Ferromagnetism and the quantum critical point in Zr 1-x Nb x Zn 2 D. Sokolov, W. Gannon, and M. C....
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Transcript of Ferromagnetism and the quantum critical point in Zr 1-x Nb x Zn 2 D. Sokolov, W. Gannon, and M. C....
Ferromagnetism and the quantum critical point in Zr1-xNbxZn2
D. Sokolov, W. Gannon, and M. C. Aronson*University of Michigan
Z. FiskFlorida State University
* Supported by the U. S. National Science Foundation
Quantum Critical Points and Superconductivity
Heavy Fermion Intermetallics
CePd2Si2 (Mathur 1998)
Complex Oxides
Quantum Criticality in Itinerant Magnets
UGe2 (Saxena 2000)Cr-V (Yeh 2002)
Antiferromagnet Ferromagnet
ZrZn2: Itinerant Ferromagnet
ZrZn2 spin density (4.2 K)
Pickart 1964
C15 Laves Phase
Ferromagnetic Quantum Critical Point in ZrZn2 : Pressure
(Grosche 1995)
Pc = 8 kbar
0.4 kbar
10.5 kbar
Zr1-xNbxZn2
m(H=0,T) = m0,0(x)(1-T/TC) =0.5
TC and m(H=0,T=0) are suppressed by Nb doping x
Polycrystalline samples
Quantum Critical Point in Zr1-xNbxZn2 (x=xC=0.085)
TC
Three dimensional Heisenberg ferromagnet (xC=0.085)
TC(d+n)/z Q (x-xC) (d=3, z=2+n=3) TC
4/3 Q (x-xC)
% Nb (x)
ZrZn2: Stoner Ferromagnet
=I N(Ef) m0 Q ()1/2 TC Q (-1)1/2 mo Q TC
Stoner ferromagnet (+ magnetic fluctuations)
E (Ry)
stat
es/R
y-ce
ll
Huang 1988
xC
• x<xC -1=o-1t t=(T-TC)/TC
• x>xC -1=o-1+CT
• x=xC -1=CT
The Initial Susceptibility
xC=8.5%
The Critical Susceptibility (x<xC)
x=0 = ot-=1.08+/- 0.05 mean field 0.01<t<100x=0.08 =ot- =1.33+/-0.05 Heisenberg ferromagnet 0.01<t<100
TC (K) reduced temperaturesFe 1044 K 1.33+/-0.02 10-5<t<10-2
Co 1388 K 1.21+/-0.04 10-3<t<10-2
Ni 627 K 1.35+/- 0.02 10-3<t<10-2
3d Heisenberg 1.33 model
Suppression of mean field behavior near quantum critical point
x=0x=0.055x=0.08
Mean Field – Heisenberg Crossover
x<<xC, large t: ~t-1 x~xC, small t: ~t-4/3/(x-xC)
Crossover function: ~t-4/3 f(t1/3/(x-xC)) ~t-4/3f(y) large y: f(y)~y-4/3 small y: f(y)~y-1
slope=-4/3
slope=-1
The Ordered Phase
xxC
Interactions become more local as xYxC, : L<<increasing importance of fluctuations
T
L>> L<<
equal reduced temperatures
Matrix more highly polarizable as xYxC: divergence of o
Paramagnetic Phase (x>xC)
-1=o-1 +
CT
xYxC: o-1Y0
T=0
x=0.14x=0.12x=0.08
Stoner ferromagnet: (T,x) = pauli/(1-(x))
0.14
0.12
0.09
The T=0 Disordered State
x>xC: (T)-1=0-1+CT4/3
x=xC (T)=C/T =d+n/z = 4/3 (3d Heisenberg FM)=1/2n=1 (n=1/d-1) (clean QC
FM)=1/n=1 (n=1/d-2) (dirty QC FM)=1- (Griffiths Phase)
FM
Criticality in Zr1-xNbxZn2
FM
Superconductivity near a Ferromagnetic QCP
2=(T=0)-1~ (x-xC)
Monthoux and Lonzarich 2001(q,) = oo2/[2+q2-i/(q)]
g2o/t60
30
20
10
5
x=xC x<<xC