ENERGY LEVELS IN IRON-DOPED SAPPHIRE.

Abstract

Energy levels of the ferric ion in a sapphire lattice are machine-calculated as a function of applied magnetic field and polar and azimuthal angles. The levels are derived for a spin 5/2 system, wherein the Spin Hamiltonian contains one coordinate system pertaining to the cubic system and another for a trigonal system. Use is made of the rotation matrix and a set of functions belonging to an irreducible tensor operator of rank L = 4 to transform the cubic part of the Spin Hamiltonian operator into the trigonal frame of reference, and matrix elements are then calculated. As a check, the matrix elements of the cubic operator are first calculated in the cubic system, and then transformed into the trigonal system. In this connection, a table of the matrix elements of the rotation operator d(5/2) (Beta) is presented, as well as some of the matrix elements of d(4) (Beta) used in the first approach. (Author)

Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1966
Accession Number
AD0648480

Entities

People

  • Irving Lessin

Organizations

  • Air Force Cambridge Research Laboratories

Tags

DTIC Thesaurus Topics

  • Coordinate Systems
  • Energy Levels
  • Magnetic Fields
  • Rotation
  • Sapphire

Fields of Study

  • Physics

Readers

  • Business Analytics
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Materials Science and Engineering.