PHYSICAL REVIEW B 97, 094514 (2018)
Unexpected effects of thickness and strain on superconductivity and magnetism
in optimally doped La
1.84
Sr
0.16
CuO
4
thin films
L. Howald,
1, 2, 3, *
E. Stilp,
1, 4, 5
F. Baiutti,
6
C. Dietl,
6
F. Wrobel,
6
G. Logvenov,
6
T. Prokscha,
4
Z. Salman,
4
N. Wooding,
7
D. Pavuna,
7
H. Keller,
1
and A. Suter
4
1
Physik-Institut der Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
2
Swiss Light Source, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
3
Hochalpines Institut Ftan AG, CH-7551 Ftan, Switzerland
4
Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
5
Materials for Energy Conversion, Empa, CH-8600 Dübendorf, Switzerland
6
Max Planck Institute for Solid State Research, Heisenbergstr. 1, D-70569 Stuttgart, Germany
7
Institute of Physics of Complex Matter, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
(Received 4 July 2017; revised manuscript received 28 January 2018; published 26 March 2018)
The magnetic field distribution of the vortex lattice of optimally doped La
1.84
Sr
0.16
CuO
4
thin films of various
thicknesses, grown on different substrates, was investigated. The influence of film thickness and biaxial strain on
the magnetic penetration depth and the superconducting number density were studied using muon spin rotation
and compared to single-crystal results. We found an effective superconducting layer thickness smaller than the
total film thickness, implying that the interfaces of the films are not or less superconducting than the bulk of
the film. The superfluid density diminished in thinner films whereas compressive strain enhanced it. This shows
that the number density of superconducting carriers is strongly affected by the boundary conditions as well
as by the strain. Furthermore, in fully relaxed optimally doped La
1.84
Sr
0.16
CuO
4
films grown on SrTiO
3
, we
found a low-temperature magnetic state which sets in at T
c
. It is reasoned that defects at the surface slow down
high-frequency magnetic fluctuations such that a “quasistatic” magnetic ground state results, which coexists with
the diminished surface superconductivity. These results indicate that the properties of the surface of optimally
doped La
1.84
Sr
0.16
CuO
4
superconductors differ substantially from the bulk.
DOI: 10.1103/PhysRevB.97.094514
I. INTRODUCTION
Since the discovery of high-temperature superconductivity
[1], understanding the phase diagram, and especially the role of
tuning parameters on superconductivity, has been the subject
of interest for many studies. In La
2−x
Sr
x
CuO
4+ǫ
the critical
temperature (T
c
) can be tuned by different techniques such
as chemical doping [2], hydrostatic pressure [3], or biaxial
pressure [4,5]. The variation of T
c
can be ascribed either to a
modification of the carrier concentration or to a modification of
the amplitude of the pairing interaction. Disentangling these
effects is one of the important challenges to understand the
mechanism of unconventional superconductivity.
The magnetic penetration depth λ offers a direct probe to
the mechanism leading to the variation of T
c
. Indeed, within
the London model
λ =
m
⋆
c
2
4πn
S
e
. (1)
λ is directly related to the density of superconducting carriers,
known as the number density n
S
, and to the effective mass
m
⋆
. Here, e is the quasiparticle (electron/hole) charge and c is
the speed of light. The mass renormalization directly depends
on the interactions affecting the quasiparticles, notably the
*
ludovic.howald@gmail.com
attracting interaction leading to superconductivity. The number
density for an invariant gap symmetry is proportional to the
carrier concentration. Therefore, within a given phase diagram,
one expects the dependence of the superconducting transition
temperature on the magnetic penetration depth to have a pos-
itive derivative dT
c
(λ)/dλ > 0 if the phase diagram is mainly
determined by a variation of pairing interaction and a negative
derivative dT
c
(λ)/dλ < 0 if the phase diagram is mainly
determined by a variation of the carrier concentration [6].
Superconductivity is defined by the absence of electrical
resistivity and expulsion of the magnetic field (Meissner
effect). The second criterion implies that superconductivity
is a bulk phase, as a certain thickness is required for super-
conducting currents to flow and expel the externally applied
magnetic field. On the other hand, the superconducting wave
function is extended and Cooper pairs can tunnel through
nonsuperconducting regions such as in Josephson junctions
[7]. Surface-sensitive techniques such as angle-resolved pho-
toemission spectroscopy (see, e.g., [8]) have claimed important
results on the superconducting phase, notably its single band
electronic structure and potential relation to other orders such
as magnetism. However, a proper understanding of these
experiments is only possible once the relation between surface
and bulk properties is established.
The application of in-plane compressive or tensile strain in
thin films has a tremendous effect on superconductivity. In the
cuprate system La
2−x
Sr
x
CuO
4+ǫ
, biaxial compressive strain
increases T
c
up to a factor 2 (see Ref. [9]) while biaxial tensile
2469-9950/2018/97(9)/094514(13) 094514-1 ©2018 American Physical Society