Temperature Controlled Fulde-Ferrell-Larkin-Ovchinnikov Instability in Superconductor-Ferromagnet Hybrids

We show that a wide class of layered superconductor-ferromagnet ($S/F$) hybrids demonstrates the emergence of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase well below the superconducting transition temperature. By decreasing the temperature, one can switch the system from uniform to the FFLO state which is accompanied by the damping of the diamagnetic Meissner response down to zero and also by the sign change in the curvature of the current-velocity dependence. Our estimates show that an additional layer of the normal metal ($N$) covering the ferromagnet substantially softens the conditions required for the predicted FFLO instability, and for existing $S/F/N$ systems, the temperature of the transition into the FFLO phase can reach several kelvins.

Figure 1

(a) The coefficients $a=\alpha (2\pi T_c{)}^2{\lambda }_c^2$ and $b=\beta (2\pi T_c{)}^4{\lambda }_c^2$ in the expansion (6) as functions of the $F$-layer thickness. (b) The dependences of the supercurrent $J=j_s{\lambda }_c^2{T}_c/({\xi }_f{T}_{c0})$ on the superconducting velocity $q$ for $T=0.8T_c(d_f)$, where ${\xi }_f=\sqrt{D_f/h}$ is the superconducting coherence length inside the ferromagnet, and $T_c(d_f)$ is the critical temperature corresponding to the thickness $d_f$ of the $F$ layer. The solid (dashed) line corresponds to $d_f=0.91{\xi }_f$ ($d_f=0.3{\xi }_f$). Here, we define ${\lambda }_c^2=ec{\mathrm{\Phi }}_0{d}_0/(16{\pi }^3{\sigma }_s{d}_s{T}_c)$ and take ${\xi }_f=10{\xi }_s$, ${\sigma }_s{d}_s/({\sigma }_f{\xi }_f)=0.06$.

Figure 2

(a)–(c) Phase diagrams of the $S/F/N$ sandwiches with $h/T_{c0}=25$ and different thicknesses $d_s$ of the $S$ layer. The ratio $d_s/{\xi }_0$ with ${\xi }_0=\sqrt{2\pi }{\xi }_s$ takes the values (a) 1.2, (b) 1.4, (c) 1.6. (d) Phase diagram of the $S/F/N$ system with $d_s/{\xi }_0=1.6$. In all panels, ${\sigma }_f/{\sigma }_s=1$, ${\sigma }_n/{\sigma }_s=150$, $d_n/{\xi }_0=1$. In panel (c), the dashed lines indicate the $d_f$ values corresponding to the curves in Fig. 3.

Figure 3

(a) The dependences of the screening parameter ${\lambda }^{-2}$ on the temperature for the $S/F/N$ sandwiches with $d_s/{\xi }_0=1.6$, the $N$-layer thickness $d_n/{\xi }_0=1$, and different thicknesses of the $F$ layer. (b) The current flowing along the layers as a function of the superconducting velocity for different $d_f$ values and $T=0.45T_{c0}$. In both panels, the black dash-dotted, blue dashed, and red solid curves correspond to $d_f=1.5{\xi }_f$, $d_f=1.2{\xi }_f$, and $d_f=0.8{\xi }_f$, respectively. The values ${\xi }_0$ and $j_0$ are defined as ${\xi }_0=\sqrt{2\pi }{\xi }_s$ and $j_0={\sigma }_s{T}_c/(e{\xi }_0)$. Other parameters are the same as in Fig. 2.