1
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Wang Y, Chen Y, Bui HT, Wolf C, Haze M, Mier C, Kim J, Choi DJ, Lutz CP, Bae Y, Phark SH, Heinrich AJ. An atomic-scale multi-qubit platform. Science 2023; 382:87-92. [PMID: 37797000 DOI: 10.1126/science.ade5050] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2022] [Accepted: 08/30/2023] [Indexed: 10/07/2023]
Abstract
Individual electron spins in solids are promising candidates for quantum science and technology, where bottom-up assembly of a quantum device with atomically precise couplings has long been envisioned. Here, we realized atom-by-atom construction, coherent operations, and readout of coupled electron-spin qubits using a scanning tunneling microscope. To enable the coherent control of "remote" qubits that are outside of the tunnel junction, we complemented each electron spin with a local magnetic field gradient from a nearby single-atom magnet. Readout was achieved by using a sensor qubit in the tunnel junction and implementing pulsed double electron spin resonance. Fast single-, two-, and three-qubit operations were thereby demonstrated in an all-electrical fashion. Our angstrom-scale qubit platform may enable quantum functionalities using electron spin arrays built atom by atom on a surface.
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Affiliation(s)
- Yu Wang
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul 03760, Korea
- Ewha Womans University, Seoul 03760, Korea
| | - Yi Chen
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul 03760, Korea
- Ewha Womans University, Seoul 03760, Korea
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Hong T Bui
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul 03760, Korea
- Department of Physics, Ewha Womans University, Seoul 03760, Korea
| | - Christoph Wolf
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul 03760, Korea
- Ewha Womans University, Seoul 03760, Korea
| | - Masahiro Haze
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul 03760, Korea
- The Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan
| | - Cristina Mier
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul 03760, Korea
- Centro de Física de Materiales CFM/MPC (CSIC-UPV/EHU), 20018 Donostia-San Sebastián, Spain
| | - Jinkyung Kim
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul 03760, Korea
- Department of Physics, Ewha Womans University, Seoul 03760, Korea
| | - Deung-Jang Choi
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul 03760, Korea
- Centro de Física de Materiales CFM/MPC (CSIC-UPV/EHU), 20018 Donostia-San Sebastián, Spain
- Donostia International Physics Center (DIPC), 20018 Donostia-San Sebastián, Spain
- Ikerbasque, Basque Foundation for Science, 48013 Bilbao, Spain
| | | | - Yujeong Bae
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul 03760, Korea
- Department of Physics, Ewha Womans University, Seoul 03760, Korea
| | - Soo-Hyon Phark
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul 03760, Korea
- Ewha Womans University, Seoul 03760, Korea
| | - Andreas J Heinrich
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul 03760, Korea
- Department of Physics, Ewha Womans University, Seoul 03760, Korea
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2
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Cahaya AB, Leon AO, Fauzi MH. Spin-orbit torque on nuclear spins exerted by a spin accumulation via hyperfine interactions. NANOTECHNOLOGY 2023; 34:505001. [PMID: 37708861 DOI: 10.1088/1361-6528/acf9ac] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2023] [Accepted: 09/14/2023] [Indexed: 09/16/2023]
Abstract
Spin-transfer and spin-orbit torques allow controlling magnetic degrees of freedom in various materials and devices. However, while the transfer of angular momenta between electrons has been widely studied, the contribution of nuclear spins has yet to be explored further. This article demonstrates that the hyperfine coupling, which consists of Fermi contact and dipolar interactions, can mediate the application of spin-orbit torques acting on nuclear spins. Our starting point is a sizable nuclear spin in a metal with electronic spin accumulation. Then, via the hyperfine interactions, the nuclear spin modifies the an electronic spin density. The reactions to the equilibrium and nonequilibrium components of the spin density is a torque on the nucleus with field-like and damping-like components, respectively. Thisnuclearspin-orbittorqueis a step toward stabilizing and controlling nuclear magnetic momenta, in magnitude and direction, and realizing nuclear spintronics.
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Affiliation(s)
- Adam B Cahaya
- Department of Physics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Depok 16424, Indonesia
- Research Center for Quantum Physics, National Research and Innovation Agency, South Tangerang, Banten, 15314, Indonesia
| | - Alejandro O Leon
- Departamento de Física, Facultad de Ciencias Naturales, Matemática y del Medio Ambiente, Universidad Tecnológica Metropolitana, Las Palmeras 3360, Ñuñoa 780-0003, Santiago, Chile
| | - Mohammad H Fauzi
- Research Center for Quantum Physics, National Research and Innovation Agency, South Tangerang, Banten, 15314, Indonesia
- Research Collaboration Center for Quantum Technology 2.0, Bandung 40132, Indonesia
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3
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Zhang X, Reina-Gálvez J, Wolf C, Wang Y, Aubin H, Heinrich AJ, Choi T. Influence of the Magnetic Tip on Heterodimers in Electron Spin Resonance Combined with Scanning Tunneling Microscopy. ACS NANO 2023; 17:16935-16942. [PMID: 37643247 DOI: 10.1021/acsnano.3c04024] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/31/2023]
Abstract
Investigating the quantum properties of individual spins adsorbed on surfaces by electron spin resonance combined with scanning tunneling microscopy (ESR-STM) has shown great potential for the development of quantum information technology on the atomic scale. A magnetic tip exhibiting high spin polarization is critical for performing an ESR-STM experiment. While the tip has been conventionally treated as providing a static magnetic field in ESR-STM, it was found that the tip can exhibit bistability, influencing ESR spectra. Ideally, the ESR splitting caused by the magnetic interaction between two spins on a surface should be independent of the tip. However, we found that the measured ESR splitting of a metal atom-molecule heterodimer can be tip-dependent. Detailed theoretical analysis reveals that this tip-dependent ESR splitting is caused by a different interaction energy between the tip and each spin of the heterodimer. Our work provides a comprehensive reference for characterizing tip features in ESR-STM experiments and highlights the importance of employing a proper physical model when describing the ESR tip, in particular, for heterospin systems.
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Affiliation(s)
- Xue Zhang
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul 03760, Republic of Korea
- Ewha Womans University, Seoul 03760, Republic of Korea
- Spin-X Institute, School of Microelectronics, South China University of Technology, Guangzhou 511442, People's Republic of China
| | - Jose Reina-Gálvez
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul 03760, Republic of Korea
- Ewha Womans University, Seoul 03760, Republic of Korea
| | - Christoph Wolf
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul 03760, Republic of Korea
- Ewha Womans University, Seoul 03760, Republic of Korea
| | - Yu Wang
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul 03760, Republic of Korea
- Ewha Womans University, Seoul 03760, Republic of Korea
| | - Hervé Aubin
- Universités Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120 Palaiseau, France
| | - Andreas J Heinrich
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul 03760, Republic of Korea
- Department of Physics, Ewha Womans University, Seoul 03760, Republic of Korea
| | - Taeyoung Choi
- Department of Physics, Ewha Womans University, Seoul 03760, Republic of Korea
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4
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Savytskyy R, Botzem T, Fernandez de Fuentes I, Joecker B, Pla JJ, Hudson FE, Itoh KM, Jakob AM, Johnson BC, Jamieson DN, Dzurak AS, Morello A. An electrically driven single-atom "flip-flop" qubit. SCIENCE ADVANCES 2023; 9:eadd9408. [PMID: 36763660 PMCID: PMC9916988 DOI: 10.1126/sciadv.add9408] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/13/2022] [Accepted: 01/09/2023] [Indexed: 06/18/2023]
Abstract
The spins of atoms and atom-like systems are among the most coherent objects in which to store quantum information. However, the need to address them using oscillating magnetic fields hinders their integration with quantum electronic devices. Here, we circumvent this hurdle by operating a single-atom "flip-flop" qubit in silicon, where quantum information is encoded in the electron-nuclear states of a phosphorus donor. The qubit is controlled using local electric fields at microwave frequencies, produced within a metal-oxide-semiconductor device. The electrical drive is mediated by the modulation of the electron-nuclear hyperfine coupling, a method that can be extended to many other atomic and molecular systems and to the hyperpolarization of nuclear spin ensembles. These results pave the way to the construction of solid-state quantum processors where dense arrays of atoms can be controlled using only local electric fields.
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Affiliation(s)
- Rostyslav Savytskyy
- School of Electrical Engineering and Telecommunications, UNSW Sydney, Sydney, NSW 2052, Australia
| | - Tim Botzem
- School of Electrical Engineering and Telecommunications, UNSW Sydney, Sydney, NSW 2052, Australia
| | | | - Benjamin Joecker
- School of Electrical Engineering and Telecommunications, UNSW Sydney, Sydney, NSW 2052, Australia
| | - Jarryd J. Pla
- School of Electrical Engineering and Telecommunications, UNSW Sydney, Sydney, NSW 2052, Australia
| | - Fay E. Hudson
- School of Electrical Engineering and Telecommunications, UNSW Sydney, Sydney, NSW 2052, Australia
| | - Kohei M. Itoh
- School of Fundamental Science and Technology, Keio University, Kohoku-ku, Yokohama, Japan
| | - Alexander M. Jakob
- School of Physics, University of Melbourne, Melbourne, VIC 3010, Australia
| | - Brett C. Johnson
- School of Physics, University of Melbourne, Melbourne, VIC 3010, Australia
| | - David N. Jamieson
- School of Physics, University of Melbourne, Melbourne, VIC 3010, Australia
| | - Andrew S. Dzurak
- School of Electrical Engineering and Telecommunications, UNSW Sydney, Sydney, NSW 2052, Australia
| | - Andrea Morello
- School of Electrical Engineering and Telecommunications, UNSW Sydney, Sydney, NSW 2052, Australia
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5
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Kim J, Noh K, Chen Y, Donati F, Heinrich AJ, Wolf C, Bae Y. Anisotropic Hyperfine Interaction of Surface-Adsorbed Single Atoms. NANO LETTERS 2022; 22:9766-9772. [PMID: 36317830 PMCID: PMC9756343 DOI: 10.1021/acs.nanolett.2c02782] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2022] [Revised: 10/20/2022] [Indexed: 06/16/2023]
Abstract
Hyperfine interactions have been widely used in material science, organic chemistry, and structural biology as a sensitive probe to local chemical environments. However, traditional ensemble measurements of hyperfine interactions average over a macroscopic number of spins with different geometrical locations and nuclear isotopes. Here, we use a scanning tunneling microscope (STM) combined with electron spin resonance (ESR) to measure hyperfine spectra of hydrogenated-Ti on MgO/Ag(100) at low-symmetry binding sites and thereby determine the isotropic and anisotropic hyperfine interactions at the single-atom level. Combining vector-field ESR spectroscopy with STM-based atom manipulation, we characterize the full hyperfine tensors of 47Ti and 49Ti and identify significant spatial anisotropy of the hyperfine interactions for both isotopes. Density functional theory calculations reveal that the large hyperfine anisotropy arises from highly anisotropic distributions of the ground-state electron spin density. Our work highlights the power of ESR-STM-enabled single-atom hyperfine spectroscopy in revealing electronic ground states and atomic-scale chemical environments.
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Affiliation(s)
- Jinkyung Kim
- Center
for Quantum Nanoscience (QNS), Institute
for Basic Science (IBS), Seoul 03760, South Korea
- Department
of Physics, Ewha Womans University, Seoul 03760, South Korea
| | - Kyungju Noh
- Center
for Quantum Nanoscience (QNS), Institute
for Basic Science (IBS), Seoul 03760, South Korea
- Department
of Physics, Ewha Womans University, Seoul 03760, South Korea
| | - Yi Chen
- Center
for Quantum Nanoscience (QNS), Institute
for Basic Science (IBS), Seoul 03760, South Korea
- Ewha
Womans University, Seoul 03760, Republic of Korea
| | - Fabio Donati
- Center
for Quantum Nanoscience (QNS), Institute
for Basic Science (IBS), Seoul 03760, South Korea
- Department
of Physics, Ewha Womans University, Seoul 03760, South Korea
| | - Andreas J. Heinrich
- Center
for Quantum Nanoscience (QNS), Institute
for Basic Science (IBS), Seoul 03760, South Korea
- Department
of Physics, Ewha Womans University, Seoul 03760, South Korea
| | - Christoph Wolf
- Center
for Quantum Nanoscience (QNS), Institute
for Basic Science (IBS), Seoul 03760, South Korea
- Ewha
Womans University, Seoul 03760, Republic of Korea
| | - Yujeong Bae
- Center
for Quantum Nanoscience (QNS), Institute
for Basic Science (IBS), Seoul 03760, South Korea
- Department
of Physics, Ewha Womans University, Seoul 03760, South Korea
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6
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Farinacci L, Veldman LM, Willke P, Otte S. Experimental Determination of a Single Atom Ground State Orbital through Hyperfine Anisotropy. NANO LETTERS 2022; 22:8470-8474. [PMID: 36305860 PMCID: PMC9650725 DOI: 10.1021/acs.nanolett.2c02783] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/14/2022] [Revised: 10/25/2022] [Indexed: 06/16/2023]
Abstract
Historically, electron spin resonance (ESR) has provided excellent insight into the electronic, magnetic, and chemical structure of samples hosting spin centers. In particular, the hyperfine interaction between the electron and the nuclear spins yields valuable structural information about these centers. In recent years, the combination of ESR and scanning tunneling microscopy (ESR-STM) has allowed to acquire such information about individual spin centers of magnetic atoms bound atop a surface, while additionally providing spatial information about the binding site. Here, we conduct a full angle-dependent investigation of the hyperfine splitting for individual hydrogenated titanium atoms on MgO/Ag(001) by measurements in a vector magnetic field. We observe strong anisotropy in both the g factor and the hyperfine tensor. Combining the results of the hyperfine splitting with the symmetry properties of the binding site obtained from STM images and a basic point charge model allows us to predict the shape of the electronic ground state configuration of the titanium atom. Relying on experimental values only, this method paves the way for a new protocol for electronic structure analysis for spin centers on surfaces.
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Affiliation(s)
- Laëtitia Farinacci
- Department
of Quantum Nanoscience, Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJDelft, The Netherlands
| | - Lukas M. Veldman
- Department
of Quantum Nanoscience, Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJDelft, The Netherlands
| | - Philip Willke
- Physikalisches
Institut, Karlsruhe Institute of Technology, 76131Karlsruhe, Germany
| | - Sander Otte
- Department
of Quantum Nanoscience, Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJDelft, The Netherlands
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7
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Li Z, Delgado F, Du M, He C, Schouteden K, Haesendonck CV, Janssens E, Arnau A, Lievens P, Cerda JI. Spin excitations of individual magnetic dopants in an ionic thin film. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:475802. [PMID: 36130609 DOI: 10.1088/1361-648x/ac93db] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2022] [Accepted: 09/21/2022] [Indexed: 06/15/2023]
Abstract
Individual magnetic transition metal dopants in a solid host usually exhibit relatively small spin excitation energies of a few meV. Using scanning tunneling microscopy and inelastic electron tunneling spectroscopy (IETS) techniques, we have observed a high spin excitation energy around 36 meV for an individual Co substitutional dopant in ultrathin NaCl films. In contrast, the Cr dopant in the NaCl film shows much lower spin excitation energy around 2.5 meV. Electronic multiplet calculations combined with first-principles calculations confirm the spin excitation induced IETS, and quantitatively reveal the out-of-plane magnetic anisotropies for both Co and Cr. They also allow reproducing the experimentally observed redshift in the spin excitations of Co dimers and ascribe it to a charge and geometry redistribution.
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Affiliation(s)
- Zhe Li
- State Key Laboratory on Tunable Laser Technology, Ministry of Industry and Information Technology Key Laboratory of Micro-Nano Optoelectronic Information System, School of Science, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, People's Republic of China
| | - Fernando Delgado
- Instituto de Estudios Avanzados IUDEA, Departamento de Física, Universidad de La Laguna, 38203 Tenerife, Spain
| | - Mei Du
- State Key Laboratory on Tunable Laser Technology, Ministry of Industry and Information Technology Key Laboratory of Micro-Nano Optoelectronic Information System, School of Science, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, People's Republic of China
| | - Chen He
- State Key Laboratory on Tunable Laser Technology, Ministry of Industry and Information Technology Key Laboratory of Micro-Nano Optoelectronic Information System, School of Science, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, People's Republic of China
| | - Koen Schouteden
- Quantum Solid-State Physics, Department of Physics and Astronomy, KU Leuven, 3001 Leuven, Belgium
- Semiconductor Physics Section, Department of Physics and Astronomy, KU Leuven, 3001 Leuven, Belgium
| | - Chris Van Haesendonck
- Quantum Solid-State Physics, Department of Physics and Astronomy, KU Leuven, 3001 Leuven, Belgium
| | - Ewald Janssens
- Quantum Solid-State Physics, Department of Physics and Astronomy, KU Leuven, 3001 Leuven, Belgium
| | - Andres Arnau
- Departamento de Polímeros y Materiales Avanzados: Física, Química y Tecnología, Facultad de Química, Universidad del País Vasco UPV/EHU, Apartado 1072, 20080 Donostia-San Sebastián, Spain
- Centro de Física de Materiales CFM/MPC (CSIC-UPV/EHU), Paseo Manuel de Lardizábal 5, 20018 Donostia-San Sebastián, Spain
- Donostia International Physics Center, Paseo Manuel de Lardizábal 4, 20018 Donostia-San Sebastián, Spain
| | - Peter Lievens
- Quantum Solid-State Physics, Department of Physics and Astronomy, KU Leuven, 3001 Leuven, Belgium
| | - Jorge I Cerda
- Instituto de Ciencia de Materiales de Madrid, CSIC, Cantoblanco 28049 Madrid, Spain
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8
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Shehada S, Dos Santos Dias M, Abusaa M, Lounis S. Interplay of magnetic states and hyperfine fields of iron dimers on MgO(001). JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:385802. [PMID: 35835084 DOI: 10.1088/1361-648x/ac8135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2022] [Accepted: 07/14/2022] [Indexed: 06/15/2023]
Abstract
Individual nuclear spin states can have very long lifetimes and could be useful as qubits. Progress in this direction was achieved on MgO/Ag(001) via detection of the hyperfine interaction (HFI) of Fe, Ti and Cu adatoms using scanning tunneling microscopy. Previously, we systematically quantified from first-principles the HFI for the whole series of 3d transition adatoms (Sc-Cu) deposited on various ultra-thin insulators, establishing the trends of the computed HFI with respect to the filling of the magnetic s- and d-orbitals of the adatoms and on the bonding with the substrate. Here we explore the case of dimers by investigating the correlation between the HFI and the magnetic state of free standing Fe dimers, single Fe adatoms and dimers deposited on a bilayer of MgO(001). We find that the magnitude of the HFI can be controlled by switching the magnetic state of the dimers. For short Fe-Fe distances, the antiferromagnetic state enhances the HFI with respect to that of the ferromagnetic state. By increasing the distance between the magnetic atoms, a transition toward the opposite behavior is observed. Furthermore, we demonstrate the ability to substantially modify the HFI by atomic control of the location of the adatoms on the substrate. Our results establish the limits of applicability of the usual hyperfine hamiltonian and we propose an extension based on multiple scattering processes.
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Affiliation(s)
- Sufyan Shehada
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich & JARA, 52425 Jülich, Germany
- Department of Physics, RWTH Aachen University, 52056 Aachen, Germany
- Department of Physics, Arab American University, Jenin, Palestine
| | - Manuel Dos Santos Dias
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich & JARA, 52425 Jülich, Germany
- Faculty of Physics, University of Duisburg-Essen & CENIDE, 47053 Duisburg, Germany
| | - Muayad Abusaa
- Department of Physics, Arab American University, Jenin, Palestine
| | - Samir Lounis
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich & JARA, 52425 Jülich, Germany
- Faculty of Physics, University of Duisburg-Essen & CENIDE, 47053 Duisburg, Germany
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9
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Kovarik S, Robles R, Schlitz R, Seifert TS, Lorente N, Gambardella P, Stepanow S. Electron Paramagnetic Resonance of Alkali Metal Atoms and Dimers on Ultrathin MgO. NANO LETTERS 2022; 22:4176-4181. [PMID: 35512394 DOI: 10.1021/acs.nanolett.2c00980] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Electron paramagnetic resonance (EPR) can provide unique insight into the chemical structure and magnetic properties of dopants in oxide and semiconducting materials that are of interest for applications in electronics, catalysis, and quantum sensing. Here, we demonstrate that EPR in combination with scanning tunneling microscopy (STM) allows for probing the bonding and charge state of alkali metal atoms on an ultrathin magnesium oxide layer on a Ag substrate. We observe a magnetic moment of 1 μB for Li2, LiNa, and Na2 dimers corresponding to spin radicals with a charge state of +1e. Single alkali atoms have the same charge state and no magnetic moment. The ionization of the adsorbates is attributed to charge transfer through the oxide to the metal substrate. Our work highlights the potential of EPR-STM to provide insight into dopant atoms that are relevant for the control of the electrical properties of surfaces and nanodevices.
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Affiliation(s)
- Stepan Kovarik
- Department of Materials, ETH Zurich, Hönggerbergring 64, Zürich CH-8093, Switzerland
| | - Roberto Robles
- Centro de Física de Materiales CFM/MPC (CSIC-UPV/EHU), Paseo Manuel de Lardizabal 5, San Sebastián 20018, Spain
| | - Richard Schlitz
- Department of Materials, ETH Zurich, Hönggerbergring 64, Zürich CH-8093, Switzerland
| | - Tom Sebastian Seifert
- Department of Materials, ETH Zurich, Hönggerbergring 64, Zürich CH-8093, Switzerland
- Department of Physics, Freie Universität Berlin, Berlin 14195, Germany
| | - Nicolas Lorente
- Centro de Física de Materiales CFM/MPC (CSIC-UPV/EHU), Paseo Manuel de Lardizabal 5, San Sebastián 20018, Spain
- Donostia International Physics Center (DIPC), Paseo Manuel de Lardizabal 4, San Sebastián 20018, Spain
| | - Pietro Gambardella
- Department of Materials, ETH Zurich, Hönggerbergring 64, Zürich CH-8093, Switzerland
| | - Sebastian Stepanow
- Department of Materials, ETH Zurich, Hönggerbergring 64, Zürich CH-8093, Switzerland
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10
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Wit B, Vranik R, Müllegger S. Enhanced conductance response in radio frequency scanning tunnelling microscopy. Sci Rep 2022; 12:6183. [PMID: 35418594 PMCID: PMC9007990 DOI: 10.1038/s41598-022-09820-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2021] [Accepted: 03/23/2022] [Indexed: 11/13/2022] Open
Abstract
Diverse spectroscopic methods operating at radio frequency depend on a reliable calibration to compensate for the frequency dependent damping of the transmission lines. Calibration may be impeded by the existence of a sensitive interdependence of two or more experimental parameters. Here, we show by combined scanning tunnelling microscopy measurements and numerical simulations how a frequency-dependent conductance response is affected by different DC conductance behaviours of the tunnel junction. Distinct and well-defined DC-conductance behaviour is provided by our experimental model systems, which include C60 molecules on Au(111), exhibiting electronic configurations distinct from the well-known dim and bright C60's reported so far. We investigate specific combinations of experimental parameters. Variations of the modulation amplitude as small as only a few percent may result in systematic conductance deviations as large as one order of magnitude. We provide practical guidelines for calibrating respective measurements, which are relevant to RF spectroscopic measurements.
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Affiliation(s)
- Bareld Wit
- Institute of Semiconductor and Solid State Physics, Johannes Kepler University Linz, 4040, Linz, Austria.
| | - Radovan Vranik
- Institute of Semiconductor and Solid State Physics, Johannes Kepler University Linz, 4040, Linz, Austria
| | - Stefan Müllegger
- Institute of Semiconductor and Solid State Physics, Johannes Kepler University Linz, 4040, Linz, Austria
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11
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Chen Y, Bae Y, Heinrich AJ. Harnessing the Quantum Behavior of Spins on Surfaces. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2022:e2107534. [PMID: 34994026 DOI: 10.1002/adma.202107534] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2021] [Revised: 12/28/2021] [Indexed: 06/14/2023]
Abstract
The desire to control and measure individual quantum systems such as atoms and ions in a vacuum has led to significant scientific and engineering developments in the past decades that form the basis of today's quantum information science. Single atoms and molecules on surfaces, on the other hand, are heavily investigated by physicists, chemists, and material scientists in search of novel electronic and magnetic functionalities. These two paths crossed in 2015 when it was first clearly demonstrated that individual spins on a surface can be coherently controlled and read out in an all-electrical fashion. The enabling technique is a combination of scanning tunneling microscopy (STM) and electron spin resonance, which offers unprecedented coherent controllability at the Angstrom length scale. This review aims to illustrate the essential ingredients that allow the quantum operations of single spins on surfaces. Three domains of applications of surface spins, namely quantum sensing, quantum control, and quantum simulation, are discussed with physical principles explained and examples presented. Enabled by the atomically-precise fabrication capability of STM, single spins on surfaces might one day lead to the realization of quantum nanodevices and artificial quantum materials at the atomic scale.
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Affiliation(s)
- Yi Chen
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul, 03760, Korea
- Department of Physics, Ewha Womans University, Seoul, 03760, Korea
| | - Yujeong Bae
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul, 03760, Korea
- Department of Physics, Ewha Womans University, Seoul, 03760, Korea
| | - Andreas J Heinrich
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul, 03760, Korea
- Department of Physics, Ewha Womans University, Seoul, 03760, Korea
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12
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Zhang X, Wolf C, Wang Y, Aubin H, Bilgeri T, Willke P, Heinrich AJ, Choi T. Electron spin resonance of single iron phthalocyanine molecules and role of their non-localized spins in magnetic interactions. Nat Chem 2021; 14:59-65. [PMID: 34764471 DOI: 10.1038/s41557-021-00827-7] [Citation(s) in RCA: 25] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2020] [Accepted: 09/27/2021] [Indexed: 11/09/2022]
Abstract
Electron spin resonance (ESR) spectroscopy is a crucial tool, through spin labelling, in investigations of the chemical structure of materials and of the electronic structure of materials associated with unpaired spins. ESR spectra measured in molecular systems, however, are established on large ensembles of spins and usually require a complicated structural analysis. Recently, the combination of scanning tunnelling microscopy with ESR has proved to be a powerful tool to image and coherently control individual atomic spins on surfaces. Here we extend this technique to single coordination complexes-iron phthalocyanines (FePc)-and investigate the magnetic interactions between their molecular spin with either another molecular spin (in FePc-FePc dimers) or an atomic spin (in FePc-Ti pairs). We show that the molecular spin density of FePc is both localized at the central Fe atom and also distributed to the ligands (Pc), which yields a strongly molecular-geometry-dependent exchange coupling.
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Affiliation(s)
- Xue Zhang
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul, Republic of Korea.,Ewha Womans University, Seoul, Republic of Korea
| | - Christoph Wolf
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul, Republic of Korea.,Ewha Womans University, Seoul, Republic of Korea
| | - Yu Wang
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul, Republic of Korea.,Ewha Womans University, Seoul, Republic of Korea
| | - Hervé Aubin
- Universités Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, Palaiseau, France
| | - Tobias Bilgeri
- Institute of Physics, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
| | - Philip Willke
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul, Republic of Korea.,Ewha Womans University, Seoul, Republic of Korea.,Physikalisches Institut, Karlsruhe Institute of Technology, Karlsruhe, Germany
| | - Andreas J Heinrich
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul, Republic of Korea. .,Department of Physics, Ewha Womans University, Seoul, Republic of Korea.
| | - Taeyoung Choi
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul, Republic of Korea. .,Department of Physics, Ewha Womans University, Seoul, Republic of Korea.
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13
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Doležal J, Merino P, Švec M. Constant amplitude driving of a radiofrequency excited plasmonic tunnel junction. APPLIED PHYSICS LETTERS 2021; 118:193301. [PMID: 34257502 PMCID: PMC7611201 DOI: 10.1063/5.0048476] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/23/2021] [Accepted: 04/17/2021] [Indexed: 06/13/2023]
Abstract
Constant-amplitude bias modulation over a broad range of microwave frequencies is a prerequisite for application in high-resolution spectroscopic techniques in a tunneling junction as e.g. electron spin resonance spectroscopy or optically detected paramagnetic resonance. Here, we present an optical method for determining the frequency-dependent magnitude of the transfer function of a dedicated high-frequency line integrated with a scanning probe microscope. The method relies on determining the energy cutoff of the plasmonic electroluminescence spectrum, which is linked to the energies of the electrons inelastically tunneling across the junction. We develop an easy-to-implement procedure for effective compensation of an RF line and determination of the transfer function magnitude in the GHz range. We test our method with conventional electronic calibration and find a perfect agreement.
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Affiliation(s)
- Jiří Doležal
- Institute of Physics, Czech Academy of Sciences, Cukrovarnická 10/112, CZ16200 Praha 6, Czech Republic
- Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, CZ12116 Praha 2, Czech Republic
| | - Pablo Merino
- Instituto de Ciencia de Materiales de Madrid, CSIC, Sor Juana Inés de la Cruz 3, E28049 Madrid, Spain
- Instituto de Física Fundamental, CSIC, Serrano 121, E28006 Madrid, Spain
| | - Martin Švec
- Institute of Physics, Czech Academy of Sciences, Cukrovarnická 10/112, CZ16200 Praha 6, Czech Republic
- Regional Centre of Advanced Technologies and Materials, CATRIN, Palacky University Olomouc, Šlechtitelů 27, CZ78371 Olomouc, Czech Republic
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14
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Feigl S, Vranik R, Wit B, Müllegger S. Frequency-independent voltage amplitude across a tunnel junction. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2021; 92:043710. [PMID: 34243382 DOI: 10.1063/5.0035388] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2020] [Accepted: 03/26/2021] [Indexed: 06/13/2023]
Abstract
Radio-frequency (rf) scanning tunneling microscopy has recently been advanced to methods such as single-atom spin resonance. Such methods benefit from a frequency-independent rf voltage amplitude across the tunnel junction, which is challenging to achieve due to the strong frequency dependence of the rf attenuation in a transmission line. Two calibration methods for the rf amplitude have been reported to date. In this Note, we present an alternative method to achieve a frequency-independent rf voltage amplitude across the tunnel junction and show the results of this calibration. The presented procedure is applicable to devices that can deliver rf voltage to a tunnel junction.
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Affiliation(s)
- Simon Feigl
- Institute of Semiconductor and Solid State Physics, Johannes Kepler University Linz, 4040 Linz, Austria
| | - Radovan Vranik
- Institute of Semiconductor and Solid State Physics, Johannes Kepler University Linz, 4040 Linz, Austria
| | - Bareld Wit
- Institute of Semiconductor and Solid State Physics, Johannes Kepler University Linz, 4040 Linz, Austria
| | - Stefan Müllegger
- Institute of Semiconductor and Solid State Physics, Johannes Kepler University Linz, 4040 Linz, Austria
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15
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Chiesa M, Giamello E. On the Role and Applications of Electron Magnetic Resonance Techniques in Surface Chemistry and Heterogeneous Catalysis. Catal Letters 2021. [DOI: 10.1007/s10562-021-03576-x] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Abstract
Abstract
Some relevant aspects of Electron Paramagnetic Resonance (EPR) applied to the fields of surface chemistry and heterogeneous catalysis are illustrated in this perspective paper that aims to show the potential of these techniques in describing critical features of surface structures and reactivity. Selected examples are employed covering distinct aspects of catalytic science from morphological analysis of surfaces to detailed descriptions of chemical bonding and catalytic sites topology. In conclusions the pros and cons related to the acquisition of EPR instrumentations in an advanced laboratory of surface chemistry and heterogeneous catalysis are briefly considered.
Graphic Abstract
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16
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McMillan SR, Harmon NJ, Flatté ME. Image of Dynamic Local Exchange Interactions in the dc Magnetoresistance of Spin-Polarized Current through a Dopant. PHYSICAL REVIEW LETTERS 2020; 125:257203. [PMID: 33416385 DOI: 10.1103/physrevlett.125.257203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2019] [Revised: 09/15/2020] [Accepted: 11/10/2020] [Indexed: 06/12/2023]
Abstract
We predict strong, dynamical effects in the dc magnetoresistance of current flowing from a spin-polarized electrical contact through a magnetic dopant in a nonmagnetic host. Using the stochastic Liouville formalism we calculate clearly defined resonances in the dc magnetoresistance when the applied magnetic field matches the exchange interaction with a nearby spin. At these resonances spin precession in the applied magnetic field is canceled by spin evolution in the exchange field, preserving a dynamic bottleneck for spin transport through the dopant. Similar features emerge when the dopant spin is coupled to nearby nuclei through the hyperfine interaction. These features provide a precise means of measuring exchange or hyperfine couplings between localized spins near a surface using spin-polarized scanning tunneling microscopy, without any ac electric or magnetic fields, even when the exchange or hyperfine energy is orders of magnitude smaller than the thermal energy.
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Affiliation(s)
- Stephen R McMillan
- Optical Science and Technology Center, and Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa 52242, USA
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
| | - Nicholas J Harmon
- Optical Science and Technology Center, and Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa 52242, USA
| | - Michael E Flatté
- Optical Science and Technology Center, and Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa 52242, USA
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
- Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands
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17
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Seifert TS, Kovarik S, Juraschek DM, Spaldin NA, Gambardella P, Stepanow S. Longitudinal and transverse electron paramagnetic resonance in a scanning tunneling microscope. SCIENCE ADVANCES 2020; 6:eabc5511. [PMID: 32998882 PMCID: PMC7527223 DOI: 10.1126/sciadv.abc5511] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/30/2020] [Accepted: 08/13/2020] [Indexed: 06/11/2023]
Abstract
Electron paramagnetic resonance (EPR) spectroscopy is widely used to characterize paramagnetic complexes. Recently, EPR combined with scanning tunneling microscopy (STM) achieved single-spin sensitivity with sub-angstrom spatial resolution. The excitation mechanism of EPR in STM, however, is broadly debated, raising concerns about widespread application of this technique. We present an extensive experimental study and modeling of EPR-STM of Fe and hydrogenated Ti atoms on a MgO surface. Our results support a piezoelectric coupling mechanism, in which the EPR species oscillate adiabatically in the inhomogeneous magnetic field of the STM tip. An analysis based on Bloch equations combined with atomic-multiplet calculations identifies different EPR driving forces. Specifically, transverse magnetic field gradients drive the spin-1/2 hydrogenated Ti, whereas longitudinal magnetic field gradients drive the spin-2 Fe. Also, our results highlight the potential of piezoelectric coupling to induce electric dipole moments, thereby broadening the scope of EPR-STM to nonpolar species and nonlinear excitation schemes.
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Affiliation(s)
- Tom S Seifert
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland.
| | - Stepan Kovarik
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | - Dominik M Juraschek
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
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18
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Willke P, Singha A, Zhang X, Esat T, Lutz CP, Heinrich AJ, Choi T. Tuning Single-Atom Electron Spin Resonance in a Vector Magnetic Field. NANO LETTERS 2019; 19:8201-8206. [PMID: 31661282 DOI: 10.1021/acs.nanolett.9b03559] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Spin resonance of single spin centers bears great potential for chemical structure analysis, quantum sensing, and quantum coherent manipulation. Essential for these experiments is the presence of a two-level spin system whose energy splitting can be chosen by applying a magnetic field. In recent years, a combination of electron spin resonance (ESR) and scanning tunneling microscopy (STM) has been demonstrated as a technique to detect magnetic properties of single atoms on surfaces and to achieve sub-microelectronvolts energy resolution. Nevertheless, up to now the role of the required magnetic fields has not been elucidated. Here, we perform single-atom ESR on individual Fe atoms adsorbed on magnesium oxide (MgO) using a two-dimensional vector magnetic field as well as the local field of the magnetic STM tip in a commercially available STM. We show how the ESR amplitude can be greatly improved by optimizing the magnetic fields, revealing in particular an enhanced signal at large in-plane magnetic fields. Moreover, we demonstrate that the stray field from the magnetic STM tip is a versatile tool. We use it here to drive the electron spin more efficiently and to perform ESR measurements at constant frequency by employing tip-field sweeps. Lastly, we show that it is possible to perform ESR using only the tip field, under zero external magnetic field, which promises to make this technique available in many existing STM systems.
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Affiliation(s)
- Philip Willke
- Center for Quantum Nanoscience , Institute for Basic Science (IBS) , Seoul 03760 , Republic of Korea
- Ewha Womans University , Seoul 03760 , Republic of Korea
| | - Aparajita Singha
- Center for Quantum Nanoscience , Institute for Basic Science (IBS) , Seoul 03760 , Republic of Korea
- Ewha Womans University , Seoul 03760 , Republic of Korea
| | - Xue Zhang
- Center for Quantum Nanoscience , Institute for Basic Science (IBS) , Seoul 03760 , Republic of Korea
- Ewha Womans University , Seoul 03760 , Republic of Korea
| | - Taner Esat
- Center for Quantum Nanoscience , Institute for Basic Science (IBS) , Seoul 03760 , Republic of Korea
- Ewha Womans University , Seoul 03760 , Republic of Korea
| | | | - Andreas J Heinrich
- Center for Quantum Nanoscience , Institute for Basic Science (IBS) , Seoul 03760 , Republic of Korea
- Department of Physics , Ewha Womans University , Seoul 03760 , Republic of Korea
| | - Taeyoung Choi
- Center for Quantum Nanoscience , Institute for Basic Science (IBS) , Seoul 03760 , Republic of Korea
- Department of Physics , Ewha Womans University , Seoul 03760 , Republic of Korea
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19
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Yang K, Paul W, Phark SH, Willke P, Bae Y, Choi T, Esat T, Ardavan A, Heinrich AJ, Lutz CP. Coherent spin manipulation of individual atoms on a surface. Science 2019; 366:509-512. [DOI: 10.1126/science.aay6779] [Citation(s) in RCA: 52] [Impact Index Per Article: 10.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2019] [Accepted: 10/01/2019] [Indexed: 11/03/2022]
Affiliation(s)
- Kai Yang
- IBM Almaden Research Center, San Jose, CA 95120, USA
| | - William Paul
- IBM Almaden Research Center, San Jose, CA 95120, USA
| | - Soo-Hyon Phark
- IBM Almaden Research Center, San Jose, CA 95120, USA
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul 03760, Republic of Korea
- Department of Physics, Ewha Womans University, Seoul 03760, Republic of Korea
| | - Philip Willke
- IBM Almaden Research Center, San Jose, CA 95120, USA
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul 03760, Republic of Korea
- Ewha Womans University, Seoul 03760, Republic of Korea
| | - Yujeong Bae
- IBM Almaden Research Center, San Jose, CA 95120, USA
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul 03760, Republic of Korea
- Ewha Womans University, Seoul 03760, Republic of Korea
| | - Taeyoung Choi
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul 03760, Republic of Korea
- Department of Physics, Ewha Womans University, Seoul 03760, Republic of Korea
| | - Taner Esat
- IBM Almaden Research Center, San Jose, CA 95120, USA
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul 03760, Republic of Korea
- Ewha Womans University, Seoul 03760, Republic of Korea
| | - Arzhang Ardavan
- CAESR, Clarendon Laboratory, Department of Physics, University of Oxford, Oxford OX1 3PU, UK
| | - Andreas J. Heinrich
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul 03760, Republic of Korea
- Department of Physics, Ewha Womans University, Seoul 03760, Republic of Korea
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20
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Yang K, Paul W, Natterer FD, Lado JL, Bae Y, Willke P, Choi T, Ferrón A, Fernández-Rossier J, Heinrich AJ, Lutz CP. Tuning the Exchange Bias on a Single Atom from 1 mT to 10 T. PHYSICAL REVIEW LETTERS 2019; 122:227203. [PMID: 31283288 DOI: 10.1103/physrevlett.122.227203] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2019] [Indexed: 06/09/2023]
Abstract
Shrinking spintronic devices to the nanoscale ultimately requires localized control of individual atomic magnetic moments. At these length scales, the exchange interaction plays important roles, such as in the stabilization of spin-quantization axes, the production of spin frustration, and creation of magnetic ordering. Here, we demonstrate the precise control of the exchange bias experienced by a single atom on a surface, covering an energy range of 4 orders of magnitude. The exchange interaction is continuously tunable from milli-eV to micro-eV by adjusting the separation between a spin-1/2 atom on a surface and the magnetic tip of a scanning tunneling microscope. We seamlessly combine inelastic electron tunneling spectroscopy and electron spin resonance to map out the different energy scales. This control of exchange bias over a wide span of energies provides versatile control of spin states, with applications ranging from precise tuning of quantum state properties, to strong exchange bias for local spin doping. In addition, we show that a time-varying exchange interaction generates a localized ac magnetic field that resonantly drives the surface spin. The static and dynamic control of the exchange interaction at the atomic scale provides a new tool to tune the quantum states of coupled-spin systems.
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Affiliation(s)
- Kai Yang
- IBM Almaden Research Center, San Jose, California 95120, USA
| | - William Paul
- IBM Almaden Research Center, San Jose, California 95120, USA
| | - Fabian D Natterer
- IBM Almaden Research Center, San Jose, California 95120, USA
- Physik-Institut, University of Zurich, CH-8057 Zurich, Switzerland
| | - Jose L Lado
- Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - Yujeong Bae
- IBM Almaden Research Center, San Jose, California 95120, USA
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul 03760, Republic of Korea
- Department of Physics, Ewha Womans University, Seoul 03760, Republic of Korea
| | - Philip Willke
- IBM Almaden Research Center, San Jose, California 95120, USA
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul 03760, Republic of Korea
- Department of Physics, Ewha Womans University, Seoul 03760, Republic of Korea
| | - Taeyoung Choi
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul 03760, Republic of Korea
- Department of Physics, Ewha Womans University, Seoul 03760, Republic of Korea
| | - Alejandro Ferrón
- Instituto de Modelado e Innovación Tecnológica (CONICET-UNNE), and Facultad de Ciencias Exactas, Naturales y Agrimensura, Universidad Nacional del Nordeste, Avenida Libertad 5400, W3404AAS Corrientes, Argentina
| | - Joaquín Fernández-Rossier
- QuantaLab, International Iberian Nanotechnology Laboratory (INL), Avenida Mestre José Veiga, 4715-310 Braga, Portugal
- Departamento de Física Aplicada, Universidad de Alicante, San Vicente del Raspeig 03690, Spain
| | - Andreas J Heinrich
- Center for Quantum Nanoscience, Institute for Basic Science (IBS), Seoul 03760, Republic of Korea
- Department of Physics, Ewha Womans University, Seoul 03760, Republic of Korea
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21
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Affiliation(s)
- Laurent Limot
- Université de Strasbourg, CNRS, IPCMS, Strasbourg, France.
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