Light-induced magnetization in a spin $S=1$ easy-plane antiferromagnetic chain

The time evolution of magnetization induced by circularly polarized light in an $S=1$ Heisenberg chain with large easy-plane anisotropy is studied numerically and analytically. Results at constant light frequency $\mathrm{\Omega }={\mathrm{\Omega }}_0$ are interpreted in terms of absorption lines of the electronic spin resonance spectrum. The application of time-dependent frequency $\mathrm{\Omega }=\mathrm{\Omega }\left(t\right)$ light, so called chirping, is shown to be an efficient procedure in order to obtain within a short time a large, controlled value of the magnetization $M^z$. Furthermore, comparison with a two-level model provides a qualitative understanding of the induced magnetization process.

Figure 1

(a) Magnetization as a function of time $M^z\left(t\right)$ calculated for $L=11, A=0.1, h=0$, and ${\mathrm{\Omega }}_0=4,6,8$. The dashed horizontal line represents the average value for ${\mathrm{\Omega }}_0=6$. Note that the results for ${\mathrm{\Omega }}_0=4$ and 8 are multiplied by factor of 5 for clarity. Inset: $M^z\left(t\right)$ induced by ${\mathrm{\Omega }}_0={\mathrm{\Omega }}_R=6$ (as in the main panel) for $t$ up to $t=250$. (b) Heat map of average net magnetization, $\overline{M^z}-M^z(t=0)$, as a function of magnetic field $h$ and frequency ${\mathrm{\Omega }}_0$, calculated for $L=10,A=0.1$. ${\omega }_B$ line (red color in the heat map) is obtained with $\mathrm{\Omega }>0$ in (2), ${\omega }_{A,G}$ (blue color) with $\mathrm{\Omega }<0$. Solid and dashed lines represent the ${\omega }_{A,B,G}$ ESR resonance lines and their continuation into the gapless regime. The vertical solid line represents the critical field $h_1$.

Figure 2

(a) Frequency ${\mathrm{\Omega }}_0$ dependence of the magnetization $M^z$ at time $t=5$ and $L=11$. Results for $h=0,2,4$ are calculated with ${\mathrm{\Omega }}_0>0$ (positive magnetization) and for $h=2,8$ with ${\mathrm{\Omega }}_0<0$ (negative magnetization). Note that for $h>h_1$ (presented for $h=4,8$) the ground state has net magnetization already at $t=0$. (b) Frequency dependence of average magnetization $\overline{M^z}$ for $h=0, L=11$ and various amplitudes $A=0.01,0.05,0.1,0.5$. Results for $A=0.01$ are multiplied by factor of 5 for clarity.

Figure 3

Time dependence of the magnetization calculated for $L=11, h=0$, and $A=0.1$. (a) Magnetization as a function of time calculated for various initial frequencies ${\mathrm{\Omega }}_I=6,8,10$ and $\nu =0.01$. The horizontal line represents the average value of magnetization for $\nu =0$ and ${\mathrm{\Omega }}_I={\mathrm{\Omega }}_R=6$ (resonance frequency). (b) Comparison of the magnetization as calculated with Eq. (3) for (i) the full Hamiltonian (2) with ${\mathrm{\Omega }}_I=8,\nu =0.01$, and (ii) the two-level model (5) and the perturbative solution ${\tilde{M}}^z$—Eq. (6) with $\mathrm{\Delta }=2, \nu =0.01$. (c) Magnetization as a function of normalized time $\nu t$ for $\nu =0.005,0.01,0.05$, initial frequency ${\mathrm{\Omega }}_I=8$, and $A=0.1$. Inset: the same results as a function of time $t$.

Figure 4

Scaling parameter $\alpha =A/\sqrt{\nu }$ dependence of the magnetization as calculated for $L=11, \nu =0.1$ (full squares), and $\nu =0.01$ (open squares). The snapshot of magnetization of the full model (squares) is taken at $\nu t=2$, i.e., $t=20$ for $\nu =0.1$ and $t=200$ for $\nu =0.01$. Circles represent the magnetization ${\tilde{M}}^z\left(\infty \right)$ dependence on $\alpha$ in the two-level model (5) and the black dashed line depicts the Landau-Zener expression.