Magnetism on the verge of breakdown

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Magnetism on the verge of breakdown
H. Aourag Laboratory for Study and Prediction of
Materials URMER University of Tlemcen
? What is magnetism? ? Examples of collective
behaviour ? Itinerant magnetism ? Disappearance
of magnetism ? Quantum critical points ?
Metamagnetism
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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 Devel
opment of quantum mechanics and relativity
permanent magnets explained
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Magnetism in pop culture
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Collective behaviour the whole is greater than
the sum of its parts
Each neuron has a binary response to fire or
not. How could we predict that 10 billion neurons
working together would do so much?
A bee colony consists of one queen and hundreds
of drones and workers. How do they organise
themselves?
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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
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Elements with magnetic order
3d- metals Cr, Mn, Fe, Co, Ni 4f- metals Ce,
Nd, Sm, Eu, Gd, Th, Dy, Ho, Er, Tm
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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
i.e. 1 UD(eF)
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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
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Schematic design of hydrostatic cell
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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)
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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 c ?
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
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Magnetically mediated superconductivity
What about the Meissner Effect?
? 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 itinerant-electron ferromagnets close to
ferromagnetic QCP? Require -low Curie
temperature (below 50 K) -long mean free paths
(above 100 mm) -low temperature probes (below 1
K)
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CePd2Si2 heavy fermion compound with
anti- ferromagnetic 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)
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high-Tc phase diagram comes to mind!
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Superconducting elements
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Phenomenological model (Landau theory of phase
transitions)
1st order transition discontinuity or jump in
order parameter M 2nd order transition
continuously broken symmetry, LRO
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Magnetic phase diagram
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Metamagnetism
Between paramagnetism and ferromagnetism
P. Vonlanthen et al, PRB (2000)
R. Perry et al, PRL (2001)
CaB6 pure (paramagnetic) and self-doped with
vacancies (ferromagnetic with TC above 600 K)
Sr3Ru2O7 shows metamagnetic behaviour for T lt 16 K
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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 ?
paramagnetic, ie nonmagnetic ? strongly enhanced,
ie close to ferromagnetism (uniaxial stress)
Park and Snyder, J Amer Ceramic Soc (1995)
Investigate interplay of superconductivity and
magnetism by application of hydrostatic pressure
to Sr3Ru2O7
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Resistance reveals diverging scattering
cross-section (effective mass) at metamagnetic
field!
r r0 AT2
T1.25 ? critical spin fluctuations as in quantum
critical metals
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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 symmetry- breaking field
can go around continuously ? possibility of new
state of matter? quantum lifeforms???
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Puzzle scaling behaviour
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
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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