First-principles study of LiNbxM1-x O3 (M= V, W, Ta, Mo,…) for holographic memory applications

Abstract: For holographic memory applications, the photorefraction of well-known ferroelectric such as lithium niobate doped with different transition metals is very important. First principles study assumes special significance in this context, as to why certain transition metal atoms are better than the other. In this work, Nb atom in LiNbO3 was substituted with transition elements having valency greater than/equal to +5 for UV photorefraction applications, and atomistic first-principles calculations were done using HSE06 functionals. The d-states of the transitional elements were found to decrease the band-gap of the host material having implications for a suitable material design. Minimum band-gap was obtained for W, while Ta showed a maximum value. Absorption coefficients were estimated for each material and based on their low values at 351 nm (i.e. for holographic applications) that is the usual UV photo-refraction wavelength, the elements found suitable were V, W, Ta, Mo. Then birefringence properties for these crystals were also studied to predict that V and W were good candidates.

Some Descriptions: Lithium Niobate (LN) has gone through intensive research for its volume holographic data storage capability (Ashkin et al., App. Phys. Lett. 1966. 9, 72). The theory of the volume phase holograms in the birefringent electro-optic crystals  (LN) has been developed a long time ago via electrically controlled light diffraction and pattern reconstruction at a "READ" wavelength different from that of the "WRITING" beams (Petrov et al, Ferroelectrics 1978, 21, 631).

        Holographic data storage is a technique that can store information at high density inside the crystals with the volume of the recording media used for data storage instead of just the surface. Opening up the inside of a material for storage, rather than just using its surface, yields huge improvements in capacity. In addition, unlike conventional technologies, which record and recover digital data bit by bit, holography has the ability to "read and write" millions of bits of data with a single pulse of light, enabling data-transfer rates of billions of bits per second with storing capacity of several Tbs.

            This subject remained dormant for quite some time. After a long break, the subject has been revived by an intensive activity on LN crystals doped with different transition elements (McMillen et al, Opt. Exp. 1998, 2, 491). The large crystal size of LN allows: (a) high capacity, (b) angular selectivity, (c) long storage lifetime, and (d) high diffraction efficiency. LN can also be used in optical "correlator type holographic data storage" applications, where analog images are accessed at high speed. In particular, angle-multiplexing type storage in LN has been observed where ‘optical correlation’ is used for data storage (Mok et al., Opt. Lett. 1993, 18, 915).

      Transition metal doped LN ferroelectric material is used for photo-refraction and volume data-storage. Although a multitude of such materials have been characterized in details, the explanation as to why only a few of them are preferred compared to others is still to be known. In the field of condensed matter physics, one of the well-studied materials is ferroelectric, which has a variety of important applications in nonlinear optics, such as electro-optics and second harmonic generation, and non-volatile memory devices (see Bandyopadhyay et al, Phys. Rev. 2010, B81, 064104, and references therein). Ferroelectrics have also emerged as important materials as piezoelectric transducers, pyroelectric detectors, surface acoustic wave (SAW) devices, four-phase mixing doublers. Such applications and many more as 'nano devices' are mentioned in the latter reference given above. One of the most important ferroelectric materials is LN that is widely used as an optical material for its various high frequency photonic and optoelectronics applications.

      Commonly Fe-doped LN is used for writing holograms in blue-green region of the visible spectrum, but in other part of electromagnetic spectrum, the ‘sensitivity’ is needed for inexpensive applications. In addition, LN:Fe has problems, such as  low response speed, strong light-induced scattering and volatility. Other transition elements such as Cu, Mn, Ni etc. have also been investigated for holography. Early attempt of doping with more than one transition elements in LN was made for various systems. Among transition elements, which were found to be suitable for holographic memory applications are: Sc, Zr, Hf, V, Mo, Mn, Fe, Ru and Cu. It was also found that the substituents occupying Li-sites were those having valence less than 5+ Hence, others were found to occupy Nb sites and were primarily used for studying UV-photo-refraction.

      Despite intensive experimental work, comparatively less theoretical investigation has been carried out on this subject, as well as on density functional theory (DFT) approach for atomistic descriptions. One of the pioneering investigations on the electronic structures and energetics of LN in comparison with those of another ferroelectric (LT) was done by Inbar and Cohen (Phys. Rev. 1996, B53, 1193) via ‘linearized augmented plane-wave’ (LAPW) frozen phonon calculations in order to shed light on phase transition and origin of ferroelectricity. Now, for the electronic and optical properties of LN, various levels of DFT calculations such as general gradient approximation (GGA) and GW calculations were carried out, and the "band gap" of LN was a crucial topic in the last few decades

            It has been evident that there is a necessity of studying the atomistic electronic properties, particularly in relation to 'band-gap engineering' of such photorefractive materials involving LN via density functional theory (DFT) approach. This assumes more importance due to the recent surge in the activity in the field of holographic memory applications. In the present work, for "holographic memory" applications, the photo-refraction of well-known ferroelectric such as lithium niobate doped with different transition metals is very important. First principles study assumes special significance in this context.

            In this work, Nb atom in LiNbO₃ was substituted with transition elements having valency greater than/equal to +5 for UV photo-refraction applications, and atomistic first-principles calculations were done using HSE06 functionals. The d-states of the transitional elements were found to decrease the band-gap of the host material having implications for a suitable material design. Absorption coefficients were estimated for each material and based on its low values at 351 nm (for holographic applications) that is the usual UV photo-refraction wavelength, the elements found suitable were V, W, Ta, Mo. Then birefringence properties for these crystals were also studied to predict that V and W were good candidates. Here, we study the dopants that have been used (or possibly used) for photo-refraction having valence more than 5+, namely V, Ta, Cr, Mo, W, Tc, Re, Ru, Os, Rh, Ir, Pt by using HSE06 hybrid functional for these calculations.

Finally, in the realm of 'band-gap engineering', the results show that tantalum (Ta) has the minimum impact, while tungsten (W) has the maximum effect on the host crystal on the reduction of 'band-gap' within the systems under the present investigation. Then, it was interesting to study the density of states (DOS) of such materials both in spin-up and spin-down conditions. It is quite pertinent to mention about an important work by Tong et al. (Phys. Rev. 2014, B89, 064404), who observed significantly different optical responses from spin-up and spin-down channels in case of multiferroic EuO via first principles DFT calculations.

Moreover, among few elements found suitable in this work, Ta is very well-known as nonlinear optical material showing the lowest absorption coefficient for LN:Ta at 0.1, although its band-gap is the highest (5.07 eV). However, for LN:W whose absorption coefficient is also very low at 0.2, its band-gap is the lowest (0.72 eV). This opens up a new field of work in the realm of "Band-Gap Engineering" of device material formulations to suit different applications. For example, in a recent work by Grinberg et al (Nature 2016, 503, 509), a 10% replacement of KNbO₃ by nickel-niobium based material decreased the band-gap to 1.39 eV to give rise to a very high level of photovoltaic efficiency in terms of high "photocurrent density for solar-energy conversion" and other important applications for this type of ferroelectric-semiconductor based materials.

It is pertinent to mention that in the present investigation with our DFT approach, a comparable band-gap was observed for LN:Re and LN:Rh and LN;Mo at 1.30 eV, 1.36 eV and 1.57 eV respectively. These materials could also be considered as competitive candidates for photoconduction based "Solar Energy" applications.

http://arxiv.org/abs/1709.01970

Multisolitons in SRR based Metamaterials in Klein-Gordon Lattice

Abstract:

             Solitons are the solutions of nonlinear partial differential equations whose modal behavior can be described by a nonlinear Klein-Gordon (NLKG) equation that is derived through variational principle based on a generalized Hamiltonian. It is known that solitons gives robust solutions that can retain their shape to a longer extent without any distortion and hence also treated as particles. In the realm of their application in nonlinear optical fibre communications as well as in various nano-structured devices, NLKG equation seems to be a better option. It is a PDE with 2^nd order spatial and temporal terms that describe the nonlinear modes in the communication systems involving both ferroelectrics and metamaterials that are well-known nonlinear optical materials. Here, we derive NLKG for metamaterials as split-ring-resonators (SRR) for the applications in antenna. Various parameters involved in the Hamiltonian indicate interesting behaviour against amplitude of magneto-inductive waves that also shows multi-soliton behaviour in the metamaterials system.

Keywords: Multi-solitons, Metamaterials, Variational Principle, K-G Equation.

            The prefix ‘meta’ in Greek means ‘beyond’ or ‘after’. This suggests that the "metamaterial" exhibits characteristics surpassing those in nature. The ‘electrodynamics of substances with both negative dielectric constant (e) and magnetic permeability (m) is very interesting indeed. They are predicted to possess a negative index of refraction, and consequently they exhibit a variety of optical properties that are not found in positive indexed materials. About fifty years ago, Veselago (Sov. Phys. Uspekhi 1968, 10, 509-514) was the first to create a theoretical foundation of whether the refractive index of materials can possess negative values, and predicted a number of unusual optical properties associated with such negative index materials (NIM). A lucid account of transforming this theory into reality, i.e. metamaterials, was later given by Litchinitser and Shalaev (J. Opt. Soc. Am. 2009, B26, 161-169) and elaborated in many other important investigations.

The fascinating world of optics deals with ‘light’ that is the ultimate means of sending information to and from the interior structure of materials. It packages data in a signal of zero mass and unmatched speed. However, light in a sense is ’one-handed’ when interacting with atoms of conventional materials. This is because from the two field components of light, i.e. electric and magnetic, only the electric-field probes the atoms of a material, whereas the magnetic-field component of light is normally weak. Metamaterials, i.e. artificial materials with rationally designed properties, can allow both field components of light to be coupled to the ‘metaatoms’, enabling entirely new optical properties and exciting applications with such ‘two-handed’ light. Among the interesting properties is a ‘negative refractive index’. The refractive index is one of the most fundamental characteristics of light–propagation in materials. With negative refractive index, metamaterials may lead to the development of a ‘superlens’ that is capable of imaging objects and fine structures, which are much smaller than the wavelength of light. Other exciting applications of metamaterials include ‘antennae’ with superior transmission properties, optical nanolithography and nanocircuits, and also ‘metacoatings’ that can make the objects invisible.        

In the field of applied physics, a fertile ground was created with the tremendous surge of research activity on nonlinear optical materials and devices involving ferroelectrics and metamaterials. For such materials, the use of non-integrable Klein-Gordon (K-G) equation with 2^nd order spatial and temporal terms is already described (see later for Bandyopadhyay et al in Phys. Rev. B) for modal behavior in various device applications including those in the nano-structured systems in terms of shape and velocity of the soliton. The main focus of this article is on the application of nonlinear K-G equation that could describe the modal behavior of soliton and multisoliton waves in metamaterials.

It may be pointed out that discrete solitons or discrete breathers (DBs) (also called ‘intrinsic localized mode’ or ILM) are observed both in the integrable (viz. sine-Gordon equation) and non-integrable systems (viz. Klein-Gordon equation). However, the integrability imposes a criterion for obtaining DBs analytically that is possible only in the integrable systems, while for the non-integrable systems it is obtained by various numerical methods viz. a) spectral collocation method, b) finite-difference method, c) finite element method, d) Floquet analysis, etc. As evident from many numerical experiments, DBs mobility is achieved by an appropriate perturbation (Tsironis et al, Phys. Rev. Lett. 1996, 77, 4776-4779). Within the ambit of integrable systems, although the above nonlinear differential equations, such as KdV equation, sine-Gordon equation and nonlinear Schrodinger equation (NLSE) give rise to soliton solutions, these equations are not discussed here in order to remain within our main focus on the derivation via Non-linear Klein-Gordon Equation, i.e. NLKG (Bandyopadhyay et al, Phys. Rev. 2010, B81, 064104-111; Phys. Rev. 2011, B84, 155429-437; Phys. Rev. 2012, B86, 184101-108)

In Book (September, 2017): "Computational Chemistry Methodology in Structural Biology & Materials Sciences", (Part II: Computational Chemistry Methodology in Materials Science) Publisher: Apple Academic Press, New Jersey (USA), Editors: T. Chakraborty, et al., pp.273-308.

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)

Discrete & Quantum Breathers in Metmaterials

Discrete Breathers:

In the field of Nonlinear Optical Materials, e.g. Metamaterials, for important applications of Discrete Breathers (DBs) or Intrinsic Localized Mode (ILM) (Sievers et al, PRL, 1988; Bandyopadhyay et al, PRB, 2010 and 2011) some systems are mentioned here: a) Solid State Mixed-Valence Transition Metal Complexes, b) Quasi-1D Antiferromagnetic Chains, c) Array of Josephson Junctions, d) Oscillators in  Micromechanical System, e) Optical Waveguide Systems, and also important molecules for biotechnology, such as f) Proteins.

DBs modify system properties viz. lattice thermodynamics and introduce the possibility of non-dispersive energy transport, because of their potential application for translatory motion along the lattice. These DBs are observed both in integrable and non-integrable systems.

Fano resonance due to DBs have also been studied by Flach et al (PRL, 2003) and were also explored in terms of some material parameters by Bandyopadhyay et al (JOSA-B, 2012). This type of study was important for various applications, e.g. in the (a) biosensing technology, (b) spectral selectivity, (c) beam filtering, etc.

Quantum Breathers:

           After DBs, next let us go to the applications of Quantum Breathers (QB) due to a possible interest in the field of Quantum Computation. To name a few: Reconfigurable Metamaterials (Quach et al, Optical Express, 2011) and Quantum Archimedean Screw for Superconducting Electronics using Metamaterials (Rakhmanov et al, PRB, 2008), and many others from Medicine to Aeorospace applications. There are so many other applications: a) Ladder Array of Josephson Junction for Superconductors, b) BEC in Optical Lattices or Nonlinear Photonic Lattices, c) Interacting Optical Waveguides, d) Cantilever Vibrations in Micro-mechanical Arrays, e) Macromolecules, such as DNA, f) Quantum Metamaterials based Superconductors, g) Modulation Instability-based Gadgets, g) Split-Ring-Resonator (SRR) based Metamaterials in Antenna Arrays, i.e. THz applications by minimizing losses (To Note: the ‘coherent quantum dynamics’ of ‘qubits’ determines the THz optical properties in the system) h) Two-Magnon Bound States (TMBS) in Antiferromagnets and  i) Two-Phonon Bound States (TPBS), i.e. Quantum Breathers as investigated by Fourier Grid Hamiltonian method. QBs can be generally described by both periodic (JAP, 2011a) and non-periodic boundary conditions (JAP, 2011b) respectively. The quantum-effect enabled systems via Metamaterials route will bring a range of exciting applications in the future (Zheludev, Opt. & Photon News, 2011).

Finally, another interesting application is mentioned here on the rectification of current density, i.e. Ratchet Solitons, (Flach et al, PRL, 2002;  Bandyopadhyay et al, JPD, 2013) through the analysis of symmetry and its violation in Metamaterials. The relevant applications are: (a) Molecular Motors and other Non-equilibrium Biological Systems, (b) Electric Currents in Superlattices, (c) Voltages in Coupled Systems, i.e. in annular Josephson Junctions revealing unidirectional Fluxon Motion that is driven by Biharmonic Microwaves, (d) Magnetic Flux Cleaning in Superconducting Films, (e) Abrikosov Vortex Diodes, and (f) Voltage Rectifiers.