Strong $(\pi ,0)$ spin fluctuations in $\beta -\mathrm{FeSe}$ observed by neutron spectroscopy

We have performed powder inelastic neutron scattering measurements on the unconventional superconductor $\beta -\mathrm{FeSe}$ $(T_{\mathrm{c}}\simeq 8\mathrm{K})$. The spectra reveal highly dispersive paramagnetic fluctuations emerging from the square-lattice wave vector $(\pi ,0)$ extending beyond 80 meV in energy. Measurements as a function of temperature at an energy of $\sim 13\mathrm{meV}$ did not show any variation from $T_{\mathrm{c}}$ to 104 K. The results show that FeSe is close to an instability towards $(\pi ,0)$ antiferromagnetism that is characteristic of the parent phases of the high-$T_{\mathrm{c}}$ iron arsenide superconductors, and that the iron paramagnetic moment is neither affected by the orthorhombic-to-tetragonal structural transition at $T_{\mathrm{s}}\simeq 90\mathrm{K}$ nor does it undergo a change in spin state over the temperature range studied.

Figure 1

(a) Magnetic susceptibility of FeSe powder. The field-cooled (FC) and zero-field-cooled (ZFC) curves confirm the onset of superconductivity at $T_{\mathrm{c}}\simeq 8$ K (left). The tetragonal-to-orthorhombic structural transition at $T_{\mathrm{s}}\simeq 90$ K is signaled by a broad magnetic anomaly (right). (b) Rietveld refinement against room temperature neutron powder diffraction data of FeSe. Peak positions for the $\beta$-FeSe phase are marked by vertical red ticks beneath the data. The other ticks indicate peak positions for Fe impurities and the vanadium sample can. (c) Temperature dependence of the orthorhombic lattice parameters of FeSe. The points at 150 K are the tetragonal parameters with $a$ multiplied by $\sqrt{2}$. The lines are visual guides.

Figure 2

Neutron powder spectra of FeSe obtained on MERLIN at $T=8$ K $\sim eq{T}_{\mathrm{c}}$. The vertical dashed lines show the 2D wave vector $(\pi ,0)$ and equivalent positions. (a) High-energy part of the spectrum recorded with an incident energy $E_{\mathrm{i}}=100$ meV. The vertical bands of scattering above the phonon cutoff at 40 meV are caused by steeply dispersing cooperative paramagnetic fluctuations. (b) Low-energy part of the spectrum from the data measured with $E_{\mathrm{i}}=34$ meV. Magnetic scattering is visible in the energy window 10–15 meV where phonon scattering is weak.

Figure 3

(a) Reciprocal lattice of the Fe square lattice. The (red) solid circles mark the $(\pi ,0)$-type wave vectors and the (green) solid diamonds the $(\pi ,\pi /4)$-type positions, including the equivalent ${90}^{\circ }$ domains. The solid and dotted large circles show the effect of powder averaging, and the table lists the corresponding values of $Q=|{\mathbf{q}}_{\mathrm{m}}|$. (b) Constant-energy cuts through the data in Fig. 2 for three different energy bands as indicated. The upper two cuts are offset vertically. The (red) symbols are the data and the (blue) lines are fits with a damped harmonic oscillator model for spin waves dispersing anisotropically from ${\mathbf{q}}_{\mathrm{m}}=(\pi ,0)$. (c) The same as in (b) but with ${\mathbf{q}}_{\mathrm{m}}=(\pi ,\pi /4)$ and an isotropic dispersion.

Figure 4

Temperature dependence of the magnetic scattering at $(\pi ,0)\approx 1.2$ Å${}^{-1}$ averaged over the energy range 11–14 meV. The solid lines are fits to a Gaussian function on a linear background (dotted). The upper three scans are offset vertically by 0.25, 0.5, and 0.75 units, respectively.