Ferromagnetism and the quantum critical point in Zr 1-x Nb x Zn 2

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Ferromagnetism and the quantum critical point in Zr 1-x Nb x Zn 2 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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Ferromagnetism and the quantum critical point in Zr 1-x Nb x Zn 2. D. Sokolov, W. Gannon, and M. C. Aronson * University of Michigan Z. Fisk Florida State University. * Supported by the U. S. National Science Foundation. Quantum Critical Points and Superconductivity. - PowerPoint PPT Presentation

Transcript of Ferromagnetism and the quantum critical point in Zr 1-x Nb x Zn 2

Page 1: Ferromagnetism and the quantum critical point in Zr 1-x Nb x Zn 2

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

Page 2: Ferromagnetism and the quantum critical point in Zr 1-x Nb x Zn 2

Quantum Critical Points and Superconductivity

Heavy Fermion Intermetallics

CePd2Si2 (Mathur 1998)

Complex Oxides

Page 3: Ferromagnetism and the quantum critical point in Zr 1-x Nb x Zn 2

Quantum Criticality in Itinerant Magnets

UGe2 (Saxena 2000)Cr-V (Yeh 2002)

Antiferromagnet Ferromagnet

Page 4: Ferromagnetism and the quantum critical point in Zr 1-x Nb x Zn 2

ZrZn2: Itinerant Ferromagnet

ZrZn2 spin density (4.2 K)

Pickart 1964

C15 Laves Phase

Page 5: Ferromagnetism and the quantum critical point in Zr 1-x Nb x Zn 2

Ferromagnetic Quantum Critical Point in ZrZn2 : Pressure

(Grosche 1995)

Pc = 8 kbar

0.4 kbar

10.5 kbar

Page 6: Ferromagnetism and the quantum critical point in Zr 1-x Nb x Zn 2

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

Page 7: Ferromagnetism and the quantum critical point in Zr 1-x Nb x Zn 2

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)

Page 8: Ferromagnetism and the quantum critical point in Zr 1-x Nb x Zn 2

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

Page 9: Ferromagnetism and the quantum critical point in Zr 1-x Nb x Zn 2

• 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%

Page 10: Ferromagnetism and the quantum critical point in Zr 1-x Nb x Zn 2

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

Page 11: Ferromagnetism and the quantum critical point in Zr 1-x Nb x Zn 2

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

Page 12: Ferromagnetism and the quantum critical point in Zr 1-x Nb x Zn 2

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

Page 13: Ferromagnetism and the quantum critical point in Zr 1-x Nb x Zn 2

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

Page 14: Ferromagnetism and the quantum critical point in Zr 1-x Nb x Zn 2

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

Page 15: Ferromagnetism and the quantum critical point in Zr 1-x Nb x Zn 2

Criticality in Zr1-xNbxZn2

FM

Page 16: Ferromagnetism and the quantum critical point in Zr 1-x Nb x Zn 2

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