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Exploring the Inverse Magnetocaloric Effect in Discrete MnII Dimers Yang Liu,† Yan-Cong Chen,† Si-Guo Wu,† Quan-Wen Li,† Wen-Bin Chen,† Jun-Liang Liu,*,† and Ming-Liang Tong*,† †

Key Lab of Bioinorganic and Synthetic Chemistry of Ministry of Education, School of Chemistry, Sun Yat-Sen University, Guangzhou 510275, P. R. China S Supporting Information *

ABSTRACT: The inverse magnetocaloric effect (IMCE) in molecular solids is explored for two antiferromagnetically coupled MnII dinuclear complexes. Magnetic studies reveal that both of them demonstrate the IMCE with negative magnetic entropy changes (−ΔSM = −3.5 J kg−1 K−1), which are in line with an analytic function derived from the quantized phenomenological model proposed in this work.

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caloric effect, namely, [MnII2(μ1,3-N3)2(bppda)2](PF6)2 (1) (bppda = N1,N3-bis(pyridin-2-ylmethylene)propane-1,3-diamine) and [MnII2(μ1,3-N3)2(bppda)2](BF4)2 (2) (Figure 1), for which the crystal structure of 1 was reported by Chandra et al.30 while 2 is new.

INTRODUCTION Ultralow temperatures can be achieved and maintained using magnetic refrigeration via the magnetocaloric effect (MCE), which was discovered in the early 20th century as a feasible and environmentally friendly cryogenic technique1−4 and has attracted much attention over the last decades.5−10 In general, the most paramagnetic coolant chills down to the desired temperature when the external magnetic field is removed adiabatically, owing to the lowering lattice entropy compensating for the increased magnetic entropy. In this way, heat can be continually pumped away upon circulating refrigeration. Indeed, the opposing situation can also happen if the magnetic entropy increases by applying a magnetic field, leading to spin disorder under specific fields, thus lowering temperatures on adiabatic magnetization instead. To the best of our knowledge, the magnetic coolants with the aforementioned inverse magnetocaloric effect (IMCE) are overwhelmingly alloys or metal oxides.11−14 Although a lot of molecular coolants with normal MCE were discovered,6−10,15−22 there are only three cases for molecule-based magnets with IMCE.19−22 However, detailed experimental and theoretical investigations on their magnetic entropies, especially simple and discrete molecules displaying IMCE in a wide temperature range, which are potentially very good prototypes, were not reported yet. In order to better study the IMCE, we prefer to choose the magnetically isotropic MnII (S = 5/2) dimers with appropriate magnetic exchange coupling. Indeed, when the versatile N3− acts as a bridging ligand, in the most general case, μ1,1 (end-on, EO) and μ1,3 (end-to-end, EE) would tend to show ferromagnetic and antiferromagnetic exchange coupling, respectively.23−29 For the sake of raising magnetic entropy on an applying field, the EE-bridged mode is favorable. Herein we report two MnII dimers for exploring the inverse magneto© XXXX American Chemical Society

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EXPERIMENTAL SECTION

Materials and General Procedures. All reactions and manipulations described below were performed under aerobic conditions. Metal salts and other reagents were commercially available and used as received without further purification. The C, H, and N elemental analyses were carried out with an Elementar vario-EL CHNS elemental analyzer. Infrared spectra (4000−400 cm−1) were recorded on KBr pellets at room temperature using a Nicolet 6700-Contiumm FT/IR spectrometer. X-ray powder diffraction (XRPD) performed on polycrystalline samples were measured at room temperature on a Rigaku D-Max 2200 VPC X-ray diffractometer (Cu Kα, λ = 1.540 56 Å) by scanning over the range 5°−50° with step of 0.2°/s. Simulated patterns were generated with Mercury. Magnetic susceptibility measurements were performed with a Quantum Design PPMS VSM. Data were corrected for the diamagnetic contribution calculated from Pascal constants. All computations were conducted with Origin 8.5. Synthesis. Caution! Azido complexes are potentially explosive, especially in the presence of organic compounds. They must be used in small amounts with special care. Received: August 18, 2017 Revised: September 27, 2017 Published: September 27, 2017 A

DOI: 10.1021/acs.jpcc.7b08271 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

Figure 1. (a) The crystal structure of the [MnII2(μ1,3-N3)2(bppda)2]2+ cation in 2. Hydrogens are omitted for clarity. Color code: Mn, violet; N, blue, C, gray. Symmetry code (A): 1 − x, 1 − y, 1 − z. (b) The chair conformation of the {MnII2(μ1,3-N3)2} unit.

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[Mn2(μ1,3-N3)2(bppda)2](PF6)2 (1). The synthetic reaction is similar to that reported previously.30 A mixture of 1,3propanediamine (0.25 mmol, 0.019 g) and picolinaldehyde (0.50 mmol, 0.054 g) was stirred in 5 mL of MeCN for a few minutes, and then the reaction solution was added slowly to MnCl2·4H2O (0.25 mmol, 0.050 g) in 4 mL of EtOH. To the resulting yellow-orange solution were added sodium azide (0.25 mmol, 0.016 g) and potassium hexafluorophosphate (0.25 mmol, 0.093 g). The solution was then filtered, the filtrate was evaporated under room temperature. After 3−5 d, yellow block crystals of 1 were obtained in ca. 20% yield. Anal. Calcd (%) for C30H32F12Mn2N14P2: C 36.42, H 3.24, N 19.83. Found (%): C 36.53, H 3.22, N 19.85. [Mn2(μ1,3-N3)2(bppda)2](BF4)2 (2). The procedure was the same as that employed for complex 1, except that potassium hexafluorophosphate was replaced by sodium tetrafluoroborate (0.25 mmol, 0.055 g). Yellow block crystals were obtained in several days by slow evaporation. Yield: 42.2%. Anal. Calcd (%) for C30H32B2F8Mn2N14: C 41.28, H 3.67, N 22.47. Found (%): C 41.28, H 3.65, N 22.08. Both of the IR spectra show a very strong band at 2105 cm−1 for the νas(N3−), and the two bands at 1655 and 1598 cm−1 are consistent with the CN of the N1,N3-bis(pyridin-2ylmethylene)propane-1,3-diamine Schiff base. The band at 840 cm−1 for 1 and 1053 cm−1 for 2 is respectively corresponding to the counteranion PF6− and BF4−. X-ray Crystallography. Diffraction data were collected on a Bruker D8 QUEST diffractometer with Mo Kα radiation (λ = 0.710 73 Å) for complexes 1 and 2 at 295.0 K. The data collection and reduction were carried out using the Bruker APEX3 program. The structures were solved by SHELXT methods, and all non-hydrogen atoms were refined anisotropically by least-squares on F2 using the SHELXL 2015 program suite.31,32 Anisotropic thermal parameters were assigned to all non-hydrogen atoms. The hydrogen atoms attached to carbon, nitrogen, and oxygen atoms were placed in idealized positions and refined using a riding model to the atom to which they were attached. CCDC 1559804 (1) and 1559805 (2) contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via http://www.ccdc.cam. ac.uk/data_request/cif.

RESULTS AND DISCUSSION Crystal Structure. The single-crystal X-ray crystallography reveals that complexes 1 and 2 crystallize in the P21/c space group (Table 1). Both complexes consist of the identical Table 1. Crystallographic Data and Structural Refinements for 1 and 2 compound empirical formula formula weight temperature/K crystal system space group a/Å b/Å c/Å β/deg V/Å3 Z ρcalc/g cm−3 F(000) μ (mm−1) goodness-of-fit on F2 R1, wR2 [I ≥ 2σ(I)]a R1, wR2 (all data)b a

1 C30H32F12Mn2N14P2 988.51 295 monoclinic P21/c 9.5331(13) 16.220(3) 12.8433(18) 94.694(4) 1979.3(5) 2 1.659 996.0 0.820 1.080 0.0464, 0.1164 0.0712, 0.1291

2 C30H32B2F8Mn2N14 872.19 295 monoclinic P21/c 9.3323(10) 16.1831(15) 12.3918(12) 95.304(3) 1863.5(3) 2 1.554 884.0 0.763 1.065 0.0656, 0.1837 0.0970, 0.2067

R1 = ∑||Fo| − |Fc||/∑|Fo|. bwR2 = [∑w(Fo2 − Fc2)2/∑w(Fo2)2]1/2.

cationic unit formulated as [MnII2(μ1,3-N3)2(bppda)2]2+ (Figure 1), with PF6− (1) or BF4− (2) anion, respectively. The MnII ions are bridged by two end-to-end azides, and each MnII is chelated by one tetradentate Schiff base, bppda. The coordination geometry of MnII is more like a trigonal prism than an octahedron (CShM: D3h, 1.208, Oh, 12.577 for 1; D3h, 1.145, Oh, 12.981 for 2; Table 2).33,34 The Mn−N bond Table 2. CShM Values Calculated by SHAPE 2.133,34 for 1 and 2a complex

HP (D6h)

PPY (C5v)

OC (Oh)

TPR (D3h)

JPPY (C5v)

1 2

33.576 33.102

13.626 13.161

12.577 12.981

1.208 1.145

17.658 17.168

a

HP = hexagon, PPY = pentagonal pyramid, OC = octahedron, TPR = trigonal prism, and JPPY = Johnson pentagonal pyramid J2.

B


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Figure 2. Temperature dependence of χMT (left) and χM (right) at 1 kOe dc field for 1 (a) and 2 (c) and field dependence of magnetization at the indicated temperatures for 1 (b) and 2 (d). The solid lines correspond to the best fits described in the text.

distance ranges from 2.225(3) to 2.314(2) Å and 2.221(4) Å (1) to 2.294(4) Å (2), and the nearest Mn···Mn distance is 5.5390(8) Å (1) and 5.5474(10) Å (2), respectively (Table S1, Supporting Information). The {MnII2(μ1,3-N3)2} units possess a chair conformation, of which the dihedral angle between the N−Mn−N plane and the idealized plane containing six nitrogen atoms from two N3− is respectively 15.7° (1) and 16.1° (2). Magnetic Properties. To probe the magnetic interactions in the Mn II dimer, the direct-current (dc) magnetic susceptibility measurement was carried out under a 1 kOe magnetic field (Figure 2a). The room-temperature χMT of 7.52 cm3 mol−1 K for 1 and 2 are both smaller than the expect value of two isolated S = 5/2 spin-only centers (8.75 cm3 mol−1 K).35,36 Upon cooling, it monotonously falls to 0.05 cm3 mol−1 K (1) and 0.04 cm3 mol−1 K (2) from 300 to 2 K, demonstrating the presence of significantly antiferromagnetic coupling between MnII ions. The spin Hamiltonian written below (eq 1) can depict a paramagnetic dimer with an isotropic g-factor and a magnetic exchange coupling (J), where S1 = S2 = 5 /2: Ĥ = −2JS1̂ S2̂ + gμB (S1̂ z + S2̂ z)H

5

F1 =

NμB 2 g 2 3kBT

[(1 − r )F1 + rF2]

T= 0

(

ST(ST + 1)(2ST + 1) exp 5

∑S

T= 0

(

(2ST + 1) exp

JST(ST + 1) kBT

JST(ST + 1) kBT

)

)

2

F2 =

∑ Si(Si + 1) i=1

The fitted curves perfectly reproduce the experimental magnetic susceptibilities, yielding g = 1.98(1), J = −5.00(3) cm−1, and r = 0.62(1)% for 1 and g = 2.00(1), J = −5.60(3) cm−1, and r = 0.47(1)% for 2. All parameters are similar to each other and typical of the azido-bridged MnII dimers.25−30 In order to investigate the inverse magnetocaloric effect of 1 and 2, we measured the variable-temperature variable-field magnetization (Figure 2b,d) and further calculated the magnetic entropy changes (Figure 3) with the Maxwell relation [−ΔSM = −∫ (∂M/∂T)H dH].5−10 The negative −ΔSM values, referred to as the inverse magnetocaloric effect, are clearly observed in the temperature range of 2−10 K under the magnetic field changes (ΔH) of 1−9 T. As the static magnetic susceptibilities are virtually identical for them, the inverse magnetocaloric effects are expected to be similar. The magnitude of both magnetic entropy changes increases with the rising of the measured ΔH; while the temperature dependence of −ΔSM shows the presence of negative peaks. The maximal IMCE is observed as −ΔSM = −3.49 J kg−1 K−1 at 3.0 K (9 T) for 1 and −ΔSM = −3.52 J kg−1 K−1 at 3.5 K (9 T) for 2 in the measured magnetic field changes and temperatures. Comparing with other molecule-based magnets exhibiting IMCE, the −ΔSM varies from −0.7 J kg−1 K−1 at 0.9 K (1 T)19,20 to ca. −2 J kg−1 K−1 at 3 K (3 T).21 Herein we propose a simple phenomenological calculation to profile the temperature- and field-dependent magnetic entropy for an antiferromagnetically coupled dimer, which helps better

(1)

In addition, as the observation of the low-temperature nonzero χM products may come from the trace amount of a mononuclear paramagnetic impurity, the ratio of the mononuclear impurity (r) is introduced into the fitting model.36 χM =

∑S

(2) C


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Scheme 1. (a) Correlation between the Magnetic Entropy (SM/R) and the Λ and G Parametersa, (b) Zeeman Splitting Diagram,b and (c) Correlation between the Magnetic Entropy Change (−ΔSM/R) and the Λ and G Parametersc

Figure 3. Temperature dependence of the magnetic entropy change (−ΔSM) under the magnetic field change from 1 to 9 T for 1 (a) and 2 (b). The solid lines are corresponding to the best fits described in the text.

understanding the inverse magnetocaloric effect on paramagnetic molecular solids. According to the statistical thermodynamics, the magnetic entropy can be shown in eq 3, which is valid in a thermal equilibrium. In terms of the paramagnetic molecular solids without hysteresis and phase transitions within the measured temperatures and magnetic fields, a thermal equilibrium is easy to achieve. SM(T ,H ) ∂ ln Z(T ,H ) = ln Z(T ,H ) + T R ∂T

(3)

where Z(T,H) = ∑ exp(−Ei/kBT) is the partition function. Moreover, each of the eigenvalues in the spin Hamiltonian (eq 1) is Ei = −JSTi(STi + 1) + MSigμB H

(4)

where ST varies from 0 to S1 + S2 and MS varies from −ST to ST. On the basis of eq 4, the Zeeman diagram can be plotted in Scheme 1b in the case of S1 = S2 = 5/2. At zero magnetic field, it is obvious that the ground state is a singlet (ST = 0) with the first excited triplet (ST = 1) lying at |2J| above. Upon applying a field, the lowest two states, namely, |ST=n−1,MS=−ST⟩ and | ST=n,MS=−ST⟩ (n = 1−5), are degenerate when the normalized field (gμBH/−J) equals each term of the 2n arithmetic sequence, where n = 1−5: gμ B H −J

= 2n

Where Λ = J/kBT and G = gμBH/kBT. bThe red circles correspond to the crossing of the two lowest states. cThe striped pattern corresponds to the magnetocaloric effect zone, while the rest corresponds to the inverse magnetocaloric effect zone. See details in the text. All data are calculated on the basis of an antiferromagnetically coupled S = 5/2 dimer. a

(5)

magnetic entropy at zero applied field is approximately R ln(1) = 0, the magnitude of −ΔSM can reach −R[ln(2) − ln(1)] = −R ln(2) at aforementioned specific fields, suggesting that the magnetic entropy can increase upon applying field, thus exhibiting IMCE.

The five simulated intersections for a Mn dinuclear molecule originate from the quantized spins, the essence of which is unique and very different from that of the bulk magnets. These equidistant fields correspond to the maximal magnetic entropy that is close to R ln(2). Considering that the II

D


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significant inverse magnetocaloric effect, with −ΔSM = −3.5 J kg−1 K−1. An analytic function derived from the phenomenological model is proposed and is in good agreement with the experiment results. Furthermore, the quantized state-degeneracy criterion, gμBH/−J = 2n (n is a positive integer), which is quite distinct from the normal magnetocaloric effect, unveils the intuitive understanding of its nature and the explicit route toward improving the inverse magnetocaloric effect of molecular solids.

Combining eqs 3 and 4, the magnetic entropy and the magnetic entropy change can be written as SM(T ,H ) = ln ∑ exp[γi(T ,H )] R i −

∑i γi(T ,H ) exp[γi(T ,H )] ∑i exp[γi(T ,H )]

−ΔSM(T ,ΔH ) = SM(T ,0) − SM(T ,H )

(6)

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(7)

where γi(T,H) = Λ(T)STi(STi + 1) − MSiG(T,H), in which Λ(T) = J/kBT is the temperature-normalized magnetic coupling and G(T,H) = gμBH/kBT is the temperature-normalized field. The simulated SM and −ΔSM corresponding to Λ and G are displayed in Scheme 1, parts a and c, respectively. Scheme 1c is the two-dimension contour with a colormap. When the magnetic parameters (g and J) and the measurement parameters (T and H) are known, we can find the corresponding horizontal (G = gμBH/kBT) and vertical (Λ = J/kBT) coordinates in Scheme 1c and thus the magnetic entropy change (−ΔSM). The state-degeneracy criterion (eq 5) can be also transformed into the quantized slopes shown in Scheme 1a,c [Λ/G = −(2n)−1 = −1/2, −1/4, −1/6, and −1/8], which perfectly match with the lowest intersections in the Zeeman diagram (Scheme 1b). In comparison to the paramagnets with normal MCE, the nonmonotonic and alternate SM (Scheme 1a) with respect to an external field suggests that the antiferromagnetically coupled dimers possessing IMCE have the potential to exhibit a normal as well as an inverse magnetocaloric effect, along with magnetizing or demagnetizing, depending on the chosen initial field and the final field. The maximum of −R ln(2) can be reached only if the ratio of the applied magnetic field (H) to the magnetic exchange constant (J) falls within the quantized state-degeneracy criterion (eq 5). Unfortunately, the magnetic field is usually 0−9 T for commercial magnets. Upon the limitation, another possible route is to tune the magnetic exchange coupling between the paramagnetic ions, namely, it cannot be too large. In other words, the quantized state-degeneracy criterion, which is valid for any antiferromagnetically coupled isotropic dimers, also reveals the key to maximize IMCE in order to compromise between magnetic exchange and applied field. Equations 6 and 7 can also be used to fit the magnetic entropy change to extract the exchange coupling constants. As shown in Figure 3, the best-fit curves are well-consistent with the temperature- and field-dependent experimental −ΔSM. The obtained exchange coupling constants of J = −5.46(1) cm−1 for 1 and J = −5.94(1) cm−1 for 2, along with the fixed g-factor and the uncoupled mononuclear impurity r obtained from the fitting of magnetic susceptibilities, are both very close to those directly fitted from magnetic susceptibilities [where J = −5.00(3) cm−1 for 1 and J = −5.60(3) cm−1 for 2]. The slight deviation of the experimental data could arise from instrumental errors and the small zero-field splitting of the MnII ion.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b08271. Infrared spectra, bond lengths and angles, and experimental and calculated X-ray powder diffraction patterns for 1 and 2 (PDF) Crystallographic data for 1 in CIF format (CIF) Crystallographic data for 2 in CIF format (CIF)

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AUTHOR INFORMATION

Corresponding Authors

*J.-L.L e-mail: [email protected]. *M.-L.T. e-mail: [email protected]. ORCID

Jun-Liang Liu: 0000-0002-5811-6300 Ming-Liang Tong: 0000-0003-4725-0798 Notes

The authors declare no competing financial interest. CCDC 1559804 (1) and 1559805 (2) contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via http://www.ccdc.cam.ac.uk/data_ request/cif.

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ACKNOWLEDGMENTS This work was supported by the NSFC (2160102002 and 91422302) and the Fundamental Research Funds for the Central Universities (Grant 17lgjc13 and 17lgpy81).

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REFERENCES

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CONCLUSIONS In conclusion, we choose two antiferromagnetically coupled MnII dinuclear complexes for exploring the rarely observed inverse magnetocaloric effect in experimental studies and in theoretical calculations. Both of the complexes show a E


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