Unconventional orbital currents and torques due to ferro-rotational orbital textures

TL;DR

This work identifies ferro-rotational order as a nonrelativistic engine for electrical generation of orbital currents, introducing an electric hexadecapole moment as the underlying multipole mechanism. Through symmetry analysis, a minimal two-orbital tight-binding model, a three-dimensional FR model, and first-principles calculations on TiAu4, the authors demonstrate rotation-induced longitudinal orbital currents and unconventional orbital Hall currents that do not rely on spin-orbit coupling or time-reversal symmetry breaking. They further show that FR order can produce orbital accumulation and a damping-like unconventional orbital torque in a FR/FM bilayer, enabling deterministic, field-free magnetization switching. Collectively, the results broaden orbitronics to ferroic materials and higher-order electric multipoles, offering new routes for nonrelativistic OAM transport and magnetic control. The findings imply a broad class of FR materials can host unconventional orbital responses, with potential applications in low-power spintronic devices and interfacial orbital filtering.

Abstract

Orbital angular momentum transport has emerged as a promising route for manipulating magnetic devices, yet its generation has largely relied on the conventional orbital Hall effect. Here, we show that ferro-rotational order enables the electrical generation of unconventional orbital currents. These orbital currents represent the orbital counterparts of spin currents due to ferromagnetic order, but arise from rotation-induced symmetry breaking rather than time-reversal symmetry breaking or spin-orbit coupling. Using tight-binding models, we identify the underlying intrinsic, nonrelativistic mechanism categorized as an electric hexadecapole moment and corroborate our findings with first-principles calculations for the ferro-rotational material TiAu$_4$. We further show that these rotation-induced orbital currents lead to surface orbital accumulation and unconventional orbital torque in a ferro-rotational/ferromagnetic metallic bilayer, allowing deterministic field-free switching. Our findings unveil a novel pathway for generating orbital currents beyond the conventional orbital Hall effect, broadening the landscape of orbitronics research to include novel ferroic materials and higher-order electric multipoles.

Figures (5)

• Figure 1: Schematic of rotation-induced orbital currents in FR systems. a Conventional orbital Hall effect in a normal metal. The electric field ($\mathbf{E}$), orbital current ($\mathbf{J}^\mathbf{L}$), and OAM ($\mathbf{L}$) are mutually orthogonal. b FM (top) and FR (bottom) orders. The FM order is described by magnetization $\mathbf{M}$, which is odd under $\mathcal{T}$. The FR order, arising from a rotational displacement of atoms by an angle $\phi$ within the unit cell, is characterized by an axial vector $\mathbf{A}$ along the rotational axis, which is even under $\mathcal{T}$. c Rotation-induced orbital currents in a FR metal for $\mathbf{E} \perp \mathbf{A}$ (left) and $\mathbf{E} \parallel \mathbf{A}$ (right). Pink and green arrows indicate longitudinal and unconventional Hall (transverse) components, respectively.
• Figure 2: Electric hexadecapole moment in a FR system. Illustrations of a electric hexadecapole moment $H_z$ and b wave function of a rotated $d_{xy}$ or $d_{x^2-y^2}$ orbital in the presence of the FR order parameter $\mathbf{A}$. c Band structure of the two-orbital model described by Eq. \ref{['eq:H_toy']}, with color indicating the expectation value of $\hat{\sigma}_x$.
• Figure 3: Three-dimensional FR model. a Crystal structure of the tight-binding model. Red arrows depict the hopping pairs considered in the model. The right panel illustrates the $xy$-plane structure, exhibiting the FR order along $\hat{\mathbf{z}}$. b Band structure of the $d$-bands, with color representing the expectation value of $\hat{H}_z$. The dotted line indicates the assumed chemical potential of 0.6 eV. c, d Orbital conductivities $\sigma_{\beta x}^{L_\gamma}$ for different values of c$\phi$ and d$\eta$.
• Figure 4: First-principles calculations for TiAu$_4$. a Crystal structure of tetragonal TiAu$_4$. b Band structure near the Fermi level (0 eV), with color representing the expectation value of $\hat{H}_z$, as defined in Eq. \ref{['eq:hexadecapole']}. c, d Nonzero orbital conductivity components $\sigma_{\beta \alpha}^{L_\gamma}$ as functions of the chemical potential, for an electric field $\mathbf{E}$ applied along c the $x$ direction and d the $z$ direction.
• Figure 5: Unconventional orbital torque in a FR/FM bilayer and its application to field-free magnetization switching. a Crystal structure of the tight-binding model for a FR/FM bilayer. The FR bulk with $\hat{H}_z$ generates the conventional and unconventional orbital Hall currents, leading to orbital accumulation $\delta L_x$ and $\delta L_y$ at boundaries, respectively. The induced spin $\delta \mathbf{S} \propto \mathbf{M} \times \delta \mathbf{L}$ in the FM layer acts as an effective field that gives rise to the damping-like torque $\mathbf{T}_\mathrm{DL} \propto \mathbf{M} \times (\mathbf{M} \times \delta \mathbf{L})$. b, c Layer-resolved induced b OAM and c spin under an applied electric field $\mathbf{E} = E_x \hat{\mathbf{x}}$. d Macrospin simulation of type-$x$ magnetization switching with conventional and unconventional damping-like orbital torques, described by Eq. \ref{['eq:llg']}. During the time $t_1 \rightarrow t_2 \rightarrow t_3$ shown in e, the magnetization direction switches from $\hat{\mathbf{x}}$ to $-\hat{\mathbf{x}}$ upon a current pulse $J_\mathrm{c} = 10^{11} \, \mathrm{A/m}^2$ without external magnetic field. e Applied charge current density as a function of time $t$. f Dynamics of $m_x$ and $m_y$ in the same time domain.