# Chapter XII Magnetic materials

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## Chapter XII Magnetic materials

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Investigation of the magnetic properties of materials is very important, because magnetic phenomena have various scientific and technical applications. The macroscopic properties of matter are a manifestation of the microscopic properties of the atoms of which it is composed. The magnetic properties of materials may be very different for types of material, depending on their nature and structure.

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## Nội dung Text: Chapter XII Magnetic materials

1. GENERAL PHYSICS II Electromagnetism & Thermal Physics 4/1/2008 1
2. Chapter XII Magnetic materials §1. Atomic magnetic moment - Bohr magneton §2. Magnetization, paramagnetism and diamagnetism §3. Ferromagnetism 4/1/2008 2
3.  Investigation of the magnetic properties of materials is very important, because magnetic phenomena have various scientific and technical applications.  The macroscopic properties of matter are a manifestation of the microscopic properties of the atoms of which it is composed.  The magnetic properties of materials may be very different for types of material, depending on their nature and structure. 4/1/2008 3
4. §1. Atomic magnetic moment – Bohr magneton: In order to understand the magnetic properties of matter we must know the magnetic properties of atoms. 1.1 The magnetic moment of an orbiting charge :  Moving electrons, protons, neutrons create currents they have magnetic dipole moments.  The motions of these particles can be decomposed into orbital motion and spinning motion The current created by the orbiting particle is 4/1/2008 4
5. • Its magnetic moment is The vector form: where L0 is angular momentum of the orbital motion. It is known that for an electron in the ground (non-excited) state of the hydrogen atom the angular momentum equals to 1.05 x 10-34 J.s (we will learn later in quantum physics), so we have for the orbital magnetic moment of electron: This quantity is the fundamental unit of magnetic moment, it is called Bohr magneton  9.22 x 10-24 A.m2. =  4/1/2008 5
6. 2.3 The magnetic moment of a spinning charge: Consider a spinning charge: A ring dq of the spinning charge creates the current: The corresponding magnetic moment of the ring is Summing over all the rings: Assume that the charge is distributed in the same way as the mass, we can write I= L The spin magnetic moment vector 4/1/2008 6
7. The particular case of an electron: An electron is known to have spin angular momentum of 0.527 x 10-34 J.s. So, its spin magnetic moment is However, experiments give the result of twice bigger. Why? The problem lies with the assumption about the charge distribution that we have used. To correct this mistake one introduces the factor g called “gyromagnetic ratio“, and writes For electrons g = 2. 4/1/2008 7
8. §2. Magnetization, paramagnetism and diamagnetisme: 2.1 Some general view on the magnetic properties of materials:  The material which has the most striking magnetic properties is iron. Similar magnetic properties are shared also by nickel, cobalt,…. That kind of magnetic properties is called ferromagnetism.  All other ordinary substances do show some magnetic effects, but very small ones – a thousand → million times less than the effects in ferromagnetic materials. This small magnetism is of two kinds. In other words, there are two signs to the magnetic effects: paramagnetism and diamagnetisme. Strong magnetic effects Weak magnetic effects in ferromagnetic materials in paramagnetic in diamagnetic materials materials 4/1/2008 8
9. Two signs to the magnetic effect: • If the small cylinder is of bismuth → it is repelled by the sharp pole • If the small cylinder is of aliminium → it is attracted by the sharp pole 4/1/2008 9
10. 2.2 Magnetization: First we consider a piece of paramagnetic material. When no external magnetic field is present, the atomic magnetic dipoles are randomly aligned (pic. a). The total magnetic field due to all the dipoles cancels to zero. If we apply an external magnetic field B 0 (pic. b), the dipoles tend to align with the applied field, and a) the vector sum of all atomic magnetic moments becomes non-zero vector, then we denote it by B’ : Applying the formula of magnetic field for a ring current on its axis, we have for each atomic current: b) 4/1/2008 10
11. Since atomic current ring is very small, we have where we have introduced the quantity M , considered as a type of average dipole moment per unit volume. We can write and we obtain the total magnetic field is The quantity M is called the magnetization of the material. 4/1/2008 11
12.  Units:  The units of magnetic moment are (current) x (area), that is A.m 2  The units of magnetization M is (A / m2) / m3 = A / m  The units of  M is the same as the units of B (as it must be):  ( T.m / A )( A / m ) = T  It is natural to think that the sum of the atomic magnetic moments tend to align with the external magnetic field, then B > B0 and M > 0 However, by experiments one observed that this is true not for all materials, but only for most common materials. Such materials are called paramagnetic. For these materials M > 0 but fairly small. 4/1/2008 12
13. 2.3 Permeability and susceptibility:  We have said that for paramagnetic materials the total magnetic field inside the material B is greater than the external field B0 . So we can write B = Km B0 where Km is a dimensionless factor, called relative permeability. The value of Km is typically ranges from 1.0001 → 1.003 (see the table In the page 1089 of the textbook).  The expression of the magnetic field in materials relates to that in vacuum by the replacement  by   Km  =  which is called the permeability of the material. 4/1/2008 13
14.  Since for paramagnetic materials the value of Km is a small deviation from unity, it is convenient to introduce the quantity χ = Km – 1 m which is called the magnetic susceptibility. 4/1/2008 14
15. 2.4 Diamagnetism: There are a type of materials for which the magnetization vector is opposite to the external magnetic field, that is M < 0. Why? We can explain this phenomenon in a simplified version as follows: a)  In the absence of external fields the electrons move randomly (pic. a).  When the external magetic field is applied (pic. b), the electrons begin move in circular orbits. This orbiting electrons create a field which is opposite to the external field. This type of materials is called diamagnetic. For it Km is typically of the order of 0.9999 → 0.99999 ( see the table). b) 4/1/2008 15
16. §3. Ferromagnetism: 3.1 Strong magnetization of ferromagnetic materials:  The third type of materials is called ferromagnetic materials, which includes iron, nickel, cobalt, … These materials manifest strong magnetic effects.  The magnetic field inside them is much larger than the applied external field, the relative permeability Km is of the order of 1.000 to 10.000. The properties of ferromagnetic materials are explained by their microscopic structure: In these materials the atomic magnetic moments are extremely easy to align together, due to strong interactions between them. Inside the material there exist regions called magnetic domains, even when no external field is applied. In each domain the atomic magnetic moments are parallel to each other. In the absence of external magnetic field the magnetic moments 4/1/2008 of different domains align randomly as shown in the picture. 16
17. When an external field B0 is applied, the domain magnetic moments tend to orient themselves paralell to the field that leads to the shift of domain boundaries: domains that have magnetic moments parallel to the external field will grow, other domains will shrink. The magnetic moment of each domain have the order of thousands of Bohr magnetons, the torques that tend to align the domains with the external field are much stronger than in paramagnetic materials. After rearrangment of domain magnetic moments the magnitude of the magnetization vector of the material is much larger than the external field. Two important features of ferromagnetism are • the saturation of magnetization • the hysteresis 4/1/2008 17
18. 3.2 Saturation of magnetization and hysteresis: Consider the dependence of the magnitude of the magnetization vector on the magnitude of external magnetic field. Increase B 0 from zero → the magnitude M of magetization increases. Msat When B0 reachs to some enough large value, further increase of the external field causes no increase in magnetization. This phenomenon is called the saturation of magnetization. B0 The saturation of magnetization is explained as follows: When the external field is enough large, all the domain magnetic moments are aligned parallel to it, and the magnetization can’t increase further. 4/1/2008 18
19. M When the material is magnetized to saturation we reduce the external field to zero, the magnetization decreases (the curve b), but some magnetization remains when B0 = 0. The material becomes then a permanent magnet. It has own magnetic moment when the external B0 field is removed. To reduce the magnetization to zero We must apply an external field in the inverse dirction. The variation of the magnetization with Hysteresis loop the change of the applied magnetic field is described by the hysteresis loop. 4/1/2008 19