# Synthesis of Manganese Mononitride with Tetragonal Structure under Pressure

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## Abstract

**:**

## 1. Introduction

_{4}N films showed ferromagnetic properties with a magnetic moment of 1.1 μ

_{B}per unit cell, and the tetragonal η-Mn

_{3}N

_{2}films exhibited antiferromagnetism with 0.4 μ

_{B}per unit cell [12]. So far, among the manganese nitrides, the most nitrogen rich-nitride is reported to be mononitride, θ-MnN (Space group:139), which has been synthesized using different methods, such as molecular beam epitaxy [13] and DC reactive sputtering [14]. Tetragonal MnN was found to have anomalous thermal expansion and be antiferromagnetic with a Néel temperature of 650 K [15]. Moreover, experimental data found that the magnetic structure of MnN consisted of ferromagnetically aligned c-planes coupled anti-ferromagnetically in the c-direction [16]. Here, we report the synthesis of the MnN compound starting from elemental Mn and liquid nitrogen in a laser-heated diamond anvil cell to explore the phase space of the Mn–N system. Tetragonal MnN was synthesized at 30 GPa and 1500 °C and was quenchable to ambient pressure. The bulk modulus and the axial compressibility were measured using in situ high-pressure diffraction. DFT results with GGA + U confirm that tetragonal MnN is energetically stable and antiferromagnetic.

## 2. Materials and Methods

^{−6}eV and 0.001 eV/Å, respectively. The k-points were automatically generated by the Monkhorst–Pack grids with a resolution of 0.03 Å

^{−1}[24]. The projector-augmented plane-wave (PAW) potentials [24,25] were used. To accurately describe the strongly correlated interaction between MnN, FeN, and CrN, GGA + U was also employed to study the stability and electronic properties with a fixed U value of 4 eV. The phonon dispersion curves were calculated using the PHONOPY code with density-functional perturbation theory (DFPT) [26].

## 3. Results and Discussion

_{0}, and its derivative with respect to pressure, ${B}_{0}^{\prime}$. Three cases are discussed. Firstly, the resulting value is B

_{0}= 160 GPa if ${B}_{0}^{\prime}$ is fixed to the canonical value of 4. Secondly, the resulting value is B

_{0}= 191 GPa (with ${B}_{0}^{\prime}$ = 2.20) when V

_{0}is fixed to the value of 37.43 Å

^{3}. Thirdly, if ${B}_{0}^{\prime}$ is allowed to freely vary, the resulting bulk modulus is 173 GPa and its derivative is 3.06. This means the data can be fitted almost equally well by decreasing the value of B

_{0}and increasing the value of ${B}_{0}^{\prime}$ or vice versa. The calculated bulk modulus is 187 GPa, in good agreement with the experimental value. Generally, for 3d transition metal nitrides with a rocksalt structure, the metals from Cr to Fe have a significantly decreasing bulk modulus with the increase of valence electrons. In addition, as shown in Figure 3b, as pressure increased, the lattice parameters show slightly anisotropic. The axial compressibility of lattice parameters shows that the decreasing of a/a

_{0}is larger than that of c/c

_{0}with increasing pressure, which means the material is much more compressible along the a direction than the c direction. At the pressure of 30 GPa, the a axis and c axis decrease by 4.59% and 4.16% relative to the ambient pressure value, respectively.

_{6}octahedrons has a slight distortion and rotation at ambient pressure. To quantitatively illustrate the pressure-induced evolution of the Mn–N bonds in octahedron MnN

_{6}, we further derived the Mn–N bond lengths from the Rietveld refinements, as depicted in Figure 3d. In the range of 0–30 GPa, the in-plane Mn–N1 bond length and the out-of-plane Mn–N2 bond length decrease gradually as pressure increases. The Mn–N1 and Mn–N2 bond lengths are 2.117 and 2.088 Å at zero pressure, respectively. The fitting curve shows that the descent rate of the Mn–N1 bond length is larger than the Mn–N2, which corresponds to the decrease rate of a/a

_{0}larger than that of c/c

_{0}, which results in much more compressibility along the a direction than along the c direction.

_{3}/mmc–MnN. At first, we looked for the most stable magnetic ground states of MnN with different candidates at ambient conditions and considered three possible magnetic configurations (non-magnetic, ferromagnetic, and antiferromagnetic) in our calculations. Our results found that the antiferromagnetic state with a magnetic moment of 4.04 μ

_{B}is the most stable magnetic configuration for all the candidates of MnN. Therefore, we only focused on the evolution of antiferromagnetic MnN structures with increasing pressure. The calculated enthalpies based on the GGA functional are plotted in Figure 4a, showing that F$\overline{4}$3m–MnN is the most stable at zero pressure. However, P6

_{3}/mmc–MnN is the most stable crystal structure at high pressures ranging from 10 GPa to 100 GPa. Furthermore, to sufficiently describe the strongly correlated system of Mn–N, we also calculated the enthalpies of MnN structures by including the U correction, and the results are shown in Figure 4b. We found that the I4/mmm–MnN observed experimentally is the most stable at ambient conditions and remains stable at high pressure up to 75 GPa. The Pmmn–MnN had smaller enthalpy than I4/mmm–MnN at 80 GPa. Later, I4/mmm–MnN becomes the most stable structure again when the pressure increases to 100 GPa. These results indicate that correcting the strongly correlated interaction is very important for a precise understanding of MnN properties. Furthermore, based on the GGA+U method, the phonon dispersion curves of I4/mmm–MnN were calculated, as shown in Supplementary Materials Figure S1. The results indicate that imaginary frequency is not observed, revealing the dynamical stability of I4/mmm–MnN again at ambient conditions.

_{F}). Assisted by the calculated density of states (DOS), we show that the conduction bands comprise of mixed Mn-d and N-p states. As we know that the magnetic ground state of I4/mmm-MnN is antiferromagnetic, the total DOS of the spin-up channel equals to that of spin-down channel. Furthermore, strong hybridization between the Mn–d orbitals and N–p orbitals is found, and both Mn–d orbitals and N–p orbitals mainly contribute to the states around the Fermi level. While formally metallic, the DOS at the Fermi energy is low (0.67 states/eV/cell). To compare the electronic properties of I4/mmm–MnN, we further investigated the stable configuration and electronic properties of FeN and CrN at zero pressure. Our results show that at ambient conditions, the most stable configuration of FeN and CrN is F$\overline{4}$3m- and Fm$\overline{3}$m-type structures, respectively. The magnetic ground state of both F$\overline{4}$3m–FeN and Fm$\overline{3}$m–CrN are antiferromagnetic with a magnetic moment of 3.85 μ

_{B}and 2.49 μ

_{B}, respectively. The band structures and PDOS are shown in Figure 5b,c. Both I4/mmm–MnN and Fm$\overline{3}$m–CrN are similar, showing metallic behaviors. However, the F$\overline{4}$3m–FeN is a semiconductor with a direct band gap of 0.5 eV at the X point.

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**X-ray diffraction pattern of Mn and liquid N before (

**a**) and after (

**b**) laser heating at 30.0 GPa; (

**c**) powder X-ray diffraction patterns of MnN from 30 GPa to ambient pressure.

**Figure 2.**(

**a**) X-ray diffraction lines’ evolution with pressure; (

**b**) crystal structure of MnN; Rietveld refinement of the XRD pattern of the MnN sample at (

**c**) 0.0 GPa and (

**d**) 30.0 GPa, respectively.

**Figure 3.**The changes of (

**a**) unit cell volume and (

**b**) lattice parameters in the entire pressure change; (

**c**) The atomic arrangement of the MnN

_{6}octahedron; (

**d**) Bond length of Mn–N as a function of pressure.

**Figure 4.**Enthalpies of MnN are shown as a function of pressure based on the DFT method (

**a**) and DFT+U method (

**b**). The enthalpy of MnN in phase A is set to zero, and contrasts between enthalpies of different phases are shown more clearly in the insets of (

**b**).

**Figure 5.**(

**a**–

**c**) show the band structures and density of states (DOS) of I4/mmm–MnN, F$\overline{4}$3m–FeN, and Fm$\overline{3}$m–CrN at zero pressure, respectively. The dashed lines show the Fermi level. For the density of states, the top, middle, and bottom part represent the total DOS, partial DOS of transitional metal elements, and partial DOS of N, respectively.

**Table 1.**Summary of crystal data of tetragonal MnN, and adjacent 3d transition metal nitrides. B

_{0}is the bulk modulus and ${B}_{0}^{\prime}$ its pressure derivative.

Compound | Space Group | Structure | Lattice Parameters (Å) | B_{0} (GPa) | ${\mathit{B}}_{0}^{\prime}$ | Ref. |
---|---|---|---|---|---|---|

CrN | Fm3m | RS | DFT: 340-430 | [27] | ||

CrN | Pnma | Orthorhombic | 243(10) | [27] | ||

MnN | I4/mmm | RS | a = 2.994(1) c = 4.175(1) | 173 DFT: 187 | 3.06 | Present |

FeN | Fm$\overline{3}$m | RS | a = 4.1041 | 186 | 4.77 | [28] |

FeN | F$\overline{4}$3m | ZB | a = 4.2250 | 266 | 6.65 | [28] |

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**MDPI and ACS Style**

Huang, D.; Niu, C.; Yan, B.; Gao, B.; Wu, L.; Zhang, D.; Wang, X.; Gou, H.
Synthesis of Manganese Mononitride with Tetragonal Structure under Pressure. *Crystals* **2019**, *9*, 511.
https://doi.org/10.3390/cryst9100511

**AMA Style**

Huang D, Niu C, Yan B, Gao B, Wu L, Zhang D, Wang X, Gou H.
Synthesis of Manganese Mononitride with Tetragonal Structure under Pressure. *Crystals*. 2019; 9(10):511.
https://doi.org/10.3390/cryst9100511

**Chicago/Turabian Style**

Huang, Dajian, Caoping Niu, Bingmin Yan, Bo Gao, Lailei Wu, Dongzhou Zhang, Xianlong Wang, and Huiyang Gou.
2019. "Synthesis of Manganese Mononitride with Tetragonal Structure under Pressure" *Crystals* 9, no. 10: 511.
https://doi.org/10.3390/cryst9100511