Figures-descripton here
Figure 2: Density of states with the respect to the magnetic structure. (a) FM, (b) AFM1, (c) AFM2.
Figure 3: Lattice deformations and spin directions related to calculations of magnetoelastic coefficients with related charge density differences. For each determined magnetoelastic coefficient bi, lattice deformations applied to the FM, AFM1, and AFM2 magnetic structures are shown with depicted spin orientations α1 and α2. Charge density difference between the system with magnetization along α1 and α2 directions from self-consistent calculations is shown for each magnetic structure and type of deformation with the applied strain ε=0.005. Fine k-mesh was used (FM: Rk = 70, AFM1: Rk = 90 and AFM2: Rk = 95). Yellow color denotes an excess of the charge density difference related to the α1 magnetization direction, whereas cyan one to the α1 direction. Deformation with respect to the FM axis is considered as in the Table 4. Below each charge density plot, the magnitude of the plotted ∆ρ isosurface is stated.
Figure 4: Magneto-crystalline anisotropy. (a,b) FM, (c,d) AFM1, (e,f) AFM2 magnetic structures. The insets (b,d,f) denote
a change of the MAE in the ab-plane. Regarding the AFM1 magnetic structure, the axis orientation according to the FM
structures is considered.
Figure 5: Atomic orbital resolved energy contributions to MAE. (a,b) FM, (c,d) AFM1, (e,f) AFM2. The energy difference ∆E= Eα2− Eα1 is related to magnetization axes as shown in Fig. 3.
Figure6: VolumedependenceofAFM1magneticexchangein- teractions. Filled circles denotes exchange interactions related to unchanged AFM1 volume V0 (Table 1). Depicted data are related to volume change between 0.9V0 and 1.1V0.
Figure 7: Strain dependence of a sum of magnetic exchange interactions. (circles) Sum of the exchange interactions up to 12th neighbor shell with respect to the unstrained system structure. (lines) Fitted slope in the vicinity of zero strain.
Figure 8: Isotropic volume mangetostrictions ωiso s for AFM1 phase. Dependence on the number of assumed interaction shells is provided. The values ωs were determined either (or- ange points) based on the radial dependence ∂J/∂r or (blue points) employing the strain dependence ∂J/∂εii (ii={xx, yy, zz}) of the exchange interactions. X-labels denote the most distant included pair exchange interactions with respect to non-deformed system.  Tables are included captions therefore self-explanatory.
Figure A.9: The room temperature X-ray diffraction pattern for the MnPt sample. The open circles represent the experi- mental data, while the solid lines depict the Rietveld-refined pattern obtained using Fullprof software. The difference pat- tern is illustrated by the solid line at the bottom. Ticks in- dicate the positions of the Bragg reflections corresponding to the tetragonal CuAu-I type structure (space group P4/mmm, No. 123). The most prominent peaks are labeled with their Miller (hkl) indices.
Figure D.10: Experimental MnPt magnetostriction. Magne- tostriction measured (olive) parallel, (blue) perpendicular, and (red)in45degtotheappliedexternalmagneticfield. Theinset depicts the magnetization curve of the sample. Measurements were performed at T = 2 K.
Figure D.11: Simulated magnetization direction of magnetic sublattices A and B in the AFM1 system depending on the external field strength. (a) Cartesian components of the A sublattice magnetization. (b) Components of the total magnetization. (c,d) Magnetization direction of the A,B sublattices in spherical coordinates. Magnetization is averaged over the atom in the supercell related to the sublattice and time. Four different relative field orientations were applied. The a axis of the AFM1 crystal cell is oriented along the Cartesian x direction, and the c axis along the z direction. Calculations were performed at T = 2 K.
