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Introduction on Magnetic Sensing and Spin Electronics

Claude Fermon

DRF/IRAMIS/SPEC/LNO, CEA CNRS Paris Saclay, 91191 Gif sur Yvette Cedex, France

This introductory chapter provides the basic knowledge of magnetism and spin electronics, which will help the reader to understand the contents of the book. Then, after a brief introduction to magnetic fields, some bases of magnetic sensing and spin electronics are proposed. The last part of the chapter provides definitions that are useful for understanding spin electronics applications. More in-depth information can be found [1,2]. A number of books have been published on nanomagnetism [3], spin electronics [4,5], GMR [6], and spin dynamics [7], where each particular topic is discussed in detail.

1.1 Magnetic Fields

1.1.1 Introduction

Magnetism and magnetic field are known since thousands of years. First magnetic sensors were compass made of magnetite stones in China during the Han dynasty rule and later used by sailors to navigate. Today, magnetic objects, such as fridge magnets, are used as ornaments or for health purpose. In parallel, electricity is associated with electrons flowing in conductors and its use in domestic applications. Rotating magnetic fields seen by a coil is today the major source of electricity and, inversely, current in a coil produces magnetic fields like in MRI devices. The fundamental reason is that both are, in fact, identical depending on the reference frame taken. This has been highlighted by the well-known Maxwell equations that link electric fields and magnetic fields, one being the derivative of the other.

In parallel to the enormous importance of electricity in our life, electromagnetism has a fundamental property that justifies the billions of magnetic sensors and antennas produced each year: it is the only long-range interaction that we can create, modify, and detect. This long-range interaction property takes various forms. Light is an electromagnetic wave. Radiofrequency transmissions used for radio, TV, or mobiles are electromagnetic waves at lower frequencies. Static or low-frequency magnetic fields are the extremely low or zero frequency aspect of the same interaction.

1.1.2 Magnetic Field, Magnetic Induction, and Units

Historically, the magnetic field has been described by two different quantities. The first one is the field created by a magnet that has been called , the magnetic field intensity. The second one is the field created by a current that has been called , the magnetic induction.

It took some time to reconcile the two quantities that are proportional in the vacuum.

Magnetic field intensity H is given in A/m or in Oersted and magnetic field induction is given in Tesla or in Gauss. They are related by the following relation:

where is the magnetization of the material at the point where the field is measured. In the presence of vacuum or in nonmagnetic materials that quantity is 0. is a constant equal to

A/m is not a very useful quantity for a common comparison, and now nearly everybody is using Tesla or Gauss as a unit both for magnetic field intensity and induction. In this book, we will follow the same use knowing that this is just a commodity.

The relationship between these quantities is given in Table 1.1.

Table 1.1 Main fields units.

1.1.3 Magnetic Materials

Materials present various states of magnetism and they are classified into three main classes: diamagnetic materials, paramagnetic materials, and ordered magnetic materials. The first one, diamagnetic materials, corresponds to the large majority of materials. These materials present a very weak magnetization that is proportional and opposite of the applied magnetic field. This magnetization is due to the reaction of electrons. Their magnetization is then simply:

where the magnetic susceptibility is negative of the order of 10-6.

Superconducting materials like Niobium at very low temperature are also diamagnetic, but in that case, the susceptibility is nearly equal to -1.

Other materials, called magnetic materials, present an internal magnetization much higher than diamagnetic materials. That magnetization is created by unpaired electrons.

Magnetic materials are disordered at high temperature and become ordered below a critical temperature. When they are disordered, they are called paramagnetic materials and their magnetization can be written as (Eq. 1.2) with ? positive and relatively large, typically 10-3. Magnetic ordered materials are ferromagnetic, antiferromagnetic, or ferromagnetic. Table 1.2 gives a list of the materials you will encounter in this book with their order type and ordering temperature.

Table 1.2 Main magnetic materials found in this book.

Here, we do not consider pure rare earths that exhibit a larger variety of magnetic ordering. Some of them have a different kind of order as function of the temperature.

1.1.4 Magnetic Field Created by a Magnet

The magnetic field created by a magnet is the sum of the fields created by the individual components of the material. This principle of superposition is very important and is included in the Maxwell equations. This principle applies for both magnetic materials and fields created by electrical currents. However, in the determination of the field created by a magnetic material, one has to take care of the magnetization induced by the field created by the other parts of the magnetic material or by external currents. This field-induced effect is very important when you have magnetic cores inserted in coils.

The field created by a small magnet having a homogeneous magnetization taken, for example, along z at a large distance from it decreases at 1/r3 and has a shape given in Figure 1.1. This shape, called dipolar shape, will appear very often in this book. The formula of this field is as follows:

where is the distance from the small magnet considered as a point (Figure 1.1).

Figure 1.1 Dipolar shape created by a small magnet.

The main features to retain are this rapid decrease, the fact that the field created along has the same direction to , and the field created perpendicular is opposite to it and for the same value of r equal to ½ of the longitudinal field.

1.1.5 Magnetic Fields Created by Electrical Currents

In 1819, Hans Christian Oersted discovered that an electric current is able to generate a magnetic field. One year later, Jean-Baptiste Biot and Félix Savart wrote the famous Biot-Savart law that gave the magnetic field intensity as function of the current in an elementary element. This law is always used to calculate the field created by an arbitrary conductor. If we consider an element of length dl with a current I, the field created at a distance r is given by

For having in mind an order of magnitude, useful for understanding the various concepts described in this book, we are giving here two simple examples.

The first one is the field created by a long wire, assumed as infinite in its neighborhood (see...