Piezomagnetism of superconducting iron chalcogenides

Experiments on the acoustoelectric transformation in superconducting compounds based on FeSe reveal the manifestation of piezomagnetism in them. It allows us to refer the family of superconducting chalcogenides to the systems with a hidden magnetic order and broken time-reversal symmetry. The anisotropy of the piezomagnetic response indicates that the crystal structure of these compounds belongs to the trigonal syngony, in the low-temperature phase.

Figure 1

The amplitude of the electromagnetic wave (the AET signal) radiated from the $\mathrm{Fe}{\mathrm{Se}}_{1-x}{\mathrm{S}}_x$ single crystals with different $x$ subjected to the transverse elastic wave. The horizontal scale is stretched in the low temperature range. The dotted line shows the approximate level of detection of the signal against the background noise. The superconductive critical temperatures $T_c$ and the temperatures of the structural transition $T_s$ are shown by dashed and dash-dotted vertical lines, respectively.

Figure 2

Polarization diagrams of the $\mathrm{Fe}{\mathrm{Se}}_{0.925}{\mathrm{S}}_{0.075}$ sample at $T=15$ K, $\mathbf{q}\parallel \left[001\right], \mathbf{u}\parallel \left[100\right]$ (red lines), and $\mathbf{u}\parallel \left[110\right]$ (green lines). (a) The amplitude of the AET signal normalized to the maximum signal, (b) the phase of the signal, (c) schematic diagram of the experiment (S is the sample, the rectangular coil A is the antenna, $\mathbf{n}$ is the normal to the plane of the coil, R is the recording device, $\mathbf{q}$ is the wave vector, and $\theta$ is the angle between the displacement $\mathbf{u}$ in the acoustic wave and $\mathbf{n}$).

Figure 3

Polarization diagrams of the $\mathrm{Fe}{\mathrm{Se}}_{0.925}{\mathrm{S}}_{0.075}$ sample at $T=15$ K, $\mathbf{q}\parallel \left[100\right], \mathbf{u}\parallel \left[010\right]$ (red lines), and $\mathbf{u}\parallel \left[001\right]$ (green lines). (a) The amplitude of the AET signal, (b) the phase of the signal.

Figure 4

Magnetic susceptibility of the detached $\mathrm{Fe}{\mathrm{Se}}_{0.925}{\mathrm{S}}_{0.075}$ single crystal (green curve) and the same crystal glued to Ge crystal (red curve) in the field $B=0.5$ T. The germanium contribution is subtracted.

Figure 5

Magnetic field dependence of the amplitude and the phase of the AET signal for the $\mathrm{Fe}{\mathrm{Se}}_{0.925}{\mathrm{S}}_{0.075}$ single crystal at $\mathbf{q}\parallel \left[001\right]$ and $\mathbf{u}\parallel \left[110\right]$. The amplitude and the phase are counted from their values at $H=0$. The even and odd components of the amplitude of the AET signal are shown in the inset.

Figure 6

Temperature dependence of the AET response of the $\mathrm{Fe}{\mathrm{Se}}_{0.5}{\mathrm{Te}}_{0.5}$ single crystal, and temperature dependence of its magnetization in the field $B=0.02$ T (curve 1) and $B=5\times {10}^{-4}$ T (curve 2).