Non-collinear magnetism contra frustration: Magnetic order and anisotropy in hexagonal MnPtGa

TL;DR

This study uses fully relativistic first-principles calculations to map the magnetic landscape of hexagonal MnPtGa, comparing collinear FM/AFM, disordered local moments, spin spirals, and canting. It finds that AFM is energetically favored over FM at zero field in the collinear sector, with lattice parameters that agree with experiments; Mn moments remain localized around $3.9~\mu_B$ even in the disordered state, while exchange splitting is reduced. Non-collinear states are nearly degenerate with collinear ones (within $\sim$ $30~\mathrm{meV}$), and spin-spiral and canting analyses reveal frustration and multiple metastable textures that could be stabilized by external fields or finite temperature, potentially including skyrmions in the appropriate geometry. The bulk centrosymmetry suppresses bulk Dzyaloshinskii–Moriya-driven spirals ($D_{\rm eff}=0$), but surfaces or thin films break inversion symmetry and can host chiral spin textures, aligning with experimental reports of varied magnetic orders under different conditions. Overall, the results reconcile diverse observations and highlight how geometry and environment tune MnPtGa’s non-collinear magnetism.

Abstract

MnPtGa is a hexagonal intermetallic compound with a rich variety of magnetic order. Its magnetic state is reported to range from collinear ferromagnetism, to non-collinear skyrmion type order. MnPtGa is a system with strongly localized magnetic moments at the Mn atoms as was demonstrated using calculations for disordered local moments. The magnetic moments at the Mn sites stay at about 3.9 bohr even above the calculated magnetic transition temperatures (TN = 220 K or TC = 285 K). In the present work, a special emphasis was focused on the possible non-collinear magnetic order using first principles calculations. The investigations included magnetic anisotropy, static noncollinear order in form of spin canting and dynamic non-collinearity in spin spirals. It is found that the energy differences between ferromagnetic, antiferromagnetic, canted, or spiral magnetic order are in the order of not more than 30 meV, which is in the order of thermal energies at ambient temperature. This hints that a particular magnetic state - including skyrmions, antiskyrmions or spin glass transitions - may be forced when an external field is applied at finite temperature.

Figures (15)

• Figure 1: Crystal and magnetic structures of MnPtGa. a) ferromagnetic, b) antiferromagnetic c) non collinear, d) antiferromagnetic in-plane. The arrows are drawn in the direction of the local magnetic moments at the Mn atoms. The angle between the magnetic moment vectors and the $z$ axis is in the canted, non-collinear state (c) is $\theta=35^\circ$ which is close to $\arctan(a/c)\approx38^\circ$.
• Figure 2: Calculated equation of state for MnPtGa with ferromagnetic (fm) or antiferromagnetic (afm), collinear magnetic order. Shown are the Energy--Volume--Pressure relations ($E(V,p)-E_{\min}$) according to the Birch--Murnaghan equation of state Mur44Bir47. $E_{\min}$ is the equilibrium energy of the antiferromagnetic state (see Table \ref{['tab:opt']}). Magnetization is along [0001]. (Note the use of atomic units for energy (mRy) and volume ($a_{0B}^3$, $a_{0B}=0.529\ldots$ Å)).
• Figure 3: Exchange coupling coefficients of MnPtGa with ferromagnetic (fm) or antiferromagnetic (afm) order. Compared are the exchange coupling coefficients $J_{ij}$ in (a, c) and the Dzyaloshinskii--Moriya coefficients $D_{ij}$ in (b, d). The distance $d_{ij}=|r_{ij}|/a$ between the Mn atoms is given relative to the lattice parameter $a$. Magnetic moments are assumed to be aligned along the $c$ axis. (Note the different energy scales.)
• Figure 4: Magnetic anisotropy of ferromagnetic (fm) and antiferromagnetic (afm) MnPtGa. The magneto-crystalline anisotropy energy $E_{a'}$ is given in meV. In the ferromagnetic state, the "easy" direction is along $z$ ($[0001]$), whereas three principle "hard" directions appear in the basal plane. The basal plane becomes an "easy" plane in the antiferromagnetic state.
• Figure 5: Disordered local moments in MnPtGa. The total (spin plus orbital) magnetic moment in the primitive cell containing 2 Mn atoms is plotted as function of the energy difference between the ferromagnetic and disordered local moment state. $\uparrow:\downarrow$ is the ratio of spin up to spin down electrons at the Mn site.