Prelude: Quantum phase transitions in correlated metals SC NFL

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

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

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

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

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

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

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

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

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

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 ~ 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?

Intermezzo:  SR basics

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

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  x  damped Gauss depolarization indicates T N

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, , 0.02, 0.05 Previous experiments for x = 0.05 showed a spontaneous  + precession frequency Heffner et al., PRB 1989

 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 = and weak magnetic signal up to ~ 2 K x = and no magnetic signal U 1-x Th x Pt 3 T=1.8 K Depolarization Time (  s) Graf et al., to be published

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

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

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

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

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

5. Summary The ZF  SR technique has been used to probe the LMAF phase in Th doped UPt 3 Magnetic signals observed for x  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

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