A high-field cryomagnet optimised for SANS measurements on superconductors

Summary: We have used this JREI grant for the purchase and subsequent use of a high-field cryomagnet, which was constructed to our specifications by Oxford Instruments, so that it would be uniquely suitable for small-angle neutron scattering, based at the SINQ neutron source at the Paul Scherrer Institut, Switzerland. The project was hugely delayed by the extremely late delivery of the cryomagnet by the manufacturers, and even after delivery it required modification because of design flaws by them. However, we now have a system that has produced high-profile results on flux line lattice phase transitions in high- and low-T_c superconductors. Its presence at PSI has ‘earned’ beamtime worth far more than the cost of the equipment. We have a long-term beam allocation, every expectation of further important results in the near future, and the possibility of uses as far afield as biology.

Introduction and Specification: Superconducting magnets are widely used in condensed matter physics experiments that require the application of high magnetic fields. However, there are special requirements when designing a superconducting magnet for use in small-angle neutron scattering (SANS). These requirements are:

(i) High homogeneity of field, so that when used for investigating the flux line lattice (FLL) in a superconductor, the flux lines are as parallel as possible and hence represent a coherent diffracting object.

(ii) A horizontal field with neutron beam access both parallel to the field (range of angles: 30° with a 1 cm sample) and perpendicular to the field (range of angles: 15° with a 1 cm sample).

(iii) A variable-temperature sample space with rapid temperature change between 300 K and 1.5 K; also with the possibility of changing samples rapidly (both of these to avoid waste of expensive neutron beamtime).

(iv) The possibility of sample rotation about a vertical axis to alter the orientation of magnetic field relative to the crystal axes of the sample.

(v) The above requirements indicate a Helmholtz pair giving a horizontal magnetic field, with vertical access between the two coils. Normally, in such geometry, superconducting magnet manufacturers place the coils at larger that the optimal Helmholtz spacing, in order to allow sufficient space for vertical access. However, by specifying very tight clearances, we were able to obtain true Helmholtz configuration and high homogeneity.

(vi) A high value of magnetic field, in order to allow the investigation of previously unexplored phenomena by the SANS technique. 11T was specified (a larger field could be obtained with a solenoid instead of a split pair, but many of the other specifications could not be achieved)

(vii) The ability to tilt and rotate the whole cryomagnet and sample by up to 10°, while at high fields, to allow various FLL diffracting planes to be brought to the Bragg diffracting angles.

(viii) Very little parasitic scattering at small angles from the cryostat.

These specifications were discussed with manufacturers before making the JREI proposal. The only acceptable quote came from Oxford Instruments.

The system is based at SINQ; we have a written agreement with them about its availability to the proposers and also, after discussion with us, other users. The project was made possible with financial contributions from the Universities of Birmingham, Warwick and Zurich, and the Paul Scherrer Institut, in addition to the JIF funds from the UK EPSRC. There were important practical contributions from Joachim Kohlbrecher, Ton Konter and Joel Mesot, all of PSI.

System Commissioning: Due to our preliminary discussions with the manufacturers, we were able to order the magnet from them within a month of the beginning of the grant, even though it was a “special”. However, partly due to internal reorganisation at Oxford Instruments and also difficulties in manufacturing the Nb₃Sn coils, the system was delivered at PSI well over a year after the scheduled delivery date and more than two years after ordering. A view of the magnet after delivery (tilted on its goniometer while at 11T) and before mounting on the beamline is shown in Fig. 1.

After the system delivery, several changes had to be implemented on the goniometer and rotation stages provided on the SANS instrument. The position sensors on this equipment were affected by large magnetic fields, and had to be replaced with optical ones. Also the motors to drive these movements and various solenoid valves associated with the vacuum system of the neutron collimation had to be relocated to avoid interference from the stray field of the magnet.

We also needed to purchase a new temperature controller for the Variable Temperature Insert (VTI), since PSI had decided to standardise on Lakeshore controllers, which we welcomed, since they are far superior to the ITC system supplied by Oxford. Fortunately, money was available to do this from the grant, since we had discovered that it was possible to avoid paying UK VAT by delivering the cryomagnet directly from Oxford to Switzerland. This saving also allowed the construction of an improved sample stick described below and the purchase of sapphire windows for the neutron beam, after tests showed that they are superior to the fused quartz windows originally specified by Oxford.

After delivery of the system, we discovered that there was a serious problem with the variable temperature insert of the cryomagnet itself. Oxford had made the ‘tail’ of the VTI (which projects into the centre of the magnet) from brass (changing to pure aluminium at the neutron beam position), although we had specified copper and aluminium. This caused poor thermal contact to the sample, which resulted in very slow thermal response at high temperatures (We had foreseen this, which is why we had specified copper). Also, the base temperature reached by the sample (on neutron scattering evidence) was only 5.5 K, while the sample thermometer which was in the VTI but outside the magnet read 1.5 K. After we had confirmed this by offline temperature measurement, Oxford agreed to replace the tail with a copper one. When delivered, this had the wrong dimensions and had to be re-machined at PSI and was installed by us. The offline tests mentioned earlier also confirmed that the sample thermometer supplied by Oxford was mis-calibrated, and they supplied us with a new one, which we installed.

The sample holder, as constructed by Oxford Instruments, did not allow for accurate sample rotation relative to the field, which is required in most SANS experiments. Phosphor-bronze springs between sample holder and VTI were intended to achieve good thermal contact. However, phosphor bronze is not a good thermal conductor (so it did not achieve what it was intended to do) and the springs pressing against the VTI made sample rotation almost impossible. We designed and constructed an entirely new sample holder, with the end-piece made of a copper cylinder, accurately machined to fit the VTI. The new sample rod allows for in-situ rotation, to an accuracy of a tiny fraction of a degree, and has been connected to a computer-controlled motor so that it can be driven by the instrument data-acquisition workstation. Further, the new sample holder also incorporates a laser, which can be used to align the sample with very high accuracy. The new sample holder design also gives much improved thermal contact between sample and VTI, so that thermal lag between sample stick and VTI is almost completely removed and the expected base temperature can be achieved. Furthermore, the accurate computer-controlled sample rotation may allow the use of the cryomagnet in large-angle diffraction or triple-axis neutron experiments if the scattering angle is in the range of angles around 90° allowed by the neutron access windows.

After several unsuccessful attempts to reach the design field of 11 T with the bottom of the helium bath cooled to 2.2 K by a “lambda-plate refrigerator”, we discovered a leak on the pumping system of the lambda plate - as supplied by Oxford Instruments. Having solved all these problems, in the last six months we now have a flexible, high performance system of general utility for measurements in high fields on anything from superconductors at 1.5 K to biological systems at room temperature.

Experiments: Our cryomagnet has already been successfully used in a number of experiments on high temperature superconductors. One PRL has already resulted and other publications will follow shortly.

(a) Our SANS measurements on the vortex lattice in YBa₂Cu₃O₇ have revealed a change in the co-ordination of the vortex lattice from triangular to square, as the applied magnetic field is increased to 11 T. This is the first microscopic investigation of the vortex lattice in high T_c superconductors at high fields (Brown et al., 2003 and appended copy of report to PSI).

(b) In our PRL publication (Gilardi et al. (2002)) our cryomagnet was used to perform the first successful SANS measurements from the vortex lattice in the high T_c superconductor La_2-xSr_xCuO_4+d, which also displayed a transition from triangular to square co-ordination, but at an applied field of just 0.6 T.

(c) We have performed SANS measurements on the vortex lattice in YNi₂B₂C and TmNi₂B₂C, in order to understand the contribution and competition between the effects of nonlocality (Fermi surface topology) and order parameter gap symmetry (Levett et al., 2003, and appended PSI report).

Future Prospects: We already have offers from sample growers to provide untwinned YBCO crystals to allow a clearer demonstration of the role of crystal anisotropy in the behaviour of this material in high fields. The dependence of FLL phase transitions on doping level is also of great interest. We have an offer of electron-doped superconducting crystals (NCCO) of sufficient purity and size to perform the first FLL investigations of these materials. This will provide an exciting opportunity to investigate the role of d-wave pairing in this class of superconductors. We still have to follow up some investigations proposed in our original proposal, for which there was insufficient time due to the delays in magnet delivery. This includes the observation of the influence of pinning on FLL structures at the high-field glass transition in YBCO and the investigation of high-field low-T_c superconductors such as Chevrel phases and Nb₃Si. We have other plans to look at previously unexplored flux lattice phase transitions in Nb, the structures produced by flux motion in low T_c alloys and the investigation of impurity pinning of flux lines by a new technique that we are developing using polarised neutrons. We envisage using the system also for magneto-structural investigation of nanostructured magnetic materials of interest to the recording industry. We have a request from a group to use the high field to align biological samples for SANS measurements at room temperature, and we are putting in place mechanisms to prevent damage to this unique equipment by unfamiliar users. It is clear from this list that having now commissioned the cryomagnet, it has a productive future.

Gilardi, R. et al., Direct evidence for an intrinsic square vortex lattice in the overdoped high-T_c superconductor La_1.83Sr_0.17CuO_4+d, Phys. Rev. Lett. 88 (2002), 217003.

Brown, S.P. et al., Observation of a triangular to square flux lattice phase transition in YBa₂Cu₃O₇ (2003, submitted to Phys. Rev. Lett.).

Levett S. et al. Flux line lattice morphology in borocarbide superconductors, (2003, in preparation for Phys. Rev. B)

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PSI Report: Observation of a Triangular to Square Flux Lattice Phase Transition in YBa₂Cu₃O₇

S.P. Brown, E.C. Jones, E.M. Forgan, D. Charalambous, School of Physics & Astronomy, University of Birmingham Birmingham B15 2TT, U K; D.McK. Paul, Department of Physics, University of Warwick, Coventry CV4 7AL, U K; A. Erb, Walther-Meissner-Institut, D-85748 Garching, Germany; J. Kohlbrecher, T. Konter, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland; H. Keller, Physik Institut der Universitat Zurich, CH-8057 Zurich, Switzerland.

Abstract: We report on small-angle neutron scattering measurements from the flux line lattice in a low twin density overdoped crystal of YBa₂Cu₃O₇ as a function of temperature and field. With the magnetic field applied perpendicular to the CuO₂ planes, the flux lattice structure changes smoothly from a distorted triangular co-ordination to almost perfect square, for field values exceeding 10 T.

The orientation of the square flux lattice relative to the crystal lattice is as expected from recent theoretical calculations assuming d (x² - y²) pairing but is at 45° from that observed in La_1.83Sr_0.17CuO_4+d. At higher temperatures, the triangular to square transition moves to higher fields, which is also expected from recent d-wave theories, but is in disagreement with a phase diagram suggested by others on the basis of macroscopic magnetisation measurements.

Introduction: Small-angle neutron scattering (SANS) is now a well-established microscopic experimental technique for the study of the vortex lattice in superconductors (e.g. [1]). Unlike Bitter decoration or STM, SANS probes the bulk of the sample and can be used to obtain information on the symmetry of the vortex lattice as well as its orientation relative to the underlying crystal lattice. Further, one can extract values for the magnetic penetration depth and coherence length under various experimental conditions from the absolute values of intensity and variation with field and temperature [2]. SANS data may even be used to reconstruct the real-space magnetic field distribution [3]. Using our recently acquired high horizontal-field cryomagnet, we have performed SANS measurements from the flux lattice in YBa₂Cu₃O₇. We have observed a phase transition from a triangular to a square flux lattice as the applied magnetic field is increased [4]. A similar transition was also observed in La_1.83Sr_0.17CuO_4+d [5].

High field measurements on YBa2Cu3O7: Our measurements were carried out on an extremely pure, low twin-density crystal of slightly overdoped YBa2Cu3O7. The sample was mounted with its c-axis parallel to the magnetic field and incoming neutron beam direction. The sample and magnet could be rotated or tilted together to put the flux lines at suitable angles to the incoming beam. Hence, the flux line planes could be rocked into the Bragg condition, allowing for the determination of the structure of the vortex lattice. Fig. 1(a) shows the diffraction pattern obtained from the flux line lattice at 5.5 T. This picture corresponds to a sum of counts on the SANS multidetector obtained from rocks about horizontal and vertical axes at 4 K, after subtracting the corresponding normal state data. The diffraction pattern has a characteristic four-fold symmetry, which arises from pinning of flux lattice planes to the average four-fold symmetry of the twinned orthorhombic structure. A {110} direction is vertical in all figures, so that the a and b axes of the orthorhombic domains are at 45° to the vertical. Careful study of the data reveals that the flux line lattices present have triangular co-ordination and the pattern in Fig. 1(a) in fact corresponds to four orientations of triangular flux-line lattices present in different domains in the sample, as illustrated in Fig. 1(b). The triangular flux line lattices are distorted by the ab anisotropy of YBCO. This interpretation is in agreement with data obtained at lower fields in a twin-free sample [6]. For an applied field of 10 T, the diffraction pattern shown in Fig. 1(c) was obtained. This picture corresponds to a single square flux lattice. The weak diffraction in the corners of Fig. 1(a) slowly transforms from ‘hexagonal’ to second-order diffraction peaks of the square lattice as the field is increased. This is reminiscent of triangular-to-square transitions in the borocarbide superconductors (e.g. [7]), although it is believed that there is a different mechanism for the transition observed in YBCO - the d (x2 - y2) nature of the order parameter.

In order to investigate the change in the vortex lattice structure with field, we rotated the crystal so that the field was 5° from the c-axis. This rotation effectively breaks the degeneracy between those flux line lattice structures giving strong vertical diffraction spots and those giving strong horizontal spots. The flux line lattice structures giving horizontal spots were suppressed. Instead, the pairs of spots near the horizontal axis could be clearly observed without being overlaid by the spots on the axis. This, in turn, allowed us to measure an ‘order parameter’ for the distortion of the flux-line lattice which is the angle between the pairs of spots, as illustrated in fig. 2(a). Fig. 2(b) shows the variation of the ‘distortion order parameter’ versus applied field. It is clear that the low field structure progressively changes with field, although in our available field range the flux-line lattice never exactly reaches a perfectly square symmetry. This is expected from the orthorhombic structure of YBCO, which should distort the square flux line lattice to be slightly rectangular. This is illustrated schematically in fig. 3, where the ellipses represent the ab anisotropy of the two orthorhombic domains within our crystal.

Temperature effects: Recent investigations of the flux lattice structure as a function of temperature at fixed field show little change at low fields. However, at high fields, the square flux lattice structure, seen at low temperatures, changes without hysteresis towards a triangular co-ordination as T_c is approached. Finally the intensity disappears as the flux lattice melts. Near T_c, the anisotropy of the gap in a d-wave superconductor becomes smaller than kT, so one would expect the behaviour to revert to that of an s-wave superconductor, as indeed we observe. These results show that a phase diagram, suggested on the basis of magnetisation results [8], is not accurate. It is also of interest to note that the changes in flux lattice structure occur at temperatures below the macroscopic irreversibility line of the sample. This means that the FLL can change its local structure, while still being sufficiently strongly pinned not to move through the bulk of the sample.

Conclusions: YBCO undergoes a transition from hexagonal to square co-ordination at much higher fields than in LSCO [5]. The orientation of the flux line lattice in YBCO is as predicted by d-wave theory [9], i.e. the nearest-neighbour direction is at 45° to the CuO₂ bonds. The fraction of H_c2 at which the transition occurs is approximately as expected from d-wave theory, and the tendency to revert to a triangular structure close to T_c is also a sign that this is an intrinsic d-wave effect. The anomalous orientation in LSCO may be due to band structure effects [10]. There is scope for much further study of the interplay of crystal anisotropy and gap symmetry and influence of doping on flux line lattice morphology in high temperature superconductors.

References

[1] E.M. Forgan, Vortices in superconductors, J. Phys.: Cond. Mat. 11, 7685-94, (1999).

[2] T.M. Riseman et al., Observation of a square flux-line lattice in the unconventional superconductor Sr₂RuO₄, Nature 396, 242-5 (1998).

[3] P.G. Kealey et al., Reconstruction from small-angle neutron scattering measurements of the real space magnetic field distribution in the mixed state of Sr₂RuO₄, Phys. Rev. Lett. 84, 6094-7 (2000).

[4] S.P. Brown et al., Observation of a triangular to square flux lattice phase transition in YBa₂Cu₃O₇, submitted to Phys. Rev. Lett. (2003).

[5] R. Gilardi et al., Direct evidence for an intrinsic square vortex lattice in the overdoped high-T_c superconductor La_1.83Sr_0.17CuO_4+d, Phys. Rev. Lett. 88, 217003 (2002).

[6] S.T. Johnson et al., Flux-line lattice structures in untwinned YBa₂Cu₃O_7-d, Phys. Rev. Lett. 82 2792-5 (1999).

[7] U. Yaron et al., Microscopic coexistence of magnetism and superconductivity in ErNi₂B₂C, Nature 382, 236-8 (1996).

[8] B. Rosenstein and A. Knigavko, Anisotropic peak effect due to structural phase transition in the vortex lattice, Phys. Rev. Lett. 83, 844-7 (1999).

[9] M. Ichioka et al., Field dependence of the vortex structure in d-wave and s-wave superconductors, Phys. Rev. B 59, 8902-16 (1999).

[10] N. Nakai et al., Re-entrant vortex lattice transformation in fourfold symmetric superconductors, Phys. Rev. Lett. 89, 237004 (2002).

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PSI Report: Flux line lattice morphology in borocarbide superconductors

S. Levett, D.McK. Paul, Department of Physics, University of Warwick, CV4 7AL, UK

Summary: We have studied the FLL in the borocarbide superconductors YNi₂B₂C and TmNi₂B₂C on the SANS instrument. In YNi₂B₂C, the interest is in understanding the contributions from, and competition between, the effects of nonlocality and superconducting order parameter symmetry. The nonlocal effects may be related to the Fermi surface topology (V.G. Kogan et al., Phys. Rev. B 55, R8693, (1997)), and the extra effects of the angular variation of the superconducting gap have been recently discussed by Nakai et al. (Phys. Rev. Lett. 89, 237004 (2002)). The latter authors suggest that the competing anisotropies each promote the formation of a square FLL but mutually rotated by 45°. They predict a magnetic phase diagram where first of all at low fields there are two domains of a distorted triangular FLL. Above a field H₂, a square FLL is formed with orientation controlled by Fermi surface anisotropy combined with nonlocal interactions. They predict that at a higher field the gap anisotropy should give a further transition into a second square FLL phase rotated by 45°.

With the SANS instrument at PSI configured into a high resolution mode, we were able to image the FLL in fields up to 3.75 T at 1.8 K with the field parallel to the tetragonal c-axis. Above this field, the intensity of the FLL diffraction signal was too low to obtain useful information in reasonable counting times. However, For all accessible fields, only one square FLL orientation was observed. This was the orientation predicted from the Fermi surface anisotropy alone, and not the higher-field orientation predicted by Nakai et al.. A diffraction pattern measured at 1.8 K with 3.75 T applied parallel to c is shown in Fig. 1. The cryostat was tilted towards the bottom RH corner of the picture, so that two {1,0} FLL reflections and a second order {1,1} FLL reflection simultaneously satisfied the Bragg condition. A crystal {110} direction is vertical, indicating that the square FLL nearest neighbour directions are parallel to the crystal {110} directions. When combined with our earlier low-field data collected at ILL it is suggestive that this square FLL phase is the only one present above H₂. An H-T phase diagram for this material is presented in Fig. 2. Clearly, data collected at higher temperatures, closer to H_c2(T), in the high-field regime would enable most of the H-T phase diagram to be mapped out. This would require significantly more beam time, given that the signal was very weak at 1.8 K. Using our cryomagnet, we collaborated with Eskildsen et al. in measuring the FLL in a LuNi₂B₂C crystal in September 2002, and we observed very similar results. The data we collected from PSI will be included in a paper currently being prepared for submission to Phys. Rev. B. (Levett et al., 2003)

In the case of TmNi₂B₂C, low-field measurements at PSI revealed that the FLL does not become square at any measurable field or temperature. An example of the resulting multi-domain FLL diffraction pattern is shown in Fig. 3, with 0.5 T applied parallel to c. The data include the FLL diffracted intensity as well as streaks arising from background from the crystal. This confirms previous reports by Eskildsen et al. (Nature 393, 242 (1998)). Our high-field measurements concentrated on FLL morphology as the external field was rotated away from the crystal c-axis. The data revealed that the direction of the flux lines changes with respect to the applied field direction. This was demonstrated by a shift in the centre of the rocking curve back towards the c-axis. This effect is thought to arise from a combination of crystal geometry and realignment of the flux lines towards the magnetic anisotropy axis.

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For completeness we also include here data from our already-published paper on the square FLL in La1.83Sr0.17CuO4+d by Gilardi et al. (Phys. Rev. Lett. 88, 217003 (2002)). Tilting of the field from the c-axis was used at low fields to produce a single-domain triangular FLL from a polycrystalline pattern, and at higher field a larger tilt angle was used to demonstrate the distortion of the square FLL by ac crystal anisotropy.