Contribution of impurity-pinned vortices to the response function in a randomly diluted easy-plane ferromagnet on a square lattice

Using spin dynamics techniques, we determine the neutron scattering function $S_{xx}(\vec{q},\omega )$ of the two-dimensional classical $XY$ model on a square lattice containing a percentage of nonmagnetic impurities on the magnetic sites. Dilution substantially transforms the shape and the position of the central and spin wave peaks. Besides the spin wave peak, an additional inelastic peak arises. We argue that the causes of this rich structure are vortex-vacancy interactions.

Figure 1

The correlation function $S_{xx}(\vec{q},\omega )$ versus $\omega$ for some impurity concentrations ${\rho }_v=0$ (dotted line), ${\rho }_v=0.16$ (dashed line), and ${\rho }_v=0.20$ (solid line). It was used for $\vec{q}=(\pi ∕4a,0)$, $L=64a$, and temperature $T=0.350J$.

Figure 2

$S_{xx}(\vec{q},\omega )$ versus frequency $\omega$ for some values of $L$.

Figure 3

(Color online) The factor $C({\rho }_v,T)$ versus impurity concentration ${\rho }_v$ for $L=96$ and $T=0.200J$. The dotted line is a good fit to the data. Note that $C({\rho }_v\to 0,T=0.200J)\to 12.09Ja$.