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

2. now at : TU Munich1, HMI Berlin2, Argonne National Lab3
Collaborators
S. Haravifard
S.R. Dunsiger 1
A.J. Berlinsky McMaster University
K.C. Rule2
J.P. Castellan3
H.A. Dabkowska
J. Bonca J. Stefan Institute
S. El Shawish University of Ljubljana, Slovenia
M.T.F. Telling ISIS Pulsed Neutron Facility, UK
T.G. Perring
Y. Qiu NIST
J.R.D. Copley
S.H. Lee
Z. Yamani CNBC, NRC, Chalk River
now at : TU Munich1, HMI Berlin2, Argonne National Lab3

3. C. G. Shull et al, 1951 Magnetic Structure of MnO
Paramagnet Ferromagnet Antiferromagnet
T>TC T<TC T<TN

4. Magnetism = Net Angular Momentum
d-electrons: 10 levels to fill 4f
14 levels 5f

5. 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

6. 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 ~ S so s=1/2 is the hardest case

7. eg orbitals
t2g orbitals

8. 3d5 : Mn2+
eg orbitals
t2g orbitals

9. 3d9 : Cu2+
eg orbitals
t2g orbitals

10. 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!

11. Large and Pristine Single Crystals Floating Zone Image Furnace
grown by
Floating Zone Image Furnace
State-of-the-art
neutron scattering
techniques
2) in pyrochlores, anisotropy makes a big difference as to whether the ground state

12. 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

13. Spin-Peierls Phase Transition
CuGeO3
Quasi-1D S=1/2 AF – structural phase transition to dimerized singlet state
Spin-Peierls Phase Transition

14. S=1/2 spin-Peierls chain: Collective Singletor
Introduce magnetic vacancies:
S=1/2 degrees of freedom occur within odd length chain segments

15. J
Singlet
Triplet

16. 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

17. SrCu2(BO3)2
| > | >
J’/J = xcrit ~ 0.69

18. 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

19. 3 Bands of Singlet-Triplet
excitations directly
observable with
neutron scattering
~ 3 meV
N=2 ~ 4.85 meV
N=3 ~ 9.5 meV

20. Temperature dependence of 1-triplet excitation
and 2-triplet excitation are identical and follow the
complement of the dc-susceptibility (1-c).

21. Time of Flight Neutron Scattering Data
B.D. Gaulin et al,
PRL 93, (2004)

22. SrCu2(BO3)2 enters collective singlet state at low temperature:
G.A. Jorge et al.
PRB, 71, , 2005.
SrCu2(BO3)2 enters collective singlet state at low temperature:
Large magnetic fields drive triplets to zero energy;
producing steps in the magnetization.

23. 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

26. Comparison to Theory Calculated dynamical spin structure factor
Calculations by S. El Shawish & J. Bonča
Calculated dynamical spin structure factor
using the zero temperature Lanczos method.

27. Starting point for spin defect around impurity
Variational Calculation
(El Shawish and Bonca, PRB 74, , 2006)
Starting point for spin defect
around impurity GS
1st ES
Starting point not an eigenfunction of H

29. Neutrons scatter from magnetic moments and nuclei in solids
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,
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.