1. Quantum phase transitions G. Aeppli (LCN) Y-A. Soh (Dartmouth) A. Yeh (NEC) T. F. Rosenbaum (UChicago) S.M. Hayden (Bristol) T.G. Perring (RAL) T.E. Mason (ORNL) H.A. Mook (ORNL) P. Evans (Wisconsin) E. Isaacs (ANL)

2. From quantum mechanics • Electrons carry spin • Spin uncompensated for many ions in solids • e.g. Cu2+ (d9,S=1/2), Ni2+ (d8,S=1), Fe2+ (d6,S=2)

3. put atoms together to make a ferromagnet-

4. Classical onset of magnetizationin a conventional transition metal alloy(PdCo)

5. Hysteresis

6. 3 mm Hysteresis comes from magnetic domain walls 300K Perpendicular recording medium

7. conventional paradigm for magnetism • Curie(FM) point Tc so that • for T<Tc, finite <Mo>=(1/N)S<Sj> • <Mo>=(Tc-T)b , x~|Tc-T|-n , c~|Tc-T|-g • for T<Tc, there are static magnetic domains, • from which most applications of magnetism are derived

8. + classical dynamics

9. Perring et al, Phys. Rev. Lett. 81 217201(2001)

10. What is special about ordinary ferromagnets? • [H,M]=0  order parameter is a conserved quantity  • classical FM eigenstates (Curie state | ½ ½ ½ … ½ >,| -½ -½ -½ … -½ > • & spin waves) are also quantum eigenstates •  no need to worry about quantum mechanics once spins exist

11. Do we ever need to worry about quantum mechanics for real magnets & phase transitions? need to examine cases where commutator does not vanish

12. Why should we ask? • Search for useable - scaleable, easily measurable - quantum • degrees of freedom, • e.g. for quantum computing • many hard problems (e.g. high-temperature superconductivity) • in condensed matter physics involve strongly fluctuating • quantum spins

13. Need look no further than Heisenberg antiferromagnet • H=SJSiSj with J>0 • classical ground state

16. outermost zone 1992 0.5 m 2002 0.1 m

17. Evans et al, Science 02 100 m

18. QCP

19. Electrical properties

20. Yeh et al, Nature ‘02

22. Lee et al, PRL 04

23. 300 T (K) 200 100 QCP DISORDER ORDER % V 2 4 6 Cr1-x Vx

26. 576 detectors 147,456 total pixels 36,864 spectra 0.5Gb Typically collect 100 million data points

27. Large magnetic fluctuations on the PM side of QCP…

29. Hayden et al PRL ‘00

31. 300 T (K) 200 100 QCP DISORDER ORDER % V 6 2 4 Cr1-x Vx CrV • Quantum criticality in car bumper • New physics easy to see near • room T using 19th century • technique! • Small science/big science • Major puzzle

32. Wider implications…

34. Quantum critical point High-Tc superconductivity

35. Aeppli et al. Science 97

36. Lake et al, Science 01 & Nature 02

37. summary • Quantum fluctuations in magnets generally neglected because ferromagnets in most • Practical circumstances don’t have them • QF important in AFM and can now be seen & do matter • QPT in AFM very common and pose unresolved issues about Fermi surface integrity, • relation to SC • Marriage of big & little science is key