[Paper Review] Current-induced Orbital and Spin Magnetizations in Crystals with Helical Structure

Taiki Yoda, Takehito Yokoyama+1 more|arXiv (Cornell University)|Jul 10, 2015

Magnetic properties of thin filmsPhysics and Astronomy30 references134 citations

TL;DR

This paper proposes that in helical crystals—such as chiral crystals of Se or Te—applying an electric current along the helical axis induces both orbital and spin magnetizations along the same axis. Using a tight-binding model, the authors show that the current-induced spin magnetization arises from a radial spin texture on the Fermi surface, contrasting with the transverse spin polarization seen in Rashba systems. The effect is chiral: right- and left-handed helices produce opposite magnetizations, mimicking a solenoid's behavior without requiring spin-orbit coupling for orbital magnetization.

ABSTRACT

We theoretically show that in a crystal with a helical lattice structure, orbital and spin magnetizations along a helical axis are induced by an electric current along the helical axis. We propose a simple tight-binding model for calculations, and the results can be generalized to any helical crystals. The induced magnetizations are opposite for right-handed and left-handed helices. The current-induced spin magnetization along the helical axis comes from a radial spin texture on the Fermi surface. This is in sharp contrast to Rashba systems where the induced spin magnetization is perpendicular to the applied current.

Motivation & Objective

• To demonstrate that electric current along a helical axis induces axial orbital and spin magnetizations in chiral crystals.
• To explain the origin of current-induced spin magnetization in helical systems, contrasting it with Rashba-type systems.
• To establish a general framework applicable to any crystal lacking mirror and inversion symmetries.
• To show that the induced magnetization is chiral—opposite for right- and left-handed helices—mirroring solenoid behavior.
• To clarify that orbital magnetization arises without spin-orbit coupling, while spin magnetization requires it.

Proposed method

• Develops a 3D tight-binding model with a helical lattice structure composed of stacked honeycomb layers, each with one orbital per site.
• Introduces helical hopping terms between same sublattices in adjacent layers that break inversion and mirror symmetries, distinguishing right- and left-handed helices.
• Uses the Hamiltonian H = t1∑⟨ij⟩c†icj + t2∑[ij]c†icj + ∆∑iξic†ici, with t2 terms encoding helicity and ∆ a staggered potential.
• Applies the semiclassical Boltzmann approximation to compute current-induced magnetization under an electric field along the z-axis (helical axis).
• Calculates orbital magnetization using the formula Morb = 2∑n∫BZ d3k/(2π)3 fnk [mnk + e/ℏ(εF−εnk)Ωnk], with mnk and Ωnk derived from the wavefunction's curvature.
• Extends the model to include spin-orbit coupling via Hso, introducing spin-dependent hoppings to study current-induced spin polarization.

Experimental results

Research questions

• RQ1 Can an electric current along the helical axis induce a net magnetization along the same axis in chiral crystals?
• RQ2 What is the origin of the current-induced spin magnetization in helical systems, and how does it differ from Rashba-type systems?
• RQ3 How does the handedness (right- vs. left-handed helix) affect the sign and magnitude of the induced magnetization?
• RQ4 Is the current-induced orbital magnetization possible in the absence of spin-orbit coupling?
• RQ5 Can the effect be generalized to any crystal lacking mirror and inversion symmetries?

Key findings

• Current along the helical axis induces a net orbital magnetization along the same axis in metals, but not in band insulators at zero temperature.
• The induced orbital magnetization is strongly enhanced near Dirac points on the K–H and K′–H′ lines in momentum space.
• The spin magnetization induced by current is axial (parallel to current), arising from a radial spin texture on the Fermi surface, unlike the transverse spin polarization in Rashba systems.
• The sign of the current-induced magnetization is reversed between right- and left-handed helices, analogous to the magnetic field direction in a solenoid.
• Orbital magnetization can be induced without spin-orbit coupling, while spin magnetization requires it.
• The results are generalizable to any crystal without mirror and inversion symmetries, suggesting potential for spintronic applications in chiral materials.