Strain-Driven Altermagnetic Spin Splitting Effect in RuO$_2$

Abstract

The non-relativistic spin-momentum locking in altermagnets gives rise to a time-reversal-odd spin Hall effect, known as the altermagnetic spin-splitting effect (ASSE). Although ASSE was first reported in RuO$_2$, subsequent experiments have yielded inconsistent results, leaving its spin-transport mechanism unclear. Here, we systematically investigate how strain, crystal orientation, and the Hubbard $U$ parameter influence the magnetic ground state and spin Hall response of RuO$_2$. Guided by recent experimental observations, we find that $U$ is likely smaller than the value required to induce intrinsic magnetism, suggesting that bulk RuO$_2$ and (001)/(101) RuO$_2$ thin films grown on TiO$_2$ are nonmagnetic in the absence of extrinsic effects. In contrast, (100) and (110) films exhibit strain-induced altermagnetic spin splitting, leading to a strong ASSE even without Hubbard $U$ corrections. These results reconcile previous experimental discrepancies and provide design guidelines for RuO$_2$-based spintronic devices.

Figures (4)

• Figure 1: (a–d) Top views of the crystal structures of RuO$_2$ with orientations (001), (101), (110), and (100), respectively. The arrows in (c) and (d) indicate the compressive strain imposed by the TiO$_2$ substrate along its [001] direction. (e) Hubbard $U$ dependent Néel vector magnitude of bulk, (001), (101), (110) and (100) RuO$_2$, respectively, without spin-orbit coupling (SOC), and that of bulk RuO$_2$ with SOC. (f-h) Electronic structures of bulk (100) and (110) RuO$_2$ without $U$ and SOC.
• Figure 2: (a) Hubbard $U$ dependent Néel vector magnitude of bulk RuO$_2$, and fully-strained (001), (101), (110) and (100) RuO$_2$ on TiO$_2$ substrates, respectively, without spin-orbit coupling (SOC), , together with the result for bulk RuO$_2$ with SOC. (b-d) Electronic structures of bulk RuO$_2$, fully-strained (100) and (110) RuO$_2$, without $U$ and SOC.
• Figure 3: (a-c) Hubbard $U$ dependent $\mathcal{T}$-even, $\mathcal{T}$-odd spin Hall conductivities, and spin Hall angles of bulk RuO$_2$ at Fermi level. $x$, $y$, and $z$ cartesian coordinates indicate corresponding directions in Fig. \ref{['fig1']} (e).
• Figure 4: The representative (a-b) $\mathcal{T}$-even and (c-d) $\mathcal{T}$-odd SHC tensor components in (100) and (110) RuO$_2$, respectively. $x$, $y$, and $z$ cartesian coordinates indicate corresponding directions in Fig. \ref{['fig1']}(g) and (h), and $\phi$ indicate the in-plane rotation angle.