Effect of the in-plane magnetic field on the neutron spin resonance in optimally doped FeSe${}_{0.4}$Te${}_{0.6}$ and BaFe${}_{1.9}$Ni${}_{0.1}$As${}_2$ superconductors

We use inelastic neutron scattering to study the effect of an in-plane magnetic field on the magnetic resonance in optimally doped superconductors FeSe${}_{0.4}$Te${}_{0.6}$ ($T_c=14$ K) and BaFe${}_{1.9}$Ni${}_{0.1}$As${}_2$ ($T_c=20$ K). While the magnetic field up to 14.5 T does not change the energy of the resonance, it partially suppresses $T_c$ and the corresponding superconductivity-induced intensity gain of the mode. However, we find no direct evidence for the field-induced spin-1 Zeeman splitting of the resonance. Therefore it is still unclear if the resonance is the long-sought singlet-triplet excitation directly coupled to the superconducting electron Cooper pairs.

Figure 1

(a) Schematic diagram of the Zeeman splitting of the exciton from singlet $|0\rangle$ to triplet $|1\rangle$ excited states. (b) Schematic diagram of the Zeeman splitting of a spin-1 resonance under 13-T field. The full width at half maximum (FWHM) of the resonance is assumed to be close to the resolutions of our instruments estimated from phonon measurements. The intensity of the central peak is set to be equal to the sum of the other two peaks, which is a requirement of isotropic spin fluctuations. The Landé factor is taken as $g=2$. (c),(d) Similar schematic diagrams as those in (a) and (b) in the case of a singlet-to-doublet excitation.

Figure 2

Constant-$Q$ scans at $Q=(0.5,0.5,1.2)$ at 1.5 and 15 K under (a) 0 and (b) 13-T field. (c),(d) Magnetic resonance at 0 and 13 T, respectively, as determined by the difference of data between 1.5 and 15 K. The solid lines are fitted results as described in the text. (e) Constant-$Q$ scans at (0.5,0.5,1.2) at 1.5 K under 0 and 11 T measured at SPINS. (f) Difference of data in (e) between 11 and 0 T. The solid line is fitted by the difference between one and three Gaussian functions as illustrated in Fig. 1b. (g) Constant-$E$ scans at 6 meV. (h) Temperature dependence of the resonance intensity at peak position ($E=7$ meV) under 13-T field.

Figure 3

Constant-$Q$ scans at (a) $Q=(0.5,0.5,0)$ and (b) $Q=(0.5,0.5,1)$. The corresponding temperature differences are shown in (c) and (d), while the ${\chi }^{″}(Q,\omega )$ are shown in (e) and (f).

Figure 4

(a) Constant-$E$ scans at 6.5 meV and $L=1$. (b) $L$ scan at 7.5 meV. (c) Temperature dependence of the resonance peak ($E=6.5$ meV) intensity at (0.5,0.5,1). The lines are guided by eye. (d) Field dependence of the resonance peak intensity at (0.5,0.5,1). The solid and dashed lines are fitted by the linear and square-root functions, respectively.