Transcript Slide 1

Neutron Scattering Studies of
Tough Quantum Magnetism Problems
B. D. Gaulin
• Magnetic Neutron Scattering
• Quantum Singlet Ground State in the Spin-Peierls System CuGeO3
• Singlet Ground State and Triplet Excited States in the
Shastry-Sutherland System SrCu2(BO3)2
• Spin Polarons in SrCu(2-x)Mg(x)(BO3)2
Collaborators
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S. Haravifard
S.R. Dunsiger 1
A.J. Berlinsky
K.C. Rule2
J.P. Castellan3
H.A. Dabkowska
• J. Bonca
• S. El Shawish
• M.T.F. Telling
• T.G. Perring
• Y. Qiu
• J.R.D. Copley
• S.H. Lee
• Z. Yamani
McMaster University
J. Stefan Institute
University of Ljubljana, Slovenia
ISIS Pulsed Neutron Facility, UK
NIST
CNBC, NRC, Chalk River
now at : TU Munich1, HMI Berlin2, Argonne National Lab3
C. G. Shull et al, 1951
Paramagnet
T>TC
Ferromagnet
T<TC
Magnetic Structure of MnO
Antiferromagnet
T<TN
Magnetism = Net Angular Momentum
d-electrons: 10 levels to fill
4f
14 levels
5f
Neutrons are s=1/2 , neutral particles
En (meV) = 81.8/ (A)2 ; so =2 A neutrons have En=20.5 meV
Neutrons scatter from nuclei and magnetic moments in solids
Neutron Scattering Cross Section:
d2s/dW dE´ = (g r0)2/(2πħ) k´/k N{1/2 g Fd(k)}2
magnetic form factor
× Sa b (da b – ka kb ) Sl exp(ik∙l)
only measure S ┴ κ
× ∫ <exp(-ik∙u0))exp(ik∙ul(t))>
× <S0a(0) Slb(t)> exp(-iw t) dt
scattering ~ S2
so s=1/2 is the hardest case
eg orbitals
t2g orbitals
3d5 : Mn2+
eg orbitals
t2g orbitals
3d9 : Cu2+
eg orbitals
t2g orbitals
Transport, structure, and magnetism
are all closely connected
Sr2+ substitutes for La3+:
- pulls electrons out of CuO2 planes
• Magnetic Mott insulator
• Strange metal
• D wave superconductor
• Conventional metal
All while doping Sr for La
at the 15% level or less!
Large and Pristine Single Crystals
grown by
Floating Zone Image Furnace
State-of-the-art
neutron scattering
techniques
DC susceptibility shows singlet
ground state
– no phase transition in
SrCu2(BO3)2
DC susceptibility shows singlet
ground state
– Spin-Peierls phase transition in
CuGeO3
CuGeO3
Quasi-1D S=1/2 AF – structural phase transition to dimerized singlet
state
Spin-Peierls Phase Transition
H = l JSl  Sl 1
H = l ( JS2l  S2l 1  J ' S2l  S2l 1)
S=1/2 spin-Peierls chain: Collective Singlet
or
Introduce magnetic vacancies:
S=1/2 degrees of freedom occur within odd length chain segments
J
Triplet

  
2
Singlet
  
2

Stot = 1
Stot = 0
SrCu2(BO3)2
• Quasi-2D Cu-BO3 planes
• Sr ions between planes
• Mott insulator
S=1/2 moments at Cu2+
sites arranged in orthogonal
dimers on square lattice
• Shastry-Sutherland model
SrCu2(BO3)2
H = J  Si  S j  J  Si  S j
nn
|
>
|
>
nnn
J’/J = xcrit ~ 0.69
Case I
Case II
J>>J’ : Ground State –
Isolated singlet dimer
on nn (diagonal) bonds
J<<J’ : Ground State –
Ordered Neel
antiferromagnetic
DC susceptibility shows singlet
ground state
– no phase transition in
SrCu2(BO3)2
DC susceptibility shows singlet
ground state
– Spin-Peierls phase transition in
CuGeO3
3 Bands of Singlet-Triplet
excitations directly
observable with
neutron scattering
~ 3 meV
N=2 ~ 4.85 meV
N=3 ~ 9.5 meV
Temperature dependence of 1-triplet excitation
and 2-triplet excitation are identical and follow the
complement of the dc-susceptibility (1-c).
Time of Flight Neutron Scattering Data
B.D. Gaulin et al,
PRL 93, 267202 (2004)
G.A. Jorge et al.
PRB, 71, 092403, 2005.
SrCu2(BO3)2 enters collective singlet state at low temperature:
Large magnetic fields drive triplets to zero energy;
producing steps in the magnetization.
Hard core Boson models for interacting triplets
(Miyahara and Ueda, J. Phys. CM 15, R327, 2003)
Plateaus appear at commensurate filling of lattice with triplets
Comparison to Theory
Calculations by S. El Shawish & J. Bonča
Calculated dynamical spin structure factor
using the zero temperature Lanczos method.
Variational Calculation
(El Shawish and Bonca, PRB 74, 174420, 2006)
Starting point for spin defect
around impurity
GS
1st ES
Starting point not an eigenfunction of H
 Conclusions:
 Neutrons scatter from magnetic moments and nuclei in solids
 New neutron scattering infrastructure leads to New Science
Remarkable new opportunities with new time-of-flight neutron
infrastructure at SNS, JSNS, 2TS@ISIS
 Quasi-1D Spin-Peierls singlet ground state in CuGeO3 occurs
via phase transition.
 Quasi-2D Shastry-Sutherland singlet ground state system
SrCu2(BO3)2 shows triplet, n-triplet excited states. Bose
condensation of triplets in presence of magnetic field.
 Weak substitution of Cu2+ with Mg2+ in SrCu(2-x)Mg(x)(BO3)2 gives
rise to in-gap states – Spin Polarons.