magnetic neutron scattering quantum singlet ground state in the spin-peierls system cugeo 3 singlet...
TRANSCRIPT
![Page 1: Magnetic Neutron Scattering Quantum Singlet Ground State in the Spin-Peierls System CuGeO 3 Singlet Ground State and Triplet Excited States in the Shastry-Sutherland](https://reader030.vdocuments.us/reader030/viewer/2022020319/56649f2f5503460f94c489dd/html5/thumbnails/1.jpg)
• 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
B. D. Gaulin
Neutron Scattering Studies of Tough Quantum Magnetism Problems
![Page 2: Magnetic Neutron Scattering Quantum Singlet Ground State in the Spin-Peierls System CuGeO 3 Singlet Ground State and Triplet Excited States in the Shastry-Sutherland](https://reader030.vdocuments.us/reader030/viewer/2022020319/56649f2f5503460f94c489dd/html5/thumbnails/2.jpg)
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
![Page 3: Magnetic Neutron Scattering Quantum Singlet Ground State in the Spin-Peierls System CuGeO 3 Singlet Ground State and Triplet Excited States in the Shastry-Sutherland](https://reader030.vdocuments.us/reader030/viewer/2022020319/56649f2f5503460f94c489dd/html5/thumbnails/3.jpg)
C. G. Shull et al, 1951 Magnetic Structure of MnO
Paramagnet Ferromagnet Antiferromagnet T>TC T<TC T<TN
![Page 4: Magnetic Neutron Scattering Quantum Singlet Ground State in the Spin-Peierls System CuGeO 3 Singlet Ground State and Triplet Excited States in the Shastry-Sutherland](https://reader030.vdocuments.us/reader030/viewer/2022020319/56649f2f5503460f94c489dd/html5/thumbnails/4.jpg)
d-electrons: 10 levels to fill
4f 14 levels 5f
Magnetism = Net Angular Momentum
![Page 5: Magnetic Neutron Scattering Quantum Singlet Ground State in the Spin-Peierls System CuGeO 3 Singlet Ground State and Triplet Excited States in the Shastry-Sutherland](https://reader030.vdocuments.us/reader030/viewer/2022020319/56649f2f5503460f94c489dd/html5/thumbnails/5.jpg)
Neutrons are s=1/2 , neutral particlesEn (meV) = 81.8/so A neutrons have En=20.5 meV
Neutrons scatter from nuclei and magnetic moments in solids
![Page 6: Magnetic Neutron Scattering Quantum Singlet Ground State in the Spin-Peierls System CuGeO 3 Singlet Ground State and Triplet Excited States in the Shastry-Sutherland](https://reader030.vdocuments.us/reader030/viewer/2022020319/56649f2f5503460f94c489dd/html5/thumbnails/6.jpg)
Neutron Scattering Cross Section:
d2/d dE´ = ( r0)2/(2πħ) k´/k N{1/2 g Fd()}2
magnetic form factor
× ( – ) l exp(i∙l)
only measure S ┴ κ
× ∫ <exp(-i∙u0))exp(i∙ul(t))>
× <S0(0) Sl
(t)> exp(-i t) dt scattering ~ S2 so s=1/2 is the hardest case
![Page 7: Magnetic Neutron Scattering Quantum Singlet Ground State in the Spin-Peierls System CuGeO 3 Singlet Ground State and Triplet Excited States in the Shastry-Sutherland](https://reader030.vdocuments.us/reader030/viewer/2022020319/56649f2f5503460f94c489dd/html5/thumbnails/7.jpg)
eg orbitals
t2g orbitals
![Page 8: Magnetic Neutron Scattering Quantum Singlet Ground State in the Spin-Peierls System CuGeO 3 Singlet Ground State and Triplet Excited States in the Shastry-Sutherland](https://reader030.vdocuments.us/reader030/viewer/2022020319/56649f2f5503460f94c489dd/html5/thumbnails/8.jpg)
eg orbitals
t2g orbitals
3d5 : Mn2+
![Page 9: Magnetic Neutron Scattering Quantum Singlet Ground State in the Spin-Peierls System CuGeO 3 Singlet Ground State and Triplet Excited States in the Shastry-Sutherland](https://reader030.vdocuments.us/reader030/viewer/2022020319/56649f2f5503460f94c489dd/html5/thumbnails/9.jpg)
eg orbitals
t2g orbitals
3d9 : Cu2+
![Page 10: Magnetic Neutron Scattering Quantum Singlet Ground State in the Spin-Peierls System CuGeO 3 Singlet Ground State and Triplet Excited States in the Shastry-Sutherland](https://reader030.vdocuments.us/reader030/viewer/2022020319/56649f2f5503460f94c489dd/html5/thumbnails/10.jpg)
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!
Transport, structure, and magnetism are all closely connected
![Page 11: Magnetic Neutron Scattering Quantum Singlet Ground State in the Spin-Peierls System CuGeO 3 Singlet Ground State and Triplet Excited States in the Shastry-Sutherland](https://reader030.vdocuments.us/reader030/viewer/2022020319/56649f2f5503460f94c489dd/html5/thumbnails/11.jpg)
State-of-the-artneutron scattering
techniques
Large and Pristine Single Crystals grown by
Floating Zone Image Furnace
![Page 12: Magnetic Neutron Scattering Quantum Singlet Ground State in the Spin-Peierls System CuGeO 3 Singlet Ground State and Triplet Excited States in the Shastry-Sutherland](https://reader030.vdocuments.us/reader030/viewer/2022020319/56649f2f5503460f94c489dd/html5/thumbnails/12.jpg)
DC susceptibility shows singletground state
– no phase transition in SrCu2(BO3)2
DC susceptibility shows singletground state
– Spin-Peierls phase transition in CuGeO3
![Page 13: Magnetic Neutron Scattering Quantum Singlet Ground State in the Spin-Peierls System CuGeO 3 Singlet Ground State and Triplet Excited States in the Shastry-Sutherland](https://reader030.vdocuments.us/reader030/viewer/2022020319/56649f2f5503460f94c489dd/html5/thumbnails/13.jpg)
CuGeO3
1 lll J SSH
)'( 122122 lllll JJ SSSSH
Quasi-1D S=1/2 AF – structural phase transition to dimerized singlet state
Spin-Peierls Phase Transition
![Page 14: Magnetic Neutron Scattering Quantum Singlet Ground State in the Spin-Peierls System CuGeO 3 Singlet Ground State and Triplet Excited States in the Shastry-Sutherland](https://reader030.vdocuments.us/reader030/viewer/2022020319/56649f2f5503460f94c489dd/html5/thumbnails/14.jpg)
S=1/2 spin-Peierls chain: Collective Singlet
Introduce magnetic vacancies: S=1/2 degrees of freedom occur within odd length chain segments
or
![Page 15: Magnetic Neutron Scattering Quantum Singlet Ground State in the Spin-Peierls System CuGeO 3 Singlet Ground State and Triplet Excited States in the Shastry-Sutherland](https://reader030.vdocuments.us/reader030/viewer/2022020319/56649f2f5503460f94c489dd/html5/thumbnails/15.jpg)
J0totS
1totS
2
2
Singlet
Triplet
![Page 16: Magnetic Neutron Scattering Quantum Singlet Ground State in the Spin-Peierls System CuGeO 3 Singlet Ground State and Triplet Excited States in the Shastry-Sutherland](https://reader030.vdocuments.us/reader030/viewer/2022020319/56649f2f5503460f94c489dd/html5/thumbnails/16.jpg)
SrCu2(BO3)2
• Quasi-2D Cu-BO3 planes• Sr ions between planes• Mott insulator
S=1/2 moments at Cu2+
sites arranged in orthogonaldimers on square lattice
• Shastry-Sutherland model
![Page 17: Magnetic Neutron Scattering Quantum Singlet Ground State in the Spin-Peierls System CuGeO 3 Singlet Ground State and Triplet Excited States in the Shastry-Sutherland](https://reader030.vdocuments.us/reader030/viewer/2022020319/56649f2f5503460f94c489dd/html5/thumbnails/17.jpg)
nn nnn
jiji SSJSSJH
Case I J>>J’ : Ground State – Isolated singlet dimer on nn (diagonal) bonds
Case II J<<J’ : Ground State – Ordered Neel antiferromagnetic
SrCu2(BO3)2
| > | > J’/J = xcrit ~ 0.69
![Page 18: Magnetic Neutron Scattering Quantum Singlet Ground State in the Spin-Peierls System CuGeO 3 Singlet Ground State and Triplet Excited States in the Shastry-Sutherland](https://reader030.vdocuments.us/reader030/viewer/2022020319/56649f2f5503460f94c489dd/html5/thumbnails/18.jpg)
DC susceptibility shows singletground state
– no phase transition in SrCu2(BO3)2
DC susceptibility shows singletground state
– Spin-Peierls phase transition in CuGeO3
![Page 19: Magnetic Neutron Scattering Quantum Singlet Ground State in the Spin-Peierls System CuGeO 3 Singlet Ground State and Triplet Excited States in the Shastry-Sutherland](https://reader030.vdocuments.us/reader030/viewer/2022020319/56649f2f5503460f94c489dd/html5/thumbnails/19.jpg)
3 Bands of Singlet-Tripletexcitations directly
observable with neutron scattering
~ 3 meV
~ 4.85 meV
~ 9.5 meV
![Page 20: Magnetic Neutron Scattering Quantum Singlet Ground State in the Spin-Peierls System CuGeO 3 Singlet Ground State and Triplet Excited States in the Shastry-Sutherland](https://reader030.vdocuments.us/reader030/viewer/2022020319/56649f2f5503460f94c489dd/html5/thumbnails/20.jpg)
Temperature dependence of 1-triplet excitation and 2-triplet excitation are identical and follow the
complement of the dc-susceptibility (1-).
![Page 21: Magnetic Neutron Scattering Quantum Singlet Ground State in the Spin-Peierls System CuGeO 3 Singlet Ground State and Triplet Excited States in the Shastry-Sutherland](https://reader030.vdocuments.us/reader030/viewer/2022020319/56649f2f5503460f94c489dd/html5/thumbnails/21.jpg)
Time of Flight Neutron Scattering Data
B.D. Gaulin et al,
PRL 93, 267202 (2004)
![Page 22: Magnetic Neutron Scattering Quantum Singlet Ground State in the Spin-Peierls System CuGeO 3 Singlet Ground State and Triplet Excited States in the Shastry-Sutherland](https://reader030.vdocuments.us/reader030/viewer/2022020319/56649f2f5503460f94c489dd/html5/thumbnails/22.jpg)
SrCu2(BO3)2 enters collective singlet state at low temperature:
Large magnetic fields drive triplets to zero energy; producing steps in the magnetization.
G.A. Jorge et al. PRB, 71, 092403, 2005.
![Page 23: Magnetic Neutron Scattering Quantum Singlet Ground State in the Spin-Peierls System CuGeO 3 Singlet Ground State and Triplet Excited States in the Shastry-Sutherland](https://reader030.vdocuments.us/reader030/viewer/2022020319/56649f2f5503460f94c489dd/html5/thumbnails/23.jpg)
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
![Page 24: Magnetic Neutron Scattering Quantum Singlet Ground State in the Spin-Peierls System CuGeO 3 Singlet Ground State and Triplet Excited States in the Shastry-Sutherland](https://reader030.vdocuments.us/reader030/viewer/2022020319/56649f2f5503460f94c489dd/html5/thumbnails/24.jpg)
![Page 25: Magnetic Neutron Scattering Quantum Singlet Ground State in the Spin-Peierls System CuGeO 3 Singlet Ground State and Triplet Excited States in the Shastry-Sutherland](https://reader030.vdocuments.us/reader030/viewer/2022020319/56649f2f5503460f94c489dd/html5/thumbnails/25.jpg)
![Page 26: Magnetic Neutron Scattering Quantum Singlet Ground State in the Spin-Peierls System CuGeO 3 Singlet Ground State and Triplet Excited States in the Shastry-Sutherland](https://reader030.vdocuments.us/reader030/viewer/2022020319/56649f2f5503460f94c489dd/html5/thumbnails/26.jpg)
Calculated dynamical spin structure factor using the zero temperature Lanczos method.
Comparison to TheoryCalculations by S. El Shawish & J. Bonča
![Page 27: Magnetic Neutron Scattering Quantum Singlet Ground State in the Spin-Peierls System CuGeO 3 Singlet Ground State and Triplet Excited States in the Shastry-Sutherland](https://reader030.vdocuments.us/reader030/viewer/2022020319/56649f2f5503460f94c489dd/html5/thumbnails/27.jpg)
Variational Calculation(El Shawish and Bonca, PRB 74, 174420, 2006)
Starting point for spin defectaround impurity
GS 1st ES
Starting point not an eigenfunction of H
![Page 28: Magnetic Neutron Scattering Quantum Singlet Ground State in the Spin-Peierls System CuGeO 3 Singlet Ground State and Triplet Excited States in the Shastry-Sutherland](https://reader030.vdocuments.us/reader030/viewer/2022020319/56649f2f5503460f94c489dd/html5/thumbnails/28.jpg)
![Page 29: Magnetic Neutron Scattering Quantum Singlet Ground State in the Spin-Peierls System CuGeO 3 Singlet Ground State and Triplet Excited States in the Shastry-Sutherland](https://reader030.vdocuments.us/reader030/viewer/2022020319/56649f2f5503460f94c489dd/html5/thumbnails/29.jpg)
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.