page_title: Voigt effect
section_title: Theory
hierarchical_section_title: Voigt effect / Theory
caption_attribution_description: English: Framework for the Voigt effect
context_page_description: The Voigt effect is a magneto-optical phenomenon which rotates and elliptizes linearly polarised light sent into an optically active medium. Unlike many other magneto-optical effects such as the Kerr or Faraday effect which are linearly proportional to the magnetization, the Voigt effect is proportional to the square of the magnetization and can be seen experimentally at normal incidence. There are several denominations for this effect in the literature: the Cotton–Mouton effect, the Voigt effect, and magnetic-linear birefringence. This last denomination is closer in the physical sense, where the Voigt effect is a magnetic birefringence of the material with an index of refraction parallel and perpendicular to the magnetization vector or to the applied magnetic field.
  For an electromagnetic incident wave linearly polarized and an in-plane polarized sample, the expression of the rotation in reflection geometry is is:
  and in the transmission geometry:
  ,
  where is the difference of refraction indices depending of the Voigt parameter, the material refraction indices and the parameter responsible of the Voigt effect and so proportional to the or in the case of a paramagnetic material.
context_section_description: As with the other magneto-optical effects, the theory is developed in a standard way with the use of an effective dielectric tensor from which one calculates systems eigenvalues and eigenvectors. As usual, from this tensor, magneto-optical phenomena are described mainly by the off-diagonal elements.
  Here, one considers an incident polarisation propagating in the z direction:  the electric field and a homogenously in-plane magnetized sample  where  is counted from the [100] crystallographic direction. The aim is to calculate  where  is the rotation of polarization due to the coupling of the light with the magnetization. Let us notice that  is experimentally a small quantity of the order of mrad.  is the reduced magnetization vector defined by  ,  the magnetization at saturation. We emphasized with the fact that it is because the light propagation vector is perpendicular to the magnetization plane that it is possible to see the Voigt effect.
caption: Framework and coordinate system for the derivation of Voigt effect. 
    
      
        
          
            
              
                
                  E
                  →
                
              
            
            
              i
            
          
        
      
      {\displaystyle {\vec {E}}_{i}}
    
  , 
    
      
        
          
            
              
                
                  E
                  →
                
              
            
            
              r
            
          
        
      
      {\displaystyle {\vec {E}}_{r}}
    
   and 
    
      
        
          
            
              
                
                  E
                  →
                
              
            
            
              t
            
          
        
      
      {\displaystyle {\vec {E}}_{t}}
    
   are referring to the incident, reflected and transmitted electromagnetic field.
exif: {}