Transcript Magnetism on verge of breakdown

Magnetism on the verge of breakdown
May Chiao
Laboratory for Solid State Physics
Swiss Federal Institute of Technology Zürich
 What is magnetism?
 Examples of collective behaviour
 Itinerant magnetism
 Disappearance of magnetism
 Quantum critical points
 Metamagnetism
A brief history of magnetism
Lodestone or magnetite Fe3O4 known
since 500-800 BC by the Greeks and
Chinese
585 BC
Thales of Miletus theorises that lodestone attracts iron because
it has a soul
~100 AD
First compass in China
1200 AD
Pierre de Maricourt shows magnets have two poles
1600 AD
William Gilbert argues Earth is a giant magnet
1820-1888
Electricity  Magnetism  Light  Classical electromagnetism
1905-1930
Development of quantum mechanics and relativity: permanent
magnets explained
Magnetism in
pop culture
Collective behaviour: the whole is greater than the sum of its parts
A bee colony consists of one
queen and hundreds of drones
and workers. How do they
organise themselves?
Each neuron has a binary
response: to fire or not. How
could we predict that 10
billion neurons working
together would do so much?
Correlated electrons
How do we calculate a system of 1023 interacting electrons?
 3 particles already a challenge to many-body theory!
Treat system as 1023 noninteracting electrons!
Landau quasiparticle picture
consider e- (or horse!) plus cloud
 same charge
 different mass and velocity
 interactions accounted for
 Landau Fermi liquid theory
Extreme case: heavy fermions
4f and 5f electron compounds like UBe13, CeAl3, CeCu2Si2 can
have electron masses up to 1000 times that of a bare electron
Elements with magnetic order
3d- metals: Cr, Mn, Fe, Co, Ni
4f- metals: Ce, Nd, Sm, Eu, Gd, Th, Dy, Ho, Er, Tm
Microscopic magnetism
-simple ferromagnet:
-simple antiferromagnet:


Itinerant electron ferromagnetism
-conduction electrons participate in magnetism
-narrow, dispersionless bands (like 3d): high density of states
D(eF) and so may fulfill Stoner criterion
B D(e F )

1 UD(eF )
2
i.e. 1 ≈ UD(eF)
Tuning out magnetism
Chemical doping: substitution of larger or smaller ions increase
or decrease lattice spacing and therefore change interactions
Pressure: clean, continuous tuning; each pressure point
equivalent to one doping level without introduction of impurities
or defects
Basic hydrostatic pressure cell: piston and cylinder design
 nonmagnetic (BeCu, Russian submarine steel)
 isotropic medium (mixture of two fluids)
 electrical leads (feedthrough with 20 wires)
 low friction (Teflon)
 hard piston material (tungsten carbide)
 maximum theoretical pressure ≈ 50 kbar or 5 GPa
Schematic design of hydrostatic cell
UGe2: first ferromagnetic
superconductor
 magnetisation shows
typical hysteresis loop
 inverse susceptibility
marks TC more sharply
S.S. Saxena et al, Nature (2000)
Phase diagram
 smooth TC  0 with pressure
 coexisting ferromagnetism
and bulk superconductivity
 FM necessary for SC?
P. Coleman, Nature (2000)
Quantum critical point
quantum  zero temperature
critical  critical phenomena/phase transitions
point  self-explanatory!
Instead of well-behaved low temperature Fermi liquid properties
 constant specific heat c/T
 constant magnetic susceptibility 
 constant scattering cross-section Dr/T2
the above quantities diverge as T  0 due to critical
fluctuations
Nature avoids high degeneracy  system
will find an escape!!!
Superconductivity often the escape route
Magnetically mediated superconductivity
 type-II superconductivity 
Consider magnetic glue for Cooper pairs. Parallel spin triplet state
 rather than singlet state  as described by the BCS model
 unconventional superconductivity
UGe2 and ZrZn2 representatives of universal class of itinerantelectron ferromagnets close to ferromagnetic QCP? Require
-low Curie temperature (below ~50 K)
-long mean free paths (above 100 m)
-low temperature probes (below 1 K)
CePd2Si2: heavy fermion
compound with antiferromagnetic ground state
Pressure-tuning to edge of
magnetic order  within
narrow range of critical
densities where magnetic
excitations dominate 
long-range order allows
superconductivity to exist
NB: inset shows resistivity
with power T1.2
N.D. Mathur et al, Nature (1998)
…high-Tc phase diagram comes to mind!
Superconducting elements
Phenomenological model (Landau theory of phase transitions)
2
F  aM  bM  dM  M  B M
2
b<0
B=0
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b<0
B0
1st order transition: discontinuity or jump in order parameter M
2nd order transition: continuously broken symmetry, LRO
Magnetic phase diagram
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Metamagnetism
Between paramagnetism and ferromagnetism
P. Vonlanthen et al, PRB (2000)
CaB6 pure (paramagnetic) and
self-doped with vacancies
(ferromagnetic with TC above
600 K)
R. Perry et al, PRL (2001)
Sr3Ru2O7 shows metamagnetic
behaviour for T < 16 K
Sr3Ru2O7
 bilayer perovskite
 Sr2RuO4 2D unconventional
superconductor Tc 1.5 K
 SrRuO3 3D itinerant electron
ferromagnet TC 160 K
 Sr3Ru2O7 on border of
superconductivity and
ferromagnetism
Ground state:
 Fermi liquid below 10 K
Park and Snyder, J Amer Ceramic Soc (1995)
 paramagnetic, ie nonmagnetic
 strongly enhanced, ie close to ferromagnetism (uniaxial stress)
Investigate interplay of superconductivity and magnetism by
application of hydrostatic pressure to Sr3Ru2O7
Resistance reveals diverging scattering cross-section
(~effective mass) at metamagnetic field!
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r = r0 + AT2
T1.25  critical spin fluctuations as in quantum critical metals
What about pressure?
 hydrostatic pressure appears
to push the system away
from the magnetic instability
 all peaks originate from one
single point at pc ~ -14 kbar
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Relate to generic phase diagram
 metamagnetism dome defined by lines of first order transitions
 we are probing positive pressure side of ferromagnetism bubble
 how to get to negative pressure side?
 how close to superconductivity? 100-200 kbar from Sr2RuO4
 what is located at (pm,Bm)?
Quantum critical end-point
 similar to tri-critical point in H2O phase diagram
 second order end-point to first order line of transitions
 no additional symmetry breaking since already in symmetrybreaking field; can go around continuously
 possibility of new state of matter? quantum lifeforms???
Puzzle: scaling behaviour
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Scaling not compatible with standard spin fluctuation theory
 major assumption that pressure mainly affects bandwidth
(DOS) not entirely correct
 rotation and distortion of octehedra important
Possible explanation:
neutron scattering suggests pressure predominantly affects
rotation angle of octehedra
 mainly metamagnetic field affected but not critical fluctuations
(probably from Fermi surface fluctuations)
Future
require magnetic probe such as a.c. susceptibility under pressure
 study rotation of applied field
higher purity samples in order to study Fermi surface changes
through metamagnetic transition
theoretical modelling must include rotation of octehedra and
differentiate between a classic quantum critical point and a
quantum critical end-point