Magnetic Neutron Scattering in Dysprosium Aluminum Garnet. I. Long-Range Order

1969 ◽  
Vol 186 (2) ◽  
pp. 557-566 ◽  
Author(s):  
J. C. Norvell ◽  
W. P. Wolf ◽  
L. M. Corliss ◽  
J. M. Hastings ◽  
R. Nathans
Keyword(s):  
Neutron Scattering ◽  
Long Range ◽  
Range Order ◽  
Long Range Order

scholarly journals Long-range order and low-energy magnetic excitations inCeRu2Al10studied via neutron scattering

2010 ◽  
Vol 82 (10) ◽  
Author(s):  
Julien Robert ◽  
Jean-Michel Mignot ◽  
Gilles André ◽  
Takashi Nishioka ◽  
Riki Kobayashi ◽  
...  
Keyword(s):  
Neutron Scattering ◽  
Long Range ◽  
Range Order ◽  
Low Energy ◽  
Long Range Order ◽  
Magnetic Excitations

Neutron Scattering Study Of Antiferromagnetic Correlations In The Zn-Mg-Ho Icosahedral Quasicrystal

1998 ◽  
Vol 553 ◽  
Author(s):  
Taku J. Sato ◽  
Hiroyuki Takakura ◽  
An Pang Tsai ◽  
Kaoru Shibata ◽  
Kenji Ohoyama ◽  
...  
Keyword(s):  
Neutron Scattering ◽  
Long Range ◽  
Diffuse Scattering ◽  
Icosahedral Phase ◽  
Range Order ◽  
Icosahedral Quasicrystal ◽  
Long Range Order ◽  
Range Magnetic Order ◽  
Powder Samples ◽  
Neutron Scattering Study

AbstractMagnetism in the Zn-Mg-Ho icosahedral quasicrystal has been studied by neutron scattering. Powder samples of the icosahedral and related crystalline phases were reexamined to clarify the origin of the previously-reported long-range magnetic order [Charrier et al., Phys. Rev. Lett. 78 (1997) 4637]. The long range order was found to originate from the related crystalline phase, which is a contaminant in the previously-used samples. Whereas for high-quality icosahedral phase, we could detect only magnetic diffuse scattering. This apparently shows the absence of the long range order in the icosahedral phase. The diffuse scattering was studied in detail by using a single quasicrystalline sample. It was found that the diffuse scattering appears as satellites from intense nuclear Bragg reflections. This indicates that corresponding spin correlations can be regarded as developed between spins on the six-dimensional virtual hypercubic lattice. A magnetic modulation vector for the correlations is proposed.

Superfluidity and Superconductivity

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Magnetic Field ◽  
Wave Function ◽  
Wave Packet ◽  
Long Range ◽  
Cooper Pair ◽  
Bose Condensation ◽  
Range Order ◽  
Condensed State ◽  
Long Range Order ◽  
Coherent Wave

Chapter 13 addresses Bose condensation in superfluids (and superconductors), which involves the field operator ψ‎ having a c-number component (<ψ(x,t)>≠0), challenging number conservation. The nonlinear Gross-Pitaevskii equation is derived for this condensate wave function<ψ>=ψ−ψ˜, facilitating identification of the coherence length and the core region of vortex motion. The noncondensate Green’s function G˜1(1,1′)=−i<(ψ˜(1)ψ˜+(1′))+> and the nonvanishing anomalous correlation function F˜∗(2,1′)=−i<(ψ˜+(2)ψ˜+(1′))+> describe the dynamics and elementary excitations of the non-condensate states and are discussed in conjunction with Landau’s criterion for viscosity. Associated concepts of off-diagonal long-range order and the interpretation of <ψ> as a superfluid order parameter are also introduced. Anderson’s Bose-condensed state, as a phase-coherent wave packet superposition of number states, resolves issues of number conservation. Superconductivity involves bound Cooper pairs of electrons capable of Bose condensation and superfluid behavior. Correspondingly, the two-particle Green’s function has a term involving a product of anomalous bound-Cooper-pair condensate wave functions of the type F(1,2)=−i<(ψ(1)ψ(2))+>≠0, such that G2(1,2;1′,2′)=F(1,2)F+(1′,2′)+G˜2(1,2;1′,2′). Here, G˜2 describes the dynamics/excitations of the non-superfluid-condensate states, while nonvanishing F,F+ represent a phase-coherent wave packet superposition of Cooper-pair number states and off-diagonal long range order. Employing this form of G2 in the G1-equation couples the condensed state with the non-condensate excitations. Taken jointly with the dynamical equation for F(1,2), this leads to the Gorkov equations, encompassing the Bardeen–Cooper–Schrieffer (BCS) energy gap, critical temperature, and Bogoliubov-de Gennes eigenfunction Bogoliubons. Superconductor thermodynamics and critical magnetic field are discussed. For a weak magnetic field, the Gorkov-equations lead to Ginzburg–Landau theory and a nonlinear Schrödinger-like equation for the pair wave function and the associated supercurrent, along with identification of the Cooper pair density. Furthermore, Chapter 13 addresses the apparent lack of gauge invariance of London theory with an elegant variational analysis involving re-gauging the potentials, yielding a manifestly gauge invariant generalization of the London equation. Consistency with the equation of continuity implies the existence of Anderson’s acoustic normal mode, which is supplanted by the plasmon for Coulomb interaction. Type II superconductors and the penetration (and interaction) of quantized magnetic flux lines are also discussed. Finally, Chapter 13 addresses Josephson tunneling between superconductors.

Sign in / Sign up

Export Citation Format

Share Document