Axial point groups: rank 1, 2, 3 and 4 property tensor tables

2015 ◽  
Vol 71 (3) ◽  
pp. 346-349
Author(s):  
Daniel B. Litvin
Keyword(s):  
Magnetic Field ◽  
Magnetic Structure ◽  
Infinite Series ◽  
Point Group ◽  
Physical Property ◽  
Induced Polarization ◽  
One Dimensional ◽  
Point Groups

The form of a physical property tensor of a quasi-one-dimensional material such as a nanotube or a polymer is determined from the material's axial point group. Tables of the form of rank 1, 2, 3 and 4 property tensors are presented for a wide variety of magnetic and non-magnetic tensor types invariant under each point group in all 31 infinite series of axial point groups. An application of these tables is given in the prediction of the net polarization and magnetic-field-induced polarization in a one-dimensional longitudinal conical magnetic structure in multiferroic hexaferrites.

On physical property tensors invariant under line groups

2014 ◽  
Vol 70 (2) ◽  
pp. 138-142 ◽  
Author(s):  
Daniel B. Litvin
Keyword(s):  
Symmetry Group ◽  
Point Group ◽  
Physical Property ◽  
One Dimensional

The form of physical property tensors of a quasi-one-dimensional material such as a nanotube or a polymer can be determined from the point group of its symmetry group, one of aninfinitenumber of line groups. Such forms are calculated using a method based on the use of trigonometric summations. With this method, it is shown that materials invariant under infinite subsets of line groups have physical property tensors of the same form. For line group types of a family of line groups characterized by an indexnand a physical property tensor of rankm, the form of the tensor for all line group types indexed withn>mis the same, leaving only afinitenumber of tensor forms to be determined.

scholarly journals Ferroelectricity and magnetic orderings in Delafossite family compounds

2014 ◽  
Vol 70 (a1) ◽  
pp. C385-C385
Author(s):  
Noriki Terada
Keyword(s):  
Magnetic Field ◽  
Magnetic Structure ◽  
Ferroelectric Phase ◽  
Point Group ◽  
Ferroelectric Polarization ◽  
Theoretical Formula ◽  
Temperature Phase ◽  
Zero Field ◽  
General Direction ◽  
Dm Effect

Since discovery of the ferroelectric polarization induced by magnetic field in CuFeO2, delafossite family compounds have attracted much attention, because some theoretical formula, which had been presented, could not explain the ferroelectric polarization of CuFeO2. We have been investigating correlation among their magnetic orderings, lattice symmetry and ferroelectric polarization in AFeO2 (A=Cu, Ag, Na) systems. In CuFeO2, the ferroelectric polarization is induced by chemical substitutions for Fe sites in CuFe1-xBxO2 (B=Al, Ga, Rh, Mn) as well as magnetic field. The magnetic structure in the ferroelectric phase is proper screw type with magnetic point group 21' determined by the neutron diffraction experiments.[1] The ferroelectric polarization parallel to the propagation vector in CuFeO2 can be explained by both extended inverse-Dzyaloshinsky-Moriya(DM) effect and d-p hybridization mechanism. We have also demonstrated that the spin-orbit interaction in Fe ions, coupling spin and orbital orders, plays a crucial role to the ferroelectricity in both of which break the crystal symmetry, by observing incommensurate 2q orbital modulation in the ferroelectric phase of CuFe1-xGaO2 by soft X-ray resonant diffraction.[2] When nonmagnetic Cu ions on A-site are substituted by Ag or Na ions, the magnetic orderings are completely modified from CuFeO2. In AgFeO2, cycloid type magnetic structure with m1' point group is stabilized, which is concomitant with ferroelectric polarization, as the lowest temperature phase in zero-field.[3] Also in alpha-NaFeO2, the other type of cycloidal ordering (m1') appears mainly in magnetic field. In these systems, taking account of extended inverse DM effect, ferroelectric polarization direction is along general direction in the ac plane and does not follow the well-known inverse DM formula. In this presentation, I will discuss the relationship between the magnetic ordering and ferroelectricity in these delafossite family compounds.

THE MAGNETIC INDUCED POLARIZATION (MIP) METHOD

Geophysics ◽  
1974 ◽  
Vol 39 (3) ◽  
pp. 321-339 ◽  
Author(s):  
Harold O. Seigel
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Current Flow ◽  
Field Tests ◽  
Physical Property ◽  
Induced Polarization ◽  
Single Frequency ◽  
Polarization Current ◽  
Galvanic Current ◽  
The Time Domain

The magnetic induced polarization (MIP) method derives information relating to the induced polarization characteristics of the earth through measurements of the magnetic fields associated with galvanic current flow. In the time domain, transient magnetic fields due to polarization current flow are measured. In the frequency domain, either the change in magnetic field with frequency or the phase shift of the magnetic field at a single frequency may be measured. The MIP method responds to regions of anomalous polarization, rather than providing physical property information. It tends to emphasize induced polarization effects in highly conducting bodies. It has special merit in certain problem areas, for example, where highly conducting overburden exists, or where the surface conditions render ground contact difficult. The results of field tests are presented where surveys using the MIP method have been carried out over “massive” and disseminated types of sulfide bodies or graphitic zones.

scholarly journals Sheath size and Child–Langmuir law in one dimensional bounded plasma system in the presence of an oblique magnetic field: PIC results

2021 ◽  
Vol 28 (8) ◽  
pp. 083501
Author(s):  
J. Moritz ◽  
S. Heuraux ◽  
E. Gravier ◽  
M. Lesur ◽  
F. Brochard ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Plasma System ◽  
One Dimensional ◽  
Bounded Plasma ◽  
Oblique Magnetic Field

scholarly journals Hamiltonian Approach to Magnetic Fields with Toroidal Surfaces

1985 ◽  
Vol 40 (10) ◽  
pp. 959-967
Author(s):  
A. Salat
Keyword(s):  
Magnetic Field ◽  
Hamiltonian System ◽  
Magnetic Fields ◽  
Constant Pressure ◽  
Time Dependent ◽  
Hamiltonian Approach ◽  
One Dimensional ◽  
Mhd Equilibrium ◽  
Magnetic Surfaces ◽  
Rotational Transform

The equivalence of magnetic field line equations to a one-dimensional time-dependent Hamiltonian system is used to construct magnetic fields with arbitrary toroidal magnetic surfaces I = const. For this purpose Hamiltonians H which together with their invariants satisfy periodicity constraints have to be known. The choice of H fixes the rotational transform η(I). Arbitrary axisymmetric fields, and nonaxisymmetric fields with constant η(I) are considered in detail.Configurations with coinciding magnetic and current density surfaces are obtained. The approach used is not well suited, however, to satisfying the additional MHD equilibrium condition of constant pressure on magnetic surfaces.

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