Spin-wave velocities, density of magnetic excitations, and NMR relaxation in iron pnictides

We perform an analysis of the experimentally known temperature dependence of the staggered magnetization in the antiferromagnetic phase. This analysis allows us to put an upper limit on the unknown value of the spin-wave velocity along the stripes of equal spin direction (spin stripes). The velocity is about ten times smaller than the velocity perpendicular to the spin stripes. The strongly anisotropic spin-wave dispersion implies a high density of low-energy magnetic excitations. We demonstrate that this high density strongly enhances the ${}^{75}\text{A}\text{s}$ NMR spin-lattice relaxation via the Raman scattering of magnons. We derive the polarization dependence of this relaxation channel and find very good agreement with experimental data. The high density of low-energy magnetic excitations deduced from our phenomenological analysis supports the scenario that ferropnictides are close to a quantum phase transition.

Figure 1

The Fe-As plane. Fe ions are shown by open circles and As ions are shown by filled circles. The Fe spins are shown by arrows. The Fe ions lie exactly in the plane while As ions are out of plane by ${\delta }_c\approx \pm 1.35\text{Å}$ in a checkerboard pattern. The pattern is shown by different fillings of the symbols for the As ions.

Figure 2

(Color online) Temperature dependence of the intensity of elastic neutron scattering at the antiferromagnetic superlattice reflection and of the spin-wave gap in ${\text{SrFe}}_2{\text{As}}_2$. Points with error bars show experimental data from Ref. 7. Blue circles show the normalized neutron-scattering intensity, $I\left(T\right)/I\left(0\right)$, and red diamonds show the normalized spin-wave gap, $\Delta \left(T\right)/\Delta \left(0\right)$. The curves show theoretical results for the normalized neutron-scattering intensity for various values of the spin-wave velocity $v_b$ along the spin stripes. Solid black curves correspond to the first scenario for the spin-wave gap, Eq. (25), and dashed red curves correspond to the second scenario, Eq. (26). The theory is justified only where the deviation of $I\left(T\right)/I\left(0\right)$ from unity is small.

Figure 3

Magnon Raman scattering on nuclear spin due to hyperfine interaction. Solid lines denote magnons, the double lines denote a nuclear spin. The dashed line denotes the hyperfine interaction.

Figure 4

NMR relaxation rates due to magnon scattering. The solid curve gives contribution of the $s$-wave transferred hyperfine coupling, see Eq. (36). The dashed curve gives contribution of the $p$-wave transferred hyperfine coupling, see Eq. (37). The parameters are given by Eqs. (1, 6, 30, 34) and $v_b=20\text{meV}$.