Room-temperature magnetism in two-dimensional metal–organic frameworks enabled by electrostatic gating

Abstract

Two-dimensional (2D) magnetism has attracted intense attention in the area of low-dimensional materials and devices, with intriguing physics emerging and significant potential for applications in energy-efficient data storage and quantum computing. Although a robust magnetic order sustainable under room temperature is the most relevant issue for its practical applications, high temperature magnetism is rarely reported. 2D magnets obtained to date are often exfoliated from van der Waals atomic crystals with bulk magnetism. In this work, we propose a new type of 2D magnets, 2D conjugated metal–organic frameworks (MOFs), which are constructed by magnetic metal ions and conjugated ligands on a honeycomb-kagome lattice. By combining chemical modifications and an electrostatic gating approach, we attain a MOF, Mn₃(THQ)₂ (THQ = tetrahydroxyquinone) possessing the square-planar Mn–O coordination and minimal-sized ligand, which exhibits an ultra-high Curie temperature of 250 K in the neutral monolayer and 300 K in the hole doped one. These findings manifest both chemical and electrical means as powerful tools to tailor the magnetism of 2D MOFs on demand, and further highlights their prospect for applications in ultracompact spintronic devices.

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1. Introduction

With the rapid development of two-dimensional (2D) materials, 2D magnets have attracted much attention for their many intriguing properties and potential applications in new magnetic and spintronic devices.¹ The most exciting news in the field includes discovery of the intrinsic long-range magnetic order in atomically thin layers^2,3 and realization of the electrical control of 2D magnetism.^4–8 The giant magnetoresistance,^9–11 stacking-dependent magnetic properties^12,13 and pressure effects^14,15 have also been observed in van der Waals layered materials and heterostructures. Representative 2D magnetic materials so far fabricated and well characterized include monolayer CrI₃,² Fe₃GeTe₂,⁸ and few-layer Cr₂Ge₂Te₆.³ The Curie temperature has been found to decrease in the 2D limit with respect to the bulk value, and is well below 300 K which severely hampers practical applications of 2D magnets. Indeed, the room-temperature ferromagnetism in ultrathin layers is strongly pursued. Methods that can enhance the magnetic ordering temperature, such as charge doping of Cr₂Ge₂Te₆via electrostatic gating¹⁶ and changing the Fe stoichiometry in Fe₃GeTe₂,^17,18 have been proposed. In addition to van der Waals atomic crystals, a new type of 2D magnets, 2D metal–organic frameworks (MOFs) have caught our attention, which also show attractive properties of high porosity, chemical diversity, and superior conductivity.^19–24 In 2D magnetic MOFs, transition metal ions are incorporated into lattices of various symmetry and linked by conjugated organic ligands through metal–ligand coordination. The large variety of metal ions, organic ligands, and topological structures render 2D MOFs an ideal platform for exploring the low-dimensional magnetism as well as its coupling to other intriguing properties, such as magneto-optics, magneto-electronics and multiferroics. Currently, theoretical investigations of 2D magnetic MOFs mainly focus on those with a Lieb lattice,^25–29 however, the most extensively explored 2D MOFs in experiments are those with a honeycomb-kagome lattice symmetry, whose magnetic properties have not been paid much attention to,^{19,21,30–33} and strong magnetic interactions and high magnetic ordering temperature, T_c, have not yet been reported. The lack of fundamental understanding of the magnetic mechanism, including exchange interactions and magneto-crystalline anisotropy in 2D MOFs significantly slows down the development of new 2D magnets with desired functionalities. In the first place, how metal ions, organic ligands, and coordination atoms impact the magnetic behavior of 2D MOFs is not clear. Secondly, control of the magnetism in 2D MOFs via electric field or electrostatic gating, which is of great relevance to their device applications, has never been proposed. Thereby, tailoring magnetic properties of 2D MOFs on demand by virtue of chemical and electrical approaches is becoming a central topic of the area.

In this work, we perform the first-principles electronic structure calculation and Monte Carlo simulation based on a generalized Heisenberg model to investigate the magnetic properties of 2D MOFs on a honeycomb-kagome lattice. Mn, Fe, and Co divalent ions are incorporated into these MOFs as metal nodes and triphenylene derivatives are organic linkers with O, N, and S as metal coordination atoms, respectively. Among these MOFs, Mn₃(HTTP)₂ (HTTP = 2,3,6,7,10,11-hexahydroxytriphenylene) with the Mn–O coordination exhibits the strongest exchange interaction and out-of-plane magneto-crystalline anisotropy. We unveil that the intralayer FM order originates from the d–π–d super-exchange interaction between metal ions on a kagome sublattice mediated by conjugated organic ligands on a honeycomb sublattice. More interestingly, either electron or hole doping above a critical value can trigger a ferromagnetic (FM) to ferrimagnetic (FIM) transition in it. By substituting HHTP with a minimal-sized organic ligand, tetrahydroxyquinone (THQ), we attain a new 2D MOF, Mn₃(THQ)₂, which exhibits a high Curie temperature of 250 K in the neutral monolayer and 300 K in the hole doped one. These findings manifest both chemical modifications and electrostatic gating as robust tools to control the magnetism in 2D conjugated MOFs.

2. Methods

2.1 DFT calculations

All the electronic structure calculations were performed within the framework of density functional theory (DFT) using the projector augmented-wave (PAW)^34,35 method and the exchange-correlation functional of Perdew–Burke–Ernzerhof (PBE), as implemented in the Vienna ab initio simulation package (VASP 5.4).^36,37 The DFT + U³⁸ method was chosen to treat the Coulomb and exchange interactions between electrons in the localized d-orbitals of transition metals. The Coulomb (U) and exchange (J) interaction parameters were set to be U = 4 eV and J = 1 eV, which have been adopted in previous studies.^{21,25,26,39–41} Our test on the U and J parameters was provided in Fig. S9.† A vacuum space of 20 Å along the z direction was applied. The lattice parameters and atomic positions were fully relaxed until the force on each atom was less than 0.01 eV Å⁻¹. The convergence criteria for the self-consistent-field energy and the energy cutoff for the plane-wave basis were 1 × 10⁻⁵ eV and 600 eV, respectively. The 3 × 3 × 1 Monkhorst–Pack k-mesh in the first Brillouin zone was used to calculate the electronic and magnetic properties of monolayer M₃X₂ (M = Mn, Fe, and Co; X = HHTP, HITP, and HTTP), and the 5 × 5 × 1 k-mesh was used for monolayer Mn₃(THQ)₂. In the calculation of DOS, the 6 × 6 × 1 k-mesh was used for the former and 15 × 15 × 1 k-mesh was used for the latter.

2.2 Monte Carlo simulation

The generalized Heisenberg model was used to describe the magnetic interactions in 2D MOFs and the Curie temperature was derived from the Monte Carlo simulation based on it. For the Hamiltonian given in eqn (4), interactions were restricted to the nearest-neighbor magnetic sites, so J_ij = J and B_ij = B. There were three identical sites in each unit cell of the honeycomb-kagome lattice, so A_i = A too. By mapping the Heisenberg model to total energies of the FM and FIM states calculated from first-principles, we derived the expressions for J, A, and B aswhere N_nn = 4 is the number of nearest-neighbor interactions and n_a = 3 is the number of magnetic sites in a unit cell. E^∥(⊥)_FM(FIM) is total energy of the FM(FIM) state from the first-principles calculation, and the superscripts ‘∥’ and ‘⊥’ represent the in-plane and out-of-plane directions of spin, respectively. MAE_FM(FIM) = E^∥_FM(FIM) − E^⊥_FM(FIM) is the magnetic anisotropy energy of the FM(FIM) state. The specific heat capacity (C_V) can be calculated by . A 20 × 20 supercell was used in the Monte Carlo simulation and the adaptive Metropolis algorithm⁴² was chosen to determine whether a new spin configuration was accepted or rejected. At each temperature, 50 trajectories with each trajectory lasting for 15 000 steps were generated and the final data was averaged over them. The method has been applied successfully to predicting the Curie temperature of monolayer CrI₃.⁴³

3. Results and discussion

3.1 Magnetic ground state of 2D MOFs

We construct a series of 2D conjugated MOFs with the same formula M₃X₂ based on divalent transition metal ions in the third period, M = Mn, Fe, and Co and organic ligands, X = HHTP (2,3,6,7,10,11-hexahydroxytriphenylene), HITP (2,3,6,7,10,11-hexaiminotriphenylene), and HTTP (2,3,6,7,10,11-hexathiolatetriphenylene) in which the coordination atoms are O, N, and S respectively. All these MOFs share the same honeycomb-kagome lattice with organic ligands located on the honeycomb sublattice and metal ions on the kagome sublattice, as shown in Fig. 1a. Their optimized lattice parameters are provided in Table S1.† Three metal ions and two ligands exist in a rhombic unit cell of M₃X₂, and each metal ion is coordinated by four donor atoms (O, N, or S), forming a square-planar configuration. According to the ligand field theory, the five degenerate d-orbitals in transition metal ions will split into four sublevels,^44,45 which are d_xy, d_xz/d_yz, d_z², and d_x²_−y², respectively as shown in Fig. S1.† The magnetism of these MOFs originates from the unpaired d-electrons and associated local spins residing on the transition metal ions. For Mn, Fe, and Co divalent ions, the number of unpaired electrons is 3, 2, and 1 respectively with a spin S = 3/2, 1, and 1/2, which is confirmed by our first-principles calculations. The magnetic ground state is determined by comparing total energies of two possible magnetic states, i.e., ferromagnetic (FM) and ferrimagnetic (FIM) states. We define the intralayer exchange energy as E_ex = E_FIM − E_FM. When E_ex > 0 the system is FM at 0 K and when E_ex < 0 it is FIM. As shown in Table 1, all the MOFs studied are FM in their ground state, whose spin-resolved band structures are shown in Fig. S2.† Both coordination atoms and metal ions have remarkable influence on the magnetic properties of MOFs. For MOFs possessing the same metal node, such as Mn₃(HHTP)₂, Mn₃(HITP)₂, and Mn₃(HTTP)₂, when the coordination atom varies from O to N and to S the E_ex reduces by more than one order of magnitude. A similar trend is observed in Fe₃X₂ and Co₃X₂ (X = HHTP, HITP, and HTTP). Among them, the magnetic exchange interaction in MOFs with Mn–O and Fe–O coordination is the strongest, whose E_ex is 110.84 meV per f.u. and 118.76 meV per f.u., respectively. In the following, we take the Mn–O MOF, Mn₃(HHTP)₂ (Fig. 1b) as an example to elucidate the magnetic mechanism of this new type of 2D magnets and the role of organic ligands in establishing magnetic interactions between metal ions.

Fig. 1 Magnetic ground state of monolayer Mn₃(HHTP)₂. (a) Schematics of 2D conjugated MOFs on a honeycomb-kagome lattice. Blue triangles and red circles represent organic ligands and metal ions, respectively. (b) Unit cell. (c) Total charge density distribution with an isovalue of 0.01 e/Bohr³. (d) Spin-resolved band structure and density of states (DOS) of the FM state. (e) Those of the FIM state. The red and blue lines represent majority and minority spin channels, respectively. The high symmetry k-points are Γ = (0, 0, 0), M = (1/2, 0, 0), and K = (2/3, 1/3, 0). The Fermi level has been shifted to 0.

Table 1 E _ex (meV per f.u.) and MAE (meV per ion, given in the parenthesis) obtained for M₃X₂ with M = Mn, Fe, and Co; X = HHTP, HITP, and HTTP in which the coordination atom is O, N, and S respectively

E ex (MAE)	Mn	Fe	Co
a The FIM state is not stable, which always relaxes to the FM one.
O	110.84 (0.430)	118.76 (−0.101)	97.34 (−0.410)
N	45.66 (0.408)	21.71 (0.308)	26.64 (−0.278)
S	3.57 (0.382)	11.91 (0.271)	N.A.^a (−0.300)

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The total charge density distribution and spin-resolved band structure of Mn₃(HHTP)₂ in its FM ground state are shown in Fig. 1c and d, respectively. The band structure in one spin channel exhibits the typical feature of organic ligands on a honeycomb lattice: four bands sit right above the Fermi level E_F, with the bottom and top ones completely dispersionless and the middle two crossing at the K point.^46,47 The partial density of states (pDOS) analysis confirms that the four electronic bands arise primarily from the p_z orbitals of C and O atoms in the organic ligands, with a small contribution from the d_xz and d_yz orbitals of Mn ions, forming the π–d conjugation. As evidenced by the partial charge density distribution at the M and K points in the Brillion zone (Fig. S3†), the bottom flat band coinciding with E_F arises mainly from the π orbitals isolated on the organic ligands with destructive interference, which was previously observed in a Cu-hexaiminobenzene framework, Cu₃(HAB)₂ where dichotomy between local spins and conjugated electrons was demonstrated.⁴⁷ The d-bands of three Mn ions on the kagome lattice show a typical feature of ‘one flat and two dispersive bands’ and are located far from the Fermi level (Fig. S4†). In the other spin channel, a bandgap of 1.80 eV shows up indicating that Mn₃(HHTP)₂ is a half metal. The metastable FIM state of Mn₃(HHTP)₂ is semiconducting with a bandgap of 0.178 eV in one spin channel while 0.051 eV in the other (Fig. 1e).

To understand the magnetic interactions in Mn₃(HHTP)₂, we plot the spin density isosurface in Fig. 2a. In the FM state, the spins residing on all three Mn ions are identical with S = 3/2, corresponding to the three unpaired d-electrons in each ion. And the spins on metal ions and organic ligands align in opposite directions, indicating the antiferromagnetic coupling between them. Since the distance between two nearest-neighbor Mn ions is 10.86 Å, the direct Coulomb exchange⁴⁸ is impossible. Because the three unpaired d-electrons are localized on d_xz/d_yz and d_z² orbitals of Mn ions (Fig. S1†), we propose two super-exchange pathways responsible for the FM order in Mn₃(HHTP)₂. One is established between d_xz/d_yz orbitals of Mn ions mediated by p_z orbitals of neighboring O and C atoms in the organic ligands (Fig. 2b). Here t_dp,t_π, and J_π represent the hopping integral between d_xz/d_yz and p_z orbitals, that between two p_z orbitals, and Coulomb exchange between two p_z orbitals, respectively. The other pathway is established between two d_z² orbitals of Mn ions, as illustrated in Fig. 2c. In this case, the direct kinetic exchange between d_z² of Mn and p_z of O is prohibited because they are orthogonal to each other, but the kinetic exchange between d_z² of Mn and p_x of O, together with Hund's coupling between p_x and p_z of O, enables the super-exchange coupling between two d_z² orbitals of Mn ions. As such, the ferromagnetic interaction between metal ions will be affected significantly by the transition matrix element t_dp, whose magnitude can be illustrated by the degree of π–d conjugation. We have obtained charge and spin density distributions (Fig. S5†) as well as the metal coordination bond length (Table S2†) in the secondary building units (SBUs)⁴⁹ of Mn MOFs. It shows that the π–d conjugation diminishes when the coordination atom goes from O to N and to S. Accordingly, the exchange energy E_ex in Mn₃X₂ (X = HHTP, HITP, and HTTP) decreases in the same order (Table 1). Similar results were also observed in metal-phthalocyanine-based 2D MOFs.²⁶

Fig. 2 Magnetic exchange mechanism and magnetic transition in monolayer Mn₃(HHTP)₂. (a) Spin density isosurface with an isovalue of 0.01 e/Bohr³. The majority and minority spins are colored in yellow and cyan, respectively. (b and c) Two ferromagnetic super-exchange pathways proposed. (d) Normalized spin per Mn ion and heat capacity changing with the temperature from the Monte Carlo simulation.

3.2 Curie temperature T_c of 2D MOFs

The magnetic exchange coupling tends to align neighboring spins at 0 K. As the temperature goes up, thermal fluctuations will destroy this long-range magnetic order and the system undergoes a phase transition above a critical temperature (T_c). The influence of thermal fluctuations depends on the dimensionality of a system. In a 3D system, the transition always occurs at a finite temperature. However, in a 1D system the macroscopic magnetic order cannot be retained at any finite temperature. In a 2D system, whether a phase transition occurs relies on the spin dimensionality,⁵⁰ which is defined as the number of spin components involved in the magnetic interaction and also known as the magnetic anisotropy. The magnetic interactions in a system can be described by a Heisenberg model, and for a 2D magnet the Mermin–Wagner–Hohenberg theorem⁵¹ states that the magnetic anisotropy plays a key role in keeping the magnetic order from the detrimental effect of thermal fluctuations; a 2D isotropic Heisenberg model with the spin dimensionality of three predicts no long-range magnetic order at any finite temperature. Here we use a generalized Heisenberg model of the form⁵²to represent the magnetic interactions in 2D MOFs on a honeycomb-kagome lattice. In this Hamiltonian, J_ij is the isotropic exchange between two nearest-neighbor magnetic sites i and j, A_i and B_ij denote the single-ion anisotropy and anisotropic exchange interaction for the spin component along the z axis, respectively. The summation runs over all the local spins, i.e., the metal ions on a kagome lattice. The extreme case of A_i = 0 and B_ij = 0 in this Hamiltonian restores the isotropic Heisenberg model, and another extreme case of J_ij = 0 and A_i = 0 corresponds to 2D Ising model for which the exact T_c > 0 has been solved by Onsager.⁵³ We can derive J_ij from the first-principles total-energy calculations of 2D MOFs in the FM and FIM states. It is directly related to the exchange energy E_ex defined earlier. When the spin–orbit coupling effect is taken into consideration, magnetic configurations where spins align along the in-plane (x/y) or out-of-plane (z) directions are no longer degenerate, which allows us to derive A_i and B_ij from the first-principles calculations. The relative energies of each MOF with different magnetic configurations: E^∥_FM, E^⊥_FM, E^∥_FIM, and E^⊥_FIM are summarized in Table S3.† The magnetic anisotropy energy (MAE) is defined as the energy difference between magnetic configurations with either in-plane or out-of-plane spin orientations: MAE = E^∥ − E^⊥. The MAEs for the FM state have been included in Table 1. It shows that the MAE in monolayer Mn₃(HHTP)₂ is 0.430 meV per ion and that in Fe₃(HHTP)₂ is −0.101 meV per ion. The single-ion anisotropy parameter A_i and anisotropic exchange parameter B_ij together reflect the magnetocrystalline anisotropy, and they can be related to the MAEs of both FM and FIM states (see methods for the expressions of A_i and B_ij). The sign of A_i is the same as MAE: A_i > 0 means MAE = E^∥ − E^⊥ > 0 so the spin tends to align along the out-of-plane direction as in Mn₃(HHTP)₂, while A_i < 0 means MAE = E^∥ − E^⊥ < 0 so the spin aligns along the in-plane direction as in Fe₃(HHTP)₂. It turns out that the exchange anisotropy B_ij is so trivial that it has a negligible influence on T_c (Table S4†). As a result, we can further simplify the Heisenberg model by considering only the single-ion anisotropy.

With all the parameters in the Heisenberg model derived, we predict T_c for 2D MOFs by performing Monte Carlo simulations. The normalized spin along the z-axis, S^z and the specific heat capacity, C_v at different temperatures are shown in Fig. 2d for Mn₃(HHTP)₂ whose easy axis is apparently the z-axis. The S^z drops abruptly to zero above a critical temperature T_c, and concurrently C_v diverges there. Since the magnetic couplings in Mn₃(HHTP)₂ and Fe₃(HHTP)₂ with Mn–O and Fe–O coordinations are the strongest of all, their Curie temperatures T_c are also the highest, 100 K and 105 K, respectively. The evolution of S^x and S^y with temperature is shown in Fig. S6a† for Mn₃(HHTP)₂. Both are nearly zero in the whole range of temperatures, which corroborates with the strong magnetocrystalline anisotropy along the z-axis. By contrast, S^x and S^y are almost identical and much larger than S^z in Fe₃(HHTP)₂ when T < T_c (Fig. S6b†), exhibiting the in-plane magnetic anisotropy.

3.3 Magnetic modulation by chemical modifications

The Curie temperature of above-mentioned 2D MOFs is still far below the room temperature. We have learned that when the magnetic anisotropy is similar, the exchange coupling will be the determining factor of the magnetic transition temperature, and the stronger coupling often leads to the higher T_c. For example, the exchange energy of Mn₃(HHTP)₂ is 110.84 meV per f.u. and T_c is 100 K, while that of Mn₃(HTTP)₂ is 3.57 meV per f.u. and T_c is 5 K (Table S4†). So, we should enhance the exchange coupling in 2D MOFs for its ferromagnetic order to sustain at a higher temperature, which is crucial for their practical applications. Since the ferromagnetism in monolayer Mn₃(HHTP)₂ originates from the super-exchange coupling between the metal d-electrons mediated by the itinerant π-electrons in organic ligand, we reasonably presume that replacement of conjugated organic ligands with small-sized ones would shorten the distance between magnetic metal ions and remarkably enhance their super-exchange interaction. MOFs constructed by small-sized organic ligands, such as hexathiolbenzene (HTB),^24,54–60 hexaiminobenzene (HIB)^23,61,62 and tetrahydroxyquinone (THQ)^63,64 have been reported, and they show many intriguing properties ranging from topological insulators and hydrogen evolution activity to high electrical conductivity, superconducting, and photo-induced charge transport. In particular, spin arrangements on the kagome lattice lead to strong geometrical magnetic frustration in Cu₃(THQ)₂.⁶⁴ Moreover, monolayer Mn₃(HTB)₂ and Mn₃(HIB)₂ with the square-planar Mn–S and Mn–N coordination, respectively, were predicted to be a half-metallic ferromagnet with T_c of about 212 K⁵⁶ and 450 K⁶⁵ based on the Ising model. Our results on M₃X₂ (X = HHTP, HITP, and HTTP with O, N, and S as coordination atoms, respectively) show that the Mn–O coordination possesses stronger π–d conjugation and exchange coupling than the Mn–S coordination. Therefore, we design a new MOF, Mn₃(THQ)₂ (Fig. 3a) with both the Mn–O coordination and the minimal-sized conjugated ligand, which should exhibit stronger magnetic coupling and higher T_c than Mn₃(HHTP)₂ and Mn₃(HTB)₂. Indeed, our calculations confirm that monolayer Mn₃(THQ)₂ is FM in its ground state and the exchange energy E_ex is 295.31 meV per f.u., more than twice that of Mn₃(HHTP)₂, which unequivocally manifests chemical modifications as an effective approach to modulate the magnetism of 2D MOFs. The charge and spin density distributions of Mn₃(THQ)₂ and simulated scanning tunneling microscopy (STM) topographies of Mn₃(THQ)₂ surfaces are plotted in Fig. S7.† The STM topography with a bias of 0 eV clearly exhibits the honeycomb feature, corresponding to the itinerant electrons of organic ligands. At the bias of −2.21 eV below the Fermi level, a kagome pattern is observed, representing the d-electrons of metals ions. The subsequent Monte Carlo simulation based on the generalized Heisenberg Hamiltonian and a new set of parameters derived from the first-principles calculations predict T_c to be 250 K (Fig. 3b), substantially higher than 100 K predicted for Mn₃(HHTP)₂. This T_c of 250 K is even higher than the highest ferromagnetic ordering temperature of 225 K⁶⁶ reported for MOFs, and the latter was observed in a mixed-valence 3D MOF Cr(tri)₂(CF₃SO₃)_0.33 (tri = 1, 2, 3-triazole). According to previous studies of van der Waals magnetic crystals including CrI₃,² Fe₃GeTe₂,^8,67 FePS₃,⁶⁸ and CrGeTe₃,³ the critical temperature T_c decreases as the layer thickness is reduced from 3D to 2D, so we anticipate the new MOF to show even higher T_c in its bulk form. Monolayer Mn₃(THQ)₂ is half metallic in its FM ground state with no bandgap in one spin channel while a bandgap of 1.51 eV in the other (Fig. 3c), and it is fully metallic in the FIM metastable state (Fig. 3d).

Fig. 3 Magnetic properties of monolayer Mn₃(THQ)₂. (a) Unit cell. (b) Normalized spin per Mn ion and heat capacity changing with the temperature from the Monte Carlo simulation. (c) Spin-resolved band structure and pDOS of the FM state. (d) Those of the FIM state. The red and blue lines represent majority and minority spin channels, respectively. The high symmetry k-points are Γ = (0, 0, 0), M = (1/2, 0, 0), and K = (2/3, 1/3, 0). The Fermi level has been shifted to 0.

3.4 Magnetic modulation by electrostatic gating

In addition to chemical modifications, which range from metal and coordination atom substitutions to the varying size of conjugated organic ligands, modulating the magnetism of 2D MOFs by physical means such as the application of an electric or magnetic field is also highly desirable and holds great promise for their device applications. Recently, the electrical control of magnetism has been realized in 2D CrI₃ (ref. 4,7) and Cr₂Ge₂Te₆.⁶ Both electric field and electrostatic gating approaches have been proved effective in these 2D magnets. Here we demonstrate modulation of the magnetism in monolayer Mn₃(HHTP)₂ and Mn₃(THQ)₂ by electrostatic gating and unravel the mechanism behind it.

In the experimental set-up of electrostatic gating, charge carriers are injected into 2D magnets by applying a gate voltage. We calculate total energies of the charged monolayer of MOFs in their FM and FIM states, respectively, following the method proposed by Reed and co-workers in their study on the structural phase transition in 2D transition metal dichalcogenides induced by electrostatic gating.⁶⁹ The energy difference between FM and FIM states, namely, the exchange energy E_ex = E_FIM − E_FM of atomically thin Mn₃(HHTP)₂ has been obtained as a function of the doping charge density (Fig. 4a). It shows that either the hole or the electron doping can trigger a transition from the FM to FIM state, when a critical hole density of 1.87 e per f.u. (4.58 × 10¹³ e cm⁻²) or electron density of 1.32 e per f.u. (3.22 × 10¹³ e cm⁻²) is reached. Now we consider a capacitor structure^70,71 with the monolayer of Mn₃(HHTP)₂ deposited on top of the dielectric layer consisting of 5 nm HfO₂ and sandwiched between two parallel metal plates, on which a gate voltage is applied. The voltage required to trigger the transition is then estimated by where is the critical charge density, d = 5 nm is the thickness and ε_r = 25 is the relative permittivity of HfO₂ dielectric, and ε₀ is the permittivity of vacuum (8.854 × 10⁻¹² F m⁻¹). The critical voltage of 1.66 V and −1.16 V is obtained for hole and electron injection, respectively, which is far below the experimental breakdown voltage for HfO₂ dielectric of similar thickness.⁶⁹

Fig. 4 Controlling the magnetism in monolayer Mn₃(HHTP)₂ and Mn₃(THQ)₂ by electrostatic gating. (a and c) Intralayer exchange energy E_ex = E_FIM − E_FM as a function of the doping charge density in (a) Mn₃(HHTP)₂ and (c) Mn₃(THQ)₂. The positive or negative charge density denotes extra hole or electron injected to the system. (b and d) DOS of the FIM and FM states in (b) Mn₃(HHTP)₂ and (d) Mn₃(THQ)₂. The red and blue lines represent majority and minority spin channels, respectively. The Fermi level has been shifted to 0.

The neutral monolayer of Mn₃(HHTP)₂ is FM in its ground state, and the energy difference between FM and FIM states decreases with charge doping (Fig. 4a). When the charge density reaches a critical value, the order of their energies is reversed and the ground state becomes FIM. This result can be understood from the total DOS of neutral Mn₃(HHTP)₂ in Fig. 4b. When the electron is injected into it, the empty electronic states above the Fermi level will be occupied in the first place. Mn₃(HHTP)₂ is a half metal in the FM state, with vanishing band gap in one spin channel whereas a wide band gap in the other channel. If one electron per formula unit is injected, the Fermi level will be lifted by +0.15 eV, where a crossing of two dispersive bands leads to abruptly reduced DOS. If the electron is further injected, it will occupy higher electronic states and the energy gain of the charged monolayer will be slowed down. In contrast, although in the FIM state there exist small band gaps in both spin channels, more low-lying unoccupied electronic states are available for both channels. If the same amount of electron is injected, the energy will decrease more rapidly. As a result, the magnetic ground state turns FIM when a critical amount of electron is injected. For the positively charged monolayer, the electron is to be removed from the occupied valence bands. There are much more states available right below the Fermi level in the FIM state than the FM one. Therefore, removal of electron in the FM state costs more energy than the FIM one, leading to more energy increase in the former which will trigger the FM-to-FIM transition when the hole density reaches a critical value.

When it comes to monolayer Mn₃(THQ)₂ (Fig. 4c), the exchange energy decreases upon the electron doping, but the FM-to-FIM transition does not show up even after a large amount of electron is injected. While upon the hole doping, the exchange energy first increases then decreases. We can understand these results from the total DOS (Fig. 4d): there are more low-lying electronic states available above the Fermi level in the FIM than the FM state, so when the same amount of electron is injected, there will be more energy gain in the former, leading to the decreased energy difference between them. Whereas in the case of hole doping, since there exist more occupied electronic states right below the Fermi level in the FM state than the FIM one, when the electron is removed, there will be less energy cost in the former, leading to the increased energy difference between them at the start. However, an energy gap shows up below these states in the FM state, so when more electron is removed, there will be more energy cost, causing the decreased energy difference thereafter. When the hole doping density reaches 1.5 e per f.u., which amounts to 9.89 e cm⁻² and can be realized by applying a gate voltage of 3.58 V based on the same capacitor model mentioned above, the energy difference between FM and FIM states, which is also known as the exchange energy, exhibits a maximum of 341.19 meV. If we ignore the effect of hole doping on the magnetic anisotropy, a T_c up to 300 K can be anticipated for the positively charged monolayer of Mn₃(THQ)₂ (Figure S8†).

4. Conclusions

To conclude, we have studied the magnetism of a new type of 2D materials, 2D conjugated MOFs with a honeycomb-kagome lattice symmetry, and unveiled how the magnetism is affected by the transition metal ions, coordination atoms, and the size of organic ligands. We demonstrate that the π–d conjugation between metal ions and organic linkers in 2D MOFs is essential for the long-distance magnetic interaction and communication. For 2D MOFs, high spin states of metal ions, strong couplings between the d-orbitals of metal ions and the p-orbitals of coordination atoms, and short distance between adjacent metal ions are required to facilitate efficient super-exchange interactions. We design a new MOF, Mn₃(THQ)₂, with the Mn–O coordination and shortest distance between adjacent metal ions to enhance the magnetic couplings between them, and it exhibits an ultra-high Curie temperature of 250 K. Other than the 2D MOFs studied here, MOFs with organic radical linkers or those combining 3d transition metal ions with high electron spins and 4d/5d transition metal ions with large spin–orbit couplings to enhance the magnetic interaction and magnetic anisotropy are also proposed to show the high temperature magnetism.⁷² The interlayer stacking and magnetic couplings can lead to the layer-dependent magnetism in 2D MOFs, which is of great interest for future studies. In addition to chemical modifications, we find that electrostatic gating offers an alternative route to modulate the magnetism of 2D MOFs. The charge doping above a critical value, which can be achieved by applying a gate voltage of a few volts, can either trigger a FM-to-FIM transition or enhance the magnetic couplings in 2D MOFs to attain the room-temperature ferromagnetism. As compared to the magnetic field, the voltage control of magnetism is more precise and convenient, which has technical importance for developing energy-efficient data storage. The successful modulation of magnetism in 2D MOFs by both chemical and electrical approaches, as showcased here, provides new opportunities for exploring applications of 2D magnets in ultracompact electrically controlled spintronic devices such as spin valves, magnetic tunnel junctions, and spin field-effect transistors.

Author contributions

D. W. supervised this study. Q. Y. performed all the calculations. D. W. and Q. Y. discussed the results and co-wrote the paper. All authors have given approval to the final version of the manuscript.

Conflicts of interest

The authors declare no conflicts of interests.

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 22073055). Computational resources are provided by the Tsinghua Supercomputing Center.

Notes and references

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d2ta08540b

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