Heterometallic M II Ln III (M = Co / Zn; Ln = Dy / Y) complexes with pentagonal bipyramidal 3d centres: syntheses, structures, and magnetic properties

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1 Supporting Information for Heterometallic M II Ln III (M = Co / Zn; Ln = Dy / Y) complexes with pentagonal bipyramidal 3d centres: syntheses, structures, and magnetic properties Fu-Xing Shen, Hong-Qing Li, Hao Miao, Dong Shao, Xiao-Qin Wei, Le Shi, Yi-Quan Zhang, * Xin-Yi Wang *. State Key Laboratory of Coordination Chemistry, Collaborative Innovation Center of Advanced Microstructures, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing, , China. wangxy66@nju.edu.cn Jiangsu Key Laboratory for NSLSCS, School of Physical Science and Technology, Nanjing Normal University, Nanjing , China. zhangyiquan@njnu.edu.cn 1

2 Table of contents Materials and Physical Measurements...4 Figure S1. Experimental and simulated powder X-ray diffraction patterns for 1 CoDy....5 Figure S2. Experimental and simulated powder X-ray diffraction patterns for 2 ZnDy....5 Figure S3. Experimental and simulated powder X-ray diffraction patterns for 3 CoY....5 Figure S4. TG curve of compound 1 CoDy at a rate of 10 K min -1 under a N 2 atmosphere....6 Figure S5. TG curve of compound 2 ZnDy at a rate of 10 K min -1 under a N 2 atmosphere....6 Figure S6. TG curve of compound 3 CoY at a rate of 10 K min -1 under a N 2 atmosphere....6 Figure S7. Crystal packing of complex 1 CoDy. Hydrogen atoms and the solvents are omitted for clarity....7 Figure S8. Crystal packing of complex 3 CoY. Hydrogen atoms and the solvents are omitted for clarity....7 Figure S9. Frequency dependence of in-phase ( ) and out-of-phase ( ) magnetic susceptibility of 1 CoDy ( Hz) measured at 2.0 K at zero field....8 Figure S10. The magnetization curves for 1 CoDy measured at 2, 3, and 5 K...9 Figure S11. The magnetization curves for 2 ZnDy measured at 2, 3, and 5 K...9 Figure S12. The magnetization curves for 3 CoY measured at 2, 3, and 5 K...9 Figure S13. Frequency dependence of the in-phase ( ) and out-of-phase ( ) magnetic susceptibilities of 2 ZnDy measured at 2.0 K in various applied fields from 0 to 4500 Oe...10 Figure S14. Frequency dependence of the in-phase ( ) and out-of-phase ( ) magnetic susceptibilities of 3 CoY measured at 2.0 K in various applied fields from 0 to 4500 Oe Figure S15. Cole Cole plots of vs. of 2 ZnDy at 2.0 K under various applied dc fields. The solid lines represent the best fit of the experimental results with the generalized Debye model Figure S16. Cole Cole plots of vs. of 3 CoY at 2.0 K under various applied dc fields. The solid lines represent the best fit of the experimental results with the generalized Debye model Figure S17. Field dependence of the magnetic relaxation time at 2.0 K for 2 ZnDy and its fitting by τ -1 = AH 4 T +B 1 /(1 + B 2 H 2 )...12 Figure S18. Field dependence of the magnetic relaxation time at 2.0 K for 3 CoY and its fitting by τ -1 = AH 4 T +B 1 /(1 + B 2 H 2 )...12 Figure S19. Variable-temperature ac susceptibility data for 2 ZnDy collected under a 1000 Oe dc field over the frequency range of 1 to 999 Hz. The solid lines are simply guides for the eye Figure S20. Variable-temperature ac susceptibility data for 3 CoY collected under a 1000 Oe dc field over the frequency range of 1 to 999 Hz. The solid lines are simply guides for the eye Table S1. SHAPE analysis of the M(II) ion in complexes Table S2. SHAPE analysis of the Ln(III) ion in complexes Table S3. The select intramolecular distance and Angles for M II and Ln III in complexes Table S4. Selected bond lengths (Å) and bond angles ( ) for compound Table S5. Relaxation fitting parameters from the least-square fitting of the Cole-Cole plots of compounds 2 ZnDy at 2 K under various dc fields according to the generalized Debye model...17 Table S6. Relaxation fitting parameters from the least-square fitting of the Cole-Cole plots of compounds 3 CoY at 2 K under various dc fields according to the generalized Debye model...17 Table S7. Relaxation fitting parameters from the least-square fitting of the Cole-Cole plots of 2 ZnDy under 1.8 K-5.0 K according to the generalized Debye model

3 Table S8. Relaxation fitting parameters from the least-square fitting of the Cole-Cole plots of 3 CoY under 1.8 K-5.0 K according to the generalized Debye model...18 Table S9. Parameters fitted from the Arrhenius plots in Figure 5 considering multiple relaxation processes for 2 ZnDy and 3 CoY Table S10. Wave functions with definite projection of the total moment m J > for the lowest two Kramers doublets (KDs) of individual Dy III fragments for complexes 1 CoDy and 2 ZnDy...19 Table S11. Calculated energy levels (cm 1 ), g (g x, g y, g z ) tensors and m J values of the lowest eight Kramers doublets (KDs) of individual Dy III fragment, and zero-field splitting parameters D (E) (cm 1 ), g tensors of the lowest spin-orbit state of individual Co II fragment of complexes 1 3 using CASSCF/RASSI with MOLCAS Table S12. Exchange energies (cm 1 ) and main values of the g z for the lowest four exchange doublets of complex 1 CoDy Reference

4 Materials and Physical Measurements Infrared spectra (IR) data were measured on KBr pellets using a Nexus 870 FT-IR spectrometer in the cm -1 range. Elemental analyses of C, H, and N were performed at an Elementar Vario MICRO analyzer. TG analyses were recorded on a NETZSCH TG209F3 thermo analyzer under N 2 atmosphere within the temperature range of K at a heating rate of 10 K min 1. Powder X-ray diffraction data (PXRD) were recorded at 298 K on a Bruker D8 Advance diffractometer with Mo-Kα X-ray source (λ = Å) operated at 40 kv and 40 ma. Magnetic susceptibility data were collected using Quantum Design SQUID VSM magnetometer on samples of crushed crystals. Direct current (dc) magnetic susceptibility measurements were performed in the temperature range of K under an applied field of 1000 Oe. Alternative current (ac) susceptibility measurements were performed with a 2 Oe ac oscillating field in an operating frequency range of Hz under a dc field of 0 or 1000 Oe. Magnetization data were collected in the 0 to 70 koe field range at 2.0 K. Experimental susceptibilities were corrected for diamagnetism of the sample holders and that of the compounds according to Pascal s constants.[s1] X-ray Crystallography Single crystal x-ray crystallographic data were collected on a Bruker APEX II or APEX Duo diffractometer with a CCD area detector (Mo-Kα radiation, λ = Å). The APEX II program was used to determine the unit cell parameters and for data collection. The data were integrated and corrected for Lorentz and polarization effects using SAINT. Absorption corrections were applied with SADABS.[S2] The structures were solved by direct method and refined by full-matrix least-squares method on F 2 using the SHELXTL crystallographic software package.[s3] All the non-hydrogen atoms were refined anisotropic. Hydrogen atoms of the organic ligands were refined as riding on the corresponding non-hydrogen atoms. Additional details of the data collections and structural refinement parameters were provided in Table 1. Selected bond lengths and bond angles of 1 3 were listed in Table S1. 4

5 Figure S1. Experimental and simulated powder X-ray diffraction patterns for 1 CoDy. Figure S2. Experimental and simulated powder X-ray diffraction patterns for 2 ZnDy. 5

6 Figure S3. Experimental and simulated powder X-ray diffraction patterns for 3 CoY. Figure S4. TG curve of compound 1 CoDy at a rate of 10 K min -1 under a N 2 atmosphere. Figure S5. TG curve of compound 2 ZnDy at a rate of 10 K min -1 under a N 2 atmosphere. 6

7 Figure S6. TG curve of compound 3 CoY at a rate of 10 K min -1 under a N 2 atmosphere. Figure S7. Crystal packing of complex 1 CoDy. Hydrogen atoms and the solvents are omitted for clarity. 7

8 Figure S8. Crystal packing of complex 3 CoY. Hydrogen atoms and the solvents are omitted for clarity. 8

9 Figure S9. Frequency dependence of in-phase ( ) and out-of-phase ( ) magnetic susceptibility of 1 CoDy ( Hz) measured at 2.0 K at zero field. 9

10 Figure S10. The magnetization curves for 1 CoDy measured at 2, 3, and 5 K. Figure S11. The magnetization curves for 2 ZnDy measured at 2, 3, and 5 K. Figure S12. The magnetization curves for 3 CoY measured at 2, 3, and 5 K. 10

11 Figure S13. Frequency dependence of the in-phase ( ) and out-of-phase ( ) magnetic susceptibilities of 2 ZnDy measured at 2.0 K in various applied fields from 0 to 4500 Oe. Figure S14. Frequency dependence of the in-phase ( ) and out-of-phase ( ) magnetic susceptibilities of 3 CoY measured at 2.0 K in various applied fields from 0 to 4500 Oe. 11

12 Figure S15. Cole Cole plots of vs. of 2 ZnDy at 2.0 K under various applied dc fields. The solid lines represent the best fit of the experimental results with the generalized Debye model. Figure S16. Cole Cole plots of vs. of 3 CoY at 2.0 K under various applied dc fields. The solid lines represent the best fit of the experimental results with the generalized Debye model. 12

13 Figure S17. Field dependence of the magnetic relaxation time at 2.0 K for 2 ZnDy and its fitting by τ -1 = AH 4 T +B 1 /(1 + B 2 H 2 ). Figure S18. Field dependence of the magnetic relaxation time at 2.0 K for 3 CoY and its fitting by τ -1 = AH 4 T +B 1 /(1 + B 2 H 2 ). 13

14 Figure S19. Variable-temperature ac susceptibility data for 2 ZnDy collected under a 1000 Oe dc field over the frequency range of 1 to 999 Hz. The solid lines are simply guides for the eye. Figure S20. Variable-temperature ac susceptibility data for 3 CoY collected under a 1000 Oe dc field over the frequency range of 1 to 999 Hz. The solid lines are simply guides for the eye. 14

15 Table S1. SHAPE analysis of the M(II) ion in complexes 1 3. Label Shape Symmetry (1) Co1 (2) Zn1 (3) Co1 HP-7 Heptagon D7h HPY-7 Hexagonal pyramid C6v PBPY-7 Pentagonal bipyramid D5h COC-7 Capped octahedron C3v CTPR-7 Capped trigonal prism C2v JPBPY-7 Johnson pentagonal bipyramid J13 D5h JETPY-7 Johnson elongated triangular pyramid J7 C3v Table S2. SHAPE analysis of the Ln(III) ion in complexes 1 3. Label Shape Symmetry (1) Dy1 (2) Dy1 (3) Y1 DP-10 Decagon D10h EPY-10 Enneagonal pyramid C9v OBPY-10 Octagonal bipyramid D8h PPR-10 Pentagonal prism D5h PAPR-10 Pentagonal antiprism D5d JBCCU-10 Bicapped cube J15 D4h JBCSAPR-10 Bicapped square antiprism J17 D4d JMBIC-10 Metabidiminished icosahedron J62 C2v JATDI-10 Augmented tridiminished C3v icosahedron J64 JSPC-10 Biaugmented trigonal prism C2v SDD-10 Staggered Dodecahedron (2:6:2) D TD-10 Tetradecahedron (2:6:2) C2v HD-10 Hexadecahedron (2:6:2) or (1:4:4:1) D4h Table S3. The select intramolecular distance and Angles for M II and Ln III in complexes 1 3. Complex M II Ln III (Å) M II 2 -O Ln III ( o ) (7) (1), (1) (12) (2), (2) (8) (8) 15

16 Table S4. Selected bond lengths (Å) and bond angles ( ) for compound 1 3. Complex 1 Complex 2 Complex 3 Dy(1)-O(2) 2.370(3) Dy(1)-O(2) 2.353(4) Y(1)-O(2) 2.367(2) Dy(1)-O(1) 2.381(3) Dy(1)-O(1) 2.375(4) Y(1)-O(2)# (2) Dy(1)-O(3) 2.399(3) Dy(1)-O(3) 2.399(4) Y(1)-O(1)# (3) Dy(1)-O(4) 2.423(4) Dy(1)-O(4) 2.425(4) Y(1)-O(1) 2.417(3) Dy(1)-O(8) 2.462(4) Dy(1)-O(8) 2.451(4) Y(1)-O(5) 2.451(3) Dy(1)-O(7) 2.470(4) Dy(1)-O(12) 2.462(4) Y(1)-O(5)# (3) Dy(1)-O(12) 2.488(4) Dy(1)-O(7) 2.462(4) Y(1)-O(3)# (3) Dy(1)-O(10) 2.532(4) Dy(1)-O(10) 2.516(4) Y(1)-O(3) 2.467(3) Dy(1)-N(3) 2.624(4) Dy(1)-N(3) 2.610(5) Y(1)-N(3) 2.618(3) Dy(1)-N(9) 2.649(4) Dy(1)-N(9) 2.654(5) Y(1)-N(3)# (3) Co(1)-N(6) 2.116(4) Zn(1)-O(3) 2.136(4) Co(1)-O(2)# (2) Co(1)-N(5) 2.126(4) Zn(1)-N(5) 2.140(5) Co(1)-O(2) 2.126(2) Co(1)-O(2) 2.133(3) Zn(1)-N(6) 2.142(5) Co(1)-N(6) 2.126(4) Co(1)-N(7) 2.133(4) Zn(1)-O(6) 2.150(5) Co(1)-N(5) 2.135(3) Co(1)-O(3) 2.137(3) Zn(1)-N(7) 2.152(5) Co(1)-N(5)# (3) Co(1)-O(5) 2.172(5) Zn(1)-O(2) 2.155(4) Co(1)-O(6)# (3) Co(1)-O(6) 2.181(5) Zn(1)-O(5) 2.175(5) Co(1)-O(6) 2.175(3) O(2)-Dy(1)-O(1) (11) O(2)-Dy(1)-O(1) (14) O(2)-Y(1)-O(2)# (11) O(2)-Dy(1)-O(3) 62.70(10) O(2)-Dy(1)-O(3) 63.80(12) O(2)-Y(1)-O(1)# (10) O(1)-Dy(1)-O(3) (14) O(1)-Dy(1)-O(3) (15) O(2)#1-Y(1)-O(1)# (9) O(2)-Dy(1)-O(4) (13) O(2)-Dy(1)-O(4) (14) O(2)-Y(1)-O(1) (9) O(1)-Dy(1)-O(4) 68.11(13) O(1)-Dy(1)-O(4) 67.86(16) O(2)#1-Y(1)-O(1) (10) O(3)-Dy(1)-O(4) (11) O(3)-Dy(1)-O(4) (13) O(1)#1-Y(1)-O(1) 66.56(14) O(2)-Dy(1)-O(8) 86.36(12) O(2)-Dy(1)-O(8) 85.05(13) O(2)-Y(1)-O(5) 75.50(9) O(1)-Dy(1)-O(8) 82.39(13) O(1)-Dy(1)-O(8) 82.19(14) O(2)#1-Y(1)-O(5) 83.62(9) O(3)-Dy(1)-O(8) (12) O(3)-Dy(1)-O(8) (13) O(1)#1-Y(1)-O(5) (10) O(4)-Dy(1)-O(8) 74.89(13) O(4)-Dy(1)-O(8) 74.73(14) O(1)-Y(1)-O(5) 75.41(10) O(2)-Dy(1)-O(7) 80.65(12) O(2)-Dy(1)-O(12) (14) O(2)-Y(1)-O(5)# (9) O(1)-Dy(1)-O(7) (13) O(1)-Dy(1)-O(12) 76.31(14) O(2)#1-Y(1)-O(5)# (9) O(3)-Dy(1)-O(7) 77.05(12) O(3)-Dy(1)-O(12) 78.97(13) O(1)#1-Y(1)-O(5)# (10) O(4)-Dy(1)-O(7) 79.45(13) O(4)-Dy(1)-O(12) 81.70(15) O(1)-Y(1)-O(5)# (10) O(8)-Dy(1)-O(7) 51.54(12) O(8)-Dy(1)-O(12) (13) O(5)-Y(1)-O(5)# (13) O(2)-Dy(1)-O(12) (12) O(2)-Dy(1)-O(7) 80.03(14) O(2)-Y(1)-O(3)# (9) O(1)-Dy(1)-O(12) 76.70(13) O(1)-Dy(1)-O(7) (15) O(2)#1-Y(1)-O(3)# (9) O(3)-Dy(1)-O(12) 79.07(12) O(3)-Dy(1)-O(7) 77.30(13) O(1)#1-Y(1)-O(3)# (10) O(4)-Dy(1)-O(12) 81.77(13) O(4)-Dy(1)-O(7) 79.15(15) O(1)-Y(1)-O(3)# (10) O(8)-Dy(1)-O(12) (13) O(8)-Dy(1)-O(7) 52.01(13) O(5)-Y(1)-O(3)# (11) O(7)-Dy(1)-O(12) (12) O(12)-Dy(1)-O(7) (14) O(5)#1-Y(1)-O(3)# (10) O(2)-Dy(1)-O(10) 73.86(12) O(2)-Dy(1)-O(10) 74.86(13) O(2)-Y(1)-O(3) (9) O(1)-Dy(1)-O(10) 79.35(13) O(1)-Dy(1)-O(10) 79.37(15) O(2)#1-Y(1)-O(3) 84.38(9) O(3)-Dy(1)-O(10) 76.08(12) O(3)-Dy(1)-O(10) 75.93(13) O(1)#1-Y(1)-O(3) 82.86(10) O(4)-Dy(1)-O(10) (13) O(4)-Dy(1)-O(10) (14) O(1)-Y(1)-O(3) 73.72(10) 16

17 O(8)-Dy(1)-O(10) (12) O(8)-Dy(1)-O(10) (14) O(5)-Y(1)-O(3) 51.49(10) O(7)-Dy(1)-O(10) (12) O(12)-Dy(1)-O(10) 50.91(14) O(5)#1-Y(1)-O(3) (11) O(12)-Dy(1)-O(10) 50.56(12) O(7)-Dy(1)-O(10) (14) O(3)#1-Y(1)-O(3) (13) O(2)-Dy(1)-N(3) 60.28(11) O(2)-Dy(1)-N(3) 60.09(14) O(2)-Y(1)-N(3) 60.14(8) O(1)-Dy(1)-N(3) 60.93(12) O(1)-Dy(1)-N(3) 60.91(15) O(2)#1-Y(1)-N(3) (8) O(3)-Dy(1)-N(3) (11) O(3)-Dy(1)-N(3) (14) O(1)#1-Y(1)-N(3) (9) O(4)-Dy(1)-N(3) (12) O(4)-Dy(1)-N(3) (15) O(1)-Y(1)-N(3) 61.16(9) O(8)-Dy(1)-N(3) 69.64(13) O(8)-Dy(1)-N(3) 69.56(15) O(5)-Y(1)-N(3) 67.12(10) O(7)-Dy(1)-N(3) (12) O(12)-Dy(1)-N(3) (14) O(5)#1-Y(1)-N(3) (10) O(12)-Dy(1)-N(3) (12) O(7)-Dy(1)-N(3) (14) O(3)#1-Y(1)-N(3) 69.39(11) O(10)-Dy(1)-N(3) 71.23(12) O(10)-Dy(1)-N(3) 70.85(14) O(3)-Y(1)-N(3) (10) O(2)-Dy(1)-N(9) (11) O(2)-Dy(1)-N(9) (13) O(2)-Y(1)-N(3)# (8) O(1)-Dy(1)-N(9) (12) O(1)-Dy(1)-N(9) (14) O(2)#1-Y(1)-N(3)# (8) O(3)-Dy(1)-N(9) 59.56(11) O(3)-Dy(1)-N(9) 59.64(13) O(1)#1-Y(1)-N(3)# (9) O(4)-Dy(1)-N(9) 60.46(11) O(4)-Dy(1)-N(9) 60.37(14) O(1)-Y(1)-N(3)# (9) O(8)-Dy(1)-N(9) (13) O(8)-Dy(1)-N(9) (14) O(5)-Y(1)-N(3)# (10) O(7)-Dy(1)-N(9) 69.65(12) O(12)-Dy(1)-N(9) 67.46(14) O(5)#1-Y(1)-N(3)# (10) O(12)-Dy(1)-N(9) 66.93(12) O(7)-Dy(1)-N(9) 68.89(13) O(3)#1-Y(1)-N(3)# (10) O(10)-Dy(1)-N(9) (12) O(10)-Dy(1)-N(9) (13) O(3)-Y(1)-N(3)# (11) N(3)-Dy(1)-N(9) (12) N(3)-Dy(1)-N(9) (14) N(3)-Y(1)-N(3)# (12) N(6)-Co(1)-N(5) 72.73(16) O(3)-Zn(1)-N(5) (16) O(2)#1-Co(1)-O(2) 71.17(12) N(6)-Co(1)-O(2) (15) O(3)-Zn(1)-N(6) (17) O(2)#1-Co(1)-N(6) (6) N(5)-Co(1)-O(2) 72.13(14) N(5)-Zn(1)-N(6) 72.90(19) O(2)-Co(1)-N(6) (6) N(6)-Co(1)-N(7) 72.66(16) O(3)-Zn(1)-O(6) 89.4(2) O(2)#1-Co(1)-N(5) (10) N(5)-Co(1)-N(7) (16) N(5)-Zn(1)-O(6) 85.7(2) O(2)-Co(1)-N(5) 72.39(9) O(2)-Co(1)-N(7) (14) N(6)-Zn(1)-O(6) 89.2(2) N(6)-Co(1)-N(5) 72.64(7) N(6)-Co(1)-O(3) (14) O(3)-Zn(1)-N(7) 72.13(16) O(2)#1-Co(1)-N(5)# (9) N(5)-Co(1)-O(3) (14) N(5)-Zn(1)-N(7) (19) O(2)-Co(1)-N(5)# (10) O(2)-Co(1)-O(3) 71.05(12) N(6)-Zn(1)-N(7) 72.82(19) N(6)-Co(1)-N(5)# (7) N(7)-Co(1)-O(3) 72.38(13) O(6)-Zn(1)-N(7) 94.1(2) N(5)-Co(1)-N(5)# (15) N(6)-Co(1)-O(5) 93.30(17) O(3)-Zn(1)-O(2) 71.66(14) O(2)#1-Co(1)-O(6)# (10) N(5)-Co(1)-O(5) 94.5(2) N(5)-Zn(1)-O(2) 71.57(16) O(2)-Co(1)-O(6)# (10) O(2)-Co(1)-O(5) 82.65(16) N(6)-Zn(1)-O(2) (17) N(6)-Co(1)-O(6)# (8) N(7)-Co(1)-O(5) 87.3(2) O(6)-Zn(1)-O(2) 96.5(2) N(5)-Co(1)-O(6)# (11) O(3)-Co(1)-O(5) 89.55(19) N(7)-Zn(1)-O(2) (17) N(5)#1-Co(1)-O(6)# (11) N(6)-Co(1)-O(6) 92.5(2) O(3)-Zn(1)-O(5) 89.35(18) O(2)#1-Co(1)-O(6) 85.66(10) N(5)-Co(1)-O(6) 85.85(17) N(5)-Zn(1)-O(5) 94.8(2) O(2)-Co(1)-O(6) 94.99(10) O(2)-Co(1)-O(6) 91.76(19) N(6)-Zn(1)-O(5) 92.40(18) N(6)-Co(1)-O(6) 89.60(8) N(7)-Co(1)-O(6) 95.87(18) O(6)-Zn(1)-O(5) 178.4(2) N(5)-Co(1)-O(6) 87.05(11) O(3)-Co(1)-O(6) 86.52(19) N(7)-Zn(1)-O(5) 86.42(19) N(5)#1-Co(1)-O(6) 92.71(11) O(5)-Co(1)-O(6) 174.0(2) O(2)-Zn(1)-O(5) 82.23(16) O(6)#1-Co(1)-O(6) (15) Symmetry transformations used to generate equivalent atoms for 3 CoY, #1: -X, Y, 0.5-Z. 17

18 Table S5. Relaxation fitting parameters from the least-square fitting of the Cole-Cole plots of compounds 2 ZnDy at 2 K under various dc fields according to the generalized Debye model. H / koe S / cm 3 mol -1 K T / cm 3 mol -1 K / s s E E E E E E E E E E E E E E E-4 Table S6. Relaxation fitting parameters from the least-square fitting of the Cole-Cole plots of compounds 3 CoY at 2 K under various dc fields according to the generalized Debye model. H / koe S / cm 3 mol -1 K T / cm 3 mol -1 K / s s E E E E E E E E E E E E E E E E E E E E E E E E-4 18

19 Table S7. Relaxation fitting parameters from the least-square fitting of the Cole-Cole plots of 2 ZnDy under 1.8 K-5.0 K according to the generalized Debye model. T / K S / cm 3 mol -1 K T / cm 3 mol -1 K / s s E E E E E E E E E E E E E E E E E E E E E E-3 Table S8. Relaxation fitting parameters from the least-square fitting of the Cole-Cole plots of 3 CoY under 1.8 K-5.0 K according to the generalized Debye model. T / K S / cm 3 mol -1 K T / cm 3 mol -1 K / s s E E E E E E E E E E E E E E E E E E E E-5 19

20 Table S9. Parameters fitted from the Arrhenius plots in Figure 5 considering multiple relaxation processes for 2 ZnDy and 3 CoY. Complex 2 Value Standard error R 2 A B B C n s U eff 32.9 K 5.57 Complex 3 Value Standard error R 2 A B B C n s U eff 7.5 K 0.59 Table S10. Wave functions with definite projection of the total moment m J > for the lowest two Kramers doublets (KDs) of individual Dy III fragments for complexes 1 CoDy and 2 ZnDy. E/cm 1 Wave functions Complex 1 Complex % ±15/2>+36% ±13/2>+6% ±11/2>+21% ±9/2>+13% ±5/2> % ±15/2>+14% ±11/2>+34% ±9/2>+14% ±5/2>+16% ±3/2>+11% ±1/2> % ±15/2>+33% ±13/2>+6% ±11/2>+9% ±9/2>+4% ±7/2> % ±11/2>+33% ±7/2>+23% ±5/2>+20% ±3/2>+12% ±1/2> 20

21 Table S11. Calculated energy levels (cm 1 ), g (g x, g y, g z ) tensors and m J values of the lowest eight Kramers doublets (KDs) of individual Dy III fragment, and zero-field splitting parameters D (E) (cm 1 ), g tensors of the lowest spin-orbit state of individual Co II fragment of complexes 1 3 using CASSCF/RASSI with MOLCAS 8.2. Complex 1 KDs Dy Co E/cm 1 g m J D (E) g ±13/ ( 0.9) ±9/ ±11/ ±3/ ±7/ ±5/ ±1/ ±15/2 Complex 3 Co D (E) g ( 1.0) Complex 2 Dy KDs E/cm 1 g m J ±15/2 21

22 ±7/2 ±13/2 ±1/2 ±9/2 ±3/2 ±5/2 ±11/2 Table S12. Exchange energies (cm 1 ) and main values of the g z for the lowest four exchange doublets of complex 1 CoDy. E/cm 1 g z

23 Reference (S1) O. Kahn, Molecular Magnetism, VCH, Weinheim, Germany, (S2) (a) SAINT Software Users Guide, Version 7.0, Bruker Analytical X-Ray Systems, Madison, WI, (b) Sheldrick, G. M. SADABS, Version 2.03, Bruker Analytical X-Ray Systems, Madison, WI, (S3) Sheldrick, G. M.; SHELXTL, Version 6.14, Structure Determination Software Suite, Bruker AXS, Inc., Madison, WI,