Thermodynamic Evidence for the Fulde-Ferrell-Larkin-Ovchinnikov State in the ${\mathrm{KFe}}_2{\mathrm{As}}_2$ Superconductor

We investigate the magnetic phase diagram near the upper critical field of ${\mathrm{KFe}}_2{\mathrm{As}}_2$ by magnetic torque and specific heat experiments using a high-resolution piezorotary positioner to precisely control the parallel alignment of the magnetic field with respect to the FeAs layers. We observe a clear double transition when the field is strictly aligned in the plane and a characteristic upturn of the upper critical field line, which goes far beyond the Pauli limit at 4.8 T. This provides firm evidence that a Fulde-Ferrell-Larkin-Ovchinnikov state exists in this iron-based ${\mathrm{KFe}}_2{\mathrm{As}}_2$ superconductor.

Figure 1

The magnetic torque as a function of the applied magnetic field of ${\mathrm{KFe}}_2{\mathrm{As}}_2$, measured at fixed temperatures. The field was aligned with a small angle of $\theta =1.7°$ to the FeAs layers. The data were measured with an increasing field. Inset: Magnetic torque at various angles close to $\theta =0°$. The linear normal state background was removed here for clarity.

Figure 2

The first-order derivative of the magnetic torque as a function of the applied field at different temperatures for the field strictly parallel to the FeAs layers ($\theta =0°$). The stars mark the upper onset of the superconducting signal and the dotted lines the constant normal state value. Vertical offsets have been added to the data. The inset shows an enlarged region of the $T=0.35\mathrm{K}$ data at $H_{c2}$.

Figure 3

Specific heat $C_p/T$ measured as a function of the magnetic field aligned with $\theta =0°$ with respect to the FeAs layers at different fixed temperatures. Solid stars mark the additional phase transitions at $H_2$ above the main transitions at $H_1$ (empty stars). Vertical offsets were added for clarity. The additional dashed lines were measured under identical conditions at 0.52 and 1.2 K but with a misalignment angle of $\theta =3°$ instead.

Figure 4

$H\text{−}T$ phase diagram of ${\mathrm{KFe}}_2{\mathrm{As}}_2$ from magnetic torque and specific heat. ${\mu }_0{H}_1$ represents the transition between the homogeneous superconducting state ($\mathbf{q}=0$) and the FFLO state. The upper transition at ${\mu }_0{H}_2$ separates the FFLO state from the normal state. The additional lines represent the $H_{c2}(T)$ lines predicted for a purely Pauli-limited superconductor ($\mathbf{q}=0$) [30] and for an in-plane isotropic $s$-wave and a $d$-wave superconductor with the FFLO state [31]. The inset shows an enlargement with the upper onset of the superconducting contribution in torque for different field orientations (0°, 0.15°, and 1.7°).