Magnetoelasticity - magnetic structure interrelation - tetragonal MnPt system study

TL;DR

MnPt exhibits magnetoelastic coupling governed by the interplay between lattice strain and magnetocrystalline anisotropy in a tetragonal system. The study combines ab-initio calculations (VASP with SOC) and atomistic spin dynamics with MEALAS/AELAS-based elasticity to quantify isotropic and anisotropic magnetostriction and their dependence on magnetic order. A key finding is that the magnetoelastic constants $b_i$ and magnetostrictive coefficients $\lambda$ vary strongly across FM, AFM1, and AFM2 states, and that the polycrystal length change follows $\langle l-l_0 \rangle = \xi + \eta (\bm{\alpha}\cdot\bm{\beta})^2$, with charge-density and orbital-resolved MAE contributions under strain explaining the differences. The experimental magnetostriction data at 2 K align with the theory, validating the approach and highlighting the potential to tailor magnetoelastic responses in tetragonal MnPt-based materials for sensors and actuators.

Abstract

Magnetic materials represent an essential ingredient for the contemporary industry. Apart from common material parameters such as magnetocrystalline anisotropy, coercivity, or saturation magnetization, magnetoelastic behavior is vital for applications serving in various devices, e.g., in acoustic actuators, transducers, or sensors providing a desirable fast response and high efficiency with respect to applied magnetic field. Magnetoelastic properties have been studied for ferromagnetic 3d elements, or especially in high symmetry systems containing rare-earth elements to achieve higher values. Since, unlike for rare earth Laves phases, in the transition metals or alloys, these effects are very weak. Here, in contrast, we analyze the magnetoelastic behavior of antiferromagnetic tetragonal system MnPt, explaining the experimentally measured data based on the theoretical calculations and discussing the influence of the magnetic structure. Particularly, we inspect the origin of magnetocrystalline anisotropy energy, as well as the size and source of the isotropic and anisotropic parts of magnetoelastic (magnetostriction) coefficients.

Figures (8)

• Figure 1: MnPt magnetic structures. (a) FM, (b) AFM1, (c) AFM2. Dashed lines in the AFM1 structure denote the primitive cell, similar to the FM one. (plotted in VESTA 3 VESTA)
• Figure 2: Experimental MnPt magnetostriction and simulated sublattice magnetization directions. (a) Magnetostriction measured (olive) parallel, (blue) perpendicular, and (red) at 45 degrees to the applied external magnetic field. The inset depicts the magnetization curve of the sample. (b-d) magnetization direction of magnetic sublattices A and B simulated in the AFM1 system depending on the external field strength. (b) Cartesian components of the total magnetization. (c,d) Magnetization directions related to the A,B sublattices in spherical coordinates. Magnetization is averaged over the atoms in the particular supercell and the 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 same as the experiment.
• Figure 3: Magneto-crystalline anisotropy. (a,b) FM, (c,d) AFM1, (e,f) AFM2 magnetic phases. 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 4: Lattice deformations and spin directions related to calculations of magnetoelastic coefficients with related charge density differences. For each determined magnetoelastic coefficient $b_{i}$, lattice deformations applied to the FM, AFM1, and AFM2 magnetic structures are shown with depicted spin orientations $\alpha_{1}$ and $\alpha_{2}$. Charge density difference between the system with magnetization along $\alpha_{1}$ and $\alpha_{2}$ directions from self-consistent calculations is shown for each magnetic phase and type of deformation with the applied strain $\varepsilon$=0.005. Fine k-mesh was used (FM: $R_{k}$ = 70, AFM1: $R_{k}$ = 90 and AFM2: $R_{k}$ = 95). Yellow color denotes an excess of the charge density difference related to the $\alpha_{1}$ magnetization direction, whereas cyan one to the $\alpha_{2}$ direction. Deformations with respect to the FM axes are considered as in the Table \ref{['Tab:multi_tab']}. Below each charge density plot, the magnitude of the plotted $\Delta\rho$ isosurface is stated. Charge density plotted in VESTA 3 VESTA.
• Figure 5: Atomic orbital resolved energy contributions to MAE. (a,b) FM, (c,d) AFM1, (e,f) AFM2. The energy difference $\Delta E = E_{\alpha_{2}}-E_{\alpha_{1}}$ is related to magnetization axes as shown in Fig. \ref{['fig:magel_chard']}.