The Utilisation of Slow Muons for Investigation of Magnetic Properties of Thin Samples and Surfaces

The low energy muon spectrometer at the Paul Scherrer Institut

Objectives

To provide a UK presence at and participation in the use of slow muons for condensed matter science, and to gain experience with this developing technique. To collaborate with others in carrying out slow muon investigations of the properties of magnetic, antiferromagnetic and superconducting layers and multilayers, in order to make use of the unique information provided by slow muons.

Introduction

Thin films and multilayers are of increasing importance in contemporary condensed matter science, with the reduced dimensionality providing insights into fundamental and emergent physical behaviour and novel applications. The development of a full understanding of observed properties requires the use of experimental probes that access the physical quantities of concern on a local scale within the material. Muon spin rotation (mSR) is a technique that is an extremely useful probe of the spatial and temporal properties of local magnetic fields within bulk materials. However, it has previously been unsuitable for studies of thin films and multilayers, because of the long stopping distance of muons in matter and noticeable straggle in the implantation depth (typically, 0.3 mm with a full width half maximum straggle of 0.07 mm). Low energy muons are prepared by slowing down a standard (4 MeV) muon beam using a cryogenic moderator of a solid noble gas or nitrogen. The large excitation energy of such moderators means that muons can exist for a long time at epithermal (~15 eV) energies and escape into the vacuum. They are then accelerated by potentials of tens of keV and deposited in the sample by an electrostatic beam transport system. At these energies implantation depths from 5 to 150 nm are accessible.

The project was a collaboration with the Paul Scherrer Institut (PSI) in Switzerland, where Elvezio Morenzoni’s group has developed a LE- (low energy) mSR beamline. In terms of count rates and instrumentation, the PSI source is by far the most successful in the world. There is a similar project based at ISIS (RAL), but unfortunately this spectrometer is limited by the much lower primary beam flux. Future developments may pull back some of their disadvantage. Our participation in the PSI project thus offers unique opportunities for condensed matter research and high returns for the UK from a relatively modest EPSRC input. Investment to the programme from the groups in Switzerland and Germany, in terms of expertise, equipment and staff, has also been considerable. Substantial support for the project is provided by PSI and also by the German Federal Ministry for Research and Technology, through funding of groups at the Technische Universität Braunschweig and the Universität Konstanz. The Birmingham Group has taken a central role in the project in providing expertise in condensed matter science, expertise that has enabled us to design experiments and apparatus, develop data analysis methods, take part in experiments and interpret the data. We are also acting as a conduit through which other UK groups may suggest samples and experiments to extend their own research. We have played a full part in staffing the beam line during experimental runs on our, and on other samples.

Summary of Principal Achievements

(i) Studies of the flux lattice inside a superconducting film in the mixed state, and the evolution of the flux distribution across a normal-superconducting boundary [1], together with developments of the theory.

(ii) A direct microscopic measurement of the functional form of the penetration of a magnetic field beneath the surface of a superconductor in the Meissner state [2], with general application to measurements of magnetic fields below surfaces.

(iii) A determination of the relaxation time and energy barrier to thermal activation in iron nanoclusters [3], which is also the demonstration of the use of slow muons to measure the properties of samples that cannot be made thick enough for the use of conventional mSR.

(iv) A series of other experiments on the interaction of slow muons with matter and their use in investigating a wide range of condensed matter systems, particularly those with magnetic properties.

(v) The design and provision of additional apparatus for the LE-muon beamline.

(vi) The development of muon implantation calculations and MAXENT analysis of low-statistics data [4].

(vii) The dissemination of our results in the literature [1-16] and at UK and international meetings.

Discussion of Achievements

(i) Apparatus

Figure 1 is a schematic diagram of the essentials of the LE-mSR apparatus at PSI. It should be noted that in operation the whole of the interior is under UHV conditions, many parts are at cryogenic temperatures, and there are applied voltages of 10’s of kV. Individual muons are detected in the presence of stray ions that may be created in these circumstances. The excellent overall operation of this complicated equipment is a tribute to Morenzoni's team. The slow muon spectrometer was originally equipped only with Helmholtz coils to provide a magnetic field perpendicular to the plane of the sample. We realised that fields parallel to the sample plane (and therefore perp-endicular to the incoming muon beam) were important for studies of thin films, partly because of demagnetising factors, partly because magnetic layers often have in-plane anisotropy, but also to enable some particular experiments that we proposed. However a magnetic field oriented perpendicular to the muon beam will cause some sideways deflection of the incoming muons due to the Lorentz force. Beam deflection is not important with fields parallel to the beam axis. An in-plane field therefore has to satisfy conflicting requirements of uniformity of field over the sample area but rapid fall-off of the field along the beam axis in order to minimise the deflection. A permanent magnet assembly, capable of applying magnetic fields up to 20 mT parallel to the plane of the sample was designed and built in Birmingham.

Figure 2 shows the magnet in position on the low energy muon spectrometer. The magnet is easily assembled in situ, to allow zero field cooling of a sample, has a small flux leakage to minimise deflection of the incoming muon beam, and provides a field uniform to within 1 % over a plane of area 13 cm2. The uniformity was achieved with shimmed pole-pieces positioned inside the sample vacuum. The pole pieces have a shallow "U" shape in cross-section. The design aim was to obtain a quartic variation of the value of the field, as a function of distance along the spectrometer axis, in the vicinity of the sample. As a consequence of the Laplace equation, the field profile within the sample plane is then very uniform.

After experience on the beamline, it became clear that rapid sample interchange was vital to provide the flexibility to enable experiments on a variety of condensed matter physics samples to be performed with the low energy muon spectrometer. This was more important than the originally proposed new sample cryostat. Therefore, a sample load-lock system and associated pump, valves and gauges was designed in Birmingham, supplied by Leybold and VAT and shipped to the Paul Scherrer Institut. With this load-lock, the sample turn around time was reduced from of the order of a day to 3 hours.

(ii) Scientific results

mSR studies of high temperature superconductors have made many contributions to understanding the mixed state, and to the determination of parameters including the temperature variation of the magnetic penetration depth l(T) from which the symmetry of the superconducting state may be deduced. We have demonstrated that LE-mSR can be used to study the flux lattice formed by a perpendicular magnetic field  applied to a thin film superconductor [1].

Figure 3

The muons can be implanted within the film, to make a "bulk" measurement of penetration depth, or they can be stopped in a thin normal layer deposited on the surface, to measure the field profile outside the superconductor. The data for the shift of the most probable field seen by the implanted muons are shown in Figure 3; they follow theoretical predictions derived from London theory (calculations by M W Long of the Theory Group in Birmingham), and provide a measure of the London penetration depth. These measurements demonstrate that a short distance within the film, the flux lattice approximates to that deep within the bulk. The spreading of the field at the surface is only important over a depth ~ flux line spacing (or penetration depth, if shorter) divided by 2p. This is an important result, for it shows that the method can be used to measure nearly "bulk" properties of superconductors which may be available as films only 200 nm thick. In this work, the magnetic field was applied perpendicular to the film plane, using the original Helmholtz coils, and the sample was field-cooled in order to obtain a uniform mixed state. The experiment represents an extension of the methods of bulk mSR, from which l(T) is determined indirectly, into the low energy regime. It has recently been published as a PRL [1].

A fundamentally different method providing a direct measure of l(T), is provided by a quite different experiment [2], in which the sample was zero-field cooled and then a magnetic field was applied in the plane of the sample, using the magnet described above. Muons were then implanted at known depths 15-150 nm below the surface, with a resolution of a few nm, by tuning the energy of the incident beam from 3-30 keV. This experiment provides a profile of the penetration of the field into the superconductor in the Meissner state without model dependent analysis; it represents the first measurement of its kind and the first direct experimental demonstration of London’s exponential decay law. In Figure 4, the points show the data and the lines are fits of the London law to the data. Such measurements can be used to measure the field and directional dependencies in l(T), and thus provide evidence of the symmetry of the superconducting order parameter in exotic superconductors. The method is not of course confined to thin films, but can be extended to observe near-surface fields in single crystals, for example. This work is also an excellent illustration of the power of low energy muons for depth-resolved measurements of the value of magnetic field: not only in superconductors, but also near the surface of magnetic structures of reduced dimensionality and in multilayers.

mSR can also be used to determine the temporal variations of magnetic fields inside materials. For example, the orientation of the magnetisation vector of sufficiently small single ferromagnetic domains is unstable against thermal activation. The relaxation time provides a signature of the mechanism of magnetic reversal and insight into the nature of the microscopic processes involved. Assemblies of iron nanoclusters with a very tight size distribution, prepared by C Binns at Leicester University, were used in these studies. The clusters were embedded in a silver thin film matrix only 500 nm thick, with an iron cluster content of only 0.1% by volume to minimise dipolar interactions [3].

The low energy muons were implanted into the silver matrix. At low temperature (up to 20 K, as shown in Figure 5 on the next page) the cluster moments are frozen in orientation and the muon relaxation rate is determined. The low energy muons were implanted into the silver matrix. At low temperatures (up to 20 K, as shown in Figure 5 on the next page), the cluster moments are "frozen" by the static distribution of dipolar fields within the sample. Simulations of the dipolar fields were in good agreement with the measured relaxation rate. At higher temperatures (above 20K – solid data points in Figure 5) thermal activation of the orientation of the cluster moments occurs, a behaviour called superparamagnetism. These fluctuations narrow the dipolar field distribution sensed by the muons. The data shown by the solid data points in Figure 5 evidence an intrinsic cluster relaxation time of 12 ± 4 ns and an energy barrier of 51 ± 9 K. We used our SQUID magnetometer at Birmingham to check that these results were consistent with more conventional laboratory measurements of the magnetisation of the clusters, as shown in Figure 6. The magnetisation curves at 10 K (full diamonds) and 25 K (open triangles) are non-hysteretic and superpose when plotted against (field/temperature).


At 5 K (open diamonds in Figure 6) the moments are beginning to freeze. (On the much shorter effective time scales of mSR, the freezing occurs at approximately 20 K, as indicated by the change from full to open symbols in Figure 5). The measured magnetic moments of the SQUID data are close to the sensitivity limit of the magnetometer. To improve the signal to noise ratio, a new data routine for analysing the raw data scans was devised and a full refurbishment of the magnetometer was undertaken. These improvements are also valuable to other work undertaken by the Condensed Matter Group in Birmingham, including the EPSRC funded research programme on superconductivity. The work with the Leicester group provides a good example of collaborations with other UK groups, where our intention is to enable the use of LE-mSR to provide complementary measurements to that obtained by their own research activities.

In addition to these Birmingham-led experiments, we staffed the beamline and provided support for other studies proposed by our collaborators. These have included investigations of magnetic ordering in thin Cr layers, magnetism in Ni/Ti layers, dimensionality effects in AuFe spin glasses, where confusion exists between previous experimental and theoretical studies, size effects in thin films of colossal magnetoresistance materials and studies of muon implantation depth and muonium formation in Al/SiO2 layers.

(iii) Analysis tools

Interpretation of mSR data requires careful computer modelling and analysis. Progress in this area has been aided considerably by input from T M Riseman, who is supported by the Superconductivity grant in Birmingham. Dr Riseman has further developed the Maximum Entropy method of analysis into a form capable of extracting the maximum information on field distributions from low-statistics LE-mSR data [4]. Without this, the experiments on superconductors described above would not have been analysable in detail. We have also made modifications to the standard MINFIT program available at PSI, to treat low energy muon data more exactly. It is essential to know accurately the implantation depth of LE-muons in materials, and we have collaborated closely with H Glückler at PSI on the development and testing of the TRIM.SP code, provided by W Eckstein (MPI, Garching). The code uses Monte-Carlo techniques, combined with mathematical representations of the various energy-loss mechanisms, to calculate the range and range distributions of ions deposited into materials. The selection of the appropriate potentials to model the atom-atom and ion-atom interactions is particularly important. The original code has also been modified to account for the known spread of kinetic energy of our low energy muons. Measurements of the depth of implantation of low energy muons into layered samples, and the agreement with theoretical expectations of the experimental results on superconducting films described above, have given substantial evidence for the accuracy of the TRIM.SP program. We in Birmingham realised early on that the better known code SRIM96 was unsuitable for muons, predicting an unphysical "pile up" at interfaces and giving longer ranges than are observed. The SRIM96 code had the advantage of being freely available over the WWW and is used elsewhere in similar projects, but makes approximations in calculating the path of the implanted particle which fail for very light projectiles. The calculated profile overestimates the mean and maximum depth and also the width of the implantation profile. The development of the TRIM.SP code, along with the ongoing programme of implantation depth measurements by our collaborators at PSI, is an important component in the systematic application of LE-muon techniques.

Staff

The project has been led by the grant holder, Prof. E M Forgan, in the Condensed Matter Group at the University of Birmingham. Dr W Nuttall worked on the project for the first year, making initial contact with the collaborating groups at PSI, Braunschweig, Konstanz and Leicester, and performing some exploratory measurements on single crystal Gd thin films grown by the LAMBE facility at Oxford University. Dr Nuttall then moved to a post at the IOP. Dr T M Riseman, supported on the Birmingham EPSRC Superconductivity programme, has provided invaluable input to the project by developing the Maximum Entropy method. Dr T J Jackson joined the project in August 1997, having worked previously on thin film growth in the Device Materials Group at the University of Cambridge. His activities have included the development of the TRIM.SP code (see above), the design and analysis of the magnetic cluster samples, the design and construction of the parallel field magnet, the dissemination of results and co-ordination of Birmingham activities with those of the collaborating institutions. In addition he has been working in the Superconductivity Group’s interdisciplinary pulsed laser ablation thin film facility, with the aim of producing very smooth high temperature superconductor thin films on vicinal substrates, for future LE-muon projects. Technical support in Birmingham has been vital, in terms of maintenance and upgrading of the film growth and cryogenic facilities, and construction of the parallel field magnet.

Future Plans

As a result of the work outlined here, a new proposal for further funding has been submitted to EPSRC: "Further Development of Slow Muon Techniques for Magnetic Properties of Thin Samples and Surfaces" reference GR/N13197. An improved moderator cryostat and a new, variable field, parallel magnet are among the equipment developments proposed. An anticipated contribution from PSI is the construction of a new high-intensity beamline dedicated to slow muons (There are also plans in the USA to create a muon and especially a LE-muon facility, attached to the new spallation neutron source). The proposal emphasises our recognition of the need to ensure that the possibilities offered by LE-mSR are extended to work by other UK groups. These include (a) Proximity coupling in superconductor/ferromagnetic multilayers (S Lee, St Andrews); (b) Vortex phase diagrams in superconducting multilayers with controlled anisotropy (Z Barber, Cambridge and M Jones and F Wellhofer, Birmingham Materials Science); (c) Surface magnetic ordering in colossal magnetoresistance materials (N Mathur, Cambridge); (d) Vortex phases and orientation-dependent field penetration in BiSCCO superconducting crystals (G Yang, Birmingham Materials Science); (e) Induced moments in transition metal multilayers (J A C Bland, Cambridge). We believe that the dissemination of our recent results will also result in new LE-muon experiments and collaborations that we have not yet foreseen. A low energy muon users group with international membership has been formed at PSI, with enthusiastic support of the director, as a forum through which international research groups may gain access to the spectrometer. We intend to participate as fully as possible in these programmes, including investigations of superconducting proximity coupling (Sonier, Los Alamos and Brewer, British Columbia) which are in principle very similar to the Meissner state experiments described previously.

Dissemination of Results

Publication in peer reviewed journals, professional magazines and presentation at conferences were the chosen methods of dissemination to the scientific community. These are detailed below. This EPSRC report may be accessed via the Bham Condensed Matter Group website: http://www.cm.ph.bham.ac.uk. A description designed more for the wider public may be found at http://www.cm.ph.bham.ac.uk/emf/slowmu2.htm.

Publications involving the Birmingham Group

[1] Ch Niedermayer et al., Direct observation of a flux line lattice field distribution across an YBa2Cu3O7-d surface by low energy muons, Phys.Rev.Lett. 83, 3932-3935 (1999).
[2] T J Jackson et al., "Depth-resolved profile of the magnetic field beneath the surface of a superconductor with a few nm resolution" submitted to Phys.Rev.Lett. (2000).
[3] T J Jackson et al., Superparamagnetic relaxation in iron nanoclusters measured by low energy muon spin rotation, Journal of Physics: Condensed Matter 12 1399-1411 (2000).
[4] T M Riseman and E M Forgan, Comparison of Maximum Entropy and FFT's of mSR Data, to be published in Physica B.
[5] T J Jackson, "Peeling the Magnetic Onion" Magnews Spring 1999
[6] M Pleines et al., Temperature dependence of the magnetic penetration depth in an YBa2Cu3O7-d film, to be published in Physica B.
[7] H Glückler et al., Range studies of low energy muons in a thin Al film, to be published in Physica B.
[8] E Morenzoni et al., Low energy mSR at PSI: present and future, to be published in Physica B.
[9] E M Forgan et al., A low energy muon study of thermal activation in single-domain iron particles, to be published in Physica B.
[10] H Luetkens et al., Magnetism of thin chromium films studied with LE-µSR to be published in Physica B.
[11] M Birke et al., LE-mSR measurements on thin Ni films to be published in Physica B.
[12] T M Riseman et al., Measurements of the Penetration Depth of an YBa2Cu3O7-d Thin Film with Low Energy Muons, to be published in Physica B.
[13] T M Riseman, Towards a single mSR data format and common high quality user-facility analysis software, to be published in Physica B.
[14] T Prokscha et al., First µSR studies on thin films with a new beam of low energy positive muons at energies below 20 keV, Hyperfine Interactions 120/121, 569-573 (1999).
[15] T Prokscha et al., µ+SR studies on thin films with low-energy muons at energies between 0 and 30 keV, to be published in Proceedings of XXXIII. Winter School of PNPI (2000).
[16] C.N.W. Darlington, T.J.Jackson, C. Roberts and F. Wellhofer, Accurate determination of the vicinal angle of substrates and characterisation of HTS thin films by X-ray diffraction submitted to J. Appl. Cryst. (1999)

Oral presentations/conference talks

E M Forgan "Information from neutron and muon measurements about the mixed state of High-Tc superconductors", invited talk at CMMP conference, University of Exeter, Xmas 1997.

E M Forgan "First experiments with low energy muons at PSI", invited talk at Workshop on Applications of Low Energy Muons, Paul Scherrer Institut, February 1999

T J Jackson "Direct measurements of the penetration of a magnetic field beneath the surface of a superconducting film" invited talk at Ampere Colloquium, Pisa June 1999

T M Riseman, "Slow muon measurements in superconductors" invited talk at University of British Columbia

T M Riseman "Measurements of the penetration depth of an YBa2Cu3O7-d thin film with low energy muons" invited talkmSR99 Conference, Les Diablerets Sept. 1999

E M Forgan "What can you do with muons and low energy muons?" invited talk at Leeds University