First-Principles Approach to Spin Excitations in Noncollinear Magnetic Systems

TL;DR

This work develops a first-principles framework to predict spin-wave excitations in noncollinear magnets by marrying density functional theory with many-body perturbation theory. It extends the Green's-function approach to general spin textures using a Wannier-basis representation and an ansatz-potential method to keep computations tractable for large spin spirals. The method yields quantitative predictions for LiCu$_2$O$_2$, including the spin-spiral pitch and detailed magnon dispersions in both ferromagnetic and helimagnetic states, in close agreement with experiments. By combining off-diagonal spin components in the Green's function with a BSE kernel, the framework captures both Stoner excitations and collective magnons beyond the localized-moment picture, offering a general tool for noncollinear spin dynamics in complex materials.

Abstract

We present a first-principles method based on density functional theory and many-body perturbation theory for computing spin excitations in magnetic systems with noncollinear spin textures. Traditionally, the study of magnetic excitations has relied on spin models that assume magnetic moments to be localized. Beyond this restriction, recent $ab~initio$ methods based on Green's functions within the local spin-density approximation have emerged as a general framework for calculating magnetic susceptibilities. However, their application has so far been largely limited to collinear ferromagnetic and antiferromagnetic systems. In this work, we extend this framework and enable the treatment of large-scale noncollinear magnetic systems by leveraging a Wannier-basis representation and implementing an ansatz potential method to reduce computational cost. We apply our method to the spin-spiral state of LiCu$_2$O$_2$, successfully capturing its steady-state spin-rotation pitch in agreement with the experimental measurement and resolving the characteristic magnon dispersion. We further analyze the interplay between the spiral spin structure and the on-site spin-exchange splitting, and elucidate the crucial role of magnetic dipoles on ligand ions in mediating effective ferromagnetic interaction among the primary spins on Cu$^{2+}$ ions. Finally, we provide a theoretical prediction of the magnon dispersion on top of the helical spin background in high agreement with the experimental measurement. Overall, this work establishes a general and computationally efficient framework for simulating collective spin dynamics in noncollinear magnetic systems from first principles, exemplified by -- but not limited to -- spin-spiral states.

Figures (11)

• Figure 1: Diagrammatic representation of (a) magnetic response function and (b) scattering kernel in the form of BSE. Compared to the collinear case in Ref. sasioglu2010wannier, we include more spin index to take account for the intrinsic spin rotation in the non-interacting Green's function, for which $G^{0}_{\alpha\beta}$ holds finite off-diagonal component under noncollinear magnetic potential.
• Figure 2: Instead of laboratory coordinate (left), we choose the local coordinate by setting the $z'$-axis to point along the local spin moment such that the spin-flipping process is well-defined in the local frame (right).
• Figure 3: (a) LiCu$_2$O$_2$ crystal structure and atomic compositions. The magnetic structure is mainly formed by the net spin momentum on $\rm Cu^{2+}~(0.52\mu_B)$ and on $\rm O^{2-}~(0.18\mu_B)$ as spin helix chains along $b$-axis. Nearby chains are connected by non-magnetic Cu$^{1+}$ ions, forming a layered structure. (b) Schematic of the Cu$^{2+}$ spin orientation from the top view along $c$-axis, while, for a clear illustration, the finite magnetic moments on O$^{2-}$ ions are hidden. Each layer (① and ②) contains four spin-helix chains rotating within the $ab$-plane and propagating along the $b$-axis. In this work, a commensurate magnetic pitch of 6 unit cells is adopted. Experimental measurements indicate a $\pi$-phase shift between chain-1 and chain-3, as well as between chain-2 and chain-4, while a $\pi/2$-phase shift between chain-1 and chain-2, as well as between chain-3 and chain-4 are expected. Between layer ① and layer ②, there is a further $5\pi/6$-phase shift in relative spin orientation.
• Figure 4: (a) Left: Band structure of $\rm LiCu_2O_2$ in non-magnetic ground state computed directly in DFT and in Wannier tight-binding model. Right: Band structure of $\rm LiCu_2O_2$ in ferromagnetic (FM) ground state computed directly in DFT (Blue line). In addition, we combine the non-magnetic Wannier tight-binding model with the magnetic potential obtained from the ansatz potential method. The spin-splitting about $1.0$ eV is correctly reproduced with an error less than 20 meV. (b) Band projection on the $d_{xy}$ orbital of $\rm Cu^{2+}$ ions and the $p_{x,y}$ orbital of $\rm O^{2-}$ ions.
• Figure 5: (a) Zero-momentum magnetic response function. Four distinct peaks correspond to the four principal spins of the Cu$^{2+}$ ions in one unit cell. D-peak represents a co-moving, in-phase rotation mode corresponding to the Goldstone mode arising from spontaneous symmetry breaking, and thus incurs no excitation energy. In contrast, the other three peaks lie in the negative energy range, indicating magnetic instability. (b) Spin precession patterns viewed along the rotation axis of each spin, as indexed in the left panel. The patterns are obtained by Eq. (\ref{['Eq:Spm_diag']}) at the respective peak positions.