Transcript Non-Fermi liquid phenomena at the quantum critical point

Prelude: Quantum phase transitions in
correlated metals
T
TM
NFL
SC
Magn.
order
TFL
FL
c

Physical background
Coleman, Physica B 1999
high T local moments
low T quasiparticles
• Ratio TK/TRKKY determines groundstate
• At T=0 control TK/TRKKY by pressure
 quantum phase transition
Quantum versus classical phase transition
•
Continuous phase transition (2nd order)
– correlation length
– correlation time
– frequency
 ~| T  Tc |
 ~z
 ~
1
z
~| T Tc |
 = correlation length exponent
z = dynamical critical exponent
•
Classical case T  Tc
– thermal fluctuations kBT» 
–  diverges and  0
– dynamics not relevant
Quantum phase transition
•
Quantum case (T=0)
– phase transition as function of control parameter 
– quantum fluctuations of the groundstate
– energy  (»kBT) of fluctuations above the groundstate
vanishes as
   ~ |    c |
z
– static and dynamical critical behaviour coupled
– d dimensional quantum system can be mapped on
classical system in d+z dimensions
NFL in specific heat and resistivity
•
Fermi liquid d=3
c  T  aT 3 ln(T / T0 )
  0  AT 2
• Quantum critical behaviour in itinerant fermion systems
Millis, PRB 1993; Moriya and Takimoto, J.Phys.Soc.Jpn 1995
d=2
– AF QCP
z=2
– FM QCP
z=3
d=3
c ~ T ln(T / T0 )
 ~ T
c ~Τ
2/3
 ~T
4/3
c ~ Τ  Τ 3/ 2
 ~T 3/ 2
c ~ T ln(T / T0 )
 ~T
5/ 3
Magnetic inhomogeneity in
heavy-fermion UPt3 doped with Th
Anne de Visser
Van der Waals-Zeeman Institute
University of Amsterdam
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)Pt3 probed by SR
• Magnetic inhomogeneity
• Summary
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
8
U(Pt1-xPdx)3
7
•
Small-moment AF
“order” for
x  0.01
•
Large-moment AF
order for
0.007  x  0.08
•
Superconductivity
suppressed
at xsc  0.006
TN or Tc (K)
6
SMAF
5
4
LMAF
3
2
1
0
SC
0
2
4
6
8
Pd concentration (at.%)
Keizer et al., PRB 1999
de Visser et al., PRL 2000
10
Evidence for fluctuating SMAF in U(Pt,Pd)3
neutrons
TN LMAF
SMAF observed by
neutrons
(time scale THz)
but not by
muons and NMR
(time scale MHz)
•
LMAF observed by
neutrons and muons
(and NMR)
TN
SMAF
muons
TN LMAF
•
Magnetic QCP at xc 0.006
2.0
TN or Tc (K)
1.5
•
U(Pt1-xPdx)3
xc,af=xc,sc  0.006
1.0
0.5
LMAF
SC
0.0
0.0
0.2
0.4
0.6
0.8
1.0
Pd concentration (at.%)
1.2
Magnetic and
superconducting
critical points
coincide
Th doped UPt3
•
AF spin density wave
optimum doping
x = 0.05, TN = 6.3 K
Ramirez et al., PRL 1986
•
Ordered moment x = 0.05
m = 0.65 B/U
ordering vector Q = (0.5,1,0)
Goldman et al., PRB 1986
•
X=0.046
U1-xThxPt3
X=0.02
X=0
X=0.17
Kadowaki et al., Physica B 1987
Superconductivity suppressed at x ~ 0.006
Vorenkamp et al., PRB 1993
U1-xThxPt3 and U(Pt1-xPdx)3
have similar magnetic and
superconducting properties
Th doping:
second case
for a QCP?
Intermezzo: SR basics
2. Magnetism in U(Pt,Pd)3 probed by SR
•
Muon depolarisation shows spontaneous oscillations
background due to
for T<TN (0.01  x  0.05)
Pt nuclear moments
A
3-parameter fit G( t )  A1Gv ( t )  A2GKL ( t )  A3GKT ( t )
•
•
3
1 muon stopping site
G (t ) 
30
25
20
G (t)
15
Run 2949/4
ZF, T = 3 K
U (Pt0.95Pd0.05)3
2 1t
1
e cos(  t )  e 1 't
3
3
polycrystalline antiferromagnet
GKL ( t ) 
A2GKL(t)
-1t
'
- 1t
A1G(t)=A1(2/3 e cos(t)+1/3 e
)
10
1 2
 ( 1  KL t )e KLt
3 3
Lorentzian distribution of
internal fields
5
0
-5
0.0
=0 for T<TN
fit constraints
0.2
0.4
0.6
t (s)
Keizer et al., JPhysCM 1999
0.8
1.0
A1  A2
A1  A2  A3  Atot
LMAF evidenced by  and KL
U(Pt
ZF-SR
 (MHz)
8
•
Pd )
1-x
x 3
6
x=0.01
4
x=0.02
f ( T )  f ( 0 )(1  ( T / TN ) )
x=0.05
with   2 and   0.37
2
0
0
2
4
6
•
KL rather than  scales with
ordered moment from neutron
diffraction
•
•
Sharp magnetic transitions
8
T (K)
10
ZF-SR
x=0.05
4
x=0.02

KL
(s-1)
8
6
2
0
x=0.01
0
2
4
T (K)
6
Order-parameter like increase of
 and KL for x = 0.01, 0.02, 0.05
8
For 0.007  x  0.009
damped Gauss depolarization
indicates TN
3. Magnetism in (U,Th)Pt3 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 U1-xThxPt3 samples (LANL)
- starting materials: U “best quality”, Th (Ames), Pt 5N
- prepared by arc-melting
- annealed at 850 oC 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
SR spectra of (U,Th)Pt3
•
2.5
T = 1.8 K
T=1.8 K
U1-xThxPt3
Depolarization
Depolarization
2.0
x = 0.05
- frequency decreases with
decreasing x
1.5
x = 0.02
1.0
0.5
•
x = 0.005 and 0.006
weak magnetic signal
up to ~ 2 K
•
x = 0.000 and 0.002
no magnetic signal
x = 0.01
0.0
0.0
x = 0.01, 0.02, 0.05
spontaneous oscillations
at T = 1.8 K
0.1
0.2
0.3
0.4
time (s)
( s)
Time
Graf et al., to be published
0.5
0.6
Spontaneous frequency in (U,Th)Pt3
Frequency (MHz)
10
8
x = 0.05
6
x
U1-xThxPt3
x = 0.02
4
0.05
0.02
0.01
2
0
0
1
2
3
4
5
6
7
TN
7.0 K
5.2 K
3.3 K
8
Temperature (K)
8
TN drops not as fast as for
Pd substitution
No clear magnetic QCP
x = 0.05
4

KL
( s
-1
)
6
2
x = 0.02
0
0
1
2
3
4
5
Temperature (K)
6
7
8
Graf et al., to be published
Temperature variation SR spectra for x=0.02
•
U0.98Th0.02Pt3
1.2
7.4 K
Depolarization
1.0
0.8
0.6
5.3 K
0.4
2.1 K
0.2
0.0
0.0
0.2
0.4
0.6
time (s)
0.8
1.0
Weak
magnetic
signal
till ~ 7 K
Fractional Magnetic Signal
4. Magnetic inhomogeneity in (U,Th)Pt3
1.0
0.8
Considerable
magnetic volume
fraction above “TN”
for x = 0.01, 0.02
•
Magnetic signal
x = 0.01, 0.02
up to ~ 7 K
5%
2%
1%
•
0.6
0.4
Pd
0.2
Th
0.0
1
2
3
4
5
6
7
8
Temperature (K)
Graf et al., to be published
A1  A2
FMS 
A1  A2  A3
Magnetic inhomogeneity for x = 0.005
Fractional Magnetic Signal
1.0
U1-xThxPt3
0.8
•
x = 0.005
0.6
0.4
0.2
0.0
0
1
2
Temperature (K)
3
Magnetic
signal
till ~ 2 K
Possisible origin inhomogeneity in (U,Th)Pt3
- 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
•
100
Crystallographic inhomogeneity ?
(U 1-x Thx )Pt 3
80
 0 ( cm)
•
60
40
20
0
0
0.01
0.02
0.03
0.04
x
Residual resistivity
Magnetic inhomogeneity ?
- percolation mechanism ?
- doping is on f-electron lattice
•
Different SMAF fluctuation rate
for Th and Pd doping ?
- always TN,max ~ TN,SMAF ~ 7 K
Kubo-Gauss relaxation rate
0.05
5. Summary
•
The ZF SR technique has been used to probe the
LMAF phase in Th doped UPt3
•
•
Magnetic signals observed for x  0.005
•
Magnetic inhomogeneity is possibly due to slowing
down of SMAF fluctuation rate
•
(U,Th)Pt3 is not a suitable system to study coinciding
SC and AFM quantum critical points
Considerable magnetic volume fractions for x = 0.01
and 0.02 above “TN”  magnetic inhomogeneity
Detailed sample characterization (x-ray line widths,
lattice parameters, EPMA etc.) is underway
Frequency and relaxation rates for U1-xThxPt3
25
(a)
8
(b)
-1
)
20
6
1
 ( s
Frequency (MHz)
10
4
Th
Pd
2
0
0
10
20
10
(d)
' ( (ss -1) )
)
-1
-1
6
1KL
KL
10
5
8
 ( s
15
4
6
10
4
2
5
2
0
00
0
0.01
0.02
0.03
x
0.04
0.05
(d)
(c)
15
8
0
0.01
0.02
0.03
x
0.04
0.05