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

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.

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

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  1. 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

  2. Quantum Critical Points and Superconductivity Heavy Fermion Intermetallics Complex Oxides CePd2Si2 (Mathur 1998)

  3. Quantum Criticality in Itinerant Magnets Antiferromagnet Ferromagnet Cr-V (Yeh 2002) UGe2 (Saxena 2000)

  4. ZrZn2: Itinerant Ferromagnet ZrZn2 spin density (4.2 K) C15 Laves Phase Pickart 1964

  5. Ferromagnetic Quantum Critical Point in ZrZn2 : Pressure (Grosche 1995) 10.5 kbar Pc = 8 kbar 0.4 kbar

  6. Zr1-xNbxZn2 Polycrystalline samples m(H=0,T) = m0,0(x)(1-T/TC)bb=0.5 TC and m(H=0,T=0) are suppressed by Nb doping x

  7. Quantum Critical Point in Zr1-xNbxZn2 (x=xC=0.085) TC % Nb (x) Three dimensional Heisenberg ferromagnet (xC=0.085) TC(d+n)/zQ (x-xC) (d=3, z=2+n=3) TC4/3Q (x-xC)

  8. ZrZn2: Stoner Ferromagnet Huang 1988 states/Ry-cell E (Ry) xC [ Stoner ferromagnet (+ magnetic fluctuations) a=I N(Ef) m0Q (a-1)1/2 TC Q (a-1)1/2 mo Q TC

  9. The Initial Susceptibility c • x<xC c-1=co-1t g t=(T-TC)/TC • x>xC c-1=co-1+CTg • x=xC c-1=CTg xC=8.5%

  10. x=0 x=0.055 x=0.08 The Critical Susceptibility (x<xC) x=0 c= cot-g g=1.08+/- 0.05 mean field 0.01<t<100 x=0.08 c=cot-gg=1.33+/-0.05 Heisenberg ferromagnet 0.01<t<100 TC (K) g reduced temperatures Fe 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

  11. Mean Field – Heisenberg Crossover slope=-1 slope=-4/3 x<<xC, large t: c~t-1x~xC, small t: c~t-4/3/(x-xC) Crossover function: c~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

  12. L>>x L<<x equal reduced temperatures T The Ordered Phase x xC Interactions become more local as xYxC, : L<<x increasing importance of fluctuations Matrix more highly polarizable as xYxC: divergence of co

  13. ParamagneticPhase (x>xC) 0.14 0.12 0.09 T=0 c-1=co-1 + CTg xYxC: co-1Y0 x=0.08 x=0.12 x=0.14 Stoner ferromagnet: c(T,x) = cpauli/(1-a(x))

  14. The T=0 Disordered State FM x>xC: c(T)-1=c0-1+CT4/3 [ • x=xCc(T)=C/Tgg=d+n/z = 4/3 (3d Heisenberg FM) • g=1/2n=1 (n=1/d-1) (clean QC FM) • g=1/n=1 (n=1/d-2) (dirty QC FM) • g=1-l (Griffiths Phase)

  15. Criticality in Zr1-xNbxZn2 FM

  16. g2co/t 60 30 20 10 5 x=xC x<<xC Superconductivity near a Ferromagnetic QCP c(q,w) = coko2/[k2+q2-iw/h(q)] Monthoux and Lonzarich 2001 k2=x(T=0)-1~ (x-xC)

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