I would like to thank all the technical assistants, academic and non-academic staff of the department who helped me in various ways during my research period. Most of the materials presented here fall into the category of magnetic form memory connections.
Martensitic transformation
Crystal twinning occurs when two separate crystals share some of the same crystal lattice points in a symmetrical manner. The atoms located at the boundary are connected by the same number of bonds in both directions of the twin crystals.
Magnetic shape memory effect(MSME)
A unique feature of these materials is that the magnetic field can affect the martensitic transformation and thus the possibility of controlling the shape memory properties. In general, the deformation caused by induced strain cannot be recovered after removal of the magnetic field.
Spintronics
Thus, the magnetic field plays an important role in sample deformation, such as mechanical loading in conventional shape memory alloys. In addition to heating the material, there are other options for recovering the induced deformation: rotating the magnetic field and applying a voltage perpendicular to the magnetic field [17].
Exchange bias
1.4 (4)), the FM spins need a smaller external force to rotate along the field direction (Fig. This shift in the hysteresis loop is called the exchange bias field, and its sign depends on the orientation of the FM spin.
Mn 2 YZ systems: Experimental and theoretical background
Depending on the number of valence electrons of the constituent elements, a system crystallizes in the regular or reverse Heusler structure. Another structural phase in Heusler compounds is the tetragonal derivative of the cubic structure, which has been widely reported in magnetic shape memory compounds.
The importances of first-principles electronic structure calculations
Over the years, these methods have become widely accepted for predicting properties of new materials where experimental evidence is not present. Therefore, the DFT-based first-principles methods are the essential tool for fundamental understanding of materials that I have worked with during my PhD research.
Outline of the thesis
We find that the martensitic phase of Mn2NiGa gradually destabilizes with an increase in the concentration of Fe/Co due to the weakening of the minority spin hybridization of Ni and Mn atoms occupying crystallographically equivalent sites. The magnetic properties of Mn2NiGa are found to be significantly improved by the substitutions due to stronger ferromagnetic interactions in the compounds.
The Born-Oppenheimer approximation
The first and third terms in the Hamiltonian are kinetic energies of nuclei and electrons, respectively. The second, fourth, and fifth terms are Coulomb interactions between nuclei and nuclei, electrons and electrons, and electrons and nuclei, respectively.
Density Functional Theory (DFT)
This mapping by Kohn and Sham resulted in a Schr¨odinger-like equation for a single particle, which gives a varying total energy and thus the ground state single particle density to a good approximation. The self-consistent equations are used to calculate the ground state energy of an electronic system with
Pseudopotential method
Norm-Conserving Pseudopotentials (NCPP)
The norm-conserving pseudopotentials (NCPP) were the first in the block of pseudopotentials that were computationally tractable. The NCPPs are generated by imposing the condition that the norm of the pseudo-wave function is the same as that of the all-electron wave function within a certain limiting distance rc.
Ultrasoft Pseudopotentials (USPP)
Projector Augmented Wave (PAW) method
Korringa, Kohn and Rostoker (KKR) Green’s Function method
The relation between GmnLL′(E) and gLLmn′(E) can be obtained by inserting the above expressions for the Green's function into the integral equation. The zeros of the KKR matrix give the poles of the Green's function; each pole corresponds to the eigenstate of the Hamiltonian.
Coherent Potential Approximation (CPA)
Next, the Green's functions of the alloy components are determined by replacing the coherent potential of the CPA medium by the actual atomic potential Pi, which is given by. Finally, the average of the individual Green's functions should reflect the single-place part of the coherent Green's functions, i.e. 2.46).
Calculation of elastic moduli
- Bulk Modulus
- Elastic Constants
- Elastic moduli in a cubic lattice
- The magnetic exchange interactions (J ij )
- The Curie temperature (T c )
- Mean field approximation (MFA)
- Monte Calro simulation (MCS)
The magnetic pair exchange parameters are calculated to understand the nature of the magnetic interactions between the systems studied in this thesis. After selecting the new spin components, we calculate the change in energy (∆E) of the system.
Calculation of phonon dispersion relations
Therefore, the potential energy of the crystal is a function of the instantaneous coordinates Rlk of the atoms. Assuming that the displacements are small, the potential of the crystal can be extended over the equilibrium positions. where α and β are the Cartesian coordinates and the coefficients φlkα and φlkα, l′k′β, are.
Summary
The modulated martensitic structures are one of the prerequisites for the observation of large reversible MFIS. The origin of the modulated structures is explained from the phonon scatterings, the functions of the Fermi surfaces and the electronic susceptibilities.
Computational Details
It was observed that the structure of the martensitic variant is quite sensitive to the residual stress in the system. In this chapter, we therefore investigate the structural properties and relative stabilities of various modulated structures of Mn2NiGa and make an attempt to understand the origin of the sequences of structural phases as the system is driven from the high-temperature cubic to the low-temperature NM tetragonal variant.
Results and Discussions
- Structural properties of cubic, non-modulated, and different
- Energetics of the modulated structures
- Electronic structures of the modulated phases
- Phonon instability, Fermi Surface Nesting and Generalised
In the case of the 14M structure, the (5¯2)2 stacking sequence was chosen, as shown in Fig. Energies of pseudocubic structures (modulated structures inscribed in an orthorhombic cell with c/a= 1) are shown. at the entrance.
Conclusions
Our results attribute the origin of the instability to the nesting features of the Fermi surface in the minority spin bands, while no supporting contribution is encountered from the electronic sensitivity of the majority spin. In both cases, the martensitic transformation disappeared rapidly indicating the stabilization of the reverse Heusler phase down to low temperature.
Computational Methods
Results and Discussions
Site preferences, stability and structural parameters
In the case of Co substitution at the Ga site in Mn2NiGa, previous work [240] showed that Co prefers to occupy the MnI sites and push the remaining MnI atoms to Ga sites (hereinafter referred to as MnIII). The only exceptions are the substitutions at the Ni site, where instead of an expected increase in the lattice constant with the concentration of the replacing element, the lattice constant decreases.
Martensitic phase transformation
In the case of Mn2Ni(Ga1−xCox), our calculated trends on the composition dependence of the martensitic transformation differ slightly from the experimental observations. We find a gradual destabilization of the martensitic phase with increasing x for the Mn2(Ni1−xCox)Ga system.
Elastic properties
The important result of the variations in C′ with compositions is that it can be considered a better predictor of. In the previous subsection, we have shown that ∆E is a good predictor of martensitic transformation.
Electronic structure
This happens mainly because of the position of the Fe-d states which are right in the gap. For co-located systems, we find that there is very little change in the overall band density characteristics of most states as Co-Content increases.
Total and atomic magnetic moments
In almost all cases, the total moment increases with the concentration of the substituent. ii) The increase in the total moment is fastest for Mn2Ni(Ga1−xXx), and is slowest for Mn2(Ni1−xXx)Ga systems. iii). The disagreement in the case of Mn2Ni(Ga1−xCox) could be due to the presence of antisite disorder in the experimental sample or due to the differences between the actual composition and the one reported in the experiment [240].
Magnetic exchange interactions and Curie temperature
The strongest ferromagnetic interaction in the co-substituted system is that of the Co-MnII pairs while the strength of the Ni-MnII interaction is significantly weaker in the concentration range. The ferromagnetic components in the exchange interactions are due to the nearest neighbors X-MnIII (X=Co, Fe), X-MnII, Ni-MnII and Ni-MnIII and the second neighbor Ni-MnI.
Conclusions
The magnetic properties of Mn2NiGa are generally improved with a greater presence of substituents. First-principles calculations of magnetic exchange interactions [262] and magnetic anisotropy [70] concluded that the new magnetic properties of Mn3Ga v.
Calculational details
For all calculations, the convergence criteria of the total energy and the convergence criteria of the force were set to 10-6 eV and 10-2 eV/˚A, respectively. The elastic constants were calculated from other derivations of the total energies with respect to the strain tensors [130].
Results and Discussions
Structural parameters and magnetic structures in various crys-
Our total Table 5.1: Calculated lattice parameters (in ˚A), total (M) and atomic magnetic moments (MX) (inµB per formula unit) of Mn2FeGa in Cu3Au, Xa, L10 and DO19 phases. A comparison with Mn3Ga in the ordered phase Cu3Au [59] shows that the replacement of one Mn atom by Fe has led to a reduction of the total moment of the system.
Stabilities of various phases: analysis from energetics, elec-
The quenching of the Fe moment in the Xa structure can also be understood from the electronic structure. The reduced hybridizations can be correlated with the instability in the Xa phase as implied by the large densities of states at the Fermi level.
Magnetic exchange interactions
The lattice of nearest-neighbor magnetic atoms in two adjacent planes in DO19. In the present case of Mn2FeGa, we find that the in-plane exchange parameters.
Conclusions
The origin of the electronic instability associated with this phase appears to be the Jahn-Teller effect. The magnetic structure in the hexagonal phase of DO19 is the one where we observe a significant influence of the presence of Fe in the system.
Computational Methods
Results and Discussions
The zero energy is the energy of the Sn1Mn3 system in the FM austenite phase. The zero energy is the energy of the Sn2Mn2 system in the FM austenite phase.
Conclusions
In Chapter 4, we have investigated the effects of Fe and Co substitutions on the stability of the martensitic phase and mechanical, electronic and magnetic properties of Mn2NiGa. Apart from the MnIII atoms, the Ni atoms on the 4d sites also play a significant role in the stability of the martensitic phases in this system.
Scopes for future work
Bhargab Deka, Ashis Kundu, Subhradip Ghosh, A Srinivasan, Experimental and ab initio studies on sublattice ordering and magnetism in Co2Fe(Ge1−xSix) alloys, Journal of Applied Physics. Ashis Kundu, Markus E Gruner, Mario Siewert, Alfred Hucht, Peter Entel, Subhradip Ghosh, Intertwining phase sequence and electronic structure in modulated Mn2NiGa martensites from first principles calculations, Physical Review B.
