Manipulation Of Pancake Vortices By Rotating A Josephson Vortex ...
IOP PUBLISHING
SUPERCONDUCTOR SCIENCE AND TECHNOLOGY
Supercond. Sci. Technol. 21 (2008) 015017 (3pp)
doi:10.1088/0953-2048/21/01/015017
Manipulation of pancake vortices by
rotating a Josephson vortex lattice
A Crisan1,2,3, S J Bending3 and T Tamegai4
1 Department of Metallurgy and Materials, University of Birmingham, Edgbaston,
Birmingham B15 2TT, UK
2 National Institute of Materials Physics, PO Box MG-7, Bucharest 077125, Romania
3 Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY, UK
4 Department of Applied Physics, University of Tokyo, Hongo, Bunkyo-ku,
Tokyo 113-8627, Japan
E-mail: I.A.Crisan@bham.ac.uk
Received 6 October 2007
Published 4 December 2007
Online at stacks.iop.org/SUST/21/015017
Abstract
Scanning Hall probe microscopy has been used to demonstrate the manipulation of pancake
vortices by rotating the Josephson vortex lattice in Bi2Sr2CaCu2O8+δ single crystals in the
interacting crossing lattices regime. Creation of one-dimensional pancake vortex chains trapped
on Josephson vortices, and the subsequent rotation of the chains were realized by independently
controlling magnetic fields in three orthogonal directions. The anisotropy parameter determined
from the in-plane distances between vortex chains in various in-plane fields is consistent with
commonly accepted values.
1. Introduction
symmetries of the projected JV and PV lattices in any given
direction are, in general, incommensurate, a rich variety of
In high critical temperature superconducting (HTS) cuprates,
broken symmetry phases can arise in the crossing lattices
a magnetic field (Hz) applied perpendicular to the super-
regime. Scanning Hall probe microscopy (SHPM) has earlier
conducting CuO2 layers (a–b planes) creates stacks of two-
been used to directly observe discrete PVs in BSCCO single
dimensional (2D) pancake vortices (PVs), with circulating su-
crystals under independently applied Hz and H fields, leading
percurrents in the CuO2 layers, weakly coupled along the c-
to an unambiguous experimental verification of the interacting
axis, which interact to form well-ordered hexagonal Abrikosov
crossing lattices scenario [5, 6].
At very low Hz a one-
lattices in disorder-free samples [1]. When the field is applied
dimensional (1D) vortex chain state was observed [5] where
in the a–b plane (H ) Josephson vortices (JV) are formed, with
all PV stacks become trapped on underlying JVs (so-called JV
‘cores’ residing in the spaces between CuO2 planes and with
‘decoration’). Distortions of the JV lattice, induced by varying
circulating currents derived partly from weak Josephson cou-
H , enabled the indirect manipulation of PVs trapped on them,
pling between them. This anisotropic current distribution leads
allowing one to conceive of vortex pumps, diodes and lenses
to strongly anisotropic JV–JV interactions and the JV lattice is
based on this principle [5, 7, 8].
a rhombic one, with the unit cell greatly stretched out in the
In this paper we demonstrate the manipulation of PVs
a–b plane.
trapped on JVs by rotating the JV lattice under independently
In weakly anisotropic layered superconductors under
controlled H
arbitrarily orientated magnetic fields, there are uniformly tilted
x and Hy magnetic fields.
vortices, composed of a staircase of pancake vortices linked
by segments of Josephson vortices. However, in extremely
2. Experimental details
anisotropic HTS, such as Bi2Sr2CaCu2O8+δ (BSCCO), the
tilted vortices are unstable with respect to the formation of
The SHPM used is a modified commercial low temperature
independent, perpendicular hexagonal PV and rhombic JV
STM in which the usual tunnelling tip has been replaced by a
lattices [2]. Furthermore, small PV displacements driven by
microfabricated GaAs/AlGaAs heterostructure chip. Electron
the underlying JV supercurrents lead to an attractive interaction
beam lithography and wet chemical etching were used to define
between these two ‘crossing’ lattices [3, 4].
Since the
a 0.6 μm Hall probe in the two-dimensional electron gas
0953-2048/08/015017+03$30.00
1
© 2008 IOP Publishing Ltd
Printed in the UK
Supercond. Sci. Technol. 21 (2008) 015017
A Crisan et al
approximately 5 μm from the corner of a deep mesa etch,
which was coated with a thin Au layer to act as an integrated
θ=0°
STM tip. The sample is first approached towards the sensor
until tunnelling is established and then retracted about 100–
200 nm allowing rapid scanning. The Hall probe makes an
H||=Hx
angle of about 1◦ with the sample plane so that the STM tip is
always the closest point to the surface, and the Hall sensor was
typically ∼500–700 nm above the sample during imaging. The
temperature-dependent scan field, ∼28 μm × 28 μm at 80 K
and ∼29 μm×29 μm at 83 K, is divided into 128×128 pixels.
The local magnetic induction at a pixel Bi, j (i, j = 1, . . . , 128)
is an average of 13 consecutive measurements. Each image
presented is an average of 25 scans, resulting in a map of the
local magnetic induction, Bi j, an average value of induction
over the entire scan area, and a greyscale, (Bmax − Bmin).
i, j
i, j
A more detailed description of the instrument and scanning
technique is given elsewhere [9]. In the studies described here
we were able to independently apply a fixed out-of-plane field,
Hz, as well as a ‘rotating’ in-plane field, H , produced by two
pairs of orthogonal Helmholtz coils outside the cryostat, each
pair generating the independent components Hx and Hy of the
in-plane field. The sample studied here was a good quality as-
Figure 1. SHPM scans at T = 80 K, H = 27.5 Oe, with the JV
lattice rotated by (left to right, top to bottom, anticlockwise rotation):
grown BSCCO (500×500×30 μm3, Tc = 90 K) single crystal
0◦, 15◦, 30◦, 45◦, 60◦, 75◦, 105◦, 120◦, 135◦, 150◦, 165◦, and 180◦.
grown by the floating zone method [10].
(Scan size ∼ 28 μm × 28 μm.)
3. Results and discussion
where γ is the anisotropy parameter and
After realizing the conditions for one dimensional (1D) PV
0 the flux quantum.
On the basis of this, the measurement of the distance between
chains (H
Hz), the rotation of the JV lattice was
achieved by gradually increasing/decreasing the current in the
1D chains at various in-plane fields H enables a fairly precise
two independent Helmholtz coils in such a way that H
= estimation of γ assuming that the JV lattice is unperturbed by
decoration, and the spacing d = ay. SHPM images of 1D PV
H 2 + H 2 = const. Starting from the initial state of 1D
x
y
chains at T = 83 K and H = 19.25, 30.25, and 52.3 Oe are
chains, SHPM images were recorded at discrete rotation angles
shown in figures 2((a)–(c)), while figure 2(d) shows a typical
θ = arctan(Hy/Hx) in steps of 15◦ at T = 80 K. The SHPM linescan used for determining the distance d between 1D PV
images of figure 1 show that 1D chains follow the rotation of
chains.
the JV lattice, with in-plane field angles, left to right and top
Figure 3 illustrates the dependence of 1/d2 versus H
to bottom, of 0◦, 15◦, 30◦, 45◦, 60◦, 75◦, 105◦, 120◦, 135◦,
obtained after constructing many such linescans through
150◦, 165◦, and 180◦. PV stacks are represented by dark dots
several SHPM images.
(negative Hz). Due to the Earth’s magnetic field, and small
It can be seen that the resulting anisotropy parameter,
parasitic Hz components from the in-plane Helmholtz coils,
γ = 550 ± 25 is well within the commonly accepted range
the exact values of Hz are not known. Moreover, changes in
for as-grown BSCCO single crystals with a similar Tc.
the density of the chains at different angles reveal that Hz was
Formation of the 1D vortex chains and their manipulation
not constant during the rotation of the JV lattice. However,
depend on the interplay between the crossing and pinning
even if the linear density of PVs trapped on JVs is not constant,
forces. The relative strengths of the crossing and pinning forces
PVs clearly follow the rotation of the JV lattice. It can also
can be estimated from known expressions. The attractive force
be seen that, at the highest PV densities (highest perpendicular
per unit length along the c-axis, fx , between a PV stack and a
field), e.g. at 30◦ and 45◦, 1D chains start to meander due to the
JV stack is given by [12]
competition between the attractive crossing lattice interaction
and the PV–PV repulsion. Nevertheless the manipulation of
PVs upon rotating the JV lattice is still evident. The bright
fx =
1.4 20
,
(2)
4π2a
dot present in the bottom right-hand side on each image is a
z γ 3s2 ln(λab/sβ f )
‘topographic’ artefact due to a small particle on the sample.
where s is the interlayer spacing, λab is the in-plane London
Within anisotropic London theory the expected rhombic
penetration depth and β f ∼ 1. In our experiments, the lowest
JV lattice produced by an in-plane magnetic induction, Bx ,
in-plane field that led to 1D chain formation was 16.5 Oe, for
in the interacting crossing lattices regime has a c-axis vortex
which, following equation (1), we find az = 5.65 × 10−6 cm.
separation, az, and a lateral stack spacing, ay, given by [11]
Inserting this value and the resulted anisotropy factor into
√
√
equation (2), fx is found to be about 1.5 × 10−5 dyn cm−1.
az =
2 0/( 3γ Bx),
ay =
3γ 0/(2Bx), (1)
As a comparison the averaged pinning force per unit length
2
Supercond. Sci. Technol. 21 (2008) 015017
A Crisan et al
6.0x10-3
γ= 550±25
)
-2
4.0x10-3
(a)
(b)
(c)
μ
(m
2
1/d 2.0x10-3
0.0
(d)
-0.2
0.0
0
10
20
30
40
50
60
H (Oe)
-0.4
)
//
(G ij
Figure 3. Dependence of the PV 1D chain separation d = a
B
y on the
-0.6
in-plane field H . The straight line is the linear fit to equation (1).
-0.8
d
of 550 ± 25 lies well within the commonly accepted range for
as-grown single crystals of this material.
-1.00
5
10
15
20
25
distance (μm)
Acknowledgments
Figure 2. ((a)–(c)) SHPM scans at T = 83 K and H = 19.25,
30.25, and 52.3 Oe, respectively (scan size ∼ 29 μm × 29 μm.
This work was supported in the UK by Engineering and Phys-
Arrows indicate the directions of the in-plane field, while dotted lines
ical Sciences Research Council grant number GR/R46489/01,
indicate the directions on the linescans used for estimation of the
by Marie Curie Excellence Grant ‘NanoTechPinningHTS’, by
anisotropy factor); (d) linescan across the indicated direction
the Romanian Ministry of Education and Research, and by the
from (b).
European Science Foundation VORTEX and NES networks.
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