Quantum corrections to the spin-wave spectrum of ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_4$ in an external magnetic field

The effects of quantum fluctuations on the magnetic field dependence of the spin-wave gaps in the lamellar antiferromagnet ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_4$ are considered. Nonlinear corrections to the spin-wave spectrum are calculated to leading order in $1∕S$, where $S$ is the localized spin. The nearest-neighbor exchange interactions between the Cu spins as well as the Dzyaloshinskii-Moriya interactions are taken into account. Using the experimental values of the components of the $g$-factor tensor, we get satisfactory agreement with the experimental results for the field dependence of the gaps by Gozar et al. [Phys. Rev. Lett. 93, 027001 (2004)] and obtain consistent values of the in-plane and interplane coupling constants. The field dependence of the dispersion of spin waves propagating perpendicular to the $\mathrm{Cu}{\mathrm{O}}_2$ planes is also discussed.

Figure 1

The four copper spins $A$, $B$, $C$, and $D$ in a unit cell. Ordered spin directions are shown by arrows. The horizontal lines refer to the $\mathrm{Cu}{\mathrm{O}}_2$ layers. The global reference axes $z$ and $y$ point along the orthorhombic crystallographic axes $c$ and $b$, respectively.

Figure 2

The field dependence of the in-plane gap for a field in the $c$ direction. Circles: experimental data from Ref. 5. Solid lines: the theoretical dependence, Eq. (55), with ${\tilde{w}}^2=2.19\mathrm{meV}$.

Figure 3

The dimensionless dispersion of the acoustical branch of the in-plane SW, $[{\omega }_{\mathit{in}}^2\left(q_z\right)-{\omega }_{\mathit{in}}^2\left(0\right)]∕{\tilde{w}}^2$, for different magnetic fields: $H\to H_c–$ (solid line), $H=H_c∕2$ (dashed line), and $H=0$ and $H>H_c$ (dash-dotted line).