Abstract
The low-energy muon facility at PSI provides nearly fully polarized positive muons with tunable energies in the keV range to carry out muon spin rotation (LE-\(\upmu \)SR) experiments with nanometer depth resolution on thin films, heterostructures, and near-surface regions. The low-energy muon beam is focused and transported to the sample by electrostatic lenses. In order to achieve a minimum beam spot size at the sample position and to enable the steering of the beam in the horizontal and vertical direction, a special electrostatic device has been implemented close to the sample position. It consists of a cylinder at ground potential followed by four conically shaped electrodes, which can be operated at different electric potential. In LE-\(\upmu \)SR experiments, an electric field at the sample along the beam direction can be applied to accelerate/decelerate muons to different energies (0.5–30 keV). Additionally, a horizontal or vertical magnetic field can be superimposed for transverse or longitudinal field \(\upmu \)SR experiments. The focusing properties of the conical lens in the presence of these additional electric and magnetic fields have been investigated and optimized by Geant4 simulations. Some experimental tests were also performed and show that the simulation well describes the experimental setup.
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References
A. Yaouanc, P.D. de Réotier, Muon Spin Rotation, Relaxation, and Resonance: Applications to Condensed Matter (Oxford University Press, Oxford, 2011)
E. Morenzoni, Physics and applications of low energy muons, Muon Science: Muons in Physics, Chemistry and Materials (Bristol and Philadelphia, 1999), vol. 51, eds. by S.L. Lee, S.H. Kilcoyne, R. Cywinski, pp. 343–404 (1998)
E. Morenzoni, H. Glückler, T. Prokscha et al., Low-energy \(\mu \)SR at PSI: present and future. Phys. B: Condens. Matter 289, 653–657 (2000). doi:10.1016/S0921-4526(00)00303-3
D. Harshman Jr., A. Mills, J. Beveridge et al., Generation of slow positive muons from solid rare-gas moderators. Phys. Rev. B 36, 8850 (1987). doi:10.1103/PhysRevB.36.8850
E. Morenzoni, F. Kottmann, D. Maden et al., Generation of very slow polarized positive muons. Phys. Rev. Lett. 72, 2793 (1994). doi:10.1103/PhysRevLett.72.2793
T. Prokscha, E. Morenzoni, K. Deiters et al., The new \(\mu \)e4 beam at PSI: a hybrid-type large acceptance channel for the generation of a high intensity surface-muon beam. Nucl. Instrum. Methods A 595, 317–331 (2008). doi:10.1016/j.nima.2008.07.081
E. Morenzoni, R. Khasanov, H. Luetkens et al., Low energy muons as probes of thin films and near surface regions. Phys. B: Condens. Matter 326, 196–204 (2003). doi:10.1016/S0921-4526(02)01601-0
E. Morenzoni, T. Prokscha, A. Suter et al., Nano-scale thin film investigations with slow polarized muons. J. Phys.: Condens. Matter 16, S4583 (2004). doi:10.1088/0953-8984/16/40/010
T. Prokscha, K. Chow, E. Stilp et al., Photo-induced persistent inversion of germanium in a 200-nm-deep surface region. Sci. Rep. 3, 2569 (2013). doi:10.1038/srep02569
E. Morenzoni, T. Prokscha, H. Saadaoui, et al., Low-energy muons at PSI: examples of investigations of superconducting properties in near-surface regions and heterostuctures, in Proceedings of the International Symposium on Science Explored by Ultra Slow Muon (USM2013), JPS Conference Proceedings, Vol. 2, id. 010201, p. 10, , p. 0201, 2014. doi:10.7566/JPSCP.2.010201
L. Schulz, L. Nuccio, M. Willis et al., Engineering spin propagation across a hybrid organic/inorganic interface using a polar layer. Nat. Mater. 10, 39–44 (2011). doi:10.1038/nmat2912
A. Suter, E. Morenzoni, T. Prokscha et al., Two-dimensional magnetic and superconducting phases in metal-insulator \(\text{ La }_{2-x}\text{ Sr }_x\text{ CuO }_4\) superlattices measured by muon-spin rotation. Phys. Rev. Lett. 106, 237003 (2011). doi:10.1103/PhysRevLett.106.237003
A. Boris, Y. Matiks, E. Benckiser et al., Dimensionality control of electronic phase transitions in nickel-oxide superlattices. Science 332, 937–940 (2011). doi:10.1126/science.1202647
A. Hofmann, Z. Salman, M. Mannini et al., Depth-dependent spin dynamics in thin films of \(\text{ TbPc }_2\) nanomagnets explored by low-energy implanted muons. ACS Nano. 6, 8390–8396 (2012). doi:10.1021/nn3031673
E. Stilp, A. Suter, T. Prokscha et al., Controlling the near-surface superfluid density in underdoped \(\text{ YBa }_2\text{ Cu }_3\text{ O }_{6+x}\) by photo-illumination. Sci. Rep. 4, 6250 (2014). doi:10.1038/srep06250
H. Saadaoui, Z. Salman, H. Luetkens et al., The phase diagram of electron-doped \(\text{ La }_{2-x}\text{ Ce }_x\text{ CuO }_{4-\delta }\). Nat. Commun. 6, 6041 (2015). doi:10.1038/ncomms7041
F. Al Ma’Mari, T. Moorsom, G. Teobaldi et al., Beating the stoner criterion using molecular interfaces. Nature 524, 69–73 (2015). doi:10.1038/nature14621
L. Anghinolfi, H. Luetkens, J. Perron et al., Thermodynamic phase transitions in a frustrated magnetic metamaterial. Nat. Commun. 6, 8278 (2015). doi:10.1038/ncomms9278
M. Flokstra, N. Satchell, J. Kim et al., Remotely induced magnetism in a normal metal using a superconducting spin-valve. Nat. Phys. 12, 57–61 (2016). doi:10.1038/nphys3486
T. Prokscha, E. Morenzoni, C. David et al., Moderator gratings for the generation of epithermal positive muons. Appl. Surf. Sci. 172, 235–244 (2001). doi:10.1016/S0169-4332(00)00857-6
P. Bakule, E. Morenzoni, Generation and applications of slow polarized muons. Contemp. Phys. 45, 203–225 (2004). doi:10.1080/00107510410001676803
Low energy muons: overview of the experimental setup. http://www.psi.ch/low-energy-muons/experimental-setup
E. Morenzoni, H. Glückler, T. Prokscha et al., Implantation studies of keV positive muons in thin metallic layers. Nucl. Instrum. Methods B 192, 254–266 (2002). doi:10.1016/S0168-583X(01)01166-1
K. Sedlak, R. Scheuermann, T. Shiroka et al., MusrSim and MusrSimAna-simulation tools for \(\mu \)SR instruments. Phys. Proced. 30, 61–64 (2012). doi:10.1016/j.phpro.2012.04.040:
S. Agostinelli, J. Allison, K. Amako et al., Geant4–a simulation toolkit. Nucl. Instrum. Methods A 506, 250–303 (2003). doi:10.1016/S0168-9002(03)01368-8
J. Allison, K. Amako, J. Apostolakis et al., Geant4 developments and applications. Nucl. Sci. 53, 270–278 (2006). doi:10.1109/TNS.2006.869826
Z. Salman, T. Prokscha, P. Keller et al., Design and simulation of a spin rotator for longitudinal field measurements in the low energy muons spectrometer. Phys. Proced. 30, 55–60 (2012). doi:10.1016/j.phpro.2012.04.039
T.K. Paraiso, E. Morenzoni, T. Prokscha et al., Geant4 simulation of low energy \(\mu \)SR experiments at PSI. Phys. B: Condens. Matter 374, 498–501 (2006). doi:10.1016/j.physb.2005.11.140
E. Morenzoni, M. Birke, H. Glückler et al., Generation of very slow polarized muons by moderation. Hyperfine Interact. 106, 229–235 (1997). doi:10.1023/A:1012610528798
K.S. Khaw, A. Antognini, P. Crivelli et al., Geant4 simulation of the PSI LEM beam line: energy loss and muonium formation in thin foils and the impact of unmoderated muons on the \(\mu \)SR spectrometer. J. Instrum. 10, 10025 (2015). doi:10.1088/1748-0221/10/10/P10025
Acknowledgements
Ran Xiao acknowledges a scholarship from the China Scholarship Council (CSC) and financial support from PSI for her stay at PSI.
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Xiao, R., Morenzoni, E., Salman, Z. et al. A segmented conical electric lens for optimization of the beam spot of the low-energy muon facility at PSI: a Geant4 simulation analysis. NUCL SCI TECH 28, 29 (2017). https://doi.org/10.1007/s41365-017-0190-2
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DOI: https://doi.org/10.1007/s41365-017-0190-2