Axelos, M. A. V. and Van de Voorde, M. (eds.)
Nanotechnology in Agriculture and Food Science
2017
Print ISBN: 9783527339891
Cornier, J., Kwade, A., Owen, A., Van de Voorde, M. (eds.)
Pharmaceutical Nanotechnology
Innovation and Production
2017
Print ISBN: 9783527340545
Mansfield, E., Kaiser, D. L., Fujita, D., Van de Voorde, M. (eds.)
Metrology and Standardization for Nanotechnology
Protocols and Industrial Innovations
2017
Print ISBN: 9783527340392
Meyrueis, P., Sakoda, K., Van de Voorde, M. (eds.)
Micro- and Nanophotonic Technologies
2017
Print ISBN: 9783527340378
Müller, B. and Van de Voorde, M. (eds.)
Nanoscience and Nanotechnology for Human Health
2017
Print ISBN: 978-3-527-33860-3
Puers, R., Baldi, L., van Nooten, S. E., Van de Voorde, M. (eds.)
Nanoelectronics
Materials, Devices, Applications
2017
Print ISBN: 9783527340538
Raj, B., Van de Voorde, M., Mahajan, Y. (eds.)
Nanotechnology for Energy Sustainability
2017
Print ISBN: 9783527340149
Sels, B. and Van de Voorde, M. (eds.)
Nanotechnology in Catalysis
Applications in the Chemical Industry, Energy Development, and Environment Protection
2017
Print ISBN: 9783527339143
All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.
Library of Congress Card No.: applied for
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
Bibliographic information published by the Deutsche Nationalbibliothek
The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.d-nb.de.
© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Boschstr. 12, 69469 Weinheim, Germany
All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law.
Print ISBN: 978-3-527-33985-3
ePDF ISBN: 978-3-527-69905-6
ePub ISBN: 978-3-527-69906-3
Mobi ISBN: 978-3-527-69907-0
oBook ISBN: 978-3-527-69850-9
Thanks to my wife for her patience with me spending many hours working on the book series through the nights and over weekends. The assistance of my son Marc Philip related to the complex and large computer files with many sophisticated scientific figures is also greatly appreciated.
Marcel Van de Voorde
Since years, nanoscience and nanotechnology have become particularly an important technology areas worldwide. As a result, there are many universities that offer courses as well as degrees in nanotechnology. Many governments including European institutions and research agencies have vast nanotechnology programmes and many companies file nanotechnology-related patents to protect their innovations. In short, nanoscience is a hot topic!
Nanoscience started in the physics field with electronics as a forerunner, quickly followed by the chemical and pharmacy industries. Today, nanotechnology finds interests in all branches of research and industry worldwide. In addition, governments and consumers are also keen to follow the developments, particularly from a safety and security point of view.
This books series fills the gap between books that are available on various specific topics and the encyclopedias on nanoscience. This well-selected series of books consists of volumes that are all edited by experts in the field from all over the world and assemble top-class contributions. The topical scope of the book is broad, ranging from nanoelectronics and nanocatalysis to nanometrology. Common to all the books in the series is that they represent top-notch research and are highly application-oriented, innovative, and relevant for industry. Finally they collect a valuable source of information on safety aspects for governments, consumer agencies and the society.
The titles of the volumes in the series are as follows:
The book series appeals to a wide range of readers with backgrounds in physics, chemistry, biology, and medicine, from students at universities to scientists at institutes, in industrial companies and government agencies and ministries.
Ever since nanoscience was introduced many years ago, it has greatly changed our lives – and will continue to do so!
March 2016 Marcel Van de Voorde
Marcel Van de Voorde, Prof. Dr. ir. Ing. Dr. h.c., has 40 years' experience in European Research Organisations, including CERN-Geneva and the European Commission, with 10 years at the Max Planck Institute for Metals Research, Stuttgart. For many years, he was involved in research and research strategies, policy, and management, especially in European research institutions.
He has been a member of many Research Councils and Governing Boards of research institutions across Europe, the United States, and Japan. In addition to his Professorship at the University of Technology in Delft, the Netherlands, he holds multiple visiting professorships in Europe and worldwide. He holds a doctor honoris causa and various honorary professorships.
He is a senator of the European Academy for Sciences and Arts, Salzburg, and Fellow of the World Academy for Sciences. He is a member of the Science Council of the French Senate/National Assembly in Paris. He has also provided executive advisory services to presidents, ministers of science policy, rectors of Universities, and CEOs of technology institutions, for example, to the president and CEO of IMEC, Technology Centre in Leuven, Belgium. He is also a Fellow of various scientific societies. He has been honored by the Belgian King and European authorities, for example, he received an award for European merits in Luxemburg given by the former President of the European Commission. He is author of multiple scientific and technical publications and has coedited multiple books, especially in the field of nanoscience and nanotechnology.
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.
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.
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.
| Quantity | Designation | Unit | Link |
| Magnetic field intensity | H | A/m (MKS) | In vacuum . |
| Oe: Oersted (CGS) | In vacuum 1Oe = 1G | ||
| Magnetic field induction | B | T: Tesla (MKS) | In vacuum . |
| G: Gauss (CGS) | 1G = 10−4 T |
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 χ 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.
| Material | Order | Temperature of ordering (K) | Comment |
| Co | Ferromagnetic | 1388 K | 3D metal |
| Fe | Ferromagnetic | 1043 K | 3D metal |
| Ni | Ferromagnetic | 627 K | 3D metal |
| Ni79Fe21 | Ferromagnetic | 553–871 | Very soft alloy called micrometal. Ordering temperature depends on crystal structure |
| CoFe | Ferromagnetic | 1360 | Used due to its large spin polarization |
| CoFeB | Ferromagnetic | 1300 | Used due to its large spin polarization and very soft material |
| PtMn | Antiferromagnetic | 1000 K | Used for spin electronics |
| IrMn | Antiferromagnetic | 700 K | Unsed for spin electronics |
| Fe3O4 | Ferrimagnetic | 948 K | Called magnetite |
| YIG (yttrium garnet) | Ferromagnetic | 560 K | Soft magnetic insulator used for its dynamic properties |
| Nd2FeB | Ferromagnetic | 593–673 | Rare earth-based hard magnet |
| Co2Sm17 | Ferromagnetic | 720 | Rare earth-based hard magnet |
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.
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.
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 Figure 1.2). The integration of the formula (1.3) is then
is the orthoradial component of the field. The two other components are 0 due to symmetry.
Figure 1.2 Field created by a wire and by a circular coil.
The field created by a circular loop can also be calculated by the (1.3) formula. Along the axis, the field is perpendicular to the coil plane and varies as follows:
Outside of the axis, the field has a dipolar shape, similar to the field created by a small magnet.
Nearly all devices presently fabricated are composed of thin films deposited on flat surfaces, typically silicon wafers. Industrial tools are now able to deposit these films on surfaces up to 300 mm with accuracy better than 0.1 nm and homogeneity on the whole surface better than 1 % of the thickness. Properties of these thin films are in general similar to bulk properties, but thin films may exhibit new features. For example, some films can be crystallized in a structure impossible to achieve with bulk materials. The second effect of thin-film geometry is to modify strongly the magnetic anisotropy of the magnetic materials.
Some films can be crystallized in relation to the wafer underneath, we are hence speaking about epitaxy. A lot of films are textured, that is, they are partially crystallized with a preferred direction imposed by the thin-film geometry. Some are nearly amorphous: an assembly of small grains with random directions. Conditions of deposition (method, temperature, and pressure) and annealing have a large impact on the final structure.
A magnetic material may have preferential axis of magnetization induced either by the crystalline anisotropy or by its shape. The crystalline anisotropy is due to the coupling between spin orientation and crystalline electric field. The minimization of the corresponding energy gives in general some preferred orientation.
That anisotropy may be very strong in crystalline materials. Rare earth-based materials present usually a very high magnetic anisotropy due to their orbital shape. It is the reason why the strongest permanent magnets are rare earth based.
A specific magnetic anisotropy appears also at the surface of the magnetic material. This is due to the breaking of the crystalline electric field symmetry at the interface. That anisotropy can be larger than the shape anisotropy and help to create magnetic thin films with a magnetization perpendicular to the plane. This is the case of, for example, a thin Co layer on Pt.
The shape anisotropy is simply due to the field created by each individual atom of the layer to the others. This field, called dipolar field or demagnetizing field, has a dipolar shape given in (Eq. 1.3). This field decreases as 1/r3, but as the number of atoms varies as r3 its impact at long distance is huge for ferromagnetic or ferrimagnetic materials. The first main effect of this shape anisotropy is to force magnetization to be in the plane of the film. This can be counteracted only by using very thin films having an additional surface anisotropy. The second effect of this shape anisotropy is to create domains, that is, parts of the films, where the magnetization has the same direction.
Dipolar interactions responsible for the shape anisotropy impose an overall magnetic configuration of the thin film that tends to minimize the overall energy. If the film is infinite, a uniform magnetization is the lowest energy state, but as soon as lateral dimensions are reduced, it costs dipolar energy to have a magnetization perpendicular to the edge more than rotating smoothly the magnetization inside the layer. For that reason, patterned objects in thin films acquire specific magnetic configurations that you will encounter in this book. Figure 1.3 gives examples of some classical shapes you will see with their stable state.
Figure 1.3 Typical magnetic domains observed in small objects. Arrows indicate the direction of magnetization and blue lines domain walls. In the cross of domain walls or in the center of the disk, the magnetization goes out of plane. This is called a vortex.
There is a large variety of magnetic sensors and it would take several books to describe all of them. Here, we are just giving some indications that will help the teacher to find more information. Some sensors such as Hall effect or inductive sensors have been developed since decades and now main innovations for these sensors are mainly coming from the integration of sophisticated electronics able to perform in real-time complicated algorithms. Others, such as NV sensors (Chapter 6), are very promising for specific applications and are at the stage of research and development. We decided to focus a part of this book on magnetoresistive sensors because they illustrate the dynamism of research in magnetism and are reaching large-volume applications that were mainly covered by Hall sensors. Table 1.3 provides some characteristic properties of the main magnetic sensors technologies.
Table 1.3 Main magnetic sensors technologies with some properties.
| Principle | Scalar/Vectorial | Operating temperature range | Field range | Frequency range | Linearity | Size | Material |
| Hall | Vect. | −200 °C/150 °C | 1 µT–10 T | DC-1 MHz | Good | µm–mm | Semiconductor |
| AMR | Vect. | −275 °C/200 °C | 1 nT–1 mT | DC-10 MHz | Limited | µm–mm | Ferromagnet |
| Optical | Vect. or scalar | Room temp. | 1 fT–1 µT | DC | Requires feedback | mm–cm | Alkali gas |
| GMI | Vect. | −50–150 °C | 10 pT–0.1 mT | DC-10 kHz | Requires feedback | mm–cm | Soft ferromagnet |
| Magnetoelectric | Vect. | −50–150 °C | 100 pT–1 mT | DC-1 kHz | Limited | 0.1 mm–cm | Composite |
| GMR/TMR | Vect. | −273–180 °C | 100 pT–10 mT | DC-GHz | Limited | µm | Multilayer |
| Coils | Vect. | −273–600 °C | 1 fT–10 T | AC | Excellent | 0.1 mm–m | Metal |
| Search coil | Vect | −50–200 °C | 1 fT–10 mT | AC | Excellent | 0.1 mm–1 m | Ferrite core |
| Fluxgate | Vect. | −50–200 °C | 5 pT–100 µT | DC-5 kHz | Good | 0.1 mm–5 cm | Ferrite core |
| SQUID | Vect. | −273–200 °C | 1 fT–10 µT | DC-100 kHz | Requires feedback | 0.1 mm–1 cm | Metallic |
The main sensor used for DC and low-frequency applications is the Hall sensor based on the Hall effect. When a field is applied on a material where a current is flowing, a voltage appears perpendicular to the current direction due to Lorentz force. This voltage is proportional to the field and the applied current through a factor RH called Hall resistance.
Today, Hall sensors represent 85 % of the world production of magnetic sensors for DC and low-frequencies applications with a growth of about 3 % per year. The main competitors are magnetoresistive sensors (AMR, GMR, and TMR) described in this book that represent only 10 % but are growing at an annual rate of about 10 %. Magnetoelectric sensors also appear in some commercial products. They present the advantage to be passive, but they cannot be integrated. Fluxgates are mainly used for very sensitive applications such as earth field mapping for field monitoring.
When the frequency is increased, the sensor used universally is the coil or antenna. The radiofrequency field creates a current inside a metallic wire that can be amplified and detected. As this current is proportional to the frequency, higher the frequency, the higher the sensitivity of a coil is. The electromagnetic wave is both an electric field and a magnetic field and antennas are designed to be more sensitive to electric fields, whereas coils are designed to be more sensitive to magnetic fields. There is, however, one specific case where coils/antennas are less competitive than magnetoresistive sensors: when the size becomes so small that it is impossible to build a performing coil. This has created two application cases for magnetoresistive sensors: nondestructive evaluation (see Chapter 5) and integrated position sensors.
The development of very sensitive sensors for low-frequency magnetic field detection is a domain where a very active research work is going on across the world. Table 1.4 describes the main sensors technologies for subpicotesla detection. Applications of very sensitive sensors are brain/body imaging like biomagnetism and low-field MRI (Chapter 2), magnetic particles detection (Chapters 8 and 9) and earth field mapping.
Table 1.4 Very sensitive magnetic sensors with their working temperature and field equivalent noise.
| Sensor type | Working temperature | Minimal detectivity for 1 cm2 | Comments |
| SQUIDs | 4 K | 1 fT/sqrt(Hz) | Extensively developed and used. This is the reference sensor |
| HTS SQUIDs | 77 K | 30 fT/sqrt(Hz) | |
| Atomic magnetometers | 150 °C | 10 fT/sqrt(Hz) | Absolute magnetometers. Need the suppression of DC fields |
| Fluxgates | RT | 1 pT/sqrt(Hz) | |
| Superconducting/GMR Mixed sensors |
4 K | 3 fT/sqrt(Hz) | Large 1/f noise |
| Superconducting/GMR Mixed sensors |
77 K | 7 fT/sqrt(Hz) | Large 1/f noise |
Spin electronics is based on the fact that electrons have not only a charge but also a magnetic moment, called spin, which is quantified. The aim is to use this magnetic moment to filter electrons, to manipulate macroscopic magnetization, and in some cases to transport information. Historically, the first spin electronic effect, called the GMR effect, was discovered by P. Grunberg and A. Fert, who were awarded the Nobel Prize in 2007 [8]. The TMR effect was proposed earlier by Julière in 1975 [9] and observed later. Spin electronics applications are today mainly magnetic sensing with GMR and TMR sensors and magnetic storage with MRAMs and magnetic logics. Both are now in their commercial phase and are still being improved in terms of their performance.
The base of spin electronics is the fact that conduction electrons in magnetic materials are polarized, that is, the direction of the spin is not arbitrary but has a preferred direction imposed by the magnetization of the material. That polarization strongly depends on the nature of the material and on its crystalline structure. CoFe is the 3D alloy mainly used in devices as it is easy to deposit and presents a large spin polarization, around 70 %.
When a polarized electron is sent inside a material, it experiences collisions. A lot of collisions are elastic and the spin is conserved, while some are inelastic and may conduct to a change in its spin orientation. The typical length on which the memory of the spin is lost is few nanometers at room temperature. This implies that in a nonmagnetic material, a spin polarization cannot be maintained beyond that distance. The impact is that all spin electronics devices have to be engineered with at least one dimension at nanometer scale. The thin-film technology and micronanofabrication techniques have hence played an essential role in the development of spin electronics.
A spin current is the propagation of a net magnetic moment. Two kinds of spin currents can be proposed. The first one is the spin wave that propagates magnetic information by elementary excitations of the magnetic material. This is discussed in Section 1.4.3. The second way is to use polarized electrons. A polarized electron current propagates magnetic information that can be used, for example, to rotate a magnetic layer through a spin torque effect. This effect is described in detail in Chapter 4.
More recently, pure spin currents carried by electrons have been created. These currents are created by two flows of polarized electrons with opposite polarities and opposite directions: there is a net magnetic moment transferred and no charge.
These spin currents can be created by a spin Hall effect where an electrical current can create a transverse spin current through spin–orbit coupling. A very recent review of spin Hall effects has been published [10], which discusses the main aspects of this subfield of spintronics.
The GMR device was the first spin electronics device proposed 25 years ago. The principle is to have magnetic thin layers separated by nonmagnetic layers having a large enough spin diffusion length. Electrons traveling inside the first layer have a spin polarization that depends on the magnetization direction. When they arrive inside the nonmagnetic layer, electrons conserve their polarization to a distance of the order of the spin diffusion length. If there is another magnetic material nearby, electrons enter it. But that entrance will be easier if the magnetization direction of this second magnetic layer is identical to the first one. Hence, electrical resistance of the stack will depend on the relative orientations of the magnetization of each magnetic layer.
The simplest GMR device is called spin valve where there are only two magnetic layers, one with a large coercivity, that is, reasonably blocked in an external field, and another one that can easily rotate in an external field. A typical spin valve is given in Figure 1.4. This device is composed of a blocked magnetic layer. The blocking is obtained by using an antiferromagnet, typically PtMn or IrMn, coupled with a CoFe layer. The antiferromagnet has the property of being insensitive to the external magnetic field. Furthermore, it has typically a blocking temperature below its ordering temperature. Below the blocking temperature, it is very hard to move it and above this temperature it becomes easy to move it with a field. The blocking temperature for IrMn is typically 240 °C and for PtMn about 340 °C. For that reason, PtMn is more interesting for high-temperature applications such as in automotive. Often an extra synthetic antiferromagnet (SAF) is added to increase the field stability.
Figure 1.4 GMR simple spin valve (a). TMR spin valve with an SAF configuration (b).
The second magnetic layer is usually a free layer, that is, able to rotate easily in external magnetic fields. It is in general composed of a bilayer of NiFe and CoFe. NiFe, called permalloy, is a very soft material, whereas CoFe ensures a high spin polarization.
The GMR spacer is generally a Cu thin layer. The typical Cu thickness is about 2 nm, and this insures a magnetic decoupling of the two magnetic layers and a low enough spin depolarization.
TMR (tunnel magnetoresistance), also called MTJ (magnetic tunnel junctions), has the same structure as GMR's, but the spacer is a very thin insulating layer called barrier. The transport through this spacer is no longer a diffusive path but requires a tunnel transport, and the TMR ratio mainly depends on the electrode spin polarization at the interface. This has several consequences. The first consequence is that the resistance of the device increases exponentially as the thickness of the barrier increases and hence has to be very well controlled; the second is that the effect can be much higher than the GMR effect; the third is that for practical devices, resistance and size are partly decoupled; and finally the current has to flow through the barrier, so it requires top and down contacts. MgO insulating barriers create a symmetry filtering that increases the TMR ratios and thus are generally used.
A spin valve gives an angular response: the resistance varies with the angle between the free layer and the hard layer. This is, for example, very different from a Hall sensor where the response is mainly linear with field. Figure 1.5 gives a typical response of a GMR sensor as function of the external field direction. For that reason, except for angle sensors (Chapter 3) the GMR response is linearized. This can be done either by a closed-loop scheme, in which a coil creates a field on the GMR device that cancels the external field, or by applying a bias field on the GMR along an axis perpendicular to the sensitive axis. The bias field has to be larger than the field range required for the device. This bias field can be created in three different ways: the first one is an external magnet, the second is to play on the shape, and the third is to use a second antiferromagnet to partly pin the free layer perpendicular to the sensitive layer. All these approaches are more thoroughly described in Chapters 3 and 9.
Figure 1.5 (a) Response of a GMR as function of external field and (b) response of a linearized GMR.
The typical variation of magnetoresistance is 6–12 % for GMR and 200 % for MgO based TMR.
Reig et al. [6] give a detailed description of noise of GMR and TMR devices. Here, we give only the main features. Electric noise in GMR and TMR has mainly three sources. The first one is a frequency-independent noise that in GMR is only the thermal noise related to the resistance of the devices. The second source is a 1/f noise that comes from resistance fluctuations in the device. For GMR, the fluctuations are related to defects and 1/f noise is comparable to usual metals and follows the classical Hooge [11] empirical formula. For TMR, the noise is mainly related to conductance fluctuations of the barrier. The 1/f noise in TMR strongly depends on the resistance and materials and is usually much higher than the noise in GMR, and this mitigates the advantages of TMR versus GMR for low-frequency applications. The third source of noise is the magnetic noise that comes mainly from domain fluctuations. This noise can be avoided by giving the device a proper shape that does not allow domain formation in the active region. The C shape, also called yoke shape, is very often used.
The sensitivity of a device is strongly related to its linearization. In practice, if a device has a magnetoresistance of 10 %, 5 % can be used as a linear range. If you bias your device so that this 5 % variation covers 1 mT, the sensitivity will be 5 %/mT. If you apply a much stronger bias on the spin valve, say 20 mT, the sensitivity decreases to 0.25 %/mT. So, the sensitivity can be tailored as function of the applications. In the various chapters, you will see how sensitivity and field dynamic range have been chosen for the targeted applications.
Very often, a magnetic sensor is characterized by the detectivity that is the field corresponding to a signal-to-noise ratio of one. It corresponds to the noise divided by the sensitivity given in V/T. The detectivity of GMR and TMR sensors depend on the size because of the 1/f noise . Table 1.5 gives a short summary of classical detectivity achieved today for magnetic sensing.
Table 1.5 Detectivity of spin electronics sensors as function of size and frequency.
| Device | Detectivity at 1 Hz | Detectivity at 1 kHz | 1/f corner | Detectivity at high frequency |
| GMR 1 mm2 | 30 pT/sqrt(Hz) | 10 pT/sqrt(Hz) | 10 Hz | 10 pT/sqrt(Hz) |
| GMR 3 µm × 20 µm | 1 nT/sqrt(hz) | 30 pT/sqrt(hz) | 10 khz | 10 pT/sqrt(Hz) |
| Array of TMR 1 mm2 |
100 pT/sqrt(Hz) | 3 pT/sqrt(Hz) | 10 kHz | 1 pT/sqrt(hz) |
| TMR 3 µm × 20 µm |
1 nT/sqrt(Hz) | 30 pT/sqrt(Hz) | 1 MHz | 1 pT/sqrt(hz) |
The basic block of a spin valve is used for magnetic storage. At present, MgO-based magnetic tunnel junctions present a typical magnetoresistance of 150–200 % at room temperature. This large magnetoresistance induces a good separation between the 0 and the 1 level. Contrary to magnetic sensors, magnetic tunnel junctions used for storage are not at all linear but should present a high stability against external field while preserving the writing possibility. This aspect of spin electronics is developed in Chapters 4 and 11.
The dynamics of small magnetic objects has been a field of intense research for the past two decades.
We can separate different main regimes: a low-frequency regime, typically below 1 GHz where the magnetization of the thin magnetic layer in small devices is able to follow the external magnetic field. In this regime, static description works well. It has, in particular, been demonstrated that the GMR effect does not decrease up to 20 GHz. The second regime corresponds to the same domain of frequency, but the size of the device is increased. Then, domains are appearing, and domain propagation, reversal, and creation dominate the dynamics of these objects. This is partly described in Chapters 10 and 11. Nevertheless, if domain propagation has been extensively studied, no devices based on their use are presently commercialized.
The third domain is the high-frequency domain between GHz and THz. In this frequency domain, natural thermal excitations of magnetic ferromagnetic order appear; these excitations, called spin waves or magnons, are the magnetic equivalent of phonons, the vibrations of crystals. They are able to propagate, to be diffused, and could be used for magnetic logic. This aspect of spintronics called magnonics is a fast-growing field, where Europe has conducted a lot a pioneering work.
Spin waves are used for small RF devices in particular circulators and dephasing devices. The two new main applications forecast today are:
These aspects of spintronics are described in Chapters 11 and 12.