Electron spin resonance in $S=\frac{1}{2}$ antiferromagnets at high temperature

We study the electron spin resonance of low-dimensional spin systems at high temperature and test the Kubo-Tomita theory of exchange narrowing. In finite-size systems (molecular magnets), we found a double-peak resonance which strongly differs from the usual Lorentzian. For infinite systems, we have predictions for the linewidth and line shape as a function of the anisotropy strength. For this, we have used an interpolation between a nonperturbative calculation of the memory function at short times (exact diagonalization) and the hydrodynamic spin diffusion at long times. We show that the Dzyaloshinskii-Moriya anisotropies generally induce a much larger linewidth than the exchange anisotropies in two dimensions, contrary to the one-dimensional case.

Figure 1

(Color online) ESR line shape of a one-dimensional chain of $N=16$ spins $\left(T⪢J\right)$. The curves are rescaled with the half width at half maximum, ${\omega }_0/J$ (shown in the inset as a function of $D/J$ for three sizes).

Figure 2

(Color online) ESR line shape (high-energy tail) for a one-dimensional chain $\left(T⪢J\right)$ for the Dzyaloshinskii-Moriya and XXZ models (using $2\delta =D^2/J^2$). The response is identical only at low energy (inset).

Figure 3

(Color online) Memory function $\Sigma \left(t\right)$ at short times ($N$ is the system size, $\delta =0.08$). Convergence to $N=\infty$ is obtained for $tJ\lesssim 6.5$. The Kubo-Tomita Gaussian holds for $tJ\lesssim 1.5$. The interpolation to the long-time spin diffusion $1/t^{1/2}$ is shown (dashed line).

Figure 4

(Color online) Memory function $\Sigma \left(t\right)$ at long times (system size $N$, $\delta =0.08$). There is a peak at $t_{a}J\sim 10–17$ whose amplitude decreases with $N$ (inset). The assumed long-time spin-diffusion tail is also shown (dashed line).

Figure 5

(Color online) Linewidth vs anisotropy for infinite one-dimensional chains (lower bound, Kubo-Tomita and self-consistent calculation).

Figure 6

(Color online) ESR line shape for infinite one-dimensional chains, assuming different cutoffs ${\tau }_0$ of the diffusive tail. The arrow (inset) indicates the self-consistent ${\tau }_c$.

Figure 7

(Color online) Memory function for the two-dimensional $S=\frac{1}{2}$ kagome antiferromagnet: effect of the Dzyaloshinskii-Moriya strength (left) and finite-size effects (right).

Figure 8

(Color online) Linewidth vs anisotropy for the $S=\frac{1}{2}$ kagome antiferromagnet (Kubo-Tomita and self-consistent calculation). The horizontal line shows the experimental linewidth of ${\text{ZnCu}}_3{\left(\text{OH}\right)}_6{\text{Cl}}_3$ (Ref. 32).

Figure 9

(Color online) ESR line shape for the two-dimensional kagome antiferromagnet, assuming different cutoffs ${\tau }_0$ of the $1/t$ diffusive tail.

Figure 10

(Color online) ESR signal (derivative of the resonance line at $\omega <h$): theory and experiment on the kagome $S=\frac{1}{2}$ ${\text{ZnCu}}_3\left({\text{OH}}_3\right){\text{Cl}}_2$ (from Ref. 32).