The MnN films were grown on MgO (001) substrates in a plasma-assisted MBE system. The background pressure in the chamber was approximately 1 × 10⁻¹⁰ mbar. Prior to the growth, MgO substrates were annealed at 900℃ for 60 minutes to remove water vapor and surface residues. The optimal growth condition for MnN films had been determined to be at the deposition temperature of 300℃. High-purity Mn (99.9999%) was evaporated from a low-temperature effusion cell operated at 750℃ to stabilize the N-rich phase. The radio frequency power supplied to the electron cyclotron resonance was set to ~ 200 W for obtaining reactive N atoms. The N partial pressure varied between 1 to 6 × 10⁻⁵ mbar. The growth was monitored by in-situ reflection high energy electron diffraction (RHEED). The X-ray diffraction (XRD) measurements were performed using a Rigaku Smart Lab (9 kW) X-ray diffractometer with a Ge (220) × 2 crystal monochromator, and the surface morphology of the films was characterized by an atomic force microscopy (Oxford Instruments). The STEM samples were prepared by focused ion beam milling. The ion-beam milling was performed using a PIPS instrument (Model 691, Gatan Inc.) with an accelerating voltage of 3.5 kV until a hole was made. Low-voltage milling was performed with an accelerating voltage of 0.3 kV to remove the surface amorphous layer and minimize damage. High-resolution high-angle annular dark-field (HAADF)-STEM images and Energy Dispersive Spectroscopy (EDS) were acquired on an aberration-corrected JEOL-ARM200F instrument with a convergence semi-angle of 30 mrad and collection semi-angles of 39 to 200 mrad. Transport properties were characterized using a Quantum Design Physical Property Measurement System (PPMS) in the van der Pauw geometry. For magnetic characterization, samples were capped with CoFeB (1.5 nm) /MgO (2 nm) /Ta layers via DC magnetron sputtering, followed by in-plane field annealing (600 K, 10 kOe). Then the magnetic measurements were performed on a Quantum Design Magnetic Property Measurement System (MPMS-3).

High-quality MnN thin films can be successfully fabricated using plasma-assisted MBE based on the following key factors: (i) Although N₂ molecules in the air are highly stable, with the N≡N triple bond having a dissociation energy as high as 9.8 eV/molecule^[31-32], the use of radio frequency plasma enables the generation of highly reactive N atoms^{[13, 32]}, which is essential for the growth of nitride films. (ii) The lattice mismatch between MgO (~ 4.211 Å) and MnN (~ 4.219 Å) is small^{[13, 15]}, promoting the epitaxial growth of high-quality MnN. (iii) By adjusting the temperature of the Mn source effusion cell or the partial pressure of N, the growth conditions can be finely tuned, allowing for precise control of the phase and quality of the MnN thin films.

Bulk MnN crystallizes in a fct rock-salt structure (space-group F4/mmm) with a = 4.219 Å and c = 4.129 Å. Fig. 1(a) shows the schematic crystal structure of θ-phase MnN, in which N atoms are embedded in the framework of Mn atoms with identical distance from each other^[14-16]. Fig. 1(b) plots the XRD θ–2θ scans of the films grown under varied N partial pressure and summarized in Tab. 1. It indicates that crystalline phase would be changed with the varied N partial pressure. For S1, the out of plane lattice parameter is almost identical to that of MgO, which corresponds to the zinc-blende type metastable MnN^[33] and requires further research. While under low N partial pressure, the S3 is identified to be η-phase Mn₃N₂^{[13, 15]}. We determine the optimal growth condition for rock-salt MnN to be deposition temperature of 300℃, Mn source effusion cell temperature of 750℃, and N partial pressure of 3 × 10⁻⁵ mbar. As shown in Fig. 1(c), in-situ RHEED and wide range of XRD spectrum reveal the good (00l) monocrystalline character of the MnN film. The streaky RHEED pattern indicates its good monocrystalline and flat surface. Layer-by-layer growth mode of the film have been obtained through in-situ RHEED oscillation (not shown). The first several oscillation periods are obvious, and the oscillation period is 40 s. Each oscillation corresponds to the growth of an atomic Mn layer, e.g., half of the MnN unit cell.

Detailed structural characterization of the MnN film is shown in Fig. 2. The small range of XRD spectrum of MnN film shows the Laue oscillations, indicating pristine interfaces and high-quality. The calculated c is ~ 4.15 ± 0.02 Å. The inset of Fig. 2(a) plots the rocking curve of the (002) peak, and the full width of half maximum is 0.108. RSM imaging around the asymmetric MgO (204) demonstrates that the film is coherently strained with the MgO substrate, sharing the same in-plane lattice constant (~4.211 Å). Above structural characterizations illustrate that the out-of-plane to in-plane lattice constant ratio (c/a) of the film is 0.98, which is consistent with previous experimental observations of tetragonal lattice distortion in MnN^{[13, 16]}. Fig. 2(c) plots a φ-scan around the MnN (204) peak, indicating the MnN film exhibits an in-plane fourfold symmetric structure and thus illustrating the tetragonal symmetry of the MnN film. Fig. 2(d) plots the experimental data and fitting results of XRR characterization. The film thickness is about 22.4 nm, the material density is about 6.35 ± 0.02 g/cm³, and the surface roughness is 0.228 nm. The roughness of the surface has also been investigated by atomic force microscopy (Fig. 2(e)). The mean roughness is about 60 pm and the root-mean-square roughness is about 70 pm.

Fig. 3 shows the HAADF-STEM images and atom-resolved EDS which were measured and analyzed on a sample that had been placed in the ambient condition for 60 days. Fig. 3(a)-(b) show HAADF-STEM images taken along the [100] zone axis of MgO. The arrangement of Mn atoms can be clearly observed (see Fig. 3(b)). Large-scale HAADF-STEM image and atom-resolved EDS spectrum analysis were carried out along the [110] zone axis of MgO (see Fig. 3(d)-(f)). The atom-resolved EDS indicates that the uniformly arranged atoms are Mn atoms.

Stability is a crucial factor for practical application of a material. Fig. 4(a) shows the structural stability of the MnN material in water. A sample prepared was soaked in water for 24 hours, and XRD measurements were carried out during the process. The results indicate that soaking in water for 24 hours does not change the structure of MnN film, implying potential use of the MnN material as a flexible material. Combined with the freestanding film technology^[34-35], the freestanding MnN film can be prepared using a suitable water-soluble sacrificial layer.

Next, the stability of MnN in ambient condition is characterized (see Fig. 4(b)-(d)). Upon exposure to ambient atmosphere for 180 days, the XRD characteristic peak of MnN would be unchanged. Moreover, to verify whether the chemical composition remains unchanged, EELS measurements were conducted on the sample that are placed in the atmospheric environment for 60 days (see Fig. 4(c)-(e)). Fig. 4(c) shows the area where EELS measurements were conducted. According to the marked lines in the region, the energy loss spectra of the Mn L-edges in the corresponding region is plotted (see Fig. 4(d)). In the film growth region, the Mn L₃/L₂ ratio remains unchanged, with an average of 2.5 (see Fig. 4(e)), indicating uniform valence state of Mn in the film. According to the analysis of energy loss spectra of Mn L-edges in manganese oxides^[36-39], the chemical valence state should be +3 when the Mn L_3,2 ratio is close to ~ 2.5. However, the L₃ peak is located at 643.5 eV, which usually corresponds to a higher valence state in literature. This inconsistency with the valence state determined by the L_3,2 ratio may be due to the existence of various chemical bonds, such as metal bonds and covalent bonds in addition to ionic bonds in the transition metal nitride^[40].

Above experimental results indicate that MnN exhibits superior stability in both atmospheric and water environments. Compared with traditional AFM materials (IrMn, PtMn, FeMn, etc.)^{[9-10, 41]}, MnN stands out for its stability and the absence of noble metals, making it more environmentally friendly and low-cost^{[18, 42]}, and thus a highly promising candidate for applications in spintronics. Although nitrides (such as TiN, AlN, CrN, etc.) generally exhibit high oxidation resistance^[43-45], possibly related to the formation of a dense oxide layer on the surface, the inevitable formation of a thermal oxide layer during heating processes remains a challenge. Previous studies on polycrystalline MnN have mentioned similar phenomenon^[19], where thermal annealing in air at high temperatures results in the formation of an oxide layer tens of nanometers thick. For single-crystal MnN films, the oxidation resistance at room temperature has been examined via EELS measurement, revealing only slight oxidation on the surface within several atomic layers (~3 nm), while the oxidation resistance at high temperature needs further investigation.

Fig. 5(a) shows the temperature dependent resistivity of the MnN film. It exhibits metallic behavior with a resistivity of 235 μΩ·cm at room temperature and a residual resistivity ratio (RRR) of 1.38. This value is consistent to that reported in the previous study^[46]. However, the resistivity curve shows an upturn at low temperatures, reaching a minimum value of 169.7 μΩ·cm at 23 K. The resistivity increases below this temperature, resulting in a relatively low RRR.

This observation could be explained by the Kondo effect. The N vacancies stabilize the rock-salt MnN, leading to the lattice distortion from a cubic to a tetragonal structure^[29-30]. The non-stoichiometric ratio between Mn and N atoms may lead to the formation of magnetic impurities, which could further induce Kondo-like behavior in MnN. In order to provide a semi-quantitative explanation for this phenomenon, the Kondo effect model was used to fit the experimental results in the low temperature section (see Fig. 5(b))^[47],

where $ {\rho }_{0} $ (~ 160 μΩ·cm) and $ {\rho }_{K} $ (~ 9 μΩ·cm) represents the residual resistivity and the Kondo resistivity, respectively. The $ {\rho }_{K} $ is relatively small, consistent with the weak increase in resistivity in the low-temperature region. $ {T}_{K} $ (~ 48 K) and s (~ 1.99) are the Kondo temperature and the impurity spin parameter, respectively. For Mn ions in MnN, the electronic configuration is 3d⁴, with the highest spin state corresponding to a spin factor of S = 2. The fitting results reveal that the value of s tends to be large, aligning with the behavior of Mn ions in a high-spin state. Furthermore, neutron diffraction experiments confirm a magnetic moment of 3.3 μ_B/Mn^[15-16], which is also indicative of a high-spin state occupation. These findings collectively demonstrate that the fitting results are in excellent agreement with the characteristics of Mn ions in MnN materials. And the last power-law term, AT^B (where A = 0.02 and B = 1.47), indicates resistivity contribution from electron–electron or electron–phonon scattering.

Fig. 5(c) plots the temperature-dependent evolution of carrier density n and mobility μ of MnN film derived from resistivity and Hall effect measurements. The carrier concentration reaches the order of 10²² cm⁻³, while the mobility remains in the range of several cm²/V·s, which may be related to Kondo scattering in the MnN system. Hall effect analysis confirms that the dominant charge carriers are electrons.

The AFM properties of MnN films are characterized through two steps. First, the magnetization curve is measured at a cooling field of 1 kOe (see Fig. 6(a)). Results show high-temperature diamagnetism and low-temperature paramagnetism of the MgO substrate, indicating the MnN film does not show obvious magnetization, consistent with the AFM configuration of MnN. Second, a 30-nm-thick sample is capped with a 1.5 nm ferromagnetic CoFeB layer, and the hysteresis loop was measured after an in-plane cooling field annealing process. Fig. 6(b) plots the experimental results, the saturation magnetization of the CoFeB layer is 5.9e⁻⁵ emu, and the unit saturation magnetization of the CoFeB layer is calculated to be 1573 emu/cc. According to the Meiklejohn-Bean model^[48-49], the interfacial exchange energy between MnN and CoFeB layers can be calculated using the formula,

the calculated value of J_eff is 0.032 mJ/m², which is an order of magnitude smaller than the value in previous study^[19]. This discrepancy arises because the corresponding exchange bias field is an order of magnitude smaller, potentially due to three reasons. First, as Meinert et al. previously noted, if the crystallinity exceeds a certain threshold, the interface can no longer be pinned^[26]. Second, it may relate to the sample preparation and measurement process. The field annealing temperature (600 K) did not reach the Néel temperature (650 K) of MnN material. Consequently, the spin configuration in the films may not completely couple with the ferromagnetic layer, further affecting the hysteresis loop symmetry during field cooling and rising process. Previous studies have pointed out that the spin glass behavior could influence the exchange bias effect in polycrystalline MnN/FM interlayer^[50]. Lastly, the relationship between lattice constants and magnetic configuration in MnN remains unclear^[15-16], and the impact of magnetic configuration to the heterostructure requires deeper investigation.

In summary, we have conducted comprehensive studies on the structure, stability, transport and magnetism of high-quality single-crystalline epitaxial MnN films prepared by MBE. Its preparation is sensitive to growth conditions, with both excessively high and low Mn/N ratio during growth being detrimental to the formation of single-crystalline epitaxial films. Its lattice structure is a rock-salt type structure with tetragonal distortion, featuring a c/a ratio of 0.98, where N atoms are inserted into the gaps between Mn atoms, generating certain N vacancies. This is a key reason for the ease of change in the lattice constant of MnN. MnN materials demonstrate excellent stability, confirmed in this work through tests in both water and atmospheric environments, showing good structural and chemical stability, and thus having the potential for practical application. Finally, we characterize the basic physical properties of the material. Its transport properties indicate that the presence of magnetic impurities, likely introduced by N-vacancy disorder. In addition, the AFM properties of the thin films were characterized. An exchange bias field of 135 Oe was found by measuring the hysteresis loop of the heterostructure composed of MnN and CoFeB, though this is not the optimal condition and requires further experimental optimization.

In the current study, we have successfully grown high-quality epitaxial MnN thin films, highlighting its potential as a promising candidate for AFM spintronics. Our work establishes a fundamental prerequisite for further investigations into several critical aspects. The relationship between the lattice constants and magnetic configurations in MnN remains to be elucidated^[15-16], particularly its impact on the EB of MnN/ferromagnet heterostructures. While MnN has recently been identified as a promising material for AFM electrical switching devices^{[28, 51]}, the fundamental mechanisms governing its switching behavior are still under debate. The fabrication of high-quality single crystals could offer deeper insight into the underlying physical mechanisms.