• Title/Summary/Keyword: Landau free energy

Search Result 6, Processing Time 0.021 seconds

Phase Diagram of Spin Density Wave and $\pi$ Phase Shifted Superconductivity in the Fe Pnictide Superconductors (철 초전도체에서 스핀 밀도 파와 $\pi$ 위상 차 초전도성의 상전이 그림)

  • Lee, Na-Young;Choi, Han-Yong
    • Progress in Superconductivity
    • /
    • v.11 no.2
    • /
    • pp.112-117
    • /
    • 2010
  • We examine phase transition of the spin density wave and $\pi$ phase shifted superconductivity in the Fe pnictide superconductors. The phase diagram is described in the plane of the temperature T and the doping x with the combination of Ginzburg-Landau expansion of the free energy near the multi-critical temperature $T_c$ and the self-consistent numerical iterations of the gap equations. The phase separation or coexistence is determined by computing the 4-th order terms of the free energy which is confirmed by the numerical calculations. We can show the phase coexistence when the spin density wave is incommensurate. And the first order phase transition is observed near the boundary between commensurate and incommensurate spin density wave.

Holographic Polymer-Dispersed Liquid Crystals and Polymeric Photonic Crystals Formed by Holographic Photolithography

  • Kyu Thein;Meng Scott;Duran Hatice;Nanjundiah Kumar;Yandek Gregory R.
    • Macromolecular Research
    • /
    • v.14 no.2
    • /
    • pp.155-165
    • /
    • 2006
  • The present article describes the experimental and theoretical observations on the formation of holographic, polymer-dispersed, liquid crystals and electrically switchable, photonic crystals. A phase diagram of the starting mixture of nematic liquid crystal and photo-reactive triacrylate monomer was established by means of differential scanning calorimetry (DSC) and cloud point measurement. Photolithographic patterns were imprinted on the starting mixture of LC/triacrylate via multi-beam interference. A similar study was extended to a dendrimer/photocurative mixture as well as to a single component system (tetra-acrylate). Theoretical modeling and numerical simulation were carried out based on the combination of Flory-Huggins free energy of mixing and Maier-Saupe free energy of nematic ordering. The combined free energy densities were incorporated into the time-dependent Ginzburg-Landau (Model C) equations coupled with the photopolymerization rate equation to elucidate the spatio-temporal structure growth. The 2-D photonic structures thus simulated were consistent with the experimental observations. Furthermore, 3-D simulation was performed to guide the fabrication of assorted photonic crystals under various beam-geometries. Electro-optical performance such as diffraction efficiency was evaluated during the pattern photopolymerization process and also as a function of driving voltage.

Magneto-optical Measurements of Semiconductor Quantum Structures in Pulsed-magnetic Fields

  • Kim, Yongmin
    • Applied Science and Convergence Technology
    • /
    • v.23 no.1
    • /
    • pp.1-13
    • /
    • 2014
  • Semiconductor quantum structures are often characterized by their energy gaps which are modified by the quantum size effect. Energy levels in semiconductors can be realized by optical transitions within confined structures. Photoluminescence spectroscopy in magnetic fields at low temperatures has proved to be a powerful technique for investigating the electronic states of quantum semiconductor heterostructures and offers a complimentary tool to electrical transport studies. In this review, we examine comprehensive investigations of magneto-excitonic and Landau transitions in a large variety of undoped and doped quantum-well structures. Strong magnetic fields change the diamagnetic energy shift of free excitons from quadratic to linear in B in undoped single quantum well samples. Two-dimensional electron gas induced by modulation doping shows pronounce quantum oscillations in integer quantum Hall regime and discontinuous transition at ${\nu}=1$. Such discontinuous transition can be explained as the formation of spin waves or Skyrmions.

Magnetoresistance Effects of Magnetic Tunnel Junctions with Amorphous CoFeSiB Single and Synthetic Antiferromagnet Free Layers (비정질 CoFeSiB 단일 및 합성형 반강자성 자유층을 갖는 자기터널접합의 자기저항 효과)

  • Hwang, J.Y.;Kim, S.S.;Rhee, J.R.
    • Journal of the Korean Magnetics Society
    • /
    • v.15 no.6
    • /
    • pp.315-319
    • /
    • 2005
  • To obtain low switching field ($H_{SW}$) we introduced amorphous ferromagnetic $Co_{70.5}Fe_{4,5}Si_{15}B_{10}$ single and synthetic antiferromagnet (SAF) free layers in magnetic tunnel junctions (MTJs). The switching characteristics for MTJs with structures $Si/SiO_2/Ta$ 45/Ru 9.5/IrMn 10/CoFe 7/AlOx/CoFeSiB 7 or CoFeSiB (t)/Ru 1.0/CoFeSiB (7-t)/Ru 60 (in nm) were investigated and compared to MTJs with $Co_{75}Fe_{25}$ and $Ni_{80}Fe_{20}$ free layers. CoFeSiB showed a lower saturation magnetization of $560 emu/cm^3$ and a higher anisotropy constant of $2800\;erg/cm^3$ than CoFe and NiFe, respectively. An exchange coupling energy ($J_{ex}$) of $-0.003erg/cm^2$ was observed by inserting a 1.0 nm Ru layer in between CoFeSiB layers. In the CoFeSiB single and SAF free layer MTJs, it was frond that the size dependence of the $H_{SW}$ originated from the lower $J_{ex}$ experimentally and by micromagnetic simulation based on the Landau-Lisfschitz-Gilbert equation. The CoFeSiB SAF structures showed lower $H_{SW}$ than that of NiFe, CoFe and CoFeSiB single structures. The CoFeSiB SAF structures were proved to be beneficial far the switching characteristics such as reducing the coercivity and increasing the sensitivity in micrometer to submicrometer-sized elements.

Shape Dependent Coercivity Simulation of a Spherical Barium Ferrite (S-BaFe) Particle with Uniaxial Anisotropy

  • Abo, Gavin S.;Hong, Yang-Ki;Jalli, Jeevan;Lee, Jae-Jin;Park, Ji-Hoon;Bae, Seok;Kim, Seong-Gon;Choi, Byoung-Chul;Tanaka, Terumitsu
    • Journal of Magnetics
    • /
    • v.17 no.1
    • /
    • pp.1-5
    • /
    • 2012
  • The coercivity of a single 27 nm-spherical barium ferrite (S-BaFe) particle was simulated using three models: 1) Gibbs free energy (GFE), 2) Landau-Lifshitz-Gilbert (LLG), and 3) Stoner-Wohlfarth (S-W). Spherically and hexagonally shaped particles were used in the GFE and LLG simulations to investigate coercivity with the different shape anisotropies. The effect of shape was not included in the S-W model. It was found that the models using a spherical shape resulted in a coercivity higher than the models using the hexagonal shape with both shapes having the same diameter. The coercivity estimated with the S-W model was approximately the same as that for the spherical-shape models, which indicates that spherical shape has no significant effect on the particle's coercivity at nanoscale.