# Publications

### Oriol T. Valls

**Tunneling Conductance and Spin Transport in Clean Ferromagnet-Ferromagnet-Superconductor Heterostructures**Chien-Te Wu, O.T. Valls, K. Halterman,

*Phys. Rev. B 90, 054523 (2014)*
Download from http://arxiv.org/abs/1408.4172

**Abstract**

We present a transfer matrix approach
that combines the
Blonder-Tinkham-Klapwijk (BTK) formalism and self-consistent
solutions to the Bogolibuov-de Gennes (BdG) equations
and use it to study the
tunneling conductance and spin transport in ferromagnet
(${\rm F}$)-superconductor (${\rm S}$)
trilayers (${\rm F_1F_2 S}$) as functions of bias voltage.
The self-consistency ensures that
the spin and charge conservation laws are properly satisfied.
We consider forward and angularly averaged conductances over a broad range of
the strength of the exchange fields and ${\rm F}$ thicknesses,
as the relative in-plane magnetization angle, $\phi$, between the two
ferromagnets varies.
The $\phi$-dependence of the self-consistent conductance
curves in the trilayers can differ substantially from that obtained %otv6
via a non-self-consistent approach.
The zero bias forward conductance peak
exhibits, as $\phi$ varies, resonance
effects intricately associated with particular
combinations of the geometrical and material parameters.
We find, when the magnetizations are non-collinear,
signatures of the anomalous Andreev reflections in the subgap
regions of the angularly averaged conductances.
When ${\rm F_1}$ is half-metallic, %otv6 half metals for the outer magnets, F$_1$,
the angularly averaged subgap conductance
chiefly arises from anomalous Andreev reflection.
The in-plane components of the spin current are strongly bias dependent,
while
the out-of-plane spin current component is only weakly
dependent upon voltage.
The components of the spin current aligned with
the local
exchange field of one of the F layers are
conserved in
that layer and in the S region, while they oscillate in the other layer.
We compute the spin transfer torques, in connection with the oscillatory
behavior of spin currents, and verify that the spin conservation law
continuity equation is strictly obeyed in our method.