Coexistence and coupling of superconductivity and magnetism in thin film structures.
ABSTRACT Superconducting and magnetic order are usually mutually exclusive, and are found to coexist in relatively few materials. We have obtained direct evidence for a spin-density wave (SDW) coexisting with bulk superconductivity in a ferromagnetic-superconducting trilayer. In the superconducting state the amplitude of the SDW is enhanced and modeling the data also suggests a pi/2 phase shift of one component of the SDW, implying a profound coupling of these two forms of order.
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ABSTRACT: The variation of a magnetic field as a function of depth beneath the surface of an YBa(2)Cu(3)O(7-delta) thin film in the Meissner state has been measured using low energy muons. The depth of implantation was varied from 20-150 nm by tuning the energy of the implanted muons from 3-30 keV. These are direct measurements of the penetration of a magnetic field beneath a superconducting surface which illustrate the power of low energy muons for near surface studies in superconductivity and magnetism.Physical Review Letters 06/2000; 84(21):4958-61. · 7.94 Impact Factor
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ABSTRACT: We have discovered a new antiferromagnetic phase in TmNi2B2C by neutron diffraction. The ordering vector is Q(A) = (0.48,0,0) and the phase appears above a critical in-plane magnetic field of 0.9 T. The field was applied in order to test the assumption that the zero-field magnetic structure at Q(F) = (0.094,0.094,0) would change into a c-axis ferromagnet if superconductivity were destroyed. We present theoretical calculations which show that two effects are important: a suppression of the ferromagnetic component of the RKKY exchange interaction in the superconducting phase and a reduction of the superconducting condensation energy due to the periodic modulation of the moments at Q(A).Physical Review Letters 06/2000; 84(21):4982-5. · 7.94 Impact Factor
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ABSTRACT: The spatially oscillating electron spin polarization in the Ag spacer of a 4 nm Fe/20 nmAg/4 nm Fe(001) epitaxial trilayer has been determined by means of low energy muon spin rotation. It oscillates with the same period as the interlayer exchange coupling, but shows a much weaker attenuation at large distances x from the interface. The measured magnetization profile from the inner 14 nm of the spacer is described by an oscillating polarization decaying as x(-0.8(1)). This unusual behavior may arise from a full confinement of electron states within the spacer.Physical Review Letters 08/2003; 91(1):017204. · 7.94 Impact Factor
Coexistence and Coupling of Superconductivity and Magnetism in Thin Film Structures
A.J. Drew,1,*S.L. Lee,1D. Charalambous,2A. Potenza,3C. Marrows,3H. Luetkens,4,†A. Suter,4T. Prokscha,4
R. Khasanov,4,‡E. Morenzoni,4D. Ucko,5,xand E.M. Forgan5
1School of Physics and Astronomy, University of St. Andrews, St. Andrews, KY16 9SS, Scotland, United Kingdom
2Department of Physics, University of Lancaster, Lancaster, LA1 4YB, United Kingdom
3School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT, United Kingdom
4Labor fu ¨r Myonspinspektroskopie, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland
5School of Physics and Astronomy, University of Birmingham, Birmingham, B15 2TT, United Kingdom
(Received 18 February 2005; published 1 November 2005)
Superconducting and magnetic order are usually mutually exclusive, and are found to coexist in
relatively few materials. We have obtained direct evidence for a spin-density wave (SDW) coexisting with
bulk superconductivity in a ferromagnetic-superconducting trilayer. In the superconducting state the
amplitude of the SDW is enhanced and modeling the data also suggests a ?=2 phase shift of one
component of the SDW, implying a profound coupling of these two forms of order.
DOI: 10.1103/PhysRevLett.95.197201PACS numbers: 75.70.Ak, 74.45.+c, 74.78.Fk, 76.75.+i
In conventional s-wave superconductors the conduction
electrons form Cooper pairs, in which the electronic spins
are oppositely aligned to form a spin-singlet state. The
presence of a magnetic impurity in such a system gives
rise to an exchange field that will tend to align the spins of
the surrounding electrons parallel to it. Thus in order to
explain the robustness of superconducting order to the
presence of magnetic species, more exotic scenarios may
have to be invoked, forexample, spin-triplet p-wave super-
conductivity. In a contrasting scenario, one considers the
spin-singlet state to persist, and the potential energy asso-
ciated with the exchange field causes each of the two
electrons to have different kinetic energy. The resultant
linear momentum of the pair leads to a spatial oscillation
of the superconducting wave function, which periodically
reverses sign [1,2]. This Larkin-Ovchinnikov-Fulde-
Ferrell (LOFF) state is thus an s-wave spin-singlet system
but possesses nonzero linear momentum, and is therefore
distinct from either a p-wave or a conventional s-wave
superconductor. It is thus of interest to study systems in
which magnetism and superconductivity coexist, in order
to probe exotic ground states.
Artificially fabricated multilayered thin-film structures,
where superconducting (S) and ferromagnetic (FM) mate-
rials are juxtaposed in neighboring layers, are an ideal
medium in which to explore the interaction of the two
order parameters at the interface. For a normal metal
?N?=FMmultilayer,the exchange field can cause a periodic
oscillation of the electron-spin density inside the normal
layer. The period of this spin-density wave (SDW) is
determined by an enhancement of the wave-vector-
dependent susceptibility at extremal spanning vectors of
the Fermi surface , as in the Ruderman-Kittel-Kasuya-
Yosida (RKKY) interaction [4,5]. In contrast, for the case
of a FM layer that is bounded on both sides by S material, a
LOFF-type scenario gives rise to a phase difference of the
superconducting wave function across the layer [6,7]. The
value of the phase difference will depend on the layer
thickness compared to the wavelength of the spatial oscil-
lation. While there are convincing reports of both spatial
modulation of the superconducting order parameter inside
the FM layer  and for the existence of a SDW inside a
normal layer bounded by FM material , relatively little
attention has been given to the related effect occurring
inside a Slayer.Herewereport sucha measurement, where
wedemonstrate that remarkably a SDW may persist in, and
couple to, the superconducting state.
The principal method of investigation is the recently
developed low energy muon-spin rotation (LE-?SR) tech-
nique . This is analogous to conventional muon-spin
rotation (?SR), with the additional advantage that with the
LE-?SR technique one can control the depth of implanta-
tion into the surface of a sample via control of the muon
energy. The technique is ideal for the investigation of
magnetism in thin films, where a typical thickness is of
the order of a few hundred nm. LE-?SR has recently been
usedto measure the depth profile of the magnetic screening
in a high-temperature superconductor thin film , to
directly observe nonlocal superconductivity effects in Pb
, and also to observe a SDW in Fe=Ag multilayers .
In our experiment, spin-polarized positive muons are
brought to rest in the sample and their spins precess in
the local internal flux density. The muon decays with a
mean lifetime of 2:197 ?s (??! e?? ? ??? ?e), emit-
ting positronspreferentially along the muon-spindirection;
the positrons are detected using an array of scintillation
detectors. By averaging over typically two million muon
events, the temporal evolution of the muon-spin polariza-
tion direction may thus be determined .
The samplewasan Fe=Pb=Fetrilayer with a Mocapping
layer to inhibit oxidation. The dimensions were 20 ?
22 mm, with Fe thickness 3:0?3? nm, Pb thickness
215?5? nm, and Mo thickness 8:9?1? nm. It was grown on
a high quality silicon wafer (100) substrate using dc sput-
PRL 95, 197201 (2005)
4 NOVEMBER 2005
© 2005 The American Physical Society
tering. The superconducting properties of the films were
characterized using dc resistivity and magnetization mea-
surements, yielding a superconducting transition tempera-
ture Tc? 5:8?1? K. Layer thicknesses were calibrated
using ex situ x-ray reflectometry and polarized neutron
reflectometry (PNR), using the CRISP instrument at ISIS.
By fitting an optical neutron reflectivity model  to the
PNR data, we determined the thickness of the magnetic
and nonmagnetic layers in our sample (shown schemati-
cally in the inset of Fig. 1) and its roughness. Using this
information, it is possible to calculate the muon implanta-
tion depth distribution p?z? for the relevant implantation
energies, shown in Fig. 1, using a well-proven Monte Carlo
Figure 2 shows examples of the time evolution of the
muon-spin polarization, for an implantation energy of
10 keV. The measurements were made in a field of
20 mT applied parallel to the film and perpendicular to
the initial muon-spin polarization, at temperatures both
above and below Tc. Since this precession signal is clearly
nontrivial, more insight can be gained from the frequency
domain data of Fig. 3, which shows the p?B? derived from
the time domain data via a maximum entropy Fourier
transform technique [15,16]. Figure 3(a) shows the mea-
sured probability distributions of values of magnetic field
p?B? inside the sample in the normal metallic state at a
temperature of 10 K, for muon implantation energies cor-
responding to those shown in Fig. 1. The unusual p?B?s
shown in Fig. 3(a) reflect a complicated flux density pro-
file, arising from a SDW induced in the Pb layer by the
exchange field from the Fe layers, as previously demon-
strated for Fe=Ag=Fe trilayers . The satellite peaks in
the data are related to the turning points of the SDW .
The fraction of muonsstopping in the Fe layer experience a
very large field and precess too fast for any oscillating
signal from them to be detected.
The fits to our data in the frequency domain are achieved
by nonlinear regression and are given in Fig. 3(a) by the
shaded areas, and simply reflect the local depth-dependent
magnetization due to the SDW. At a given temperature, an
identical model isusedforall energies,and anydifferences
arise only from the muon stopping profile of Fig. 1. The
magnetization within the Pb spacer layer is given by the
addition of the magnetization, M?z?, induced in the Pb,
originating from each of the two Fe=Pb interfaces. In our
model, M?z? is assumed to take the following form :
where kiare the wave vectors of the SDW, z the distance
into the spacer layer, and Aiis an adjustable parameter for
the coupling strength of the spin-density wave of wave
vector ki. Our polycrystalline Pb films grow preferentially
with the ?111? direction perpendicular to the surface of the
film. The fits were found to converge to two wave vectors,
k1? 2:3?2? nm?1and k2? 15:8?2? nm?1. These values
are in excellent agreement with those obtained from de
Haas–van Alphen quantum oscillation measurements of
Pb (2:31 nm?1and 15:81 nm?1) [17,18] and correspond to
wave vectors that connect flat pieces of the Fermi surface
along the (111) direction in reciprocal space. One addi-
tional complication, which has been accounted for in the
model, arises from the aliasing effect due to the discrete
sampling steps of the muons, which reside at fixed sites
within the crystal lattice . This has been incorporated
using the known lattice parameters for Pb, without any
adjustment. On fixing thewavevectors to those found from
the de Haas–van Alphen measurements, the only adjust-
able parameters in the model are the phase of the oscil-
sin?2kiz ? ?i?
in the sample, plotted for different incident energies. Inset: the
composition and structure of the sample, as determined by PNR.
The calculated implantation profile for muons stopping
Time / µS
planted into the sample with an energy of 10 keV, as revealed by
the asymmetry in the number of detected positrons. The solid
lines correspond to fits to the data using the same model as
Figs. 3(a) and 3(b) (see text). The measurements were made in
an applied field of 20 mT in (a) the normal state, at a temperature
of 10 K and (b) the superconducting state, at a temperature of
The time evolution of the polarization of muons im-
PRL 95, 197201 (2005)
4 NOVEMBER 2005
lation ?i, the amplitude Ai, and the exponent ni. The
phases of the two oscillations, ?1and ?2, were found to
be 3?=2 ? 0:2 and ?=2 ? 0:2, respectively, and the ex-
ponent was found to be 0.86(2) for both oscillations, which
is surprisingly close to the value obtained for a similar
SDW in a Fe=Ag=Fe trilayer . The exponent niis much
smaller than fora simple RKKYmodel [3–5], although not
dissimilar to that for theories of electron confinement in
FM=N=FM trilayers . The result is that the electron-
spin polarization decays relatively slowly in amplitude as a
function of depth, and is thus evident even at our largest
We now turn to data taken at T ? 2:5 K, below the
superconducting transition temperature, measured by field
cooling immediately after the measurements were taken
above Tc. Figure 3(b) shows the p?B?s for the same en-
ergies under identical conditions as those measured above
Tc. The resemblance of the rawdata between Figs.2(a) and
2(b)demonstrate that remarkably the SDWpersistsinto the
superconducting state, and this coexistence is also sup-
ported by the satellite peaks of Fig. 3(b). To understand
the subtle differences that occur below Tcwe first turn to
the field profile across a pure Pb thin film. We performed
PNR measurements on a 220 nm Pb film, where we use the
fact that the neutron spin is sensitive to the flux profile
inside the sample. We used a nonmagnetic sample since
PNR measurements to study the effects of superconductiv-
ity are not currently feasible on FM=S=FM trilayers. This
is because the much stronger spin-dependent scattering
from the magnetic layers masks the much weaker, subtle
effects from the superconductor. The local nature of the
LE-?SR technique avoids this difficulty and allows us to
see effects inside the Pb film without interference from the
Fefilms.Fitsto the PNRspinasymmetry [Fig.4(b)]clearly
indicate that the flux profile, given in Fig. 4(a), is rather
different from that of a simple Meissner state . Rather,
the model shown comprises a highly concentrated row of
vortices down the center of the sample, leading to a flux
profile that exhibits flux expulsion near the surface and a
maximum in the center, in the vicinity of the normal cores
of the vortices [21,22]. The London penetration depth and
Ginzburg-Landau coherence length were found to be
50?2? nm and 55?2? nm respectively, with a vortex spacing
of 450?10? nm. Fits to the LE-?SR data, independent to
the PNR fits, reveal a very similar flux profile inside the
FM=S=FM trilayer, only with less flux expulsion and a
slightly larger core size, as might be expected if the ferro-
magnetism acts to suppress the superconductivity. In order
to increase the spin-dependent signal the PNR measure-
ments were also taken at the somewhat higher field of
The presence of vortices alone, however, does not ac-
count for the p?B? observed in the LE-?SR data below Tc
[Fig. 3(b)]. In order to model successfully the field profile
inside the Pb=Fe film, one must also take into account the
spatial phase of the oscillations. The model shown in
Fig. 3(b) includes a ?=2 change in phase of one of the
spin-density wave components compared to the value
found in the normal state, such that ?1and ?2are 2? ?
0:2 and ?=2 ? 0:2, respectively. The fits also require a
25% increase in amplitude for both oscillations to describe
the data, suggesting an increase in the coupling of spins
below the superconducting transition. To illustrate this
further, Fig. 4(c) compares a set of data taken below Tc
using a model identical to that shown in Fig. 3(b), except
that the phases were constrained to the values found above
Tc. Thus it is clear that this ?=2 phase shift to the model
provides a much better description of the frequency distri-
bution below Tc, which is true for the data taken at all
implantation energies [Fig. 3(b)]. For example, this phase
change also reduces the local flux density in the vicinity of
the Fe=Pb interface, allowing a description of the addi-
tional satellites observed below Tcat 4 keV [Fig. 3(b)].
These are not visible above Tc[Fig. 3(a)] because the
muons in this region are rapidly depolarized outside of
the time window.
While a number of previous experimental and theoreti-
cal studies have suggested the existence of LOFF-type
states in the FM layers of hybrid multilayer systems
[e.g., [7,8]], relatively little theoretical or experimental
study has been carried out on the related effects inside
the S layer. In a recent model calculation , it was found
that spontaneous currents may flow near a superconductor/
FM interface. The currents in the FM flowed in the oppo-
site direction to those in the superconductor, which died
away exponentially on the scale of the FM coherence
implantation depths into the sample, revealing the presence of
a spin-density wave inside the Pb layer (see text). The points and
shaded areas correspond to the data and fit, respectively. It was
measured in an applied field of 20 mTin (a) the normal state, at a
temperature of 10 K and (b) the superconducting state, at a
temperature of 2.5 K.
The field probability distribution p?B? for different
PRL 95, 197201 (2005)
4 NOVEMBER 2005
length. The results presented in this Letter show a much
longer range penetration of oscillatory spin polarization
inside the S layer and it remains uncertain as towhether the
LOFF mechanism is appropriate in this case.
It was proposed by Anderson and Suhl  that mag-
netic impurities present in a superconducting system could
couple to the superconducting state. They suggested that
the suppression of the spin susceptibility ??q? around q ?
0 in the BCS superconducting state leads to a broad
maximum in ??qs? at finite q. By analogy with the
RKKY interaction this gives rise to a spatial variation of
spin density characterized by a wave vector qs?
cussed in the context of the magnetic superconductor
TmNi2B2C, to explain the uncharacteristically long length
scale for magnetic order observed in the superconducting
state . Substituting the values obtained from our fits
gives qs? 3:2 nm?1, close to that of the firstcomponent of
the SDW found in the normal state. This proximity to the
natural wavelength for spin polarization may help explain
why it is only this component of the SDW that appears to
undergo a phase change in the superconducting state.
In conclusion, we have demonstrated the remarkable
coexistence of a SDW with bulk superconductivity in the
S layer in a FM=S=FM trilayer. Furthermore, the apparent
0?1=3. This mechanism has recently been dis-
enhancement of the SDWamplitude and ?=2 phase shift of
one component of the SDW below Tcindicate a profound
coupling of these two forms of spin order. It remains,
however, a challenge to theory to explain fully this persis-
tence of the SDW and its accommodation to the onset of
bulk superconductivity in these systems.
We thank S. Langridge, R. Dalgleish, and H.P. Weber
for their support during the beamtime and T.M. Riseman
for her version of the maximum entropy code. This work
was performed at the Swiss Muon Source, Paul Scherrer
Institute, Villigen, Switzerland and at ISIS, Rutherford
Appleton Laboratory, Oxfordshire, UK.
*Electronic address: email@example.com
†Also at Institut fu ¨r Metallphysik und Nukleare Festko ¨rper-
physik, Technische Universita ¨t Braunschweig, D-38106
‡Also at Physik Institut, Universita ¨t Zu ¨rich, CH-8057
Zu ¨rich, Switzerland.
xCurrent Address PR/PRL Editorial Offices, One Research
Road, Box 9000, Ridge, NY 11961-9000.
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220 nm in an applied field of 50 mT, deduced from a PNR
experiment (solid). A similar profile is deduced from the fits to
the LE-?SR data below Tcin the Fe=Pb=Fe trilayer at 20 mT
(dashed line). (b) The PNR spin asymmetry and fit to a model
involving a single row of vortices in the middle of the film
[21,22]. (c) One of the data sets shown in Fig. 2(b) is compared
with an identical model, except that the phases were constrained
to the values found above Tc.
(a) The field profile across a Pb film of thickness
PRL 95, 197201 (2005)
4 NOVEMBER 2005