Fulde-Ferrel-Larkin-Ovchinnikov Inhomogeneous Superconducting State and Phase Transitions Induced by Spin Accumulation in a Ferromagnet-$d_{x^2-y^2}$-Wave Superconductor-Ferromagnet Tunnel Junction

Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) inhomogeneous superconducting (SC) state, first- and second-order phase transitions, and quantum criticality induced by spin accumulation in a ferromagnet-$d_{x^2-y^2}$-wave superconductor-ferromagnet tunnel junction are theoretically predicted. A complex phase diagram in the temperature-bias voltage plane is determined. It is found that the phase transitions from the homogeneous BCS state to the inhomogeneous FFLO state, and from the FFLO state with the momentum $\mathbf{% q}${}^{\mathrm{\prime }}sazimuthalangle$\theta_{$\mathbf{q}$}=0$tothatwith$\theta_{% $\mathbf{q}$}=\pi /4$, are of the first-order; while the transitions from all SC states to the normal state at critical voltages are of the second-order. A Lifshitz point, a bicritical point and a quantum critical point are identified.