olivier isnard institut néel -...
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Olivier ISNARD Institut Néel
What is the susceptibility ?
Answer which one?
M
H
χi
χm
Hst
Mst
M0 χ0
χ
Initial susceptibility
Mean susceptibility
High field susceptibility
0==
HdH
dMχ
Olivier ISNARD Institut Néel
What is the susceptibility ?Answer which one?
HM
=χ
''' χχχ i−=
Initial susceptibility
Mean susceptibility
High field susceptibility
Tensor of susceptibility
Differential susceptibility
dc or ac susceptibility…
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
333231
232223
131211
χχχχχχχχχ
HMrr
χ=
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛=
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
3H2H1H
333231232221131211
3M2M1M
χχχχχχχχχ
),,( HTfmaterial ωχ =
M
H
ijHijMd
ij ∂
∂=χ
Susceptibility often express/ mass or/ volume or/ molecule
Olivier ISNARD Institut Néel
What is the physical meaning of real and imaginary part of susceptibility ?
''' χχχ i−=tacHHtH ωcos)( +=
)cos()( φω −+= tacMMtM
)sinsincos(cos)( φωφω ttacMMtM −+=
''' χχχ i−=acH
acM φχ cos' =acH
acM φχ sin'' =and
)exp()( tiacHHtH ω+= )exp()( tiacMacMtM ωχ+=
2''21
acHacP χω=power absorbed per unit volume
Phase shift
Olivier ISNARD Institut Néel
acHacM φχ cos' =
acHacM φχ sin'' =
Real part
Imaginary part
Reflects sensitivity of material to H appliedEventually in the different directions (tensor rank 2)
),,( HTfmaterial ωχ =
Non zero values of χ’’ related to dispersion centered at a frequency of ωτ =1/τ τ being a relaxation time ie: domain wall motions, relaxation irreversibility, magnetic phase transition, Tc, spin reorientation …
Remember
Tm2Fe17
Tm2Fe17D3
Reflects :•phase shift of H applied•dissipation energy lost absorption of energy
Ac susceptibility is a very sensitive technique !!
From Hz to 10 KHz…
F. Grandjean, O. Isnard, G.J. Long
What is the physical meaning of realand imaginary part of susceptibility ?
Olivier ISNARD Institut Néel
After Lemoine thesis Univ. Nancy
Signal at the ordering of the rare earth
Olivier ISNARD Institut Néel
What is the susceptibility ?
Differential susceptibility
ijHijMd
ij ∂
∂=χ
In ferromagnetic materials the relation between M and H is not linear
Differential susceptibility also referred to
M
H
χi
χm
Hst
Mst
M0 χ0
χ 0==
HdH
dMχ
Olivier ISNARD Institut Néel
In which measurement can you see difference between superparamagnetism and spin glass behaviour?
Similar behaviour from magnetization measurements
What is spin glass ?
What is superparamagnetism ?
T
MField cooling
Zero Field cooling
T critical = T blocking or T freezingsuperparamagnetism
Olivier ISNARD Institut Néel
Superparamagnetism
•Ferromagnetic particles => J>0 •Small particles => single domain (cf lecture Olivier)•Anisotropy M preferentially aligned along one direction energy KV
Competition between kT and KV => limit on particle sizeIf V decreases then anisotropy energy also and Magnetization of the particle no longer force to be along the easy direction because of kT
⇒ Fluctuation of the magnetization direction intrinsically ferromagnetic particles but appearing like para (superpara)
The particle behaves like a macrospin
Coherence length larger than the particle size at T> Tblocking
k Tblocking ~ K V SuperparaFe particles
20 nm
Olivier ISNARD Institut Néel
Spin glasses ie: Fe diluted in Au or Cu1-xMnx and x 0
• Diluted system• Mixed interaction competing• J>0 and J<0 (RKKY int.)• Random• Transition from not ordered to low T metastable state (no
long range order)
Opposite limit percolation between clusters => ordering
ZFCFC
Tspin freezing
The term "glass" comes from an analogy between the magnetic disorder in a spin glass and the positional disorder of a conventional, chemical glass
Olivier ISNARD Institut Néel
In which measurement can you see difference between superparamagnetism and spin glass behaviour?
ac susceptibility in particular frequency dependence
superparamagnetism and spin glass exhibit similar behavior from magnetization measurements
For more detailsJ.A. Mydosh, Spin Glasses : An experimental Introduction, Taylor & Francis : London, 1993.
Specific heat (magnetic one) independent of T below Tfreezing
Local probe of the internal magnetic field•Mössbauer spectroscopy 10-7-10-10s•Muon spectroscopy 10-5-10-10s•Neutron spectroscopies 10-10-10-12s• NMR …
Access to relaxation time
ie: Relaxation time of the moment in the superparamagnet
B. Idzikowski et al 1999 Europhys. Lett. 45 714
Olivier ISNARD Institut Néel
Signature of Spin Glass from M(T) and Xac
''' χχχ i+=
''χ
'χ
Follow the frequency dependence For more detailsJ.A. Mydosh, Spin Glasses : An experimental Introduction, Taylor & Francis : London, 1993.
Olivier ISNARD Institut Néel
What is superparamagnetism ?
Co
Ni
CoPt
FePt
FeCo
Fe3O4
Fe2O3
CoFe2O4
0 20 40 60 80 100 120
Nanoparticle diameter (nm)
Dsd
Dsp
Usuallly of interest for Crystalline materialsLarge anisotropy
Olivier ISNARD Institut Néel
alloysystem
material K:anisotropyin 1e7erg/cc
Ms:saturationmagnetization inemu/cc
Hk:anisotropyfield inkOe
Dp:minimalstablediameterin nm
CoCrPtX 0.20 200-300 15-20 8-10Co-alloys Co 0.45 1400 6.4 8
hex Co3Pt 2.0 1100 36 4.8
FePd 1.8 1100 33 5.0L10phases
FePt 6.6-10 1140 116 2.8-3.3
CoPt 4.9 800 123 3.6MnAl 1.7 560 69 5.1
RE-TM Nd2Fe14B 4.6 1270 73 3.7Co5Sm 11-20 910 240-400 2.2-2.7
KTkD B
P⋅⋅
=60Minimal Stable Grain Diameter
A few nm
Olivier ISNARD Institut Néel
0.0
5.0
10
15
20
25
30
250 300 350 400 450 500
YCo4Si
M2 (u
.a.)
T(K)
Tc=320(5)K
µ0H=1T
Ideally In practise
Olivier ISNARD Institut Néel
Origin of this behavior ?Short range ordering = correlation between neighbouring spins even just above Tc
Existence of a typical correlation length which is infinite in the ordered stateTends to zero at high temperatureTypical scale where there is correlation between the magnetic moments⇒No longer independent => not strictly paramagnetic ⇒Reminiscent of magnetic order for a certain T range
How to observe it experimentallyNeutron scatteringsince short range order => diffuse neutron scatteringSmall angle scattering depending upon coherence length
