Magnetic Vortex Induced by Nonmagnetic Impurity in Frustrated Magnets

We study the effect of a nonmagnetic impurity inserted in a two-dimensional frustrated ferromagnet above its saturation magnetic field $H_{\mathrm{sat}}$ for arbitrary spin $S$. We demonstrate that the ground state includes a magnetic vortex that is nucleated around the impurity over a finite range of magnetic field $H_{\mathrm{sat}}\le H\le H_{\mathrm{sat}}^I$. Upon approaching the quantum critical point at $H=H_{\mathrm{sat}}$, the radius of the magnetic vortex diverges as the magnetic correlation length: $\xi \propto 1/\sqrt{H-H_{\mathrm{sat}}}$. These results are derived both for the lattice and in the continuum limit.

Figure 1

Binding energies ${\mathrm{\Delta }}_b^l$ for $l=0$, 1, 2 as a function of ${\mathrm{\Delta }}_0$ for (a) $r_0=4$ and (b) $r_0=2$. Panels (c) and (d) show the difference between the energies of the $l=1$, 2 and the $l=0$ bound states for $r_0=4$ and $r_0=2$, respectively.

Figure 2

Vortex solutions for $H_{\mathrm{sat}}<H<H_{\mathrm{sat}}^I$ obtained from numerical simulations of $\mathcal{H}$ in the classical limit ($S\to \infty$). (a) Vortex bound to a single-site nonmagnetic impurity for different field values. The vortex helicity is arbitrary due to the U(1) symmetry of $\mathcal{H}$. (b) Giant vortex solution ($l=\pm 2$) obtained after removing the spins from the six sites indicated with black dots, for $J_3=-0.2777J_1$ and $Q=2\pi /12$. The saturation field is $H_{\mathrm{sat}}=0.02235|J_1|$ and $H_{\mathrm{sat}}^I=0.04725|J_1|$.

Figure 3

Binding energy ${\mathrm{\Delta }}_b$ of the $l=\pm 1$ bound state around a nonmagnetic impurity inserted in the TL model described by $\mathcal{H}$. Here, $|{\mathrm{\Delta }}_b|$ is equal to the difference between the saturation field around the impurity, $H_{\mathrm{sat}}^I$, and the bulk saturation field $H_{\mathrm{sat}}$. The lower inset shows the ratio $(H_{\mathrm{sat}}^I-H_{\mathrm{sat}})/H_{\mathrm{sat}}$ as a function of $J_3/|J_1|$. The contour plots correspond to the amplitude of the ground state wave function for selected values of $J_3/|J_1|$.