Scissors modes

1. Scissors Modes: Overtones and Spin-Orbit Locking in rare earth crystalsK. Hatada, K. Hayakawa and F. Palumbo • Scissors modes Oscillations of the axes of two different systems of particles which conserve their shape. Predicted and observed in all deformed atomic nuclei (protons against neutrons) By extension: oscillation of a cloud of particles with respect to a structure at rest: predicted in Bose-Einstein condensates in magnetic traps, in quantum dots, metal clusters and crystals, observed in Bose-Einstein condensates • Overtones (second excitations) For the charged systems the theoretical relation was experimentally confirmed B(M1)scissors ~ B(E2)scissors B(M)\ B(E), magnetic\ electric strengths We found the surprising result B(M1)scissors ~ B(E2)scissors ~ B(E2)overtones K.Hatada, K.Hayakawa and F.Palumbo, arXiv:1105.1319 [nucl-th], subm. Phys. Rev. C, Rapid Communications LF61

2. K. Hatada, K. Hayakawa and F. Palumbo, arXiv:1004.2220 [cond-mat] revised, submitted to Annals of Physics. • Spin-Orbit Locking Conjecture: When the Spin-Orbit interaction is much stronger than the crystal field, a magnetic field should rotate both spin and charge density profile of an ion in a crystal cell We propose experiments to investigate Spin-Orbit Locking by studying Scissors Modes in rare earth crystals. Such a crystal is set in a magnetic field, which will align spin and charge density profile away from the axis of the cell. Then the magnetic field is suddenly switched off. The rare earth ion will align its axis along the axis of the cell after some oscillations (Scissors Modes) with emission of photons of given energy and polarization. We want to study Scissors modes associated with the interaction of the electronic cloud with the atomic nucleus.

3. Fermi level Published in Europhysics Letters 2011 Co O Valence band Photoemission Above Néel temperature Below Néel temperature No important difference in XPS spectra ! 3

4. Instead, Auger M23VV – 3p photoemission coincidence spectra are different above and below NéelTemperature. Besides, dicroic effect: NN and AN refer to different geometries Ground state: Co d7 Auger final state: d5 strong correlation 4

5. Auger line shape analysis:where we stand Filled bands theory explains band-like and atomic-like spectra Almost filled bands case Strongly correlated bands with incomplete filling: the general framework predicting that the spectrum shows relaxed and unrelaxed features But no detailed studies to date Review 5

6. Present analysys of CoO spectra: M.Cini et al, in preparation (essentially, a calculation of the unrelaxed features) CoO6 cluster: Oh Group A…E Oxygens  3 p orbitals each Co 5 d orbitals Cluster model with correct atomic multiplet in atomic limit Exact diagonalization for a range of occupations Comparison with photoemission spectroscopy fixes hopping and repulsion parametrs Optimal parameters used in Auger simulations with computed Auger matrix elements 6

7. (indices run on the symmetry-adapted basis, Slater-Coster analysis determines overlaps and hopping terms from distances and angles, essentially no free parameters here) 7

8. Comparison between theory and experimental position of features fixes parameter A Theory must line up main features (an unknown background exists) The following Auger analysis is parameter-free 8

9. M.Cini et al, in preparation 9

10. This assignement is achieved for the first time: the existence of such detailed info in the spectra was not known before. The success is due to a strong interplay between experimental and theoretical advances. Outlook Work which is under way: Other cases study Attempt to produce a theory of spin-angular interrelation in DEAR-APECS Attempt to produce a theory of interrelation between DEAR-APECS and magnetism, thereby opening a ‘local’ window of magnetism in nano-systems and low dimensional systems. 10

11. Ab initio model of carbon nanotubes growth on nano-structured Ni catalyst in a nanoporous Al2O3 membrane and resistance calculations for their junctions with various metal substrates Stefano Bellucci, Federico Micciulla LNF INFN (Frascati) Eugene Kotomin, Sergey Piskunov,Yuri Shunin, Yuri Zhukovskii,LUCFI(Riga)

12. Outlook 1) Description of model of carbon nanotubes growth on nano-structured Ni catalyst 2) resistance calculations

13. Formation of SW CNTs mainly requires the presence of transition-metal element or alloy catalysts (Co, Ni, Fe, Y, etc.) [2]. SW CNTs can be synthesized via the interaction of the metal catalyst nanoparticles with the hydrogen-carbon or hydrocarbon vapor at relatively high temperature. Fig. 2. Growth of SW CNT from the metallic nanocluster [2]. The microscopic images of CNTs growing from the catalytic nanoclusters help to clarify how the models of the Me-CNT junction can be drawn (Fig. 2). The optimal performance of CNTs requires control of their structure properties, e.g., size, length, chirality, which remains a significant difficulty for widespread application of CNTs in high-technology devices [2] S. Hofmann, R. Sharma, C. Ducati, G. Du, C. Mattevi, C. Cepek, M. Cantoro, S. Pisana, A. Parvez, F. Cervantes-Sodi, A.C. Ferrari, R. Dunin-Borkowski, S. Lizzit, L. Petaccia, A. Goldoni, J. Robertson, Nano Lett. 7 (2007) 602.

14. To understand a relation between the chirality of the growing CNT and the chemical composition of the catalyst, a comprehensive study of the interaction between graphitic fragments and metallic particles is required. However, such a study is computationally prohibitive because of the large configuration space involved [5]. To address this issue, one can focus on the binding of minimal structural units of armchair (ac) and zigzag (zz) edges to either flat or stepped surfaces. The binding energies are quantified by the chemical potential per edge atom edge defined as: , Fig. 8. Binding of zz (left) and ac (right) CNT to a flat (111) surface of the catalyst nanoparticle where is the chemical potential per edge atom for an unbound edge, Efrag the total energy of an isolated model fragment, and nC the number of edge carbon atoms. The value of can be estimated via the calculations of ideal graphene and suitable graphenenanoribbons. (2)

15. SUMMARY AND PREDICTIONS[Yuri F. Zhukovskii; Sergei Piskunov; Eugene A. Kotomin; Stefano Bellucci, Simulations on the mechanism of CNT bundle growth upon smooth and nanostructured Ni as well as θ-Al2O3 catalysts, Central European Journal of Physics, 2011] Our results predict quite effective and reproducible growth of carbon nanotubes upon the nickel nanostructured substrate. In absence of catalyst nanoparticles upon the bottom of the nanopores inside alumina membrane the carbon structures could grow from the walls towards the centers of nanopores: either carbon nanoscrolls or rather thick amorphous (soot-like) microtubes. At the bottom level of the multiscale modeling, ab initio methods can be used for determining the electronic structure of the assumed carbon-metal nanocomposites. Moreover, the obtained results can be employed in the construction of single-particle Hamiltonian used in the analytical tight-binding calculations of the conducting channels in the Me/MW-CNT interconnects, as well as in further MD and KMC simulations.

16. 1. In this study, simulations of conductivity and resistivity are performed using the multiple scattering theory and effective media cluster approach. The main problems at the current stage of researches on CNT interconnect resistance appear due to the influence of chirality effects in interconnects of SW and MW CNT with the fitting metals (Me = Ni, Cu, Ag, Pd, Pt, Au) for predefined CNT geometry. 2. The main task of this study is the implementation of advanced ab initio simulation models for construction of nanocircuits containing CNTs and their junctions with metallic contacts. Both the local and integral CNT properties have been simulated using prototype NT models such as a dispersion law, the electronic density of states (EDOS), the conductivity, resistivity, effective masses, etc.

17. The scattering theory approach allows us to calculate both the electronic structure and elastic properties of condensed matter considered as the static phenomena simultaneously with the dynamical phenomena of electron transport. Computational procedure developed for these calculations [1] is based on construction of the cluster potentials and evaluation of the S-and T-matrices for scattering and transfer (Fig. 1), respectively. Fig. 1. The wave packet -scattering principle The coherent-potential approach (CPA [2]) is considered as an effective-medium-approximation (EMA). [1] Yu.N. Shunin, K.K. Schwartz. In: Computer Modelling of Electronic and Atomic Processes in Solids (Eds. R.C. Tennyson, A.E. Kiv; Kluwer Academic Publisher, Dodrecht, Boston, London, 1997) p. 241-257. [2] E.L. Economou. Green's Functions in Quantum Physics (3rd Ed., Solid State Ser. Vol. 7, Springer Verlag, Berlin, Heidelberg, 2006).

18. c) hot electrons All resistance calculations have been performed taking into account that not all the electrons participate in a conduction process with the Fermi velocity vf. For this aim, we must take into account the thermally activated electrons (Fig. 3), i.e., only the small part of n: , where n is a quasi-free electron concentration, kT = 0.0258 eV for T=3000 K. Fig. 3. Evaluation of hot conductivity electrons, f(E) is a Fermi-Dirac distribution function, and (E) is EDOS.

19. d. simulations of contacts between metal substrates and SW NTs The ’effective bonds’ model means that the conductivity of CNT-metal interconnect is proportional to the number of direct chemical bonds between CNT and metal, which depend on the CNT chirality and metal substrate atomic configuration (Fig. 4). Thus, we can evaluate the Landauer’s multiplier for conductance calculations. We have also proposed a parameter  (chirality angle) for the identification of nanotube chirality (Fig. 5). Fig. 4. Model of the CNT-Me interconnect

20. Fig. 5. Modeling of chirality effects Fig. 6 shows effects of diameter and chirality on CNT-Ni interconnect resistivity. The larger the diameter, the larger the number of direct junction bonds and the total conductance (i.e., the resistance is smaller). Similar effect is observed for varying chirality: number of direct bonds is higher for armchair and zigzag CNT chiralities. Fig. 6. The CNT-Ni interconnect resistance vs.: (a) nanotube diameter and (b) nanotube chirality.

21. In Fig. 7 we compare resistance for the interconnects of the same SW CNT with various metal substrates (Ag, Au, Cu, Ni, Pd and Pt). Although nickel is a good catalyst for CNT growth, resistance of its interconnect with nanotube has been found to be noticeably higher as compared to that for silver, gold and platinum substrates. Fig. 7. Resistances of various zigzag-type metal-SW CNT interconnects for nanotube diameter ~20 nm.

22. e) simulations of contacts between metal substrates and given MW NT Using the simulation models presented above we have developed a model of multi-wall CNT-Me junction resistance based on the interface potential barriers evaluation and Landauer’s formalism described above. For these simulations, we have used the MW CNT model which is present in Fig. 8:

23. Comparing Figs. 7 and 9 we can conclude that for the interconnects of metals with both SW and MW CNTs, the smaller resistance is again observed for Ag, Au and Pt. Obviously, resistance of the metal interconnect with MW CNT is several times smaller than that with SW CNT since the number of direct junction bonds is substantially larger in the former case. Fig. 9. Calculated values of resistance for various MW CNT-Me interconnects.

24. f) evaluation of current losses between the adjacent shells in MW CNT Using the model of interwall potential in MW CNT we also evaluate the coefficient of transparency which determines the possible ‘radial current’ losses (Fig. 10): Fig. 10. Interwall transparency and interwall potential model, where a is an interwall distance (~0.34 nm). Transparency Tper one C-C bond along the interwall distance (a) determines the radial current losses. Two different cases may be considered in this case: For example, if the larger shell possesses the zigzag chirality whereas chirality of the smaller one is armchair while distance between them is a = 13.54-12.88 = 0.66 nm (Fig.10), the radial current loss factor can be estimated as T = 3.469*10-6 per one C-C bond.

25. Radial Effects on physical Models for Multiwall Carbon-Nanotube Interconnects S. Bellucci, P.Onorato NANOSCIENCE AND NANOTECHNOLOGY, Frascati, September 22, 2010

29. Outline • We discuss potential performances of nanotube based interconnects,starting from the dependence of the number of electrically active channels on both the temperature and radii of the innermost, as well as the outermost tube. • For a small innermost radius, we show that the presence of a geometrical potential can be quite relevant, while the intershell tunneling can be quite relevant in determining  the number of electrically active channels, when the radius of the outermost shell becomes of the order of hundreds of nm.

32. Conclusions

33. Thank you for your attention! stefano.bellucci@lnf.infn.it This research is supported by grant EC FP7 ICT-2007-1, Proposal for 21625 CATHERINE Project (2008-2010): Carbon nAnotube Technology for High-speed nExt-geneRation nano-InterconNEcts. S. Bellucci and P. Onorato, The role of the geometry on Multiwall Carbon-Nanotube Interconnects, JOURNAL OF APPLIED PHYSICS 108, 1 2010

34. Effectiveness of microwave electromagnetic shielding in carbon based epoxy nanocompositesS. Bellucci, L. Coderoni, F. Micciulla, I. Sacco,Frascati National Laboratory, National Institute of Nuclear Physics, Italy P. Kuzhir, A. Paddubskaya, D. Bychanok, A. Plyusch, S.Slepyan, M. Shuba,S. Maksimenko,Institute for Nuclear Problem, Belarusian state University, Belarus G. Rinaldi,University of Rome “Sapienza”, Rome, Italy J. Macutkevic, D.Seliuta, G. Valusis,Semiconductor Physics Institute, Lithuania J. BanysUniversity of Vilnius, Lithuania FrascatiNationalLaboratories, Frascati, 29 November 2010

35. Motivation EM pulse in airplanes Unauthorized access to information networks EM Shielding EM-Shielding Information Technology Shielding Wireless Handset Shielding • Nano-sized inhomogeneities in dielectric media (i) spatial confinement of charge carriers, thereby providing a discrete spectrum of energy states (ii) nanoscale inhomogeneity of electromagnetic fields in them. • New materials with high shielding effectiveness and suitable mechanical and physical-chemical properties (weight, corrosive resistance, mechanical properties, etc) can significantly increase Electromagnetic compatibility; prevent unauthorized access to information networks; reduce impact on electronic devices from EM pulse attack; reduce parasitic radiation from junctions, trailers, transmission lines; improve technical characteristics of microwave elements, circuits and devices. • Design of wide-band electromag-netic coatings with controlled properties.

36. FP7-INCO-2010-6 BY-NanoERA: Institutional Development of Applied Nanoelectromagnetics: Belarus in ERA Widening New research discipline comprising classical Electrodynamics of microwaves and present day concepts of condensed matter physics covered by FP7 Theme 4 'Nanoscience, Nanotechnology, Materials and new Production Technologies – NMP'. (nanocarbon) Based on research results and their applications in material sciences and medicine the activities will support RTD in applied nanoelectromagnetics contributing to creation of European research network 2010-2013

37. Coordination and support actions Coordinator: Sergey Maksimenko

38. ISTC projectB-1708 and the Italian Ministry PRIN 2008 research program Development and Electromagnetic Characterization of Nano Structured Carbon Based Polymer CompositEs (DENSE) 2010-2012

39. Coordination and support actionsCoordinator: Vincenzo Tucci

40. Influence of CNT topology (including constraints and defects) on nanocomposites. Both phenomenological and atomistic models to be involved. • Stability of CNT (graphene)- polymeric matrix interface, influence of defects beginning with single vacancies on their atomic and electronic structure (quantum chemical + MD simulations). • Simulation of electrical and mechanical properties for perfect and defective CNT (using both continuum and atomistic models). • Statistics of defect concentration in the proximity of the interface with the polymer matrix and along the CNT. • Innovative aspects of the research proposed by the LNF unit: • -The development of multi-scale models, in order to simulate carbon nanostructures for nanocomposites • -Simulation procedures taking into account defects and doping.

41. EM analysis in quasi-static regime • SWNT in small percentage give a significant impact into permittivity • Since Re and Im dielectric function are approx equal for SWNT/resin composites they should yield high absorption of EM radiation • MWNT contribute significantly, but 3 orders of magnitude less than SWNT • CB in small percentage (0.5wt%) does not have an impact into EM response of CB/resin samples

42. Percolation effect Percolation networks Sheng Wang, “Characterization and analysis of electrical conductivity properties of nanotube composites”, FSU master’s thesis, 2004 Philippe Gonnet, “Thermal Conductivity and Coefficients of Thermal Expansion of SWNTs/Epoxy Nanocomposites”, FSU master’s thesis, 2004 Schematic view of a representative 3D element with randomly dispersed CNTs. Ning Hu et al.“The electrical properties of polymer nanocomposites with carbon nanotube fillers”(April 2008) Nanotechnology 19:215701 Scheme of percolation phenomenon in composite material

43. Microwave probing Ka-band(26-37,5 GHz), X-band (8-12GHz) and W-band (78-118GHz) Figure. S-parameters collected for nanocarbon (0.5 wt.%) based resin composites in X-, Ka- and W-bands • In contrast to low-frequency data microwave probing does not demonstrate significant impact of the type of CNTs used for the EM analysis. The reason is that in microwave frequencies the internal shells of MWNT are less effectively involved in the EM interaction due to screening effect of outer one. The multiple-reflection within MWNT internal shells could also affect the overall EM shielding effectiveness. • As distinct from classical electromagnetic CB-based materials, whose EM response is caused mostly by absorbing mechanism, the EM shielding effectiveness provided by both types of CNT incorporated into resin is determined in X-band (8-12 GHz) equally by EM reflection and absorption. Contrary, in W-band the contribution of microwaves absorption is 3 times higher for SWNT/resin and 1,5 times higher for MWNT based composites than EM reflection. In Ka-band, the contribution of EM reflectance is decisive: the reflection provided by MWNT/resin composites is 20 times higher than absorption; SWNT provided 4.4 times higher reflection.

44. Modeling: electromagnetic response theory Maxwell Garnett homogenisation procedure N- number of CNT in the unit volume Boltzmann transport equation Fermi distribution function Dependence of reconstructed and theoretically modified permittivity for SWNT/epoxy composite

45. Modeling: electromagnetic response theory • We see that SWNT produced via ultra large-scale technology way do not demonstrate high EM shielding effectiveness in X-, Ka and W-bands in such a small CNT concentration as 0.5 wt%. • The easiest way to improve the EM shielding ability is to increase the CNT concentration up to at least 1.5 wt%: the increase of nanocarbon concentration from 0.5 to 1.5wt% shall lead to the decrease of the EM transmittance through the sample by a factor 2.

46. Modeling: electromagnetic response theory.Conclusions • The theoretical predictions prove that the EM shielding effectiveness for the CNT based polymer composites is determined mostly by the CNT conductivity. • Consequently, utilizing well purified or defect-free CNT (that is CNT with higher conductivity) can improve significantly the EM shielding effectiveness of such composites not changing the fraction of nanocarbon inclusions. • One more way to improve drastically the conductivity of CNT and therefore to suppress the microwave signal transmittance through the CNT based polymer composite is to use chemically modified (boron- or nitrogen doped) CNT. Indeed, in that case semiconducting CNTs that normally interact weakly with the electromagnetic radiation become metallic due to the increase of the charge carriers in the Fermi level, which could lead finally to the significant rise of the EM shielding performance.

47. Conclusions SWNT/epoxyand MWNT/epoxy composites could offer could good shielding performances in the microwave frequency range with very low percolation thresholdthat cannot be achieved by classical EM materials BOTH types of CNT could be used for fabrication of effective electromagnetic materials on the basis of epoxy resin