Transcript NEC physical sciences seminar Nov 3 2000

Resolving a Magnetic Quandary
Collin Broholm
Johns Hopkins University and NIST Center for Neutron Research
 Introduction
 Magneto-elastic transitions
 Magnetic frustration
 Order by coupling to lattice or charge
 Spin Peierls like transition in ZnCr2O4
 Resolving frustration in Y2Mo2O7
 orbital fluctuations and magnetism in (V1-xCrx)2O3
 Conclusions
Supported by the NSF through DMR-0074571
Collaborators
S.-H. Lee
G. Aeppli
W. Bao
S. A. Carter
S.-W. Cheong
P. Dai
J. S. Gardner
B. D. Gaulin
NEC 11/3/00
J. E. Greedan
J. M. Honig
T. H. Kim
P. Metcalf
N. P. Raju
W. Ratcliff III
T. F. Rosenbaum
Magnetic Neutron Scattering

ki
2

kf



Q  ki  k f
  E  E
i
f

Q
The scattering cross section is proportional to the
Fourier transformed dynamic spin correlation function
S


(Q ,  ) 
1
2 
 dt e
 i t
1
N


RR '
e
  
i Q  ( R  R ')

Fluctuation dissipation theorem:
 " Q ,     g  B   1  e
2
NEC 11/3/00
 

 S R ( t ) S R ' ( 0 ) 
 S Q ,  
Jahn-Teller Theorem
Any molecule or complex ion in an
electronically degenerate state will be
unstable relative to a configuration
of lower symmetry in which the
degeneracy is absent
NEC 11/3/00
Is exchange constant ?
H 
 ij J ij S i  S j
Jij is controlled by higher energy physics
that we like to consider irrelevant at low energies
• atomic spacing
• Orbital overlap
• Orbital occupancy
• localized or itinerant electronic states
 These degrees of freedom can become relevant
if H produces “degenerate” state
 The result can be intricate interplay between
spin charge and lattice sectors
NEC 11/3/00
D<3 magnets can have extensive soft
modes
Cu
Copper Benzoate Dender et al. (1996)
Spin Peierls Transition
H    l ( JS
2l
 S 2 l  1  J ' S 2 l  S 2 l 1 )
H    l J S  S l 1
l
M. Arai et al. (1996)
NEC 11/3/00
Q
Q
Spins with AFM interactions on corner-sharing
tetrahedra
What is special about this lattice?
 Low coordination number
 Triangular motif
 Infinite set of mean field ground states
 with zero net spin on all tetrahedra
 No barriers between mean field ground state
 Q-space degeneracy for spin waves
NEC 11/3/00
SPIN TYPE
SPIN
VALUE
LOW T
PHASE
M ETHOD
REFERENCE
Isot ropic
S= 1/ 2
Spin Liquid
Exact Diag.
Canals and Lacroix
PRL'9 8
Isot ropic
S= 
Spin Liquid
M C sim.
Anisot ropic
S= 
Reimers PRB'9 2
M oessner, Chalker
PRL'9 8
Neel order
M C sim.
Bramwell, Gingras,
Reimers
J. Appl. Phy s. '9 4
Pyrochlore
B-spinel
spins on corner sharing tetrahedra
M at erial
spin
t y pe
spin
value
 CW
( K)
M gV 2 O4
isot rop.
1
- 75 0
45
LRO
Balt zer et al '6 6
ZnV 2 O4
isot rop.
1
-60 0
40
LRO
Ueda et al '9 7
CdCr 2 O4
isot rop.
3/2
-8 3
9
LRO
Balt zer et al '6 6
M gCr 2 O4
isot rop.
3/2
-3 50
15
LRO
Blasse and Fast '6 3
ZnCr 2 O4
isot rop.
3/2
-3 9 2
12 .5
LRO
S.- H. Lee et al '9 9
FeF3
isot rop.
5/2
-23 0
20
LRO
Ferey et al. '8 6
Y 2 M o 2 O7
isot rop.
1
-20 0
2 2 .5
spin glass
Gingras et al. '9 7
Y 2 M n 2 O7
isot rop.
3/2
17 spin glass
Reimers et al '9 1
Tb 2 M o 2 O7
anisot r.
6 and 1
Gd 2 Ti 2 O7
isot rop.
7/ 2
Er 2 Ti 2 O7
anisot r.
-25
Tb 2 Ti 2 O7
anisot r.
- 19
Yb 2 Ti 2 O7
anisot r.
0
Dy 2 Ti 2 O7
Ising
7.5
Ho 2 Ti 2 O7
Ising
8
NEC 11/3/00
1/ 2
Low T phase
25
- 10
1/ 2
Tc
( K)
0 .5
1.9
spin glass
1 LRO
1.2 5
Greedan et al '9 1
Radu et al '9 9
LRO
Ramirez et al '9 9
spin liquid?
Gardner et al '9 9
0 .2 1 LRO
1.2
Ref .
Ramirez et al '9 9
spin ice
Ramirez et al '9 9
spin ice
Harris et al ''9 7
Subjects of this talk
ZnCr2O4 : Corner sharing tetrahedra
M aterial
M gV 2 O 4
Z nV 2 O 4
C dC r 2 O 4
M gC r 2 O 4
Z nC
r2O 4
NEC
11/3/00
 CW
-750
-600
-83
-350
-392
TN
45
40
9
15
12.5
 C W /T N
17
15
9
23
31
NIST Center for Neutron
Research
NEC 11/3/00
NEC 11/3/00
Signs of frustration: short range order for T<|CW|
Points of interest:
h (meV)
• 2/Qr0=1.4
=> nn. AFM correlations
• No scattering at low Q
=> satisfied tetrahedra
• Relaxation rate of order kBT
=> quantum critical
0
NEC 11/3/00
0.5
1.0
1.5
Q (A-1)
2
2.5
Approaching quantum criticality
  0 .8
C  0 .6
Lorentzian
relaxation spectrum:
 " (Q ,  ) 
k B   0 . 76 meV
 Q Q 

2
 Q
2
Near Quantum Critical
spin system:
T 
 Q (T )  C k B T  
 
Q
2
 Q (T ) 
1
3 k B 1  T
No indication of finite T cross over or phase transition in cubic phase
NEC 11/3/00
 1

First order phase transition in
ZnCr2O4
Dynamics:
• Low energy PM.
Fluctuations form
resonance
Statics:
• Staggered magnetization
• tetragonal distortion
NEC 11/3/00
Local spin resonance in ordered phase
Paramagnetic
fluctuations in
frustrated AFM
Local spin resonance
in magneto-elastic
LRO phase
NEC 11/3/00
Low T excitations in ZnCr2O4:
Magnetic DOS
Q-dep. of E-integ. intensity
C
C
A: Bragg peaks
B: Spin waves
C: Resonance
D: Upper band
D
B
A
B
A
NEC 11/3/00
Spectra at specific Q
Resonance
Spin waves
NEC 11/3/00
Dispersion relation for resonance
ZnCr2O4 single crystals T=1.5 K
NEC 11/3/00
Structure factor for resonance
ZnCr2O4 T=1.4 K 3 meV     6 meV
Extended sharp
structures in
reciprocal space
Fluctuations satisfy
local constraints
NEC 11/3/00
Comparing resonance and PM fluctuations
3 meV     6 meV
1.4 K
   0 . 7 meV
15 K
• Paramagnetic fluctuations and resonance satisfy
same local constraints.
• Transition pushes low energy fluctuations into a resonance
NEC 11/3/00
How can this frustrated system
order?
Edge sharing n-n exchange in ZnCr2O4 depends strongly on Cr-Cr distance, r
Cr3+
(JAFM<0)
O2-
r
From series of Cr-compounds:
 J ||

J 

a  c
2
 a r0
r0
dJ
dr
dJ
 40 meV

/A
  0 . 04 meV
dr
dJ
 0 . 06 meV
dr
The effect for a single tetrahedron is to make 4 bonds more AFM and two bond
less AFM. This relieves frustration!
Tetragonal dist.
NEC 11/3/00
Magnetic order in ZnCr2O4
•tetrahedra have zero net moment
this is a mean field ground
state for cubic ZnCr2O4
•Tetragonal distortion lowers energy
of this state compared to other
mean field ground states:
 HS
MF

1
2
5  J ||   J     0 .07
meV
•In a strongly correlated magnet
this shift may yield
-NEC
View
along tetragonal c-axis
11/3/00
k B T N t   H
S
MF
Ftet, Fcub
Analysis of spin and lattice energies at
TC
Cubic paramagnet
Tetrag. AFM
TC
T
From first moment sum-rule
 Hs  
3
2


 0  1  e
 S Q  
  0 . 40 ( 7 ) meV/Cr
sin Qr 0
1
Qr 0
2

 
Based on scattering data above and below TC and
assuming that nearest neighbor exchange dominates
NEC 11/3/00
Change in lattice energy at TC
Free energy of the two phases coincide at TC
0   F   Hs  
Hl  T c  S
From this we derive increase in lattice energy at transitio
TC  S

 0 . 16
 Hs

 0 . 40 ( 7 ) meV/Cr
 Hl

0 . 24 ( 7 ) meV/Cr
meV/Cr
Compare to tetragonal strain energy
 Hl
t
 v0

1
2



c11  c  2  a  c12  a  2  a  c
2
2
2
  0 . 026
meV/Cr
Discrepancy calls for additional lattice changes at TC
NEC 11/3/00
Analogies with Spin Peirls transition?
SpinPeirls
Quant um c rit ic al above TC
Order suppressed t o | T/  CW | < < 1 due t o
ZnCr 2 O4
y es
y es
low D
f rust rat ion
Change of lat t ic e sy mm et ry at TC enables
lower energy spin st at e
y es
y es
Low energy m agnet ic spec t ral weight is
pushed int o resonanc e
y es
y es
Order of phase t ransit ion
sec ond
f irst
Low T phase
isolat ed
singlet
Neel
LRO
no
y es
TC  S is signif ic ant energy sc ale
There are similarities as well as important distinctions!
NEC 11/3/00
Short range correlations in Y2Mo2O7
NEC 11/3/00
Spin-glass transition in Y2Mo2O7
Elastic scattering intensity:
• Development of spin correlations
static on the 50 ps time-scale
of the experiment.
Inelastic scattering intensity:
• Inelastic scattering decreases
as spins cease to fluctuate.
Spin relaxation rate:
• (T) decreases linearly with
T and extrapolates to
Tg=23 K derived from
AC-susceptibility
NEC 11/3/00
EXAFS Evidence for disorder in
Y2Mo2O7
NEC 11/3/00
Booth et al (2000)
Metal Insulator transition in V2O3
Hole doping
Increase U/W
The World according to Bill Gates
Mott, Sir Nevill Francis
Mott (mt), Sir Nevill Francis
Born 1905
British physicist. He shared a 1977 Nobel Prize
for developments in computer memory.
- from Microsoft Bookshelf Basics circulation >50,000,000?
on every Windows 98 based PC with Office
NEC 11/3/00
Short Range order in Paramagnetic
Insulator
B.Z.
NEC 11/3/00
Correlations in (V1-xCrx)2O3 and
La2CuO4
(V1-xCrx)2O3
Bao et al.
TC
TC
La2CuO4
NEC 11/3/00
Keimer et al.
First order phase transition in (V1-xCrx)2O3
Neel order
Spin Waves
Paramagnetic
Short Range Order
NEC 11/3/00
Spin wave dispersion
constants
Exchange
0.6 meV
Bao et al. Unpublished (2000)
NEC 11/3/00
Orbital fluctuations
order
Magnetic SRO
Magnetic order
T>TC
T<TC
Why orbital fluctuations at low T ?
An interesting possibility:
•Bonds occupy kagome’ lattice
•Ising model on kagome’ lattice
has no phase transition whence
the low TC
•Orbital occupational order
occurs to lower energy of
spin system
NEC 11/3/00
Conclusions
ZnCr2O4
• Quantum critical fluctuations in PM phase
• strain relieves frustration, enables Neel order
Y2Mo2O7
• Short range order at all temperatures T<|CW|
• spin freezing due to quenched lattice disorder ?
(V1-xCrx)2O3
-2
E (meV)
2
• MIT visible due to orbital occupational frustration ?
• Short range order due to orbital fluctuations
• Orbital occupational order enables spin order
Is there a Jahn-Teller like theorem for quantum critical magnets?
NEC 11/3/00