Transport spin current driven by the moving kink crystal in a chiral helimagnet

Abstract

We show that the bulk transport magnetic current is generated by the moving magnetic kink crystal (chiral soliton lattice) formed in the chiral helimagnet under the static magnetic field applied perpendicular to the helical axis. The current is caused by the non-equilibrium transport momentum with the kink mass being determined by the spin fluctuations around the kink crystal state. An emergence of the transport magnetic currents is then a consequence of the dynamical off-diagonal long range order along the helical axis. We derive an explicit formula for the inertial mass of the kink crystal and the current in the weak field limit. PACS numbers: Valid PACS appear hereHow to create, transport, and manipulate spin currents is a central problem in the multidisciplinary field of spintronics.1 The key theoretical concepts there include the current-driven spin-transfer torque 2 and resultant force acting on a domain wall (DW) 3 in metallic ferromagnetic/nonmagnetic multilayers, the dissipationless spin currents in paramagnetic spin-orbit coupled systems, 4 and magnon transport in textured magnetic structures.5 A fundamental query behind the issue is how to describe transport magnetic currents.6 Conventionally, the charge current is defined by the product of the carrier density and the drift velocity related via the continuity equation. In the case of spin current, the deviation of the spin projection from its equilibrium value plays a role of a charge. Then, an emergence of the transport magnetic currents may be expected in non-equilibrium state as a manifestation of the dynamical off-diagonal long range order (ODLRO).7 Historically, Döring first pointed out that the longituidal component of the slanted magnetic moment inside the Bloch DW emerges as a consequence of translational motion of the DW.8 An additional magnetic energy associated with the resultant demagnetization field is interpreted as the kinetic energy of the wall.Recent progress of material synthesis sheds new light on this problem. In a series of magnets belonging to chiral space group without any rotoinversion symmetry elements, the crystallographic chirality gives rise to the asymmetric Dzyaloshinskii interaction that stabilizes either left-handed or right-handed chiral magnetic structures.9 In these chiral helimagnets, magnetic field applied perpendicular to the helical axis stabilizes a periodic array of DWs with definite spin chirality forming kink crystal or chiral soliton lattice.10 In this paper, we demonstrate that the magnetic transport analogous to Döring effect 8 occurs in the moving kink crystal of chiral helimagnets and serves an example of the dynamical ODLRO in non-equilibrium state. An essential point is that the kink crystal state has a degeneracy originating from the translational symmetry. Consequently, the transport momentum has a form MẊ, where M and X represent the kink mass and the collective coordinate of the kink in the laboratory frame. The kink crystal behaves as a heavy object with the inertial mass M .We start with a spin...

Theory of Monoaxial Chiral Helimagnet

“…The standing CSL enables the new soliton to emerge and transport the magnon density. As compared with the motion of the whole kink crystal with a heavy mass [16,54], our new soliton is a well localized object with a light mass. This new traveling soliton can be regarded as a promising candidate to transport magnetic information by using chiral helimagnet.…”

“…This resembles the situation in a pure metal at T ¼ 0, when there is no resistance, but this is not superconductivity, which is an absence of resistance in "dirty" metals at T > 0. A remarkable feature of the chiral helimagnet is an existence of spin currents of both types (I) and (II) [16,54]. To maintain the spin current of the type (I), some external sources are required, for example, an electric current of free-carriers supporting a dissipationless spin current in a subsystem of localized moments due to the spin-transfer torque, or an external magnetic field in the case of insulators.…”

“…where we used (54) and the relation @ z φ 0 ' q 0 . Here, we introduced the nonadiabatic spin-transfer torque (STT) on the local moments defined by…”

Electronic structure of the chiral helimagnet and3d-intercalated transition metal dichalcogenideCr1/3NbSirica1, Mo2, Bondino3 et al. 2016Phys. Rev. B

“…From a technological viewpoint, the CSL can be thought of as a tunable magnetic superlattice acting as an effective potential for itinerant electron spins [17]. Beyond the possibility of exercising precise control over the transport properties of spin carriers, the high stability and robustness of the CSL phase has made Cr 1/3 NbS 2 an attractive candidate for a wide range of other spintronic applications [18][19][20].…”

Monopole and topological electron dynamics in adiabatic spintronic and graphene systems

“…Of interest recently is the spin orbital (SO) effect [11][12][13][14] , particularly the Rashba and the Dresselhaus in semiconductor materials. The SO effect has direct implication to the spin and the momentum dynamics of electrons, leading to recent interest that spans fundamental, device and engineering physics, and subjects that range from spin Hall [15][16][17] to spin current 18 transistor. In fact, SO effect is highly relevant to spintronics, ranging from the well-known anisotropic magnetoresistance, the anisotropy energy of local moment density, the keenly studied spin Hall and spin current in semiconductor spintronics, to more subtle implications like spin torque, spin dynamics, spin oscillations, and Zitterbewegung.…”