1. 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

2. A brief history of magnetism Lodestone or magnetite Fe 3 O 4 known since 500-800 BC by the Greeks and Chinese 585 BCThales of Miletus theorises that lodestone attracts iron because it has a soul ~100 ADFirst compass in China 1200 ADPierre de Maricourt shows magnets have two poles 1600 ADWilliam Gilbert argues Earth is a giant magnet 1820-1888Electricity  Magnetism  Light  Classical electromagnetism 1905-1930Development of quantum mechanics and relativity: permanent magnets explained

3. Magnetism in pop culture

4. 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?

5. Correlated electrons How do we calculate a system of 10 23 interacting electrons?  3 particles already a challenge to many-body theory! Treat system as 10 23 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 UBe 13, CeAl 3, CeCu 2 Si 2 can have electron masses up to 1000 times that of a bare electron

6. Elements with magnetic order 3d- metals: Cr, Mn, Fe, Co, Ni 4f- metals: Ce, Nd, Sm, Eu, Gd, Th, Dy, Ho, Er, Tm

7. Microscopic magnetism -conduction electrons participate in magnetism -narrow, dispersionless bands (like 3d): high density of states D(  F ) and so may fulfill Stoner criterion i.e. 1 ≈ UD(  F ) -simple ferromagnet:  -simple antiferromagnet:  Itinerant electron ferromagnetism

8. 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

9. Schematic design of hydrostatic cell

10. UGe 2 : first ferromagnetic superconductor Phase diagram S.S. Saxena et al, Nature (2000) P. Coleman, Nature (2000)  magnetisation shows typical hysteresis loop  inverse susceptibility marks T C more sharply  smooth T C  0 with pressure  coexisting ferromagnetism and bulk superconductivity  FM necessary for SC?

11. Quantum critical point Instead of well-behaved low temperature Fermi liquid properties  constant specific heat c/T  constant magnetic susceptibility   constant scattering cross-section  /T 2 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

12. 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 UGe 2 and ZrZn 2 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)

13. CePd 2 Si 2 : 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 T 1.2

14. …high-T c phase diagram comes to mind!

15. Superconducting elements

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

17. Magnetic phase diagram

18. Metamagnetism Between paramagnetism and ferromagnetism CaB 6 pure (paramagnetic) and self-doped with vacancies (ferromagnetic with T C above 600 K) Sr 3 Ru 2 O 7 shows metamagnetic behaviour for T < 16 K P. Vonlanthen et al, PRB (2000) R. Perry et al, PRL (2001)

19. Sr 3 Ru 2 O 7  bilayer perovskite  Sr 2 RuO 4 2D unconventional superconductor T c 1.5 K  SrRuO 3 3D itinerant electron ferromagnet T C 160 K  Sr 3 Ru 2 O 7 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 Sr 3 Ru 2 O 7

20. Resistance reveals diverging scattering cross-section (~effective mass) at metamagnetic field! T 1.25  critical spin fluctuations as in quantum critical metals  =  0 + AT 2

21. 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

22. Relate to generic phase diagram Quantum critical end-point  similar to tri-critical point in H 2 O 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 Sr 2 RuO 4  what is located at (p m,B m )?

23. 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

24. 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