Exploring Quantum Magnetism
through Neutron Scattering
Collin Broholm,
Johns Hopkins University and NIST Center for Neutron Research
What is Quantum Magnetism?
Where do we find it?
Why is it interesting?
Summary & Prospects
Magnetism & Quantum Magnetism
 Ferromagnetism : Fundamental & essential collective phenomenon
— macroscopic semi-classical dynamics
 Non-magnetic materials: intra-atomic singlet formation
 Quantum Magnetism:
— Inter-atomic singlet formation
— Macroscopic singlet formation
— Strong correlations without static order
— Emergent quantum particles
— Quantum T=0 Phase Transitions
 
1
2
 
 

Overview of quantum magnetism
 Fundamental Questions:
– What types of collective phases are possible
– What are the corresponding quasi-particles
 Elements of the research
– Materials Synthesis (bulk and nano-structured)
– Advanced Characterization
– Theory
 Applications
– Model systems for quantum correlated physics
– Sensors and filters via strong collective response
– Quantum computing by manipulating emergent
quasi-particles
Probing matter through scattering
pf
Q 1



Q

Q

p

p


p

p
1
2
i
f
i
f
Q
 i EEi f E f
 Q 1 QQ2 E
Q 2
Intensity
ћw
Single Particle
Process
pi
Q
Intensity
ћw
Multi Particle
Process
May 6, 2009
ICNS 2009
Q
4
Quasi-particles “live” within solids
Bound spinons in spin-1 chain
Free spinons in spin-1/2 chain
≈ 10 mm
≈ 40 mm
Y2BaNiO5
Cu(C4D4N2)(NO3)2
≈ 0.1 mm
ZnCr2O4
May 6, 2009
Cu2(quinox)2Cl4
ICNS 2009
5
Acknowledgements
G. Aeppli
UCL
C. D. Batista
Los Alamos
Y. Chen
NIST
D. C. Dender
NIST
T. Hong
ORNL
M. Kenzelmann
PSI
C. P. Landee
Clarke University
K. Lefmann
Copenhagen Univ.
Y. Qiu
NIST & Univ. of Maryland
D. H. Reich
JHU
C. Rische
Univ. of Copenhagen
J. Abalardo-Rodriguez NIST & Univ. of Maryland
C. Stock
ISIS
M. B. Stone
Penn State University
M. M. Turnbull
Clarke University
G. Xu
BNL
I. Zaliznyak
BNL
Y. Zhao
JHU
+ many more friends & colleagues
Decoupled spin pairs: singlet ground state
 ,
1
2
 ,  ,  , 
 
,

S tot  1
H  JS1  S 2

1
2
JS tot 
2
3
4
J
1
2
May 6, 2009
 
ICNS 2009
 
7
 
 S 0
tot
A mobile triplet exciton
k B T  J
May 6, 2009
ICNS 2009
Xu et
8 al PRL (2000)
Description of weakly interacting dimers
 A spin-1/2 pair with AFM exchange has a singlet - triplet gap:
J
S tot  1
S tot  0
 Inter-dimer coupling allows coherent triplet propagation and
produces well defined dispersion relation
 Triplets can also be produced in pairs with total Stot=1
May 6, 2009
ICNS 2009
9
Creating two triplets with one neutron
Two magnons
One magnon
Tennant et al (2000)
w (meV)
Strongly Interacting Dimers in PHCC
2    max
(C H N )Cu2Cl6
May 6, 2009 4 12 2
(PHCC)
Stone et al. PRB (2001)
Magnon decay in two-magnon continuum
May 6, 2009
Stone et al. Nature (2006)
Neutron Scattering from Spin-1/2 chains
KCuF3: orb. order
Tenant, Lake, Nagler (2005)
SrCuO2: orb. order
CuPzN: Pyrazine
Stone et al., PRL (2003)
q / 2
Zaliznyak et al (2004)
Spinons on MACS
Large monochromator & 20 analyzers
Total
ofK2.7 hours counting time
T=1.6
3.5 hrs
Counting
T=5 K
3.5 hrs
Counting
MACS @ NCNR
May 6, 2009
Disintegration of a spin flip
Spinon
May 6, 2009
Spinon
/J
w J
From band-structure to bounded continuum
Q ()
q ()
S  Q , w   2
May 6, 2009


G SQ 
2
 w  w  
Quantum Criticality: T is only energy scale
TS
 qc , w  
A
1  exp(  w / k B T )
Im  
Lake et al (2005)
Lake et al (2005)
w / k BT

w / k BT

Quantum Critical Spin-1/2 chain
 
 J
2
S 2 n  S 2 n 1  J 1S 2 n 1S 2 n  2 
n
1
2
3
4

5
 
May 6, 2009
0
J 2  J1
J 2  J1
Damle and Huse PRL (2002)
Two & one-particle scattering in spin chains
CuCl2.2(DMSO):
 0 H  11 Tesla
Spin-1/2 chains in a crystal
Kenzelmann
May
6, 2009 et al. PRL (2004)
Why staggered field yields bound states
Zero field state quasi-long range AFM order
Without staggered field distant spinons don’t interact
With staggered field solitons separate “good” from “bad”
domains, which leads to interactions and “soliton” bound state
May 6, 2009
Corner-sharing
tetrahedra
Hao & Tchernyshyov (2009)
Triangular
Frustration &
weak connectivity
stunt growth of
correlations
Quantum Magnetism
Kagome
Frustrating outcomes
Lattice distorts
Long range order
ZnCr2O4
Weak disorder
Spin freezing
Stock et al. (2009)
40 K
15 K
1.5 K
S. H. Lee et al. (2000)
Nakatsuji et al (2006)
Frustration + Fermions = spin liquid
La2CuO4
Coldea et al 2001
k-ET2Cu2CN3 Kurosaki et al (2005)
Summary
Quantum magnetism: beyond spin to collective
quantum correlations
Stabilized by
– Low dimensionality
– Frustration
– Proximity to metal insulator transition
Examples
–
–
–
–
Spin dimers: Propagating triplet excitons
2-magnon continuum and magnon decay
Spinons and quantum criticality in spin-1/2 chain
Spin-liquids beyond one dimension?
Accelerated progress from new instruments
May 6, 2009