Magnetic Anisotropy from Trigonal Prismatic to Trigonal Antiprismatic

Article Cite This: Inorg. Chem. 2018, 57, 3903−3912

pubs.acs.org/IC

Magnetic Anisotropy from Trigonal Prismatic to Trigonal Antiprismatic Co(II) Complexes: Experimental Observation and Theoretical Prediction Jing Zhang,† Jing Li,† Li Yang,† Chen Yuan,‡ Yi-Quan Zhang,*,‡ and You Song*,† †

State Key Laboratory of Coordination Chemistry, Collaborative Innovation Center of Advanced Microstructures, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China ‡ Jiangsu Key Laboratory for NSLSCS, School of Physical Science and Technology, Nanjing Normal University, Nanjing 210023, China S Supporting Information *

ABSTRACT: A family of trigonal antiprismatic Co(II) complexes was synthesized, which exhibited field-induced Raman process dominated singlemolecule magnet behavior. Despite the coordination environment of Co(II) being of similar symmetry, the four complexes exhibit distinct dynamic magnetic properties owing to their packing arrangements and dipole−dipole interactions. On the basis of computational results we have demonstrated that the gz and giso values follow a cosine relation with respect to the rotated angle φ (twist angle φ defined as the rotation angle of one coordination square away from the eclipse conformation to the other).

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INTRODUCTION In recent years, single-molecule magnets (SMMs)1 have manifested themselves in the information storage2 and quantum computing fields.3 The first complex that exhibited SMM behavior was discovered in the 1990s, [Mn12],1 initiating a field for studying the magnetic properties of multinuclear transition-metal complexes. However, the limitation of high relaxation energy barriers (Ueff) and high blocking temperatures (TB) still hinders practical applications, motivating scientists to resort to new methods. Slow magnetic relaxation was observed in the mononuclear complex [Tb(III)Pc2]4 in 2003, whose energy barrier is up to 331 K. These kinds of complexes are also termed single-ion magnets (SIMs). Subsequently, efforts have shifted to mononuclear SMMs thanks to their strong spin− orbital coupling and high magnetic anisotropy.5−8 Research on 3d and 4f SIMs has since begun to emerge. Recently, Goodwin and co-workers and Guo and co-workers have reported a dysprosium complex whose magnetic hysteresis is up to 60 K, close to the temperature of liquid nitrogen. Further progress can be anticipated in the practical application of SMMs.9−11 In the past few decades, the research for new SIMs has extended to Cr(II),12 Mn(III, IV),13−15 Fe(I, II, III),16−24 Co(I, II),25−49 Ni(I, II),50,51 and Re(IV).52,53 The reversal energy barrier can be predicted by U = |D|S2 or U = |D|(S2 − 1/4) for integer or half-integer spin, respectively. More importantly, according to Kramer’s theory,54 quantum tunnelling of magnetization can be suppressed for a non-integer spin system. For an ideal spin carrier candidate, an exceptional zero field © 2018 American Chemical Society

splitting parameter (D) and large half-integer spin are important. It is natural that high spin Co(II) became the preferred candidate for building an excellent SIM. Many kinds of two-,33,49 three-,34 four-,28,29 five-,35,47,48 six-,27,36,37,40−46 seven-,38 and eight-coordinate26 complexes have already been reported. Some of them exhibit SMM behavior with easy-plane magnetic anisotropy.27,31,38,39 For a six-coordinate complex there are many kinds of spatial configurations with different symmetries, of which trigonal antiprism and trigonal prism are two special configurations with C3 symmetry. In recent years, several Co(II)-based complexes with trigonal prism have shown SMM behavior in a zero applied dc field.37,40−44 In 2016, our group and Dunbar and co-workers reported the first trigonal antiprismatic Co(II) field-induced single-molecule magnets, [Co(Tp*)2]36 (5), [Co(TPm)2][BPh4]2,45 and [Co(TPm)2][ClO4]2,45 which exhibit Raman process dominated relaxation. In this report, we synthesized a series of complexes possessing trigonal antiprism, among which the structures of complexes 1 and 4 have been reported;55 similar structures of 1, 2, and 4 based on non-cobalt ions can also be found.55b,56 Herein our research focuses on only the magnetostructural correlation. Additionally, we designed a series of model complexes with different rotation angles φ from trigonal antiprism to trigonal prism, combined with ab inito calculations, to determine the correlation between structure and magnetic relaxation. Received: January 7, 2018 Published: March 12, 2018 3903

DOI: 10.1021/acs.inorgchem.8b00055 Inorg. Chem. 2018, 57, 3903−3912

Article

Inorganic Chemistry Table 1. Crystal Data for Complexes 1−4

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formula Mr crystal system space group a (Å) b (Å) c (Å) α (deg) β (deg) γ (deg) V (Å3) T (K) Z ρcalcd (g cm−3) λ (Å) number of ind reflns number of reflns with I > 2σ(I) number of parameters final R1, wR2 [I > 2σ(I)] R1, wR2 all data goodness of fit, GOF CCDC

1

2

3

4

C18H20N12B2Co 485.01 monoclinic P21/c 9.7349(17) 17.631(3) 15.450(18) 90.00 121.523(7) 90.00 2260.5(6) 293(2) 4 1.425 0.71073 5165 3646 298 0.0357, 0.0829 0.0586, 0.0911 0.984 1545684

C18H20N12B2Co 485.01 tetragonal P42/ncm 17.5540(15) 17.5540(15) 7.4948(6) 90.00 90.00 90.00 2309.5(3) 296(2) 4 1.395 0.71073 1393 1037 89 0.0474, 0.1011 0.0711, 0.1095 1.140 1545685

C36H56N18B2S12Co3 1324.12 triclinic P1̅ 7.7964(14) 12.272(2) 16.425(3) 110.123(3) 101.657(3) 90.800(3) 1439.2(5) 296(2) 1 1.528 0.71073 6591 4349 331 0.0517, 0.1325 0.0880, 0.1525 0.993 1545686

C32H40N16B2Co 729.35 monoclinic P21/c 10.1333(8) 12.1956(11) 14.2613(10) 90.00 98.075(2) 90.00 1745.0(2) 296(2) 2 1.388 0.71073 4022 3074 236 0.0568, 0.1277 0.0804, 0.1375 1.038 1545683

yield of 31% based on Co. Elemental analysis calcd (%) for C36H56B2Co3N18S12 (3): C (32.62), N (19.03), H (4.26); found C (32.69), N (19.13), H (4.27). IR data (cm−1): 3421.25s, 2925.68w, 2856.55w, 2464.19w, 1637.60w, 1519.80s, 1389.33s, 1306.58m, 1252.06w, 1210.19m, 1141.06s, 1113.80s, 1051.49s, 976.52w, 782.78w, 769.15m, 721.44s, 659.13w, 625.05w, 445.91w. Synthesis of (pzTpMe)2Co (4). The synthesis of complex 4 is different from the published method.55b KpzTpMe (0.2 mmol, 55 mg) and Co(ClO4)2·6H2O (0.1 mmol, 36.5 mg) were added to MeOH (1 mL). After the metallic salt dissolved, CH2Cl2 (10 mL) and i-PrOH (2 mL) were added. Twenty minutes later, the yellow solution was filtered and left in a beaker until crystallization occurred. Yellow crystals were isolated with a yield of 81%. Elemental analysis calcd (%) for C32H40B2CoN16 (4): C (52.70), N (30.73), H (5.53); found C (52.5), N (30.72), H (5.50). IR data (cm−1): 3434.88m, 3159.35w, 3125.27w, 2925.68w, 1630.79w, 1519.80s, 1485.72m, 1444.83w, 1362.07m, 1237.45w, 1182.93s, 1066.10s, 1003.79m, 851.90s, 804.20s, 769.15s. X-ray Crystallography. The X-ray measurements of compounds 1−4 were carried out on a Bruker Smart CCD area-detector diffractometer with Mo Kα radiation (λ = 0.71073 Å) by using an ω scan mode at 296 K (293 K for 1). The diffraction data were treated using SAINT,58a and all absorption corrections were applied by using SADABS.58b All non-hydrogen atoms were located by Patterson’s method58c using the SHELXS programs of the SHELXTL package and by subsequent difference Fourier syntheses. The hydrogens bonded to carbon were determined theoretically and refined with isotropic thermal parameters riding on their parents. H atoms of methanol were first located by difference Fourier E-maps and then treated isotopically as riding. All non-hydrogen atoms were refined by a full-matrix leastsquares technique based on F2. All calculations were performed by SHELXTL-97.58d Physical and Magnetic Measurements. The IR spectral measurements were carried out with a Nexus 870 FT-IR spectrometer using KBr pellets in the range of 400−4000 cm−1. Elemental analyses of C, H, and N were recorded on a PerkinElmer 240C elemental analyzer. The ac magnetic susceptibility data were collected using a Squid VSM magnetometer with an ac field of 2 Oe and frequencies ranging from 1 to 999 Hz, under different external dc fields. The dc magnetic susceptibility data were measured in the temperature range of 1.8−300 K. Experimental susceptibilities were corrected for the

EXPERIMENTAL SECTION

Reagents and General Procedures. All the reagents and solvents were commercially available and used as received without further purification. Potassium hydridotris(pyrazole) borate (KTp) and potassium tetra(3-methylpyrarole) borate (KpzTpMe) were prepared by literature procedures.57 Synthesis of (Tp)2Co-1 (1). The synthesis of complex 1 is based on the procedure from ref 55a with a slight modification. KTp (0.2 mmol, 50 mg) and Co(ClO4)2·6H2O (0.1 mmol, 36.5 mg) were added to MeOH (1 mL). After the metallic salt dissolved, CH3CN (10 mL) was added. Twenty minutes later, the yellow solution was filtered and left in a beaker until crystallization occurred. Yellow crystals were isolated with a yield of 93%. Elemental analysis calcd (%) for C18H20B2CoN12 (1): C (44.58), N (34.66), H (4.16); found C (44.55), N (34.32), H (4.15). IR data (cm−1): 3449.48w, 3111.64w, 2464.19m, 1733.99w, 1623.97w, 1506.17m, 1402.96s, 1306.58s, 1210.19s, 1113.80s, 1044.68s, 976.52m, 879.16m, 755.52s, 721.44s, 659.13m, 618.24m. Synthesis of (Tp)2Co-2 (2). KTp (0.2 mmol, 50 mg) and Co(ClO4)2·6H2O (0.1 mmol, 36.5 mg) were added to MeOH (1 mL). After the metallic salt dissolved, CH2Cl2 (10 mL) and i-PrOH (2 mL) were added. Twenty minutes later, the yellow solution was filtered and left in a beaker until crystallization occurred. Yellow crystals were isolated with a yield of 93%. Elemental analysis calcd (%) for C18H20B2CoN12 (2): C (44.58), N (34.66), H (4.16); found C (44.55), N (34.32), H (4.15). IR data (cm−1): 3441.69w, 3132.08w, 2918.87w, 2849.74w, 2608.29w, 2477.82m, 1623.97w, 1500.32m, 1402.96s, 1306.58s, 1210.19s, 1113.80s, 1044.68s, 972.52m, 886.95w, 789.59w, 748.70s, 714.62s, 665.94m, 618.24m. Synthesis of Tp2Co·2[(CH3)2NCS2]3Co (3). Tp2Co (0.1 mmol, 48.5 mg) and [(CH3)2NCS2]3Co (0.1 mmol, 41.9 mg) were dissolved in CH3CN (20 mL), and the resulting mixture was filtered and left in a beaker undisturbed. A week later, black crystals were isolated with a yield of 80%. This crystal can also be obtained by one-pot synthesis, which is depicted as follows: KTp (0.2 mmol, 51 mg) and Co(ClO4)2·6H2O (0.2 mmol, 73 mg) were added to MeOH (1 mL). After the metallic salt dissolved, CH3CN (10 mL) was added. After the mixture stirred for 20 min, sodium dimethyldithiocarbamate (0.2 mmol, 28.6 mg) was added. Thirty minutes later, the green solution was filtered and then left in a beaker until crystallization occurred. Black crystals were isolated with a 3904


Article

Inorganic Chemistry diamagnetism of the samples as estimated from Pascal’s tables59 and of the sample holder by a previous calibration. Computational Details. The CASPT2/RASSI method with the MOLCAS 8.0 program package60 was performed on complexes 1−4 (see the Supporting Information for details). Then, the Single_Aniso61 program was used to obtain the g tensors, energy levels, magnetic axes, etc., based on the above CASPT2/RASSI calculations. For CASPT2 calculations, the basis sets for all of the atoms are the atomic natural orbitals from the MOLCAS ANO-RCC library: ANORCC-VTZP for the Co(II) ion, VTZ for close N, and VDZ for distant atoms. The calculations employed the second-order Douglas−Kroll− Hess Hamiltonian, where scalar relativistic contractions were taken into account in the basis set and the spin−orbit coupling was handled separately in the restricted active space state interaction (RASSI-SO) procedure. The active electrons in 5 + 5′ active spaces, considering the 3d double shell effect, include all d electrons (CAS (7 in 10) for complexes 1−4 in the CASPT2 calculation). To exclude all doubts, we calculated all of the roots in the active space. We have mixed the maximum number of spin-only states, which was possible with our hardware (from all 10 quadruplets and 20 from 40 doublets for Co(II)).

Figure 1. (a) Structures of 1−4. The green arrow represents the orientations of the main local magnetic axes of the ground doublets on the magnetic center. The hydrogen atoms and substituent group in pyrazole have been omitted for clarity. (b) 3d energy levels. (c, d) Illustration of the angular parameters α (c) and φ (d). All panels show the variables used in the structural analysis of the Tp2Co part, assuming ideal D3 symmetry.

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RESULTS AND DISCUSSION Structure Descriptions. The crystallized products of this series were obtained in different ways. Complex 1 was obtained using CH3CN as the solvent. CH2Cl2 and i-PrOH were used instead as a mixed solvent for both 2 and 4. For 3, the synthesis process was similar to that of 1 except that Co[HB(pz)3]2· 2[(CH3)2NCS2]3Co was added as a coformer. Further, the ligand of 4 was changed from KTp to KpzTpMe. The structures of complexes 1 and 4 have been depicted in related references,55 with a slight difference in bond lengths and angles from those we synthesized. Because we pay attention mainly to the rotated angle φ for a better comparison, we describe the structures of all four complexes here in another way. The single-crystal XRD analysis revealed that compounds crystallized in the monoclinic space group P21/c for 1 and 4, tetragonal space group P42/ncm for 2, and triclinic space group P1̅ for 3. Selected crystallographic data are listed in Table 1. Details of bond lengths and angles for the four compounds are contained in Table S2 in the Supporting Information. The molecular geometry of the chelates is shown in Figure 1, from which we could see that the central Co(II) ion in all four complexes is coordinated to six N atoms, forming a quasitrigonal antiprism with different bond angles and lengths, similar to our published complex.36 Often, when it comes to trigonal antiprism, two angle values φ and α are considered to describe the structural features.43 The twist angle φ indicates the distortion by trigonal rotation. For trigonal antiprism and trigonal prism, the values of φ are 60° and 0°, respectively. The angle α describes the distortion by trigonal compression (α > 54.74°) or elongation (α < 54.74°). For complexes 1, 2, and 4, the values of φ are 56.77°, 59.40°, and 58.66°, respectively, while the angle α is in the range of 51.03−52.89°, so Co(II) is in an elongated trigonal ligand field. The nearest neighbor distances of Co···Co are 8.491, 7.495, and 9.382 Å, respectively. Complex 3 is a bit different as BVS calculations (Table S3) reveal two valence states of the Co ion in CoII[HB(pz)3]2 and CoIII[(CH3)2NCS2]3. The central Co(II) ion, as mentioned above, is coordinated to six nitrogen atoms, giving rise to a slightly distorted triangular antiprism of D3 symmetry with a twist angle φ of 59.34°. The angle α is 52.01°, 52.14°, and 52.36°. As for the central Co(III) ion, which is coordinated to six sulfur atoms, it has a distorted octahedron with the Co2···S distance ranging from 2.256 to 2.283 Å. The shortest distance

between the paramagnetic Co(II) ions of neighboring units is 7.796 Å. dc Magnetic Measurements and Theoretical Calculations. Static direct current (dc) magnetic measurements were performed on polycrystalline samples of 1−4 in the 1.8− 300 K temperature range under 1 kOe. As shown in Figure 2, the χMT values at 300 K for 1−4 were 3.05, 3.08, 2.99, and 3.20 cm3 K mol−1, respectively. These values are considerably larger than the 1.87 cm3 mol−1 K value for the mononuclear high spin Co(II) with S = 3/2 and g = 2.0, which can be attributed to the unquenched orbital contribution.25 For all of the complexes, the χMT curves roughly remain constant at high temperature and then exhibit a gradual decrease, giving an ultimate value of 2.37, 2.16, 2.30, and 2.16 cm3 mol−1 K at 1.8 K, respectively. The decrease of χMT observed in the low temperature range is, to a great extent, due to the intrinsic magnetic anisotropy of the Co(II) ions.25 Additionally, the χMT curve of 3 decreases to 2.40 cm3 mol−1 K at 12 K and then increases, reaching 2.41 cm3 mol−1 K at 7 K before dropping to 2.30 cm3 mol−1 K at 1.8 K. The principal reason for this rising part is the strong anisotropic dipole interaction between two spin carriers.47,62 The fielddependent magnetizations of 1−4 were measured at fields ranging from 0 to 7 T between 1.8 and 10.0 K (Figure 2 inset). All the M versus H data below 5 K show a rapid magnetization at the low magnetic field, while the magnetization tends to increase slower at higher fields, following a linear slope without saturation. The unsaturated M versus H curves indicate the presence of strong magnetic anisotropy in this series of complexes, which also can be proven by the non-superposition of the M versus H/T plot (Figure S2). Because of the strong first-order orbital contribution in the trigonal antiprismatic geometry (distorted octahedral geometry), zero field splitting parameters D and E are not suitable to describe the magnetic energy levels.63 A simple approach for understanding the firstorder orbital angular momentum associated with the 4T1g ground state is to employ the T, P isomorphism, that is, the orbital triplet T1 coming from the 4F term and the triplet L = 1 from a P term (ML = 0, ±1) which has a correspondence of ∥T1∥ = −α∥P∥, where α considers the ligand field strength and 3905


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Inorganic Chemistry

Figure 2. Temperature dependence of χMT under a 1.0 kOe applied dc field at 1.8−300 K for a polycrystalline sample of 1−4 by MPMS-XL7. Red solid lines are the calculated magnetic susceptibilities within CASPT2, and blue solid lines represent the fitted results from eq 1. Isothermal fielddependent magnetization at different temperatures is shown in the insets, where dotted lines represent the measured experimental data while solid lines are the fitted results of eq 1.

Table 2. Structure Parameters α and φ, N−Co Bond Lengths, and Calculated Effective geff Values (x, y, z) for the Lowest KDs and the Energy Difference between the Two Lowest Spin-Only States (Δ′) and Two Lowest KDs (Δ) Using CASPT2 geff 1 2 3 4 5

α (deg)

φ (deg)

N−Co (Å)

Co−Co (Å)

gx

gy

gz

Δ′ (cm−1)

Δ (cm−1)

51.63−51.87 51.87−51.95 52.01−52.36 51.03−52.89 52.43−52.76

56.77 59.40 59.34 58.66 58.54

2.124−2.143 2.121−2.129 2.097−2.107 2.133−2.178 2.133−2.151

8.491 7.495 7.796 9.382 8.825

0.871 0.998 0.848 1.047 1.015

0.892 1.001 0.873 1.059 1.041

8.702 8.747 8.801 8.726 8.685

39.1 7 66.0 10.4 32

211.5 222.9 218.4 223.1 217.6

Figure 3. Frequency dependence of out-of-phase (χM″) magnetic susceptibility for 1−3 in 800 and 3000 Oe and for 4 in 1000 and 3000 Oe dc fields (1−999 Hz, by MPMS Squid VSM).

covalency effects.63,64 Here, the PHI program65 was employed to analyze the dc susceptibility and magnetization data, using a spin Hamiltonian with spin−orbital coupling (λ), crystal field parameter (B20), and orbital reduction parameter (α):

parameter and orbital reduction parameter. All of the B20 parameters are negative, indicating the Co(II) has strong axial magnetic anisotropy.64 To understand the magnetic anisotropy in depth, ab initio calculations using the experimental geometry and the CASSCF/CASPT2 approach with MOLCAS 8.060 were performed. For a mononuclear Co(II) complex in a trigonal antiprismatic geometry, the expected splitting of the d orbitals is shown in Figure 1(b). The calculated χMT curves were in good agreement with the experimental data (Figure 2). From the results, the splitting of the two lowest Kramers doublets (KDs) was much larger than the energy separation between the two lowest spin-only states for all four of the complexes (Table 2), which is in line with the fitted results using the PHI program,65 indicating that the contribution of the orbital is

2 2 Ĥ = −αλLŜ ̂ + α 2B2 0 [3L̂ z − L̂ ] + βH[−αL̂ + geS]̂

(1)

where λ is close to −170.1 cm−1 and α is 1.5 for a Co(II) in Oh symmetry and a weak ligand field. The best fit results were obtained with parameters λ = −150.5 cm−1, α = 1.50, and B20 = −219 cm −1 for 1; λ = −150.2 cm−1, α = 1.50, and B20 = −194 cm−1 for 2; λ = −150.0 cm−1, α = 1.48, and B20 = −300 cm−1 for 3; and λ = −150.1 cm−1, α = 1.49, and B20 = −187.6 cm−1 for 4. The low symmetry distortions of the octahedral coordination induce the deviation of the spin−orbital coupling 3906


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Inorganic Chemistry

Figure 4. Arrhenius plots of ln(τ) versus the inverse temperature T−1, as calculated from data under a respective dc field. The blue and green lines show the fit of the data with the Arrhenius expression τ = τ0 exp(Ueff/kBT) in the high temperature range. The red and black solid curves show the fit results with eq 4 in the whole temperature range.

in 2, which is the same as that of reported complexes in literature.45 Cole−Cole plots66 are fitted (Figures S11−S14) to a modified Debye model, allowing for the extraction of τ and α (Tables S8−S11). The relaxation times τ obtained by the fitting program were plotted versus T−1, generating the Arrhenius-like diagram (Figure 4). Fitting to the Arrhenius law affords the estimations of anisotropy barriers Ueff/kB = 60.3 K (51.5 K), 14.99 K (43.0 K), 32.57 K (63.4 K), and 29.7 K (22.4 K) for 1, 2, and 3 at 800 (3000) Oe and for 4 at 1000 (3000) Oe dc fields, respectively, with exponential prefactors of τ0 = 3.07 × 10−8 s (8.76 × 10−8 s), 9.36 × 10−6 s (3.66 × 10−7 s), 1.32 × 10−6 s (1.82 × 10−8 s), and 4.08 × 10−7 s (1.40 × 10−6 s), respectively (Figure 4). The fitted energy barriers of all four complexes are far smaller compared to the calculated energies (Δ), suggesting a virtual state existing in the magnetic relaxation pathway, indicating the presence of the Raman process in the high temperature range. Since multiple relaxation processes may exist in field-induced Co(II)-based SIMs, in an ideal case, the general eq 2 containing four relaxation processes should be employed for analysis, where A is the coefficient of the direct process, τQTM represents the QTM process, C is the coefficient of the Raman process, U is the energy barrier to magnetization reversal, kB is the Boltzmann constant, and T is temperature.

strong. The strong unquenched orbital contribution at low temperature made the Co(II) ion similar to a lanthanide ion, proving again that zero field splitting parameters D and E are indeed not suitable here. Based on the observed g value of the lowest KDs, the ground and the first excited states are not pure Ising states and are mixed by several mJ states,26,28 indicating that strong quantum tunnelling of magnetization (QTM) might exist in the spin relaxation without an external dc field. ac Magnetic Measurements. In order to investigate the slow magnetization relaxation behavior of complexes 1−4, temperature and frequency dependence analyses of the alternating current (ac) magnetic measurements were performed on the polycrystalline samples at low temperature. Unfortunately, none of them showed an out-of-phase signal (χM″) without an applied dc field, which is attributed to QTM. However, with small external dc fields, all of the samples show an obvious out-of-phase signal (Figure S3). In order to study the magnetostructure correlation and the effect of packing arrangements on the crystal lattice, we chose 800 and 3000 Oe (400, 1000, and 3000 Oe for 4) external dc fields to test the dynamic spin relaxation behaviors (Figure 3), where double spin relaxation processes were observed in complex 4 below 800 Oe and dc fields higher than 800 Oe led to only one relaxation process. Under an 800 Oe dc field (4 was studied under 1000 Oe), all of the complexes exhibit an obvious slow spin relaxation behavior, and only one slow magnetic relaxation is observed. The maximum out-of-phase (χM″) magnetic susceptibility signals can be observed in the ranges of 1.8−6.6 K for 1, 1.8−5.2 K for 2, 1.8−6.3 K for 3, and 1.8−4.2 K for 4 in the frequency range of 1−999 Hz (Figure 3). The Cole−Cole plots of χM″ versus χM′ for 1−4 are fitted by the CCFIT program66 using a modified Debye function (Figures S7−S10). The extracted τ and α values are listed in Tables S4−S7. The α values are in the ranges of 0−0.13, 0.03−0.18, 0−0.23, and 0.04−0.25 for 1−4, respectively. All of the α values are very small, indicating a narrow distribution of relaxation times for each complex. In order to explore the effect of an applied external field on the spin relaxation processes67 (Orbach, Raman, and direct processes), a further comparison was made by increasing the external dc field from 800 to 3000 Oe. A maximum of χM″ can be observed in the range of 1.8−6.3 K for 1, 1.8−6.5 K for 2, 1.8−6.9 K for 3, and 1.8−3.9 K for 4 over the whole frequency range (Figure 3). For complexes 2 and 3, these peaks appeared at lower frequencies, while the maximums of χM″ for complexes 1 and 4 are shifted to higher frequencies, which might be ascribed to a direct process due to its field dependence. An obvious second relaxation process appeared at low temperature

τ −1 = τQTM −1 + AT + CT n + τ0−1 exp( −U /kBT )

(2)

However, this may lead to overparametrized fit results. A common way to avoid overparametrization is to fit the dependence of τ with the field to obtain direct and tunnelling parameters, and then the temperature-dependent data considering the four processes in eq 2 are fitted by fixing the obtained parameters.16,44,45 Field dependence of the relaxation time τ was studied (Figure S4), and attempts were made to fit the field-dependent data using eq 3, where the direct process for Kramers ions, QTM, and a non-zero contribution of Raman and Orbach processes are taken into account consecutively.45 Unfortunately we did not obtain satisfactory results due to the complexity of the dependence of τ with the field. τ −1 = A′H 4 + B1/(1 + B2 H2) + D

(3)

Referring to Dunbar group’s work,45 an alternative approach is adopted by analyzing the temperature-dependent τ by different temperature regions. Through a similar analysis procedure and to avoid overparametrization, the best fit results are obtained when we consider only the direct and Raman processes, as in the following equation τ −1 = AT + CT n 3907

(4) DOI: 10.1021/acs.inorgchem.8b00055 Inorg. Chem. 2018, 57, 3903−3912

Article

Inorganic Chemistry

Table 3. Calculated Energy Barrier between the Two Lowest KDs Δ, the Experimental Ueff Values under Different dc Fields, and Fitting Results from eq 4 for 1−5 Arrhenius’ law

1 2 3 4 5 a

direct + Raman

800 Oe

3000 Oe

800 Oe

Δ (cm−1)

Ueff (K)

Ueff (K)

A

C

n

A

3000 Oe C

n

211.5 222.9 218.4 223.1 217.6

60.3 15.0 32.6 29.7a 30.5a

51.5 43.0 63.4 22.4

6.6 618.6 65.3 456.1a 0a

0.007 5.500 0.102 2.500a 0.023a

7.0 3.8 5.6 4.8a 7.0a

21.4 273.0 34.7 444.4

0.187 0.0008 0.134 17.764

5.4 7.9 5.6 3.7

Data from measurements under a 1000 Oe dc field.

the results of which are shown in Figure 4 and the obtained parameters are listed in Table 3. The parameter n differs under different dc fields, which might be ascribed to two main reasons: one is the low energy vibration and the other is magnetic field-induced single or double relaxation process transitions.68 As mentioned above, when a 400 Oe dc field is applied, two slow magnetic relaxations can be observed in complex 4 (Figure S15). Fitting the Cole−Cole plots successfully extracts the relaxation time τ (Figure S15 and Table S12). The ln(τ) versus the inverse temperature T−1 are plotted in Figure S16, with a platform in the low temperature regime, indicating the presence of quantum tunnelling. The best fits are obtained when Raman, QTM, and the direct process are considered, giving parameters τQTM−1 = 900.64 s−1, A = 704.77 s−1 K−1, C = 0.00399 s−1 K−8.845, and n = 8.845. Magnetostructural Correlations. The Co(II) part in 1, 2, and 3 is using the same ligand Tp with a slight difference in local symmetry due to the packing arrangement.48 In terms of all the complexes 1−5, the Co(II) part has similar symmetry. The calculated energy barriers between the two lowest KDs (ca. 220 cm−1) are not influenced by the local symmetry and the slight difference in the Co−N length. However, a significant difference was observed in the dynamic magnetic properties. Among these five complexes, 1, 3, and 5 exhibit comparatively good SMM performance. There are many factors that can impact SMM properties.16,69 The discrepancies in the nearest Co···Co distances among the five complexes first come into consideration (Table 2). Complex 4 possesses the longest Co··· Co distance, while complex 2 has the shortest. Nevertheless, both show poor SMM behavior, which indicates that dipolar interaction is not the unique factor related to the magnetic properties. In a recent work48 the packing arrangement also played an important role in the spin relaxation process. In terms of c orientation, the arrangement of molecules in the lattice is extracted, and the main local magnetic axes of the ground doublets (along the B−Co−B direction, Figure 1) represent every molecule (Figure 5). The arrangements of the main magnetic axes are parallel in the lattices of 3 and 5 and are crossed with a small angle in 1 (nearly parallel). However, in 2 and 4 the main magnetic axes are vertically aligned, where the transverse dipolar fields generated by these packing arrangements promote quantum tunnelling.48 For 4 and 5, two processes are observed under a low external dc field and only one process is observed under high dc field. As we earlier reported, the second relaxation process of 5 is from dipole− dipole intermolecular interactions.36 Although the magnetically diluted experiments proved the dipole−dipole intermolecular interaction has a certain contribution to the multiprocess,

Figure 5. Packing arrangements of complexes 1−5. Only the atoms defining the C3 axes are shown for the sake of clarity. (a) 1, (b) 2, (c) 3, (d) 4, (e) 5. Color code: Co, purple; B, blue.

according to our recent studies and references, the vibration of the C−H bond from the methyl in the ligand is also nonnegligible.9 So far we have compared the properties of complexes 1−4, and relevant reasons have been given. However, a fact that cannot be neglected is that these four trigonal antiprismatic complexes are all field-induced SMMs. We recalled some trigonal prismatic Co(II) SMMs also with C3 symmetry reported by other groups showing zero field relaxation. An idea that there may be some regularity among them naturally comes to us . Table 4 comprehensively summarizes the key structural and magnetic factors for all reported C3 symmetrized six-coordinated Co(II) SMMs. It indicates that the complexes showing a slow magnetic relaxation behavior without an external dc field have a φ smaller than 23.5°. In contrast, all other complexes are field-induced SMMs when φ values are close to 60°. Given the obviously different dynamic magnetic properties in a zero external dc field, a study of the correlations between φ and uniaxial anisotropy is meaningful. We designed a series of model complexes, changing the angle φ from 5° to 60° through rotating the Tp ligand along the B2−Co−B1 axis of 2, while the Co−N length and the angle α remained unchanged. It can be seen from the calculated results in Figure 6 that gx and gy are close to 1.0 when φ is 60° (trigonal antiprismatic), indicating that transversal anisotropy is nonnegligible and QTM induced by a transversal magnetic field70 (2Δtun = μB[gx2Hx2 + gy2Hy2]1/2) might be strong in this situation. As φ decreases, gx and gy decrease and nearly vanish when the structure is close to trigonal prismatic symmetry (φ = 5°), whereas the gz value increases with decreasing φ. That is to say, the axiality of the ground KD increases as φ decreases. As a result, QTM can be suppressed effectively in the spin relaxation process without a dc field. To look for the periodic regularity between the g values and angle φ, we extend the range of φ 3908


Article

Inorganic Chemistry Table 4. Literature Survey for the Co(II) SMMs with Trigonal Antiprismatic and Trigonal Prismatic Configurations complex

a

SMM without dc field

field (kOe)

Ueff (cm−1)

τ0 (s)

φ (deg)

0 0 1.5 0 1.2 0 1 2.0 0 1.5 0 1.5 0 1.5 0 1.5 0 1.5 0 1.5 0 1.5 0 1.5 0.8 3.0 0.4 1.0 0.5 1.5 1.0 3.0 1.0 0.5 3.0 0.8 3.0 0.8 3.0

109.4 71 101 not extracted 56.65 180.2 191.4 23 73.6 86.1 102.8 113.3 88.8 90.9 90.2 93.7 95.8 97.2 26.6 28.7 36.4 37.8 30.0 31.5 42.9a 35.8a 25.6 21.18 42.5(6)a 44.7(6)a 20.6a 15.6a 35.2 30.6a 33.6a 22.6a 44.0a 10.4a 29.9a

2.65 × 10−9 4.3 × 10−7 5.1 × 10−8 not extracted 2.24 × 10−10 8.87 × 10−10

0.11 0.27

42 44

3

41

3.58

42

12.86 16.01

40 37

16.56

43

16.58

43

16.64

43

17.76

43

20.54

43

21.43

43

23.47

43

56.77

this work

58.54

36

58.59

45

58.66

this work

59.1 59.24

46 45

59.34

this work

59.40

this work

1 2

β−Co [CoII(Pzox)3(BC6H5)]Cl

yes yes

3

[CoII(L)]

yes

4

α−Co

yes

5 6

[CoII(P(S)(N)3)](NO3)2 (NHEt)3[CoIICoIII3(L1)6]

yes yes

7

(nBu4N)[CoIICoIII3(L5)6] (8R)

yes

8

(HDBU)[CoIICoIII3(L4)6] (5R)

yes

9

(HDIPEA)[CoIICoIII3(L5)6] (6R)

yes

10


yes

11

(NHEt)3[CoIICoIII3(L2)6] (2R)

yes

12


yes

13

(NHEt)3[CoIICoIII3(L3)6] (4R)

yes

14

1

no

15

Tp*2CoII

no

16

[Co(TPm)2][BPh4]2

no

17

4

no

18 19

[Co(SDZ)2bpy] [Co(TPm)2][ClO4]2

no no

20

3

no

21

2

no

4 × 10−6 1.7 × 10−7 6.3 × 10−8 2.5 × 10−8 1.2 × 10−8 5.8 × 10−8 5.4 × 10−8 5.7 × 10−8 4.5 × 10−8 5.3 × 10−8 4.6 × 10−8 8.3 × 10−7 6.4 × 10−7 5.0 × 10−7 2.8 × 10−7 2.0 × 10−7 2.4 × 10−7 3.07 × 10−8 8.76 × 10−8 1.47 × 10−7 4.85 × 10−7 1.5 × 10−7 1.0 × 10−7 4.08 × 10−7 1.40 × 10−6 4.61 × 10−8 3.3 × 10−7 2.0 × 10−7 1.32 × 10−6 1.82 × 10−8 9.36 × 10−6 3.66 × 10−7

ref

Complexes that are Raman dominated at high temperatures; the values of Ueff are just listed for reference.

from 0° to 120°. Interestingly, gz and giso ( g iso =

(gx 2 + gy 2 + gz 2)/3 ) versus φ plots can be fitted

with a simple cosine function very well (Figures 6 and S17): gz = 9.29 + 0.48 cos(2π/120 × φ) and giso = 5.38 + 0.25 cos(2π/ 120 × φ). This might result from the rotation of the ligand (group) which exerts the ligand field effect. The energy difference between the two lowest spin-only states with different φ can be a proof of this (Table S13). On the basis of the two functions, we can easily obtain the g factor with φ and predict the possible dynamic properties from the crystal structure. It gives strong evidence as to why the complexes with symmetry close to trigonal prism can be observed with a slow magnetic relaxation behavior in a zero dc field while all other complexes with trigonal antiprismatic symmetry are fieldinduced SMMs. Changing φ leads to the transformation of the ligand field from trigonal prismatic to distorted octahedral (trigonal antiprismatic) symmetry, further influencing the anisotropy of the molecule.

Figure 6. Relationship among gx,y (red dots), gz (black panes), and the angle parameter φ. The blue solid line is the fitting result with gz = 9.29 + 0.48 cos(2π/120 × φ).

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(6) Craig, G. A.; Murrie, M. 3d single-ion magnets. Chem. Soc. Rev. 2015, 44, 2135−2147. (7) Gómez-Coca, S.; Aravena, D.; Morales, R.; Ruiz, E. Large magnetic anisotropy in mononuclear metal complexes. Coord. Chem. Rev. 2015, 289-290, 379−392. (8) Frost, J. M.; Harriman, K. L. M.; Murugesu, M. The rise of 3-d single-ion magnets in molecular magnetism: towards materials from molecules? Chem. Sci. 2016, 7, 2470−2491. (9) Goodwin, C. A. P.; Ortu, F.; Reta, D.; Chilton, N. F.; Mills, D. P. Molecular magnetic hysteresis at 60 K in dysprosocenium. Nature 2017, 548, 439−442. (10) Guo, F.-S.; Day, B. M.; Layfield, R. A.; Chen, Y.-C.; Tong, M.-L.; Mansikkamäki, A. A Dysprosium metallocene single-molecule magnet functioning at the axial limit. Angew. Chem., Int. Ed. 2017, 56, 11445. (11) Sessoli, R. Magnetic molecules back in the race. Nature 2017, 548, 400−401. (12) Deng, Y.-F.; Han, T.; Wang, Z.; Ouyang, Z.; Yin, B.; Zheng, Z.; Krzystek, J.; Zheng, Y.-Z. Uniaxial magnetic anisotropy of squareplanar chromium(II) complexes revealed by magnetic and HF-EPR studies. Chem. Commun. 2015, 51, 17688−17691. (13) Vallejo, J.; Pascual-Alvarez, A.; Cano, J.; Castro, I.; Julve, M.; Lloret, F.; Krzystek, J.; De Munno, G.; Armentano, D.; Wernsdorfer, W.; Ruiz-Garcia, R.; Pardo, E. Field-induced hysteresis and quantum tunnelling of the magnetization in a mononuclear manganese(III) complex. Angew. Chem., Int. Ed. 2013, 52, 14075−14079. (14) Ding, M.; Cutsail Iii, G. E.; Aravena, D.; Amoza, M.; Rouzieres, M.; Dechambenoit, P.; Losovyj, Y.; Pink, M.; Ruiz, E.; Clerac, R.; Smith, J. M. A low spin manganese(IV) nitride single molecule magnet. Chem. Sci. 2016, 7, 6132−6140. (15) Ishikawa, R.; Miyamoto, R.; Nojiri, H.; Breedlove, B. K.; Yamashita, M. Slow relaxation of the magnetization of an MnIII single ion. Inorg. Chem. 2013, 52, 8300−8302. (16) Zadrozny, J. M.; Atanasov, M.; Bryan, A. M.; Lin, C.-Y.; Rekken, B. D.; Power, P. P.; Neese, F.; Long, J. R. Slow magnetization dynamics in a series of two-coordinate iron(II) complexes. Chem. Sci. 2013, 4, 125−138. (17) Weismann, D.; Sun, Y.; Lan, Y.; Wolmershaeuser, G.; Powell, A. K.; Sitzmann, H. High-spin cyclopentadienyl complexes: a singlemolecule magnet based on the aryl-iron(II) cyclopentadienyl type. Chem. - Eur. J. 2011, 17, 4700−4704. (18) Eichhoefer, A.; Lan, Y.; Mereacre, V.; Bodenstein, T.; Weigend, F. Slow magnetic relaxation in trigonal-planar mononuclear Fe(II) and Co(II) bis (trimethylsilyl) amido complexes: a comparative study. Inorg. Chem. 2014, 53, 1962−1974. (19) Zadrozny, J. M.; Xiao, D. J.; Long, J. R.; Atanasov, M.; Neese, F.; Grandjean, F.; Long, G. J. Mössbauer spectroscopy as a probe of magnetization dynamics in the linear iron(I) and iron(II) complexes [Fe (C (SiMe3) 3) 2] 1−/0. Inorg. Chem. 2013, 52, 13123−13131. (20) Harman, W. H.; Harris, T. D.; Freedman, D. E.; Fong, H.; Chang, A.; Rinehart, J. D.; Ozarowski, A.; Sougrati, M. T.; Grandjean, F.; Long, G. J.; Long, J. R.; Chang, C. J. Slow magnetic relaxation in a family of trigonal pyramidal iron(II) pyrrolide complexes. J. Am. Chem. Soc. 2010, 132, 18115−18126. (21) Lin, P.-H.; Smythe, N. C.; Gorelsky, S. I.; Maguire, S.; Henson, N. J.; Korobkov, I.; Scott, B. L.; Gordon, J. C.; Baker, R. T.; Murugesu, M. Importance of out-of-state spin-orbit coupling for slow magnetic relaxation in mononuclear FeII complexes. J. Am. Chem. Soc. 2011, 133, 15806−15809. (22) Mossin, S.; Tran, B. L.; Adhikari, D.; Pink, M.; Heinemann, F. W.; Sutter, J.; Szilagyi, R. K.; Meyer, K.; Mindiola, D. J. A mononuclear Fe(III) single molecule magnet with a 3/2↔ 5/2 spin crossover. J. Am. Chem. Soc. 2012, 134, 13651−13661. (23) Samuel, P. P.; Mondal, K. C.; Amin Sk, N.; Roesky, H. W.; Carl, E.; Neufeld, R.; Stalke, D.; Demeshko, S.; Meyer, F.; Ungur, L.; Chibotaru, L. F.; Christian, J.; Ramachandran, V.; van Tol, J.; Dalal, N. S. Electronic Structure and slow magnetic relaxation of low-coordinate cyclic alkyl (amino) carbene stabilized iron(I) Complexes. J. Am. Chem. Soc. 2014, 136, 11964−11971.

CONCLUSION We synthesized a series of trigonal antiprismatic Co(II) complexes showing field-induced single-molecule magnet behavior. The dynamic magnetic relaxation processes are all Raman process dominated and strongly dependent on the packing arrangements. Through a survey of literature reports, in combination with theoretical calculations, the angle φ in trigonal antiprismatic and trigonal prismatic configurations is a key factor for designing excellent Co(II) SIMs due to the results from the rotation of the ligand (group) which exerts the strongest ligand field effect. When the angle φ is small (0° < φ < 60°), the magnetic anisotropy becomes stronger, and QTM can be suppressed without an applied dc field. Therefore, guidance is given to help chemists design excellent SMMs.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.8b00055. Structural and magnetic characterizations and theoretical calculations (PDF) Accession Codes

CCDC 1545683−1545686 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by emailing [email protected], or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Yi-Quan Zhang: 0000-0003-1818-0612 You Song: 0000-0002-0289-7830 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Key R&D Program of China (2017YFA0303203), the National Natural Science Foundation of China (91622115 and 21571097), the Natural Science Foundation of Jiangsu Province of China (BK20151542), and the Specialized Research Fund for the Doctoral Program of Higher Education.

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REFERENCES

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