Optical control of spin-splitting in an altermagnet

Abstract

Manipulating and controlling the band structure and the spin-splitting in the newly discovered class of magnetic materials known as 'altermagnets' is highly desirable for their application in spintronics. Based on real-time simulations for an interacting multiband tight-binding model, we propose optical excitations as an effective way to selectively control the spin-splitting of an altermagnet. The consistent treatment of electronic interactions and electron-phonon coupling in the model allows for a systematic study of the effect of these interactions on the spin-splitting of the altermagnet in the ground as well as in the excited-state. Our simulations reveal that optical excitations modify the band structure and thus lead to significant changes in the spin-splitting within 50 fs. The relative spin-splitting in the conduction band grows up to four times in the optically excited altermagnet. We disentangle the roles of Coulomb $U$ and $J$ in the enhancement of the spin-splitting in the photoexcited state. Our study elucidates the potential for exploiting optical control of spin-splitting gaps to obtain desirable properties in altermagnets on the fastest possible timescales.

Figures (4)

• Figure 1: Altermagnetic ground state of the TB model described in the text before photoexcitation. (a) Spin and orbital order hosting altermagnetism: The rectangles describe the spin and orbital polarization of the TM sites. Blue and red specify the two opposite spin orientations directions. The orientation, horizontal vs. vertical, encodes the orbital polarization of the $e_g$-electron in the xy-plane along the x and y directions, respectively. (b) Average local magnetic moment $\langle|\mu_R|\rangle$ (bottom) and octahedral modes $\langle|Q_{2,R}|\rangle$ (top) in the $U/J-U/t$ plane. (c-d) Density of states (DOS) (c) and band structure (d) projected on local orbitals $|\Theta_l\rangle$ (green) and $|\Theta_u\rangle$ (orange). The left and right DOS shows spin-up and spin-down contributions. The thickness of the color represents the intensity of each component in the band structure. (e) Band structure of the altermagnetic state projected onto spin-up (blue) and spin-down (red) components, with the thickness of the colors representing the intensity of each component. The band structures are plotted along high symmetry points $M(\pi,\pi)-Y(0,\pi)-\Gamma(0, 0)-X(\pi, 0)-M(\pi,\pi)$. The plots in (b) use $U{=}2.50$ eV. The plots c-e use $t=0.833$ eV, $U/t=3.0$ and $U/J=7.0$.
• Figure 2: Spin-splitting gaps in the altermagnetic ground state as functions of $U/t$ (a) and $U/J$ (b). The color codes are the same as \ref{['fig:fig1']}-e. The other model parameters are set to reference values, which are specified in the main text. The vertical dashed line in (b) indicates $U/J{=}7.0$ used to study photoexcitation.
• Figure 3: (a) Evolution of the local magnetic moment of the spin-up (blue) and spin-down (red) TM-sites during and after light-pulse with photon energy $h\omega_p=2.39$ eV for different $N^{exci}$. The inset shows the photon absorption density $D_p$ versus the excitation energy $\hbar\omega$, where the horizontal line indicates $h\omega_p=2.39$. (b) Relative change in spin-splitting $\Delta^s(t_o)/\Delta^s(t{=}0)$ at the high-symmetry point X at $t_f{=}50$ fs. (c) Evolution of percentage of excited electrons (inset) and $\Delta^s(t)/\Delta^s(t{=}0)$ (main) at X-point after photoexcitation for various light intensities. Lines with triangles, circles, and without symbols correspond to $N^{exci}{=}$ 8.50%, 18.30% and 20.30%, respectively, after $t_f$=50 fs in both figures b and c. The vertical line marks the zero point of the 30-fs Gaussian light pulse. The model parameters are consistent with the panel (e) in Figure 1.
• Figure 4: (a) Band structure of the photoexcited altermagnet at $\hbar\omega_p=2.39$ eV and $N^{exci}{=}18.30\%$, showing also the electron distribution in the valence and conduction bands. The size of the circles represents the occupancy of the electronic levels. The horizontal dashed line indicates the Fermi level. The vertical arrows indicate the electronic transitions. (b) Spin-splitting gaps as a function of the percentage $N^{exci}$ (%) of photoexcited electrons with $\hbar\omega_p=2.39$ eV. The vertical line indicates $N^{exci}{=}18.30\%$.