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 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 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

What about the Meissner Effect? 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)

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)

…high-Tc phase diagram comes to mind!

Superconducting elements

Phenomenological model (Landau theory of phase transitions) b < 0 B = 0 B  0 1st order transition: discontinuity or jump in order parameter M 2nd order transition: continuously broken symmetry, LRO

Magnetic phase diagram

Between paramagnetism and ferromagnetism 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 < 16 K

 Sr2RuO4 2D unconventional superconductor Tc 1.5 K  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

Resistance reveals diverging scattering cross-section (~effective mass) at metamagnetic field! 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

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???

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

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