M versus ν plot occurs (Figures 4 and 5). In both 1 and 2, the intensity of the χ″M peaks increases with increasing the external dc magnetic field.       The U eff values for 1 are similar between them at both 1000 and 5000 G, and much higher (approximately five/six times) than that of compound 2 (Table 2). Besides, the energy barrier value of 2 remains practically unaffected with increasing the dc applied magnetic field. The τ o parameter for 1 and 2 shows values that are in agreement with those that were reported for similar Re IV complexes displaying SIM behaviour [20][21][22][23].
In the low-temperature region of the ln(τ) versus 1/T plots, curved lines are only observed for 1, which are better defined when the H dc = 5000 G is applied (Figures 4 and 5). These features would account for the occurrence in such conditions of several relaxation processes, especially in compound 1.
All the four mechanisms were considered during the fitting process of the ln(τ) versus 1/T curve for 1 that was obtained at the optimal magnetic field of 5000 G, whereas in the case of the treatment of the experimental data acquired with H dc = 1000 G, the fourth term (QTM) was kept equal to zero ( Table 3). The least-squares fit of the experimental data of 1 through Equation (2) leads to the set of parameters listed in Table 3. From these results, it is worthy to point out that the U eff values thus obtained for compound 1 are somewhat higher than those calculated through the Arrhenius law and listed in Table 2. Besides, the U eff parameter for 1 remains higher than that of 2. Indeed, the effective energy barrier value obtained at the optimal dc field (H dc = 5000 G) for 1 [ [21,22]. The computed values of τ o and τ QTM for 1 agree with those that were reported for other 5d-SIMs [20][21][22][23]. On the other hand, the n values for 1 lie between 4.3 and 5.5 and fall into the range typical of metal ions with relaxation through optical and acoustic Raman-like process (n being equal to 9 for the Raman relaxation of Kramer ions) [12]. These n values are very close to those that were obtained for similar 5d-SIMs (Table 3) [24][25][26]. Table 3. Parameters of the magnetic relaxation obtained through the dc applied magnetic fields of 1000 and 5000 G and the Equation (2) for 1. The frequency-dependent ac magnetic susceptibility data of compounds 1 and 2 were modelled to give the Cole-Cole plots that are shown in Figure 6. The obtained values for the α parameter are in the ranges of 0.09-0.17 (1) and 0.06-0.11 (2), with these values suggesting a narrow distribution of the relaxation times for these mononuclear Re IV complexes [20][21][22][23][24][25].
Magnetochemistry 2020, 6, x FOR PEER REVIEW 7 of 11 Table 3. Parameters of the magnetic relaxation obtained through the dc applied magnetic fields of 1000 and 5000 G and the Equation (2)  The frequency-dependent ac magnetic susceptibility data of compounds 1 and 2 were modelled to give the Cole-Cole plots that are shown in Figure 6. The obtained values for the α parameter are in the ranges of 0.09-0.17 (1) and 0.06-0.11 (2), with these values suggesting a narrow distribution of the relaxation times for these mononuclear Re IV complexes [20][21][22][23][24][25].

Reagents and Instruments
All of the manipulations were performed under aerobic conditions, using materials as received (reagent grade). The Re IV precursors, namely, the K2ReBr6 and K2ReI6 salts, were prepared following the synthetic methods described in the literature [29,30].
Elemental analyses (C, H, N) were performed by the Central Service for the Support to

Reagents and Instruments
All of the manipulations were performed under aerobic conditions, using materials as received (reagent grade). The Re IV precursors, namely, the K 2 ReBr 6 and K 2 ReI 6 salts, were prepared following the synthetic methods described in the literature [29,30].
Elemental analyses (C, H, N) were performed by the Central Service for the Support to Experimental Research (SCSIE) at the University of Valencia. Infrared spectra of 1 and 2 were recorded with a PerkinElmer Spectrum 65 FT-IR spectrometer in the 4000-400 cm −1 region. The powder X-ray diffraction (PXRD) patterns of 1 and 2 confirmed the homogeneity of their bulk samples ( Figure S2). Variable-temperature, solid-state direct current (dc) magnetic susceptibility data down to 2.0 K were collected on a Quantum Design MPMS-XL SQUID magnetometer that was equipped with a 5 T dc magnet. Experimental magnetic data were corrected for the diamagnetic contributions of the involved atoms by using Pascal's constants [46].

X-ray Data Collection and Structure Refinement
X-ray diffraction data from single crystals of dimensions 0.28 × 0.26 × 0.20 (1) and 0.18 × 0.13 × 0.08 mm 3 (2) were collected on a Bruker D8 Venture diffractometer with graphite-monochromated Mo-K α radiation (λ = 0.71073 Å). Crystal parameters and refinement results for 1 and 2 are summarized in Table 1. The data were processed through SAINT [47] reduction and SADABS [48] multi-scan absorption software. The structure was solved with the SHELXS structure solution program through the Patterson method. The model was refined with version 2013/4 of SHELXL against F 2 on all data by full-matrix least squares [49][50][51]. In the two samples, all non-hydrogen atoms were anisotropically refined. All of the hydrogen atoms of the PPh 4 + cations were set in calculated positions and refined isotropically by using the riding model. The graphical manipulations were performed with the DIAMOND program [52]. The CCDC codes are 1956543 and 1956544 for 1 and 2, respectively.

Conclusions
In summary, the X-ray structures and magnetic properties of two mononuclear Re IV complexes, of general formula (PPh 4 ) 2  interactions are present. The study of the relaxation dynamics reveals that 1 and 2 are not equally affected by the external dc magnetic fields, the bromo-derivative complex 1 exhibiting the higher value of the energy barrier (U eff ) for the reverse of the magnetisation in this family of hexahalo [ReX 6 ] 2− compounds. Indeed, the U eff value for 1 is higher than those previously reported for Re IV -based SIMs. Hence, the information generated by these results could be very useful in designing future magnetic materials that are based on Re IV SIMs.