Upload
others
View
2
Download
0
Embed Size (px)
Citation preview
KITP KITP –– Moments and Multiplets in Mott Materials (August 13 - December 14, 2007)
Michel GingrasDepartment of Physics & Astronomy, University of Waterloo, Waterloo, Ontario, CanadaandCanadian Institute for Advanced Research/Quantum Materials Program
Experimentally Motivated Problems Experimentally Motivated Problems in Some Highly Frustrated Rarein Some Highly Frustrated Rare--
Earth Magnetic Materials Earth Magnetic Materials
Collaborators• Ali Tabei (Waterloo)• Pawel Stasiak (Waterloo)• Taras Yavors’kii (Waterloo)• Hamid Molavian (Waterloo) • Adrian del Maestro (Harvard)• Francois Vernay (Waterloo PSI)• Matt Enjalran (USC)• Ying-Jer Kao (Nat. U. Taiwan,Tapei)• Jean-Yves Fortin (CNRS, Strasbourg)• Benjamin Canals (CNRS, Grenoble)
• Steve Bramwell (U.Coll. London)• Tom Fennell (U. Coll. London)• Jan Kycia (Waterloo)• Jeff Quilliam (Waterloo)• Kate Ross (Waterloo)• Linton Corruccini (UC Davis)• Oleg Petrenko (Warwick)
Theory
Experiment
Insulating Rare-Earth Magnetic Materials
• 4f orbitals are burried under 5s, 6s, 5d orbitals: exchange interactions Jij are “small”: θCW ~ 100 —101 K
• Re3+ can have large magnetic moments µ ~ 100 —101 µB• Magnetic dipolar interactions, D ~ 10-1 — 100 K ~ θCW
GENERAL SPIN HAMILTONIAN
20B 3 5
C BF
J J 3
(
(J )(J )
J J
J B
(
)
)4
J
ij i jj i
ii
i j i ij j ij
j i ij ij
i
H
r rg
r r
V
J
gα
µ µπ
µ
>
>
=
+
−
−
−
+
∑
∑
∑
i i
i
i
i
Crystal field part of H. This is a single-particle part of the Hamiltonian.it describes how the local electrostatic/chemical environment lifts the otherwise (2J+1) degeneracy of the otherwise free rare-earth ion.
Pyrochlore lattice:(Gd,Tb,Ho,Dy)2(Ti,Sn)2O7
Body-centered tetragonal lattice:LiHoxY1-xF4
Garnet lattice:Gd3Ga5O12
Spin IcePyrochlore lattice:(Ho,Dy)2(Ti,Sn)2O7
Ho2Ti2O7, Dy2Ti2O7, Ho2Sn2O7, Dy2Sn2O7,
Real materials show manifestations of Pauling’s ground state entropy magnetic analogues of water ice
2
12 1
( )( ) ( )T
T
C TS T S T dTT
− = ∫
Ramirez et. al, Nature 399, 333 (1999)
Dipolar Ising Spin Ice Model
Moved from J=15/2 S=1/2 effective classical Ising spin
( ),
3 5
ˆ ˆ
ˆ ˆ ˆ ˆ3( )( )
ji
ji
zzi j i j
i j
zi j i ij j ij zi j
i j ij ij
H z z
z z z r z r
rD
J
r
σ σ
σ σ>
= − +
• •−
∑
∑
i
iNot known
Known
den Hertog and Gingras, Phys. Rev. Lett. 84, 3430 (2000).
Real materials show manifestations of Pauling’s ground state entropy magnetic analogues of water ice
den Hertog and Gingras, Phys. Rev. Lett. 84, 3430 (2000).
Neutron scattering in Ho2Ti2O7
(h,h,0)
(0,0,l)
nn-spin ice
dipolar spin iceS. T. Bramwell, et al., Phys. Rev. Lett. 87, 047205 (2001).
Monte Carlo Phase Diagram of the Dipolar Spin Ice ModelMonte Carlo Phase Diagram of the Dipolar Spin Ice Model
Ho2Ti2O7
Jnn/Dnn ≈ - 0.22Dy2Ti2O7
Jnn/Dnn ≈ - 0.52
Tb2Ti2O7
Jnn/Dnn ≈ - 1.1
PM
2nd
OPT • LRO
• 1st OPT
910 .DJ
nn
nn −≈
C
TNo PT
C
T
Neutron Scattering in Dy2Ti2O7
T=400 mK
Experiment Monte Carlo
Gives exchange Jnn
??
Brillouin zone boundary scattering
ZnCr2O4 spinelθCW ~ -390 KTc =12.5 K
Experiment Cluster
Monte Carlo on dipolar spin ice model
Cluster
Fit to many experiments: M(H), Cv(T,H)
Consistent determination
0.7K<T<1.49K 1.5<T<2.8K
( ),
3 5
ˆ ˆ
ˆ ˆ ˆ ˆ3( )( )
ji
ji
zzi j i j
i j
zi j i ij
i
j ij zi j
i j ij ij
jH z z
z z z r z rD
r r
J σ σ
σ σ>
=− +
• •−
∑
∑
i
i
Conclusion about Dy2Ti2O7 Spin Ice
• At least in this system, it appears that “cluster-like” / “composite-spin” – like correlations are not emergent.
• They are accidentally fined-tuned by Nature.• They are the signature of the development of
“superstructure” in S(q) arising from ancillary perturbations to H0 in the “spin liquid” state.
Yavorsk’ii, Fennell, Gingras and Bramwell; arXiv:0707.3477
Gd3Ga5O12 Garnet (GGG)
•Complex lattice with 24 atoms in conventional cubic unit cell
Yavors’kii, Enjalran and Gingras; Phys. Rev. Lett. 97, 267203 [2006]
AFM
Re-entrance,4He-like P-T phase
diagram
Fiel
d (T
esla
)
0.40.2
1.0
0.5PM - SL
Temperature (K)
Gd3Ga5O12 garnet
Spin Glass or Extended SRO
• H~0T, T< 180mK, spin glass phase or extended SR correlations, ξ=100A? • No LRO at H=0.• Spin Liquid phase at intermediate fields.• AFM phase at stronger fields.• Reentrance resembles 4He melting.
1 K
Zero field experimental picture of: neutrons
Isotopically enriched 160Gd
Petrenko et al., Phys. Rev. Lett. 80, 4570 (1998)Pict: Roger Melko
Zero field experimental picture of : neutrons
1. How can the existence of sharp peaks in neutron scattering be understood in the context of the bulk measurements finding glassy behavior and muon spin relaxation finding persistent spin dynamics down to 20 mK?
2. There has been some skepticism in the field as to the correctness/accuracy/intrinsicness of those neutron data.
1) Determine the ordering wavevector using Gaussian approximation(i.e.) mean-field theory
20B 3 5
J J
J J 3(J )(J ) ( )4
ij i jj i
i j i ij j ij
j i ij ij
H J
r rg
r r
µ µπ
>
>
=−
+ −
∑
∑
i
i i i
2) Determine the right J2 and J3 by comparing the experimental vs theoretical critical neutron scattering calculated using MFT[similar conclusion reached by considering paramagnetic S(q)]
√
XX
X
Theoretical CalculationsBy allowing a fine-tuning of the exchange interactions beyond nearest neighbors, we are able to suggest that the incommensurate ordering seen in Gd3Ga5O12 garnet (GGG) may be “intrinsic” to the would-have been “idealized/disorder-free system”.
( )ord2 0.29,0.29,0qaπ
≅
Similar results reached with MCTc
MC ~0.2K / Tcexp ~0.14K
What does that mean?What kind of state is GGG in at low temperatures?
T. Yavors’kii, M. Enjalran, and M. J. P. Gingras Physical Review Letters 97, 267203 (2006)
Fluctuating “spin liquid”
regions
Ordered/ “spin solid” regions with glassy
“components”
Conclusions as per Gd3Ga5O12 (GGG)
Conclusion about Gd3Ga5O12
• Gd3Ga5O12 is displaying incommensurate order – system is on the verge …
• Bulk is akin to a spin slush…
Transverse Field LiHoxY1-xF4
Bx
The Transverse-Field Ising Model
Pierre-Gilles de GennesParis, France 1932 PGdG introduced the TFIM to describe
collective low energy proton excitations & tunneling effects in ferroelectrics:
∑∑ Γ−=i,
- xi
ji
zj
ziij SSSJH
Quantum mechanics (tunneling between the “up” and “down” direction) is introduced by the transverse field term (proportional to Г)
[ ] 0, ≠zi
xi SSP.G. de Gennes,
Collective Motions of Hydrogen BondsSolid. State. Comm. 1, 132 (1963).
Essentials of Γ-T Phase Diagrammfz
iS Γ< Γc
TTc
T
Γ
Γc
Tc(Γ=0)
Paramagnetic/disordered
Ordered/Frozen
Ordered/Frozen
Paramagnetic/disordered
R. J. Elliott, P. Pfeuty, and C. Wood,Ising Model with a Transverse FieldPhys. Rev. Lett. 25, 443(1970).
x-T Phase Diagram of LiHoxY1-xF4
x
41 FYLiHo xx −
Tc(x)PM
FM
SG
Г~ħ disorder- Г plane
AG
“ferroglass”composition
x
41 FYLiHo xx −Tc(x)PM
FMSG
Transverse field (Γ) vs temperature (T) phase diagram of LiHoxY1-xF4; x=0.44
Г
J. Brooke, U. Chicago; Ph.DThesis.
Transverse field (Transverse field (ΓΓ)) vsvs temperature (T) phase diagram of temperature (T) phase diagram of LiHoLiHoxxYY11--xxFF44; x=0.167; x=0.167
Spin glass composition
M T H T H T H( , ) ( ) ( ) ...= − +χ χ1 33
x
41 FYLiHo xx −
Tc(x)PM
FMSG
Microscopic origin of transverse field Ising model in LiHoxY1-xF4
e x
2
3 5
3 ( )1
z zi j
i j
zi j z z
i ji j i j i j
xi
i
H J S S
rD S S
r r
S
>
=
⎛ ⎞⎜ ⎟+ −⎜ ⎟⎝ ⎠
− Γ
∑
∑
∑
CF ex,
3 5
B x
({J }) J J
J • J 3(J )(J )
B
i i ji j
i j i ij j ij
i j ij ij
xi
i
H V J
r rD
r r
g J
α
µ
>
= + •
• •+ −
−
∑
∑
∑Remember: moved from J=8 S=1/2 effective spin
!!!!!!
Leading Interactions in LiHoxY1-xF4: long-range magnetic dipole-dipole REVISITED:
( )∑>
−••−•=ji
ijjijijijijinn rJrrJJJDRH 33 ˆˆ3εε
• In presence of the randomness, there will be random terms of the form:
zi
xi
zij
xijji JJrrεε
• Since there is broken symmetry along thex direction by the applied transverse field, the x-component of Ji will be nonzero:
zi
zi
j
zi
xj
zij
xijj JhJJrr ≈∑ ε
• This means that there is a random field along the z direction introduced by the combination of (i) the applied transverse field along the x direction and (ii) the random dilution of Ho3+ Y3+.
Generation of Longitudinal Random Fieldsa) Pure case z
x
Bx=0T>Tc
mirror plane
Bx≠0T>Tc
average Jx component
No local magnetic fieldalong z at reference point Bx
Generation of Longitudinal Random Fieldsb) Diluted case
z
Bx≠0T>Tc
average Jx component
x
A component of thelocal (magnetic) field is inducedalong z at reference point
Hence, the minimal model that we have is:
• Not only random Ising systems only in a transverse field:
∑∑ Γ−−=i,
xi
ji
zj
ziijJH σσσ
• But random Ising systems in a transverse field andcorrelated random longitudinal field:
, i, - z z x
ij iz
j ii j
i z ii
H hJ σσ σ σ=− − Γ∑∑ ∑
Effective Hamiltonian MethodEffective Hamiltonian Method
( ) 3 5
J J (J )(J )( 3 ) c
i j i ij j iji j
j i ij ij
R RH D
R RVε ε
>
• • •= − +∑
∑∉ −
=P EE
Rβ
βα
ββ
00
αα= ∑∈α P
P
effH PHP PHRHP= + + ⋅ ⋅ ⋅
eff, ,
0
1 12 2
z z x zij i j ij i j
i j i j
x z zrii i
ii
iz
ih S
H J S S K S S
S h S
= − −
−Γ −−
∑ ∑
∑ ∑ ∑
Mean-Field Phase Diagram
Toy Model
∑∑∑∑∑ −−Γ−−−=i
ziri
i
ziz
i
xi
zj
xi
jiij
zj
zi
jiij ShShSSSKSSJH 0
,, 21
21
( )2221
2 2exp2
)( JNJJ
NJP ijij −⎟⎠⎞
⎜⎝⎛=π
( )2221
2 2exp2
)( KNKKNKP ijij −⎟
⎠⎞
⎜⎝⎛=π
( )∆−⎟⎠⎞
⎜⎝⎛
∆= 2exp
21)( 2
21
riri hhPπ
field) magnetic e transvers(external of functions are J
and J
, 2 xBJK Γ∆
Tabei, Gingras, Kao et al., Phys. Rev. Lett., 97, 237203 (2006).
Conclusion about LiHoxY1-xF4 in a Transverse Field
• This system is a new realization in a magneticcontext of the random field Ising model.
Yavors’kii et al., Phys. Rev. Lett. 97, 267203 [2006]
• Similar conclusion reached by Schechter et al.M. Schechter and N. Laflorencie; Phys. Rev. Lett. 97, 137204 (2006)
• Some evidence from experiment that RFIM is at work in LiHoxY1-xF4 in FM regime of x: D. M. Silevitch et al.; Nature 448, 567-570 (Aug. 2007)
Tb2Ti2O7 Pyrochlore•Complex lattice with 16 atoms in conventional cubic unit cell
,1 ,2 ,3 ,4 0S S S S∆ ∆ ∆ ∆+ + + =
However, crystalline field effects and dipolar interactions playan important role in Re2Ti2O7 pyrochlores.
H. Molavian, B. Canals and M.J.P. Gingras , Phys. Rev. Lett. 98, 157204 (2007).
Monte Carlo Phase Diagram of the Dipolar Spin Ice ModelMonte Carlo Phase Diagram of the Dipolar Spin Ice Model
Ho2Ti2O7
Jnn/Dnn ≈ - 0.22Dy2Ti2O7
Jnn/Dnn ≈ - 0.52
Tb2Ti2O7
Jnn/Dnn ≈ - 1.1
PM
2nd
OPT • LRO
• 1st OPT
910 .DJ
nn
nn −≈
C
TNo PT
C
T
1/T 1
(µs-1
)
Tf
Muon Spin Relaxation Study of Tb2Ti2O7
J.S. Gardner et al. Phys. Rev. Lett. 82, 1012 (1999)
Exp
erim
ent
MonteCarlo
M.C. of Tb2Ti2O7 with <111> Ising spins at T=5K
⎥mJ⟩ wavefunction decomposition
Dy3+ (J=15/2)Ho3+ (J=8)
⎥±15/2⟩ + O(10-1)
~ 350 K
⎥±8⟩ + O(10-1)
~ 280 K
Tb3+ (J=6)(should be a nonmagnetic singlet, as Tm3+ !)
⎥±4⟩ + εg ⎥±1⟩; εg ~ O(10-1)
~ 20 K⎥±5⟩ + εe⎥±2⟩; εe ~ O(10-1)
~ 20 K
{⎥-3⟩,⎥+6⟩, -6⟩}
{⎥+3⟩, ⎥-3⟩,⎥+6⟩, -6⟩}
~ 80 K
Gingras et al., Phys. Rev. B 61, 6496 (2000)
⎥±4⟩ + εg ⎥±1⟩; εg ~ O(10-1)
~ 20 K⎥±5⟩ + εe⎥±2⟩; εe ~ O(10-1)
~ 80 K
~ 20 K
{⎥-3⟩,⎥+6⟩, -6⟩}
{⎥+3⟩, ⎥-3⟩,⎥+6⟩, -6⟩}
• The issue is that this gap is not very much larger than the exchangeand dipolar interactions, Hint.
• Hence, Hint induces admixing via virtual transitions among CEF levels.• This problem is not unrelated to the one of multispin (ring-exchange)
interactions generated via double-occupancy in the Hubbard model.
Gingras et al., Phys. Rev. B 61, 6496 (2000)
Quantum Fluctuations via Excited StatesQuantum Fluctuations via Excited States
e 15 4ψ β≈ + − e 2
5 4ψ β≈ − − +
0 14 5ψ α≈ − − 0 2
4 5ψ α≈ − +
J+ Jz
There is a mechanism for spin flips, and some isotropy can be restored.
Is Tb2Ti2O7 a spin liquid down to T=0with nearby quantum critical points?
Temperature
Jnn/Dnn
Paramagnetic
Q=0Néel Spin Ice
~ 20 K
~ 80 K
~ 20 K
The “third axis” (e.g. finite anisotropy {crystal field gap ∆} controls quantum fluctuations)
Exact Diagonalization of Single Tetrahedron
⎥±4⟩ + εg ⎥±1⟩; εg ~ O(10-1)
~ 20 K⎥±5⟩ + εe⎥±2⟩; εe ~ O(10-1)
~ 80 K
~ 20 K
{⎥-3⟩,⎥+6⟩, -6⟩}
{⎥+3⟩, ⎥-3⟩,⎥+6⟩, -6⟩}
Shed some light on quantum fluctuation channels
Single Tetrahedron Exact Diagonalization
0 0.01 0.02 0.03 0.04 0.05 0.060.15
0.16
0.17
0.18
0.19
0.2
0.21
Singlet
Doublet
1/∆ (K−1)
Jc (
K)
0 0.02 0.04 0.06
0.15
0.16
0.17
0.18
0.19
0.2
Doublet
Sextet
Effective Hamiltonian MethodEffective Hamiltonian Method
3 5,
J J (J )(J )J J ( 3 )i j i ij j ij
i ji j j i ij ij
R RH J D
R R>
• • •= • + −∑ ∑
∑∉ −
=P EE
Rβ
βα
ββ
00
αα= ∑∈α P
P
effH P H P P H R H P= + + ⋅ ⋅ ⋅
ex ex
e
eff
x dip dip ex dip dip
ex dip
( )
PH RH P
PH RH P PH RH P P
H
H
PH P
RH P
PH P
+ + +
= + +
0 0.01 0.02 0.03 0.04 0.05 0.060.15
0.16
0.17
0.18
0.19
0.2
0.21
Singlet
Doublet
1/∆ (K−1)
Jc (
K)
0 0.02 0.04 0.06
0.15
0.16
0.17
0.18
0.19
0.2
Doublet
Sextet
N-body quantum effectsplay an important rolein the renormalizationof the Néel – spin-ice boundary.
+ + + +=
+ + …+ + ++
Is Tb2Ti2O7 a spin liquid down to T=0with nearby quantum critical points?
Temperature
Jnn/Dnn
The “third axis” (e.g. finite anisotropy {1 over the crystal field gap∆} controls quantum fluctuations)
Paramagnetic
Q=0Néel Spin Ice
~ 20 K
~ 80 K
~ 20 K
Conclusion about Tb2Ti2O7
• Tb2Ti2O7 is an exotic material system – akin to a genuine 3D spin liquid. Why? Perhaps is pushed into a quantum disordered “quantum spin ice” regime. More experiments and calculations are needed.
Gd2Sn2O7 Pyrochlore
• A. Del Maestro, M. J. P. Gingras; Phys. Rev. B 76, 064418 (2007).• J.A. Quilliam, K.A. Ross, A.G. Del Maestro, M.J.P. Gingras, L.R. Corrucciniand J.B. Kycia; Phys. Rev. Lett. 99, 097201 (2007).
The neutron diffraction below T=1 K is well described by the so-called Palmer-Chalker ground states (3 discrete g.s. (×2))
S. E. Palmer and J. T. Chalker, Phys. Rev. B 62, 488 (2000).
Top view
“top” (001) view
NMR/muSR Relaxation Regimes
[ ] [ ] ( )B B
2 2ex ex ex
2( / ) ( / ) 1
~
For , Raman process
Conv
; ~ exp( / ) ;
~ / ; ~ ( 1)
ersely
(
/ ;
)
,
c
c
c
n k T n k T d
T T TT T
J zS S T T
T T
gµ
λ ε ε
λ
ω
εε
λ
λ ω
∞
∆× +
∆
−∆ ∆
Λ +
∫∼
ω0
bω aω
Y2Mo2O7
22 K
No order seen via any techniques down to ~ 50 mK
• Two-step transition to long-range order.• Mechanisms and ground state not fully understood.• Yet, neutron sees long-range order below 700 mK.
But neutron scattering sees a long-range ordered spin ice state: Mirebeau et al., Phys. Rev. Lett. 94, 246402 (2005).
Summary
• (Tb,Gd,Er,Yb)2(Ti/Sn)2O7 pyrochlores display λ>0 down to the lowest temperature.
• This persistent spin dynamics suggests unconventional ground state and/or excitations.
• “Psychologically”, one may be able to accept λ>0 in the previous materials since the ground state is all of them lacks a complete understanding.
• Not so for the next material (Gd2Sn2O7) since neutron scattering reveals long range order.
MuSR on Gd2Sn2O7
Sharp transition
P. Dalmas de Réotier, P. C. M. Gubbens and A. YaouancJ. Phys.: Condens. Matter 16, S4687(2004).
10-1 100 101
T [K]
100
101
102
Cp
[Jm
ol−
1 K−
1 ]
T 2 fit
0.2 0.4 0.60.8T [K]
10-1
100
101
Cp
[Jm
ol−
1K
−1]
Interestingly … the specific heat has also been interpreted as unconventional
2~C T
In conventional three-dimensionallong-range ordered antiferromagnets one expects T:
3~ ; ~ exp( / ) ;
cC T T TC T T
∆
−∆ ∆
P. Bonville et al, J. Phys. Condens. Matter 15, 7777 (2003).
But neutron scattering sees long-range order below 1 K: T=0.1 K
The neutron diffraction below T=1 K is well described by the so-called Palmer-Chalker ground states (3 discrete g.s. (×2))
S. E. Palmer and J. T. Chalker, Phys. Rev. B 62, 488 (2000).
Top view
“top” (001) view
This is “interesting” …
The identification of the PC ground state via neutron diffraction motivates a microscopic description.
A. G. del Maestro and M. J. P. Gingras; “Low temperature specific heat andpossible gap to magnetic excitations in the Heisenberg pyrochloreantiferromagnet Gd2Sn207”; Phys. Rev. B 76, 064418 (2007).
10-1 100 101
T [K]
100
101
102C
p[J
mol
−1 K
−1 ]
T 2 fit
0.2 0.4 0.60.8T [K]
10-1
100
101
Cp
[Jm
ol−
1K
−1]
Maybe a gap is opening up
Magnetic Interactions Involved
20B 3 5
CF
(| |) J J
J J 3(J )(J ) ( )
4
(J )
ij ij i jj i
i j i ij j ij
j i ij ij
i
H J r
r rg
r r
V α
µ µπ
>
>
= −
+ −
+
∑
∑
i
i i i
Crystal field part of H. This is a single-particle part of the Hamiltonian.it describes how the local electrostatic/chemical environment lifts the otherwise (2J+1) degeneracy of the otherwise free rare-earth ion.
Knowing the classical ground state of H, one can do 1/S spin-wave expansion away from it. After some work … one can recast H as:
†0 , ,( ) 1/ 2k k
k
H H k a aα α αα
ω ⎡ ⎤= + +⎣ ⎦∑∑
Γ X W L K Γ
0.0
1.0
2.0
3.0
4.0
ε(k
)[K
]
J2/|J1| = 0.00, J31/|J1| = 0.00
J2/|J1| = 0.03, J31/|J1| = −0.03
J2/|J1| = −0.03, J31/|J1| = 0.03
2
31
32J
J
J
J1
J2/|J1| = 0.02, J31/|J1| = 0.0
Exp. data
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
T [K]
10-1
100
Cv
[Jm
ol−
1 K−
1 ]
Spin Wave TheoryExp. data
0.2 0.4 0.6 0.8T [K]
5.5
6.0
6.5
7.0
m[µ
B/G
d3+
]
“Evidence for gapped spin-wave excitations in the frustrated Gd2Sn2O7pyrochlore antiferromagnet from low-temperature specific heat measurements”J. A. Quilliam, K. A. Ross, A. G. Del Maestro, M. J. P. Gingras, L. R. Corruccini, and J. B. Kycia (Phys. Rev. Lett. 99 097201 [2007]).
Pushing the study further …
350 mK
Gap-like behavior, C~ exp(-∆/T) Fit to spin-wave theory
0.01
0.1
1
10
100
Spe
cifi
c H
eat (
J / K
mol
Gd)
0.12 3 4 5 6 7 8 9
12 3
Temperature (K)
Total C (this work) C (from Bonville et al.)
T 2
power law
T 3
power law Nuclear contribution
Conclusions as per Gd2Sn2O7 pyrochlore- Neutron seemingly “sees” long range order.- That order is semi-classical (very weak quantum fluctuations ~ 3%).- That order agrees with simplest theoretical expectations.- Specific heat reveals gapped magnetic excitations below ~350 mK- The magnetic excitations are spin-wave like. - These quantitatively characterize the experimental specific heat.- Yet muSR “sees” persistent spin dynamics down to the lowest
temperature.- What is it that gives rise to this persistent spin dynamics in this
material?- Most/more interestingly, what is the influence of this “cause” in
Gd2Sn2O7 on the observed PSD in other (rare-earth oxide) HFMs?
THE END