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

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

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

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

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

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 Singlet Triplet

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 | > | > J’/J = xcrit ~ 0.69

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)

SrCu2(BO3)2 enters collective singlet state at low temperature: 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 Calculated dynamical spin structure factor Calculations by S. El Shawish & J. Bonča Calculated dynamical spin structure factor using the zero temperature Lanczos method.

Starting point for spin defect around impurity 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

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, 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.