{"id":102942,"date":"2025-08-28T09:37:12","date_gmt":"2025-08-28T09:37:12","guid":{"rendered":"https:\/\/www.newsbeep.com\/ca\/102942\/"},"modified":"2025-08-28T09:37:12","modified_gmt":"2025-08-28T09:37:12","slug":"chemical-tuning-of-quantum-spin-electric-coupling-in-molecular-magnets","status":"publish","type":"post","link":"https:\/\/www.newsbeep.com\/ca\/102942\/","title":{"rendered":"Chemical tuning of quantum spin\u2013electric coupling in molecular magnets"},"content":{"rendered":"<p>The Mn(Me6tren)X compounds<\/p>\n<p>The crystallographic structure of Cl derivative 1 is the same as that reported for its Ni(II) and Co(II) counterparts<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Ruamps, R. et al. Giant Ising-type magnetic anisotropy in trigonal bipyramidal Ni(II) complexes: experiment and theory. J. Am. Chem. Soc. 135, 3017&#x2013;3026 (2013).\" href=\"#ref-CR27\" id=\"ref-link-section-d151643489e733\">27<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Ruamps, R. et al. Ising-type magnetic anisotropy and single molecule magnet behaviour in mononuclear trigonal bipyramidal Co(ii) complexes. Chem. Sci. 5, 3418&#x2013;3424 (2014).\" href=\"#ref-CR28\" id=\"ref-link-section-d151643489e733_1\">28<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 29\" title=\"Rubin-Osanz, M. et al. Chemical tuning of spin clock transitions in molecular monomers based on nuclear spin-free Ni(II). Chem. Sci. 12, 5123&#x2013;5133 (2021).\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#ref-CR29\" id=\"ref-link-section-d151643489e736\" rel=\"nofollow noopener\" target=\"_blank\">29<\/a>. None of the reported Br derivatives with any metal ion crystallize in a trigonal space group. We thus prepared a new compound with Br in the axial position and [PF6]\u2212 as the counter anion that turned out to crystallize in a trigonal space group. For the I derivative, despite trying several counter anions, they all crystallized in a cubic space group. We therefore prepared the Mn complex based on the reported Zn(II) one, which crystallizes in a cubic space group (Supplementary Tables <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">1<\/a> and <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">2<\/a>)<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 30\" title=\"Naveen, K., Ji, H., Kim, T. S., Kim, D. &amp; Cho, D.-H. C3-symmetric zinc complexes as sustainable catalysts for transforming carbon dioxide into mono- and multi-cyclic carbonates. Appl. Catal. B Environ. 280, 119395 (2021).\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#ref-CR30\" id=\"ref-link-section-d151643489e751\" rel=\"nofollow noopener\" target=\"_blank\">30<\/a>. Mn(II) is pentacoordinate, surrounded by one axial (N1) and three equatorial (N2) nitrogen atoms belonging to the tetradentate me6tren ligand, and one halogen (X). Its coordination sphere has a trigonal bipyramidal (tbp) geometry of C3 point group symmetry, with the three-fold axis along the N1\u2013Mn\u2013X direction (Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#Fig1\" rel=\"nofollow noopener\" target=\"_blank\">1a<\/a> and Supplementary Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">1<\/a>). The Mn\u2013N1 and Mn\u2013N2 bond lengths and the N1MnN2 angles differ by less than 1% for the three complexes (Supplementary Table <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">3<\/a>). The main difference is the Mn\u2013X distance: 2.3458(3)\u2009\u00c5, 2.5026(18)\u2009\u00c5 and 2.7133(6)\u2009\u00c5, for X\u2009=\u2009Cl, Br and I, respectively. 1 and 2 crystallize in the R3c and the R3m trigonal space group, with the C3 molecular axis along the crystal c axis and all the N1\u2013Mn\u2013X bonds aligned. 3 crystallizes in the cubic P213 space group with the C3 molecular axes along the cubic unit cell diagonal. For each compound, we used the corresponding isostructural diamagnetic Zn(II)-containing compounds to provide a diamagnetic host crystal with dilute Mn(II)-complex impurities (Supplementary Sections <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">I<\/a> and <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">II<\/a>).<\/p>\n<p>Fig. 1: ESR spectra and spin relaxation measurements for 1 and 2.<a class=\"c-article-section__figure-link\" data-test=\"img-link\" data-track=\"click\" data-track-label=\"image\" data-track-action=\"view figure\" href=\"https:\/\/www.nature.com\/articles\/s41557-025-01926-5\/figures\/1\" rel=\"nofollow noopener\" target=\"_blank\"><img decoding=\"async\" aria-describedby=\"Fig1\" src=\"https:\/\/www.newsbeep.com\/ca\/wp-content\/uploads\/2025\/08\/41557_2025_1926_Fig1_HTML.png\" alt=\"figure 1\" loading=\"lazy\" width=\"685\" height=\"301\"\/><\/a><\/p>\n<p>a, Ball-and-stick representation of the [Mn(me6tren)X] molecules. H atoms are omitted for clarity. b, Representative low-temperature ESR spectra for 1 recorded with different sample forms at different frequencies. The single-crystal spectrum (middle) was recorded at the Q-band using an echo-detected field sweep (EDFS), whereas the ESR experiments for the powder sample (top and bottom) were conducted using the continuous-wave method. c, Low-temperature relaxation times for 1 and 2 molecules measured on the \u22125\/2\u2009\u2194\u2009\u22123\/2 and +3\/2\u2009\u2194\u2009+5\/2 transitions, respectively. Upper panel: the spin\u2013lattice relaxation time, T1, and quantum phase memory time, Tm, for 1 and 2 as a function of temperature. T1 is described by a single exponential decay over the experimental temperature range. Lower panel: in contrast, Tm follows a stretched exponential, whose stretch parameter varies with temperature.<\/p>\n<p><a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM3\" rel=\"nofollow noopener\" target=\"_blank\">Source data<\/a><\/p>\n<p>We characterized the magnetic properties using electron spin resonance (ESR) at three frequencies. Representative data for 1 are shown in Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#Fig1\" rel=\"nofollow noopener\" target=\"_blank\">1b<\/a> (Supplementary Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">2<\/a> presents more data). The results can be described by an electron spin S\u2009=\u20095\/2 and a nuclear spin I\u2009=\u20095\/2 under the Hamiltonian<\/p>\n<p>$${\\hat{H}}={D{\\hat{S}}_{z}^{2}+{\\mu }_{\\rm{B}}g{{\\bf{B}}}_{0}\\cdot \\hat{{\\bf{S}}}+A\\hat{{\\bf{I}}}\\cdot \\hat{{\\bf{S}}}}$$<\/p>\n<p>\n                    (1)\n                <\/p>\n<p>where B0 is the applied magnetic field, g and A are the isotropic g-factor and hyperfine coupling, respectively, and D is the axial ZFS parameter. No evidence of a transverse anisotropy was observed for any of the three compounds, consistent with the three-fold rotational symmetry of the molecules. D exhibits a systematic trend through the series, with 1 possessing easy-axis-type anisotropy (D\u2009&lt;\u20090) and 2 and 3 exhibiting easy-plane-type anisotropy (D\u2009&gt;\u20090). By contrast, the hyperfine coupling is almost identical across the family (Table <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"table anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#Tab1\" rel=\"nofollow noopener\" target=\"_blank\">1<\/a>).<\/p>\n<p>Table 1 Spin Hamiltonian parameters<\/p>\n<p>We measured low-temperature spin relaxation times for 1 and 2 using magnetically diluted single crystals [Mn0.001Zn0.999(me6tren)X]Y (for 3, see Supplementary Figs. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">3<\/a>, <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">4<\/a> and <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">8<\/a>). The results are shown in Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#Fig1\" rel=\"nofollow noopener\" target=\"_blank\">1<\/a> (Supplementary Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">4<\/a> presents representative relaxation data). The spin lattice relaxation time T1 for both molecules increases monotonically as the temperature falls, showing no sign of saturation down to our base temperature. At 3.5\u2009K, T1 for 1 (2.3\u2009ms) is approximately six times that for 2 (0.36\u2009ms). Such a difference in T1 is probably due to the difference between the Mn\u2013Cl (2.3458(3)\u2009\u00c5) and Mn\u2013Br (2.5026(18)\u2009\u00c5) bond lengths: the longer Mn\u2013Br distance leads to a weaker bond and lower energy vibrational modes, leading to faster spin\u2013lattice relaxation rates at all temperatures that we studied. This is also consistent with the difference in the ESR spectra for 1 and 2: although the hyperfine structure of 1 is clearly resolved for all transitions (Supplementary Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">2a,e<\/a>), we could only distinguish it for the ms\u2009=\u2009\u00b11\/2 transition in 2 (Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#Fig2\" rel=\"nofollow noopener\" target=\"_blank\">2b<\/a> and Supplementary Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">2b<\/a>), indicating the presence of a substantial D strain.<\/p>\n<p>Fig. 2: SEC in Mn triangle molecules.<a class=\"c-article-section__figure-link\" data-test=\"img-link\" data-track=\"click\" data-track-label=\"image\" data-track-action=\"view figure\" href=\"https:\/\/www.nature.com\/articles\/s41557-025-01926-5\/figures\/2\" rel=\"nofollow noopener\" target=\"_blank\"><img decoding=\"async\" aria-describedby=\"Fig2\" src=\"https:\/\/www.newsbeep.com\/ca\/wp-content\/uploads\/2025\/08\/41557_2025_1926_Fig2_HTML.png\" alt=\"figure 2\" loading=\"lazy\" width=\"685\" height=\"369\"\/><\/a><\/p>\n<p>a, The microwave and E-field pulse sequence measuring SEC in single crystals. b, The Q-band EDFS spectrum for 2 recorded at 3.5\u2009K. c, The in-phase spin echo signals for different ms transitions as a function of tE recorded on 2. The data were recorded with both B0 and the pulsed electric field parallel to the Mn\u2013Br bond. d, The in-phase (black) and quadrature (red) echo signals for the +3\/2 to +5\/2 transition in MnBr with the electric field applied parallel (top), perpendicular (middle) and antiparallel (bottom) to the Mn\u2013Br direction. Note that the polarity of the quadrature signal is reversed for the top and bottom data, consistent with a linear SEC. e, Orientation dependence of the E-field-induced shift in the ZFS parameter D (errors are smaller than the symbol sizes).<\/p>\n<p><a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM4\" rel=\"nofollow noopener\" target=\"_blank\">Source data<\/a><\/p>\n<p>The phase coherence times (Tm) for 1 and 2 are described by a stretched exponential decay with a temperature-dependent stretch parameter, indicating an interplay between multiple decoherence mechanisms<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 31\" title=\"Wedge, C. J. et al. Chemical engineering of molecular qubits. Phys. Rev. Lett. 108, 107204 (2012).\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#ref-CR31\" id=\"ref-link-section-d151643489e1625\" rel=\"nofollow noopener\" target=\"_blank\">31<\/a>. At 3.5\u2009K, both compounds show similar Tm values, with their stretched parameters close to 2, suggesting that the decoherence is dominated by the nuclear spin bath surrounding Mn spins. On raising the temperature, the coherence of 2 decreases rapidly, with the stretch parameter dropping below 1 at 5\u2009K. By comparison, both Tm and the stretch parameter for 1 remain almost temperature-independent up to 10\u2009K (Supplementary Table <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">4<\/a> provides more details).<\/p>\n<p>The average Mn\u2013Mn distance in our 0.1% diluted crystals is less than 8\u2009nm, so electron spin\u2013spin dipolar interactions are of the order of ~1\u2009MHz. The difference in the temperature dependences of Tm is probably related to the short T1 associated with 2 (Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#Fig1\" rel=\"nofollow noopener\" target=\"_blank\">1c<\/a>): T1 relaxation in 2 leads to magnetic fluctuations in the local environment, inducing contributions to the phase decoherence. Above 10\u2009K, both the Tm and the stretch parameter for 1 start to decrease rapidly with increasing temperature, suggesting that the nuclear spin bath is no longer the dominant decoherence source.<\/p>\n<p>SECs<\/p>\n<p>We measured SECs for all three molecules by embedding a square d.c. E-field pulse into a Hahn-echo sequence (Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#Fig2\" rel=\"nofollow noopener\" target=\"_blank\">2a<\/a> and Supplementary Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">5<\/a>). We recorded the spin echo signal as a function of the duration\/amplitude of the E-field pulse<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 22\" title=\"Liu, J. et al. Quantum coherent spin&#x2013;electric control in a molecular nanomagnet at clock transitions. Nat. Phys. 17, 1205&#x2013;1209 (2021).\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#ref-CR22\" id=\"ref-link-section-d151643489e1700\" rel=\"nofollow noopener\" target=\"_blank\">22<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 32\" title=\"Liu, J. et al. Electric field control of spins in molecular magnets. Phys. Rev. Lett. 122, 037202 (2019).\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#ref-CR32\" id=\"ref-link-section-d151643489e1703\" rel=\"nofollow noopener\" target=\"_blank\">32<\/a> (more details are provided in Supplementary Figs. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">6<\/a>\u2013<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">8<\/a>). Representative data (recorded on 2) are shown in Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#Fig2\" rel=\"nofollow noopener\" target=\"_blank\">2<\/a>. The echo signals for the inter-Kramers transitions exhibit clear oscillations as a function of the duration of the E-field pulse (tE), with the oscillation frequency for the +5\/2\u2009\u2194\u2009+3\/2 signal almost exactly double that for the +3\/2\u2009\u2194\u2009+1\/2 signal. The E-field-induced change in the spin transition frequency, \u03b4fE, is calculated by a fast Fourier transform of the oscillating echo signal. By comparison, the \u22121\/2\u2009\u2194\u2009+1\/2 transition shows only a weak SEC coupling. Measuring on different hyperfine peaks yields the same weak SEC.<\/p>\n<p>When the magnetic field B0 is parallel to the magnetic anisotropy axis, the transition within the \u00b11\/2 doublet depends only on g and A, whereas the inter-Kramers transitions also depend on the ZFS parameter D. Hence, the lack of E-field dependence for the \u00b11\/2 transition suggests both A and g show negligible SEC, and the oscillations observed with the inter-Kramers transitions are, therefore, attributable to the E-field modulation of the anisotropy parameter D. This is further supported by the fact that the ZFS for the +5\/2\u2009\u2194\u2009+3\/2 transition, 4D, is exactly twice that for the +3\/2\u2009\u2194\u2009+1\/2 transition, 2D. Accordingly, an E-field-induced modification in D, \u03b4D, lead to oscillation in the +5\/2\u2009\u2192\u2009+3\/2 echo at frequency 4\u03b4D, double that for the +3\/2\u2009\u2192\u2009+1\/2 echo, 2\u03b4D.<\/p>\n<p>Both 1 and 2 crystallize in a polar space group with all molecules co-aligned. Consequently, all molecules should exhibit the same linear response upon application of an external E-field, allowing us to measure both the amplitude and sign of \u03b4fE. (The sign of \u03b4fE is inaccessible for random orientated samples, such as frozen solutions<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 32\" title=\"Liu, J. et al. Electric field control of spins in molecular magnets. Phys. Rev. Lett. 122, 037202 (2019).\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#ref-CR32\" id=\"ref-link-section-d151643489e1812\" rel=\"nofollow noopener\" target=\"_blank\">32<\/a> or single crystals with inversion-related molecules<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 22\" title=\"Liu, J. et al. Quantum coherent spin&#x2013;electric control in a molecular nanomagnet at clock transitions. Nat. Phys. 17, 1205&#x2013;1209 (2021).\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#ref-CR22\" id=\"ref-link-section-d151643489e1816\" rel=\"nofollow noopener\" target=\"_blank\">22<\/a>.) The in-phase and quadrature parts of the echo signal should follow cos(2\u03c0\u03b4fEtE) and sin (2\u03c0\u03b4fEtE), respectively, where the sign of \u03b4fE is determined by the polarity of the quadrature component, as illustrated in Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#Fig2\" rel=\"nofollow noopener\" target=\"_blank\">2d<\/a> (more details are provided in Supplementary Figs. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">6<\/a>\u2013<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">8<\/a>). When the orientation of the electric field is rotated from the Mn\u2013Br (top) to the Br\u2013Mn (bottom) direction, the quadrature part of the signal is inverted, whereas the in-phase part remains virtually identical, as expected for a linear SEC.<\/p>\n<p>The full orientation dependence of the SECs is mapped by rotating the E-field against the crystals. We present the E-field-induced changes in D for all three molecules for direct comparison (Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#Fig2\" rel=\"nofollow noopener\" target=\"_blank\">2e<\/a>). For all molecules the maximum SECs occur with the applied electric field parallel or antiparallel to the Mn\u2013X bond, with a near-complete extinction of the effect for the perpendicular orientation. This highlights the importance of the molecular electric dipole: an E-field is coupled to the molecular spin via its electric dipole. Hence, even though the triangular plane perpendicular to the Mn\u2013X bond also does not possess an inversion symmetry, allowing first-order SEC<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 6\" title=\"Trif, M., Troiani, F., Stepanenko, D. &amp; Loss, D. Spin&#x2013;electric coupling in molecular magnets. Phys. Rev. Lett. 101, 217201 (2008).\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#ref-CR6\" id=\"ref-link-section-d151643489e1874\" rel=\"nofollow noopener\" target=\"_blank\">6<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 33\" title=\"Trif, M., Troiani, F., Stepanenko, D. &amp; Loss, D. Spin electric effects in molecular antiferromagnets. Phys. Rev. B 82, 045429 (2010).\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#ref-CR33\" id=\"ref-link-section-d151643489e1877\" rel=\"nofollow noopener\" target=\"_blank\">33<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 34\" title=\"Mims, W. The Linear Electric Field Effect in Paramagnetic Resonance (Oxford Univ. Press, 1976).\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#ref-CR34\" id=\"ref-link-section-d151643489e1880\" rel=\"nofollow noopener\" target=\"_blank\">34<\/a> by symmetry, an E-field applied in this plane cannot couple to the spin efficiently due to the lack of an electric dipole in this orientation.<\/p>\n<p>The observed E-field-induced frequency shifts (~4.8\u2009Hz\u2009(V\u2009m\u22121)\u22121 for 2) are substantial, especially considering that Mn(II) ions are typically associated with a weak spin\u2013orbit interaction due to their half-filled 3d5 outer shell. The coupling to the spin spectrum (\u03b4fE\/E) is much stronger than that for molecular magnets containing Mn(II) (~0.68\u2009Hz\u2009(V\u2009m\u22121)\u22121)<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 24\" title=\"Fang, Y.-H. et al. Spin-electric coupling with anisotropy-induced vanishment and enhancement in molecular ferroelectrics. J. Am. Chem. Soc. 144, 8605&#x2013;8612 (2022).\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#ref-CR24\" id=\"ref-link-section-d151643489e1917\" rel=\"nofollow noopener\" target=\"_blank\">24<\/a> and comparable with the shift for a lanthanide-based molecule (~11\u2009Hz\u2009(V\u2009m\u22121)\u22121) with giant SOC<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 22\" title=\"Liu, J. et al. Quantum coherent spin&#x2013;electric control in a molecular nanomagnet at clock transitions. Nat. Phys. 17, 1205&#x2013;1209 (2021).\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#ref-CR22\" id=\"ref-link-section-d151643489e1926\" rel=\"nofollow noopener\" target=\"_blank\">22<\/a>. The E-field effect on the ZFS parameter, \u03b4D\/E\u2009=\u20091.7\u2009Hz\u2009(V\u2009m\u22121)\u22121 for 3, is also comparable to those found for Mn2+ spins doped in inorganic crystals: 1.26, 2.25, 1.33 and 3.3\u2009Hz\u2009(V\u2009m\u22121)\u22121 for CaWO4 (ref. <a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 35\" title=\"Kiel, A. &amp; Mims, W. B. Electric field shift in electron paramagnetic resonance for Mn2+ in CaWO4. Phys. Rev. 153, 378 (1967).\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#ref-CR35\" id=\"ref-link-section-d151643489e1956\" rel=\"nofollow noopener\" target=\"_blank\">35<\/a>), SrWO4 (ref. <a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 36\" title=\"Kiel, A. &amp; Mims, W. B. Electric field effect in paramagnetic resonance for Mn2+ in SrWO4. Phys. Rev. B 3, 2878 (1971).\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#ref-CR36\" id=\"ref-link-section-d151643489e1962\" rel=\"nofollow noopener\" target=\"_blank\">36<\/a>), PbMoO4 (ref. <a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 37\" title=\"Kiel, A., Mims, W. B. &amp; Masuhr, G. J. Electric field effect in paramagnetic resonance for Mn2+ in PbMoO4. Phys. Rev. B 7, 1735 (1973).\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#ref-CR37\" id=\"ref-link-section-d151643489e1968\" rel=\"nofollow noopener\" target=\"_blank\">37<\/a>) and ZnO (ref. <a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 26\" title=\"George, R. E., Edwards, J. P. &amp; Ardavan, A. Coherent spin control by electrical manipulation of the magnetic anisotropy. Phys. Rev. Lett. 110, 027601 (2013).\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#ref-CR26\" id=\"ref-link-section-d151643489e1973\" rel=\"nofollow noopener\" target=\"_blank\">26<\/a>), respectively. For the scheelite lattices<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Kiel, A. &amp; Mims, W. B. Electric field shift in electron paramagnetic resonance for Mn2+ in CaWO4. Phys. Rev. 153, 378 (1967).\" href=\"#ref-CR35\" id=\"ref-link-section-d151643489e1977\">35<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Kiel, A. &amp; Mims, W. B. Electric field effect in paramagnetic resonance for Mn2+ in SrWO4. Phys. Rev. B 3, 2878 (1971).\" href=\"#ref-CR36\" id=\"ref-link-section-d151643489e1977_1\">36<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 37\" title=\"Kiel, A., Mims, W. B. &amp; Masuhr, G. J. Electric field effect in paramagnetic resonance for Mn2+ in PbMoO4. Phys. Rev. B 7, 1735 (1973).\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#ref-CR37\" id=\"ref-link-section-d151643489e1980\" rel=\"nofollow noopener\" target=\"_blank\">37<\/a>, the SEC is largely attributed to the displacement of the spin-carrying ion in the applied electric field. In ZnO (ref. <a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 26\" title=\"George, R. E., Edwards, J. P. &amp; Ardavan, A. Coherent spin control by electrical manipulation of the magnetic anisotropy. Phys. Rev. Lett. 110, 027601 (2013).\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#ref-CR26\" id=\"ref-link-section-d151643489e1984\" rel=\"nofollow noopener\" target=\"_blank\">26<\/a>), the SEC is associated with the piezoelectric nature of the host lattice, allowing a substantial E-field-induced distortion of the lattice geometry. These previous works are consistent with our findings: a strong SEC is probably due to the substantial molecular electric dipole and the fact that it is directly correlated to the molecular magnetic anisotropy. An E-field distorts the geometry of the molecule, modulating the ZFS of the Mn2+ spins.<\/p>\n<p>The SECs for the complexes could be adequate for practical spin control with an E-field generated by sufficiently localized electrodes. For example, with a d.c. E-field of 107\u2009V\u2009m\u22121, that is, 10\u2009mV\u2009nm\u22121, the resonance frequency of 3 can be shifted by ~68\u2009MHz, corresponding to the excitation bandwidth of a 15-ns microwave pulse. A high-frequency resonance a.c. E-field of the same amplitude can drive coherent spin transitions with the Rabi rate of ~15\u2009MHz and ~1.7\u2009MHz for standard \u03b4ms\u2009=\u20091 and double \u03b4ms\u2009=\u20092 transitions, respectively (applying B0 perpendicular to the anisotropy axis), potentially allowing hundreds of coherent E-field-driven spin operations within Tm. E-fields on this scale are routinely accessible in reported molecular break-junction devices<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 7\" title=\"Thiele, S. et al. Electrically driven nuclear spin resonance in single-molecule magnets. Science 344, 1135&#x2013;1138 (2014).\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#ref-CR7\" id=\"ref-link-section-d151643489e2041\" rel=\"nofollow noopener\" target=\"_blank\">7<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 38\" title=\"Burzur&#xED;, E., Zyazin, A. S., Cornia, A. &amp; van der Zant, H. S. J. Direct observation of magnetic anisotropy in an individual Fe4 single-molecule magnet. Phys. Rev. Lett. 109, 147203 (2012).\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#ref-CR38\" id=\"ref-link-section-d151643489e2044\" rel=\"nofollow noopener\" target=\"_blank\">38<\/a> and scanning tunnelling microscopy experiments<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 11\" title=\"Zhang, X. et al. Electron spin resonance of single iron phthalocyanine molecules and role of their non-localized spins in magnetic interactions. Nat. Chem. 14, 59&#x2013;65 (2022).\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#ref-CR11\" id=\"ref-link-section-d151643489e2049\" rel=\"nofollow noopener\" target=\"_blank\">11<\/a>.<\/p>\n<p>Despite the fact that D\u2009&lt;\u20090 for X\u2009=\u2009Cl and D\u2009&gt;\u20090 for X\u2009=\u2009Br and I, we note that \u03b4D\u2009&lt;\u20090 for all three compounds when an electric field is applied pointing from the X halogen ion towards Mn2+ (Supplementary Table <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">5<\/a>). Such behaviour showcases the possibility of controlling magnetic anisotropy and SEC independently, allowing the design of molecular magnets with strong SEC while maintaining operability within the microwave frequency range convenient for (quantum) information technologies. This can be understood qualitatively by considering the origin of the magnetic anisotropy and the symmetry of their electronic states (see next section).<\/p>\n<p>Electronic structure calculations<\/p>\n<p>We performed wavefunction-based ab initio calculations to understand the origin of D and its interaction with an external E-field<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 10\" title=\"Pradines, B., Cahier, B., Suaud, N. &amp; Guih&#xE9;ry, N. Impact of the electric field on isotropic and anisotropic spin Hamiltonian parameters. J. Chem. Phys. 157, 204308 (2022).\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#ref-CR10\" id=\"ref-link-section-d151643489e2094\" rel=\"nofollow noopener\" target=\"_blank\">10<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Maurice, R. et al. Universal theoretical approach to extract anisotropic spin Hamiltonians. J. Chem. Theory Comput. 5, 2977&#x2013;2984 (2009).\" href=\"#ref-CR39\" id=\"ref-link-section-d151643489e2097\">39<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Bouammali, M.-A., Suaud, N., Martins, C., Maurice, R. &amp; Guih&#xE9;ry, N. How to create giant Dzyaloshinskii-Moriya interactions? Analytical derivation and ab initio calculations on model dicopper(II) complexes. J. Chem. Phys. 154, 134301 (2021).\" href=\"#ref-CR40\" id=\"ref-link-section-d151643489e2097_1\">40<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 41\" title=\"Bouammali, M.-A., Suaud, N., Maurice, R. &amp; Guih&#xE9;ry, N. Extraction of giant Dzyaloshinskii-Moriya interaction from ab initio calculations: first-order spin-orbit coupling model and methodological study. J. Chem. Phys. 155, 164305 (2021).\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#ref-CR41\" id=\"ref-link-section-d151643489e2100\" rel=\"nofollow noopener\" target=\"_blank\">41<\/a>. The ZFS parameters for all molecules (without external E-field) were calculated using two geometries: the X-ray structures and the molecular geometries optimized in density functional theory (DFT) while preserving C3 symmetry. Both calculations reproduce the trend of D observed in ESR measurements; that is, the ZFS shifts from easy-axis type (D\u2009&lt;\u20090) to easy-plane type (D\u2009&gt;\u20090) as the halogen atom varies from Cl to I. Here we focus on results obtained using the DFT-optimized geometry, as this allows us to investigate the E-field-induced distortions to the geometry of the molecules.<\/p>\n<p>Detailed analysis was performed with 1 and 3 to rationalize the origin of the ZFS. For a high-spin Mn(II) (S\u2009=\u20095\/2) ground state, all five d orbitals are singly occupied, leading to a sextuplet ground state 6A. Therefore, the ZFS can only emerge due to interactions between the electronic ground state and the excited quadruplet states, 4Yi, via SOCs. It is worth noting that the spin\u2013spin contribution to D (ref. <a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 42\" title=\"Duboc, C. et al. Origin of the zero-field splitting in mononuclear octahedral dihalide Mn II complexes: an investigation by multifrequency high-field electron paramagnetic resonance and density functional theory. Inorg. Chem. 46, 4905&#x2013;4916 (2007).\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#ref-CR42\" id=\"ref-link-section-d151643489e2154\" rel=\"nofollow noopener\" target=\"_blank\">42<\/a>), which is considered in the calculations, is very small.<\/p>\n<p>For analysis purposes, we can consider the second-order perturbation expression of the SOC contributions. The SOC interaction between the ground electronic state \\({{| }^{6}{A}_{{m}_{\\rm{s}}}\\left.\\right\\rangle}\\) with the spin projection ms and the msl component in an excited electronic state 4Yi leads to a contribution to D of the ground state, \\({c(D)[{4\\atop}{Y}_{{m}_{\\rm{sl}}}^{\\,i}]}\\):<\/p>\n<p>$${c(D)\\left[{4\\atop}{Y}_{{m}_{\\rm{sl}}}^{i}\\right]}={\\sum _{k}\\frac{\\left| \\left\\langle {6\\atop}{A}_{{m}_{\\rm{s}}}| {\\zeta }_{k}\\left[\\left({\\hat{L}}_{k}^{+}{\\hat{S}}_{k}^{-}+{\\hat{L}}_{k}^{-}{\\hat{S}}_{k}^{+}\\right)\/2+{\\hat{L}}_{k}^{z}{\\hat{S}}_{k}^{z}\\right]| {4\\atop}{Y}_{{m}_{\\rm{sl}}}^{\\,i}\\right\\rangle \\right| ^{2}}{{\\mathcal{E}}\\left({4\\atop}{Y}^{i}\\right)}}$$<\/p>\n<p>\n                    (2)\n                <\/p>\n<p>where the sum runs over all electrons k of the d shell. \\({\\mathcal E} ({4\\atop}{Y}^{\\,i})\\) is the energy of the 4Yi excited state with respect to the ground state and \u03b6k is the SOC constant, which depends on the two orbitals involved in the excitation. By summing over the ms and msl components of both the ground and excited states, one obtains the full contribution C(D) of each excited state. The sum of the contributions of all 4Yi excited states, \u2211C(D), leads to the ZFS. Ab initio calculations show that the main contributions to D arise from the ten excited quadruplet states. Among them, four doubly degenerate states Ei (i\u2009= 1 to 4) that couple to the ground state through the \\(({\\hat{L}}_{k}^{+}{\\hat{S}}_{k}^{-}+{\\hat{L}}_{k}^{-}{\\hat{S}}_{k}^{+})\/{2}\\) term lead to negative contributions to D, and the two non-degenerate states Ai (i\u2009=\u20091 or 2) that couple to the ground state through \\({\\hat{L}}_{k}^{\\,z}{\\hat{S}}_{k}^{\\,z}\\) lead to positive contributions to D (ref. <a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 43\" title=\"Suaud, N. et al. Playing with magnetic anisotropy in hexacoordinated mononuclear Ni(II) complexes, an interplay between symmetry and geometry. Appl. Magn. Reson. 51, 1215&#x2013;1231 (2020).\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#ref-CR43\" id=\"ref-link-section-d151643489e3138\" rel=\"nofollow noopener\" target=\"_blank\">43<\/a>).<\/p>\n<p>The excitation energies are driven by the ligand field and follow the halogen spectrochemical series (Supplementary Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">9<\/a> and Supplementary Section <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">V.A<\/a>). However, although for many series of complexes the excitation energies govern the magnitude and nature of D, here the variation of the SOCs plays the most important role. Indeed, one may notice that the increase or decrease in the contributions to D of an excited state is directly correlated with the decrease or increase of the SOCs (Supplementary Table <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">6<\/a>). The variation in SOCs can have two origins: either the coefficient on the 4Y state determinants involved in the coupling varies between 1 and 3, or the spin\u2013orbit constants \u03b6k vary. In the present case, both variations need to be considered. However, the dominant effect concerns the spin\u2013orbit constants. Indeed, for an excitation involving an orbital with a z component (that is pointing towards the halogen), the constant \u03b6k is weaker for the iodine-containing complex than for the chlorine-containing one due to the relativistic nephelauxetic effect, inducing weaker couplings and therefore lower negative contributions. Concerning the A2 state, it is essentially carried by the two excitations from dxy to \\({d}_{({x}^{2}-{y}^{2})}\\) (Supplementary Table <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">7<\/a>) and vice versa, and the weight on these two configurations (Supplementary Table <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">8<\/a>) is larger in 3 than in 1, inducing a stronger coupling and therefore a larger positive contribution. To summarize, the negative contributions to D due to the quadruplet Ei states decrease from 1 to 3, whereas the positive contributions brought by the Ai states increase, resulting in an overall ZFS shifting from easy-axis to easy-plane type, as experimentally observed.<\/p>\n<p>The application of an E-field modifies both the electronic structure and the geometry of the molecules, thus changing D. To appreciate the spin\u2013electric effect due to each contribution individually, we calculated D using the following three cases: (1) an E-field only modifies the electronic structure, with the molecular geometry unperturbed; (2) an E-field distorts the geometry of the molecule, leading to a new structure (optimized using DFT in the presence of the E-field) with which D is calculated; (3) D is calculated using the new geometry in the presence of an E-field affecting the electronic structure. To reduce relative digital errors in the ab initio calculation, a strong electric field is used (~109\u2009V\u2009m\u22121), substantially larger than those applied in experiments (~105\u2009V\u2009m\u22121). Nevertheless, the calculations produce a linear E-field dependence of D (Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#Fig3\" rel=\"nofollow noopener\" target=\"_blank\">3a<\/a>), allowing us to draw a direct comparison between calculations and experiments.<\/p>\n<p>Fig. 3: Theoretical calculations for 3.<a class=\"c-article-section__figure-link\" data-test=\"img-link\" data-track=\"click\" data-track-label=\"image\" data-track-action=\"view figure\" href=\"https:\/\/www.nature.com\/articles\/s41557-025-01926-5\/figures\/3\" rel=\"nofollow noopener\" target=\"_blank\"><img decoding=\"async\" aria-describedby=\"Fig3\" src=\"https:\/\/www.newsbeep.com\/ca\/wp-content\/uploads\/2025\/08\/41557_2025_1926_Fig3_HTML.png\" alt=\"figure 3\" loading=\"lazy\" width=\"685\" height=\"402\"\/><\/a><\/p>\n<p>a, Theoretical calculation for 3 showing a linear SEC. A positive E corresponds to an E-field applied from I\u2212 to Mn2+. The calculations were performed with three cases as described in the main text. b, Molecular orbital energy diagram for 3 with the application of an E-field.<\/p>\n<p><a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM5\" rel=\"nofollow noopener\" target=\"_blank\">Source data<\/a><\/p>\n<p>Representative results for 3 are shown in Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#Fig3\" rel=\"nofollow noopener\" target=\"_blank\">3<\/a> (Supplementary Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">10<\/a> presents results for 1 and 2). When an E-field is applied pointing from the halogen ion towards the Mn(II) ion, it distorts the molecular geometry such that the Mn\u2013X distance increases (Supplementary Table <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">9<\/a>) while the Mn\u2013N bond length decreases. This changes the electronic structure of the molecule such that all energy differences between the orbitals increase, as shown in Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#Fig3\" rel=\"nofollow noopener\" target=\"_blank\">3b<\/a>. Note that this increase is larger in the iodine-containing complex than in the chlorine one due to the larger polarizable character of iodine; that is, a stronger deformation of the electronic cloud induces a larger geometric distortion of the molecule. More importantly and as explained in the Supplementary Information (Supplementary Tables <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">10<\/a>\u2013<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">13<\/a>), the application of an E-field varies the SOCs, leading to a weaker D\u2009&gt;\u20090 contribution by the Ai states and a stronger D\u2009&lt;\u20090 contribution by the Ei states. These two modulations combine constructively and give rise to the overall E-field-induced modulation of D.<\/p>\n<p>The results are summarized in Table <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"table anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#Tab1\" rel=\"nofollow noopener\" target=\"_blank\">1<\/a>. The calculations successfully reproduce the trend observed in experiments, with increasing effects when the halogen is changed from Cl to I. The variations in dipole moment also follow the expected trends (\u0394\u03bce\u2009=\u20092.063 D, 2.194 D and 2.465\u2009D for 1, 2 and 3, respectively; Supplementary Table <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">14<\/a>); that is, a positive (negative) E-field increases (decreases) the dipole moment. As the geometric distortions follow the displacements of the electron cloud, the two effects in cases (1) and (2) add up almost perfectly (Supplementary Table <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">14<\/a>). The comparison of the dipole moments in the spectrochemical series also shows that the E-field-induced effect is stronger for 3 than that for 1, as I\u2212 is more polarizable than Cl\u2212, so applying an E-field leads to a larger distortion in 3 and a stronger modulation of D, despite the SOC constant being stronger for 1.<\/p>\n<p>To check that the effect of the electric field on the crystallographic structures follows the same trend as on the optimized ones, we performed the same analysis (case (1)) on the experimental structures of 1 and 3 (Supplementary Tables <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">15<\/a> and <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">16<\/a>) and found the same results: the variation of the contributions to D follows the variations of the SOCs and can therefore be attributed to changes in the ground- and excited-state wavefunctions. Overall, we can conclude that the structural distortions follow the field-induced deformations of the electron cloud and are therefore stronger for 3 than for 1, as I\u2212 is more polarizable than Cl\u2212. Crucially, our analysis reveals that the distortions to the molecular geometry play the major role for all three molecules<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 22\" title=\"Liu, J. et al. Quantum coherent spin&#x2013;electric control in a molecular nanomagnet at clock transitions. Nat. Phys. 17, 1205&#x2013;1209 (2021).\" href=\"http:\/\/www.nature.com\/articles\/s41557-025-01926-5#ref-CR22\" id=\"ref-link-section-d151643489e3547\" rel=\"nofollow noopener\" target=\"_blank\">22<\/a>.<\/p>\n<p>Finally, we note that, compared to the optimized structures used in the calculation, which are obtained considering single molecules in vacuum, the actual crystal structure contains counterions that can lead to larger distortions. Therefore, it is conceivable that the calculations underestimate the electric-field effect. Nevertheless, the theoretical results are in reasonable agreement with the experimental data.<\/p>\n","protected":false},"excerpt":{"rendered":"The Mn(Me6tren)X compounds The crystallographic structure of Cl derivative 1 is the same as that reported for its&hellip;\n","protected":false},"author":2,"featured_media":102943,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[24],"tags":[24717,13929,49,48,1793,24716,30301,3673,4489,59273,24718,24719,314,66],"class_list":{"0":"post-102942","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-physics","8":"tag-analytical-chemistry","9":"tag-biochemistry","10":"tag-ca","11":"tag-canada","12":"tag-chemical-physics","13":"tag-chemistry-food-science","14":"tag-computational-chemistry","15":"tag-general","16":"tag-inorganic-chemistry","17":"tag-magnetic-materials","18":"tag-organic-chemistry","19":"tag-physical-chemistry","20":"tag-physics","21":"tag-science"},"_links":{"self":[{"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/posts\/102942","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/comments?post=102942"}],"version-history":[{"count":0,"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/posts\/102942\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/media\/102943"}],"wp:attachment":[{"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/media?parent=102942"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/categories?post=102942"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/tags?post=102942"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}