Ferromagnetism and the quantum critical point in Zr1-xNbxZn2

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Ferromagnetism and the quantum critical point in
Zr1-xNbxZn2

• D. Sokolov, W. Gannon, and M. C. Aronson
• University of Michigan
• Z. Fisk
• Florida State University

Supported by the U. S. National Science
Foundation
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Quantum Critical Points and Superconductivity
Heavy Fermion Intermetallics
Complex Oxides
CePd2Si2 (Mathur 1998)
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Quantum Criticality in Itinerant Magnets
Antiferromagnet
Ferromagnet
UGe2 (Saxena 2000)
Cr-V (Yeh 2002)
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ZrZn2 Itinerant Ferromagnet
ZrZn2 spin density (4.2 K)
C15 Laves Phase
Pickart 1964
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Ferromagnetic Quantum Critical Point in ZrZn2
Pressure
(Grosche 1995)
10.5 kbar
Pc 8 kbar
0.4 kbar
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Zr1-xNbxZn2
Polycrystalline samples
m(H0,T) m0,0(x)(1-T/TC)b b0.5
TC and m(H0,T0) are suppressed by Nb doping x
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Quantum Critical Point in Zr1-xNbxZn2 (xxC0.085)
TC
Nb (x)
Three dimensional Heisenberg ferromagnet
(xC0.085) TC(dn)/z Q (x-xC) (d3, z2n3)
TC4/3 Q (x-xC)
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ZrZn2 Stoner Ferromagnet
Huang 1988
states/Ry-cell
E (Ry)
xC

Stoner ferromagnet ( magnetic fluctuations)
aI N(Ef) m0 Q (a-1)1/2 TC Q (a-1)1/2
mo Q TC
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The Initial Susceptibility c
xC8.5

• xltxC c-1co-1t g t(T-TC)/TC
• xgtxC c-1co-1CTg
• xxC c-1CTg

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The Critical Susceptibility (xltxC)
x0 c cot-g g1.08/- 0.05 mean field
0.01lttlt100 x0.08 ccot-g
g1.33/-0.05 Heisenberg ferromagnet 0.01lttlt100
TC (K) g reduced temperatures Fe 1044
K 1.33/-0.02 10-5lttlt10-2 Co 1388
K 1.21/-0.04 10-3lttlt10-2 Ni 627 K 1.35/-
0.02 10-3lttlt10-2 3d Heisenberg 1.33 model
Suppression of mean field behavior near quantum
critical point
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Mean Field Heisenberg Crossover
slope-1
slope-4/3
xltltxC, large t ct-1 xxC, small
t ct-4/3/(x-xC)
Crossover function ct-4/3 f(t1/3/(x-xC))
t-4/3f(y) large y f(y)y-4/3
small y f(y)y-1
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The Ordered Phase
x
xC
Interactions become more local as xYxC,
Lltltx increasing importance of fluctuations
Matrix more highly polarizable as xYxC
divergence of co
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Paramagnetic Phase (xgtxC)
0.14
0.12
0.09
T0
c-1co-1 CTg xYxC co-1Y0
x0.14
x0.12
x0.08
Stoner ferromagnet c(T,x) cpauli/(1-a(x))
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The T0 Disordered State
FM
xgtxC c(T)-1c0-1CT4/3

xxC c(T)C/Tg gdn/z 4/3 (3d
Heisenberg FM) g1/2n1 (n1/d-1)
(clean QC FM) g1/n1 (n1/d-2) (dirty
QC FM) g1-l (Griffiths Phase)
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Criticality in Zr1-xNbxZn2
FM
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Superconductivity near a Ferromagnetic QCP
c(q,w) coko2/k2q2-iw/h(q)
Monthoux and Lonzarich 2001
k2x(T0)-1 (x-xC)