2. Magnetic Instabilities

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2. Magnetic Instabilities -- Types of magnetic
phase boundaries
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Ranges of magnetic order detection (34 examples)
Sereni, J Phys Soc Jpn 67 (1998) 1767
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Sorting magnetic phase boundaries
Sereni, J.Phys.Soc.Jpn, 70 (2001) 2139
Type III TN nearly constant
Type II TN vanishes at finite temperature
Type I TN,C tarced down to 10 of TN,C (x 0)
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Comparison of ordering temperature dependences
Ligand-doping
Magnetic field
Pressure
Inter-ligand substitution
J.Phys.Soc.Jpn, 70 (2001) 2139
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2a. Physical properties of Type III systems
Exaempleary system hexagonal CePd2-xNixAl3
Sereni et al., PRB (2004) accepted Cond. Mat.
0303154-March 5.2004
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Lattice parameters
doping pressure
Inter-atomic distances
Ce -T spacing expands Ce -Al spacing contracts
For Ce-ligands spacing criteria see
Sereni et al., JMMM 140 (1995) 885. Handb.
Phys. Chem. RE, Vol 15, Ch 98 (1991)
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High temperature properties T gtgtTN T ?CF
(crystal field splitting)
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Magnetic Susceptibility
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Crystal field Effects
Crystal Field Effect TK
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Comparison between pressure and alloying effects
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Scale of energy related to T?max (x, p) Measured
resistance
R(T) l/s ?o ?(T/?E) ?ph(T)
?E intensive parameter, better computed
from maximum curvature than T?max Best fit

R(T) Ro L tanh(T/?tgh) Rph(T)
Sereni et al., Cond. Mat. 0303154 - March
5th.2004
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Comparison between concentration and pressure
dependence
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Low temperature properties T TN (magn.
Order) T ltlt ?CF
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Fermi Liquid (FL) vs Non-Fermi Liquid (NFL)
Conduction electron (Fermi gas - Sommerfeld)
Cel / T ? ?o ? ?ensity of states(?F) ? f (T)
(TltltT F) ?o ? ?o (Pauli susc.) ? ?A ( A
?/T2) Heavy quasiparticles (Fermi Liquid) Cel /
T f (T) ?(T) ? ?T (density of excitations) ?
?ensity of states(?F) ?(T?0) ? ? (T?0) ? ?A
(TltltTK) ? ?(T?0) Wilson ratio
Kadowaky-Woods First order corrections Cel / T ?
1- (T/To)2 ? ? 1 (T/To)2 ? ? A T 2 NFL
behavior Cel / T ?(T) ?T ? Logarithmic (Cel
/ T ? - Ln T) divergences ?(Cel / T)/ ?T ? 1/T
divergence ? Analytical Cel / T ?
1- ? T divergences No divergence in the Entropy
(S?Cp/T dT ) for T?0 ! ?(T) ? divergent for T?0
?(T) ? T Q (1.5 lt Q lt 2) or ? A (T) T 2
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Expected behavior for 3D Antiferromagnetic
systems

• ? T ?
• ?0 -?(T/T0)

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Pressure dependence of the exponent
? T n
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Comparison between two concentrations
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Magneto resistence
Scaling with field
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Specific Heat at the LR-MO region
For x lt 0.2 T lt TN Cm / T ?0BT 2 B Jex
For x gt 0.2 broad maximum
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Specific Heat at the critical concentration
Const.
?T scale
Cm / T ? ? - a?T
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Normalized Entropy
Sereni Physica B 320 (2002) 376
T-scaling
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Phase Diagram combining x and p
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Conclusions for CePd2-x Nix Al3

• Three regions in the magnetic phase diagram
• 0 lt x lt 0.2 LR-MO (TN nearly independent of x
  )
• 0.2 lt x lt 0.45 SR-Corr coexistence with NFL
  behavior ? Cm / T ? ?o (1 - ?T/D) D 18K
• x 0.45 critical concentration
• 0.4 lt x lt 0.9, exponent of ? ? T Q ? 1lt Q lt 2
• x 0.9 onset of Fermi Liquid behavior (Q 2)

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2b. Physical properties of Type II systems
(pressure induced superconductors)
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Also for CePd2Si2 CeCu2 CeInGa3
Evanescent phase boundaries (Type II )
Rev.Esp de Fisica
Sereni, J.Phys.Soc.Jpn 70 (2001) 2139
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Hydrostatical pressure
x2
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CeCu2Si2 has a shaped superconducting phase
similar to pure Ce
? ?
? 6 9 12
15 Pure Ce
Wittig PRL 21 (1968) 1250
Holmes et al., PRB 69 (2004) 024508
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Proof for LR-Order evanescence
TN ? temp of ?(?T)/?Tmax does not extrapolate to
0
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Specific Heat of type-II systems
There is an entropy compensation respect to
Cp/T (T gtgt TN), extrapolated from the
paramagnetic state
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Comparison of transition involving band states
ZrCe2
NpSn3
Pure itinerant magnetism Ref
Superconductor Sereni et al. Phill Mag Lett 68
(1993) 231
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Entropy compensation
Magnetic free energy gain
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Spin Density Waves ordering in

heavy fermion (narrow band) systems
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SDW formed by nesting of quasi-particle (HF) bands
1 0.97 0.95
Takeuchi et al., JJAP Ser.11 (1999) 151
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Further example
1
10
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Conclusions
Magnetic Instabilities may have different origins
LR-magnetic order may vanish at finite
temperature (not necessarily at T 0)
LR order may be due to localized moments
interaction or to SDW effect
In pressure induced superconductors, TN,C (p)
phase boundary vanishes at finite temperature