Controllable half-metallicity in MnPX3 monolayer

Spintronics, which is based on the spin degree of freedom, is a field of science and technology that will most likely have a significant impact on the future electronics. Among various spintronic materials, one of the most promising candidates is half-metal (HM)^1,2, which has the ability to provide 100% spin-polarized electrons due to its special band structure, i.e., one spin channel is metallic and the other is semiconducting^3,4,5,6,7. According to the previous reports, HM can be obtained in the semi-Heusler alloys^8,9, the manganese perovskites¹⁰, and the oxides such as chromium dioxide and magnetite^11,12,13, etc.

Recently, with the rapid development of two-dimensional (2D) materials^14,15,16, many 2D HM has been reported^{17,18,19,20,21,22}. One outstanding approach to obtaining 2D HM is based on a new type of semiconductor, i.e., bipolar magnetic semiconductor (BMS)²³, whose conductance band minimum (CBM) and valence band minimum (VBM) have full spin polarization with opposite directions. In BMS, ±100% spin-polarized HM and the switching between them can be easily obtained by applying positive/negative gate voltage (hole/electron doping). In 2023, we reviewed the development of 2D BMS²⁴. Until now, some intrinsic 2D BMS have been proposed, for example, 2H-VX₂ (X = S and Se)^25,26, GdI₂²⁷ and NbS₂²⁸, etc. To obtain more BMS, various approaches have been proposed to tailor BMS band structures^{29,30,31,32,33,34}. For example, BMS can be obtained in 2D AFM by destroying the balance of the crystal field of the antiferromagnetically coupling magnetic ions^{35,36,37,38,39,40}. A typical case is that 2D AFM semiconductor Cr₂TiC₂ becomes a BMS by adsorbing F and Cl atoms on its top and down surfaces, respectively^35,36.

Layered transition-metal phosphorus trichalcogenides MPX₃ (M = Mn, Fe, Ni, and V; X = S, Se, and Te)⁴⁰ are an important family of materials that can be exfoliated in two dimensions. MnPSe₃ monolayer has been characterized experimentally⁴¹, and has attracted much attention due to its excellent electrical and magnetic properties^42,43,44,45. Interestingly, 2D MnPSe₃ has achieved AFM-FM transition through strain³⁸ or carrier doping^39,40. In this work, we investigate the magnetic properties of MnPSe₃ monolayer adsorbed by Li and F atoms and MnPS₃ contacting with Au(111), using density-functional theory (DFT). We find that both MnPSe₃ and MnPS₃ monolayers can become half-metallic, due to the extra charge they obtain from surroundings.

Ground states of MnPS₃ and MnPSe₃

Due to the weak interlayer van der Waals (vdW) force, 2D MnPX₃ (X = S and Se) can be easily exfoliated^41,46. The unit cell of the MnPX₃ monolayer is composed of two Mn²⁺ and one [P₂Se₆]⁴⁺ cluster⁴⁷. The side view of MnPX₃ can be seen in Fig. 1a. We optimize the lattice structure of MnPX₃ monolayer and obtain the lattice constants of MnPSe₃ about 6.387 Å and MnPS₃ about 6.080 Å, which are in good agreement with the experimentally reported values of 6.402 Å for MnPSe₃³⁹ and 5.997 Å for MnPS₃⁴⁰. Although FM MnPX₃ shown in Fig. 1b is not the ground state, several approaches have been proposed to induce AFM-FM transition in MnPX₃. For example, gate modulation through hole/electron doping can induce AFM-FM transition in MnPSe₃³⁹. In addition, in the multiferroic MnPS₃/Sc₂CO₂, AFM-FM transition in MnPS₃ can be tuned by reversing the ferroelectric polarization direction of Sc₂CO₂⁴⁸. In Fig. 1c, we summarize the approaches that can induce AFM-FM transition in MnPX₃, in which adsorption doping and metal contract will be discussed in our present work.

a, b The side views of AFM and FM monolayer MnPX₃ (X = S and Se), in which the red/blue arrows represent the spin-up and -down, respectively. c The transition from AFM to FM MnPX₃ by gate doping, multiferroic heterostructure, adsorption doping, and metal contact.

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According to the calculation, the total energy of AFM MnPSe₃ is lower than that of the FM state by about 40.10 meV/unit cell (u.c.). We plot the band structures of AFM and FM MnPSe₃, as shown in Fig. 2a, b, respectively. We can see that the band gap of AFM MnPSe₃ is obviously larger than that of FM MnPSe₃. In addition, we notice that the CBM and VBM of FM MnPSe₃ have the opposite spin polarization, which means that FM MnPSe₃ is a BMS. Fig. 2c, d show the band structures of AFM and FM MnPS₃, which are similar to MnPSe₃. The total energy of AFM MnPS₃ is lower than that of the FM state by about 54.77 meV/u.c.

AFM and FM band structures of a, b MnPSe₃ and c, d MnPS_3. Blue and red represent spin-down and -up states, respectively.

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Half-metallic ferromagnetism in the Li- and F-doped MnPSe₃

In order to study the adsorption effects on the electronic structures of 2D MnPSe₃, we construct 2 × 2 × 1 supercells, as shown in Fig. 3, in which solid blue circles represent the Li/F atoms and the red diamond indicates the unit cell of MnPSe₃. Adsorption sites of Li/F on the top of P, Mn, and Se atoms are all considered. Fig. 3a–d shows the atomic structures of Li/F adsorption on the top of P atoms with concentrations of 25%, 50%, 75%, and 100%, respectively. The atomic structures of the MnPSe₃ monolayer with Li/F atoms on the top of Se and Mn atoms can be seen in Figs. S1 and S2, respectively. According to the total energy, Li/F adsorptions on the top of P atoms are more stable.

Atomic structures of MnPSe₃ monolayer with different Li/F atoms adsorption concentrations: a 25%, b 50%, c 75%, and d 100%.

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We also check the ground states of MnPSe₃ with different adsorption concentrations. According to the total energy calculation, FM MnPSe₃ is more stable with Li/F adsorption, as can be seen in Table 1. For the Li adsorption, ΔE is from 45.8 to 85.7 meV, and for the F adsorption, ΔE is from 28.8 to 155 meV. For both Li and F adsorptions, all the concentrations, including 25%, 50%, 75%, and 100%, can induce AFM-FM transition in MnPSe₃. With the increasing concentration from 25% to 100%, the Bader charge linearly increases from 0.224 to 0.868 e/u.c. for the Li adsorption and −0.175 to −0.683 e/u.c. for the F adsorption. In the previous reports³⁹, electron, and hole doping with the carrier concentration of 1.4 × 10¹⁴ cm⁻² can induce AFM/FM transition in MnPSe₃. It is clear that the Bader charge induced by the Li/F adsorption exceeds the electron and hole doping mentioned above.

Band structures of MnPSe₃ monolayer with different Li/F concentrations are also calculated. As shown in Fig. 4a, b, the MnPSe₃ monolayer has a complete spin-down polarization in blue with 25% and 50% Li concentrations and remains an HM. When the adsorption concentration increases to 75% and 100%, as shown in Fig. 4c, d, both spin-up and -down channels cross the Fermi Level and show metallicity. Fig. 4e–h shows the band structures of MnPSe₃ with the F adsorption. It is clear that for all four concentrations, the F-adsorbed 2D MnPSe₃ remains an HM_. In summary, MnPSe₃ can exhibit a complete spin-up polarization with the Li adsorption, and a full spin-down polarization with the F adsorption. When MnPSe₃ is adsorbed with the Li atom, electrons will easily transfer from the Li atom to MnPSe₃, i.e., MnPSe₃ will gain electrons. It will gain more electrons with the increasing adsorption concentration, and the Fermi level will shift up into the conduction bands of MnPSe₃. However, for the F atom adsorption, electrons will transfer from MnPSe₃ to the F atom, and the Fermi level will shift down into the valence bands of MnPSe₃.

Band structures of MnPSe₃ monolayer with different Li and F adsorption concentrations: a, e 25%, b, f 50%, c, g 75%, and d, h 100%.

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The band structures of the MnPSe₃ monolayer with Li/F adsorption on the top of Se/Mn atoms can be seen in Figs. S3 and S4. Other atoms, such as Ca, O, and Cl are also considered, as shown in Figs. S5 and S6. For all the adsorptions, we can obtain AFM-FM transition, which means that FM MnPSe₃ can be easily obtained, and actually, it is an important spintronic material.

To well understand the AFM-FM transition induced by the adsorption, we perform density of states (DOS) calculations for the Li/F-adsorbed MnPSe₃ with 50% concentration, as shown in Fig. 5. We plot the non-magnetic (NM) and FM DOS for comparison. For the NM DOS of both the Li/F-adsorbed MnPSe_3, sharp peaks appear at the Fermi level, while for the FM DOS, the sharp peaks disappear. According to the Stoner criterion^49,50, the extremely large DOS at the Fermi level cannot be stable, which will induce magnetic transition.

NM and FM DOS of MnPSe₃ with 50% adsorption concentration: a, b Li adsorption and c, d F adsorption.

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MAE is defined as the total energy difference between E[001] and E[100], i.e., MAE = E[001] − E[100]. The positive and negative MAE corresponds to the in-plane and out-of-plane magnetization easy axis, respectively. To obtain MAE, we include spin-orbit coupling (SOC) in the calculations⁵¹, and the results are shown in Fig. 6a. It is clear that the pure MnPSe₃ with positive MAE has the in-plane magnetization axis. For the Li adsorption, the easy axis reverses from in-plane to out-of-plane, when the adsorption concentration is around 25%. In contrast, for the F atom adsorption, MAE of MnPSe₃ remains positive for all the concentrations, i.e., the F-adsorbed MnPSe₃ has the in-plane easy axis. In addition, we notice that the absolute value of MAE of the F-adsorbed MnPSe₃ is much larger than that of the Li-adsorbed MnPSe₃. This is because the 3d-orbitals of the Mn atom dominate the valence band maximum and they cross the Fermi level when F is adsorbed, while p-orbitals of the Se and P atoms dominate the conduction band minimum, and they cross the Fermi level when Li is adsorbed. Mn-3d-orbitals have a larger influence than p-orbitals of the Se and P atoms.

a MAE and b the Curie temperature of MnPSe₃ with different Li/F adsorption concentrations.

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We also calculate the total energy of FM, AFM-Néel, AFM-Zigzag, and AFM-Stripy MnPSe₃ with different Li/F adsorptions, and obtain the parameters J₁, J₂, J₃, and the Curie temperature. The structures of FM, AFM-Néel, AFM-Zigzag, and AFM-Stripy MnPSe₃ are shown in the previous reports⁴⁰. The relation between the adsorption concentration and the Curie temperature is shown in Fig. 6b. The Curie temperature of the pristine 2D MnPSe₃ is about 86 K, which is in good agreement with the previous research (88 K)³⁹, confirming the validity of our model. For the F adsorption, T_c increases with the adsorption concentration and nearly reaches the room temperature for 100% adsorption. For the Li adsorption, T_c can reach 240 K when the concentration is 50%, and it does not change for 75% and 100%.

Half-metallic ferromagnetism at the MnPS₃/Au(111) interface

Since hole/electron doping can induce AFM/FM transition in MnPX₃, contact with metal may also induce AFM/FM transition in MnPX₃. In Fig. 7a, we schematically draw the field-effect transistor, which has the electrodes of Au(111) and transport material of MnPS₃ monolayer. We construct the heterostructure MnPS₃/Au(111), as shown Fig. 7b, to investigate the influence of the metal contact on the magnetic properties of MnPS₃. The lattice constant of MnPS₃ and Au(111) is 6.08 Å and 5.90 Å, respectively, resulting in a relatively small mismatch of about 2.96%. According to the structural relaxation, we get an interlayer space of about 2.40 Å between MnPS₃ and Au(111). The planar average of the electrostatic potential energy of MnPS₃ and Au(111) are shown in Fig. 8a and b, respectively, from which we can see that the work functions of MnPS₃ and Au(111) are 5.871 eV and 5.825 eV, respectively. Since the work function of Au(111) is smaller, electrons will transfer from Au(111) to MnPS₃, forming the Ohmic contact, which can also be confirmed in the band structure.

a The schematic field-effect transistor and b atomic structure of MnPS₃/Au(111).

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a, b The planar average potential energy of MnPS₃ and Au(111), and c the band structure of FM MnPS₃/Au(111).

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We test the AFM and FM states for the heterostructure and find that the FM states have lower total energy. For each unit cell of the heterostructure, the energy difference (ΔE) between AFM and FM is about 22.5 meV. The calculated band structure of the FM MnPS₃/Au(111) is shown in Fig. 8c, in which the atomic orbitals of MnPS₃ are picked out and their weight is indicated by the circles in blue (spin-down) and red (spin-up). We can see that the Fermi level crosses the conduction band of MnPS₃, which means that MnPS₃ obtains electrons from Au(111), and the Ohmic contact is formed. In addition, we notice CBM of MnPS₃ is fully spin-polarized in blue, which is consistent with the Li adsorption.

Through first-principles calculations, we investigate the AFM/FM transition in monolayer MnPX₃. We find that both the Li- and F-adsorbed MnPSe₃ monolayers can become HM, and HM is well preserved for a large range of concentrations. The curie temperature and the magnetic anisotropy of the Li- and F-adsorbed MnPSe₃ are calculated. It is found that the Curie temperature can be obviously enhanced by the adsorption (~240 K for the Li adsorption and ~280 K for the F adsorption). The magnetization easy axis of the Li-adsorbed MnPSe₃ can switch from in-plane to out-of-plane, while that of the F-adsorbed MnPSe₃ remains in-plane. In addition, in the heterostructure MnPS₃/Au(111), charge transfers from Au(111) to MnPS₃ and Ohmic contact is formed, and AFM/FM transition is also obtained.

Both adsorption and contact with metal surfaces commonly exist in devices, which, however, give rise to quantitative change for MnPX₃. Our study shows that 2D MnPX₃ can show ferromagnetic half-metallicity in reality, although it is intrinsically an antiferromagnet, which means that 2D MnPX₃ can be regarded as an important spintronic material.

All calculations are based on the Vienna ab initio simulation package (VASP) in the framework of density-functional theory (DFT)^52,53. The projector augmented wave (PAW) method and the Perdew–Burke–Ernzerhof (PBE) general functional with the generalized gradient approximation plus on-site Coulomb interaction U (GGA + U) with U = 5 eV^46,54 is used. For the MnPSe₃ monolayer, to avoid interactions between neighboring layers, 20 Å of vacuum space along the z-axis is inserted. A cutoff energy of 450 eV is set for the plane wave expansion. Monkhorst k-mesh grids of 8 × 8 × 1 and 4 × 4 × 1 are used for the Brillouin-zone sampling of 1 × 1 × 1 and 2 × 2 × 1 MnPSe₃, respectively. For geometry optimization, all of the internal coordinates are relaxed until the Hellmann-Feynman force is less than 0.01 eV·Å⁻¹ for each ion, and total energy convergence is within 10⁻⁵ eV.