{"id":399,"date":"2016-03-14T21:05:27","date_gmt":"2016-03-14T20:05:27","guid":{"rendered":"http:\/\/labfiz.uwb.edu.pl\/lab\/magmicroscope\/?page_id=399"},"modified":"2016-03-14T21:12:50","modified_gmt":"2016-03-14T20:12:50","slug":"description-changeability-domain-structure-in-magnetic-fields","status":"publish","type":"page","link":"http:\/\/labfiz.uwb.edu.pl\/lab\/magmicroscope\/?page_id=399&lang=en","title":{"rendered":"Description changeability domain structure in magnetic fields"},"content":{"rendered":"

Interesting problem is describe magnetic material magnetization process, and define relationship magnetization M(H)<\/b> depending on external magnetic fields H<\/b>. For solving this problem we need knowledge about magnetic domain structure. We consider model based on sample with thickness h<\/b> (Picture O1). The magnetization M<\/b> measurred as a macro value we involve with domain structure size d+<\/sub><\/b> i d–<\/sub><\/b>:<\/p>\n

M=Ms<\/sub>*(d+<\/sub> -d–<\/sub>)\/(d+<\/sub> +d–<\/sub>)=Ms<\/sub>*m <\/b>~~<\/p><\/blockquote>\n

where Ms<\/sub><\/b> is a magnetization of saturation which occur in single domain. On this page we can show changeability domain structure d+<\/sub>(H)<\/b> id–<\/sub> (H)<\/b> as esily as possible. On the next\/linked pages we give precisly mathematic equations helpful for domain structure descriptions and software for aid this problem<\/p>\n

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Rys. O1<\/b> Struktura domenowa w polu magnetycznym H<\/p>\n

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On the start we introduce concept energy of unit sample surface E<\/b>. Applying magnetic fields with force lines perpendicular to sample surface we incrase volume of domain with the same direction of manetization vector. Respecting domain structure geometry introduced on picture O1 we can easy define energy of unit sample surface in magnetic fields H<\/b> Eh<\/sub>=-h*H*m*Ms<\/sub>.<\/b> (Or1)<\/p>\n

With border between light and dark domains (domain wall) is associate energy [1]. For the unit sample surface we have energy Sw<\/sub><\/b>. Repeated analysis geometry from picture O1 give in simple way define the energy of the domain wall (unit of surface our layer) as:<\/p>\n

Ew<\/sub>=2*h*Sw<\/sub>\/p<\/b>(Or2)<\/p><\/blockquote>\n

For the sake of domain wall good for minimum enrgy is incrase period of magnetic structure p<\/b>.<\/p>\n

More dificult to understend (mostly in mathematics structure) is take into consideration division magnetic material onto separately, light and dark doamins. It is a result magnetostatic influence its magnetic domain parts. Each one give magnetic fields (demagnetisation fields Hd<\/sub><\/b>) in whole space and in neighbouring areas of sample too. This field want arrange in these areas magnetisation in antiparallel direction to domain magnetisation. Demagnetization field try to make most as possible numbers of domain, and decrace period of structure p=d+<\/sub> + d–<\/sub><\/b>. Simple mathematical description for demagnetization field and demagnetization energy Ed<\/sub> <\/b>can introduce in case 'ideal’ magnetic layer<\/p>\n

Hdi<\/sub>=-4*Pi*M=-4*Pi*m*Ms<\/sub> <\/b>(Or3a)<\/p><\/blockquote>\n

and demagnetization energy<\/p>\n

Edi<\/sub>=2*Pi*h*m2<\/sup>*Ms<\/sub>2<\/sup><\/b> (OR3b)<\/p><\/blockquote>\n

For derive formula Or3b<\/b> we use the equation Or1 where field H<\/b> changing by Hd<\/sub><\/b> and result two times decrase (interaction parts\/areas of the sample). In the sample with homogenous magnetization |Hdj<\/sub>|=4*Pi*Ms<\/sub><\/b> and demagnetization energy have the biggest as possible valueEdj<\/sub>=2*Pi*h*Ms<\/sub>2<\/sup><\/b>. In the case domain structure with any period demagnetization energy we can describe by formula:<\/p>\n

Ed<\/sub>= 4*Pi*h*Ms<\/sub>2<\/sup> *F(h\/p,m)<\/b> (Or3c)<\/p><\/blockquote>\n

The exactly form of function F(h\/p,m)<\/b> is given on the next pages.<\/p>\n

When we known magnetization of saturation Ms<\/sub>,<\/b> domain wall energy Sw<\/sub><\/b> and thickness of magnetic layer h<\/b> we can calculate two geometric parameters of structure: m(H)<\/b> and p(H)<\/b> (or d+<\/sub>(H)<\/b> and d– <\/sub>(H)<\/b>).To do this we look the minimum of complet layer energy Et<\/sub><\/b> which is a sum of energy Eh<\/sub> + Ew<\/sub> + Ed<\/sub>=Et<\/sub><\/b>. We introduce relationship beetween two „domains” parameters m<\/b> and p<\/b> from four quantities (three materialsMs<\/sub><\/b>, Sw<\/sub><\/b>, h<\/b> and magnetic fields H<\/b>) is on the first look very complicated problem If we take the Et<\/sub><\/b> form we can see that the problem can be simplify by reduced uantities. This way permit reduce problem to analyse geometric parameters of structure as a analyze function two parameters: material and reduced magnetic fields. When we divide Et<\/sub><\/b> by 4*Pi*h*Ms<\/sub>2<\/sup><\/b> then:<\/p>\n

Etn<\/sub>(l\/h,hg,m,h\/p)=Et<\/sub>\/(4*Pi*h*Ms<\/sub>2<\/sup>) = 2*(l\/h)*(h\/p) Hg*m + F(m,h\/p)<\/b> (Or4e)<\/p><\/blockquote>\n

where parameter<\/p>\n