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• 1.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, The Institute of Technology.
Complex magnetism in nanolaminated Mn2GaC2014Manuscript (preprint) (Other academic)

We have used first-principles calculations and Heisenberg Monte Carlo simulations to search for the magnetic ground state of Mn2GaC, a recently synthesized magnetic nanolaminate. We have, independent on method, identified a range of low energy collinear as well as non-collinear magnetic configurations, indicating a highly frustrated magnetic material with several nearly degenerate magnetic states. An experimentally obtained magnetization of only 0.29 per Mn atom in Mn2GaC may be explained by canted spins in an antiferromagnetic configuration of ferromagnetically ordered sub-layers with alternating spin orientation, denoted AFM[0001]$\smal\text{A}\atop\text{4}$. Furthermore, low temperature X-ray diffraction show a new basal plane peak appearing upon a magnetic transition, which is consistent with the here predicted change in inter-layer spacing for the AFM[0001]$\smal\text{A}\atop\text{4}$ configuration.

• 2.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Magnetically driven anisotropic structural changes in the atomic laminate Mn2GaC2016In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 93, no 1, p. 014410-Article in journal (Refereed)

Inherently layered magnetic materials, such as magnetic M(n+1)AX(n) (MAX) phases, offer an intriguing perspective for use in spintronics applications and as ideal model systems for fundamental studies of complex magnetic phenomena. The MAX phase composition M(n+1)AX(n) consists of M(n+1)AX(n) blocks separated by atomically thin A-layers where M is a transition metal, A an A-group element, X refers to carbon and/or nitrogen, and n is typically 1, 2, or 3. Here, we show that the recently discovered magnetic Mn2GaC MAX phase displays structural changes linked to the magnetic anisotropy, and a rich magnetic phase diagram which can be manipulated through temperature and magnetic field. Using first-principles calculations and Monte Carlo simulations, an essentially one-dimensional (1D) interlayer plethora of two-dimensioanl (2D) Mn-C-Mn trilayers with robust intralayer ferromagnetic spin coupling was revealed. The complex transitions between them were observed to induce magnetically driven anisotropic structural changes. The magnetic behavior as well as structural changes dependent on the temperature and applied magnetic field are explained by the large number of low energy, i.e., close to degenerate, collinear and noncollinear spin configurations that become accessible to the system with a change in volume. These results indicate that the magnetic state can be directly controlled by an applied pressure or through the introduction of stress and show promise for the use of Mn2GaC MAX phases in future magnetoelectric and magnetocaloric applications.

• 3.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Linköping University, Faculty of Science & Engineering. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Electronic structure, bonding characteristics, and mechanical properties in (W2/3Sc1/3)(2)AIC and (W2/3Y1/3)(2)AIC i-MAX phases from first-principles calculations2018In: Journal of Physics: Condensed Matter, ISSN 0953-8984, E-ISSN 1361-648X, Vol. 30, no 30, article id 305502Article in journal (Refereed)

With the recent discovery of in-plane chemically ordered MAX phases (i-MAX) of the general formula ((M2/3M1/32)-M-1)(2)AC comes addition of non-traditional MAX phase elements. In the present study, we use density functional theory calculations to investigate the electronic structure, bonding nature, and mechanical properties of the novel (W2/3Sc1/3)(2)AlC and (W2/3Y1/3)(2)AlC i-MAX phases. From analysis of the electronic structure and projected crystal orbital Hamilton populations, we show that the metallic i-MAX phases have significant hybridization between W and C, as well as Sc(Y) and C states, indicative of strong covalent bonding. Substitution of Sc for Y (M-2) leads to reduced bonding strength for W-C and Al-Al interactions while M-2-C and M-2-Al interactions are strengthened. We also compare the Voigt-Reuss-Hill bulk, shear, and Youngs moduli along the series of M-1 = Cr, Mo, and W, and relate these trends to the bonding interactions. Furthermore, we find overall larger moduli for Sc-based i-MAX phases.

• 4.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Linköping University, Faculty of Science & Engineering. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Electronic structure, bonding characteristics, and mechanical properties in (W2/3Sc1/3)(2)AIC and (W2/3Y1/3)(2)AIC i-MAX phases from first-principles calculations2018In: Journal of Physics: Condensed Matter, ISSN 0953-8984, E-ISSN 1361-648X, Vol. 30, no 30, article id 305502Article in journal (Refereed)

With the recent discovery of in-plane chemically ordered MAX phases (i-MAX) of the general formula ((M2/3M1/32)-M-1)(2)AC comes addition of non-traditional MAX phase elements. In the present study, we use density functional theory calculations to investigate the electronic structure, bonding nature, and mechanical properties of the novel (W2/3Sc1/3)(2)AlC and (W2/3Y1/3)(2)AlC i-MAX phases. From analysis of the electronic structure and projected crystal orbital Hamilton populations, we show that the metallic i-MAX phases have significant hybridization between W and C, as well as Sc(Y) and C states, indicative of strong covalent bonding. Substitution of Sc for Y (M-2) leads to reduced bonding strength for W-C and Al-Al interactions while M-2-C and M-2-Al interactions are strengthened. We also compare the Voigt-Reuss-Hill bulk, shear, and Youngs moduli along the series of M-1 = Cr, Mo, and W, and relate these trends to the bonding interactions. Furthermore, we find overall larger moduli for Sc-based i-MAX phases.

• 5.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, The Institute of Technology.
A theoretical investigation of Tin+1AlCn and Mn2GaC MAX phases: phase stability and materials properties2014Licentiate thesis, comprehensive summary (Other academic)

This thesis presents theoretical research on MAX phases (M=transition metal, A=A-group element, X=carbon and/or nitrogen), with focus on predictions of phase stability as well as of physical properties.

The first part is an investigation of the phase stability of the MAX phases Ti2AlC, Ti3AlC2, and Ti4AlC3 at elevated temperatures, where the former two phases have been obtained experimentally. Phase stability calculations of MAX phases usually do not take temperature dependent effects such as electronic excitations and lattice vibrations into consideration due to significantly increased computational cost. The results have nevertheless so far been quite accurate, with good agreement between theory and experiments. Still, the question whether the inclusion of temperature into the calculations could significantly alter the results as compared to previous 0 K calculations needs to be investigated, since this has bearing on the reliability of future predictions of the stability of not yet known MAX phases. However, it is shown that for Tin+1AlCn, the different temperature dependent effects largely cancel each other. The results therefore suggest that to go beyond 0 K calculations for phase stability predictions of MAX phases is motivated only for borderline cases.

The second part investigates the Mn2GaC MAX phase, which was recently predicted from theoretical phase stability calculations and subsequently synthesized. As a new member of the MAX phase family as well as being one of the first known MAX phases to exhibit magnetism, it is of interest to explore its physical properties. Here, we have used firstprinciples calculations to determine the electronic, vibrational and elastic properties. Analysis of the electronic band structure indicates anisotropy in transport properties, while the electronic and phonon density of states shows that the relative orientation of the Mn magnetic moments over the Ga layers affects the distribution of the electronic and vibrational states for both Mn and Ga.

The Voigt bulk, Voigt shear, and Young's modulus is also investigated, together with the Poisson's ratio, the elastic anisotropy, and the  machinability via two machinability indices. In relation to experimental results of the moduli of other M2AC phases, the Voigt bulk and shear moduli are concluded to be fairly low, 157 and 93 GPa, respectively, while the magnitude of the Young's modulus at 233 GPa is intermediate. The Poisson's ratio, which is 0.25, on the other hand, is comparatively high. The phase is shown to be elastically quite isotropic, and, just as other M2GaC phases, also machinable. As all here investigated properties are affected by the choice of magnetic spin configuration, the results show the importance of identifying the correct magnetic ground state in future theoretical work on magnetic MAX phases.

1. Temperature dependent phase stability of nanolaminated ternaries from first-principles calculations
Open this publication in new window or tab >>Temperature dependent phase stability of nanolaminated ternaries from first-principles calculations
2014 (English)In: Computational materials science, ISSN 0927-0256, E-ISSN 1879-0801, Vol. 91, p. 251-257Article in journal (Refereed) Published
##### Abstract [en]

Methods based on first-principles calculations have proven effective for predicting the thermodynamic stability of materials that have not previously been considered. However, the vast majority of these predictions are based on 0 K calculations, which means that little is known about the effects of temperature on their accuracy. This causes considerable uncertainty with respect to stability predictions of new hypothetical phases. In this work we combine first-principles calculations with an optimization procedure to calculate the phase stability as a function of temperature for Ti2AlC, Ti3AlC2 and Ti4AlC3 MAX phases with respect to their most competing phases in the Ti-Al-C phase diagram, in a temperature interval from 0 to 2000 K. To model nonzero temperatures, we include effects from the electronic and vibrational free energies to the Gibbs free energy for all relevant competing phases. We show that, due to a mutual cancellation of the temperature dependent energy terms, the results of neither the harmonic nor the quasiharmonic calculations differ significantly from the calculated 0 K formation energies. We thus provide a plausible explanation for the success of previous 0 K predictions, an explanation which also serves as evidence for the hypothesis that the phase stability in many materials systems is primarily governed by the 0 K energy terms.

##### Place, publisher, year, edition, pages
Elsevier, 2014
##### Keywords
First-principles; Phase stability; Ternary carbides; Harmonic approximation; Quasiharmonic approximation; Density functional theory
##### National Category
Physical Sciences
##### Identifiers
urn:nbn:se:liu:diva-109360 (URN)10.1016/j.commatsci.2014.04.055 (DOI)000339129100032 ()
Available from: 2014-08-15 Created: 2014-08-15 Last updated: 2017-12-05Bibliographically approved
2. First-principles calculations of the electronic, vibrational, and elastic properties of the magnetic laminate Mn2GaC
Open this publication in new window or tab >>First-principles calculations of the electronic, vibrational, and elastic properties of the magnetic laminate Mn2GaC
2014 (English)In: Journal of Applied Physics, ISSN 0021-8979, E-ISSN 1089-7550, Vol. 116, no 10, p. 103511-Article in journal (Refereed) Published
##### Abstract [en]

In this paper, we report the by first-principles predicted properties of the recently discovered magnetic MAX phase Mn2GaC. The electronic band structure and vibrational dispersion relation, as well as the electronic and vibrational density of states, have been calculated. The band structure close to the Fermi level indicates anisotropy with respect to electrical conductivity, while the distribution of the electronic and vibrational states for both Mn and Ga depend on the chosen relative orientation of the Mn spins across the Ga sheets in the Mn–Ga–Mn trilayers. In addition, the elastic properties have been calculated, and from the five elastic constants, the Voigt bulk modulus is determined to be 157 GPa, the Voigt shear modulus 93 GPa, and the Young's modulus 233 GPa. Furthermore, Mn2GaC is found relatively elastically isotropic, with a compression anisotropy factor of 0.97, and shear anisotropy factors of 0.9 and 1, respectively. The Poisson's ratio is 0.25. Evaluated elastic properties are compared to theoretical and experimental results for M 2 AC phases where M = Ti, V, Cr, Zr, Nb, Ta, and A = Al, S, Ge, In, Sn

##### Place, publisher, year, edition, pages
American Institute of Physics (AIP), 2014
##### National Category
Physical Sciences
##### Identifiers
urn:nbn:se:liu:diva-111954 (URN)10.1063/1.4894411 (DOI)000342833700023 ()
Available from: 2014-11-11 Created: 2014-11-11 Last updated: 2017-12-05Bibliographically approved
• 6.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Phase stability and physical properties of nanolaminated materials from first principles2016Doctoral thesis, comprehensive summary (Other academic)

The MAX phase family is a set of nanolaminated, hexagonal materials typically comprised of three elements: a transition metal (M), an A-group element (A), and carbon and/or nitrogen (X). In this thesis, first-principles based methods have been used to investigate the phase stability and physical properties of a number of MAX and MAX-like phases.

Most theoretical work on MAX phase stability use the constraint of 0 K conditions, due to the very high computational cost of including temperature dependent effects such as lattice vibrations and electronic excitations for all relevant competing phases in the ternary or multinary chemical space. Despite this, previous predictions of the existence of new MAX phases have to a large extent been experimentally verified. In an attempt to provide a possible explanation for this consistency, and thus help strengthen the confidence in future predictions, we have calculated the temperature dependent phase stability of Tin+1AlCn, to date the most studied MAX phases. We show that both the electronic and vibrational contribution to the Gibbs free energies of the MAX phases are  cancelled by the corresponding contributions to the Gibbs free energies of the competing phases. We further show that this is the case even when thermal expansion is considered.

We have also investigated the stability of two hypothetical MAX-like phases, V2Ga2C and (Mo1-xVx)2Ga2C, motivated by a search for ways to attain new two-dimensional MAX phase derivatives, so-called MXenes. We predict that it is possible to synthesize both phases. For x≤0.25, stability of (Mo1-xVx)2Ga2C is indicated for both ordered and disordered solid solutions on the M sublattice. For x=0.5 and x≥0.75, stability is only indicated for disordered solutions. The ordered solutions are stable at temperatures below 1000 K, whereas stabilization of the disordered solutions requires temperatures of up to 2100 K, depending on the V concentration.

Finally, we have investigated the electronic, vibrational, and magnetic properties of the recently synthesized MAX phase Mn2GaC. We show that the electronic band structure is anisotropic, and determine the bulk, shear, and Young’s modulus to be 157, 93, and 233 GPa, respectively, and Poisson’s ratio to be 0.25. We further predict the magnetic critical order-disorder temperature of Mn2GaC to be 660 K. We base the predictions on Monte Carlo simulations of a bilinear Heisenberg Hamiltonian constructed from magnetic exchange interaction parameters derived using two different supercell methods: the novel magnetic direct cluster averaging method (MDCA), and the Connolly-Williams method (CW). We conclude that CW is less computationally expensive than MDCA for chemically and topologically ordered phases such as Mn2GaC.

1. Temperature dependent phase stability of nanolaminated ternaries from first-principles calculations
Open this publication in new window or tab >>Temperature dependent phase stability of nanolaminated ternaries from first-principles calculations
2014 (English)In: Computational materials science, ISSN 0927-0256, E-ISSN 1879-0801, Vol. 91, p. 251-257Article in journal (Refereed) Published
##### Abstract [en]

Methods based on first-principles calculations have proven effective for predicting the thermodynamic stability of materials that have not previously been considered. However, the vast majority of these predictions are based on 0 K calculations, which means that little is known about the effects of temperature on their accuracy. This causes considerable uncertainty with respect to stability predictions of new hypothetical phases. In this work we combine first-principles calculations with an optimization procedure to calculate the phase stability as a function of temperature for Ti2AlC, Ti3AlC2 and Ti4AlC3 MAX phases with respect to their most competing phases in the Ti-Al-C phase diagram, in a temperature interval from 0 to 2000 K. To model nonzero temperatures, we include effects from the electronic and vibrational free energies to the Gibbs free energy for all relevant competing phases. We show that, due to a mutual cancellation of the temperature dependent energy terms, the results of neither the harmonic nor the quasiharmonic calculations differ significantly from the calculated 0 K formation energies. We thus provide a plausible explanation for the success of previous 0 K predictions, an explanation which also serves as evidence for the hypothesis that the phase stability in many materials systems is primarily governed by the 0 K energy terms.

##### Place, publisher, year, edition, pages
Elsevier, 2014
##### Keywords
First-principles; Phase stability; Ternary carbides; Harmonic approximation; Quasiharmonic approximation; Density functional theory
##### National Category
Physical Sciences
##### Identifiers
urn:nbn:se:liu:diva-109360 (URN)10.1016/j.commatsci.2014.04.055 (DOI)000339129100032 ()
Available from: 2014-08-15 Created: 2014-08-15 Last updated: 2017-12-05Bibliographically approved
2. Phase stability of the nanonlaminates V2Ga2C and (Mo1-xVx)2Ga2C from first-principles calculations
Open this publication in new window or tab >>Phase stability of the nanonlaminates V2Ga2C and (Mo1-xVx)2Ga2C from first-principles calculations
##### Abstract [en]

We here use first-principles calculations to investigate the phase stability of the hypothetical laminated materials V2Ga2C and the related alloy (Mo1-xVx)2Ga2C, the latter for a potential parent material for synthesis of (Mo1-xVx)2C, a new two-dimensional material in the family of so called MXenes. We predict that V2Ga2C is thermodynamically stable with respect to all identified competing phases in the ternary VGa-C phase diagram. We further predict the stability for ordered and disordered configurations of Mo and V in (Mo1-xVx)2Ga2C and predict that ordered (Mo1-xVx)2Ga2C for 𝑥 ≤ 0.25 is stable, with an orderdisorder transition temperature of ~1000 K. Furthermore, (Mo1-xVx)2Ga2C for 𝑥 = 0.5 and 𝑥 ≥ 0.75 is suggested to potentially be stable, but only for disordered Mo-V configurations, and only at elevated temperatures. We have also investigated the electronic and elastic properties of V2Ga2C; the calculated bulk, shear, and Young’s modulus are 141, 95, and 232 GPa, respectively.

##### National Category
Physical Sciences
##### Identifiers
urn:nbn:se:liu:diva-124561 (URN)
Available from: 2016-02-03 Created: 2016-02-03 Last updated: 2017-11-03Bibliographically approved
3. First-principles calculations of the electronic, vibrational, and elastic properties of the magnetic laminate Mn2GaC
Open this publication in new window or tab >>First-principles calculations of the electronic, vibrational, and elastic properties of the magnetic laminate Mn2GaC
2014 (English)In: Journal of Applied Physics, ISSN 0021-8979, E-ISSN 1089-7550, Vol. 116, no 10, p. 103511-Article in journal (Refereed) Published
##### Abstract [en]

In this paper, we report the by first-principles predicted properties of the recently discovered magnetic MAX phase Mn2GaC. The electronic band structure and vibrational dispersion relation, as well as the electronic and vibrational density of states, have been calculated. The band structure close to the Fermi level indicates anisotropy with respect to electrical conductivity, while the distribution of the electronic and vibrational states for both Mn and Ga depend on the chosen relative orientation of the Mn spins across the Ga sheets in the Mn–Ga–Mn trilayers. In addition, the elastic properties have been calculated, and from the five elastic constants, the Voigt bulk modulus is determined to be 157 GPa, the Voigt shear modulus 93 GPa, and the Young's modulus 233 GPa. Furthermore, Mn2GaC is found relatively elastically isotropic, with a compression anisotropy factor of 0.97, and shear anisotropy factors of 0.9 and 1, respectively. The Poisson's ratio is 0.25. Evaluated elastic properties are compared to theoretical and experimental results for M 2 AC phases where M = Ti, V, Cr, Zr, Nb, Ta, and A = Al, S, Ge, In, Sn

##### Place, publisher, year, edition, pages
American Institute of Physics (AIP), 2014
##### National Category
Physical Sciences
##### Identifiers
urn:nbn:se:liu:diva-111954 (URN)10.1063/1.4894411 (DOI)000342833700023 ()
Available from: 2014-11-11 Created: 2014-11-11 Last updated: 2017-12-05Bibliographically approved
4. Magnetic exchange interactions and critical temperature of the nanolaminate Mn2GaC from first-principles supercell methods
Open this publication in new window or tab >>Magnetic exchange interactions and critical temperature of the nanolaminate Mn2GaC from first-principles supercell methods
2016 (English)In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 93, no 5Article in journal (Refereed) Published
##### Abstract [en]

In this work, we employ and critically evaluate a first-principles approach based on supercell calculations for predicting the magnetic critical order-disorder temperature 𝑇𝑐 . As a model material we use the recently discovered nanolaminate Mn2GaC.

First, we derive the exchange interaction parameters 𝐽𝑖𝑗 between pairs of Mn atoms on sites 𝑖 and 𝑗 of the bilinear Heisenberg Hamiltonian using the novel magnetic direct cluster averaging method (MDCA), and then compare the 𝐽’s from the MDCA calculations to the same parameters calculated using the Connolly-Williams method. We show that the two methods yield closely matching results, but observe that the MDCA method is computationally less effective when applied to highly ordered phases such as Mn2GaC.

Secondly, Monte Carlo simulations are used to derive the magnetic energy, specific heat, and 𝑇𝑐 . For Mn2GaC, we find 𝑇𝑐 = 660 K. The uncertainty in the calculated 𝑇𝑐 caused by possible uncertainties in the 𝐽’s is discussed and exemplified in our case by an analysis of the impact of the statistical uncertainties of the MDCA-derived 𝐽’s, resulting in a 𝑇𝑐 distribution with a standard deviation of 133 K.

##### National Category
Physical Sciences
##### Identifiers
urn:nbn:se:liu:diva-124563 (URN)10.1103/PhysRevB.93.054432 (DOI)000371391800004 ()
##### Note

Funding agencies: European Research Council under the European Community Seventh Framework Program (FP7)/ERC Grant [258509]; Swedish Research Council (VR) [621-2011-4417, 330-2014-6336]; Knut and Alice Wallenberg (KAW) Fellowship program; SSF synergy grant FUNCASE

Available from: 2016-02-03 Created: 2016-02-03 Last updated: 2017-11-30Bibliographically approved
• 7.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, The Institute of Technology.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, The Institute of Technology.
First-principles calculations of the electronic, vibrational, and elastic properties of the magnetic laminate Mn2GaC2014In: Journal of Applied Physics, ISSN 0021-8979, E-ISSN 1089-7550, Vol. 116, no 10, p. 103511-Article in journal (Refereed)

In this paper, we report the by first-principles predicted properties of the recently discovered magnetic MAX phase Mn2GaC. The electronic band structure and vibrational dispersion relation, as well as the electronic and vibrational density of states, have been calculated. The band structure close to the Fermi level indicates anisotropy with respect to electrical conductivity, while the distribution of the electronic and vibrational states for both Mn and Ga depend on the chosen relative orientation of the Mn spins across the Ga sheets in the Mn–Ga–Mn trilayers. In addition, the elastic properties have been calculated, and from the five elastic constants, the Voigt bulk modulus is determined to be 157 GPa, the Voigt shear modulus 93 GPa, and the Young's modulus 233 GPa. Furthermore, Mn2GaC is found relatively elastically isotropic, with a compression anisotropy factor of 0.97, and shear anisotropy factors of 0.9 and 1, respectively. The Poisson's ratio is 0.25. Evaluated elastic properties are compared to theoretical and experimental results for M 2 AC phases where M = Ti, V, Cr, Zr, Nb, Ta, and A = Al, S, Ge, In, Sn

• 8.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Magnetic exchange interactions and critical temperature of the nanolaminate Mn2GaC from first-principles supercell methods2016In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 93, no 5Article in journal (Refereed)

In this work, we employ and critically evaluate a first-principles approach based on supercell calculations for predicting the magnetic critical order-disorder temperature 𝑇𝑐 . As a model material we use the recently discovered nanolaminate Mn2GaC.

First, we derive the exchange interaction parameters 𝐽𝑖𝑗 between pairs of Mn atoms on sites 𝑖 and 𝑗 of the bilinear Heisenberg Hamiltonian using the novel magnetic direct cluster averaging method (MDCA), and then compare the 𝐽’s from the MDCA calculations to the same parameters calculated using the Connolly-Williams method. We show that the two methods yield closely matching results, but observe that the MDCA method is computationally less effective when applied to highly ordered phases such as Mn2GaC.

Secondly, Monte Carlo simulations are used to derive the magnetic energy, specific heat, and 𝑇𝑐 . For Mn2GaC, we find 𝑇𝑐 = 660 K. The uncertainty in the calculated 𝑇𝑐 caused by possible uncertainties in the 𝐽’s is discussed and exemplified in our case by an analysis of the impact of the statistical uncertainties of the MDCA-derived 𝐽’s, resulting in a 𝑇𝑐 distribution with a standard deviation of 133 K.

• 9.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Max Planck Institute Eisenforsch GmbH, Germany. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Phase stability of the nanolaminates V2Ga2C and (Mo1-xVx)(2)Ga2C from first-principles calculations2016In: Physical Chemistry, Chemical Physics - PCCP, ISSN 1463-9076, E-ISSN 1463-9084, Vol. 18, no 18, p. 12682-12688Article in journal (Refereed)

We here use first-principles calculations to investigate the phase stability of the hypothetical laminated material V2Ga2C and the related alloy (Mo1-xVx)(2)Ga2C, the latter for a potential parent material for synthesis of (Mo1-xVx)(2)C, a new two-dimensional material in the family of so called MXenes. We predict that V2Ga2C is thermodynamically stable with respect to all identified competing phases in the ternary V-Ga-C phase diagram. We further calculate the stability of ordered and disordered configurations of Mo and V in (Mo1-xVx)(2)Ga2C and predict that ordered (Mo1-xVx)(2)Ga2C for x &lt;= 0.25 is stable, with an order-disorder transition temperature of similar to 1000 K. Furthermore, (Mo1-xVx)(2)Ga2C for x = 0.5 and x &gt;= 0.75 is suggested to be stable, but only for disordered Mo-V configurations, and only at elevated temperatures. We have also investigated the electronic and elastic properties of V2Ga2C; the calculated bulk, shear, and Youngs modulus are 141, 94, and 230 GPa, respectively.

• 10.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Phase stability of the nanonlaminates V2Ga2C and (Mo1-xVx)2Ga2C from first-principles calculations2016Manuscript (preprint) (Other academic)

We here use first-principles calculations to investigate the phase stability of the hypothetical laminated materials V2Ga2C and the related alloy (Mo1-xVx)2Ga2C, the latter for a potential parent material for synthesis of (Mo1-xVx)2C, a new two-dimensional material in the family of so called MXenes. We predict that V2Ga2C is thermodynamically stable with respect to all identified competing phases in the ternary VGa-C phase diagram. We further predict the stability for ordered and disordered configurations of Mo and V in (Mo1-xVx)2Ga2C and predict that ordered (Mo1-xVx)2Ga2C for 𝑥 ≤ 0.25 is stable, with an orderdisorder transition temperature of ~1000 K. Furthermore, (Mo1-xVx)2Ga2C for 𝑥 = 0.5 and 𝑥 ≥ 0.75 is suggested to potentially be stable, but only for disordered Mo-V configurations, and only at elevated temperatures. We have also investigated the electronic and elastic properties of V2Ga2C; the calculated bulk, shear, and Young’s modulus are 141, 95, and 232 GPa, respectively.

• 11.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, The Institute of Technology.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, The Institute of Technology.
Temperature dependent phase stability of nanolaminated ternaries from first-principles calculations2014In: Computational materials science, ISSN 0927-0256, E-ISSN 1879-0801, Vol. 91, p. 251-257Article in journal (Refereed)

Methods based on first-principles calculations have proven effective for predicting the thermodynamic stability of materials that have not previously been considered. However, the vast majority of these predictions are based on 0 K calculations, which means that little is known about the effects of temperature on their accuracy. This causes considerable uncertainty with respect to stability predictions of new hypothetical phases. In this work we combine first-principles calculations with an optimization procedure to calculate the phase stability as a function of temperature for Ti2AlC, Ti3AlC2 and Ti4AlC3 MAX phases with respect to their most competing phases in the Ti-Al-C phase diagram, in a temperature interval from 0 to 2000 K. To model nonzero temperatures, we include effects from the electronic and vibrational free energies to the Gibbs free energy for all relevant competing phases. We show that, due to a mutual cancellation of the temperature dependent energy terms, the results of neither the harmonic nor the quasiharmonic calculations differ significantly from the calculated 0 K formation energies. We thus provide a plausible explanation for the success of previous 0 K predictions, an explanation which also serves as evidence for the hypothesis that the phase stability in many materials systems is primarily governed by the 0 K energy terms.

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