Recent progress in simulations of the paramagnetic state of magnetic materials

Abrikosov, Igor A.; Ponomareva, A. V.; Steneteg, Peter; Баранникова, С. А.; Alling, Björn

doi:10.1016/j.cossms.2015.07.003

Cited by 88 publications

(60 citation statements)

References 152 publications

(296 reference statements)

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“…This remains then an unquantified potential inaccuracy in our calculations. If needed, it should be possible to capture the effect of this phenomenon on the FE perturbatively at each temperature, starting from the results developed here and using emerging methods for quantifying combined electronic-magnetic-vibrational effects [81][82][83] . The computational framework developed here can be used as a basis for calculation of regions of stability for various phases of iron at high pressure and temperature, solely based on ab initio methods.…”

Section: Discussionmentioning

confidence: 99%

Accurate and precise ab initio anharmonic free-energy calculations for metallic crystals: Application to hcp Fe at high temperature and pressure

et al. 2017

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A framework for computing the anharmonic free energy (FE) of metallic crystals using BornOppenheimer ab initio molecular dynamics (AIMD) simulation, with unprecedented efficiency, is introduced and demonstrated for the hcp phase of iron at extreme conditions (up to ≈ 290 GPa and 5000 K). The advances underlying this work are: (1) A recently introduced harmonically-mapped averaging temperature integration (HMA-TI) method reduces the computational cost by order(s) of magnitude compared to the conventional TI approach. The TI path starts from zero Kelvin, where it assumes the behavior is given exactly by a harmonic treatment; this feature restricts application to systems that have no imaginary phonons in this limit. (2) A Langevin thermostat with the HMA-TI method allows use of a relatively large MD time step (4 fs, which is about eight times larger than the size needed for the Andersen thermostat) without loss of accuracy. (3) AIMD sampling is accelerated by using density functional theory (DFT) with a low-level parameter set, then the measured quantities of selected configurations are robustly reweighted to a higher level of DFT. This introduces a speedup of about 20-30× compared to directly simulating the accurate system. (4a) The temperature (T ) dependence of the hcp equilibrium shape (i.e. c/a axial ratio) is determined (including anharmonicity), with uncertainty less than ±0.001. (4b) Electronic excitation is included through Mermin's finite-temperature extension of the T = 0 K DFT. A simple FE perturbation method is introduced to handle the difficulty associated with applying the TI method with a Tdependent geometry and (due to electronic excitation) potential-energy surface. (5) The FE in the thermodynamic limit is attained through extrapolation of only the (computationally inexpensive) quasiharmonic FE, because the anharmonic FE contribution has negligible finite-size effects. All methods introduced here do not affect the AIMD sampling -results are obtained through postprocessing -so established AIMD codes can be employed without modification. Analytical formulas fitted to the results for the variation of the equilibrium c/a ratio and FE components with T are provided. Notably, effects of magnetic excitations are not included, and may yet prove important to the overall FE; if so, it is plausible that such contributions can be added perturbatively to the FE values reported here. Notwithstanding these considerations, FE values are obtained with an estimated accuracy and precision of 2 meV/atom, suggesting that the capability to compute the phase diagram of iron at Earth's inner core conditions is within reach.

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Section: Discussionmentioning

confidence: 99%

Accurate and precise ab initio anharmonic free-energy calculations for metallic crystals: Application to hcp Fe at high temperature and pressure

et al. 2017

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“…While lattice expansion is believed to be the most important contribution to the temperature dependence of elastic moduli, it would be worthwhile to develop methods which enable us to directly investigate the full effect of the temperature. Unfortunately, a consistent description of a paramagnetic state of a magnetic material is a highly nontrivial theoretical task [7]. In particular, we are not aware of any theoretical calculation of elastic moduli, where lattice vibrations and magnetic disorder are included on the same footing.…”

Section: Introductionmentioning

confidence: 99%

Finite-temperature elastic constants of paramagnetic materials within the disordered local moment picture fromab initiomolecular dynamics calculations

et al. 2016

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We present a theoretical scheme to calculate the elastic constants of magnetic materials in the high-temperature paramagnetic state. Our approach is based on a combination of disordered local moments picture and ab initio molecular dynamics (DLM-MD). Moreover, we investigate a possibility to enhance the efficiency of the simulations of elastic properties using the recently introduced method: symmetry imposed force constant temperature-dependent effective potential (SIFC-TDEP). We have chosen cubic paramagnetic CrN as a model system. This is done due to its technological importance and its demonstrated strong coupling between magnetic and lattice degrees of freedom. We have studied the temperature-dependent single-crystal and polycrystalline elastic constants of paramagentic CrN up to 1200 K. The obtained results at T = 300 K agree well with the experimental values of polycrystalline elastic constants as well as the Poisson ratio at room temperature. We observe that the Young's modulus is strongly dependent on temperature, decreasing by ∼14% from T = 300 K to 1200 K. In addition we have studied the elastic anisotropy of CrN as a function of temperature and we observe that CrN becomes substantially more isotropic as the temperature increases. We demonstrate that the use of Birch law may lead to substantial errors for calculations of temperature induced changes of elastic moduli. The proposed methodology can be used for accurate predictions of mechanical properties of magnetic materials at temperatures above their magnetic order-disorder phase transition.

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“…These oxides have a low-temperature antiferromagnetic (AFM) phase, in which they exhibit slightly distorted rock salt structures, and a high-temperature paramagnetic (PM) phase, having macroscopically the cubic rock salt structure and a globally zero magnetic moment. In simplified band structure calculations [2][3][4][5][6][7] it has been customary to evaluate the electronic structure for the macroscopically observed average rock salt configuration 0 , leading to zero local magnetic moment ( 0 ) at each metal site , and therefore, by symmetry, to zero band gaps Eg( 0 ). Here, 0 was taken as the non-magnetic, cubic rock salt configuration in which all TM sites are equivalent (a monomorphous representation).…”

Section: Introductionmentioning

confidence: 99%

Polymorphous band structure model of gapping in the antiferromagnetic and paramagnetic phases of the Mott insulators MnO, FeO, CoO, and NiO

2018

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A band structure description of the observed large band gaps and moments in both the antiferromagnetic (AFM) and paramagnetic (PM) phases of the classic NaCl-structure Mott insulators MnO, FeO, CoO, and NiO is provided by ordinary, single-determinant density functional theory (DFT) method. This is enabled by permitting unit cells that can lift the degeneracy of the d orbitals and develop large on-site magnetic moments without violating the global, averaged NaCl symmetry. As noted by previous authors, the ordered AFM phases already show in band theory significant band gaps when one uses the observed NaCl crystal structure but doubles the unit cell by permitting different potentials for transition metal atoms with different spins; for the degenerate d band cases of CoO and FeO, energy-lowering atomic displacements remove the band degeneracies, whereas for MnO and NiO the spin-dependent crystal field symmetry already does so. However, for the disordered PM phases the commonly used band model has been to assume the macroscopically observed, averaged NaCl structure, where all transition metal (TM) sites are forced to be symmetry-equivalent (a monomorphous description); for the PM phase this forces zero moment on an atom by atom basis, thus producing a gapless PM state, in sharp conflict with experiment. We do not follow this description. Instead, we allow larger NaCltype supercells where each TM site can have different local bonding and spin environments (a polymorphous description) and thus the geometric flexibility to acquire symmetry-lowering distortions that lower the total energy and can break the symmetry of the d orbitals. It turns out that such a polymorphous description of the structure (the existence of a distribution of different local spin and bonding environments) allows large on-site magnetic moments to develop spontaneously in the self-consistent DFT+U leading to significant (1-3 eV) band gaps in the AFM, FM, and PM phases of the classic NaCl-structure Mott insulators MnO, FeO, CoO, and NiO. We adapt to the spin disordered configurations in the PM phases the "special quasi-random structure" (SQS) construct known from the theory of random substitutional alloys whereby supercell approximants which represent the best random configuration average (not individual snapshots) for finite (64, 216 atoms or larger) supercells of a given lattice symmetry are constructed. Thus, avoiding a monomorphous description of the disordered magnetic phases allows even ordinary DFT+U, which represents the N electron system with a single-determinant wavefunction, to describe the gapping not only in the AFM phases but also in the PM phases of the classic Mott insulators MnO, FeO, CoO, and NiO.

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Recent progress in simulations of the paramagnetic state of magnetic materials

Cited by 88 publications

References 152 publications

Accurate and precise ab initio anharmonic free-energy calculations for metallic crystals: Application to hcp Fe at high temperature and pressure

Accurate and precise ab initio anharmonic free-energy calculations for metallic crystals: Application to hcp Fe at high temperature and pressure

Finite-temperature elastic constants of paramagnetic materials within the disordered local moment picture fromab initiomolecular dynamics calculations

Polymorphous band structure model of gapping in the antiferromagnetic and paramagnetic phases of the Mott insulators MnO, FeO, CoO, and NiO

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