• 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

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

d-electrons: 10 levels to fill

4f 14 levels 5f

Magnetism = Net Angular Momentum

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

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

eg orbitals

t2g orbitals

eg orbitals

t2g orbitals

3d5 : Mn2+

eg orbitals

t2g orbitals

3d9 : Cu2+

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

State-of-the-artneutron scattering

techniques

Large and Pristine Single Crystals grown by

Floating Zone Image Furnace

DC susceptibility shows singletground state

– no phase transition in SrCu2(BO3)2

DC susceptibility shows singletground state

– Spin-Peierls phase transition in CuGeO3

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

S=1/2 spin-Peierls chain: Collective Singlet

Introduce magnetic vacancies: S=1/2 degrees of freedom occur within odd length chain segments

or

J0totS

1totS

2

2

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 orthogonaldimers on square lattice

• Shastry-Sutherland model

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

DC susceptibility shows singletground state

– no phase transition in SrCu2(BO3)2

DC susceptibility shows singletground state

– Spin-Peierls phase transition in CuGeO3

3 Bands of Singlet-Tripletexcitations directly

observable with neutron scattering

~ 3 meV

~ 4.85 meV

~ 9.5 meV

Temperature dependence of 1-triplet excitation and 2-triplet excitation are identical and follow the

complement of the dc-susceptibility (1-).

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:

Large magnetic fields drive triplets to zero energy; producing steps in the magnetization.

G.A. Jorge et al. PRB, 71, 092403, 2005.

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

Calculated dynamical spin structure factor using the zero temperature Lanczos method.

Comparison to TheoryCalculations by S. El Shawish & J. Bonča

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

Conclusions:

Neutrons scatter from magnetic moments and nuclei in solids

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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.