Magnetic susceptibility anisotropies in a two-dimensional quantum Heisenberg antiferromagnet with Dzyaloshinskii-Moriya interactions

The magnetic and thermodynamic properties of the two-dimensional quantum Heisenberg antiferromagnet (QHAF) that incorporates both a Dzyaloshinskii-Moriya and pseudodipolar interactions are studied within the framework of a generalized nonlinear sigma model. We calculate the static uniform susceptibility and sublattice magnetization as a function of temperature and we show that (i) the magnetic response is anisotropic and differs qualitatively from the expected behavior of a conventional easy-axis QHAF; (ii) the Néel second-order phase transition becomes a crossover, for a magnetic field $B\perp \mathrm{Cu}{\mathrm{O}}_2$ layers. We provide a simple and clear explanation for all the recently reported unusual magnetic anisotropies in the low-field susceptibility of ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_4$ [L. N. Lavrov et al., Phys. Rev. Lett. 87, 017007 (2001)], and we demonstrate explicitly why ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_4$ cannot be classified as an ordinary easy-axis antiferromagnet.

Figure 1

Left: The hatched circles represent the ${\mathrm{O}}^{--}$ ions tilted above the $\mathrm{Cu}{\mathrm{O}}_2$ plane; the empty ones are tilted below it; small black circles are ${\mathrm{Cu}}^{++}$ ions; $bac$ orthorhombic coordinate system. Right: Schematic arrangement of the staggered magnetization (small black arrows) and DM vectors (open arrows). Center: Continuum definition of ${\mathbf{D}}_{+}$.

Figure 2

(Color online) Temperature dependence of the magnetic susceptibilities ${\chi }_a$, ${\chi }_b$, and ${\chi }_c$ from (11). Insets: (a) temperature dependence of $M_{a,b,c}$ and (b) ${\xi }^{-1}$.

Figure 3

(Color online) Plot of ${\sigma }_0$, $M_b$, and $M_b^{\mathit{exp}}$ from Eqs. (21, 20). $M_b^{\mathit{exp}}$ is fitted to the experimental data for the inverse correlation length above $T_N$, see discussion in the text below Eq. (21). Inset: ${\chi }_c$ in units of emu/g and experimental points from Ref. 4. ${\chi }_c^{\mathit{exp}}$ is obtained from Eqs. (11) using $M_b^{\mathit{exp}}$. Here ${\rho }_s=0.07J$, $\gamma =0.5$, $a=5.3\mathrm{\AA }$, the out-of-plane lattice parameter $d=13.5\mathrm{\AA }$, and we added a $T$-independent shift of ${\chi }_{\mathrm{vV}}\approx 1.0\times {10}^{-7}\mathrm{emu}∕\mathrm{g}$ to account for the van Vleck paramagnetic susceptibility (see Ref. 4).