## Abstract

Diagram methods are applied for evaluating the off‐diagonal (Hall) components of the ac effective magnetoconductivity tensor σ yx*(ω) in an inhomogeneous material for the case of low magnetic field. Closed expressions for σ ik*(ω) are obtained in two approximations, namely in the self‐consistent cumulant approximation and in the effective‐medium approximation (EMA). Our expression for σ ik*(ω) in the EMA coincides with the one obtained earlier by Fishchuk. The obtained results are applied to the model of a random binary mixture consisting of two conducting materials 1 and 2 with conductivity tensors σ ik(1) and σ ik(2) and volume fractions x and 1 − x, respectively. In the special case of σ ik(2) = 0 and ω = 0 the (dc) Hall conductivity σ yx* in both above‐mentioned approximations has a percolation threshold at some critical value X_{c}. In each approximation the value of x_{c} coincides with the one for the dc diagonal (ohmic) conductivity σ* taken in the same approximation: the self‐consistent cumulant approximation gives x_{c} = 1 – exp (−1/3), while in the EMA x_{c} is equal to 1/3.

Original language | English |
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Pages (from-to) | 431-440 |

Number of pages | 10 |

Journal | physica status solidi (b) |

Volume | 180 |

Issue number | 2 |

DOIs | |

State | Published - 1 Jan 1993 |

Externally published | Yes |

## ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics