Spin waves and magnetic exchange interactions in the spin-ladder compound ${\mathrm{RbFe}}_2{\mathrm{Se}}_3$

We report an inelastic neutron scattering study of the spin waves of the one-dimensional antiferromagnetic spin ladder compound ${\mathrm{RbFe}}_2{\mathrm{Se}}_3$. The results reveal that the products, $SJ$'s, of the spin $S$ and the magnetic exchange interaction $J$ along the antiferromagnetic (leg) direction and the ferromagnetic (rung) direction are comparable with those for the stripe ordered phase of the parent compounds of the iron-based superconductors. The universality of the $SJ$'s implies nearly universal spin wave dynamics and the irrelevance of the fermiology for the existence of the stripe antiferromagnetic order among various Fe-based materials.

Figure 1

(a) A schmatic of the ladder structure of ${\mathrm{RbFe}}_2{\mathrm{Se}}_3$. The cuboid indicates one unit cell. (b) The one-dimesnional (1D) edge-shared FeSe tetrahedra in ${\mathrm{RbFe}}_2{\mathrm{Se}}_3$. The red arrows represent the moment directions of iron atoms. The $J_L,J_R,J_2,J_5,J_6,$ and $J_7$ are the magnetic exchange interactions between the corresponding iron atoms.

Figure 2

INS spectra $S(Q,\omega )$ of ${\mathrm{RbFe}}_2{\mathrm{Se}}_3$ at (a) 5 K and (b) 300 K with $E_i=50$ meV. The color represents intensities in arbitrary units. (c) Constant $Q$ cuts between $1.1<Q<1.3$ (${\AA }^{-1})$ at 5 and 300 K, respectively. The intensities have been corrected the Bose factor. (d) Constant energy cuts at 11, 18, 25, and 29 meV at 5 K. The cuts are averaged between $E\pm 1$ meV.

Figure 3

(a) Spin excitation spectra $S(Q,\omega )$ collected with $E_i=150$ meV and (b) $E_i=250$ meV at 5 K. The red dashed rectangle highlights a branch of dispersive spin waves. (c) Constant energy cuts at $E=23$, 57, and 80 meV averaged within $E\pm 2$ meV with $E_i=150$ meV. Cuts at $E=101$ and 117 are obtained in panel (b) averaged within $E\pm 3$ meV. The intensities for $E=23$ meV have been reduced by multiplying a factor of 0.5 for comparison. (d) $S(Q,\omega )$ collected with $E_i=450$ meV at 5 K. (e) Constant $Q$ cuts obtained in panel (d) at $Q=5.25$, 5.75, 6.25, and 6.75 ${\AA }^{-1}$ averaged within $Q\pm 0.24{\AA }^{-1}$. The solid lines in panels (c) and (e) are fits to Gaussian functions. (f) A plot of the intensities at $E=205\pm 5$ meV after subtracting an averaged background at $E=160\pm 5$ and $250\pm 5$ meV. The solid line is the squared magnetic form factor of ${\mathrm{Fe}}^{2+}$.

Figure 4

SpinW simulations on the $S(Q,\omega )$ with parameters described in the text. The spectrum has been convoluted an instrumental resolution of (a) 3, (b) 10, and (c) 15 meV in order to compare with the data for $E_i=50$, 250, and 450 meV, respectively. The white points are extracted from the experimental data. The bars in panel (c) along the vertical direction represent the FWHM. The others indicate the standard deviations of the data. (d) Simulated dispersion relation along high-symmetry directions in the [H, L] 2D Brillouin zone, as shown in the inset. The color represents intensities. We convolute a constant 5-meV instrumental resolution for visualization.