Anomalous Hall effect formula

Unravel the Anomalous Hall Effect and its formula in this concise article. Dive into its terms, coefficients, and explore a practical calculation example.

Anomalous Hall Effect: Unraveling the Formula

The Anomalous Hall Effect (AHE) is a phenomenon that captures the essence of the interplay between charge carriers and magnetic fields in a solid state. Distinguished from its traditional counterpart, the ordinary Hall effect, AHE occurs even without an external magnetic field, being induced by the internal magnetic moments of the material.

The Fundamental Formula

The heart of the understanding of AHE lies in its formula:

1. σ_yx = R₀ρ + R_sM

Here, σ_yx is the Hall conductivity, ρ is the resistivity, M is the magnetization, and R₀, R_s are coefficients. It’s noteworthy to mention that the first term represents the ordinary Hall effect, whereas the second term introduces the anomalous component.

Unveiling the Terms

• σ_yx: It symbolizes the transverse conductivity – a measure of how effectively charge carriers can move perpendicular to an applied electric field.
• R₀ and R_s: These are called the ordinary and anomalous Hall coefficients, respectively. They represent the material’s intrinsic properties and can vary with temperature.
• ρ: This signifies the resistivity of the material, highlighting how strongly it can oppose the flow of electric current.
• M: The magnetization of the material, this term indicates the density of its internal magnetic moments.

In essence, the Anomalous Hall Effect formula eloquently encapsulates the complex relationship between a material’s electrical and magnetic properties. Understanding it offers us a potent tool to delve into the depths of condensed matter physics, spurring advancements in the realms of spintronics and magnetic data storage.

Example Calculation: Anomalous Hall Effect

Let’s illustrate how to calculate the Hall conductivity (σ_yx) using the Anomalous Hall Effect formula:

σ_yx = R₀ρ + R_sM

Suppose we have the following data for a ferromagnetic material:

• Ordinary Hall coefficient (R₀) = 0.1 Ω^-1 cm^-1
• Anomalous Hall coefficient (R_s) = 0.05 Ω^-1 cm^-1
• Resistivity (ρ) = 1.0 Ω cm
• Magnetization (M) = 1000 Gauss

First, we calculate the Ordinary Hall conductivity:

σ_{yx, ordinary} = R₀ρ

σ_{yx, ordinary} = 0.1 Ω^-1 cm^-1 x 1.0 Ω cm = 0.1 Ω^-1 cm^-1

Next, we compute the Anomalous Hall conductivity:

σ_{yx, anomalous} = R_sM

σ_{yx, anomalous} = 0.05 Ω^-1 cm^-1 x 1000 Gauss = 50 Ω^-1 cm^-1

Finally, we add the Ordinary and Anomalous conductivities to get the total Hall conductivity:

σ_yx = σ_{yx, ordinary} + σ_{yx, anomalous}

σ_yx = 0.1 Ω^-1 cm^-1 + 50 Ω^-1 cm^-1 = 50.1 Ω^-1 cm^-1

Thus, the Hall conductivity for this specific ferromagnetic material, according to the Anomalous Hall Effect, is 50.1 Ω^-1 cm^-1.