Bulk photovoltaic effect in antiferromagnet: Role of collective spin dynamics

Inspired by recent advancements in the bulk photovoltaic effect which can extend beyond the independent-particle approximation (IPA), this study delves into the influence of collective spin dynamics in an antiferromagnet on photocurrent generation using a time domain calculation. In the linear and photocurrent conductivity spectra, we observe peaks below the band gap regime, attributed to the resonant contributions of collective modes, alongside broadband modifications resulting from off-resonant spin dynamics. Notably, the emergence of spin dynamics allows various types of photocurrent, which are absent in the IPA framework. Furthermore, we emphasize the importance of energy scale proximity between electronic and spin degrees of freedom in enabling efficient feedback. These findings offer new avenues for efficient energy harvesting and optoelectronic applications.

Figure 1

(a) One-dimensional chain model with canted antiferromagnetic order. (b) Band dispersion of the system with the parameters $t_h=1,\lambda =0.8,J=0.6,K_z=0.2,h_y=0.2$.

Figure 2

Collective mode of canted antiferromagnetic moment. The red (blue) arrow indicates the spin moment in the $A$ ($B$) sublattice, respectively. The black arrow denotes the summation of the sublattice spin moment.

Figure 3

(a) Linear electromagnetic susceptibility to the external light field. (b) Linear optical conductivity of the system. The red solid line and the blue dashed line indicate the calculation with and without updating the spin configurations, respectively. The black dashed line indicates the band gap frequency.

Figure 4

(a) Photocurrent spectra. The blue dashed and red solid lines indicate the IPA calculation and calculation incorporating the spin dynamics, respectively. (b), (c) Dependence of photocurrent conductivity at the above-band-gap frequency (${\omega }_p=0.8$) on (b) electric-field strength $E_0$ and (c) relaxation time $\tau$. The blue and red lines indicated the IPA calculation and calculation incorporating the spin dynamics, respectively. The black solid line in (b) indicates the line which is proportional to $E_0^2$.

Figure 5

(a) Schematic picture of three different processes of the photocurrent in the presence of collective spin dynamics. The wavy and dashed lines indicate the light field and interaction $J$, respectively. $\otimes$ represents the output photocurrent. The solid triangles describe the photocurrent susceptibility evaluated with the IPA. $\mathrm{\Delta }\mathbf{S}$ is the light-induced spin dynamics. (b) Photocurrent spectra originating from the three different processes. The inset shows the magnified view of ${\sigma }_{\text{col-E}}$ component around the collective mode frequency ${\omega }_p\sim 0.35$.

Figure 6

Relaxation time dependence of photocurrent conductivity given by (a) Eq. (38), (b) Eq. (39), and (c) Eq. (40). The insets in (b) and (c) show the magnified view of photocurrent spectra around the collective mode frequency ${\omega }_p\sim 0.35$.

Figure 7

(a) Magnetic field dependence of linear electromagnetic susceptibility $Im{\chi }_{{\mathrm{L}}^{x}E}\left(\omega \right)$ to the external light field. (b) Photocurrent spectra $\sigma (\omega =0;{\omega }_p)-{\sigma }_0(\omega =0;{\omega }_p)$ with modulating the canted angle of antiferromagnetic moments by changing the magnetic field along the $y$ direction.

Figure 8

(a) $J,\lambda$ dependence of amplitude of electromagnetic susceptibility. The white dashed lines indicate the band. The parameters $t_h=1,K_z=0.2,h_z=0.2,\gamma =0.01$ were used. (b) Change of Photocurrent spectra arising from spin dynamics $\sigma (\omega =0;{\omega }_p)-{\sigma }_0(\omega =0;{\omega }_p)$. Parameters are $t_h=1,\lambda =0.8,K_z=0.2,h_y=0.2$.

Figure 9

Photocurrent spectra with smaller spin-orbit coupling. The parameters $t_h=1,\lambda =0.1,J=0.4,K_z=0.2,h_z=0.2,\gamma =0.01$ were used. The blue dashed and red solid lines indicate the IPA calculation and calculation incorporating the spin dynamics, respectively.