Dzyaloshinskii-Moriya Interaction and Hall Effects in the Skyrmion Phase ofMn1−xFexGe

Abstract

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...

First-Principles Evaluation of the Dzyaloshinskii–Moriya Interaction

“…50 3.2 DM interaction using E(q) Figure 5 shows the spin stiffness and the DM interaction calculated using E(q) for Mn 1−x Fe x Ge and Fe 1−x Co x Ge in two different studies. 25,52) Although there is a slight difference in the two studies due to the treatment of the alloys, the results well reproduce the sign change of the DM interaction observed in the experiments, that is, at x = 0.8 in Mn 1−x Fe x Ge and x = 0.6 in Fe 1−x Co x Ge. In addition, a recent spin-wave spectroscopy experiment has shown that the DM interaction for FeGe is ∼ -3.6 meVÅ, which is also consistent with the calculation.…”

Composition-dependent magnetic response properties of Mn1−xFexGe alloys

“…The dependence of the DMI parameter D xx (x) on x is plotted in Fig. 1 (a) in comparison with available theoretical results from other groups [12,30]. The results calculated using an explicit expression for D xx derived recently [20] are given by open diamonds, while those based on the interatomic interaction parameters D ij are given by solid circles.…”

“…Experimentally, it was found [9,11] that the size of Skyrmions in this material can be tuned by changing the Fe concentration, reaching a maximum at x ∼ 0.8 [11], i.e., at the concentration when the Skyrmion helicity changes sign without a change of the crystal chirality. This behavior was investigated theoretically [12,13] via first-principles calculations of the DMI and analyzing the details of the electronic structure that may have an influence on it. Gayles et al [12] have demonstrated that the sign of the DMI in Mn 1−x Fe x Ge can be explained by the relative positions in energy of the d ↑ xy -and d ↓ x 2 −y 2 -states of Fe which change when the Fe concentration increases above x ∼ 0.8.…”

“…This behavior was investigated theoretically [12,13] via first-principles calculations of the DMI and analyzing the details of the electronic structure that may have an influence on it. Gayles et al [12] have demonstrated that the sign of the DMI in Mn 1−x Fe x Ge can be explained by the relative positions in energy of the d ↑ xy -and d ↓ x 2 −y 2 -states of Fe which change when the Fe concentration increases above x ∼ 0.8. As a consequence a flip of the chirality of the magnetic texture occurs.…”

“…While these calculations have been done treating chemical disorder within the virtual crystal approximation (Ref. 12) or even employing the rigid band approximation (Ref. 13), the present work is based on the coherent potential approximation (CPA) alloy theory, which should give more reliable results for the electronic structure of disordered alloys.…”