Phase-controlled proximity effect in ferromagnetic Josephson junctions: Calculation of the density of states and the electronic specific heat

We study the thermodynamic properties of a dirty ferromagnetic $\text{S}\left|\text{F}\right|\text{S}$ Josephson junction with $s$-wave superconducting leads in the low-temperature regime. We employ a full numerical solution with a set of realistic parameters and boundary conditions, considering both a uniform and nonuniform exchange field in the form of a Bloch domain wall. Our main result is that it is possible to strongly modify the electronic specific heat of the system by changing the phase difference between the two superconducting leads from zero up to nearly $\pi$. This is explained in terms of the proximity-altered density of state in the ferromagnetic region, and we discuss possible methods for experimental detection of the predicted effect.

Figure 1

(Color online) The normalized local density of states vs energy and phase difference between two $s$-wave superconducting leads for a uniform magnetization texture with (a) $d_F/{\xi }_S=0.3$ and (b) $d_F/{\xi }_S=1.0$. The DOS is evaluated in the middle of the junction, i.e., $x=0$, and $h/{\Delta }_0=0.5$.

Figure 2

(Color online) The normalized local density of states vs energy and phase difference between two $s$-wave superconducting leads and inhomogeneous magnetization texture for (a) $d_F/{\xi }_S=0.3$ and (b) $d_F/{\xi }_S=1.0$. The DOS is evaluated in the middle of the junction, i.e., $x=0$, and $h/{\Delta }_0=0.5$.

Figure 3

(Color online) The normalized electronic specific heat of the diffusive $\text{S}\left|\text{F}\right|\text{S}$ Josephson junction vs phase difference between two $s$-wave superconducting leads with a ferromagnetic layer featuring a homogeneous and an inhomogeneous Bloch domain-wall magnetization texture. The arrows indicate an increasing value of $h$.

Figure 4

(Color online) The normalized local density of states of the diffusive $\text{S}\left|\text{F}\right|\text{S}$ junction vs phase difference and energy for homogeneous structure of ferromagnetic layer with exchange field $h/{\Delta }_0=1.1$ and thickness $d_F/{\xi }_S=0.3$.