Exchange bias and coercivity of ferromagnetic/antiferromagnetic multilayers. Klaus D. Usadel

Transcription

1 Exchange bas and coercvty of ferromagnetc/antferromagnetc multlayers Klaus D. Usadel Unverstät Dusburg-Essen, Germany Contents: exchange bas: ntroducton doman state model: results from MC smulatons mean feld approach for Isng AFM: coercvty and exchange bas generalsaton to local vector spn models: dynamcal consequences conclusons Coworkers: U. Nowak, A. Msra, B. Beckmann, R. Stamps

2 Exchange bas exchange bas (EB) = shfted hysteress loop frst observaton n Co/CoO partcles (Meklejohn and Bean, Phys. Rev. 12,1413 (1956)) typcal for FM/AFM compounds lke multlayers, nanopartcles ntal procedure: coolng the system n an external feld from above to below Neel temperature of the AFM loop s shfted upwards and asymmetrc; enhancement of the coercvty B Hyst. FC T N T

3 Applcatons: sensors 1.5 F(Sx) magnetzaton -.5 H 2 < H 1 H = 1 < -1 1 S x external feld F(S x ) = DSx 2 BS x The felds B and B + at whch the magnetzaton of the FM swtches are obtaned from F = at S x = 1 and S x = 1, respectvely: B = 2D, B + = 2D.

4 Understandng EB: problems external feld and exchange feld of the FM nterface layer polarzes the AFM nterface layer why s the polarsaton stable durng a hysteress cycle? why s the symmetry broken? uncompensated compensated perfect nterface rough nterface Doman wall formaton

5 Soluton: doman walls n the AFM breakng the symmetry necessary for EB by ntroducng frozen domans perpendcular doman walls n the AFM due to nterface roughness (Malozemoff, Phys. Rev. B 35, 3679 (1987)) but: doman wall formaton unlkely for large AFM thcknesses dea: ntroducng defects n the AFM to stablze domans: doman state model (Mlteny, Gerlngs, Keller, Beschoten, Güntherodt, Nowak, and Usadel, PRL 84, 4224 (2))

6 Experments wth dluted AFM Idea: generate defects n AFM: CoO Co 1 x Mg x O nterface layer wthout defects vary bulk dluton FM: Co AFM: CoO CoMgO bulk dluton enhances exchange bas(eb) assocated wth EB s an enhancement of the coercvty see also: Mewes et al., APL 76, 157 (2) Sh et al., JAP 91, 7763 (22) Mlteny, Gerlngs, Keller, Beschoten, Güntherodt, Nowak, Usadel, PRL 84, 4224 (2)

7 Local spn model FM M AFM z y EB x B H = H F + H AF + H nt H F = J F S S j,j H AF = J AF ǫ ǫ j σ σ j,j H nt = J nt ( ) DS 2 x + S x B ǫ S x σ, ǫ σ B D > ; J AF = J F /2; J nt = +/ J AF ; Monte Carlo smulaton, system sze up to (9 + 1) up to 136 MCS per hysteress, average over up to 1 runs local mean feld theory (nt)

8 Hysteress of FM and AFM nterface: MC smulatons system cooled n a feld B c =.25J F down to 1.5 B + k B T =.1J F AFM frozen n a doman state wth nterface magnetzaton m (FM) B_ ts rreversble part leads to exchange bas B EB.3J nt D =.1J F m (AFM Interface) m I B

9 Structure of the AFM domans B FC Hyst. T N T Staggered AFM magnetzaton after feld coolng above: large dluton, p =.5, small domans, below: small dluton, p =.3, larger domans.

10 Magnetzaton reversal of the FM layer 1 θ = 8 4 Magnetzaton my coherent rotaton of the FM magnetzaton no asymmetry for θ local FM spns S = S replaced by a macro spn -1 1 Magnetzaton m z F(S x ) = NlDSx 2 NlBS x k B T Tr e β(h AF+H nt ) F (S x ) = 2NlDS x NlB J nt σ F (S x ) = 2NlD βj 2 nt nt ( ) 2 (σ σ ) nt m nt = nt σ l number of FM monolayers N spns per FM monolayer

11 Ñ ¼ ½µ Â ÒØ Ñ ¼ Ñ ¼ ½µ Â ÒØ Swtchng felds ½ F(Sx) À H 2 < H 1 H = 1 < -1 1 S x ½ F (S x ) = 2NlDS x NlB J nt m nt Felds B and B + for magnetzaton swtchng from F = at S x = 1 and S x = 1, respectvely: À B = 2D J nt m nt ( B, S x = 1 ) /l, B + = 2D J nt m nt ( B+, S x = 1 ) /l, m nt = m + m rev m rev = χ (1) AF J nts x + χ (2) AF B

12 Hysteress of FM and AFM nterface: MC smulatons system cooled n a feld B c =.25J F down to 1.5 B + k B T =.1J F AFM frozen n a doman state wth nterface magnetzaton m (FM) B_ ts rreversble part leads to exchange bas B EB.3J nt D =.1J F m (AFM Interface) m I B

13 Lnear approxmaton m nt (B, S x = ±1): AFM nterface magnetzaton determnes coercvty and EB B ± = ±2D J nt m nt (B ±, S x = 1)/l m nt = m + m rev m rev = χ (1) AF J nts x + χ (2) AF B B ± = ±2D J ntm /l±j 2 nt χ(1) AF /l 1+J nt χ (2) AF /l B eb = 1 2 (B + + B ) = J ntm /l 1+J nt χ (2) AF /l B c = 1 2 (B + B ) = 2D+J2 nt χ(1) AF /l 1+J nt χ (2) AF /l dependence on the sgn of J INT H c /J AF H c ln H c num (1) T/T N mean feld approach

14 MF approxmaton; no dluton σ = m = tanh (β ( J AF j m j + J nt S x + B )).18 (a).18 (b) H c /J AF.1 H c /J AF L=1 L=2 L=3 L=8.6.2 L=1 L=2 L=3 L= (1) T/T N (1) T/T N Coercve feld as functon of reduced temperature for dfferent AFM layer thcknesses l. left: J nt = J AF rght: J nt = J AF D/J F =.5 large ncrease of the coercvty n the vcnty of the Neel temperature T N (Scholten, Usadel, Nowak, Phys. Rev. B 71, (25))

15 Dluted systems Local mean feld equatons: m = ǫ tanh (β ( J AF j ǫ j m j + J nt S x + B )) Coolng: Iteraton at a fxed temperature untl a (metastable) self-consstent soluton s obtaned, then reducng temperature n small steps.

16 Coercvty and bas felds: dfferent AFM dluton p H c /J AF.1 H c /J AF H eb /J AF p=. p=.1 p=.3 p=.6 H eb /J AF p=. p=.1 p=.3 p= (1,) T/T N l = 3 and J nt = J AF (1,) T/T N l = 3 and J Int = J AF maxmum of the coercvty ndependent of dluton: χ max = x/t N (x); x concentraton of magnetc stes

17 Generalzaton to AFM vector spns H o = BS x () D S x () 2 + H ex h α () = S α () H o + J nt σ α () h α () = S α () H o + J nt m α () m α () = χ (1) αβ B β + J nt χ (2) αβ S β() + m,α () Effectve (free) energy of the FM layer: separaton of tme scales and/or slow varaton n space: thermal average restrcted to the AFM AFM eqlbrum susceptbltes χ (1) αβ and χ (2) αβ and exchange feld as response to external feld F = H o J nt S α ()χ (1) αβ B β 1 2 J2 nt S α ()χ (2) αβ S β() S α ()m,α () enhanced moment; enhanced ansotropy

18 F = H o J nt S α ()χ (1) αβ B β 1 2 J2 nt S α ()χ (2) αβ S β() S α ()m,α () maxmum lowerng of symmetry occurs when only one component of the susceptblty tensor, χ x,x, s nonzero: Isng antferromagnet H o = BS x () DS 2 x() + H ex S α ()m,α () B = B[1 + (J nt /l)χ] D = D + [Jnt/(2l)]χ 2 = B c /2 strong dependence on temperature relatvely weak ansotropy n the ferromagnet: maxmum value of h c /J nt.1 for 2D/J nt =.2. Ths corresponds to ( B/B) max 1.1 and ( D/D) max 5. Dynamcal consequences: doman wall wdth and doman wall energy E DW : ( ) max (ẼDW) max J/ D; J D wall velocty v DW : ṽ DW B. Stamps, Usadel,Europhys. Lett., 74, 512 (26)

19 Conclusons Doman state model explans exchange bas and many effects assocated wth t wthout explctely assumng some net AFM nterface magnetzaton frozen AFM nterface magnetzaton leads to EB reversble part of the AFM nterface magnetzaton leads to enhanced coercvty provdng the AFM s ansotropc for slow FM dynamcs and slow spatal varaton of ts magnetzaton an effectve FM energy can be obtaned after ntegratng out the AFM degrees of freedom