Spin Dynamics in Pyrochlore Heisenberg Antiferromagnets

We study the low temperature dynamics of the classical Heisenberg antiferromagnet with nearest neighbor interaction on the frustrated pyrochlore lattice. We present extensive results for the wave vector and frequency dependence of the dynamical structure factor, obtained from simulations of the precessional dynamics. We also construct a solvable stochastic model for dynamics with conserved magnetization, which accurately reproduces most features of the precessional results. Spin correlations relax at a rate independent of the wave vector and proportional to the temperature.

Figure 1

Evidence for spin diffusion. (a) Dependence of $S(q,\omega )$ on $q$ and $\omega$ at small $q$. (b) Scaling collapse following Eq. (7) at multiple temperatures ($\beta J=20,40,60,80$) and four of the wave vectors plotted in (a). Also plotted is the prediction of Eq. (6).

Figure 2

Main panel: Decay rate of $S(\mathbf{q},t)$ as a function of $T$ at wave vectors as indicated. Upper inset: $S(\mathbf{q},\omega )$ at $\beta J=40$ (red curve) and 100 (blue curve), for $\mathbf{k}=(1,1,1)$. Lower inset: $S(\mathbf{q},\omega )$ on a nodal line at $\mathbf{k}=(0,0,1.25)$.

Figure 3

Intensity map of $\beta S(\mathbf{q},\omega )$ in the $(q_x,q_x,q_z)$ plane at $\beta J=500$. (a) Lower panel: Zero frequency (data divided by $1.25\times {10}^5$); white line is path $\mathcal{P}$. Upper panel: $\omega =2.5J$; black circle is centered on a pinch point. (b) Section along path segment ${\mathcal{P}}_1$ (see text).

Figure 4

Solid blue lines: Normalized correlation function $S(\mathbf{q},t)/S(\mathbf{q},0)$. Dashed red lines: Prediction from Eq. (6) with $\Gamma =0.167$, both shown at 3 times, $t$.