Magnetism on the verge of breakdown

H. AouragLaboratory 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

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

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?

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, Ni4f- metals: Ce, Nd, Sm, Eu, Gd, Th, Dy, Ho, Er, Tm

Microscopic magnetism

-conduction electrons participate in magnetism

-narrow, dispersionless bands (like 3d): high density of states D(F) and so may fulfill Stoner criterion

B

2D(F )1 UD(F )

i.e. 1 ≈ UD(F)

-simple ferromagnet: -simple antiferromagnet:

Itinerant electron ferromagnetism

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 ferromagneticsuperconductor

Phase diagram

S.S. Saxena et al, Nature (2000)

P. Coleman, Nature (2000)

magnetisation shows typical hysteresis loop inverse susceptibility marks TC more sharply

smooth TC 0 with pressure coexisting ferromagnetism and bulk superconductivity FM necessary for SC?

Quantum critical point

Instead of well-behaved low temperature Fermi liquid properties

constant specific heat c/T constant magnetic susceptibility constant scattering cross-section /T2

the above quantities diverge as T 0 due to critical fluctuations

quantum zero temperature

critical critical phenomena/phase transitions

point self-explanatory!

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 itinerant-electron 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 anti-ferromagnetic ground state

N.D. Mathur et al, Nature (1998)

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

…high-Tc phase diagram comes to mind!

Superconducting elements

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F aM2 bM 4 dM6 M2 BM

b < 0 B = 0

b < 0B 0

1st order transition: discontinuity or jump in order parameter M2nd order transition: continuously broken symmetry, LRO

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Metamagnetism

Between paramagnetism and ferromagnetism

CaB6 pure (paramagnetic) and self-doped with vacancies (ferromagnetic with TC above 600 K)

Sr3Ru2O7 shows metamagnetic behaviour for T < 16 K

P. Vonlanthen et al, PRB (2000)R. Perry et al, PRL (2001)

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

Park and Snyder, J Amer Ceramic Soc (1995)

Ground state: Fermi liquid below 10 K 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!Title: Print File Creator: PSCRIPT.DRV Version 4.0 Preview: This EPS picture was not saved with a preview (TIFF or PICT) included in it Comment: This EPS picture will print to a postscript printer but not to other types of printers T1.25 critical spin fluctuations as in quantum critical metals

= 0 + AT2

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to push the system away from the magnetic instability

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Relate to generic phase diagram

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???

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)?

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