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An Ab Initio Study of Pressure-Induced Changes of Magnetism in Austenitic Stoichiometric Ni_{2}MnSn

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. Quantum-Mechanical Calculations

#### 2.2. Experiments

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Graf, T.; Felser, C.; Parkin, S.S. Simple rules for the understanding of Heusler compounds. Prog. Solid State Chem.
**2011**, 39, 1–50. [Google Scholar] [CrossRef] - Recarte, V.; Pérez-Landazábal, J.I.; Sánchez-Alarcos, V.; Cesari, E.; Jiménez-Ruiz, M.; Schmalzl, K.; Chernenko, V.A. Direct evidence of the magnetoelastic interaction in Ni
_{2}MnGa magnetic shape memory system. Appl. Phys. Lett.**2013**, 102, 201906. [Google Scholar] [CrossRef][Green Version] - Lee, S.J.; Lee, Y.P.; Hyun, Y.H.; Kudryavtsev, Y.V. Magnetic, magneto-optical, and transport properties of ferromagnetic shape-memory Ni
_{2}MnGa alloy. J. Appl. Phys.**2003**, 93, 6975–6977. [Google Scholar] [CrossRef] - Brown, P.J.; Crangle, J.; Kanomata, T.; Matsumoto, M.; Neumann, K.U.; Ouladdiaf, B.; Ziebeck, K.R.A. The crystal structure and phase transitions of the magnetic shape memory compound Ni
_{2}MnGa. J. Phys. Condens. Matter**2002**, 14, 10159–10171. [Google Scholar] [CrossRef] - Entel, P.; Siewert, M.; Gruner, M.E.; Herper, H.C.; Comtesse, D.; Arróyave, R.; Singh, N.; Talapatra, A.; Sokolovskiy, V.V.; Buchelnikov, V.D.; et al. Complex magnetic ordering as a driving mechanism of multifunctional properties of Heusler alloys from first principles. Eur. Phys. J. B
**2013**, 86, 65. [Google Scholar] [CrossRef] - Kaštil, J.; Kamarád, J.; Isnard, O.; Skourski, Y.; Míšek, M.; Arnold, Z. Effect of pressure and high magnetic field on phase transitions and magnetic properties of Ni
_{1.92}Mn_{1.56}Sn_{0.52}and Ni_{2}MnSn Heusler compounds. J. Alloys Compd.**2015**, 650, 248–255. [Google Scholar] [CrossRef] - Sutou, Y.; Imano, Y.; Koeda, N.; Omori, T.; Kainuma, R.; Ishida, K.; Oikawa, K. Magnetic and martensitic transformations of NiMnX(X=In,Sn,Sb) ferromagnetic shape memory alloys. Appl. Phys. Lett.
**2004**, 85, 4358–4360. [Google Scholar] [CrossRef] - Brown, P.J.; Gandy, A.P.; Ishida, K.; Kainuma, R.; Kanomata, T.; Neumann, K.U.; Oikawa, K.; Ouladdiaf, B.; Ziebeck, K.R.A. The magnetic and structural properties of the magnetic shape memory compound Ni
_{2}Mn_{1.44}Sn_{0.56}. J. Phys. Condens. Matter**2006**, 18, 2249–2259. [Google Scholar] [CrossRef] - Çakır, A.; Righi, L.; Albertini, F.; Acet, M.; Farle, M. Intermartensitic transitions and phase stability in Ni
_{50}Mn_{50-x}Sn_{x}Heusler alloys. Acta Mater.**2015**, 99, 140–149. [Google Scholar] [CrossRef] - Khan, M.; Pathak, A.K.; Paudel, M.R.; Dubenko, I.; Stadler, S.; Ali, N. Magnetoresistance and field-induced structural transitions in Ni
_{50}Mn_{50-x}Sn_{x}Heusler alloys. J. Magn. Magn. Mater.**2008**, 320, L21–L25. [Google Scholar] [CrossRef] - Maheswar Repaka, D.V.; Chen, X.; Ramanujan, R.V.; Mahendiran, R. Magnetic field dependence of electrical resistivity and thermopower in Ni
_{50}Mn_{37}Sn_{13}ribbons. AIP Adv.**2015**, 5, 097116. [Google Scholar] [CrossRef][Green Version] - Kaštil, J.; Kamarád, J.; Míšek, M.; Hejtmánek, J.; Arnold, Z. Complex transport properties of the Ni
_{1.92}Mn_{1.56}Sn_{0.52}Heusler alloy and its magnetic behavior. J. Magn. Magn. Mater.**2018**, 466, 260–266. [Google Scholar] [CrossRef] - Aksoy, S.; Acet, M.; Deen, P.P.; Mañosa, L.; Planes, A. Magnetic correlations in martensitic Ni-Mn-based Heusler shape-memory alloys: Neutron polarization analysis. Phys. Rev. B
**2009**, 79, 212401. [Google Scholar] [CrossRef] - Khan, M.; Dubenko, I.; Stadler, S.; Ali, N. Exchange bias in bulk Mn rich Ni-Mn-Sn Heusler alloys. J. Appl. Phys.
**2007**, 102, 113914. [Google Scholar] [CrossRef][Green Version] - Webster, P.J. Heusler alloys. Contemp. Phys.
**1969**, 10, 559–577. [Google Scholar] [CrossRef] - Alves, A.L.; Magnus Gomes Carvalho, A.; Cápua Proveti, J.R.; Nascimento, V.P.; Passamani, E.C. EXAFS studies of enhancement of L2
_{1}-B2 chemical disorder induced by ball milling in martensitic Ni_{50}Mn_{36}Sn_{14}pseudo-Heusler alloy. Mater. Charact.**2019**, 158, 109972. [Google Scholar] [CrossRef] - Kuzmin, R.N.; Ibraimov, N.S.; Zhdano, G.S. Mössbauer effect in Heusler alloys. Sov. Phys. JETP
**1966**, 23, 219. [Google Scholar] - Leiper, W.; Geldart, D.J.W.; Pothier, P.J. Hyperfine field at the tin sites in the Heusler alloy Ni
_{2}MnSn. Phys. Rev. B**1971**, 3, 1637–1640. [Google Scholar] [CrossRef] - Williams, J.M.; Danson, D.P. A Mössbauer study of the Heusler alloys series Ni
_{2}Mn_{x}Ti_{1-x}Sn. Le J. Phys. Colloq.**1979**, 40, C2-169–C2-171. [Google Scholar] [CrossRef] - Gavriliuk, A.G.; Stepanov, G.N.; Sidorov, V.A.; Irkaev, S.M. Hyperfine magnetic fields and Curie temperature in the Heusler alloy Ni
_{2}MnSn at high pressure. J. Appl. Phys.**1996**, 79, 2609–2612. [Google Scholar] [CrossRef] - Şaşıoğlu, E.; Sandratskii, L.M.; Bruno, P. Pressure dependence of the Curie temperature in Ni
_{2}MnSn Heusler alloy: A first-principles study. Phys. Rev. B**2005**, 71, 214412. [Google Scholar] [CrossRef][Green Version] - Bose, S.K.; Kudrnovský, J.; Drchal, V.; Turek, I. Magnetism of mixed quaternary Heusler alloys: (Ni,T)
_{2}MnSn(T=Cu,Pd) as a case study. Phys. Rev. B**2010**, 82, 174402. [Google Scholar] [CrossRef][Green Version] - Bose, S.K.; Kudrnovský, J.; Drchal, V.; Turek, I. Pressure dependence of Curie temperature and resistivity in complex Heusler alloys. Phys. Rev. B
**2011**, 84, 174422. [Google Scholar] [CrossRef][Green Version] - Fichtner, T.; Kreiner, G.; Chadov, S.; Fecher, G.H.; Schnelle, W.; Hoser, A.; Felser, C. Magnetic and transport properties in the Heusler series Ni
_{2-x}Mn_{1+x}Sn affected by chemical disorder. Intermetallics**2015**, 57, 101–112. [Google Scholar] [CrossRef] - Comtesse, D.; Gruner, M.E.; Ogura, M.; Sokolovskiy, V.V.; Buchelnikov, V.D.; Grünebohm, A.; Arróyave, R.; Singh, N.; Gottschall, T.; Gutfleisch, O.; et al. First-principles calculation of the instability leading to giant inverse magnetocaloric effects. Phys. Rev. B
**2014**, 89, 184403. [Google Scholar] [CrossRef][Green Version] - Jezierski, A. Electronic structure, magnetic, optical and thermodynamic properties of Ni
_{2}Mn_{1-x}Re_{x}Sn and NiMn_{1-x}Re_{x}Sn Heusler alloys-ab-initio study. J. Alloys Compd.**2019**, 803, 153–164. [Google Scholar] [CrossRef] - Saunders, N.; Miodownik, A. CALPHAD (Calculation of Phase Diagrams): A Comprehensive Guide; Elsevier Ltd.: New York, NY, USA, 1998. [Google Scholar] [CrossRef]
- Lukas, H.; Fries, S.; Sundman, B. Computational Thermodynamics (The Calphad Method), 1st ed.; Cambridge University Press: New York, NY, USA, 2007. [Google Scholar] [CrossRef]
- Guo, C.; Du, Z. Thermodynamic optimization of the Mn–Ni system. Intermetallics
**2005**, 13, 525–534. [Google Scholar] [CrossRef] - Miettinen, J. Thermodynamic solution phase data for binary Mn-based systems. Calphad
**2001**, 25, 43–58. [Google Scholar] [CrossRef] - Walnsch, A.; Kriegel, M.J.; Rudolph, M.; Motylenko, M.; Fabrichnaya, O.; Leineweber, A. Thermodynamic assessment and experimental investigation of the Al–Mn–Ni system. Calphad
**2019**, 64, 78–89. [Google Scholar] [CrossRef] - Miettinen, J. Thermodynamic description of the Cu–Mn–Sn system in the copper-rich corner. Calphad
**2004**, 28, 71–77. [Google Scholar] [CrossRef] - Rababah, M.; Itradat, A.; Almagableh, A.; Aljarrah, M.; Obeidat, S.; Al-Hadeethi, R. Thermodynamic calculations of the Mn–Sn, Mn–Sr and Mg–Mn–{Sn, Sr} systems. IET Sci. Meas. Technol.
**2015**, 9, 681–692. [Google Scholar] [CrossRef][Green Version] - Zemanová, A.; Kroupa, A.; Dinsdale, A. Theoretical assessment of the Ni–Sn system. Monatshefte Chem. Chem. Mon.
**2012**, 143, 1255–1261. [Google Scholar] [CrossRef] - Liu, H.S.; Wang, J.; Jin, Z.P. Thermodynamic optimization of the Ni–Sn binary system. Calphad
**2004**, 28, 363–370. [Google Scholar] [CrossRef] - Li, J.; Zhang, Z.; Sun, Y.; Zhang, J.; Zhou, G.; Luo, H.; Liu, G. The thermodynamic, electronic and magnetic properties of Ni
_{2}MnX (X=Ge, Sn, Sb) Heusler alloys: A quasi-hormonic Debye model and first principles study. Phys. B Condens. Matter**2013**, 409, 35–41. [Google Scholar] [CrossRef] - Podgornykh, S.; Streltsov, S.; Kazantsev, V.; Shreder, E. Heat capacity of Heusler alloys: Ferromagnetic Ni
_{2}MnSb, Ni_{2}MnSn, NiMnSb and antiferromagnetic CuMnSb. J. Magn. Magn. Mater.**2007**, 311, 530–534. [Google Scholar] [CrossRef] - Vřešťál, J. Recent progress in modelling of sigma-phase. Arch. Metall.
**2001**, 46, 239–247. [Google Scholar] - Havránková, J.; Vřešťál, J.; Wang, L.G.; Šob, M. Ab initio analysis of energetics of σ-phase formation in Cr-based systems. Phys. Rev. B
**2001**, 63, 174104. [Google Scholar] [CrossRef] - Burton, P.; Dupin, N.; Fries, S.; Grimvall, G.; Guillermet, A.F.; Miodownik, P.; Oates, W.A.; Vinograd, V. Using ab Iiitio calculations in the CALPHAD environment. Z. Für Met.
**2001**, 92, 514–537. [Google Scholar] - Kaufman, L.; Turchi, P.; Huang, W.; Liu, Z.K. Thermodynamics of the Cr-Ta-W system by combining the ab initio and CALPHAD methods. Calphad
**2001**, 25, 419–433. [Google Scholar] [CrossRef] - Dutta, B.; Opahle, I.; Hickel, T. Interface effects on the magnetic properties of layered Ni
_{2}MnGa/Ni_{2}MnSn alloys: A first-principles investigation. Funct. Mater. Lett.**2016**, 9, 1642010. [Google Scholar] [CrossRef] - Entel, P.; Gruner, M.E.; Acet, M.; Çakır, A.; Arróyave, R.; Duong, T.; Sahoo, S.; Fähler, S.; Sokolovskiy, V.V. Properties and decomposition of Heusler alloys. Energy Technol.
**2018**, 6, 1478–1490. [Google Scholar] [CrossRef] - Waske, A.; Dutta, B.; Teichert, N.; Weise, B.; Shayanfar, N.; Becker, A.; Hütten, A.; Hickel, T. Coupling phenomena in magnetocaloric materials. Energy Technol.
**2018**, 6, 1429–1447. [Google Scholar] [CrossRef] - Zhang, K.; Tian, X.; Tan, C.; Guo, E.; Zhao, W.; Cai, W. Designing a new Ni-Mn-Sn ferromagnetic shape memory alloy with excellent performance by Cu addition. Metals
**2018**, 8, 152. [Google Scholar] [CrossRef][Green Version] - Buchelnikov, V.D.; Sokolovskiy, V.V.; Miroshkina, O.N.; Zagrebin, M.A.; Nokelainen, J.; Pulkkinen, A.; Barbiellini, B.; Lähderanta, E. Correlation effects on ground-state properties of ternary Heusler alloys: First-principles study. Phys. Rev. B
**2019**, 99, 014426. [Google Scholar] [CrossRef][Green Version] - Benguerine, O.; Nabi, Z.; Benichou, B.; Bouabdallah, B.; Bouchenafa, H.; Maachou, M.; Ahuja, R. Structural, elastic, electronic, and magnetic properties of Ni
_{2}MnSb, Ni_{2}MnSn, and Ni_{2}MnSb_{0.5}Sn_{0.5}magnetic shape memory alloys. Rev. Mex. Fis.**2020**, 66, 121–126. [Google Scholar] [CrossRef] - Zagrebin, M.A.; Sokolovskiy, V.V.; Buchelnikov, V.D. Ab initio calculations of structural and magnetic properties of Ni-Co-Mn-Cr-Sn supercell. Intermetallics
**2017**, 87, 55–60. [Google Scholar] [CrossRef] - Pramanick, S.; Dutta, P.; Chatterjee, S.; Majumdar, S.; Chatterjee, S. Anomalous pressure effect on the magnetic properties of Ni-Mn based shape memory alloys. J. Appl. Phys.
**2018**, 124, 133901. [Google Scholar] [CrossRef] - Sokolovskiy, V.V.; Zagrebin, M.A.; Buchelnikov, V.D.; Entel, P. The effect of anti-site disorder on structural and magnetic properties of Ni-Co-Mn-In alloys: Ab initio and Monte Carlo studies. IEEE Trans. Magn.
**2018**, 54, 1–5. [Google Scholar] [CrossRef] - Sokolovskiy, V.; Zagrebin, M.; Buchelnikov, V.D. First-principles study of Ni-Co-Mn-Sn alloys with regular and inverse Heusler structure. J. Magn. Magn. Mater.
**2019**, 476, 546–550. [Google Scholar] [CrossRef] - Sokolovskiy, V.; Miroshkina, O.; Zagrebin, M.; Buchelnikov, V. Prediction of giant magnetocaloric effect in Ni
_{40}Co_{10}Mn_{36}Al_{14}Heusler alloys: An insight from ab initio and Monte Carlo calculations. J. Appl. Phys.**2020**, 127, 163901. [Google Scholar] [CrossRef][Green Version] - Kresse, G.; Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. Rev. B
**1993**, 47, 558–561. [Google Scholar] [CrossRef] [PubMed] - Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B
**1996**, 54, 11169–11186. [Google Scholar] [CrossRef] [PubMed] - Hohenberg, P.; Kohn, W. Inhomogeneous electron gas. Phys. Rev. B
**1964**, 136, B864–B871. [Google Scholar] [CrossRef][Green Version] - Kohn, W.; Sham, L.J. Self-consistent equations including exchange and correlation effects. Phys. Rev. A
**1965**, 140, A1133–A1138. [Google Scholar] [CrossRef][Green Version] - Blöchl, P.E. Projector augmented-wave method. Phys. Rev. B
**1994**, 50, 17953–17979. [Google Scholar] [CrossRef] [PubMed][Green Version] - Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B
**1999**, 59, 1758–1775. [Google Scholar] [CrossRef] - Perdew, J.P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett.
**1996**, 77, 3865–3868. [Google Scholar] [CrossRef][Green Version] - Kamarád, J.; Machátová, Z.; Arnold, Z. High pressure cells for magnetic measurements - Destruction and functional tests. Rev. Sci. Instrum.
**2004**, 75, 5022–5025. [Google Scholar] [CrossRef] - Sokolovskiy, V.V.; Buchelnikov, V.D.; Zagrebin, M.A.; Entel, P.; Sahoo, S.; Ogura, M. First-principles investigation of chemical and structural disorder in magnetic Ni
_{2}Mn_{1+x}Sn_{1-x}Heusler alloys. Phys. Rev. B**2012**, 86, 134418. [Google Scholar] [CrossRef] - Szytuła, A.; Kołodziejczyk, A.; Rżany, H.; Todorović, J.; Wanic, A. Atomic and magnetic structure of the Heusler alloys Ni
_{2}MnSb, Ni_{2}MnSn, and Co_{2}MnSn. Phys. Status Solidi (a)**1972**, 11, 57–65. [Google Scholar] [CrossRef] - Chen, X.Q.; Wolf, W.; Podloucky, R.; Rogl, P.; Marsman, M. Ab initio study of ground-state properties of the Laves-phase compound ZrMn
_{2}. Phys. Rev. B**2005**, 72, 054440. [Google Scholar] [CrossRef] - Unzueta, I.; Sánchez-Alarcos, V.; Recarte, V.; Pérez-Landazábal, J.I.; Zabala, N.; García, J.A.; Plazaola, F. Identification of a Ni-vacancy defect in Ni-Mn-Z (Z = Ga, Sn, In): An experimental and DFT positron-annihilation study. Phys. Rev. B
**2019**, 99, 064108. [Google Scholar] [CrossRef] - Momma, K.; Izumi, F. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr.
**2011**, 44, 1272–1276. [Google Scholar] [CrossRef]

**Figure 1.**Schematic visualizations of 4-atom rhombohedral primitive unit cell (

**a**) and 16-atom computational supercell (

**b**) of the stoichiometric Ni${}_{2}$MnSn with the austenitic structure (L2${}_{1}$, so-called full Heusler structure). Arrows in part (

**a**) indicate the orientation of local magnetic moments and numbers accompanying them are their magnitudes in Bohr magnetons with negative values indicating an antiparallel orientation (also underlined for the sake of clarity).

**Figure 2.**Computed total energy difference of the austenitic stoichiometric Ni${}_{2}$MnSn with different values of the fixed total magnetic moment with respect to the energy of the ground state (

**a**). Arrows indicate experimental value of the magnetic moment and the theoretical value corresponding to the minimum of the energy. Part (

**b**) shows calculated pressure-induced changes of the total magnetic moment $\mu $ relative to its zero-pressure value ${\mu}_{0}$. The inset contains a linear fit through the values in the lower-pressure region and its parameters including the value of d(ln$\mu )/$dp close to the zero-pressure magnetic moment ${\mu}_{0}$ approximated as $(1/{\mu}_{0})$ d$\mu /$dp = d$(\mu /{\mu}_{0})/$dp = −0.0036 GPa${}^{-1}$.

**Figure 3.**A 16-atom computational supercell of the austenitic stoichiometric Ni${}_{2}$MnSn with one Mn atoms swapping one Sn atom as indicated by the red arrow (

**a**) with the local magnetic moment of the swapped Mn atom (on the Sn sublattice) having the orientation equal as that of Mn atoms at the Mn sublattice. Included are also values of local magnetic moments (in Bohr magnetons) corresponding to a minimum-energy zero-pressure state. Part (

**b**) shows the calculated pressure-induced changes of the total magnetic moment of the state in part (

**a**) together with the corresponding linear fit. Figure (

**c**) shows a state with the swapped Mn atom having its local magnetic moments anti-parallel to the Mn atoms on the Mn sublattice. Part (

**d**) shows calculated pressure-induced changes of the total magnetic moment of the state shown in part (

**c**) together with the corresponding linear fit. Magnitudes of local magnetic moments are listed in Bohr magnetons and negative underlined values mean antiparallel orientation.

**Figure 4.**A schematic visualization of a 16-atom computational supercell of the austenitic stoichiometric Ni${}_{2}$MnSn (

**a**) with one Mn atom swapping with one Ni atom (indicated by the red arrow) with the local magnetic moments of the swapped Mn atom having the orientation equal as that of the Mn atoms at the Mn sublattice. Part (

**b**) shows calculated pressure-induced changes of the total magnetic moment of this state (the computed data points are accompanied by a linear fit and its parameters). Figure (

**c**) shows a state with the swapped Mn atom having its local magnetic moments anti-parallel to those of Mn atoms on the Mn sublattice. Part (

**d**) exhibits calculated pressure-induced changes of the total magnetic moment of the state shown in part (

**c**) together with the corresponding linear fit. Magnitudes of local magnetic moments are listed in Bohr magnetons and negative underlined values mean antiparallel orientation.

**Figure 5.**Similar set of figures as in Figure 4 but with three times more swapped atoms (three Mn atoms swapping with three Ni atoms, see red arrows). Schematic visualizations including local magnetic moments are shown in parts (

**a**,

**c**) for states FM and AFM coupled Mn atoms, respectively. The corresponding pressure-induced changes are presented in parts (

**b**,

**d**). Magnitudes of local magnetic moments are listed in Bohr magnetons and negative values indicate antiparallel orientation.

**Figure 6.**A 16-atom computational supercell of the stoichiometric Ni${}_{2}$MnSn with the inverse Heusler structure (

**a**) and local magnetic moments corresponding to a minimum-energy zero-pressure state. Part (

**b**) shows calculated pressure-induced changes of the total magnetic moment of the state shown in part (

**a**) together with the corresponding linear fit.

**Figure 7.**A schematic visualization of a 16-atom computational supercell of the austenitic stoichiometric Ni${}_{2}$MnSn with one Sn atoms swapping one Ni atom as indicated by the red arrows (

**a**) accompanied by values of local magnetic moments (in Bohr magnetons) corresponding to a minimum-energy zero-pressure state. Part (

**b**) shows calculated pressure-induced changes of the total magnetic moment of the state shown in part (

**a**) together with the corresponding linear fit.

**Figure 8.**Computed changes of the magnetic moment of individual Mn atoms (

**a**) as well as those of Ni atoms and in the interstitial region (

**b**) in the case of FM-coupled single Mn-Ni swap.

**Figure 9.**Computed compositional dependence of formation energy of systems with Mn-Ni swaps as a function of their number in 16-atom supercells modeling stoichiometric Ni${}_{2}$MnSn (

**a**). Part (

**b**) shows a pressure-dependence of the energy difference between AFM and FM-coupled states.

**Table 1.**Computed properties of the studied systems including the lattice parameters of the 16-atom supercells, formation energies ${E}_{\mathrm{f}}$ (in eV per atom), total magnetic moments ${\mu}^{\mathrm{TOT}}$ (in ${\mu}_{\mathrm{B}}$ per 4-atom formula unit, f.u.) and its pressure derivatives d$(ln\mu )$/d p. States with a lower formation energy (from the pair of either FM-coupled or AFM-coupled one) have their formation energy printed in bold.

System | Mn-Mn Coupling | Lattice Parameter | ${\mathit{\mu}}^{\mathbf{TOT}}$ | ${\mathit{E}}_{\mathbf{f}}$ | $\mathit{d}(ln\mathit{\mu})/\mathit{d}\mathit{p}$ |
---|---|---|---|---|---|

(Å) | (${\mathit{\mu}}_{\mathbf{B}}$/f.u.) | (eV/atom) | (GPa${}^{-1}$) | ||

Ni${}_{8}$Mn${}_{4}$Sn${}_{4}$ L2${}_{1}$ full Heusler | FM | 6.059 | 4.09 | −0.167 | −0.0036 |

Ni${}_{8}$Mn${}_{4}$Sn${}_{4}$ Mn swaps Sn | FM | 6.083 | 4.03 | −0.074 | −0.0035 |

Ni${}_{8}$Mn${}_{4}$Sn${}_{4}$ Mn swaps Sn | AFM | 6.076 | 1.87 | −0.066 | −0.0047 |

Ni${}_{8}$Mn${}_{4}$Sn${}_{4}$ Mn swaps Ni | FM | 6.058 | 3.75 | −0.113 | -0.0119 |

Ni${}_{8}$Mn${}_{4}$Sn${}_{4}$ Mn swaps Ni | AFM | 6.053 | 2.09 | −0.107 | −0.0037 |

Ni${}_{8}$Mn${}_{4}$Sn${}_{4}$ 3 Mn swap 3 Ni | FM | 6.054 | 3.58 | −0.029 | −0.0098 |

Ni${}_{8}$Mn${}_{4}$Sn${}_{4}$ 3 Mn swap 3 Ni | AFM | 6.049 | 1.57 | −0.040 | −0.0107 |

Ni${}_{8}$Mn${}_{4}$Sn${}_{4}$ inverse Heusler | FM | 6.048 | 3.51 | −0.019 | −0.0070 |

Ni${}_{8}$Mn${}_{4}$Sn${}_{4}$ Ni swaps Sn | FM | 6.106 | 4.04 | −0.012 | −0.0048 |

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Friák, M.; Mazalová, M.; Turek, I.; Zemanová, A.; Kaštil, J.; Kamarád, J.; Míšek, M.; Arnold, Z.; Schneeweiss, O.; Všianská, M.;
et al. An Ab Initio Study of Pressure-Induced Changes of Magnetism in Austenitic Stoichiometric Ni_{2}MnSn. *Materials* **2021**, *14*, 523.
https://doi.org/10.3390/ma14030523

**AMA Style**

Friák M, Mazalová M, Turek I, Zemanová A, Kaštil J, Kamarád J, Míšek M, Arnold Z, Schneeweiss O, Všianská M,
et al. An Ab Initio Study of Pressure-Induced Changes of Magnetism in Austenitic Stoichiometric Ni_{2}MnSn. *Materials*. 2021; 14(3):523.
https://doi.org/10.3390/ma14030523

**Chicago/Turabian Style**

Friák, Martin, Martina Mazalová, Ilja Turek, Adéla Zemanová, Jiří Kaštil, Jiří Kamarád, Martin Míšek, Zdeněk Arnold, Oldřich Schneeweiss, Monika Všianská,
and et al. 2021. "An Ab Initio Study of Pressure-Induced Changes of Magnetism in Austenitic Stoichiometric Ni_{2}MnSn" *Materials* 14, no. 3: 523.
https://doi.org/10.3390/ma14030523