High-field behavior: the law of approach to saturation (Is there an equation for the magnetization at high fields?)

Transcription

1 High-field behavior: the law of approach to aturation (I there an equation for the magnetization at high field? In the high-field region the magnetization approache aturation. The firt attempt to give an equation decribing the behavior in thi region wa Lamont law Lamon' t law : dm dh contant ( M M Which tate imply that at high field the uceptibility i proportional to the diplacement from aturation The high field behavior can be modeled by the law of approach to aturation a given by Becker and Doring and Bozorth. a b M M (... kh H H kh: the force magnetization that i the field induced increae in pontaneou magnetization which i a very mall contribution except at high field H 0 5 ~0 6 Oe, the lat term become ignificant.

2 In the high-field region, domain rotation i the predominant effect. The relation between M and H in thi region i called the law of approach to aturation and i uually written a b M M (... kh H H. Thi term i very mall at temperature well below T c and may be neglected. kh repreent the forced magnetization, that i the field induced increae in pontaneou magnetization There remain the term a / H and b / H a i generally interpreted a due to incluion or microtre b a due to crytal aniotropy In field over a few thouand Oe, the term a / H i uually dominant, the above expreion reduce to a M M ( H High-field meaurement of M can be plotted againt / H, the extrapolated to / H = 0 in order to find the value of M.

3 Domain rotation

4 The Barkhauen effect (Doe the magnetization change moothly with magnetic field? The Barkhauen effect i the phenomenon of dicontinuou change in the flux denity B within a ferromagnet a the magnetic field H i changed continuouly. A the H field wa increaed moothly a erie of click were heard over the loudpeaker, which were due to mall voltage pule induced in the econdary coil. V N d db NA dt dt Thee voltage were caued through the law of electromagnetic induction by mall change in flux denity through the coil ariing from dicontinuou change in M and in B. If the initial magnetization curve, which look to be a mooth variation of B with H under normal circumtance i greatly magnified, then the dicontinuou change in B. In Fig(c, where the magnification factor applied to one portion of the curve i of the order 0 9.

5 A earch coil i wound on a pecimen(iron and connected through an amplifier to loudpeaker or earphone. No matter how moothly and continuouly the field i increaed, a crackling noie i heard from the peaker. If the earch coil i connected to an ocillocope, intead of a peaker, irregular pike will be oberved. Thee voltage pike are known a Barkhauen noie. The Barkhauen effect wa originally thought to be due to udden rotation of the M vector from one orientation to another in variou mall volume of the pecimen. It i due mainly to domain wall making udden jump from one poition to another. 5

6 Magnetotriction (Do the dimenion of a pecimen change when it i magnetized? The magnetization of a ferromagnetic material i in nearly all cae accompanied by change in dimenion. The reulting tarin i called the magnetotriction λ. Two main type magnetotriction Spontaneou: ariing from the ordering of magnetic moment into domain at the curie temperature Field-induced: arie when domain that have pontaneou magnetotriction are reoriented under the action of a magnetic field The fractional change in length d The proce of magnetization occur by two mechanim, domain-wall motion and domain rotation; mot of the magnetotrictive change in length uually occur during domain rotation Meauremen method ( Reitive tarin gauge ( Optical technicque 6

7 Magnetotriction occur in all pure ubtance. However, even in trongly magnetic ubtance, the effect i mall, λ ~0-5 λ Between the demagnetized tate and aturation the volume of a pecimen remain contant, to a quite good approximation. λ t (tranvere magnetotriction Thi mean that there will be a tranvere magnetotriction λ t, very nearly equal to one-half the longitudinal and oppoite in ign 7

8 Spontaneou magnetotriction in iotropic material. (Doe the length of a pecimen change when it become forromagnetic? Let u conider pherical volume of untrained olid withhin the olid above T c and hence in the diorder phae. At T=T c, pontaneou magnetization appear within the domain and with it an aociated pontaneou train or magnetotriction λ 0, along a particular direction. When a ferromagnetic material T < T c, the diorder magnetic moment become order over volume containing larger no. of atom. Thee volume in which all moment lie parallel are calleddomain The diretion of ponaneou M varie from domain to domain throughout the material to enure that the bulk magnetization i zero. 8

9 For the preent iotropic cae the amplitude of thee puntaneou magnetotriction are independent of crytallographic direction. Within each iotropic domain, pontaneou train varie with angle (θ from the direction of pontaneou magnetization according to the relation e(θ = e co θ The average deformation throughout the olid due to the onet of ponteneou magnetotriction can then be obntained by intregration auming that the domain are oriented at random o that any particular direction i equally likely 0 eco ind e Spontaneou magnetotriction caued by ordering of the magnetic moment at the onet of ferromagnetim Since we have aumed an iotropic material the domain are arranged with equal probability in any direction and therefore the train i equivalent in all direction. Saturation magnetotriction (λ (What i the maximum change in length when a ferromagnet i magnetized e 0 e The tranition from the ordered but demagnetized tate to the ordered aturated tate by application of a magnetic field Thi give u a method of meauring of the pontaneou train within a material due to magnetic ordering along a particular direction, by 9 meauring λ.

10 Technical aturation and forced magnetotriction (can the aturation increae even after the magnetization ha reached technical aturation? Technical aturation of magnetization occur when all magnetic domain within a material have been aligned in the ame direction to form a ingle-domain pecimen. However, if the magnetic field i increaed further there i till a very low rie in M and thi proce i calledforced magnetization. Similar behavior i oberved in the magnetotriction. Technical aturation magnetotriction i reached when the pecimen ha been converted to a ingle domain. However a very low change in magnetotriction, called forced magnetotriction, i oberved a the field i increaed further. Forced magnetotriction, i a very mall effect, being appreciable only at field of the order of 800 ka/m. (0,000 Oe From wall motion to aturation, rotation predominate; in thi region work mut be done againt the aniotropy force, and a rather larger increae in H i require to produce a relative mall increae in M. 0

11 Domain wall motion Domain rotation

12 Magnetotriction at an angle θ to the magnetic field (How doe the aturation magnetotriction vary a a function of angle? conider a completely iotropic medium ( (co aturation magnetotriction along the direction of magnetization for λ (θ at any angle θ to the field direction λ // : the field parallel to a given direction λ : the field perpendicular to a given direction, The difference between them give the pontaneou train within a ingle domain // e // 0, 90, (0 ( (90 (0

13 Aniotropic material (Are the magnetic propertie identical in all direction in a ingle crytal? Although ingle crytal Ni come fairly cloe to having iotropic propertie uch a magnetotriction, the reality i that all olid are aniotropic to ome degree, and therefore the aturation magnetotriction need to be defined in relation to the crytal axi along which the magnetization lie. The magnetotriction or pontaneou train are defined along each the principal axe of crytal. For cubic material there are two independent magnetotriction contant λ 0 0 λ The aturation magnetotriction in ingle domain, ingle crytal cubic material i then given by a generalized verion of the eq. for iotropic material 00 ( ( α α α are the direction coine, relative to the field direction, of the axi along which the magnetic moment are aturated. β β β are the direction coine, relative to the field direction, in which the aturation magnetotriction i meaured. λ 00 : the aturation magnetotriction meaured along <00> direction λ : the aturation magnetotriction meaured along <> direction

14 We often wih to know the aturation magnetotriction in the ame direction a the field, then β = α, β = α, β = α ( ( 00 Thee eq only apply to the magnetotriction within a domain ( ( ( ( ( ( ( ( ( ( a polycrytal can only be calculated by averaging the effect. It i aumed that the material conit of a larger no. of domain and the train i uniform in all direction. In a randomly oriented polycrytalline cubic material thi formula implifie further to become

15 Field induced bulk magnetotriction (λ (How doe the length of a ferromagnet change with magnetic field The variation λ(h or λ(b are very tructure enitive o that it i not poible to give any general formula for the relation of magnetotriction to field. In thi cae, magnetization take place entirely by rotation of magnetization. So we may make the ubtitution M= M coθ, which give the magnetization along the field axi in term of the angle θ which the aturation magnetization within the domain make with thi axi. The magnetotriction along the field axi i given by co M ( M M= M coθ (The variation of oberved magnetotriction with magnetization M M 5