MAGNETIC BEHAVIOUR OF CORE/SHELL NANOPARTICLE ASSEMBLIES: INTERPARTICLE INTERACTIONS EFFECTS

Transcription

1 IMS MAGNETIC BEHAVIOUR OF CORE/SHELL NANOPARTICLE ASSEMBLIES: INTERPARTICLE INTERACTIONS EFFECTS Kalliopi Trohidou Computational Materials Science Group Institute of Materials Science, NCSR Demokritos, Athens, Greece.

2 Study of the Magnetic Behaviour of Nanoparticles Understanding of Physical Properties Finite size effects Surface and interface effects Interparticle Interactions effects Applications Magnetic recording media Biomedical applications

3 Outline of the talk Introduction Core/shell nanoparticles, basic characteristics Interparticle interaction effects Granular Solids 2D ordered arrays single spin core/shell nanostructures Concluding remarks

4 Magnetic Domains Magnetic Materials Ferromagnets Energy Minimisation

5 Nanoparticles are single domain N Μ= Σ m i i=1

6 How big? 100 atoms Co 1.3 nm diameter 500 atoms Co 2.2 nm diameter 1000 atoms Co 2.8 nm diameter Co-fcc structure 5000 atoms Co 4.7 nm diameter

7 NANOPARTICLE ASSEMBLIES Langevin Function μ=μ L(μ. Η/ΚΤ)=cot(μ. Η)-ΚΤ/μ. Η μ>> μ atomic Superparamagnetism The assembly becomes superparamagnetic above the Blocking Temperature (T B ) For μ. Η << ΚΤ For μ. Η >> ΚΤ μ=μ 2 Η/ 3ΚΤ μ=μ(1-κτ/μη)

8 Magnetic Nanoparticles Α. Modified Bulk Properties Temperature dependence of the Magnetization Higher anisotropies (at least an order of magnitude) than the bulk materials Different anisotropy strength and type on the surface because of the reduced symmetry Β. Properties Non-observable in bulk materials Influence on the Coercive field Finite magnetization in antiferromagnetic particles. High coercive fields in antiferromagnetic and ferrimagnetic nanoparticles Shifted Hysteresis Loops and High coercive fields on composite core/shell particles Monte Carlo studies on surface and interface effects of magnetic nanoparticles Chapter in Surface Effects in Magnetic Nanoparticles. Editor D. Fiorani, Springer Verlang Series on Nanostructure Science and Technology (2005)

9 Storage Densities on Single Particles 20 nm 600 Gb/in 2 10 nm 2.4 Tb/in 2 Unstable at RT < 5 nm >10 Tb/in 2 Required by 2012

10 Scientific challenges Storage medium (hard disk) Areal density > 100 Gbits/in 2 Need to overcome magnetic instability (superparamagnetic limit) high anisotropy Ordered arrays (self-organisation)

11 Core-Shell Nanoparticles Exchange anisotropy The interaction between the ferromagnetic(fm) core and the antiferromagnetic(afm) or ferrimagnetic(fi) shell, leads to a unidirectional anisotropy which is called exchange anisotropy. The exchange anisotropy results in : Enhanced coercivity. Shifted hysteresis loops after a field cooling procedure. Reversal in the temperature dependence of coercivity with particle size

12 Shifted Hysteresis Loops Exchange Bias Field Hex= (H 1 -H 2 )/2 Coercive Field Hc= (H1+H2)/2 Vertical Shift DM=M1-M2

13 System Morphology FM Core and AFM or FI shell Atomic-scale modeling Ε = J ur ur S S K ur ( S e) ² J urur S S FM i j ifm i i SH i j i, j FM i FM i, j SH ur urur uur ur K ( S e$ ) ² J S S H S ish i i IF i j i i SH i FM, j SH i Energy minimization method Metropolis Monte Carlo

14 Numerical Modelling of magnetic nanoparticles with core/shell morphology in an atomic scale Origin of the exchange bias effects Effect of the core/shell ratio Critical shell thickness for the appearance of Hex Effect on the exchange bias properties of J SH and J IF Origin of the vertical (DM) shift Training Effect Aging Effect Phys. Rev B71, (2005) Phys. Rev B74, (2006) Modern Phys.Lett. B21, 1169(2007) J. Phys. Cond.Matt.19, (2007) Phys. Stat. Sol. (A), Vol. 205, 1865(2008) Phys. Rev B79, (2009)

15 Magnetic Behavior of Assemblies of Nanoparticles Modification of the magnetic and blocking behavior with the interparticle distance due to interparticle interactions To study the dependence of the coercive (H C ), the exchange bias field (H E ) and the magnetisation curves in granular solids and ordered arrays consisted of nanoparticles with FM core/afm shell morphology on the interparticle interactions and to compare their magnetic behavior with that of single spin nanoparticle assemblies. Aim of Work

16 System Morphology AFM Shell (2 sublattices) AFM Interface (2 sublattices) FM Interface FM Core Granular solids Multiscale Modeling : Beyond the single-spin (SW) model 2D ordered arrays

17 Numerical Modeling Atomic-scale modeling AFM Shell AFM Interface (alloying with the FM interface) FM Interface (alloying with the AFM interface) FM Core PR B 71, (2005) Scaling parameters for the magnetisation in AFM Shell (2 sublattices-2 spins) AFM Interface (2 sublattices-2 spins) FM Interface FM Core

18 Numerical Modeling Magnetic state of a nanoparticle : Four regions and six spins AFM Shell (2 sublattices) AFM Interface (2 sublattices) FM Interface FM Core Ŝ 4 H r Ŝ 2 Ŝ 1 Ŝ 5 Ŝ 3 ê Ŝ 6 E (Intra-particle) = Anisotropy + Exchange + Zeeman

19 Granular film Numerical Modeling Ordered arrays E (Inter-particle) = Dipole-Dipole Interactions (DDI) E= g i ( mˆ mˆ )-3( mˆ rˆ )( mˆ rˆ ) i j R 3 ij i ij j ij

20 Total Energy Total E = E (Intra-particle) + E (Inter-particle) Energy Minimisation by Metropolis Monte Carlo algorithm Exchange parameters Anisotropy parameters Dipolar Strength J FM J FM J AFM K FM K IF K AFM M s2 /K The magnetic field and the anisotropy constant are expressed in units J FM /gμ Β and the temperature in units J FM /k.

21 Single-spin nanoparticle assemblies Granular film hcp bilayer Mesoscopic scale model Coherent rotation model (Stoner-Wolfarth) ( mˆ Rˆ )( mˆ Rˆ ) ( mˆ mˆ ) ( ) ( ) 2 3 i ij j E = h mˆ Hˆ + k mˆ eˆ + g i 1 i i 3 i j Rij Energy parameters g=m 2 /D 3 Dipolar k=k 1 V Anisotropy h=mh Zeeman ij i j

22 Modeling of Isothermal Hysteresis System initially at positive saturation Positive external field reduced gradually Magnetization recorded at H=0 : Positive Remanence Negative applied field reduced gradually Field recorded when M=0 : Coercivity Hc1 Negative saturation Magnetization recorded at H=0 : Negative Remanence Applied field increased gradually Field recorded when M=0 : Coercivity Hc2 Positive external field increased gradually

23 MC simulations on the Hysteresis behaviour of FM core and AFM shell random assemblies of nanoparticles Co/Mn c=10% c=5% c=1.5% 0,1 Experimental results Nanospin Samples Co in Mn M/Ms H(J FM /gµ B ) m/ m sat (a.u.) 0,0-0, H 0(T) 2000 T = 5K VFF=9,8% VFF=4,7% VFF=1,5% Preformed Co clusters (2 nm diam.) codeposited with Mn from MBE source Increase of Hc with VF Co@Mn: Competing ordering Co: FM Mn: AFM

24 Co in Mn Comparison with Co in Ag: Experimental results Hc bigger for the Co in Mn system C=4.7% J. Phys D Appl. Phys. 41, (2008)

25 Comparison of Co/Mn and Co/Ag Hysteresis Behaviour : Numerical simulations 1,0 0,8 0,6 0,4 0,2 Co/Mn c=10% c=5% c=1.5% Co/Ag c=5% 1,0 0,8 0,6 0,4 0,2 Co/Mn Co/Ag M/Ms 0,0-0,2 M/Ms 0,0-0,2-0,4-0,4-0,6-0,6-0,8-0,8-1, , H(J FM /gµ B ) H(J) C=5% Hc bigger for the Co@Mn system in agreement with the experimental findings

26 Numerical Modelling of the Temperature dependence of Hc and Hex 0,5 0,5 Hex (J FM /gµ B ) Hc(J FM /gµ B ) 0,4 0,3 0,2 0,1 0,0 Hc Hex T(J/K B ) Hex(J FM /gµ B ) Hc(J FM /gµ B ) 0,4 0,3 0,2 0,1 0, T(J/K B ) Co/Mn Hc Hex Co/Ag Hc C=5% Exponential decay of Hex and Hc with temperature for the core/shell nanoparticles, in agreement with the experimental findings.

27 Co/CoO granular systems Sample S1 VF~8% Sample S3 VF~33% Very big increase of Hex with VF Exponential decay of Hc and Hex at VF 8% J. Nogues, V. Skumryev, J. Sort, S. Stoyanov, and D. Givord PRL 97, (2006)

28 Modeling of Temperature Dependent Magnetization (ZFC/FC) System initially at high-t and H=0 (M=0) Temperature lowered gradually to zero limit (Ground state) Weak field applied & temperature raised gradually - M ZFC (T) Field remains & temperature lowered gradually M FC (T)

29 NUMERICAL SIMULATIONS OF THE ZFC MAGNETIZATION CURVES OF ASSEMBLIES OF NANOPARTICLES WITH FM CORE AND RANDOM AFM SHELL c=10% c=5% c= M 0.06 Increase of Tmax with the concentration T(J/K B )

30 Simulated ZFC/FC for Ag Concentration Effects c=10% c=5% c=1.5 Mz Increase of Tmax with the concentration T(K)

31 ZFC/FC Measurements: 3,0x10-7 VFF= 9,8% VFF= 4,7% VFF= 1,5% H = 100 Oe χ (emu/oe) 0, T (K) Co in Mn T Max S1 9.2% 64 K S2 4.7% 65 K S3 1.3% 58 K χ (emu/ cm 3 Co ) 3.0 H = 100 Oe VFF = 9,8% VFF = 4,7% VFF = 1,5% T (K) T B 8.9% 18 K Co in Ag 4.7% 17 K 1.5% 9.5 K

32 Comparison of Co/Mn and Co/Ag ZFC curves C~5% x10-2 FC Mtot χ (emu/cm 3 ) Co@Mn 1.0x x10-3 FC ZFC ZFC χ (emu/cm 3 ) Co@Ag T(J/K B ) T (K) Left:Simulated ZFC curves for Co@Mn(full circles) and Co@Ag (open circles) nanoparticle assembliesm. Right: Measurered ZFC/FC curves. Co@Mn has higher T B

33 Concluding Remarks for Random Assemblies Random Assemblies of the composite FMcore/AFMshell nanoparticles exhibit: Higher Hc than the SW type nanoparticle assemblies and appearance of Hex Increase in Hc with the particle density. Exponential decay of Hex and Hc with temperature Training effect in Hex Higher T B than the SW type nanoparticle assemblies In agreement with the Co/Mn experiments

34 Single spin Ordered Arrays Film morphology TEM image of 5.8-nm fcc Co nanoparticles (Petit and Pileni, Adv Mat 1998) TEM image of 8-nm fcc Co nanoparticles (Murray et al MRS Bulletin 2001) Almost identical spherical nanoparticles (σ<10%) Located on nodes of a hexagonal quasi 2-d lattice

35 Experimental Results - Increase of T b X.X.Zhang et al JMMM (2003) C. Petit, et al, Adv. Mater. 10 (1998) 259

36 T B dependence from the simulations Ordered arrays granular solids 0,8 0.6 Magnetization (M/M s ) 0,6 0,4 0,2 (D/d) ,0 0,0 0,1 0,2 0,3 0,4 0,5 0,6 Temperature (k B T/K 1 V) Blocking Temperature (k B T b /K 1 V) Volume Fraction (x v ) Exchange g/k=0 J/k=0 J/k=0.5 J/k=10. Exchange+Dipolar g/k=0.5 J/k=0 J/k=0.5 J/k=10. Appl. Phys. Lett. 81 (2002) 4574 J.Mag.Mag.Mater. 262, 107(2003)

37 Dependence of T b on inter-particle distance 0,8 Magnetization (M/M s ) 0,6 0,4 0,2 (D/d) ,0 0,0 0,1 0,2 0,3 0,4 0,5 0,6 Temperature (k B T/K 1 V) The blocking temperature (T b ) increases when the inter-particle spacing (d) decreases (interactionsinduced anisotropy) T b / T b 0 1,5 Scaling behavior : T b 1/d 3 T b (dipolar strength) Dipolar interactions increase the single-particle energy barrier 1,0 0,0 0,2 0,4 0,6 1/d 3 Appl. Phys. Lett. 81 (2002) 4574

38 Dependence of T b on coverage Magnetization (M/M s ) 0,6 0,5 0,4 0,3 0,2 0,1 Coverage ,0 0,0 0,1 0,2 0,3 0,4 0,5 0,6 Temperature (k B T/K 1 V) The blocking temperature (T b ) increases with layer coverage - due to increase of coordination number and the macroscopic Lorentz field. 1,4 Saturation of T b at approximately 1ML T b / T b 0 1,2 1,0 MC data fitting curve Coverage (ML) Predominantly in-plane dipolar interactions modify blocking behavior Appl. Phys. Lett. 81 (2002) 4574

39 2D Self-Organization of Core/Shell Cohcp/CoO Nanocrystals I. Lisiecki, M. Walls, D. Parker, and M. P. Pileni Langmuir, 2008, 24 (8), 4295

40 Ordered Arrays Decrease of the interparticle distance reduction of Hc increase of Hex H E H C 0,62 0,60 0,58 0,56 0,22 0,20 (a) R C =5 R o =9 M s 2 / K FM = 1. H E H C 0,24 0,22 0,20 0,18 0,16 0,10 0,08 (b) M s 2 / K FM = 6.5 Increase of the dipolar strength reduction of Hc reduction of Hex 0, d 0 / a 0, d 0 / a Coercivity (H C ) and exchange bias field (H E ) as a function of the interparticle spacing (d 0 ) in a 2D hexagonal array R C =5a and external radius R=9a. (a) weakly dipolar (M 2 s/k=1.0) and (b) strongly dipolar (M 2 s/k=6.5) material.

41 Coercivity and Exchange Bias Size dependence Shell Thickness = 4a // Weakly Dipolar Material M s2 /K FM =1.0 R FM =5a R FM =12a 0.62 H E H C d/a H E H C d/a The smaller core size results to higher Hc and Hex Coercivity (H C ) and exchange bias field (H E ) as a function of the interparticle spacing (d) in a 2D hexagonal array of nanoparticles.

42 Experimental results K. Temst, E. Popova, H. Loosvelt, M.J. Van Bael, S. Brems, Y. Bruynseraede,C. Van Haesendonck, H. Fritzscheb, M. Gierlings, L.H.A. Leunissen, R. Jonckheere. Journal of Magnetism and Magnetic Materials 304 (2006) 14 18

43 Concluding Remarks on Ordered Arrays Ordered arrays of Single Spin nanoparticles: Increase of T B with coverage Decay of T B with cube of interparticle distance Dipolar Interparticle Interactions in ordered arrays of FMcore/AFMshell nanoparticles: facilitate the magnetization reversal in both directions Small reduction of Hc have an asymmetric effect on the two branches Small increase of Hex The reduction of H C is more pronounced in strongly dipolar materials and large nanoparticles.

44 Collaborators Modelling Computational Materials Science Group, IMS Demokritos, M. Vasilakaki E. Eftaxias G. Margaris J.A. Blackman (University of Reading) Experiments C. Binns (Leicester, UK) D. Fiorani (Rome, Italy) A. M. Testa(Rome, Italy) N. Domingo(Barcelona, Spain) X. Tejada(Barcelona, Spain) The work was supported by EU STREP project No. NMPCT NANOSPIN (SELF-ORGANISED COMPLEX-SPIN MAGNETIC NANOSTRUCTURES )