Upload
lawrence-melton
View
217
Download
0
Tags:
Embed Size (px)
Citation preview
Solving Impurity Structures Using Inelastic Neutron Scattering
Quantum Magnetism - Pure systems - vacancies - bond impuritiesConclusions
Collin Broholm*Johns Hopkins University and NIST Center for Neutron Research
*supported by the NSF through DMR-0074571
Ca2+
Y3+
Y2-x Ca
x BaNiO
5
ACA 7/24/00
Collaborators
G. Aeppli M. E. BisherJ. F. DiTusa C. D. FrostT. Ito T. H. Kim
K. Oka R. PaulD. H. Reich H. TakagiM. M. J. Treacy G. Xu
I. A. Zaliznyak
ACA 7/24/00
Inelastic Neutron Scattering
fi kkQ
fi EE
ikfk
Q
2
t
Nedt ti
QQQ
01
2
1),(
S
Nuclear scattering
RR'RR
RRQQ )(S)0(1
2
1),( '
' tSeN
edt iti
S
Magnetic scattering
ACA 7/24/00SPINS Cold neutron triple axis spectrometer at NCNR
ACA 7/24/00
Simple example of “Quantum” magnet
Cu(NO3)2.2.5D2O : dimerized spin-1/2 system
Only Inelastic magnetic scatteringOnly Inelastic magnetic scattering
ACA 7/24/00
A spin-1/2 pair has a singlet - triplet gap:
inter-dimer coupling yields dispersive mode
Why dimerized chain is a spin liquid
J0totS
1totS
ACA 7/24/00
Types of Quantum magnets
Definition: small or vanishing frozen moment at low T:
Conditions that yield quantum magnetism Low effective dimensionality Low spin quantum number geometrical frustration dimerization low connectivity interactions with fermions
Quantum magnets can display novel coherent states
JTkS B S for
ACA 7/24/00
Why study Quantum magnets ?
Coherent many body states are fascinating and useful Superconductivity Fractional Quantum Hall effect Bose Condensation Quantum magnets without static order at T=0
Each phenomenon provides different experimental info about macroscopic quantum coherence
Only in quantum magnets are dynamic correlations directly accessible (through neutron scattering)
ACA 7/24/00
Why study impurities in quantum magnets ?
Impurities are inevitable or even necessary to produce coherence
Probing the response to impurities reveals the building blocks of a macroscopic quantum state.
Impurities in quantum magnets can be explored at the microscopic level.
Ca2+Y3+
ACA 7/24/00
Dynamic condensed matter: 1D antiferromag.
q~2
Ni 2+
Y2BaNiO5 : spin 1 AFM
Impure
Pure
ACA 7/24/00
Macroscopic singlet ground state of S=1 chain
• This is exact ground state for spin projection Hamiltonian
• Magnets with 2S=nz have a nearest neighbor singlet covering with full lattice symmetry.
• Excited states are propagating bond triplets separated from the ground state by an energy gap .J
Haldane PRL 1983Affleck, Kennedy, Lieb, and Tasaki PRL 1987
i
iii
iiiii
toti SP 12
131
12 SSSSSSH
ACA 7/24/00
Coherence in a fluctuating system
Probing spatialcoherence of Haldane mode
Probing equal time correlation length
ACA 7/24/00
Impurities in Y2BaNiO5
Ca2+
Y3+
• Mg2+on Ni2+ sites finite length chains• Ca2+ on Y3+ sites mobile bond defectsMg
Ni
Kojima et al. (1995)
Mg
Ca2+
Pure
ACA 7/24/00
Zeeman resonance of chain-end spinsI(
H=
9 T
)-I(
H=
0 T
) (
cts.
per
min
.)
Hg B
h (
meV
)
H (Tesla)0 2 4 6 8
g=2.16
0 0.5 1 1.5 2
-5
0
10
15
20
Hg B
meV)(
ACA 7/24/00
Form factor of chain-end spins
Q-dependence revealsthat resonating objectis AFM.
The peak resemblesS(Q) for pure system.
Q-dependence revealsthat resonating objectis AFM.
The peak resemblesS(Q) for pure system.
Chain end spin carryAFM spin polarizationof length back into chain
Chain end spin carryAFM spin polarizationof length back into chain
Y2BaNi1-xMgxO5 x=4% Hg B
ACA 7/24/00
Sub gap excitations in Ca-doped Y2BaNiO5
Pure 9.5% Ca
•Ca-doping creates states below the gap
•sub-gap states have doubly peaked structure factor
Y2-xCaxBaNiO5:
G. Xu et al. Science (2000)
ACA 7/24/00
Incommensurate modulations in high TC superconductors
Hayden et al. (1998)
YBa2Cu3O6.6 T=13 K E=25 meV
h (rlu)
k
(rl
u)
Yamada et al. (1998)
La2-xSrxCuO4
ACA 7/24/00
Why is Y2-xCaxBaNiO5 incommensurate?
Charge ordering yields incommensurate spin order
Quasi-particle Quasi-hole pair excitations in Luttinger liquid
Single impurity effect
xq
q indep. of xq indep. of x
ACA 7/24/00
Does q vary with calcium concentration?
q not strongly dependent on x
q not strongly dependent on x
single impurity effectsingle impurity effect
G. Xu et al. Science (2000)
ACA 7/24/00
(b)
Ca
Ba
Ni
Y
c
b
a
(e)
(f)
(c)
(d)
a
O
Bond Impurities in a spin-1 chain: Y2-
xCaxBaNiO5
(a)
Form-factor for FM-coupled chain-end spins
2/)(Re2)( iqeqMqS
A symmetric AFM droplet
22/*2/ )()()(
ll
iql
iqlll eqMeqMPqS
Ensemble of independent randomly truncated AFM droplets
ACA 7/24/00
ConclusionsQuantum Magnets
low dimensional frustrated and/or weakly connected Coherent low T states rather than magnetic order Challenging to describe because fluctuations are essential
Probing impurities with neutrons Spectroscopic separation yields unique sensitivity to
impurity structures (in quantum magnets) through coherent diffuse inelastic neutron scattering
Impurities in spin-1 chain They create sup-gap composite spin degrees of freedom Edge states have extended AFM wave function Holes create AFM spin polaron with phase shift