We carry out density functional theory calculations which demonstrate that the electron dynamics in the skyrmion phase of Fe-rich Mn1−xFexGe alloys is governed by Berry phase physics. We observe that the magnitude of the Dzyaloshinskii-Moriya interaction, directly related to the mixed space-momentum Berry phases, changes sign and magnitude with concentration x in direct correlation with the data of Shibata et al., Nature Nanotech. 8, 723 (2013). The computed anomalous and topological Hall effects in FeGe are also in good agreement with available experiments. We further develop a simple tight-binding model able to explain these findings. Finally, we show that the adiabatic Berry phase picture is violated in the Mn-rich limit of the alloys.Recently, there has been strong interest in skyrmionic systems for applications in spintronic devices. Skyrmions in magnetic systems are whirls of magnetization that have a nonzero topological charge, also known as the winding number. These topologically protected structures are particularly promising in magnetic memory devices [1], where memory bits can be packed denser and are more robust due to their topological nature. In addition, it has been experimentally shown that current densities used to manipulate these particle-like magnetic whirls are five orders of magnitude lower than in magnetic switching devices based on spintransfer torque [2,3].Chiral skyrmions were first seen to exist in the so-called B20 compounds, of which the most prominent representatives are MnSi, FeCoSi, FeGe and MnGe based alloys [4][5][6]. What makes the B20 materials so special is the real space inversion asymmetry, itinerant magnetism and often relatively small spin-orbit interaction (SOI). The electronic and magnetic properties of these alloys are very sensitive to various parameters, such as pressure, temperature and alloy composition. The phase diagram of many B20 compounds with respect to temperature and magnetic field consists of several phases. Most importantly, it often exhibits the A-phase characterized by formation of a chiral skyrmion lattice below a critical temperature in a finite external field [4,7]. Recently, it was shown experimentally that in Mn 1−x Fe x Ge alloys the skyrmions in the A-phase drastically change their size and chirality as a function of chemical composition [8,9].The fundamental interaction behind the formation of chiral skyrmions in B20 compounds is the antisymmetric Dzyaloshinskii-Moriya exchange interaction (DMI) [10][11][12][13][14][15]. The DMI arises in crystals with broken inversion symmetry and it favors a certain chirality of the magnetization − the condition, necessary for formation of chiral magnetic structures such as skyrmions or spin-spirals of unique rotational sense. For slowly varying magnetic textures the contribution to the total energy of the system due to the DMI reads, where i stands for cartesian coordinates, D i is the i'th Dzyaloshinskii-Moriya vector, andm is the unit vector of the space-dependent magnetization. The DMI has been known sinc...
We investigate the chiral magnetic order in free-standing planar 3d-5d bi-atomic metallic chains (3d: Fe, Co; 5d: Ir, Pt, Au) using first-principles calculations based on density functional theory. We found that the antisymmetric exchange interaction, commonly known as Dzyaloshinskii-Moriya interaction (DMI), contributes significantly to the energetics of the magnetic structure. For the Fe-Pt and Co-Pt chains, the DMI can compete with the isotropic Heisenberg-type exchange interaction and the magneto-crystalline anisotropy energy (MAE), and for both cases a homogeneous left-rotating cycloidal chiral spin-spiral with a wave length of 51Å and 36Å, respectively, were found. The sign of the DMI, that determines the handedness of the magnetic structure changes in the sequence of the 5d atoms Ir(+), Pt(−), Au(+). We used the full-potential linearized augmented plane wave method and performed self-consistent calculations of homogeneous spin spirals, calculating the DMI by treating the effect of spin-orbit interaction (SOI) in the basis of the spin-spiral states in first-order perturbation theory. To gain insight into the DMI results of our ab initio calculations, we develop a minimal tight-binding model of three atoms and 4 orbitals that contains all essential features: the spin-canting between the magnetic 3d atoms, the spin-orbit interaction at the 5d atoms, and the structure inversion asymmetry facilitated by the triangular geometry. We found that spin-canting can lead to spin-orbit active eigenstates that split in energy due to the spin-orbit interaction at the 5d atom. We show that, the sign and strength of the hybridization, the bonding or antibonding character between d-orbitals of the magnetic and non-magnetic sites, the bandwidth and the energy difference between states occupied and unoccupied states of different spin projection determine the sign and strength of the DMI. The key features observed in the trimer model are also found in the first-principles results.
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