Topic: Studying magnetic field in ferromagnets

2. Goal of the work:

2.1. Study magnetic field induction dependence in ferromagnets on magnetic field intensity magnitude.

2.2. Study magnetic permeability dependence in ferromagnets on magnetic field intensity magnitude.

Main concepts

Difference between the magnetic intensity and magnetic induction

The magnetic field is being characterized by two main quantities: vector of magnetic induction and vector of magnetic intensity .

Magnetic induction B is a force characteristic of magnetic field, because its magnitude is equal to the force which acts on unit element of current oriented perpendicularly to the vector of magnetic induction (85). Both magnetic induction and magnetic force are being determined by macro-currents in wires and by atomic micro-currents of medium, therefore both depend on magneticpermeability of medium m.

Magnetic intensity H is additional quantity which characterize only external magnetic field of macro-currents in wires and is independent from medium in which magnetic field occurs (88). For example in center of circular current (91) we obtain:

=> and [ H ]= . (96)

Absolute value of magnetic intensity in center of circular current of unit diameter is equal to simply value of current. From (96) we can see, that the SI unit for magnetic intensity is ampere per meter (A / m).

Magnetic induction in center of circular current:

. (97)

And, if circular current coats the iron core (m~3000), then in center of core the magnetic induction approximately 3000 times greater, than in air.

 

Permeability of medium mis a ratio between the magnetic force in medium and magnetic forcr in vacuum:

; [m]=1, (98)

it shows in how many times the magnetic induction in given medium is more, htan in vacuum. Permeability of medium is a dimensionless quantity.

 

Magnetic Properties of different materials

Circular motion of electron in atom can be considered as circular current loop (Fig. 28). Moving elementary charge q ₀ creates an elementary current i ₀. Elementary circular current i ₀ creates an elementary magnetic moment:

, (99)

where S – area of plane of orbit of electron, - unit normal vector to the area of the loop.

Direction of magnetic moment is being defined by corkscrew rule(Fig. 26 or 28) and coincides whith a direction of own magnetic intensity.

 

The magnetic moment of a current loop is a vector quantity defined as (Fig. 3):

,

where I – is a current, S – area of the loop, - unit normal vector to the area of the loop. Circular motion of charged particle (an electron in atom) can be considered as such current loop and characterized by its orbital magnetic moment . Beside the orbital moment electrons has self magnetic moment called a spin. Spin does not related with any motion, it is a self characteristic of electron, such as charge, and it is only shows that immovable electrons in external magnetic field behave as current loops with moments .Like a charge in electric field experiences a force, the magnetic moment experiences a torque in external magnetic field tend to re-align it in the direction of the field.

Total moment of electron:

Total moment of an atom:

 

,

where summing provided for valence electrons.

So the magnetic behavior of a substance depends on a presence of magnetic moment in its atoms.

Magnetic Properties of different materials

Materials may be classified by their response to externally applied magnetic fields as diamagnetic, paramagnetic, or ferromagnetic. These magnetic responses differ greatly in strength. Diamagnetism is a property of all materials and opposes applied magnetic fields, but is very weak. Paramagnetism, when present, is stronger than diamagnetism and produces magnetization in the direction of the applied field, and proportional to the applied field. Ferromagnetic effects are very large, producing magnetizations sometimes orders of magnitude greater than the applied field and as such are much larger than either diamagnetic or paramagnetic effects.

Diamagnetism

The orbital motion of electrons creates tiny atomic current loops, which produce magnetic fields. When an external magnetic field is applied to a material, these current loops will tend to align in such a way as to oppose the applied field. Materials in which this effect is the only magnetic response are called diamagnetic. All materials are inherently diamagnetic, but if the atoms have some net magnetic moment as in paramagnetic materials, or if there is long-range ordering of atomic magnetic moments as in ferromagnetic materials, these stronger effects are always dominant. Diamagnetism is the residual magnetic behavior when materials are neither paramagnetic nor ferromagnetic.

Any conductor will show a strong diamagnetic effect in the presence of changing magnetic fields because circulating currents will be generated in the conductor to oppose the magnetic field changes. A superconductor will be a perfect diamagnet since there is no resistance to the forming of the current loops.

Paramagnetism

Some materials exhibit a magnetization which is proportional to the applied magnetic field in which the material is placed. These materials are said to be paramagnetic.

Paramagnetism is a form of magnetism which occurs only in the presence of an externally applied magnetic field. Paramagnetic materials are attracted to magnetic fields, hence have a relative magnetic permeability µ greater than one. The force of attraction generated by the applied field is linear in the field strength and rather weak. It typically requires a sensitive analytical balance to detect the effect. Paramagnets do not retain any magnetization in the absence of an externally applied magnetic field, because thermal motion causes the spins to become randomly oriented without it. Thus the total magnetization will drop to zero when the applied field is removed. Even in the presence of the field there is only a small induced magnetization because only a small fraction of the spins will be oriented by the field. This fraction is proportional to the field strength and this explains the linear dependency.

Ferromagnetism

Iron, nickel, cobalt and some of the rare earths (gadolinium, dysprosium) exhibit a unique magnetic behavior which is called ferromagnetism because iron (ferrum in Latin) is the most common and most dramatic example. Samarium and neodymium in alloys with cobalt have been used to fabricate very strong rare-earth magnets.

Ferromagnetic materials exhibit a long-range ordering phenomenon at the atomic level which causes the unpaired electron spins to line up parallel with each other in a region called a domain. Within the domain, the magnetic field is intense, but in a bulk sample the material will usually be unmagnetized because the many domains will themselves be randomly oriented with respect to one another. Ferromagnetism manifests itself in the fact that a small externally imposed magnetic field, say from a solenoid, can cause the magnetic domains to line up with each other and the material is said to be magnetized. The driving magnetic field will then be increased by a large factor which is usually expressed as a relative permeability for the material. There are many practical applications of ferromagnetic materials, such as the electromagnet.

Ferromagnets will tend to stay magnetized to some extent after being subjected to an external magnetic field. This tendency to "remember their magnetic history" is called hysteresis. The fraction of the saturation magnetization which is retained when the driving field is removed is called the remanence of the material, and is an important factor in permanent magnets.

Ferromagntic materials will respond mechanically to an impressed magnetic field, changing length slightly in the direction of the applied field. This property, called magnetostriction, leads to the familiar hum of transformers as they respond mechanically to 60 Hz AC voltages.

The long range order which creates magnetic domains in ferromagnetic materials arises from a quantum mechanical interaction at the atomic level. This interaction is remarkable in that it locks the magnetic moments of neighboring atoms into a rigid parallel order over a large number of atoms in spite of the thermal agitation which tends to randomize any atomic-level order. Sizes of domains range from a 0.1 mm to a few mm. When an external magnetic field is applied, the domains already aligned in the direction of this field grow at the expense of their neighbors.

For a given ferromagnetic material the long range order abruptly disappears at a certain temperature which is called the Curie temperature for the material.

In ferromagnetic materials the permeability µ depends on applied field and may be very large, up to 105.

Hysteresis

When a ferromagnetic material is magnetized in one direction, it will not relax back to zero magnetization when the imposed magnetizing field is removed. It must be driven back to zero by a field in the opposite direction. If an alternating magnetic field is applied to the material, its magnetization will trace out a loop called a hysteresis loop. The lack of retraceability of the magnetization curve is the property called hysteresis and it is related to the existence of magnetic domains in the material. Once the magnetic domains are reoriented, it takes some energy to turn them back again. This property of ferrromagnetic materials is useful as a magnetic "memory". Some compositions of ferromagnetic materials will retain an imposed magnetization indefinitely and are useful as "permanent magnets". The magnetic memory aspects of iron and chromium oxides make them useful in audio tape recording and for the magnetic storage of data on computer disks.

 

Hysteresis loop