Supercurrent diode effect, spin torques, and robust zero-energy peak in planar half-metallic trilayers
Klaus Halterman, Mohammad Alidoust, R. S. Smith, Spencer Starr
Abstract
We consider trilayer ${\mathrm{F}}_{1}{\mathrm{F}}_{2}{\mathrm{F}}_{3}$ Josephson junctions that are finite in two dimensions and have arbitrary magnetizations in each ferromagnet ${\mathrm{F}}_{i}\phantom{\rule{0.28em}{0ex}}(i=1,2,3)$. The trilayers are sandwiched between two $s$-wave superconductors with a macroscopic phase difference $\mathrm{\ensuremath{\Delta}}\ensuremath{\varphi}$. Our results reveal that when the magnetizations have three orthogonal components, a supercurrent can flow at $\mathrm{\ensuremath{\Delta}}\ensuremath{\varphi}=0$. With our generalized theoretical and numerical techniques, we study the planar spatial profiles and $\mathrm{\ensuremath{\Delta}}\ensuremath{\varphi}$ dependencies of the charge supercurrents, spin supercurrents, spin torques, and density of states. Remarkably, upon increasing the magnetization strength in the central ferromagnet layer up to the half-metallic limit, the self-biased current and induced second harmonic component become dramatically enhanced while the critical supercurrent reaches its maximum value. Additionally, for a broad range of exchange-field strengths and orientations, the ground state of the system can be tuned to an arbitrary phase difference ${\ensuremath{\varphi}}_{0}$. For intermediate exchange-field strengths in the middle layer ${\mathrm{F}}_{2}$, a ${\ensuremath{\varphi}}_{0}$ state can arise that creates a superconducting diode effect, whereby $\mathrm{\ensuremath{\Delta}}\ensuremath{\varphi}$ can be tuned to create a one-way dissipationless current flow. The spin currents and effective magnetic moments reveal a long-ranged spin torque in the half-metallic phase. Moreover, the density of states unveils the emergence of zero-energy peaks for the mutually orthogonal magnetization configurations. Our results suggest that this simple trilayer Josephson junction can be an excellent candidate for producing experimentally accessible signatures for long-ranged self-biased supercurrents and supercurrent diode effects.