6.4 Results and discussions for systems under pressure
6.4.2 Mn-based compounds
Figure 6.22: Effect of pressure on the lattice parameters for all the Mn-based compounds along with available experimental results.
(a) (b)
Figure 6.23: (a) Density of states under compression for all the Mn-based compounds and (b) magnetic moment of Mn under compression for all the Mn-based compounds.
the FS topology as shown in Fig. 6.24. In the same way, we found the absence of pockets at X point in minority spin case compared to ambient one. Similarly, absence of pockets at Γ point in MnGaGe for both majority and minority spin cases is observed as shown in Fig. 6.25 compared to ambient. At the same compression we have found the sudden drop in the total DOS of minority spin in MnAlGe and a sudden increase in the minority spin case in MnGaGe is observed. The pressure corresponding to these compression in MnAlGe and MnGaGe is around 12.9 and 12.5 GPa respectively. In the case of MnZnSb, absence of one FS in minority spin case is observed at V/V0=0.96 (pressure of 4.2 GPa) and a drastic change in the complete band and FS topology is observed at V/V0=0.92 (pressure of 8.5 GPa). Band and FS topology of these two compressions is given in Fig. 6.26 and Fig. 6.27. Experimentally Matsuzaki et al [133] observed small anomalies in the lattice parameters
‘a’ and ‘c’ in the pressure range between 4.2 and 6 GPa. In our study, we have observed changes in the band structure, FS topology in MnZnSb around the experimentally mentioned pressures. A drastic decrease in the magnetic moment of Mn atom in MnZnSb is also confirmed at V/V0=0.92 as shown in Fig. 6.23(b).
As pressure increase further, a continuous change in both band and FS are observed. The band structure and FS topology is given for the final compression V/V0=0.90 for all the compounds to observe the effect of pressure in Fig. 6.28-6.30. In majority spin case, additional band is found to cross EF in MnAlGe around Γ point and the corresponding FS is shown in Fig. 6.28. As pressure increases, EF is found to shift towards lower energy regions which will effect the size and shape of the FS topology as compared to ambient. Similar to MnAlGe, we have also observed changes in the FS topology in MnGaGe and MnZnSb and the plots are given in Fig. 6.29 and Fig. 6.30 respectively. At the final compression the band and FS topology are found to be same in all the investigated compounds. The pressure values corresponding to the final compression for MnAlGe,
(a) (b)
(c) (d) (e)
(f)
Figure 6.24: Band structure for MnAlGe at V/V0=0.92 (a) majority spin (b) minority spin case.
FS of (c, d) majority spin and (e, f) minority spin case.
(a) (b)
(c) (d) (e)
(f) (g)
Figure 6.25: Band structure for MnGaGe at V/V0=0.92 (a) majority spin (b) minority spin case.
FS of (c, d, e) majority spin and (f, g) minority spin case.
(a) (b)
(c) (d)
(e) (f) (g)
Figure 6.26: Band structure for MnZnSb at V/V0=0.96 (a) majority spin (b) minority spin case.
FS of MnZnSb at V/V0=0.96 (c, d, e, f) majority spin and (g) minority spin case.
(a) (b)
(c) (d) (e)
(f)
Figure 6.27: Band structure for MnZnSb at V/V0=0.92 (a) majority spin (b) minority spin case and FS of MnZnSb at V/V0=0.92 (c, d) majority spin and (e, f) minority spin case.
MnGaGe and MnZnSb are around 17.10 GPa, 16.6 GPa and 11.15 GPa respectively. Now let us analyse the enhancement of quasi two dimensional nature under pressure. If we look at MnAlGe, at ambient conditions state itself the system is quasi two dimensional which we have already shown, and in the compressed state, the two dimensional character is found to increase which is evident from the FS shape. The last FS in minority spin case clearly indicate the enhanced two dimensionality.
The possibility of Fermi surface nesting is also found to be increased, each FS might show nesting nature in this compressed state. Similar behaviour is observed for other compounds also. For the last FS of minority spin, schematic representation of nesting vector is given in Fig. 6.31 along Γ-X direction and the nesting vector is around∼0.48×2π/a for all the compounds.
The calculated single crystalline elastic constants under compression for all the compounds is given in Fig. 6.32, where we observed a non-monotonic variation in all the compounds. In MnZnSb, under compression, negative values are observed in C12(at V/V0=0.96 (pressure of 4.66 GPa)), C13
and C33 (both at V/V0=0.94 (pressure of 6.44 GPa)) elastic constants. The pressure values for these compressions are the same where the experimental [133] anomalies are observed in the lattice parameters under pressure. This further confirms either the structural instability or an ETT in MnZnSb. To check the possible structural transition in MnZnSb, we have calculated total energies under compression for different possible phases (cubic-α,β,γand Orthorhombic, Hexagonal phases) and are plotted in Fig. 6.33. From this figure we are not able to find any phase transition among the given structures. It may lead to the phase transition to another new structure which needs further studies on MnZnSb and will serve as the future scope of this work. It might be possible that the ETT observed at V/V0 around 0.96 might have lead to the mechanical instability and this can be observed from the FS topology.
From the above discussions it is found the quasi two dimensional nature is found to increase in all the compounds with pressure and is evident from the calculated FS topology. With pressure decrease in the magnetic moment of the Mn atom is observed.