Research articlesMesoscopic orbital paramagnetism: The role of zero-point energy
Introduction
An unusual magnetic phenomenon is sometimes observed in oxides that contain none of the unpaired 3d electrons that are normally required for magnetic order at room temperature and above. The experimental syndrome is illustrated in Fig. 1 for a nanoporous amorphous alumina membrane [1], but similar effects have been observed in a variety of other oxide systems, including reduced strontium titanate powder [2], cerium dioxide nanoparticle clusters [3] and Sc-doped ZnO thin films [4].
After correcting raw magnetization data obtained by SQUID magnetometry for a linear paramagnetic or diamagnetic background, the residual signal illustrated in Fig. 1 is obtained. The following are the characteristic features:
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The signal is independent of temperature, from cryogenic temperatures to room temperature and above. The curves measured at different temperatures superpose directly, without any need to normalize the vertical axis.
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There is little or no hysteresis at any temperature.
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The value of the saturation magnetization Ms is from one to four orders of magnitude smaller than the saturation field 100 kAm-1 extrapolated from the initial susceptibility. For clarity, M is plotted against H in Fig. 1, with both in multiples of the same SI unit of Am-1.
A simplified but unconventional model was able to account for the characteristic features listed above, and make testable predictions for the cerium dioxide nanoparticle system [3]. In that case, measurements on dispersed powder samples established that there was a characteristic length scale of order 100 nm for the appearance of the magnetism, in agreement with prediction. Furthermore, UV absorption at a specific frequency was predicted for magnetic samples of CeO2 nanopowders, and it was subsequently observed [3].
The originality of the model is to consider effects of the zero-point electromagnetic field on the orbitals of bound electrons in the oxides. The results are explained in terms of saturating orbital paramagnetism. The main idea is that coherence may be possible within a mesoscopic region containing millions of atoms due to mixing of the ground and excited atomic orbital states. The stabilization energy of the coherent electrons is about 1 percent of their UV excitation energy. The coherent multi-electron state formed in this way is much more likely to be stable at the surface of the mesoscopic region than in the bulk. The effect of an applied magnetic field B is then to form a new mixture of the the coherent ground and excited states that exhibits a saturating paramagnetic response similar to the one observed experimentally. In view of the unfamiliarity of these concepts in magnetism, it is worthwhile to explain the underlying physics in more detail, and suggest further developments and experimental tests of the ideas.
Section snippets
The model
The model considers a collection of N spinless charged electrons that are each bound to a molecule with an orbital ground state and an orbital excited state several eV higher in energy. By ‘molecule’ we mean some collection of atoms or ions that constitute a defect in the structure, particularly at the surface of the bulk material. We comment on this point later. Coulomb interactions between electrons are neglected, but their wave functions turn out to be correlated nonetheless, because
The mesoscopic system
Consider next a well-defined mesoscopic cluster of N bound electrons in a volume . In the presence of zero-point radiation, the length scale of the system l increases by [18] where is defined by Eq. 4. This is a key result. The positions of relativistic electrons buffeted by zero-point photons undergo uncorrelated fluctuations known as zitterbewegung. So when the square of the sum of these fluctuations is averaged over their respective space and time
Discussion
Motivated by experimental results on the magnetism of some oxides, we have outlined how the zero-point electromagnetic field can lead to the emergence of a coherent electronic state for some mesoscopic systems with bound electrons that have an excited state at an energy within the bandgap. The basis of the effect is the tiny expansion of the one-electron orbitals that gives rise to the Lamb shift in atomic hydrogen. In a mesoscopic assembly of these two-level systems, the tiny orbital
Conclusions and future work
Our model is based on some basic physical ideas and it introduces a new mesoscopic control parameter into quantum field theory. It neglects many possible effects which will be the subject of further investigation. Nevertheless, the principal prediction is that a stable coherent electronic state can form on a mesoscopic scale at the surface of oxides or other compounds where electrons occupy bound ground and excited states that form in the gap between valence and conduction bands. The
CRediT authorship contribution statement
Siddhartha Sen: Conceptualization, Writing - original draft, Writing - review & editing. Lucy Prendeville: Writing - original draft, Writing - review & editing. J.M.D. Coey: Conceptualization, Supervision, Writing - original draft, Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This work was supported by Science Foundation Ireland as part of the ZEMS project, 16/IA/4534. Lucy Prendeville was supported by the Irish Research Council Government of Ireland Postgraduate Scholarship Programme, GOIPG/2019/4430. We thank Katarzyna Siewierska for her helpful discussions.
References (26)
- et al.
Generation and stability of freestanding aqueous microbubbles
Electrochem. Commun.
(2017) - et al.
Protein folding: understanding the role of water and the low Reynolds number environment as the peptide chain emerges from the ribosome and folds
J. Theor. Biol.
(2014) - et al.
d-zero magnetism in nanoporous amorphous alumina membranes
Phys. Rev. Mater.
(2018) - et al.
Surface magnetism of strontium titanate
J. Phys.: Condens. Matter
(2016) - et al.
Collective magnetic response of CeO2 nanoparticles
Nat. Phys.
(2016) - et al.
Anisotropic ferromagnetism in substituted zinc oxide
Phys. Rev. Lett.
(2004) - K. Khalid, A. Setzer, M. Ziese, P. Esquinazi, D. Spemann, A. Pöppl, E. Goering, Ubiquity of ferromagnetic signals in...
- et al.
Sources of experimental errors in the observation of nanoscale magnetism
J. Appl. Phys.
(2009) Magnetism in d0 oxides
Nat. Mater.
(2019)Principles of Quantum Mechanics
(1994)
Approximate methods of Quantum Mechanics
History and some aspects of the lamb shift
Physics
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