The free electron model and the electronic energy losses of protons at low velocities interacting with polycrystalline tantalum

Abstract

In this letter, we report experimental data and theoretical work on the electronic energy loss and energy loss straggling of protons transmitted through self-supported thin films of tantalum in a polycrystalline tetragonal phase $(\beta \text{-}Ta)$. Low-energy protons with energies below 10 keV and Ta films with nominal thickness of 6, 9 and 12 nm are used. The aim of this work is to understand the unexpected values of the Ta stopping power for low-energy proton backscattering reported recently, which are far from the prediction of the standard free electron gas model and semi-empirical approaches. This had led the authors to conclude the failure of the free electron model. Our transmission measurements confirm these experimental results. In this work, a qualitative discussion and quantitative explanation of our experimental results is given, using an approach based on the density functional theory within the framework of the free electron gas (FEG) model. We performed semiclassical deterministic trajectory simulations and employ the local density approximation model, using an inhomogeneous electron density distribution and the polycrystalline character of Ta samples.

KEYWORDS:

• ion scattering
• stopping
• protons
• tantalum
• DFT
• free electron model

Acknowledgements

This work has been financially and partially supported by DGIIE internal project #PI_LI_19_17. M. Mery acknowledges support of FONDECYT Postdoctoral project 3210785; V. A. Esaulov acknowledges support of DGIIE internal project #MEC-USM-2019, and the Physics Department at USM for its hospitality; C. Garcia acknowledges the financial support received by FONDECYT Regular 120110; C. González-Fuentes and C. García acknowledge the financial support received by ANID PIA/APOYO AFB180002.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Mario Mery

Mario Mery is presently a postdoctoral researcher in Universidad Técnica Federico Santa María (UTFSM). He graduated from UTFSM, Chile, Department of Physics with a Master of Science in experimental physics. His PhD from UTFSM was on topics related to low energy ion interaction with nanostructures. His research interests include proton interaction with graphene, nanotube and metallic thin films. Also, synthesis, study and applications of nanoparticles.

Claudio González-Fuentes

Claudio González-Fuentes is currently asociate researcher at Centro Científico y Tecnológico de Valparaíso. Much of his research has been dedicated to scientific instrumentation for spintronics, with a special focus on ferromagnetic resonance and magneto-optical detection of spin-orbit torques.

Cristian Romanque-Albornoz

Cristian Romanque-Albornoz received the B.Sc. degree in physics from the Pontifical Catholic University of Valparaíso, Valparaíso, Chile, in 2010. He is currently pursuing the Ph.D. degree in physics with Federico Santa María Technical University, Valparaíso. His research focuses mainly on fabrication and characterization of magnetic thin films and scientific instrumentation for spin caloritronics and thermoelectric phenomena, with an emphasis on the spin Seebeck and anomalous Nernst effects.

Carlos García

Carlos García is an associate professor at the Physics Department of the Federico Santa María Technical University (UTFSM), Valparaíso, Chile. He is the head of the Applied Magnetism and Spintronic group, his research focus on magnetotransport properties of magnetic materials, particularly thin films.

Andrea M. León

Andrea M. León is currently a postdoctoral researcher at the Technical Dresden University, Dresden, Germany. Her main research field is the study of the electronic and structural properties of materials through first-principles calculations and theoretical models. Her current investigation addresses the modeling of new quantum materials including superconductors, ferroelectrics and 2D magnetic heterostructures.

Néstor R. Arista

Néstor R. Arista is a former senior staff member of the Atomic Energy Commission of Argentina and Professor of the Universidad Nacional de Cuyo. He is currently a Professor Emeritus of this University.

Vladimir A. Esaulov

Vladimir A. Esaulov is Research Director Emeritus of the Centre National de Recherche Scientifique (CNRS) at the Institut des Sciences Moléculaires d'Orsay, Université Paris Sud, and Université Paris Saclay, Orsay, France. His research interests include interaction of atomic and molecular ions with matter, characteristics of nanostructured materials and molecular self-assembly on surfaces.

Jorge E. Valdés

Jorge E. Valdés is currently Senior Researcher at the Physics Department of the Federico Santa María Technical University (UTFSM), Valparaíso, Chile. As head of the Atomic Collision Laboratory at UTFSM, he has developed methods and experiments related to the interaction of charged particles with solids and surfaces.