Proximity Effects in Ferromagnet/Superconductor Layered Heterostructures with Inhomogeneous Magnetization

Abstract

In this thesis, we present a theoretical investigation of the proximity effects in ferromagnet/superconductor heterostructures with inhomogeneous magnetization, including ferromagnet/ferromagnet/superconductor (<italic>F₁F₂S</italic>) trilayers and conical-ferromagnet/superconductor bilayers. We numerically obtain the self-consistent solutions of the Bogoliubov-de Gennes (BdG) equations and use these solutions to compute the relevant physical quantities. In <italic>F₁F₂S</italic> trilayers, we find that the critical temperature, <italic>T_c</italic>, can be a non-monotonic function of the angle <italic>&alpha</italic> between magnetizations in F layers. The minimum <italic>T_c(&alpha)</italic> often occurs when magnetizations are mutually perpendicular (<italic>&alpha=&pi/2</italic>). In addition, we demonstrate that the <italic>T_c</italic> minimum corresponds to the maximum of the penetration of the long-range triplet amplitudes. We compare our theoretical results with experiment and find that they are in excellent agreement. We also study other aspects of proximity effects such as the local density of states, local magnetizations, and thermodynamic functions. In conical-ferromagnet/superconductor bilayers, we obtain the relation between <italic>T_c</italic> and the thickness <italic>d_F</italic> of the magnetic layer, and find that the <italic>T_c(d_F)</italic> curves include multiple oscillations. Moreover, for a range of <italic>d_F</italic>, the superconductivity is reentrant with temperature <italic>T</italic>: as one lowers <italic>T</italic> the system turns superconducting, and when <italic>T</italic> is further lowered it returns to normal. We demonstrate that the behavior of both <italic>m=0</italic> and <italic>m=&plusmn1</italic> triplet amplitudes are related to the intrinsic periodicity of conical ferromagnet. Our theoretical fits of <italic>T_c(d_F)</italic> are in good agreement with experimental data. The transport properties, including the tunneling conductance and the spin polarized transport, in <italic>F₁F₂S</italic> trilayers are investigated. To fully take into account proximity effects, we adopt a transfer matrix method incorporated with the Blonder-Tinkham-Klapwijk formalism and self-consistent solutions to the BdG equations. We show that our method ensures that conservation laws are properly satisfied. Our results indicate that the behavior of tunneling conductance depends on the misorientation angle between magnetizations, and also exhibits resonance effects. We also investigate the bias dependence of non-equilibrium spin transfer torque and its connection to both spin currents and local magnetizations.