Stabilization of skyrmion textures by uniaxial distortions in noncentrosymmetric cubic helimagnets

Abstract

In cubic noncentrosymmetric ferromagnets uniaxial distortions suppress the helical states and stabilize Skyrmion lattices in a broad range of thermodynamical parameters. Using a phenomenological theory for modulated and localized states in chiral magnets, the equilibrium parameters of the Skyrmion and helical states are derived as functions of the applied magnetic field and induced uniaxial anisotropy.These results show that due to a combined effect of induced uniaxial anisotropy and an applied magnetic field Skyrmion lattices can be formed as thermodynamically stable states in large intervals of magnetic field and temperatures in cubic helimagnets, e.g., in intermetallic compounds MnSi, FeGe, (Fe,Co) where L is a vector order parameter (e.g. the magnetization vector M in magnetic materials or the director n in chiral liquid crystals), ∂ k L i ≡ ∂L i /∂x k are spatial derivatives of the order parameter. In condensed matter physics there are no physical interactions underlying energy contributions with higherorder spatial derivatives. [7] On the contrary, the invariants of type (1) arise in systems with intrinsic [9, 10] and induced chirality.[6] Particularly, in noncentrosymmetric magnetic materials such interactions stem from the chiral part of spin-orbit couplings (Dzyaloshinskii-Moriya interactions).[9] Chiral interactions of type (1) stabilize helical [9,11] and Skyrmionic structures [5,12] with fixed rotation sense (Fig. 1) [15]. Therefore, additional effects are necessary to stabilize Skyrmionic states in these systems. [2,13] In this paper we demonstrate that uniaxial distortions suppress the helical phases and enable the thermodynamic stability of the Skyrmion lattice in a broad range of applied magnetic fields. The calculated magnetic phase diagram allows to formulate practical recommendations on the possibility to stabilize Skyrmion states at low temperatures in MnSi, FeGe, (Fe,Co)Si and similar intermetallic compounds with B20-structure.Following the phenomenological theory developed in Refs. [9,11] we write the magnetic energy density for a cubic helimagnet with uniaxial distortions along z-axis aswhere A is the exchange stiffness, the second term is the Zeeman energy,zy ) =D M·rotM is the chiral energy with the Dzyaloshinskii constant D,i ] includes exchange (B) and cubic (K c ) anistropies [11]. The last term in (2) is uniaxial anisotropy induced by distortions.The Dzyaloshinskii-Moriya energy w D (2) favours spatially modulated chiral states where the magnetization rotates with a fixed turning sense in the plane perpendicular to the propagation direction (Fig. 1). The sign and magnitude of the Dzyaloshinskii constant D determine the modulation period and the sense of rotation, respectively. Thus, in zero magnetic field, H = 0, and for zero anisotropies, B = K c = K = 0, a flat helix forms the magnetic ground state as a single harmonic mode with wave number q 0 = D/(2A), where the phase angle φ of the magnetization varies linearly along the

Tailoring magnetic skyrmions in ultra-thin transition metal films

“…Figure 3d shows that for fcc Pd stacking the exchange interaction favours the skyrmion over the ferromagnetic state (Eo0). This is in contradiction to the predictions from the micromagnetic model that assumes a ferromagnetic exchange stiffness [1][2][3][4]13,14,[21][22][23]32 . In Pd/Fe/Ir(111), however, we need to consider a ferromagnetic NN exchange that competes with antiferromagnetic interactions beyond the NNs.…”

“…A skyrmion is characterized by an integer winding number or topological charge Q defined as Q ¼ 1 4p R n Á @n @x  @n @y dxdy, where n(x,y) is the unit vector of the local magnetization and the integral is taken over the surface area. Chiral skyrmions induced by the Dzyaloshinskii-Moriya (DM) interaction are stable against continuous deformations 3,13,14 , for example, due to external perturbations such as an applied magnetic field. Besides the fundamental interest in magnetic skyrmions due to their intriguing topological properties, they hold promise for magnetic data storage and spintronic applications 14,15 .…”

Universal current-velocity relation of skyrmion motion in chiral magnets

“…The DM interaction naturally leads to a helical spin order (HL), which turns into a triangular skyrmion crystal (SkX) under an external magnetic field B (refs 11,12) as observed in a narrow region of the B-T phase diagram for bulk samples by neutronscattering experiments 13 . Enhanced stability of the SkX in twodimensional (2D) systems or in thin-plate samples was predicted theoretically 14,15 , and was indeed confirmed by Lorentz microscope experiments 16,17 . Figure 1 shows a phase diagram at T ¼ 0 as well as schematic pictures of spin configurations in the HL, SkX and ferromagnetic phases in the 2D system.…”

Skyrmionic spin Seebeck effect via dissipative thermomagnonic torques

“…Skyrmion crystal (SkX) is particularly stable in twodimensional (2D) systems or thin films as was predicted theoretically [35,36] and later confirmed experimentally [37,38]. Just like other textures, such as domain walls, skyrmions can be manipulated by temperature gradients [39,40].…”