Breaking the Magic Border of One Second for Slow Magnetic

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Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

Breaking the Magic Border of One Second for Slow Magnetic Relaxation of Cobalt-Based Single Ion Magnets Roman Bocǎ ,*,† Cyril Rajnaḱ ,† Jań Moncol,‡ Jań Titiš,† and Dušan Valigura† †

Department of Chemistry, Faculty of Natural Sciences, University of SS Cyril and Methodius, SK-917 01 Trnava, Slovakia Institute of Inorganic Chemistry, Slovak University of Technology, SK-812 37 Bratislava, Slovakia

‡

Inorg. Chem. Downloaded from pubs.acs.org by UNIV OF SUNDERLAND on 11/08/18. For personal use only.

S Supporting Information *

ABSTRACT: Instead of assembling complex clusters and/or expensive lanthanide-based systems as single ion magnets, we are focusing on mononuclear cobalt(II) systems among which the complex under study, [Co(pydca)(dmpy)]2·H2O (1), shows a field supported slow magnetic relaxation on the order of seconds at low temperature (pydca = pyridine-2,6-dicarboxylato, dmpy = 2,6-dimethanolpyridine). The low-frequency relaxation time is as slow as τ(LF) = 1.35(6) s at T = 1.9 K and BDC = 0.4 T. The properties of 1 are compared to the previously reported nickel and copper analogues which were the first examples of single ion magnets in the family of Ni(II) and Cu(II) complexes.

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INTRODUCTION Nanosized objects possess unique properties where the quantum effects show their importance. Single molecule magnets (SMMs) span this class of materials as they bring the possibility of constructing new devices possessing a giant capacity for data storage. One of the characteristic properties of SMMs is the slow magnetic relaxation that is typically on the order of microseconds and rarely breaks the limit of milliseconds. Where are the SMMs? The answer is “Everywhere. They are waiting to be discovered.” Polynuclear and/or mononuclear transition metal complexes bearing unpaired electrons bring magnetic response, and their assembly can be polarized in the external magnetic field. A paramagnetic material obeys a fast relaxation when the magnetic field is switched off when the information carried by the magnetic polarization is lost. On the contrary, the SMM holds its magnetic orientation for a long enough time (typically ms at low temperature; extrapolated relaxation time for infinite temperature is on the order τ0 ≈ 10−6 s). The SMM exhibits a slow magnetic relaxation that can be identified by DC and/or AC magnetic experiments. The family of mononuclear complexes showing slow magnetic relaxation, termed as single ion magnets (SIMs), is represented by a variety of transition metal complexes, e.g., V(IV), low-spin Mn(IV), Cr(II), Mn(III), Fe(III), Fe(II), Fe(I), Co(II), Ni(II), Ni(I), and Cu(II) systems; only a single representative for each central ion (a pioneering work) is quoted.1−11 The basic properties of these SIMs were subjected to a number of review articles.12−15 A common feature of these systems is that the relaxation time hardly exceeds milliseconds at low temperature (around 2 K): τ ≈ 10−3 s. A mononuclear complex [Ni(pydca)(dmpy)]·H2O (2) was reported as the first SMM based upon the Ni(II) central atom © XXXX American Chemical Society

(dmpy = 2,6-dimethanolpyridine, pydca = pyridine-2,6dicarboxylato).9 Magnetic susceptibility in a small AC field reveals that this system exhibits two relaxation channels: at T = 1.9 K and the external magnetic field BDC = 0.2 T the highfrequency relaxation time is τHF = 0.54 ms, whereas the lowfrequency channel possesses τLF = 91 ms. The high-frequency branch obeys a usual relaxation equation with several contributions τ −1 = τ0−1 exp( −U /kBT ) + CT n + ABmT + D1/(D2 + B2 )

(1)

that involve the thermally activated Orbach process (characterized by the extrapolated relaxation time τ0 and the barrier to spin reversal U), the field independent two-phonon Raman process (parameters n and C), the direct process (the constants m and A), and eventually the quantum tunneling process (that is, field dependent but temperature independent). The low-frequency channel does not obey the above equation, and its thermal evolution stays unmodeled so far: on heating, the relaxation time tends to decrease, but over some temperature it is prolonged. Experiments with doped salts into a diamagnetic Zn-matrix confirm that the opening of the lowfrequency channel originates in the intermolecular contacts such as hydrogen bonds, π-H contacts, or π−π stacking. It seems that an assembly of the faster-relaxing mononuclear entities forms oligomers on cooling (such as finite chains, plates, blocks)a process that resembles a nucleation, and these assemblies are relaxing more slowly. Received: August 24, 2018

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DOI: 10.1021/acs.inorgchem.8b02287 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Figure 1. Structure of 1 and 1b, and DC magnetic properties of 1. (a) Molecular structure of [Co(pydca)(dmpy)]2·H2O (1) showing two structural units connected by the crystal water molecule. (b) DC magnetic data for 1; lines − fitted using the zfs model. (c) and (d) Molecular structure of [Co0.52Zn1.48(pydca)(dmpy)]·H2O (1b) showing independent structural units.

Continuing on these lines, we prepared the cobalt(II) complex, [Co(pydca)(dmpy)]·0.5H2O (1), that is subjected to a deep theoretical and magnetochemical analysis.

The copper(II) complex [Cu(pydca)(dmpy)]·0.5H2O (3) was reported as the first example of the Cu(II)-based SIMs.11 Unlike other S > 1/2 spin systems, it is not characterized by the axial zero-field splitting D-parameter; this parameter was accepted as a key factor influencing the barrier to spin reversal U via relationships U = |D|S2 non-Kramers systems and U = |D| (S2 − 1/4) for Kramers systems, respectively. Therefore, the identification of the slow magnetic relaxation in 3 is a rarity, though some parallel reports for S = 1/2 spin systems already appeared.1,2 In this case, two relaxation channels were identified with the low-frequency relaxation path strongly supported by the external magnetic field: the relaxation time was τ = 0.8 s at T = 1.9 K and BDC = 1.5 T. The relaxation mechanism via the HF mode at low temperature includes a dominating Raman process along with the quantum tunneling term.

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RESULTS Crystal Structure. X-ray structure analysis for 1 revealed that the independent unit is C14H12CoN2O6.38 with the formula weight Mr = 369.26 (CCDC code BEZDAN).16 A redetermination in this report confirms the composition (C14H12CoN2O6)2·H2O, the same space group P21/n, similar cell parameters, and Mr = 744.39 (Figure 1). There are a number of intermolecular contacts and hydrogen bonds in the crystal lattice (for details, see Supporting Information). The crystal structure of 1 is formed of two crystallographically independent neutral [Co(pydca)(dmpy)] units (containing Co1 and Co2 centers) interconnected by crystal water molecule. These complexes exhibit similar coordination features but show visible differences in bond lengths and bond B


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Inorganic Chemistry angles (Table S2). The Co(II) ion is hexacoordinated by neutral tridentate 2,6-dimethanolpyridine molecule and tridentate pyridine-2,6-dicarboxylato dianion. The chromophore trans-{CoO4N2} exhibits a strong axial compression (along the N−Co−N axis in D4h approximation) accompanied by significant angular distortions reducing the symmetry to D2d (O−Co−O angles deviating from 180°); the exact symmetry is C1. The structural anisotropy parameter Dstr = dz − (dx + dy)/2 in the approximation of right angles becomes Dstr = −0.228 and −0.208 Å, respectively. Also a pure Zn-analogue, [Zn(pydca)(dmpy)]·0.5H2O (1c), has been prepared and structurally characterized; it is isostructural to 1. A doping of Co into the Zn matrix led to the single crystals of the composition [Co0.52Zn1.48(pydca)(dmpy)]·H2O (1b) possessing four independent structural units with Co1, Co2, Zn1, and Zn2 centers (Figure 1c,d). DC Magnetic Data. Magnetic data taken in a static magnetic field (DC data) show a typical behavior of hexacoordinate Co(II) complexes (Figure 1b). The effective magnetic moment at the room temperature adopts a value of μeff = 4.84 μB as compared to the spin-only value for S = 3/2 spin system (3.87 μB). It slowly decreases on cooling, more rapidly below 100 K, to the value of μeff = 3.93 μB at T = 1.9 K. The magnetization per formula unit M1 = Mmol/NAμB saturates to M1 = 1.85 that is far below the spin-only value (3.0). These data indicate a considerable zero-field splitting (with unassigned sign). A simultaneous fitting of the susceptibility and magnetization data to the standard model of the zero-field splitting (zfs) gave gx = 2.27, gy = 2.69, gz = 2.00, D/hc = +55 cm−1, E/ hc = 19 cm−1, and some temperature-independent magnetism χTIP = 11 × 10−9 m3 mol−1 (SI units are employed). Although the discrepancy factors of the fit R(χ) = 0.0073 and R(M) = 0.041 confirm that the reconstructed data match experiment, an application of the spin Hamiltonian formalism is still questionable for hexacoordinate Co(II) complexes. Ab Initio Calculations. Calculations using the ORCA package (CASSCF followed by NEVPT2)17 for individual units A and B in their experimental geometry confirm a splitting of the electronic ground term 4T1g into 4Eg and 4A1g daughter terms and a further splitting of 4Eg on symmetry lowering to D2d symmetry. The ground (0) and the first (1) excited states stay quasidegenerate (i.e., Δ01 = 797 and 389 cm−1 for units A and B, respectively) which means that the spin Hamiltonian parameters calculated by means of the perturbation theory might be problematic. The spin−orbit corrected energies of the six lowest Kramers doublets show a rather large energy gap (e.g., δ01 = 138 and 248 cm−1), and one could assume |D| ≈ δ01/2 = 69 and 124 cm−1. A theoretical modeling for the compressed tetragonal bipyramid with D4h symmetry shows that the ground term 4 A1g is orbitally nondegenerate and facilitates the application of the spin Hamiltonian formalism resulting in evaluation of the zero-field splitting D and E parameters.17 However, the angular distortion due to O−Co−O angle ∼150 deg causes a crossing of the Eg/A1g terms so that 4Eg becomes the ground term; this is indicated also by data in Table 1. In such a case, the spin− orbit multiplets refer to Γ6, Γ6, Γ7, Γ7, Γ6, Γ7 irreducible representations of the D4h′ double group (Bethe notation), and evidently the spin Hamiltonian formalism (that assumes either Γ6, Γ7 or Γ7, Γ6 ordering) fails.18 [However, activation of the spin Hamiltonian calculations gave D/hc = −68 cm−1, for the unit A and −121 cm−1 for the unit B, respectively. This is a

Table 1. Results of Ab Initio Calculations for 1 energies of terms (NEVPT2)/cm−1

energies of Kramers doublets (spin−orbit multiplets)/cm−1

g-factorsa

D/cm−1 E/D a

Unit A

Unit B

0 797 (Δ01) 2571 0

0 389 (Δ01) 1763 0

138 (δ01) 971 1176 2753 2853 2.081 2.162 2.882 (−67.7) (0.10)

248 (δ01) 731 997 2089 2212 1.812 2.137 3.292 (−121) (0.13)

Spin-Hamiltonian parameters might be virtual.

virtual set of magnetic parameters owing to the (quasi) degeneracy of the electronic ground term for which the perturbation theory tends to diverge. The large negative contribution to the D-parameter is given just by the first excitation energy: D ≈ 1/Δ01.] AC Susceptibility Data. AC susceptibility data were acquired first at low temperature T = 2.0 K for four representative frequencies of the oscillating field (BAC = 0.38 mT) and the external magnetic field varying between BDC = 0 to 1.5 T (Figure 2a). In the zero field the out-of-phase susceptibility component χ″ is silent. It is observed that χ″ rises with the applied field until a maximum and then attenuates at higher fields; this behavior is frequency dependent. It confirms that 1 shows field induced slow magnetic relaxation. A more detailed mapping of the AC susceptibility components depending upon the frequency f of the AC field for a set of external magnetic fields BDC is presented in Figure 2b. This is a rather unusual behavior representing the key result of this communication. Normally a single peak at the out-of-phase susceptibility component χ″ is expected; the position of its maximum defines the relaxation time τ = 1/ (2πf max″). In the present case three absorption peaks can be distinguished. The high-frequency (HF) peak at about 500 Hz possesses a low height. The low-frequency (LF) peak around f ≈ 0.1 Hz, on the contrary, is the most intense. In between, an intermediate-frequency (IF) peak exists at around f ≈ 1 Hz. At temperature of the data taking (T = 1.9 K) the peak heights determine the mole fractions that are normalized to xLF + xIF + xLF = 1. The data confirm that the mole fraction of the LF phase dominates and the relaxation time scales to seconds τLF ≈ 1 s in a rather tight interval of the external magnetic fields. The experimental data points in Figure 2c were fitted to the extended Debye model χk − χk − 1 χ (ω) = χS + ∑ 1 + (iωτk)1 − αk (2) k This formula contains several relaxation channels (distinguished by the index k), for which relaxation times τk, distribution parameters αk, and isothermal susceptibilities χk are characteristic, along with the adiabatic susceptibility χS (see Supporting Information). The data set contains 22 in-phase and 22 out-of-phase values that have been processed by fitting to a three-set Debye model that involves 10 free parameters. C


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Inorganic Chemistry

Figure 2. AC susceptibility data for 1. (a) The field dependence of the AC susceptibility components at T = 2.0 K: in-phase χ′ and out-of-phase χ″ molar susceptibility (in SI units). Lines serve as a visual guide. (b) Frequency dependence of the AC susceptibility components at fixed external fields. (c) Frequency dependence of the AC susceptibility components at fixed temperatures. Lines − fitted, using a three-set Debye model; dashed − one-set model for the HF peak. (d) Fitted AC susceptibility data at BDC = 0.4 T. Left − Argand diagram (fixed temperature), lines − calculated using fitted parameters; right − Arrhenius-like plot, lines − guide for eyes.

χ″) vs the reciprocal temperature. It can be seen that the HF branch on cooling increases according to the curved line and tends to saturate to a constant value. This is a usual behavior that can be modeled by eq 1 reflecting the Orbach, Raman, direct, and quantum tunneling relaxation processes. However, below some temperature (T < 3.5 K) the relaxation time decreases, which cannot be recovered by the standard models of the relaxation. Thus, a “strange term” EsT−k has been added to the Raman term CT n and probed as a competitive phenomenological contribution in the truncated relaxation equation τ−1 = CTn + EsT−k. The fitting of the relaxation time resulted in a set of parameters listed in Table 2 and drawn in Figure 3. This table is enriched by the relaxation data calculated for 2 and 3, which are Ni- and Cu-analogues of 1,

The fitting procedure can be controlled by the standard deviation for each optimized parameter σp, and discrepancy factors for the susceptibility components R(χ′) and R(χ″), respectively. Upon the basis of the fitted parameter the extrapolation/ interpolation lines were calculated, and they are drawn in Figure 2b. This procedure allows determining parameters for the IF mode represented by a shoulder and HF mode when the maximum of the out-of-phase susceptibility falls outside the hardware limit (1500 Hz). There are unique properties of the LF relaxation channel: (i) the relaxation time varies between τLF = 1.34(5) s at BDC = 0.4 T and 1.87(5) s at 1.2 T (T = 1.9 K); (ii) the distribution parameter is very small (αLF < 0.01); (iii) the mole fraction increases from xLF = 0.28 at BDC = 0.4 T to xLF = 0.78 at BDC = 1.2 T. To this end, the external magnetic field strongly supports the slow magnetic relaxation via the low-frequency mode; this field no longer can be termed “small external field”. A temperature variation of the AC susceptibility components vs frequency of the AC field is shown in Figure 2c for a representative value of BDC = 0.4 T. It can be seen that the height of the LF peak decreases progressively on heating in favor of the HF peak. In the other words, with increasing temperature the mole fraction of the LF species decreases and that of the HF species increases. For instance, xLF = 0.28, 0.20, and 0.04 at T = 1.9, 3.7, and 6.1 K, whereas xHF = 0.14, 0.59, and 0.93 (a complement to 1 is xIF). Figure 2d, left displays the Argand diagram for the fixed temperature; it consists of three distorted and overlapping arcs. Figure 2d, right shows the Arrhenius-like plot: the fitted relaxation times (referring to the frequencies of the maxima on

Table 2. Parameters of the Relaxation Process for the HighFrequency Channela parameter

1, BDC = 0.4 T

2, BDC = 0.4 T

3, BDC = 0.5 T

n C/K−n s−1 k Es/Kk s−1

[5.7] 0.213(6) [0.63] 3172(67)

[4.7] 10.3(2) [0.58] 3414(99)

[2.3] 16.7(5) [0.23] 1746(42)

Truncated relaxation equation τ−1 = CTn + EsT−k. The data fitting in the whole temperature region was preceded by linear fits: (a) ln τ = −lnC − n ln T in the intermediate temperature region, and (b) ln τ = −ln Es + k ln T in the lowest temperature region. This facilitates fixation of the power coefficients n and k [in square brackets]. 1: [Co(pydca)(dmpy)]2·H2O; 2: [Ni(pydca)(dmpy)]·H2O; 3: [Cu(pydca)(dmpy)]·0.5H2O. a

D


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Inorganic Chemistry

Figure 3. Plot of the relaxation rates for high-frequency relaxation channel of 1. Inset: error bars. Solid lines − fitted with the truncated relaxation equation τ−1 = CTn + EiT−k. Straight lines − linear dependence in the intermediate temperature region (Raman term) and the lowest temperature region (“strange term”); full points − selection for the linear fit.

i.e., [Ni(pydca)(dmpy)]·H 2 O and [Cu(pydca)(dmpy)]· 0.5H2O, respectively.11,29 In the Orbach process, absorption of a phonon is followed by phonon emission and relaxation from an excited state. It is assumed that under the thermal activation the system climbs the barrier to spin reversal between − MS and + MS states that is proportional to the axial zero-field splitting parameter D via formula U = |D|(S2 − 1/4) that for S = 3/2 reduces to U = 2| D|. With D ≈ 100 cm−1 (as for many hexacoordinate Co(II) systems), the energy barrier cannot be overcome by thermal activation at T = 2−10 K so that the Co(II) complex behaves as an effective spin S* = 1/2 system.20 In the other words, the Orbach process is discriminated and it can be omitted. In order to clarify the role of the intermolecular interaction, Co(II) centers were doped into a diamagnetic Zn(II) matrix. The single crystals of the composition C28H26Co0.52N4O13Zn1.48 (1b) were grown and fully characterized by X-ray structure analysis (see Supporting Information). The powder material was subjected to AC susceptometry at various external magnetic fields ranging between BDC = 0.1 to 0.7 T. In this substance the out-of-phase susceptibility displays only a single peak in the intermediate range of frequencies whose position is strongly field dependent (Figure 4): the relaxation time decreases from τ(IF) = 376 ms (BDC = 0.1 T) to 19.5 ms (BDC = 0.4 T) and 1.6 ms (BDC = 0.7 T) at T = 2.0 K.

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Figure 4. AC susceptibility components for doped Co/Zn = 1:3 crystals 1b. Top − frequency dependence at various external fields and fixed temperature; bottom − frequency dependence at various temperatures and a fixed external field.

DISCUSSION An alternative approach utilizes the spin−orbit Hamiltonian which is based upon the spin- and orbital- kets |L = 1,ML,S,MS⟩ as outlined by Griffith and extended by Figgis and Lines21−23

DC Magnetic Data. The spin Hamiltonian (SH) formalism involves the axial zero-field splitting D-parameter, the rhombic zero-field splitting E-parameter, and the g-tensor components gx, gy, and gz. This set of magnetic parameters is appropriate in reconstructing the magnetic data (field dependence of the magnetization and temperature dependence of the magnetic susceptibility) only in the case of the nondegenerate ground electronic term. For hexacoordinate Co(II) complexes, there is an obstacle, since in the octahedral geometry the ground term is orbitally degenerate 4T1g. On symmetry lowering to the compressed tetragonal bipyramid of D4h symmetry it splits into the ground 4A1g and excited 4Eg daughter terms, and then the SH formalism can be applied. On the opposite distortion to an elongated tetragonal bipyramid, the ground 4Eg term does not allow application of the SH. A further symmetry descent to D2h causes its splitting, but there is no guarantee whether quasi-degeneracy occurs.

2 GF 2 Ĥ = −(Aκλ)(L⃗p ·S ⃗)ℏ−2 + Δax (L̂p, z − L⃗p /3)ℏ−2

+ μB ge(B⃗ ·S ⃗)ℏ−1 − μB (Aκ )(B⃗ ·L⃗p)ℏ−1

(3)

The spin−orbit coupling involves the free-ion spin−orbit splitting parameter λ = −ξ/2S = −155 cm−1, the orbital and spin Zeeman terms, and the axial splitting parameter Δax. The remaining parameters involve the orbital reduction factor κ, and the Figgis CI parameter A. Due to the T-p isomorphism the orbital angular momentum is Lp = 1. This Hamiltonian can be treated by a numerical procedure. The magnetic susceptibility and magnetization were fitted by the following set of magnetic parameters: (Aκλ)/hc = −152 cm−1, gL = −(Aκ) = −1.15, Δax/hc = −846 cm−1, and an additional temperature-independent term χTIM = +5 × 10−9 m3 mol−1 E


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Inorganic Chemistry (the discrepancy factors were R(χ) = 0.008 and R(M) = 0.036). The calculated energies of six lowest Kramers doublets were 0, 156, 303, 498, 1158, and 1192 cm−1. The first excitation energy relates to energy gaps δ01 = 138 and 248 cm−1 predicted by the ab initio NEVPT2 method for the crystallographic centers A and B, respectively. A 3D mapping of the magnetization confirms that the system refers to the easy-axis type (Figure S4). AC Susceptibility Data. Normally the relaxation time of SIMs decreases upon heating. Usually the relaxation time extrapolated to the infinite temperature, τ0, is used to as one characteristics of the Orbach relaxation process. Typically, τ0 ≈ 10−6 s is met in SIMs as opposed to spin glasses for which τ0 ≈ 10−20 s.24 The relaxation time interrelates to the barrier to spin reversal: with increasing U the value of τ0 decreases. Moreover, the effective U-value extracted from the relaxation experiments is approximately a half of that predicted from the D-value: 2Ueff ≈ U ≈ 2|D|. This effect has been explained by the employment of the anharmonic phonons into the relaxation model.25 As already quoted, the Orbach process for hexacoordinate Co(II) complexes is discriminated owing to a large energy gap. For the Cu(II) analogue (3), the Orbach process is ineffective since the D-parameter is undefined and then the barrier to spin reversal U does not exist. Therefore, the slow magnetic relaxation in these systems is attributed to the Raman process eventually combined with the quantum tunnelling of the magnetization at low temperature. The phenomenological involvement of the “strange term” operative at the lowest temperatures for 1, 2, and 3 lacks a rational explanation so far. In small molecular systems with aromatic rings, the intermolecular contacts such as π−π stacking, π-H interaction, hydrogen bonds, etc., are common cases. The magnetic field supports a formation of “finite oligomers” (finite chains, plates, blocks), whereas temperature causes their disintegration to monomeric units. At higher temperature, only the monomeric units exhibit the slow relaxation (HF branch), whereas the LF branch is attenuated since the oligomers disintegrate to monomers. Field Effect and Zn-Doping. The intermolecular origin of the LF relaxation branch can be examined by doping experiments into a diamagnetic Zn(II) matrix.20,26−28 The dilution of Co(II) centers causes a disruption of the exchange coupling paths so that formation of oligomers is less probable. Indeed, the relaxation times found in 1, i.e., τLF = 1.34 s, τIF = 107 ms, and τHF = 456 μs at T = 1.9 K and BDC = 0.4 T, drop to a single mode relaxation with τ = 19.5 ms at the same conditions in 1b. At the magnetic field BDC = 0.7 T, however, an additional relaxation channel is opened with τLF = 68 ms and τHF = 1.6 ms (Table 3). Structurally analogous complex to 1, [Co(dmpy)2](dnbz)2 (hereafter 4), shows a slow magnetic relaxation with several relaxation modes.19 At small external field BDC = 0.2 T and T = 1.9 K, only an asymmetric peak at χ″ is seen; this can be fitted by means a two-set Debye model yielding τLF = 29 ms (xLF = 0.48) and τHF = 2.6 ms. With increasing temperature, this peak visibly splits into two components having τLF = 8.7 ms (xLF = 0.46) and τHF = 0.54 ms at T = 3.1 K. An increase of the magnetic field to BDC = 0.4 T causes the former peak to splits into two components even at T = 1.9 K: τLF = 131 ms and τHF = 0.96 ms. At the elevated temperature T = 3.1 K, the relaxation times increase to τLF = 172 ms and τHF = 0.69 s. Further heating causes an additional splitting of the HF channel and then τLF = 387 ms, τIF = 0.82 ms, and τHF = 0.095

Table 3. Relaxation Times for Related Co(II) Complexes system

T/K

B/T

τLF, ms

τIF, ms

τHF, ms

1, [Co(pydca)(dmpy)]2·H2O

1.9 1.9 1.9 1.9 1.9 2.0 2.0 2.0 2.0 2.0 1.9 1.9 1.9 1.9 1.9 1.9 1.9

0.4 0.6 0.8 1.0 1.2 0.1 0.3 0.4 0.5 0.7 0.2 0.4 0.2 0.4 0.6 0.8 1.0

1340 1270 1440 1650 1870 376 51 20 54 68 29 131 44 57 90 147 192

107 88 86 94 76

0.46 0.21 0.11 0.16 0.23

1b, wCo = 0.25

4, [Co(dmpy)2](dnbz)2 4b, wCo = 0.41

7.3 1.6 2.6 0.96 5.8 2.33 0.40 0.13 0.056

ms. A doping of the complex 4 into a diamagnetic Zn matrix with wCo = 0.41 causes the following effects: (i) at small field BDC = 0.2 T the dilution influences the basic features of the χ″ only slightly; i.e., there exists a dominating LF peak with an arm referring to the HF peak; (ii) in the elevated magnetic field BDC = 0.4 T the HF peaks become better developed (higher in intensity) in gain of the LF peaks; (iii) at BDC = 0.4 T the doping xCo = 1.00 → 0.41 causes a relative decrease of the height of the LF peak. These findings point to a complex interplay of several factors in the multimode Co(II) SIMs relative to the single-mode cases. It can be said that the effect of the magnetic field to the slow magnetic relaxation in 1 is expressive. The magnetic field supports the low-frequency relaxation channel, and it shifts the relaxation time τLF close and above the border of seconds. The complex interplay of the LF and HF relaxation modes at the lowest temperatures manifests itself in an unexpected acceleration of the relaxation for the HF phase. Ni(II) and Cu(II) Analogues. The Ni(II) analogue to 1 (hereafter 2) has been reported as a field induced SIM with two relaxation modes at BDC = 0.2 T.9 A reinvestigation of the AC susceptibility at higher magnetic fields revealed a progressive support of the LF relaxation channel:29 small LF peak at BDC = 0.2 T (xLF = 0.16) turned to the dominant peak above 0.4 T; at BDC = 1.2 T the relaxation time is as slow as τLF = 876 ms with the mole fraction xLF = 0.81. Doping experiment confirm that the Ni/Zn-complex with 55% of Ni possesses a lower mole fraction xLF = 0.20 relative to the pure Ni(II) complex with xLF = 0.28 at the same conditions (T = 1.9 K, BDC = 0.2 T). The Cu(II) analogue of 1 (hereafter 3) also exhibits a field supported slow magnetic relaxation.11 The effect of the external magnetic field to the relaxation parameters is also very expressive: at BDC = 0.5 T the mole fractions of the lowfrequency relaxation mode are xLF = 0.61, 0.53, and 0.46 for T = 1.9, 2.3, and 2.7 K. At BDC = 1.5 T, they increase to xLF = 0.82, 0.78, and 0.75 for the same set of temperatures. The external magnetic field considerably supports the efficiency of the LF relaxation mode (expressed by xLF), which indicates that the intermolecular interactions influenced by the magnetic field are in the play. F


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Inorganic Chemistry

molar magnetization per formula unit per Bohr magneton, i.e., M1 = Mmol/(NAμB). AC susceptibility was taken with the same magnetometer at small oscillating field BAC = 0.38 mT; for each temperature, 22 frequencies ranging between f = 0.1−1500 Hz were selected. These measurements were conducted in an external magnetic field BDC up to 0.7 T. Ab initio quantum chemical calculations were performed in the complete active space self-consistent field (CASSCF method) followed by the second-order N-electron valence perturbation theory (NEVPT2).17 ZORA-TZV basis set for all elements was employed and the active space was represented by seven electrons distributed into five cobalt d-orbitals, CAS(7,5).

The slow magnetic relaxation in Co(II) complexes can be influenced also by the hyperfine interaction because of the nuclear spin I = 7/2 for the 59Co isotope.20 In the hexacoordinated Co(II) complexes, the zero-field splitting adopts very high D-values ∼100 cm−1 so that at low temperature only one Kramers doublet is thermally populated. Consequently the real spin S = 3/2 can be substituted for an effective spin S* = 1/2. After considering the electron−nuclear hyperfine interaction, 16 sublevels |S*,I,MS*,MI⟩ are in the play, and at the applied field some transitions among them are allowed. In the Cu(II) complexes with S = 1/2 an analogous situation occurs: both natural isotopes 63Cu and 65Cu have the nuclear spin I = 3/2. Therefore, there are eight hyperfine levels among which four transitions are allowed: ΔMS = ± 1 and ΔMI = 0. The natural abundance of the isotope 61Ni (I = 3/2) is only 1.2%, and in such a case the hyperfine interaction in the Ni(II) analogue of 1 is suppressed.

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The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.8b02287.

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Details about the synthesis, crystal and molecular structure (CCDC 1526142, 1526143, 1825175, 1825176), ab initio calculations, and DC and AC magnetic data and their analysis (PDF)

CONCLUSIONS AC susceptibility measurements reveal that the system under study, 1, refers to the first case of Co(II) complexes in which the slow magnetic relaxation has been observed with the relaxation time τ > 1 s at low temperature and applied magnetic field. There are three relaxation channels in 1: lowfrequency, intermediate-frequency, and the high-frequency one. The former exhibits the relaxation time τLF = 1.34 s at T = 1.9 K and BDC = 0.4 T. The latter possess a relaxation time typical for Co(II) SIMs: τHF ≈ 0.45 ms at the same conditions. The relaxation time is prolonged at higher magnetic fields, e.g., τLF = 1.87 s at T = 1.9 K and BDC = 1.2 T when the mole fraction of the low-frequency fraction is xLF = 0.78. The existence of the low-frequency relaxation mode is caused by the intermolecular interactions in the solid state as confirmed by doping experiments into the diamagnetic Zn(II) matrix. Ab initio calculations show that the ground electronic term is followed by a close lying excited one so that the application of the perturbation theory in calculating the spin Hamiltonian parameters can fail. The DC magnetic data were fitted by means of a spin−orbit Hamiltonian of the Griffith-Figgis-Lines type, and the 3D visualization of the magnetization refers to the easy axis system.

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ASSOCIATED CONTENT

S Supporting Information *

Accession Codes

CCDC 1585697−1585699 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 Author

*E-mail: [email protected]. ORCID

Roman Boča: 0000-0003-0222-9434 Dušan Valigura: 0000-0001-7834-7395 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Slovak grant agencies (APVV-14-0078 and VEGA 1/0534/16) and the Research and Development Operational Program (University Science Park of STU Bratislava, ITMS 26240220084), cofunded by the European Regional Development Fund, are acknowledged for financial support.

METHODS

Synthesis of the complexes 1, 1b, and 1c is described in the Supporting Information along with the analytical data and spectral characterization. The Eulerian-cradle diffractometer Stoe StadiVari was used in the X-ray structure determination of 1, 1b, and 1c at 100 K. CuKα radiation microfocused source Xenocs Genix3D and Pilatus3R 300 K HPAD detector were utilized. Lorentz and polarization factors were applied in correcting the diffraction intensities. The structure was solved by software SUPERFLIP or SHELXT,30,31 and refined by the full-matrix least-squares procedure with SHELXL (ver. 2017/1).32 The crystal structure was drawn using the OLEX2 and MERCURY programs.33,34 Crystal data, data collection details, and refinement are reported in Table S1. DC magnetic data were acquired using the SQUID magnetometer (MPMS-XL7, QuantumDesign) in the reciprocating sample option at a small field BDC = 0.1 T. Sample was weighed into a diamagnetic gelatin holder. Raw magnetic susceptibility was corrected to the underlying diamagnetism and drawn in the form of the temperature dependence of the effective magnetic moment. The magnetization data were taken at low temperature T = 2.0 and 4.6 K at the fields approaching BDC = 7.0 T; it is drawn as the field dependence of the

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Breaking the Magic Border of One Second for Slow Magnetic

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