Neutron diffraction from the flux line lattice

Physica C 185-189 (1991) 247-252 North-Holland

NEUTRON DIFFRACTION FROM THE FLUX LINE LATrlCE E. M. FORGAN, DMcK. PAUL*, H. A. MOOK + , S. L. LEE, R. CUBITT, J. S. ABELL, F. GENCER and

P. TIMMINSx Superconductivity Research Group, University of Birmingham, Birmingham BI5 2TT, UK

We review the detection of flux lattice structure by neutron diffraction and describe recent results of this technique in YBazCu3OT.6. We have observed flux lattice structures in fields up to 4T, which is the highest field at which the mixed state has been imaged in any superconductor. There is strong pinning of flux lattice planes to twin planes and no clear signs of melting of the flux lattice in this material. The distortion of the flux lattice structure by the crystal anisotropy has also been observed.

2. NEUTRON DIFFRACTION

1. INTRODUCTION The behaviour of flux lines in type It superconductors

Neutrons are sensitive to magnetic fields because of

is of great importance both for understanding fundamental

their magnetic moment; in a spatially varying magnetic

aspects of superconductivity and for practical applications.

field, each neutron has a Zceman energy, wl':ch is a

surface of the

function of position and this can give rise to diffraction of

The arrangement of flux lines at the

superconductor may be established either by imaging the

the neutron beam.

field lines, by "decoration" with small magnetic particles l,

average value of the magnetic induction B vdthin the

or by detecting the electron states in the flux line cores by

sample determines the spacing of the flux lines, which

tunnelling2. However, these techniques can only show the

varies as " 450Ad(B/Tesla) I/2.

surface, which may not represent the bulk; in addition, the large value of penetration depth in high-Tc

fields, this spacing is much larger than the typical

superconductors limits the first technique to very low

angles are small: 0 " 1°.

fields in these materials, and the second technique has so far only succeeded in a Iow-Tc material. For investigation of the

bulk, we need a penetrating local probe of the

Because of flux quantisafion, the

For easily achievable

wavelength of cold neutrons, " 10A, so that the diffraction The

intensity of the diffracted signal depends on the

mean square or the "field contrast" AB between the flux line cores and the spaces between them.

For a high-~

magnetic field in the mixed state. One such probe is the

superconductor, not too close to upper or lower critical

positive muon: the damping of its precession reveals the

fields, the London equations apply over most of the bulk,

distribution of field va/ues within the material3. However,

and may be solved to predict the magnitude of the field

r,,. infe..rm..afion abeut mh,~,,~,;,,/,,~,-;at;on of the magm..efie

contrast*. Under the above stated conditions, the absolute

field due to the flux lines, neutron diffraction is the ideal

magnitude of AB is

probe.

* Department of Physics, University of Warwick, Coventry CV4 7AL, UK + Oak Ridge National Laboratory, P. O. Box 2008, Oak Ridge TN37831, USA x Institut Laue-Langevin, 38042, Grenoble Cedex, France

independent of field (although the

248

E.M. Forgan et a£ / Neutron diffraction.from the flux line lattice

relative contrast, ABIB, falls as the flux lines overlap more at higher fields).

Ca)

The field contrast gives rise to an "q~""- B

integrated intensity i of first order Bragg reflection, from flux lattice planes of spacing d, which has the following important dependencies: i oc d l h 4L

(1)

(b)

where h L is the London penetration depth. The total intensity, h is measured as an integral over sample rotation angle as the diffracting planes are rocked

..

through the Bragg angle. If the flux lattice is not well-

...<

ordered, the contributions to ! will be spread over a wide range of angles (the "mosaic spread"), and the diffracted intensity at any particular sample angle will be small and hard to detect. In addition, the penetration depth is long in high-Tc superconductors; the stror, g dependence on hL in (1) makes the diffracted signal difficult to detect in the

FIGURE 2 (a) Longitudinal, and (b) transverse field geometries for small-angle neutron diffraction by the flux lattice. 0 is the Bragg angle, exaggerated for clarity.

presence of background scattering from any defects in the samples.

diffractions,6, although the technique in low T c materials

It is for these reasons that the flux lattice has only recently been observed in high T c materials by neutron

has a history which goes back over 25 years7. In figure 1 is represented a typical diffraction pattern from niobium. It arises from a slightly distorted hexagonal lattice, and shows many higher-order diffraction spots.

It should be

noted that the scale is logarithmic and the higher order C~

©

©

spots are much weaker than the first order ones. The penetration depth depends on the density n s and effective mass m* of superconducting carriers via: l

×[

Ponse2 m

*

(2)

® The huge v,'duc of m* for UPt3 makes the recent observation of the flux lattice in this materials particdarly noteworthy. It was probably made possible by the small mosaic spread of the flux lattice. The diffraction geometry used to observe the flux lattice is also important; two possibilities are illustrated in FIGURE 1 Contour plot (logarithmic scale) of a neutron diffraction pattern by the flux lattice in Nb, taken at B=0.1T, T f 2.5K.

figure 2. The former is to be preferred because all the various Bragg planes can be brought into the diffracting condition either by the mosaic spread of the flux lattice, or by small (" 20) tilts of the field, up or down, or out of the

E.M. Forgan et aL / Neutron chffraction from the flux line lattice

2.t,~

page. in the latter geometry, for most orientations of the

state, after cooling through T c in an applied field, minus a

flux lattice, no diffraction at all will be observed.

background acquir~.d above T c.

If the

flux lattice is disordered, or its orientation is unknown, it may be difficult to detect in this geometry 9.

Usually. Ihe flux laai~-~.

was sufficiently perfect that only some of the Bragg planes would give stnmg diffraction for a part/cular sample angle.

(figure 3. EXPERIMENTAL DETAILS

4}.

To give a complete p/cture of ",he flux

structure, independent of scattering geometry, the resultg

The single crystal YBCO sample was " 200mg in

for several different tilts can be added together.

weight and was grown by the halide-flux method t°. After growth, it was subjected to a 200 hr anneal in oxygen at 200 bar at 4250C. It was heavily twinned. The neutron diffraction experiments were performed using the smallangle diffractomctcrs D11 and D I 7 at the Institut Lauel.,angevin. A collimated incident beam of neutrons passed through the sample and the scattered neutrons were registered by a {64, x 64,) cmz multidetcctor set at distances from 3 - 15 m behind the sample.

The

unseattered beam was intercepted by a beam stop. The scattering by the sample in the normal state is shown in figure 3.

The lobes arise from scattering both by twin

planes parallel to { I I 0 } directions and cracks parallel to {I00} directions. The extra signal due to the flux lattice was comparable with or smaller than this .~zattering.

RESULTS: FLUX PINNINC Such a comlmfite pattern is ~ o w n

in figure 5.

Somewhat surprisingly, it has a fourfold, not .~xfold symmetry; the strong spots reprc~nt diffraction by flux lattice planes that are parallel to twin planes, although there is weaker diffraction in nlhcr directions as weD. When the ~ m p l c was rotated .so that the field was at 45 ° from the crystal e-direction, and the flux lattice was regrown, the results of figure 6 were obtained.

The

sample was rotated in such a direction that the ficld. perpendicular to the page, still lies within one set of {i !0} twin planes, which are horizontal. The flux lattice planes parallel to this dinzctinn giw: rise to the two strong diffraction spots, but the. other s[mL,, complete a distorted

Subsequent diagrams show results obtained in the mixed

65, /

\

FIGURE 3 Contour plot (logarithmic scale) of the background scattering by the YBCO sample in the normal state with the neutron beam parallel to e.

FIGURE 4 Contour plot of a flux lattice diffraction pattern for one ~-ticular till of the YBCO sample: towards the bouom right.

E.M. Forgan et al / N e u ~ n d,'ffraction from the flux line lam'ce

250

0 FIGURE 5 Fourfold diffraction pattern at 10K ;n YBCO for B=O.6T applied parallel to g.

FIGURE 6 Distorted hexagonal pattern at 10K for B = 0 . 6 T applied at 45* to e. Detailed measurements of a strong diffraction spot

heragona/ understood:

pattern.

The

distortion

may be easily

it arises from the anisotropy of penetration

depth 3, and the observed axial ratio of this pattern is close to the "~f7/2 expected at this angle for a material of large uniaxial anisotropy t I. It seems clear that the difference in intensities of the

shape and its intensity variation with sample angle can be analysed to give more information about the flux lattice perfection 12. The flux lattice planes have a mosaic spread of < 1°, which is comparable with that of the host crystal. However, the radial width of a spot indicates that the lattice plane spacing is not constant, but has a standard

diffracted spots arises mainly because the twin boundaries

de,dation of order 10%.

control the orientation of some of the flux lattice planes to

the twin plane spacing is not in general commensurate

be parallel to {110} directions.

with the flux lattice spacing.

The other diffracting

This doubtless arises because

planes thread through twin planes at 45* and will give

These observations are the £L,'St confirmation, at high

lower intensities if they are less well-formed and hence

field and in the bulk of the material, of pinning of flux

have a wider mosaic spread (another cause of intensity

lines by twin planes.

differences is the anisotropy of penetration depth).

We

from resistivity la and magnetisation l'* measurements (with

believe that the intensity pattern for B parallel to c (figure

a different field orientation) and seen at low fields in

5) arises from similar causes. In this case, there will be

decoration experiments TM. We have also observed ",hat

different domains of the sample having twin planes

the flux lattice planes remain pinned to the twin planes

running either vertically or horizontally.

In each region,

when the applied field is moved a few degrees from the c-

the flux lattice orientation will be pinned to the local twin

direction. It is likely in this case that the flux lines have a

plane orientation, so that the resultant pattern is a

zig-zag shape tT.

superposition of the effects of two flux lattice orientations.

record that the flux lattice diffraction pattern remained

The weaker scattering between the four strong spots is due

when we reduced the external field of 0.6T to zero at low

to the less well-formed planes in the hexagonal latticcs.

temperatures: this is consistent with " 90% flux trapping

Similar patterns to fig. 5 have been observed in fields up to 4T.

at 0.6T which we have observed by magnetisation

This pinning has been suspected

As ~ final comment on pinning, we

measurements on the same sample.

E.M. Forgan et a L / Neutron diffraction from the flux line lattice

•

i

|

q

•

•

-

i

251

would be of great interest to continue these measurements in detwinned crystals. We are not aware of any successful

t~

observations by diffraction of the flux latace in a bismuthbased

In cq)

high-temperature

superconductor.

experiments are a challenge, both b e c a ~

Such of their

difficulty (the signals are even weaker than from YBCO) 4o0

but also because of the possible reward:

detection, by

microscopic means, of flux lattice melting in a mater;.al o

which is expected to show this effect over a wide range of conditions.

#

Temperature (K)

There is also great intecest in the exotic flux lattice structures predicted for uniaxial superconductors with the

FIGURE 7 Temperature dependence of intensity of a strong diffracted spot from YBCO, with B = 2"1"applied parallel to ¢; line : theory.

field at a large angle to the c-axist.21;

this has not yet

been investigated by diffraction techniques.

Clearly,

much more work remains to be done on flux lattice structures in low- and high-T c and hea D- fermion superconductors.

5. RESULTS: TEMPERATURE DEPENDENCE The temperature-dependence of the diffracted signal

REFERENCES

is of interest because it may give information about the variation of penetration depth and lattice perfection with temperature s.

in YBCO, we see no significant variation

I. See e . g . G . J , l)olan. F. Ho:zbcrg, C. Feud and T. R. Dingcr, Phys. Rev. l.ett. 62 (1989) 2184.

with temperature of the size of the strong diffracted spots, which argues against melting ta of the flux lattice under our experimental conditions.

In figure 7, we show the

2. H. F. Hess, II. II. Robinson, R. C. Dynes, J. M. Valles Jr and J. V. Waszcr'_,!:, Phys. Rev. Left. 6.__2211989) 214.

temperature dependence of intensity observed at B = 2T, which is very similar to that seen by us in another sample at much lower fieldss.

3. See e . g . E . M . Forgan, Nature 329 (1987) 483.

The theoretical curve is derived

from the two fluid model s for the temperature-dependence of hi., modified to take account of the loss of intensity due to thermal vibrations of the flux lattice (the Debye-Wallcr factor). We have used the nonlocal theory of flux lattice vibrations ~9, to make estimates of this effect, which is small except near T c (as soon as the lattice vibrations arc large enough to give a big D-W factor for the first-order reflections, the lattice mclts anyway), it is clear that there is some deviation, of unexplained

origin, from the

4. J. Schelten, 14. Ullmaier, G. Lippman and W. Schmatz in: Proc. of the 13th Int. Conf. on Low Temperature Physics, part III (North Holland, Amsterdam, 1974) p.54. 5. E. M. Forgan, D. McK. Paul, H. A. Mook, P. A. Timmins, H. Keller, S. Sutton and J. S. AbcU, Nature 343 (1990) 735. 6. E. M. Forgan, Physica B 169 (I 991 ) 107.

theoretical expectations; rather stronger deviations have bccn observed 2° in Ba/KBiO 3.

7. i"or a comprehensive list of references, see: E.H. Brandt, Phys. Rcv. BI8 (1978) 6022.

6. CONCLUSIONS AND FUTURE WORK

8. D. Bishop et al., this volume.

We have observed the effects of twin boundary pinning on the flux lattice structures in YBazCu307.,s. It

252

E.M. Forgan et aL / Neutron &'ffractionfrom the flux line lattice

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