Quantum Criticality in the Itinerant Antiferromagnet Cr-V

Quantum Criticality in the
Itinerant Antiferromagnet Cr-V
**
D. A. Sokolov, G. Strycker,
M. C. Bennett, M. C. Aronson
University of Michigan, Ann Arbor MI
S. E. Nagler and M. Lumsden
HFIR, Oak Ridge TN
** Work at the University of Michigan supported by the U. S. National Science Foundation

Heavy Fermion Intermetallics
CePd 2 Si 2 (Mathur 1998)
Quantum Critical Points
Complex Oxides
Need for simpler model systems: itinerant magnets

T>T N
T

Quantum critical point in Cr 1-x V x (x=x C =0.035)
x x C : simultaneous suppression of T N and staggered moment μ
Cr: [Ar]3d 5 4s 1
V: [Ar]3d 3 4s 2
Fawcett 1994
x C ~0.038
Koehler 1966

Electron Microprobe
45 g single crystal grown by arc-zone melting (Ames Laboratory)
1. rectangular slab
spark-cut from
interior of crystal
top view of slab
after polishing
2. Surface damaged by
spark cutting, removed by
polishing.
Composition of crystal interior is nominal 3.5 +/- 0.2 at. % V.
3. Microprobe performed on
indicated area.
at. %V

Electrical Resistivity of Cr 0.965 V 0.035
Takeuchi 1980
V concentration 3.5%

Elastic Scattering: Magnetic Modulation
Triple axis spectroscopy: HB-3 at High Flux Isotope Reactor
Collimation: 48’-40’-80’-120’
no filter with λ/2 filter
Elastic scattering:
2 K
h+k+l =2n+1 magnetic satellites SDW
h+k+l =2n bcc structure factor

Cr – 3.5%V
Incommensurate Elastic Scattering
Pure Cr: T N =311 K
Elastic scattering: critical SDW fluctuations,
T N ~311 K
Commensurability δ: x~1 %
Werner 1967
Part of crystal is electronically like lightly doped Cr

Evidence for Phase Separation
Elastic scattering from regions which are at least
500 A in size
Sample is large single crystal, no appreciable
twinning (Laue, rocking curve)
Averaging over length scales larger than ~1 μm,
our crystal: 3.5 at. % V
(microprobe, resistivity)
Phase diagram: continuous V solubility in Cr
Cr V

Inelastic Scattering in Chromium
Boni 2002
Sternlieb 1993
Nearly dispersionless spin waves emanating from SDW satellites at (1+/-δ,0,0).
Fincher-Burke excitations near (1,0,0).

Inelastic Scattering in Cr 0.965 V 0.035
Cr – 3.5%V
q*=(0,0,1+/-δ) S(q)=S o /(1+4((q+/-q*/Γ) 2 ) + S g exp(-0.5q 2 /Γ 2 )
Resolution corrections with RESLIB
Pure Cr
6 meV
5.4 meV
4 meV
2.6 meV
Burke 1983
230 K

Commensurate Scattering in Cr 0.965 V 0.035
q=(0,0,1) 2π/a q=(0,0,1) 2π/a
Detailed balance corrected intensity: constant energy
scale for T

Dispersion of the Incommensurate Excitations
Cr-3.5%V: Spin wave velocity greatly reduced relative to pure Cr
New branch of excitations , perhaps observed by Burke (1983)
Sternlieb 1993

Incommensurate vs Commensurate Scattering
Response most enhanced at q*=(0,0,1-δ)2π/a and as T0.
Consistent with χ -1 ~ [ a(T-T N ) γ + θ(q-q*) +f(E) ] where θ 0 when q q*
Critical scattering (T>T N ) for q=q*=(0,0,1+/-δ)2π/a

Critical Incommensurate Correlations
Spatial correlations for q=(0,0,1+/-δ)2π/a diminished by
increased temperature T>T N and increased energy transfer E
Critical susceptibility χ q -1 ~ [ Γ(E,T) + θ(q-q*) ] Γ~a(T-TN ) γ + f(E)
Γ conv (A -1 )

Incommensurate Scattering
q*=(0,0,1+/-δ)2π/a: temperature independent scattering T0.
S(q,E,T) = [n(E/k B T)+1] χ”(q,E,T)
E/ k B T1 n(E/k B T)+1 ~ 1 χ”~G(E)
Quantum Criticality: Scale Invariant Excitations

QCP
q
Neutron Scattering Study of Cr 0.0965 V 0.035
Elastic scattering: similar to pure Cr. Electronic phase separation?
Commensurate scattering: Fermi – liquid like, E F ~ 18 meV
Incommensurate scattering: critical, divergence in the susceptibility
controlled by distance from (quantum) critical point
E
q-q * ,
q-q*, E, T-T N
T
T T N (=30 K?) E 0 q q*=2π/a(0,0,1+/-δ)
Generalized Critical Susceptibility:
χ -1 ~ [ (T-T N ) γ + iE + θ(q-q*)]
χ -1 ~ [(aT-iE) α + θ(q-q*) α ] CeCu 6-xc Au xc (Schroder2001)
χ -1 ~ [aT-iE + θ(q-q*)] α Ce(Ru 1-xc Fe xc ] 2 Ge 2 (Montfrooij2003)