Magnetoresistance

Table of Contents

Introduction

Magnetoresistance is the property of a material to change its electrical resistance in response to an applied magnetic field. This quantum mechanical phenomenon has profound applications in modern electronics and computing.

Basic Explanation

When a magnetic field is applied to a conductive material, the trajectories of the charge carriers (electrons or holes) can be curved due to the Lorentz force. This deflection leads to an increased path length for the charge carriers to traverse, leading to an increase in electrical resistance, a phenomenon referred to as magnetoresistance.

The basic magnetoresistance effect can be quantified as the relative change in resistance, $\Delta R/R_0$ , where $R_0$ is the resistance without the magnetic field and $\Delta R$ is the change in resistance due to the field:

$\dfrac{\Delta R}{R_0} = \dfrac{R(B) - R_0}{R_0}$

where $R(B)$ is the resistance in the presence of a magnetic field $B$ .

Types of Magnetoresistance

Classical Magnetoresistance

In metals at high temperatures or in high magnetic fields, the magnetoresistance tends to be positive, meaning the resistance increases with increasing magnetic field. This behavior is described by the Kohler’s rule:

$\dfrac{\Delta R}{R_0} = f\left(\dfrac{B}{\rho}\right)$

where $f$ is a scaling function and $\rho$ is the resistivity of the material with no magnetic field present.

Quantum Magnetoresistance

In certain systems at very low temperatures, resistance oscillations occur as a function of the magnetic field. This quantum magnetoresistance arises due to the quantum mechanical nature of the electrons and includes phenomena such as the Shubnikov–de Haas oscillations and the Quantum Hall effect.

Giant Magnetoresistance (GMR)

Giant magnetoresistance is a quantum mechanical magnetoresistance effect observed in thin film structures composed of alternating ferromagnetic and nonmagnetic layers. The resistance of the GMR structure changes significantly when the alignment of the magnetization in adjacent ferromagnetic layers changes relative to each other. The discovery of GMR led to a breakthrough in gigabyte hard disk drives and won the 2007 Nobel Prize in Physics.

Applications

Hard Disk Drives: Magnetoresistance is exploited in the read heads of hard disk drives. The resistance of the read head changes based on the magnetic field from the disk, enabling the reading of data.
Magnetic Field Sensors: Devices to measure magnetic fields can be designed using magnetoresistance effects, including sensors used in anti-lock braking systems in cars and in magnetic resonance imaging (MRI).
Magnetic Random Access Memory (MRAM): MRAM is a type of non-volatile memory that uses magnetic states (instead of electric charges) to store information. MRAM devices use magnetoresistance to read the stored information.

Conclusion

Magnetoresistance embodies the interplay between magnetism and electrical transport, two of the most fundamental properties in solid-state physics. Its discovery and exploitation continue to drive advances in data storage technology, sensing applications, and the development of magnetic memory devices.

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Introduction

Basic Explanation