Chapt. 4 Magnetic properties of materials Prof. Kee-Joe Lim School of Electrical and Computer Engineering Chungbuk National University /3/1

2 Scope of this chapter some fundamental concepts concerning magnetic fields essence of the atomic theory of magnetic dipoles atomic interpretation of dia-, para-, ferro-, antiferro- and ferri-magnetism application of magnetic materials

3 Summary of concepts pertaining to magnetic fields Definition of magnetic flux density ; B defined in terms of the force exerted by a magnetic field on a current- carrying wire magnetic fields are produced by electric currents [law of Biot-Savart] ; relative permeability – depended on materials This quantity is the parameter which can be interpreted in terms of the atomic properties of the medium ; No physical significance

4 magnetic field ; H Ampere’s law; the line integral of H around a single closed path is equal to the current enclosed relation between B and H Linear and isotropic medium only -Nonlinear ; ferromagnetic materials - anisotropic ; single crystal- tensor expression

5 4.2 Magnetic dipole moment of a current loop difference between electricity and magnetism 정자기학 magnetic dipole = motion of electric charges Relation between a current loop and magnetic dipole P Q R S B F I n    F  x y z Current loop The results can be apply for a current loop of any shape

6 Magnetization from a macroscopic viewpoint H dA dl How can we achieve a flux density inside the cavity that remains the same as it was when the material was present ? I dI Cavity 내부 자계를 만큼 증가시키기 위하여는 솔레노이드 전류 와 동일 방향으로 의 전류를 소코일에 흘리면 된다. - 자계가 인가된 자성체는 단위체적당 M 의 자기쌍극자 모멘트를 가지고 있다. ( 거시적 특성량과 원자론적 의미 관계 )

7 Magnetization from a macroscopic viewpoint correspondence or? comparison between magnetism and electricity …………

8 Orbital magnetic dipole moment and angular momentum in circular Bohr orbit model +e -e R 1 Bohr magneton ( M a has same dimension as h )

9 Orbital magnetic dipole moment and angular momentum in spherical charge cloud model -e +e R h   결과식은 두 모델에서 동일하며,  에도 무관함 Hold for any volume element of charge distribution

10 [ 보충자료 ] 운산과정

Lenz’s law and induced dipole moments The current remains constant for t > t 0. Thus, a permanent change has been accomplished; the current can be made equal to zero only by reducing the flux to zero.

12 Induced dipole moment in circular Bohr orbit model(1) B R E -e +e v0v0 F = -eE : Larmor angular frequency Induced dipole moment has a direction opposite to the applied magnetic flux density. This results is independent of the initial direction of rotation. It will also keep its new angular frequency  as long as B remains constant. B 인가시도 R 은 일정으로 가정

13 Induced dipole moment in circular Bohr orbit model(2) B R +e -e v

14 Induced dipole moment in homogeneous spherical charge distribution model B B +e  R E   d  F Induced dipole moment is independent of the initial angular frequency  0 of the charge distribution. Hence, a magnetic dipole moment will be induced in the atomic model, independent of whether the model has a “permanent” magnetic dipole moment or not.

classification of magnetic materials 분류 기준 : 영구자기쌍극자 모멘트 유무, 쌍극자모멘트간 상호작용 classification Permanent dipole interaction diamagnetic No- paramagnetic YesNegligible ferromagnetic YesParallel orientation antiferromagnetic YesAntiparallel orientation of equal moments ferrimagnetic yesAntiparallel orientation of unequal moments Curie law Curie-Weiss law

Diamagnetism( 반자성 ) This expression is valid for diamagnetic and paramagnetic materials at all temperatures, but for the other classes only above a certain temperature. Table 4.2 the susceptibility of some diamagnetic materials As long as the electronic structure of the material is independent of temperature, the magnetic susceptibility is also essentially independent of temperature. Comparing with experimental value and theoretical value (by Lenz’s law)in solid with an atom contains 10 electrons; eq. (4.57) Superconductor is a perfect diamagnetic material; susceptibility =-1

17 Origin of permanent magnetic dipoles in matter Whenever a charged particle has an angular momentum, the particle will contribute to the permanent dipole moment. - There are three contributions to the angular momentum of a atom (i) orbital angular momentum of electrons (ii) electron spin angular momentum (iii) nuclear spin angular momentum - Orbital angular momentum of electrons -Orbital (angular) momentum quantum number l determines the orbital angular momentum which is measured in units of h/2  -Magnetic quantum number m l determines the component of angular momentum along an external field direction

18 a completely filled shell l=1 m l =1(h/2  h  orbital dipole moment -eh/4  m, 0, +eh/4  m a completely filled electronic shell contributes nothing to the orbital permanent dipole moment of a atom. Incomplete outer shell no contribution because of “frozen in” Transition elements (incomplete inner shell) Iron group(Z=21 ~ 28; 3d) (Z=39~45; 4d) Rare earth group(Z=58~71; 4f) (Z=89~92; 6d) In case of the elements of the rare earths group, the permanent orbital dipole moments do contribute to the magnetic susceptibility, but contribution from orbital magnetic dipoles will be neglected. 1 Bohr magneton( 보아磁子 ) = eh/4  m =9.27 x [Am 2 ]

19 Electron spin magnetic dipole moment spin angular momentum along a given direction is either +1/2(=+h/4  or - 1/2(=-h  S=1, angular momentum=h/4  dipole moment=-eh/4  m = - 1Bohr magneton complete electronic shell incomplete outer shell incomplete inner shell (transition element; iron group) Hund ’ s rule Iron group ; 1s 2, 2s 2, 2p 6, 3s 2, 3p 6, 3d 0~10, 4s 2

20 Nuclear magnetic moments angular momentum associated with the nuclear spin is measured in units h/2 , and is of the same order of magnitude as electron spin and orbital angular momentum of the electrons. Mass of the nucleus is larger than that of an electron by a factor of the order of The magnetic dipole moment associated with nuclear spin is of the order of Bohr magnetons. Since nuclear magnetic dipole moments are small compared to those associated with electrons, its contribution may be neglected

21 Paramagnetic spin system 가정 ; 자화에는 전자 spin 만 기여, 원자당 dipole moment = 1 Bohr magneton(  =eh/4  m) 체적당 원자수 N( 개 /m 3 ) 자계와 평향한 원자수 Np, 반평행 Na

22 ( i ) ( ii ) (for ) ( At room temperature ) Curie law Saturation, see fig Table 4.4 susceptibility of some paramagnetic materials

23 Diamagnetic contribution 도 있으나 미미함 (-10 -5, ) 대표적인 응용 분야 –To obtain very low temperature(<1 o K] by adiabatic demagnetization –MASER ( microwave amplification through stimulated emission by radiation ) s entropy T, temperature