Supporting information. Realizing Two-Dimensional Magnetic Semiconductors with. Enhanced Curie Temperature by Antiaromatic Ring Based

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1 Supporting information Realizing Two-Dimensional Magnetic Semiconductors with Enhanced Curie Temperature by Antiaromatic Ring Based Organometallic Frameworks Xingxing Li and Jinlong Yang* Department of Chemical Physics, Hefei National Laboratory for Physical Sciences at the Microscale, and Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei, Anhui , China. Computational method Theoretical simulations are carried out by using the PBE-D3 functional 1-3 with strong-correlation correction 4 implemented in Vienna ab initio simulation package (VASP). 5 The Coulomb interaction parameter (U) and exchange interaction parameter (J) are set to 4.0 and 1.0 ev, respectively. 6 For accurate calculations of magnetic and electronic properties, we adopt the well-performed hybrid HSE06 functional. 7,8 The projector augmented wave (PAW) potential 9 is employed with a planewave cut-off energy of 520 ev. Monkhorst-Pack k-point meshes of and are used for structure optimization and property calculation, respectively. The criterion for convergence of total energy and fore are set as ev and 0.01 ev/å, respectively. To investigate the thermodynamic stability of designed organometallic frameworks at PBE+U level, phonon band structure is calculated with finite displacement method by the Phonopy package 10 interfaced to VASP, and ab initio molecular dynamics (AIMD) are performed in NVT ensemble, which last for 14 ps with a timestep of 1 fs. 2D Cr-pentalene organometallic lattice with pristine, fully fluorinated and hydroxylated pentalene rings Test calculations show that with pristine pentalene, 2D Cr-pentalene MOF in which pentalene rings all rotate by 90 is a magnetic metal rather than a magnetic semiconductor, mainly due to the strongly covalent nature of Cr-C bonds and highly conjugated network [Figure S1(a)]. To induce semiconducting property, a viable route is to increase the Cr-C bond ionicity by introducing electron-withdrawing groups on the pentalene ring, such as fluorination. Indeed, based on fluorinated pentalene, 2D Cr-pentalene MOF becomes a semiconductor, resulting from the enhanced charge transfer from Cr to pentalene (~ 0.1e from Bader charge analysis), and also the reduction of conjugation by staggered torsion of neighboring pentalene rings [Figure S1(b)]. Other electronegative groups like OH are also applicable to achieve semiconducting property (Figure S2). For simplicity, the 2D MOF with fluorinated pentalene is still labeled as 2D Cr-pentalene. S1

2 Figure S1. Test calculations on 2D Cr-pentalene organometallic lattice with (a) pristine and (b) fully fluorinated pentalene rings at PBE+U level. Insets are the optimized structures. The 2D Cr-pentalene with pristine pentalene is characterized by 90 rotation of all pentalene rings and behaves as a magnetic metal, while after fluorination, 2D Cr-pentalene becomes a magnetic semiconductor with staggered torsion of neighboring pentalene rings with a rotation angle of 63. Fermi levels are all set to zero. Figure S2. Test calculations on 2D Cr-pentalene organometallic lattice with fully hydroxylated pentalene rings at PBE+U level. The (a) optimized structure and (b) density of states are given. Like fluorination, a magnetic semiconductor property is obtained. Besides, a hydrogen bonding network with bond lengths of and Å is observed. Fermi level is set to zero. 2D organometallic lattice with transition metals other than Cr We have tested other transition metals (V, Mn-Ni) in the similar lattice structure of 2D Crpentalene, and found that except the paramagnetic 2D Ni-pentalene, they are all magnetic metals with significant exchange energies. As an example, 2D Mn-pentalene is predicted to be a half metal with an exchange energy of ev per unit cell (see Figure S3). These materials may be useful for developing 2D magnetic metals, but are beyond the theme of 2D magnetic semiconductors in this communication. S2

3 Figure S3. The density of states for 2D Mn-pentalene at PBE+U level. Fermi level is set to zero. 2D hexagonal or triangular organometallic lattice We have explored the possibility of 2D Cr-pentalene in a hexagonal or triangular lattice. Triangle lattice with six surrounding pentalene rings around each Cr atom is not stable and tends to be dissociated after structure optimization due to the steric hindrance effect among neighboring pentalene rings. Whereas stable hexagonal lattice where each Cr atom is coordinated to three pentalene rings is attainable 11 (see Figure S4), the material itself is predicted to be paramagnetic with tiny induced magnetic moment on pentalene rings and very small exchange energy (~ 10 mev), thus is excluded for further study. Figure S4. Optimized structure for 2D Cr-pentalene in a hexagonal lattice. Purple, grey and cyan balls represent Cr, C and F atoms, respectively. Thermal stability of 2D Cr-pentalene By applying ab initio molecular dynamics (AIMD) in NVT ensemble, we investigate the thermal stability of free-standing 2D Cr-pentalene at 200 and 300 K, respectively. As shown in Figures S5 (a) and S5 (b), during 200 K AIMD, the temperature and total energy all fluctuate around their equilibrium values with the spin magnetic moment and structure kept well, indicating 2D Crpentalene in its free-standing state is thermally stable at 200 K. While at 300 K, we observe a trend of dimerization of neighboring pentalene rings [indicated by the blue circle in the snapshot structure of Figure S5 (c)], accompanied by a sudden jump of spin magnetic moment from 16 to 18 μ B [Figure S5 (d)]. When 2D Cr-pentalene is implemented in a practical semiconductor device, there will be insulating dielectrics surrounding it. Therefore, it is more realistic to consider the stability of 2D Cr- S3

4 pentalene when dielectrics exist. As an example, we sandwich the 2D Cr-pentalene between two insulating hexagonal BN sheets [Figure S6 (a)] and investigate its thermal stability by performing AIMD at 300 K. From the results in Figures S6 (b) and S6 (c), it is clear no jump of spin magnetic moment and structure destruction occur, indicating the encapsulated 2D Cr-pentalene stabilizes at room temperature. The underlying mechanism may be that the interaction between BN sheet and 2D Cr-pentalene hinders the pentalene rings to move together and dimerize. Noe that the structure of 2D Cr-pentalene sandwiched between BN sheets becomes flatter with the rotation angle changing from 63 in the free-standing state to 43, while the magnetic semiconductor property remains with a somewhat bigger exchange energy (-2.01 ev) compared to the free-standing one (-1.97 ev). Above all, 2D Cr-pentalene is expected to be working as a magnetic semiconductor at room temperature when insulating dielectrics such as hexagonal BN sheets are integrated around. Figure S5. Ab initio molecular dynamics (AIMD) for free-standing 2D Cr-pentalene. (a) and (b) are the fluctuation of temperature, total energy and spin magnetic moment at 200 K, while (c) and (d) are those at 300 K. Insets are the snap shots at 0 and 14 ps, respectively. S4

5 Figure S6. Ab initio molecular dynamics (AIMD) for 2D Cr-pentalene sandwiched between two hexagonal BN monolayer sheets. (a) Top (left panel) and side (right) views of the BN/Crpentalene/BN sandwich structure. The supercell structure consists of 4 unit cells of 2D Cr-pentalene and 112 unit cells of BN in each layer with a lattice mismatch of ~ 1%. The equilibrium distance d is determined to be around 4.5 Å. (b) and (c) are the fluctuation of temperature, total energy and spin magnetic moment at 300 K AIMD. Insets are the snap shots at 0 and 14 ps, respectively. Easiness of spin polarization of antiaromatic rings in 2D organometallic lattices To give a quantitative measurement for the easiness of spin polarization of antiaromatic rings in the designed 2D organometallic lattices, we evaluate the spin polarization energy of antiaromatic rings, which is defined as the energy difference between the ground ferrimagnetic state and the magnetic state where the antiromantic rings are paramagnetic with little moments while keeping the spins of transition metals (see Figure S8). The spin polarization energy for pentalene is determined to be ev per unit cell, while it is and ev per unit cell for cyclobutadiene and s- indacene, respectively. These positive values directly indicate antiaromatic rings prefer to be spin polarized in the 2D organometallic lattices. S5

6 Figure S7. The spin charge density for an intermediate magnetic state where the antiromantic rings are little spin polarized. The isovalue is set as 0.05 e/å 3. Red and blue indicate up and down spins, respectively. Purple, grey and cyan balls represent Cr, C and F atoms, respectively. Distribution of magnetic moment on pentalene rings Figure S8. Side-viewed plot of spin magnetic charge density of ferrimagnetic state for 2D Crpentalene with an isovalue of 0.05 e/å 3. Red and blue indicate up and down spins, respectively. Purple, grey and cyan balls represent Cr, C and F atoms, respectively. Magnetic coupling mechanism Figure S9. The scheme of magnetic coupling for (a) our proposed materials and (b) traditional ferromagnetic semiconductors. In our proposed materials, the strong direct exchange J 0 determines the magnetic coupling, while it is missing in traditional ferromagnetic semiconductors and only the S6

7 weak 90 superexchange J 1 exists. 2D organometallic lattice constructed by cyclobutadiene with 4 п electrons and s- indacene with 12 п electrons Figure S10. The study of 2D organometallic lattice constructed by cyclobutadiene (fluorinated) with 4 п electrons at HSE06 level. (a), (b) and (c) are the optimized structure, classic Heisenberg model Monte Carlo (MC) simulation and density of states. Fermi level is set to zero. With a ferrimagnetic Curie temperature of 640 K, 2D Cr-cyclobutadiene is a bipolar magnetic semiconductor with a gap of 2.26 ev. Bipolar magnetic semiconductors feature in oppositely spin polarized valence band and conduction band edges. Figure S11. The study of 2D organometallic lattice constructed by s-indacene (fluorinated) with 12 п electrons at HSE06 level. (a), (b) and (c) are the optimized structure, classic Heisenberg model Monte Carlo (MC) simulation and density of states. Fermi level is set to zero. With a ferrimagnetic Curie temperature of 453 K, 2D Cr- s-indacene is nearly a spin gapless semiconductor with a tiny gap of 0.09 ev. The deduction of eq (2) In eq. (2), the factor 16 emerges as follows: In the unit cell of 2D Cr-pentalene, there are eight exchange interactions between Cr and pentalene. Thus, the magnetic energy for ferrimagnetic (FIM) and ferromagnetic (FM) states can be written as E(FIM) = 8J S 1S 2, E(FM) = -8J S 1S 2, respectively, where S 1 = 2 and S 2 = 1/2 is the spin value for Cr and pentalene, respectively. Therefore, the exchange parameter J can be obtained as J = [E(FIM) E (FM)]/16 = E ex/16. S7

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