Optical selection rules of the magnetic excitation in the $S=\frac{1}{2}$ one-dimensional Ising-like antiferromagnet ${\mathrm{BaCo}}_2{\mathrm{V}}_2{\mathrm{O}}_8$

In this study, we clarify the selection rules of optical transitions from the ground state to the magnetic excited states in the quasi-one-dimensional quantum Ising-like antiferromagnet ${\mathrm{BaCo}}_2{\mathrm{V}}_2{\mathrm{O}}_8$ with spin $S=\frac{1}{2}$ using the high-field electron spin resonance measurement with illuminating polarized electromagnetic waves. We demonstrate that the unconventional magnetic excitation via the pair creation of quasipaticles at wave numbers $q_z$ = $\pi /2$ and $\pi$ in the field-induced quantum critical state can couple with both oscillating magnetic and electric fields. Our density matrix renormalization group calculations indicate that the observed selection rules can be explained by two- and four-fold periodical spin interactions, originating from the screw chain structure in ${\mathrm{BaCo}}_2{\mathrm{V}}_2{\mathrm{O}}_8$, in addition to the magnetoelectric coupling between spins and electric dipoles.

Figure 1

(a) ESR resonance points observed in ${\mathrm{BaCo}}_2{\mathrm{V}}_2{\mathrm{O}}_8$ for $H\parallel c$ [17]. The bold solid curves above $H_c$ are the magnetic excitation energies at $q=0, \pi /2$, and, $\pi$, obtained from our previous calculations [17]. The thin solid lines below $H_c$ are guides for the eyes. The magnetic structure factors (b) $S^{+-}(q,\omega )$ and (c) $S^{-+}(q,\omega )$ obtained from the DMRG calculation for the $S=\frac{1}{2}$ quantum Ising-like chain with $\epsilon$ = 0.46 in the longitudinal magnetic field, where the total magnetization reaches to 1/4 of the saturation. The ESR signals $B$ and $L$ in the quantum critical phase emerge from the psinon-antipsinon pair excitation at $q_z$ = 0 and the psinon-psinon pair excitation at $q_z$ = $\pi /2$, respectively. The $M$ and $P$ originate from the two-string excitations at $q_z$ = $\pi /2$ and $q_z$ = $\pi$, respectively. For the calculation of the $S^{+-}(q,\omega )$ and $S^{-+}(q,\omega ), J_{\pi }$ and $J_{\pi /2}$ are not included.

Figure 2

ESR spectra observed in ${\mathrm{BaCo}}_2{\mathrm{V}}_2{\mathrm{O}}_8$ for $H\parallel c$ at (a) 730.5 GHz, (b) 490 GHz, and (c) 1839 GHz. The upper and middle curves are spectra, observed by illuminating electromagnetic waves with the magnetic component polarized parallel and perpendicular to the $c$ axis, respectively, in the Voigt configuration. The lower curves are the spectra, observed by illuminating unpolarized electromagnetic waves in the Faraday configuration.

Figure 3

The four-fold screw Co-O chain in ${\mathrm{BaCo}}_2{\mathrm{V}}_2{\mathrm{O}}_8$.

Figure 4

Results of the DMRG calculations for (a) $S^x(q=0,\omega )$, (b) $S^z(q=0,\omega )$, (c) $T_{\pi /2}^x\left(\omega \right)$, and (d) $T_{\pi }^x\left(\omega \right)$ obtained with $J=65$ K, $\epsilon =0.46, J_{\pi }/J=0.2, J_{\pi /2}/J=0.2$, and $g=6.2$. The calculated intensities are presented with the scale given in color bar. The symbols are the experimental resonance points obtained from the previous ESR measurements [17].

Figure 5

Schematic pictures for distribution of the Bethe quantum numbers $I_j$ for (a) psinon-psinon, (b) antipsinon-psinon, and (c) two-string excitation. $I_F$ = $N/4-M/2\text{−}1$/2 is the maximum Bethe quantum number, which is occupied by the magnon in the ground state. Thus, a region shown by a bold curve is occupied by the magnons in the ground state. Note that the energy dispersion $\epsilon$ is not precisely depicted and is nonlinearly renromalized by changes in the distribution of the $I_j$'s due to the interaction effect amoung spins.