# Publications

### Oriol T. Valls

**Proximity Effects in Conical-Ferromagnet/Superconductor bilayers**Chien-Te Wu, O.T. Valls, K. Halterman,

*Phys. Rev. B 86, 184517 (2012)*
Download from http://arxiv.org/abs/1210.3636

**Abstract**

We present a study of various aspects of proximity effects
in $F/S$ (Ferromagnet/Superconductor) bilayers, where $F$
has a
spiral magnetic texture such
as that found in Holmium, Erbium and other materials, and
$S$ is a conventional
$s$-wave superconductor.
We numerically solve the Bogoliubov-de Gennes (BdG)
equations self-consistently
and use the solutions to compute physical quantities relevant
to the proximity effects in these bilayers. We obtain the relation
between the superconducting transition temperature $T_c$ and
the thicknesses $d_F$ of the magnetic layer by solving the
linearized BdG equations.
We find that the $T_c(d_F)$ curves include multiple oscillations.
Moreover, the system may be reentrant not only
with $d_F$, as is the case when the magnet is
uniform, but also with temperature $T$:
the superconductivity disappears in certain ranges of $d_F$ or $T$.
The $T$ reentrance reported here occurs when $d_F$
is larger than the spatial period of the conical exchange field.
We compute the condensation free energies and entropies from
the full BdG equations and find the results are
in agreement with $T_c$ values obtained
by linearization. The inhomogeneous nature
of the magnet makes it possible for all odd triplet pairing components
to be induced.
We have investigated their properties and
found that, as compared to the singlet amplitude, both the
$m=0$ and $m=\pm 1$ triplet components exhibit long range penetration.
For nanoscale bilayers, the proximity lengths for
both layers are also obtained.
These lengths oscillate with $d_F$ and they are found to be
long range on both sides. These results are shown to be
consistent with recent experiments.
We also calculate
the reverse proximity effect described by the three dimensional
local magnetization, and the local DOS, which reveals
important energy resolved signatures
associated with the
proximity effects.