Itinerant Magnetic Excitations in Antiferromagnetic ${\mathrm{CaFe}}_2{\mathrm{As}}_2$

Neutron scattering measurements of the magnetic excitations in single crystals of antiferromagnetic ${\mathrm{CaFe}}_2{\mathrm{As}}_2$ reveal steeply dispersive and well-defined spin waves up to an energy of $\sim 100\mathrm{meV}$. Magnetic excitations above 100 meV and up to the maximum energy of 200 meV are however broader in energy and momentum than the experimental resolution. While the low energy modes can be fit to a Heisenberg model, the total spectrum cannot be described as arising from excitations of a local moment system. Ab initio calculations of the dynamic magnetic susceptibility suggest that the high energy behavior is dominated by the damping of spin waves by particle-hole excitations.

Figure 1

Observed (left panel) and calculated (right panel) magnetic excitations in ${\mathrm{CaFe}}_2{\mathrm{As}}_2$ single crystals at temperature $T=10\mathrm{K}$ with an incident energy $E_i=450\mathrm{meV}$. The projections are in the scattering plane formed by the energy transfer axis and ($H$, 0, 0) direction and averaged over $-0.1<K<0.1$. An estimated background away from the magnetic zone center averaged over $1.8<H<2.0$ and $-0.25<K<0.25$ has been subtracted from the data. The intensities have been multiplied by the energy transfer for viewing purposes. Because of the fixed crystal orientation with incident beam along $L$, the $L$ component of the wave vector varies with the energy transfer. The calculation is from a Heisenberg spin wave model with a small damping parameter ($\Gamma =3\mathrm{meV}$) (see text).

Figure 2

Constant energy slices through spin waves in ${\mathrm{CaFe}}_2{\mathrm{As}}_2$ at $T=10\mathrm{K}$ as observed on MAPS (left panel) (intensity shown in absolute units from background level) compared with calculations using the fitted exchange parameters in the text (right panel) with small damping ($\Gamma =3\mathrm{meV}$) (see text).

Figure 3

Intensity of observed spin wave excitations in ${\mathrm{CaFe}}_2{\mathrm{As}}_2$ along [$H00$] direction at $T=10\mathrm{K}$, compared with the resolution convoluted spin wave calculations including damping shown in Fig. 5. The calculations with energy independent damping ($\Gamma$ held fixed at 3 meV) are also shown for comparison.

Figure 4

The dispersion of magnetic excitations in ${\mathrm{CaFe}}_2{\mathrm{As}}_2$: theory (lines) and experiment (solid circles). The dashed black lines are from Eq. (1) using exchange parameters derived from band-structure calculations (see Ref. 10). The solid lines represent the best global fit of Eq. (1) to the data. Variations of the fits with changing BZ boundary energy are shown for $E_{\mathrm{BZ}}=50$ and 150 meV. Also shown with open circles are the location of maxima in $\mathrm{Im}\{\chi (\mathbf{q},\omega )\}$ from ab initio band-structure results.

Figure 5

Spectral half width at half maximum derived from band-structure calculated peaks in $\mathrm{Im}\{\chi (\mathbf{q},\omega )\}$ (open circles) compared to the spin wave relaxation rate, $\Gamma (E)$ required to fit the neutron scattering data (solid circles).