Non-Linear Modes in Lithium Niobate Ferroelectrics with niobium antisite defects

Ferroelectric belongs to an important class of materials showing very interesting non-linear optical properties that have a variety of application in photonic devices In a discrete Hamiltonian, if we consider the space and time dependence of polarization vectors with an interaction term between two polarization domains, it gives rise to a nonlinear Klein-Gordon (K-G) equation that has been shown in some systems [Phys. Rev. B 86, 184101 (2012), and Phys. Rev.-B 81, 064104 (2010)]. This equation as a governing equation enables multiple time-scale analysis (MTSA) to be performed on a real ferroelectric material that reveals new type of information on both linear (known as soft modes) and the nonlinear parts of frequencies and amplitudes of oscillations. MTSA was described in a K-G system based on staggered polarization where more emphasis was given to reveal the presence of intrinsic localized modes (ILM). Here, detailed results for the first three linear modes and their frequencies as a function of a wide range of niobium antisite defects or, impurities in lithium niobate ferroelectric are presented. It is found that when an external excitation (i.e. the input) is only harmonic in nature, it could not be ascertained whether the even modes of the solitonic waves (i.e. the output) will have phase-locking with this type of harmonic external force.

The paper is organized as follows: In Section II, a brief description of the MTSA technique is given, in both linear and nonlinear forms, and at the end of this section three cases are presented for electric field and damping. In Section III, the results and discussion are given for linear modes and frequencies that are shown to depend on impurity content of lithium niobate as well as on upper limit of domain wall width. In Section III, the nonlinear modes, their frequencies and amplitudes are also shown. In Section IV, the conclusions are given.

A Bhattacharya, K Choudhary, S Das, L Vu-Quoc, and A K Bandyopadhyay - arXiv preprint arXiv: …, 2016

Molecular Bose-Einstein Condensation and Bound States in Lithium Niobate

The most outstanding experimental discovery in recent times is Bose-Einstein condensation (BEC) in 1995 and excellent reviews on BEC exist in the vast ocean of literature (Ketterle, Rev. Mod. Phys. 74, (2002)1131). This has triggered both theoretical and experimental works on this fascinating topic of research. The reasons for these vigorous activities are: a) it gives an opportunity to open a new window for a macroscopic view of quantum mechanics, and b) it makes such studies most interesting in the field of matter-wave relations. Experiments show nonlinear excitation within the wave that is known as solitons, and the properties of such bosonic particles in a condensate could manipulate them in periodic or other potential. Some evidence exists for the formation of both dark and bright solitions in the condensate, but the concept of bound state still remains somewhat illusive, despite a lot of activities on nonlinear optical systems that are important for many devices. This could create motivation to study bound state with a connection to BEC.

      Further, both lower and upper bounds are found out in relation to frequency and the extent of condensation in the bound state. Although ferroelectrics data are used for general theoretical study, it can also be extended to other relevant systems, e.g. in magnon system with two-well Landau potential (Demokritov, Nature, 433, (2006) 430). This effort is made through Klein-Gordon (K-G) model which on perturbation gives rise to NLSE that is a variant of GPE, which is somehow popular and commonly used for studying BEC. Landau-Ginzburg (L-G) potential is used in our discrete Hamiltonian for nonlinear optical materials like ferroelectrics (Phys. Rev. B 81, (2010) 064104) and metamaterials (Phys. Rev. B 84, (2011) 155429) to probe localization for discrete breathers. Also, a perturbation on our K-G model gives rise to NLSE (Phys. Rev. B 86, (2012) 184101) and showed both bright and dark solitons with ‘discrete energy levels’, estimated via hypergeometric function.

      The coherent molecular BEC was shown in one-dimension by mean field theories of parametric nonlinearities that convert two solitons to one (and vice-versa) for non-integrable equations (Drummond, Phys. Rev E 54, (1996) 896). Molecular BEC was invoked for a reaction between molecules to engineer condensates of heavier molecules where macroscopic occupation of single molecular quantum state gives rise to the coherent bosonic stimulation (Kokkelman, Phys Rev. A 63, (2001) R031601).  BEC was also reported on lithium molecules in an optical trap with spin mixture of fermionic Li atoms by measuring a collective excitation mode (Denschlag, Science 302, (2003) 2101). This gives rise to further motivation to theoretically explore BEC in the realm of bound state that might help towards better understanding of switching phenomenon in a vast area of devices including many nano devices involving lithium niobate. The intention is to show that molecular BEC formation is possible in this system that is described by frequency and temperature in the bound state.

      The dark and bright solitons in lithium niobate ferroelectric are already established in Klein-Gordon lattice. For small oscillations, the modal dynamics is characterized as bound states, revealed via associated Legendre polynomial. Bose Einstein condensation takes place around bosonic particles having different wave functions within the bound states in the temperature region T = 0 to T_c. The pairing and interplay between the dark and bright solitons occur with their effect on the condensation. The bound state disappears after a critical frequency (i.e. equivalent to a critical temperature). The quasi-particles then become phonons in the unbound states that propagate through the domains, when scattering length increases.

      Despite mathematical rigour, the physics of the above work may not be palatable by many relevant Physics Journals. However, a recent effective mass calculation shows the temperature of BEC formation lies in the range of micro-Kelvin.

https://arxiv.org/abs/1612.09494

Quantum Breathers and Phonon Bound State in the Ferroelectric System

Lithium niobate and lithium tantalate are technologically very important ferroelectric materials with a low poling field that have several applications in the field of photonics and memory switching devices. In a Hamiltonian system, such as dipolar system, the modal dynamics of such ferroelectrics can be well-modeled by a nonlinear Klein-Gordon (K-G) equation. Due to strong localization coupled with discreteness in a nonlinear K-G lattice, there is a formation of breathers and multi-breathers that manifest in the localization peaks across the domains in polarization-space-time plot. Due to the presence of impurities in the structure, dissipative effects are observed. To probe the quantum states related to discrete breathers, the same K-G lattice is quantized to give rise to quantum breathers (QBs) that are explained by a periodic boundary condition (Bloch state). The gap between the localized and delocalized phonon-band is a function of impurity content that is again related to the effect of pinning of domains due to antisite defects, i.e. a point of easier switching, which is related to Landau coefficient (read, nonlinearity). Secondly, in a non-periodic boundary condition approach, the temporal evolution of quanta shows interesting behavior in terms of ‘critical’ time of redistribution of quanta that is proportional to QB’s lifetime in femtosecond having a possibility for THz and other applications in quantum computation.  Hence, the importance of both of these methods for characterizing quantum breathers is shown in these perspectives.

In Book (January, 2014): "Computational and Experimental Chemistry", (Chapter: New Developments in Computational and Experimental Chemistry), Publisher: Apple Academic Press, New Jersey, Editors: T. Chakraborty, M. J. Bucknum, E. A. Castro, pp.245-278

Spin-exchange interaction between transition metals and metalloids in soft-ferromagnetic metallic glasses

High performance magnetic materials are of immense industrial and scientific importance in wide ranging electronic, electromechanical, and medical device technologies. Metallic glasses, with fully amorphous structure, are particularly suited for advanced soft-magnetic applications due to their homogeneous and isotropic structure down to the atomic scale. However, fundamental scientific understanding of spin-exchange interaction between the metal and metalloid atoms (that typically constitute a metallic glass) and the resulting desirable magnetic behavior is lacking. Using an integrated experimental and molecular dynamic approach, we demonstrate the mechanism of electron interaction between transition metals and metalloids which results in the enhanced magnetic properties of amorphous metallic alloys. Spin-exchange interactions were investigated for a Fe-Co metallic glass system of composition [(Co_1−xFe_x)_0.75B_0.2Si_0.05]₉₆Cr₄. The saturation magnetization was found to increase with increasing Fe concentration. Ab-initio molecular dynamics simulation was used to identify the ferromagnetic/anti-ferromagnetic interaction between the transition metals and metalloids. The overlapping band-structure and density of states represent “Stoner type” magnetization for the amorphous alloys in contrast to “Heisenberg type” in crystalline iron. The enhancement of magnetization by increasing iron was attributed to the interaction between Fe 3d and B 2p bands, which was further validated by valence-band study.

Recent research on engineered magnetic materials is primarily driven by cutting-edge technologies in magnetic storage, electro-magnetic shielding, magnetic flux-gate sensors, magnetic switches, micro-electromechanical systems (MEMS), and medical devices. Amorphous metals are particularly of interest in this regard due to their grain boundary-free isotropic structure, which results in exceptional magnetic properties. This paper deals with the issue with a good back-up of DFT calculations.

J. Phys. – Cond. Matter, Vol. 28 (2016) 216003 (9 pages)