Inverse Faraday effect in 3d, 4d, and 5d transition metals

TL;DR

This work develops and applies a gauge‑invariant framework for the spin part of the inverse Faraday effect (IFE) across 3d, 4d, and 5d transition metals, decomposing the response into $M^{\rm IFE} = M^{\rm IFE}_{\rm elec} - M^{\rm IFE}_{\rm hole} + M^{\rm IFE}_{\rm ndr}$. Using first‑principles calculations with spin–orbit coupling and Wannier interpolation, it reveals that doubly‑resonant electron–hole processes largely control the IFE in heavy 5d metals, while overall IFE depends sensitively on electron–hole asymmetry and non‑doubly‑resonant terms. Pt yields the strongest IFE in the 1–2 eV range, Os dominates the 2–4 eV window (opposite sign), and neighboring elements can be tuned to match IFE responses by shifting the Fermi level, illustrating band‑structure engineering as a viable route to control opto‑magnetic effects. The findings link the IFE to valence electron filling and spin Hall conductivity trends, while highlighting the nuanced role of band structure and resonances in shaping the total response, with potential implications for all‑optical magnetic switching and spintronic applications.

Abstract

Using first-principles calculations, we systematically investigate the spin contributions to the inverse Faraday effect (IFE) in transition metals. The IFE depends on the d-electron filling and asymmetry between excited electron and hole spin moments. Our results reveal that even elements with smaller electron magnetic moments, like Os, can exhibit higher IFE due to greater electron-hole asymmetry. Pt shows the highest IFE in the 1-2 eV frequency range, while Os dominates in the 2-4 eV range. In addition, we demonstrate that the IFE of neighboring elements with similar crystal structures (e.g., Ir, Pt, and Au) can be tuned by adjusting their Fermi levels, indicating the importance of d-electron filling on IFE. Finally, we find that the trend in electron (or hole) contributions to the IFE closely follows that of the spin Hall conductivity, however, the total IFE involves more complex interactions.

Figures (16)

• Figure 1: Schematic illustration of the dominant contributions to the IFE in metals with doubly degenerate band structures. Band doublets are shown as pairs of solid lines at each energy level. Panels (a) and (b) depict the doubly-resonant contributions to the IFE from excited electron ($M^{\rm IFE}_{\rm elec}$) and hole ($M^{\rm IFE}_{\rm hole}$) moments, respectively. Panels (c) and (d) illustrate the dominant non-doubly-resonant contributions from electrons ($M^{\rm IFE}_{\rm ndr,a}$) and holes ($M^{\rm IFE}_{\rm ndr,e}$), respectively.
• Figure 2: Average spin IFE of 3$d$, 4$d$, and 5$d$ metals as a function of the number of valence ($d$+$s$) electrons. The IFE values are averaged over three frequency ranges: 1$-$2 eV (left), 2$-$3 eV (middle), and 3$-$4 eV (right). The full frequency dependence of IFE is given in Figs. \ref{['fig:3d-metals']}$-$\ref{['fig:5d-metals']} of the Appendix \ref{['app:IFE-with-freq']}. For clarity, the IFE for 3$d$ and 4$d$ metals are scaled by factors of 10 and 2, respectively.
• Figure 3: Relationship between the mean absolute value of IFE and JDOS$/\omega^2$ for 3$d$, 4$d$ and 5$d$ metals in three frequency ranges 1$-$2 eV (left), 2$-$3 eV (middle) and 3$-$4 eV (right). The vertical axis for mean IFE values is shown on a logarithmic scale.
• Figure 4: (a) Calculated mean value of $M^{\rm IFE}_{\rm elec}$ for 3$d$, 4$d$ and 5$d$ transition metals in the 1$-$2 eV frequency range, plotted as a function of valence electron filling. (b) The real part of spin hall conductivity (SHC) $\sigma_{\rm xy}^{\rm spin z}$ as a function of valence electrons. The SHC is computed at zero frequency ($\omega$=0) and at each metal's Fermi energy, using a broadening parameter $\eta$=0.1 eV.
• Figure 5: Mean absolute values of $M^{\rm IFE}_{\rm hole}$ versus $M^{\rm IFE}_{\rm elec}$ for 3$d$, 4$d$ and 5$d$ metals in the 1$-$2 eV frequency range. Both axes are shown on a logarithmic scale. The black dashed line represents the line of equality and serves as a visual guide for comparing the electron and hole contributions.