Q2. What have the authors stated for future works in "Slater-pauling behavior in limgpdsn-type multifunctional quaternary heusler materials: half-metallicity, spin-gapless and magnetic semiconductors" ?
The effect of deformations and defects on the properties of these alloys still remains an open issue to be addressed in future studies.
Q3. What method is used in Ref. 22?
The authors have used an all-electron full-potential firstprinciples electronic structure method while in Ref. 22 a pseudopotentials method is employed.
Q4. How many valence electrons are in the majority spin-up band structure?
The remaining 14 electrons in the majority spin-up band structure occupy also the eu states and in order to have a spin-gapless semiconductor the non-bonding eu bands should not overlap with the antibonding eg states.
Q5. How many minority spin-down states are there?
In the majority spin-up band structure, the t1u states are occupied while the eu states are above the Fermi energy and the authors have in total 12 occupied majority spin-up states and 9 minority spin-down states and thus a total spin magnetic moment of 3 lB.
Q6. What is the relative orientation of the spin magnetic moments of the nearest neighboring atoms?
The relative orientation of the spin magnetic moments of the nearest neighboring atoms follows the Bethe-Slater curve26 and the equilibrium lattice constants are larger when early transition-metal atoms are present since their d-wavefunctions are more extended in space with respect to the late transition-metals.
Q7. What are the common types of Heusler compounds?
28Among the LiMgPdSn-type Heusler compounds, which the authors have studied, the authors have identified ten compounds which behave like spin-gapless or magnetic semiconductors.
Q8. what is the d orbital of the y atom?
The d orbitals of the X atoms hybridize strongly creating (i) 5 bonding d-hybrids (the double-degenerated eg and the triple-degenerated t2g hybrids) which obey the tetrahedral symmetry and can in their turn hybridize with the d-orbitals of the Y atom creating at the end five bonding and five antibonding hybrids and (ii) five non-bonding d-states (the double-degenerated eu states and the triple-degenerated t1u states), which are of octahedral symmetry, cannot couple with the d-orbitals of the Y atoms since the latter obey the tetrahedral symmetry.
Q9. What is the slater-Pauling behavior of the compounds?
All compounds included in the tables follow a Slater-Pauling behavior since their total spin magnetic moments, Mt, in lB scales linearly with the total number of valence electrons.
Q10. How many valence electrons are in CrVTiAl?
For the 26 valence electron compounds, the minority spin-down band structure is similar to the usual full-Heusler compounds and contains exactly 12 electrons.
Q11. What is the d-wavefunction of the transition metals?
These bands are important since they accommodate charge from the transition-metal atoms reducing the effective d-chargeTABLE I. Calculated equilibrium lattice constant and spin magnetic moments in lB for the LiMgPdSn-type Heusler compounds under study obeying the Mt ¼ Zt 18 Slater-Pauling rule.
Q12. how many occupied states are there in the spin-down band?
The energy gap in the spin-down band is between the occupied t1u and the unoccupied eu states and thus in total in the spin-down band, there are exactly 12 occupied states leading to the Mt ¼ Zt 24 SlaterPauling rule.13