Ferromagnetism

Ferromagnetism (from the Latin ferrum 'iron' ) is the property of certain materials to align their elementary magnets parallel to each other. This means that pieces of these materials cause either itself or a static magnetic field are attracted to the magnetic pole of an external magnetic field. This attraction is independent of the polarity of the external magnetic field and is caused by the fact that the direction of the parallel-aligned elementary magnets is rotated in the ferromagnetic material such that it is parallel to the external magnetic field.

There are three ferromagnetic at room temperature, the elements iron, nickel and cobalt. At lower temperatures, some of the lanthanides are ferromagnetic, such as gadolinium for up to 19.3 ° C. Ferromagnetism is the to in everyday life most clearly observed expression form of magnetism of matter. Other manifestations are paramagnetism and diamagnetism.

Ferromagnetic materials magnetized in an external magnetic field so that the magnetic flux density is greatly increased in the interior compared to the exterior, the field lines in the material are therefore closer together. A ferromagnetic body undergoes - as well as a paramagnetic - in an inhomogeneous magnetic field, a force toward the location of the strongest magnetic field, it is attracted by a magnet, for example. This results in the total field a lower-energy state. It is performed mechanical work that needs to be applied in the removal of the attracted body from the field in the same strength again.

The factor of the flux density increase compared to the empty space ( ĩr or magnetic susceptibility - 1 ) by the magnetic permeability of the material determines ĩr applies for the ferromagnet ĩr >> 1 (see paramagnetism ).

Ferromagnetic materials are usually solid. Known applications of these materials include permanent magnets, electric motors, transformers, and the various forms of magnetic data storage ( magnetic tape, diskette, hard drive, etc.).

The hysteresis curve of the ferromagnetism is caused by effects in two different orders of magnitude:

• Microscopically, the rectified magnetic order of the elementary magnets (eg, the electron spins, see below) in the atomic scale
• Macroscopically the arrangement of the white areas ( the so-called " domains") in the order of micrometers to nanometers

Many considerations in theoretical solid state physics are limited to the microscopic aspect and are already calling the rectification of the elementary magnets as ferromagnetism. On the other hand, enter the White districts also occur with other magnetic ordering.

• 6.1 hysteresis
• 6.2 Hard and soft ferromagnets
• 6.3 practice covers the hysteresis

Introduction

A material is " ferromagnetic" called when it is a separate and independent from the external magnetic field, so called " spontaneous" magnetization in an external magnetic field. This is not " induced ", as in " diamagnetic " and " paramagnetic " material. Rather, the external magnetic field determines only the direction of the elementary magnets, while the amount of which is independent of it. The external and the hazards arising from the ferromagnetic material magnetic field have A., the same orientation, therefore, is formed between the external object and the magnet a magnetic attraction. A ferromagnetic material is attracted for this reason both of magnetic north poles and south poles of the same way.

In soft magnetic materials, these magnetization for the most part immediately loses if the object is removed from the external magnetic field, especially after alternating fields have been created. In general, only a small residual magnetism called the remanence is left behind. However, there are materials in which these retentivity is fairly large and permanent ( persistent ) strong magnetization can be achieved. Such hard magnetic materials, such as hardened steel can be magnetized permanent magnet or exist from the outset as permanent magnets, that is, assume a distinct recognizable ( macroscopic ) magnetization permanently.

The remanent magnetization can be eliminated by applying a magnetic field opposite of what happens when it reaches the coercive field. In hard magnetic materials, the amount of the necessary counter- field is larger than that of soft magnetic materials. Wherein the permanent magnet both high remanence and a high coercive force is desired.

From the ferromagnetism of ferrimagnetism is to be distinguished (eg ferrites ), the macroscopic although it has similar properties, but is microscopically related to the antiferromagnetism. For him, the elementary magnets are each as alternately oppositely directed the antiferromagnetism in the two directions, however, less pronounced, which is why - unlike the antiferromagnetism - for each pair remains a magnetization.

Materials with ferromagnetic properties

Among the elements or metals in pure form include iron, cobalt and nickel at room temperature ferromagnetic properties. At lower temperatures, the lanthanides gadolinium, terbium, dysprosium, holmium and erbium are ferromagnetic.

In practice, one commonly used, ferromagnetic alloys such as AlNiCo, SmCo, Nd2Fe14B, Ni80Fe20 ( " permalloy ") or NiFeCo alloys ( " mu-metal "). It is noteworthy that in certain circumstances, some of the compounds are generally non-ferromagnetic elements comprise ferromagnetic behavior, for example chromium dioxide, Manganarsenid, europium (II ) oxide or superfluid A -1 phase of He-3, and also the so-called Heusler alloys.

Is also noteworthy that the known ferromagnetic material, iron, as a main component of an austenitic alloy has no effect ferromagnetic. Austenitic structure are part of many stainless steels and stainless steel varieties. (Iron crystallizes at room temperature in the body-centered cubic lattice. Austenitic alloys, however, are predominantly face-centered. )

In general, the presence of ferromagnetic properties is dependent on that are present in the electron configuration of the ground state of the metal in question or of the connection unpaired electrons, which essentially occurs only in transition metals and rare earths.

Ferromagnetism normally occurs only in the solid state, because the Curie temperature of these materials is lower than the melting temperature. Ferromagnetism was, however, observed in a supercooled melt. Ferrofluids are suspensions of solid magnetic particles in a non-magnetic fluid.

Physical origin

Carriers of the elementary magnetic moments are the electron spins. As with other cooperative magnetic phenomena, the magnetic dipole -dipole interaction is also the ferromagnetism far too weak to be responsible for the ordering of the spins. But it has, in contrast to the exchange interaction (see below), very long range, and is therefore still important for the applications. In the ferromagnetic phase has the added that the parallel alignment of magnetic moments for the dipole -dipole interaction is energetically unfavorable. Is responsible for the parallel spin ordering of the ferromagnet the quantum mechanical exchange interaction, which has to do with the existence of singlet and triplet states in two-electron systems, and related to the Pauli principle. So there is a real non- classical phenomenon that is not easy to understand:

In detail, the corresponding spin wave function must be symmetric according to the Pauli principle for an antisymmetric spatial wave function (eg with parallel spins in the two-electron system ). It can be shown that the average distance between the two particles is larger at the antisymmetric spatial wave function and hence for the particles of the same charge a low Coulomb repulsion. The exchange interaction causes therefore here an effective lowering of the potential energy. On the other hand, the electrons with parallel spins can not reside in the same local state and must occupy successively higher levels, reducing their kinetic energy increases by the Pauli principle. The spontaneous parallel position of the spins and thus a ferromagnetic order is therefore only occur if the lowering of the potential energy than offset the increase in kinetic energy. This is the reason why only the few above-mentioned materials are ferromagnetic, but the vast majority do not.

An illustrative representation of this is the Bethe- Slater curve, which shows the exchange interaction as a function of relative atomic distance, eg for common materials (Cr, Mn, Fe, Co, Ni). The relative distance between the atoms in this case the ratio of the atomic spacing of the neighboring atoms to the diameter of the non- closed electron shell.

In one sentence:

The magnetic permeability and hence the magnetic susceptibility is not constant in the ferromagnet, but a complicated function of the applied field strength and depends on the magnetization history. Most, therefore, the (differential) magnetic susceptibility is considered to be derivative of the magnetization after the field strength. It disappears in the saturation region.

The relationship between magnetization and magnetic flux density is considered in the rest of the relationship

White districts, domains and domain walls

Ferromagnetism arises from the fact that elementary magnetic moments have a sibling order that persists through the interaction of the moments with each other even without an external magnetic field. The regions of equal magnetization called domains or white districts. They occur in sizes from 0.01 micron to 1 micron and are not uniformly oriented in the unmagnetized state of the substance.

The exchange interaction acts only between fermions whose wave functions have a substantial overlap, which is generally only between nearby particles. The magnetic interaction, however, also acts between distant magnetic moments. Therefore, in an extended ferromagnet exceeds the magnetic energy consumption sometime the energy gain of the exchange interaction. The ferromagnetic ordering of the solid body then breaks down into differently oriented domains. The ranges of the solid body in which meet differently oriented domains, called domain wall. Depending on the rotation of the magnetization in the wall is called Bloch walls or Néel walls ( Bloch walls, the rotation of the magnetization occurs in the direction perpendicular to the wall plane, in Néel walls it is done, however, within the plane of the wall; Néelwände dominate only in very thin magnetic layers ). There are also other types of wall topological singularities so-called Bloch lines and Bloch points that are associated with changes in the rotational behavior of the wall. These differences, which can move in the 10 - nanometer range, are subtle, but interesting for current applications in information technology.

The formation of the domain wall requires to perform work against the exchange interaction; the reduction of the domain ( the volume of a continuous domain ) reduces the magnetic energy of a solid.

Due to the non - continuously running direction of the white areas under the influence of external magnetic fields so-called Barkhausen jumps can be observed.

The magnetic order is broken at high temperatures, the ferromagnets are then only paramagnetic. The temperature above which the ferromagnetic order disappears is called the Curie temperature ( after Pierre Curie, the husband of Marie Curie ). The susceptibility can be calculated above the Curie temperature according to the Curie- Weiss law. Paramagnetism remains for all temperatures above the Curie temperature maintained even after the transfer of the solid into the liquid or gas phase.

Saturation

Under saturation magnetization is understood that the magnetization in the causes in a mostly ferromagnetic material an increase in the external magnetic field strength does not increase the magnetization of the substance more. The latter has reached a constant material-specific " saturation ." The (differential) is magnetic susceptibility in other words considered as a derivative of magnetization according to the field strength. It disappears in the saturation region.

A particularly good conductivity in the magnetic flux is the essential property in particular ferromagnetic materials such as soft iron dynamo sheet or certain ferrites. This explains the use of these materials, where it depends on the spatial guidance of magnetic fluxes, for example in iron cores of transformers. By increasing the magnetic field strength in these materials, the range of the saturation magnetization is reached where there is a sharp drop of the magnetic conductivity. The magnetic saturation is these technical applications therefore usually undesirable.

Plotting for a material with the magnetic flux density compared to the externally applied magnetic field strength in a chart that gives the hysteresis loop ( magnetization curve). The flattening of the slope characterizes clearly the beginning of the saturation magnetization.

Practice covers the saturation

• Geophysics: identify materials by measuring the specific Curie temperature by determining the dependence of the saturation magnetization of the temperature.
• In industrial applications, such as transformers or motors, the magnetic saturation of the core is undesirable and leads to massive waste of the efficiency and the power transmitted. ( An exception is the reluctance motor in which the saturation is desired to increase the power factor). To avoid saturation, magnetic cores in transformers and the electric motors must have a suitable minimum cross -sectional area.
• In magnetic voltage regulators, the magnetic saturation of a transformer core is used to stabilize short-term variations in problematic power grids.
• By incorporating an air gap (perpendicular to the magnetic flux ) in a closed coil core, the saturation of any ferromagnetic core material can prevent or greatly reduce. However, the effective inductance is reduced greatly compared to ungapped core coils. Application found this measure, for example, earlier at the same current-carrying NF- transmitters in the classic tube -A amplifiers.

Hysteresis

The term hysteresis (Greek: hysteros = after, later ) characterizes a system whose variable output not only depends on the input size, but also by the course of history. Such hysteresis occurs with ferromagnetic, magnetic conductive materials such as iron, cobalt, nickel and alloys thereof. Increasing the magnetic field strength in a not previously magnetized ferromagnetic material, increases in the vicinity, the magnetic flux density. Reducing the field strength to zero, the magnetic flux density on a non-zero value will stop. The ferromagnetic material retains some residual magnetism back ( remanence ). The magnetic flux density does not depend only on the magnetic field strength, but also on the Timeline.

The magnetic flux density in a ferro- magnetic material is determined by the strength of the ambient magnetic field (). Is increased sufficiently, increases due to the saturation of only very slightly. Go back the external magnetic field, the flux density decreases again. The magnetic flux density reaches the same value at a field strength that is on the wane, a higher value than he appeared during the Zunehmens the field strength. Is reduced entirely to zero, does not return to zero, but only up to a so-called remanence. To cause the magnetization to zero, therefore, a reverse magnetic field with the coercive force has to be built. There is still applied an external magnetic field, we speak here not of demagnetization, for which several steps are necessary rather. A renewed reversing the field strength of the result that the lower branch of the hysteresis curve is traversed. This Hysteresevorgang can be well illustrated by the history of the hysteresis curve or hysteresis loop. A complete traversing the hysteresis curve is called hysteresis. The hysteresis curve is point symmetric about the origin. Only a decaying in amplitude alternating magnetic field through the gradual approximation of hysteresis cycles at zero for complete demagnetization.

The cause of the behavior are the so-called white areas. They are characterized by the fact that the spins of the electrons, which can be regarded as elementary magnets are parallel to one another within a district. The boundaries between districts are called Bloch walls. If now an external magnetic field is applied, the districts whose orientation corresponds to the orientation of the magnetic field, at the expense of other districts by electrons thus be aligned parallel to the magnetic field " fold " in the other districts. Grow Clearly, this corresponds to a shift of the Bloch walls.

Imperfections that exist in each of ferromagnetic material ( iron, for example carbon in the inclusions), however, that prevent the shifting of the Bloch walls is uniform. When a domain wall encounters a defect when you move, it remains first hang on her, and it is located behind the impurity a kind of bubble in which not simply fold down the spins of the electrons. Only above a certain field strength agrees that bubble, which leads to a sudden change in the magnetization. This process is called Barkhausen jump. Through this non-uniform wall displacements demagnetization along the new curve is impossible. They are the reason for the emergence of the hysteresis curve. If all the electron spins are aligned with the field in the ferromagnet, the saturation is reached. If now the external field is removed, do not return all the electrons back to the original orientation. The magnetization drops to the remanence level. Only by supplying additional energy of the material can be demagnetized again. Substances with high remanence are not necessarily hard -magnetic. Hard magnetic materials ( permanent magnets ) require a high coercivity. The remanence in a transformer core is less of the core material dependent, but depends heavily on the design of the core from: A toroidal core has a very high remanence, because no air gaps lie in the magnetic circuit. A transformer with technologically related or intentionally built-in air gaps, however, has by shear ( tilt) of the hysteresis curve a low remanence, although the core material itself may have a high remanence.

Typical of the hysteresis, the occurrence of a bistable behavior. With the same environmental conditions, the state of the past, the acting voltage time before switching off, depending. According to a certain point in the phase diagram is reached.

Considering the shape of the hysteresis loop can magnetize a substance specifically. Appropriate methods are used in the manufacture of permanent magnets or when writing to magnetic storage media (magnetic tape, disk, core memory ).

Hysteresis

If materials are magnetically reversed, energy for changing the orientation of the white districts must be expended. This rotation causes heat generation in the material. The losses generally are proportional to the area within the hysteresis curve and the frequency at which is remagnetized. It should be noted that the hysteresis curve is not statically determined, but narrows with increasing frequency, up to an oval.

The area enclosed by the hysteresis curve area corresponding to the energy which is converted in the fuel at its full magnetization reversal to heat. With electromagnetic components makes itself felt as a " core loss " or additional expenditure of energy. This integral should be in the case of storage media to be as high as possible. In the case of cores of transformers should be as small as possible in order to cause minimal energy losses. Which applies in a similar way for other contexts.

Hard and soft ferromagnets

In the case of high coercive force is called magnetically hard material, as to their reorientation high field strengths are needed. For storage media, this corresponds to a high data security, as the written information is not reoriented by random stray fields. At low coercive force is called contrast of magnetically soft material. The names derive from the fact that pure (ie soft ) iron compared to magnetic steel is rather soft magnetic. Very soft magnetically, the aforementioned permalloy, Ni80Fe20. Alloying of 5 % molybdenum obtained the extremely soft magnetic Supermalloy with which you as shields rooms that you can measure extremely weak magnetic fields generated by brain activity. Very soft magnetic metallic glasses are also the so-called iron-based or cobalt-based amorphous alloys which are similar in structure, the liquid metal alloy close to the melting point.

Practice covers the hysteresis

• The course and the shape of a hysteresis curve is not only by properties of the material of the magnetic conductor ( such as low loss, grain orientation and their alignment to the field lines ), but also strongly influenced by its design, particularly with or without air gaps.
• In the formerly common core save the computer memory were rings that frequently changed their condition, warm and reacted differently to the current pulses as storage rings that were rarely addressed. Remedy was a vigorous circulation of the air, so that all cores had the same temperature as possible.
• In many applications small hysteresis cycles are points in the - driven surface; see also small-signal behavior. Due to the dependent of the magnetization permeability have cycles near the origin to a higher permeability.
• Importantly, the hysteresis property, for example, in audio technology when recording to tape (see tape, bias ).
• For the understanding and the interpretation and calculation of transformers knowledge of the hysteresis behavior of the core material is fundamentally important.
• If materials are magnetically reversed, energy for the altered orientation of the white districts must be expended. This rotation causes heat in the iron ( hysteresis ).
• This hysteresis for example, play a role in induction cooktops, where in ferromagnetic pots 1/3 of the heating power provided by hysteresis.

Applications

Ferromagnetic materials have a high permeability with. Characterized the magnetic field lines are well managed (for example air ) compared to the surrounding material. Therefore find ferromagnetic materials such as in electromagnets and transformers use.

Other applications (eg in electronic storage media) are currently mainly in connection with the information technologies to date, such as the so-called GMR and TMR, the it comes to reading heads for magnetic hard disks for the applications. For this, the Nobel Prize in Physics was awarded in 2007, namely to Peter Grünberg of the Jülich and Albert Fert of Paris.