Thin films and multilayers are of increasing scientific and technological importance in contemporary condensed matter science, with the reduced dimensionality providing insights into fundamental and emergent physical behavior 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 is a technique that has proven extremely useful to measure the spatial and temporal properties of local magnetic fields within bulk materials.
The muon, as a local sensitive probe with complementary observational time window to other probes or techniques, can also offer new insights into new objects of investigation. 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).
Based on a moderation technique of surface muons in cryocrystals, the LEM group has developed a beam of ~ 100% polarized muons with tunable energy between ~0 and 30 keV. At these energies implantation depths in matter typically extend from the subnanometer region to 200-300 nm. The ultrahigh vacuum apparatus includes a µSR spectrometer and sample environment. This development, allowing all the advantages of µSR to be obtained in thin samples, near surfaces, and as a function of depth below and above surfaces, has set the basis of the LE-µSR method and opened new fields of µSR investigations [1,2].
The LE-µSR technique has been recently used to investigate the microscopic magnetic field distribution in the vortex state of a thin epitaxial film of a high-temperature superconductor. By varying the energy of the muons and using films with a thin normal layer deposited at the surface, the muons could be implanted below, across and above the surface of the superconducting film to monitor the spatial evolution of the magnetic field distribution as the flux lines emerge through the surface [3].
In another experiment the spatial variation on a scale of some nm of the magnetic flux penetration beneath the surface of a high-temperature superconductor in the Meissner state was observed for the first time. The determination of the spatial dependence of the field is a microscopic test of the London equations and has made possible the first absolute model-independent measurement of the magnetic penetration depth (an important quantity directly related to the superconducting carrier density), since no assumption about the functional form of the magnetic field needs to be made in this experiment [4]. This experiment is perhaps the most powerful demonstration of the new capabilities offered by a local, depth-dependent magnetic probe and has been covered by reports in Physical Review Focus and in Physics News Update [5]. The possibility to measure local field distributions on some nm scale demonstrated on a single layer superconductor will be used to investigate more complex structures. For instance, studies of the influence of increasing anisotropy on the vortex state in artificially grown multilayers consisting of superconducting, metallic and insulating materials are planned (in collaboration with the Universities of Geneva, Zürich, Birmingham, and Columbia University). Another example is the search for spontaneous magnetization below the surface of a HTc-superconductor as a consequence of broken time reversal symmetry, where the local probe character of the muons implanted a few nm below the surface can be used to give a direct proof of the magnetic field and to quantify its magnitude (in collaboration with the Universities of Urbana-Illinois and Zürich).
Investigations of magnetization reversal in nanometer size clusters of ferromagnetic materials such as iron are an example of the application of LE-µ+ to measure properties of samples that cannot be made thick enough to stop the normally available surface muons. Assemblies of iron nanoclusters with a very tight size distribution embedded in a silver thin film matrix and only 500 nm thick were used in these studies [6] as a first step toward investigations of the activated magnetic behavior in monodispersed cluster with controlled anisotropy. Measurement of finite size effects in the freezing character of spin glasses (in collaboration with the University of Leiden) [7] and determination of magnetic order in thin magnetic Cr multilayers further demonstrate the potential of LE-µSR [8].
For a correct analysis of the data it is often essential to know accurately the implantation depth and implantation profiles of LE-muons in multilayers and their behavior at interfaces and surfaces. We have developed Monte Carlo codes to simulate the behavior of low energy muons stopped in multilayered materials of variable composition and performed experiments to test their reliability [9]. The development of these codes, along with the ongoing program of implantation depth measurements and diffusion studies in multilayers is an important component in the systematic application and extension of LE-µSR techniques. These measurements have also shed new light onto the understanding of the behavior of particles implanted in matter.
We have closely collaborated with the University of Birmingham group on development and testing of the Maximum Entropy method of analysis into a form capable of extracting the maximum information on field distributions from low-statistics LE-µSR data [10]. Without this, the experiments on superconductors described above would not have been analyzable in detail.
References
The muon, as a local sensitive probe with complementary observational time window to other probes or techniques, can also offer new insights into new objects of investigation. 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).
Based on a moderation technique of surface muons in cryocrystals, the LEM group has developed a beam of ~ 100% polarized muons with tunable energy between ~0 and 30 keV. At these energies implantation depths in matter typically extend from the subnanometer region to 200-300 nm. The ultrahigh vacuum apparatus includes a µSR spectrometer and sample environment. This development, allowing all the advantages of µSR to be obtained in thin samples, near surfaces, and as a function of depth below and above surfaces, has set the basis of the LE-µSR method and opened new fields of µSR investigations [1,2].
The LE-µSR technique has been recently used to investigate the microscopic magnetic field distribution in the vortex state of a thin epitaxial film of a high-temperature superconductor. By varying the energy of the muons and using films with a thin normal layer deposited at the surface, the muons could be implanted below, across and above the surface of the superconducting film to monitor the spatial evolution of the magnetic field distribution as the flux lines emerge through the surface [3].
In another experiment the spatial variation on a scale of some nm of the magnetic flux penetration beneath the surface of a high-temperature superconductor in the Meissner state was observed for the first time. The determination of the spatial dependence of the field is a microscopic test of the London equations and has made possible the first absolute model-independent measurement of the magnetic penetration depth (an important quantity directly related to the superconducting carrier density), since no assumption about the functional form of the magnetic field needs to be made in this experiment [4]. This experiment is perhaps the most powerful demonstration of the new capabilities offered by a local, depth-dependent magnetic probe and has been covered by reports in Physical Review Focus and in Physics News Update [5]. The possibility to measure local field distributions on some nm scale demonstrated on a single layer superconductor will be used to investigate more complex structures. For instance, studies of the influence of increasing anisotropy on the vortex state in artificially grown multilayers consisting of superconducting, metallic and insulating materials are planned (in collaboration with the Universities of Geneva, Zürich, Birmingham, and Columbia University). Another example is the search for spontaneous magnetization below the surface of a HTc-superconductor as a consequence of broken time reversal symmetry, where the local probe character of the muons implanted a few nm below the surface can be used to give a direct proof of the magnetic field and to quantify its magnitude (in collaboration with the Universities of Urbana-Illinois and Zürich).
Investigations of magnetization reversal in nanometer size clusters of ferromagnetic materials such as iron are an example of the application of LE-µ+ to measure properties of samples that cannot be made thick enough to stop the normally available surface muons. Assemblies of iron nanoclusters with a very tight size distribution embedded in a silver thin film matrix and only 500 nm thick were used in these studies [6] as a first step toward investigations of the activated magnetic behavior in monodispersed cluster with controlled anisotropy. Measurement of finite size effects in the freezing character of spin glasses (in collaboration with the University of Leiden) [7] and determination of magnetic order in thin magnetic Cr multilayers further demonstrate the potential of LE-µSR [8].
For a correct analysis of the data it is often essential to know accurately the implantation depth and implantation profiles of LE-muons in multilayers and their behavior at interfaces and surfaces. We have developed Monte Carlo codes to simulate the behavior of low energy muons stopped in multilayered materials of variable composition and performed experiments to test their reliability [9]. The development of these codes, along with the ongoing program of implantation depth measurements and diffusion studies in multilayers is an important component in the systematic application and extension of LE-µSR techniques. These measurements have also shed new light onto the understanding of the behavior of particles implanted in matter.
We have closely collaborated with the University of Birmingham group on development and testing of the Maximum Entropy method of analysis into a form capable of extracting the maximum information on field distributions from low-statistics LE-µSR data [10]. Without this, the experiments on superconductors described above would not have been analyzable in detail.
References
- [1] E. Morenzoni et al., Phys. Rev. Lett. 72 (1994) 2793.
- [2] E. Morenzoni et al., Physica B289-290 (2000) 653.
- [3] C. Niedermayer et al., Phys. Rev. Lett. 83 (1999) 3932.
- [4] T. Jackson et al., Phys. Rev. Lett. 84 (2000) 4958.
- [5] Phys. Rev. Focus 5 Story 22 15 May (2000) and Physics News Update, May 2000
- [6] T.J. Jackson et al., J. Phys.: Cond. Matt. 12 (2000) 1399.
- [7] H. Luetkens et al., Physica B 289-290 (2000) 326.
- [8] G.J. Nieuwenhuys et al., in preparation.
- [9] H. Glückler et al., Physica B 289-290 (2000) 658 and in preparation.
- [10] T.M. Riseman, E.M. Forgan, Physica B 289 (2000) 718.