1. Prelude: Quantum phase transitions in correlated metals SC NFL

2. Physical background Coleman, Physica B 1999 high T local moments low T quasiparticles Ratio T K /T RKKY determines groundstate At T=0 control T K /T RKKY by pressure  quantum phase transition

3. Quantum versus classical phase transition Continuous phase transition (2 nd order) – correlation length – correlation time – frequency = correlation length exponent z = dynamical critical exponent Classical case T  T c – thermal fluctuations k B T»   –  diverges and   0 – dynamics not relevant

4. Quantum case (T=0) – phase transition as function of control parameter  – quantum fluctuations of the groundstate – energy   (»k B T) of fluctuations above the groundstate vanishes as – static and dynamical critical behaviour coupled – d dimensional quantum system can be mapped on classical system in d+z dimensions Quantum phase transition

5. Fermi liquid d=3 Quantum critical behaviour in itinerant fermion systems Millis, PRB 1993; Moriya and Takimoto, J.Phys.Soc.Jpn 1995 d=2 d=3 – AF QCP z=2 – FM QCP z=3 NFL in specific heat and resistivity

6. Magnetic inhomogeneity in heavy-fermion UPt 3 doped with Th Contents Introduction: - The magnetic phase diagram of U(Pt,Pd) 3 - Th doping Magnetism in U(Pt,Pd) 3 probed by  SR Magnetism in (U,Th)Pt 3 probed by  SR Magnetic inhomogeneity Summary Anne de Visser Van der Waals-Zeeman Institute University of Amsterdam

7. Thanks to ……. Mike Graf, Cy Opeil Physics Department, Boston College Jason Cooley, Jim Smith Los Alamos Nat. Lab. Alex Amato, Chris Baines Paul Scherrer Institute, Villigen Alex Schenck ETH Zürich and PSI ESF/FERLIN for financial support

8. 1. Magnetic phase diagram of U(Pt,Pd) 3 Small-moment AF “order” for x  0.01 Large-moment AF order for 0.007  x  0.08 Superconductivity suppressed at x sc  0.006 Keizer et al., PRB 1999 de Visser et al., PRL 2000

9. Evidence for fluctuating SMAF in U(Pt,Pd) 3 SMAF observed by neutrons (time scale THz) but not by muons and NMR (time scale MHz) LMAF observed by neutrons and muons (and NMR) muons neutrons T N SMAF T N LMAF

10. Magnetic QCP at x c  0.006 x c,af =x c,sc  0.006 Magnetic and superconducting critical points coincide

11. Th doped UPt 3 AF spin density wave optimum doping x = 0.05, T N = 6.3 K Ordered moment x = 0.05 m = 0.65  B /U ordering vector Q = (0.5,1,0) Superconductivity suppressed at x ~ 0.006 U 1-x Th x Pt 3 and U(Pt 1-x Pd x ) 3 have similar magnetic and superconducting properties Ramirez et al., PRL 1986 U 1-x Th x Pt 3 X=0.17 X=0 X=0.02 X=0.046 Vorenkamp et al., PRB 1993 Goldman et al., PRB 1986 Kadowaki et al., Physica B 1987 Th doping: second case for a QCP?

12. Intermezzo:  SR basics

13. 2. Magnetism in U(Pt,Pd) 3 probed by  SR Keizer et al., JPhysCM 1999 Muon depolarisation shows spontaneous oscillations for T<T N (0.01  x  0.05) 3-parameter fit 1 muon stopping site polycrystalline antiferromagnet Lorentzian distribution of internal fields background due to Pt nuclear moments A 3 =0 for T<T N fit constraints

14. LMAF evidenced by and KL Order-parameter like increase of and KL for x = 0.01, 0.02, 0.05 with   2 and   0.37 KL rather than scales with ordered moment from neutron diffraction Sharp magnetic transitions For 0.007  x  0.009 damped Gauss depolarization indicates T N

15. 3. Magnetism in (U,Th)Pt 3 probed by  SR Zero field  SR at PSI Experiments in GPS (T>2 K) and LTF (T>0.05 K) at  M3 beam line Polycrystalline U 1-x Th x Pt 3 samples (LANL) - starting materials: U “best quality”, Th (Ames), Pt 5N - prepared by arc-melting - annealed at 850 o C for 5 days - concentrations x = 0.00, 0.002, 0.005, 0.006, 0.009 0.01, 0.02, 0.05 Previous experiments for x = 0.05 showed a spontaneous  + precession frequency Heffner et al., PRB 1989

16.  SR spectra of (U,Th)Pt 3 x = 0.01, 0.02, 0.05 spontaneous oscillations at T = 1.8 K - frequency decreases with decreasing x x = 0.005 and 0.006 weak magnetic signal up to ~ 2 K x = 0.000 and 0.002 no magnetic signal U 1-x Th x Pt 3 T=1.8 K Depolarization Time (  s) Graf et al., to be published

17. Spontaneous frequency in (U,Th)Pt 3 U 1-x Th x Pt 3 x T N 0.05 7.0 K 0.02 5.2 K 0.01 3.3 K T N drops not as fast as for Pd substitution No clear magnetic QCP Graf et al., to be published

18. Temperature variation  SR spectra for x=0.02 U 0.98 Th 0.02 Pt 3 Weak magnetic signal till ~ 7 K

19. 4. Magnetic inhomogeneity in (U,Th)Pt 3 Considerable magnetic volume fraction above “T N ” for x = 0.01, 0.02 Magnetic signal x = 0.01, 0.02 up to ~ 7 K Pd Th Graf et al., to be published

20. Magnetic inhomogeneity for x = 0.005 U 1-x Th x Pt 3 Magnetic signal till ~ 2 K

21. Possisible origin inhomogeneity in (U,Th)Pt 3 Crystallographic inhomogeneity ? - no second phases observed (x-rays) -  0 varies smoothly with x - clustering of Th ? - 1 and 1 Th, Pd comparable - no magnetism for x = 0 - homogeneous for x = 0.05 Magnetic inhomogeneity ? - percolation mechanism ? - doping is on f-electron lattice Different SMAF fluctuation rate for Th and Pd doping ? - always T N,max ~ T N,SMAF ~ 7 K Kubo-Gauss relaxation rate Residual resistivity

22. 5. Summary The ZF  SR technique has been used to probe the LMAF phase in Th doped UPt 3 Magnetic signals observed for x  0.005 Considerable magnetic volume fractions for x = 0.01 and 0.02 above “T N ”  magnetic inhomogeneity Magnetic inhomogeneity is possibly due to slowing down of SMAF fluctuation rate (U,Th)Pt 3 is not a suitable system to study coinciding SC and AFM quantum critical points Detailed sample characterization (x-ray line widths, lattice parameters, EPMA etc.) is underway

23. Frequency and relaxation rates for U 1-x Th x Pt 3