the role of exchange bias in domain dynamics control

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Information about the role of exchange bias in domain dynamics control

Published on January 5, 2017

Author: AndreaBenassi3

Source: slideshare.net

1. The  Role  of  Exchange  Bias  in    Domain  Dynamics  Control   A.  Benassi1,  M.A.  Marioni1,  D.  Passerone1  and  H.J.  Hug1,2               1-­‐  EMPA  Swiss  Federal  InsHtute  for  Materials  Science  and  Technology,  Dübendorf  (Switzerland)   2-­‐    Department  of  Physics,  Universität  Basel,  Basel  (Switzerland)  

2. Sample  and  measurements   A  perpendicular  anisotropy  ferromagneHc  film  (FF)  is  anH-­‐coupled  with  a  thinner   anHferromagneHc  film  (AF)  grown  on  top     Upon  cooling  below  the  Neel  temperature,  the  AF  becomes  ordered  except  for  few   atomic   layer   at   the   interface,   here   the   defects   at   the   interface   give   rise   to   a   distribuHon  of  uncompensated  spins  (UCS)   Being  the  Neel  temperature  of  the  AF  smaller  than  the  Curie  temperature  of  the  FF,  the  presence  of  the  ferromagneHc   domains   can   orient   the   uncompensated   spin   at   the   interface   during   the   cooling.   This   allow   us   to   fix   stably   the   FF   domain  structure  on  the  cooled  AF.       the  domains  image  is   taken  through  the  AF   layer  because  the  FF   field  is  orders  of   magnitude  stronger   the  UCS  image  is  taken   saturaHng  the  FF   domains  with  an   external  field   Schmid  e  al.  PRL  105  197201  (2010)            Joshi  et  al.  Appl.Phys.LeY.  98  082502  (2011)   Hext uncompensated   frustrated   AF   FF  

3. The  model  system   The  Landau-­‐Lifshitz-­‐Gilbert  (LLG)  equaHon  rules  the  precession  of  a  magneHc  dipole  in  an  external  field:   ∂m ∂t = − γ 1 + ξ2 m × B + ξ m × B B = − 1 Ms δH[m] δm + Q(R, t) Q(R, t) = 0 Q(R, t)Q(R , t ) = δ(t − t )δ(R − R )2KBTξ/Msγ Bm precession  term   Bm damping  term   dissipaHon  by   microscopic  degrees   of  freedom     Bm stochasHc  term   thermal  fluctuaHons   Under  the  following  approximaHons:       •  scalar  magneHzaHon  uniform  along  the  FF  thickness  d •  domain  walls  smaller  than  the  domain  size   •  small  FF  thickness  d the  magneHzaHon  in  the  FF  can  be  described  by  the   following  hamiltonian  power  expansion:     Gilbert  IEEE  Trans.  On  MagneHcs  40  3434  (2004)            Brown  Phys.Rev.  130  1677  (1963)            Usadel  PRB  73  212405  (2006)   m(r, t) = m(x, y, t)ˆz H = d3 R − Ku(R) m2 2 + A 2 (∇Rm)2 + µ0M2 s d 8π d2 R m(R )m(R) |R − R|3 − µ0Msm(Hext − HUCS(R))

4. The  model  system   ∂m ∂t = − γ 1 + ξ2 m × B + ξ m × B B = − 1 Ms δH[m] δm + Q(R, t) Q(R, t) = 0 Q(R, t)Q(R , t ) = δ(t − t )δ(R − R )2KBTξ/Msγ Bm Bm Under  the  following  approximaHons:       •  scalar  magneHzaHon  uniform  along  the  FF  thickness  d •  domain  walls  smaller  than  the  domain  size   •  small  FF  thickness  d the  magneHzaHon  in  the  FF  can  be  described  by  the   following  hamiltonian  power  expansion:     Jagla  PRB  72  094406  (2005)            Jagla  PRB  70  046204  (2004)     m(r, t) = m(x, y, t)ˆz The  Landau-­‐Lifshitz-­‐Gilbert  (LLG)  equaHon  rules  the  precession  of  a  magneHc  dipole  in  an  external  field:   precession  term   Bm damping  term   dissipaHon  by   microscopic  degrees   of  freedom     stochasHc  term   thermal  fluctuaHons   H = d3 R − Ku(R) m2 2 + A 2 (∇Rm)2 + µ0M2 s d 8π d2 R m(R )m(R) |R − R|3 − µ0Msm(Hext − HUCS(R))

5. The  model  system   Under  the  following  approximaHons:       •  scalar  magneHzaHon  uniform  along  the  FF  thickness  d •  domain  walls  smaller  than  the  domain  size   •  small  FF  thickness  d the  magneHzaHon  in  the  FF  can  be  described  by  the   following  hamiltonian  power  expansion:     m(r, t) = m(x, y, t)ˆz Jagla  PRB  72  094406  (2005)            Jagla  PRB  70  046204  (2004)     anisotropy  term:   its   fluctuaHons   around   an   average   value   provides   strong   pinning   points   for   the   domain   walls   Ku(R) = Ku(1 − P(x, y)) P(R) = 0 P(R)P(R ) = θδ(R − R ) H = d3 R − Ku(R) m2 2 + A 2 (∇Rm)2 + µ0M2 s d 8π d2 R m(R )m(R) |R − R|3 − µ0Msm(Hext − HUCS(R))

6. H = d3 R − Ku(R) m2 2 + A 2 (∇Rm)2 + µ0M2 s d 8π d2 R m(R )m(R) |R − R|3 − µ0Msm(Hext − HUCS(R)) The  model  system   anisotropy  term:   its   fluctuaHons   around   an   average   value   provides   strong   pinning   points   for   the   domain   walls   Under  the  following  approximaHons:       •  scalar  magneHzaHon  uniform  along  the  FF  thickness  d •  domain  walls  smaller  than  the  domain  size   •  small  FF  thickness  d the  magneHzaHon  in  the  FF  can  be  described  by  the   following  hamiltonian  power  expansion:     m(r, t) = m(x, y, t)ˆz Ku(R) = Ku(1 − P(x, y)) P(R) = 0 P(R)P(R ) = θδ(R − R ) Jagla  PRB  72  094406  (2005)            Jagla  PRB  70  046204  (2004)     anisotropy  term:   it  represents  the  energy  cost  for   the  domain  walls.           we   do   not   have   real   Block   or   Neel  walls,  just  their  projecHon   along  z      

7. H = d3 R − Ku(R) m2 2 + A 2 (∇Rm)2 + µ0M2 s d 8π d2 R m(R )m(R) |R − R|3 − µ0Msm(Hext − HUCS(R)) The  model  system   anisotropy  term:   its   fluctuaHons   around   an   average   value   provides   strong   pinning   points   for   the   domain   walls   Under  the  following  approximaHons:       •  scalar  magneHzaHon  uniform  along  the  FF  thickness  d •  domain  walls  smaller  than  the  domain  size   •  small  FF  thickness  d the  magneHzaHon  in  the  FF  can  be  described  by  the   following  hamiltonian  power  expansion:     m(r, t) = m(x, y, t)ˆz Ku(R) = Ku(1 − P(x, y)) P(R) = 0 P(R)P(R ) = θδ(R − R ) Jagla  PRB  72  094406  (2005)            Jagla  PRB  70  046204  (2004)     anisotropy  term:   it  represents  the  energy  cost  for   the  domain  walls.           we   do   not   have   real   Block   or   Neel  walls,  just  their  projecHon   along  z       stray  field  energy:   responsible   for   the   domain   formaHon               non  local  term  to  be  treated  in   reciprocal  space  

8. H = d3 R − Ku(R) m2 2 + A 2 (∇Rm)2 + µ0M2 s d 8π d2 R m(R )m(R) |R − R|3 − µ0Msm(Hext − HUCS(R)) The  model  system   anisotropy  term:   its   fluctuaHons   around   an   average   value   provides   strong   pinning   points   for   the   domain   walls   Under  the  following  approximaHons:       •  scalar  magneHzaHon  uniform  along  the  FF  thickness  d •  domain  walls  smaller  than  the  domain  size   •  small  FF  thickness  d the  magneHzaHon  in  the  FF  can  be  described  by  the   following  hamiltonian  power  expansion:     m(r, t) = m(x, y, t)ˆz Ku(R) = Ku(1 − P(x, y)) P(R) = 0 P(R)P(R ) = θδ(R − R ) Jagla  PRB  72  094406  (2005)            Jagla  PRB  70  046204  (2004)     anisotropy  term:   it  represents  the  energy  cost  for   the  domain  walls.           we   do   not   have   real   Block   or   Neel  walls,  just  their  projecHon   along  z       stray  field  energy:   responsible   for   the   domain   formaHon               non  local  term  to  be  treated  in   reciprocal  space   UCS   field:   as   measured   in  the  experiment  

9. H = d3 R − Ku(R) m2 2 + A 2 (∇Rm)2 + µ0M2 s d 8π d2 R m(R )m(R) |R − R|3 − µ0Msm(Hext − HUCS(R)) The  model  system   anisotropy  term:   its   fluctuaHons   around   an   average   value   provides   strong   pinning   points   for   the   domain   walls   Under  the  following  approximaHons:       •  scalar  magneHzaHon  uniform  along  the  FF  thickness  d •  domain  walls  smaller  than  the  domain  size   •  small  FF  thickness  d the  magneHzaHon  in  the  FF  can  be  described  by  the   following  hamiltonian  power  expansion:     m(r, t) = m(x, y, t)ˆz Ku(R) = Ku(1 − P(x, y)) P(R) = 0 P(R)P(R ) = θδ(R − R ) Jagla  PRB  72  094406  (2005)            Jagla  PRB  70  046204  (2004)     anisotropy  term:   it  represents  the  energy  cost  for   the  domain  walls.           we   do   not   have   real   Block   or   Neel  walls,  just  their  projecHon   along  z       stray  field  energy:   responsible   for   the   domain   formaHon               non  local  term  to  be  treated  in   reciprocal  space   UCS   field:   as   measured   in  the  experiment   External  field:  uniform   but  Hme  dependent    

10. Pueng  this  approximate  hamiltonian  inside  the  LLG  equaHon  we  obtain  the  following  equaHon  of  moHon:           where  everything  is  now  in  dimensionless  units:                 the  model  contains  only  three  non-­‐independent  dimensionless  parameters  related  to  the  material  proper.es:     ∂m ∂τ = (1 − m2 ) α(1 − p(r)) m − 1 4π d2 r m(r ) |r − r|3 + hext(t) − hUCS(r) + q(r, τ) + β∇2 rm The  model  system   Jagla  PRB  72  094406  (2005)            Jagla  PRB  70  046204  (2004)            Zhirnov  Zh.Eksp.Teor.Fiz.  35  1175  (1958)     r = R/d τ = tγµ0Ms/ξ hext = Hext/Ms hUCS = HUCS/Ms q(r, τ) = Q(R, t)/µ0Ms KBT = KBT/µ0M2 s d3 dimensionless  posiHon     dimensionless  Hme   dimensionless  fields   η = θ/d3 β = A/µ0M2 s d2 α = Ku/µ0M2 s dimensionless  temperature   dimensionless  thermal  noise   p(r)p(r ) = ηδ(r − r ) dimensionless  anisotropy  noise   uniaxial  anisotropy     exchange  sHffness   anisotropy  fluctuaHons   (strength  on  the   pinning  disorder)  

11. Pueng  this  approximate  hamiltonian  inside  the  LLG  equaHon  we  obtain  the  following  equaHon  of  moHon:           where  everything  is  now  in  dimensionless  units:                 the  model  contains  only  three  non-­‐independent  dimensionless  parameters  related  to  the  material  proper.es:     The  model  system   Jagla  PRB  72  094406  (2005)            Jagla  PRB  70  046204  (2004)            Zhirnov  Zh.Eksp.Teor.Fiz.  35  1175  (1958)     r = R/d τ = tγµ0Ms/ξ hext = Hext/Ms hUCS = HUCS/Ms q(r, τ) = Q(R, t)/µ0Ms KBT = KBT/µ0M2 s d3 dimensionless  posiHon     dimensionless  Hme   dimensionless  fields   η = θ/d3 β = A/µ0M2 s d2 α = Ku/µ0M2 s dimensionless  temperature   dimensionless  thermal  noise   p(r)p(r ) = ηδ(r − r ) dimensionless  anisotropy  noise   uniaxial  anisotropy     exchange  sHffness   anisotropy  fluctuaHons   (strength  on  the   pinning  disorder)   ∂m ∂τ = (1 − m2 ) α(1 − p(r)) m − 1 4π d2 r m(r ) |r − r|3 + hext(t) − hUCS(r) + q(r, τ) + β∇2 rm

12. Pueng  this  approximate  hamiltonian  inside  the  LLG  equaHon  we  obtain  the  following  equaHon  of  moHon:           where  everything  is  now  in  dimensionless  units:                 the  model  contains  only  three  non-­‐independent  dimensionless  parameters  related  to  the  material  proper.es:     The  model  system   Jagla  PRB  72  094406  (2005)            Jagla  PRB  70  046204  (2004)            Zhirnov  Zh.Eksp.Teor.Fiz.  35  1175  (1958)     r = R/d τ = tγµ0Ms/ξ hext = Hext/Ms hUCS = HUCS/Ms q(r, τ) = Q(R, t)/µ0Ms KBT = KBT/µ0M2 s d3 dimensionless  posiHon     dimensionless  Hme   dimensionless  fields   η = θ/d3 β = A/µ0M2 s d2 α = Ku/µ0M2 s dimensionless  temperature   dimensionless  thermal  noise   p(r)p(r ) = ηδ(r − r ) dimensionless  anisotropy  noise   uniaxial  anisotropy     exchange  sHffness   anisotropy  fluctuaHons   (strength  on  the   pinning  disorder)   domain  wall  energy   domain  wall  width     domain  size   domain  morphology  ∝ β/α ∝ αβ ∂m ∂τ = (1 − m2 ) α(1 − p(r)) m − 1 4π d2 r m(r ) |r − r|3 + hext(t) − hUCS(r) + q(r, τ) + β∇2 rm

13. Model  validaHon:  from  micro  to  macro   The  procedure  for  the  determinaHon  of  the  three  material  parameters  is  made  in  such  a  way  to  fit  both  macroscopic  and   microscopic  properHes  of  the  sample:   A   good   iniHal   guess   for   α,β   and   η   makes   the   measured  domain  image  at  0  mT  a  steady  state   of  our  equaHon  of  moHon.  A  good  choice  of  α,β   and   η   is   such   that,   if   we   use   the   measured   image  as  the  iniHal  condiHon  of  our  equaHon  of   moHon  and  we  let  it  evolve  in  Hme,  it  will  not   change.     Benassi  et  al.  (waiHng  for  PRL  rejecHon)  

14. Model  validaHon:  from  micro  to  macro   The  procedure  for  the  determinaHon  of  the  three  material  parameters  is  made  in  such  a  way  to  fit  both  macroscopic  and   microscopic  properHes  of  the  sample:   A   good   iniHal   guess   for   α,β   and   η   makes   the   measured  domain  image  at  0  mT  a  steady  state   of  our  equaHon  of  moHon.  A  good  choice  of  α,β   and   η   is   such   that,   if   we   use   the   measured   image  as  the  iniHal  condiHon  of  our  equaHon  of   moHon  and  we  let  it  evolve  in  Hme,  it  will  not   change.     The  measured  field  from  the  UCS  distribuHon  is     also  included  in  the  equaHon  of  moHon  and  it   helps  in  stabilizing  the  domain  configuraHon.       Benassi  et  al.  (waiHng  for  PRL  rejecHon)  

15. Model  validaHon:  from  micro  to  macro   The  procedure  for  the  determinaHon  of  the  three  material  parameters  is  made  in  such  a  way  to  fit  both  macroscopic  and   microscopic  properHes  of  the  sample:   Than  we  ramp  up  the  external  uniform  field  and   we   trim   the   parameters   in   such   a   way   to   reproduce   the   correct   path   to   saturaHon   looking  also  at  the  MFM  taken  at  100  mT,  200   mT  and  300  mT.   Benassi  et  al.  (waiHng  for  PRL  rejecHon)  

16. Model  validaHon:  from  micro  to  macro   The  procedure  for  the  determinaHon  of  the  three  material  parameters  is  made  in  such  a  way  to  fit  both  macroscopic  and   microscopic  properHes  of  the  sample:   Once   that   the   microscopic   properHes   are   well   reproduced  we  can  check  the  macroscopic  ones   (hysteresis  loops).   We  can  sHll  trim  a  bit  the  model  parameters  to   adjust  the  fine  detail.   Eventually   we   have   to   go   back   and   control   again  the  microscopic  behavior.         The  loops  were  measured  with  a  sample  cooled   in   a   saturaHng   field   so   the   printed   UCS   distribuHon  is  different  from  the  previous  one.   Benassi  et  al.  (waiHng  for  PRL  rejecHon)  

17. Model  validaHon:  from  micro  to  macro   The  procedure  for  the  determinaHon  of  the  three  material  parameters  is  made  in  such  a  way  to  fit  both  macroscopic  and   microscopic  properHes  of  the  sample:   Benassi  et  al.  (waiHng  for  PRL  rejecHon)   αinit = 6.25 βinit = 0.85 ηinit = 1.5 × 10−4 α = Ku/µ0M2 s = 6.6 → Ku = 3.1 × 106 J/m3 β = A/µ0M2 s d2 = 0.88 → A = 2.2 × 10−10 J/m η = 1.88 × 10−4 perfectly  in    the   expected  range   too  big  but  our  1D  walls  are  less  expensive  than  a   real  block  wall  and  A  must  compensate!  

18. Path  to  saturaHon:  the  full  dynamics     Now  that  the  parameters  are  fixed,  the  theoreHcal  model  allows  us  to  access  the  full  dynamics  in  Hme,  we  can  thus   invesHgate  the  domain  behavior  with  more  than  few  MFM  images       Benassi  et  al.  (waiHng  for  PRL  rejecHon)   As   demonstrated   by   the   experiments   the   domains,   retracHng  with  increasing  external  field,  will  try  to  avoid  the   frustrated  F/AF  coupling  regions.      

19. UnmounHng  the  machinery   Benassi  et  al.  (waiHng  for  PRL  rejecHon)   Now  we  can  switch  off  separately  the  different  hamiltonian  terms  and  try  to  understand  and  quanHfy  their  contribuHon:     The  UCS  distribuHon  alone  has  not  enough  strength  to  pin   the   domains   and   even   at   0   mT   the   shape   of   the   steady   configuraHon  is  quite  different  from  the  original  one.     The  saturaHon  occurs  too  early!       The  anisotropy  fluctuaHons  have  enough  strength  to  keep   the  iniHal  configuraHon  pinned,  however,  without  the  help   of  the  UCS  local  field,  the  pinning  sHll  occurs    too  early.  

20. Now  we  can  also  try  to  predict  which  is  the  effect  of  a  different  UCS  distribuHon  on  the  exchange-­‐bias  (EB)  effect  and  on  the   coercivity  of  the  FF.                                     •  As  expected,  switching  off  the  UCS  field  the  EB  effect  goes  to  zero     •  Doubling  the  average  value  of  the  UCS  field,  without  changing  the  fluctuaHons  strength,  increases  the  EB  effect  without   affecHng  the  coercivity   •  Doubling  the  fluctuaHons  of  the  UCS  field,  without  shiking  its  average,  increase  strongly  the  coercivity  with  minor   changings  in  the  EB  loop  shik.   Some  predicHons  on  the  macroscopic  properHes   calc. 10 K -0.5 0.0 0.5 1.0 -1.0 -0.4 -0.2 -0.1 0.0 0.1 0.2 0.4-0.3 0.3 no UCS double UCS average double UCS fluctuations Benassi  et  al.  (waiHng  for  PRL  rejecHon)  

21. Up  to  now  the  fluctuaHons  of  the  uniaxial  anisotropy  have  been  considered  to  be  uncorrelated  (white  noise),  however  they   have  something  to  do  with  the  granularity  of  the  sample.  Something  more  about  the  strength  and  the  correlaHon  of  these   fluctuaHon  can  be  inferred  from  Barkhausen  noise  measurements.                                   The  presence  of  Chromium  atoms  in  the  AF  decouples  the  magneHc  moment  of  neighboring  grains,  increasing  the  UCS  field   by  the  40%.  The  model  will  be  used  to  study  this  new  sample  in  which  the  role  of  the  UCS  map  as  been  enhanced.  ParHcular   aYenHon  will  be  given  to  the  return  point  memory  effects.     The  code  is  easily  parallelizable  allowing  for  the  descripHon  of  lager  system  or  for  the  coupling  of  two  interacHng   magneHzed  films         Further  developments   Benassi  et  al.  PRB  84  214441  (2011)  

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