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![Page 1: Vivien Zapf National High Magnetic Field Laboratory Los Alamos National Lab Bose-Einstein Condensation and Magnetostriction in NiCl 2 -4SC(NH 2 ) 2](https://reader036.vdocument.in/reader036/viewer/2022062320/56649d795503460f94a5c729/html5/thumbnails/1.jpg)
Vivien ZapfNational High Magnetic Field Laboratory
Los Alamos National Lab
Bose-Einstein Condensation and Magnetostriction in NiCl2-4SC(NH2)2
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National High Magnetic Field Laboratory
Pulsed magnets to 75 TM(H), (H), magnetostriction, ESR, optics, etc
300 T single-turn (s pulse)
Coming soon: 60 T and 100 T long pulse magnets (2 s)
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300 T single-turn nondestructive magnetChuck Mielke, Ross McDonald, et al
Capacitor bank pulses a short (s) mega-amp current pulse to achieve ultra high magnetic fields.
10 mm long.10mm ID.
2 s rise time, dB/dt ≈ 108 Ts-1
3 orders of magnitude faster than standard short pulse magnets at the NHMFL.
Low inductance capacitor bank.L = 18 nH, C = 144 F, V = 60 kV, E = 259kJ.
Single turn magnet coil, L = 7 nH.
Peak current 4 MA.
1st megagauss shot (February 8th 2005)
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Ni
Cl
Jplane/kB = 0.17 K
c
a
a
Ni S = 1
Cl
NiCl2-4SC(NH2)2 (DTN)No Haldane gap
Other BEC compoundsAll Cu spin-1/2 dimers
•TlCuCl3 (wrong symmetry)
•BaCuSi2O6
(3D -> 2D crossover)
• CsCuCl4
Jchain/kB = 1.72 K
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0.2
0.4
0.6
0.8
1
-1 -0.5 0 0.5 1
kz
- -/2 -/20
Hc2 = 12.6 THc1 = 2.1 T
kz=0 (FM)
kz= (AFM)
Antiferromagnetic exchange
jiijv
v SSJ
NiCl2-4SC(NH2)2 (DTN)
2j
z
jSDH
Spin-orbitcoupling Zeeman term
j
zzB jSHg
Sz = +1
H
D~8K
E
Sz = 0
Sz = -1
Ni2+ S = 1: Triplet split by spin-orbit coupling Tetragonal lattice
Sz = +1
Sz = 0
Sz = -1
D~8K
Hc
Sz
a
S=1 M. Kenzelmann et al
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Ni spins
Mz
(x10
3 em
u/m
ol)
0
2
4
6
8
10
12
14
0 5 10 15H (T)
H || c
A. Paduan-Filho et al, Phys. Rev. B 69, 020405(R) (2004)
Hc
a
BEC/AFM
Hc1 Hc2
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10 ibea
10 zz SbeSa i spin language
boson language
H ~ Mz ~ N (# of bosons)
Sz = 1D
H || c
E
or T(K)
XY AFM orderAFMFM
b or N0 1
Boson filling fraction/Number of bosons
Occupied bosonEmpty site
Note: Approximate theory neglects Sz = -1 state. Complete theory:
H.-T. Wang and Y. Wang, Phys. Rev. B 71, 104429 (2005) K.-K. Ng and T.-K. Lee, cond-mat/0507663
Example: treat upper state as an energetically unfavorable double occupancy state
Sz = -1
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jji
ii
ziB
i
zi SSJSHgSD
,
Η2
i
iieffji
ijjijjii bbDhbbbbbbbbJ
,
H
AFM exchangeSpin-orbit coupling
Zeeman term
Repulsion (2nd order in N)
hopping number operator
Spin language Hamiltonian
Boson language Hamiltonian (neglecting Sz = -1 term)
S+ -> b+ (boson creation operator)
(Hardcore Constraint: One boson per site)
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Spins Bosons
|Sz = 1> state occupied boson |1>
|Sz= 0> state unoccupied boson |0>
Order parameter: Order parameter:Staggered magnetization Mx Boson creation operator b† = S+
Magnetic field Chemical potential (H ~ N ~ )
Boson mapping
This also works for S=1/2: |↑> = occupied, |↓> = unoccupied
Spins are prevented from obeying fermion statistics since no real-space overlap between states allowed
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Why do the bosons obey number conservation?
Tetragonal symmetry of crystal:
U(1) symmetry of spins. Symmetric under rotation by in a-b plane
• Hamiltonian must be independent of
• Rotation by : b† → b† eiand b → be-i
• H can only contains b†b or bb† terms ( = number operator)
• (b† eibe-ib† b = N
• Hamiltonian commutes with boson number operator
• Boson number is conserved.
a
b
|Sz = 1> = occupied boson |Sz = 0> = unoccupied bosonb† = boson creation operator H
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X
Energy landscape of spins
S
Symmetry in plane
X
Ni
HXY
model
Ising model
E()
Ni
H
• Boson number only conserved in statistical average• Spin fluctuations, lattice fluctuations limit super current
lifetimes• Small corrections to XY model: DM interactions, dipole-
dipole, and spin-orbit coupling
Limitations
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Experimental Tests for BEC
Sz = 1D
H || c
E or T(K)
XY AFM order
0N
230
0 1
11
1
/
/
/
TMN
eNN
en
z
kTk
Tkk
Bk
Bk
23
32
32
/
/
/
~
~
~~
~
TH
HT
HMN
NT
C
C
C
0
2
4
6
8
10
12
14
0 5 10 15H (T)
H || c
Mz
2kk ~where
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H
T
Hc1Hc2
Quantum Phase Transition (BEC)amplitude driven (d=3, z=2)
XY AFM
Thermal phase transition (XY AFM) phase driven (d=3, z=1)
Quantum Phase Transition:universality class of a BEC
• BaCuSi2O6
(3D -> 2D crossover)
• CsCuCl4
• NiCl2-4SC(NH2)2
THH
TM
cc
z
1
3D BEC: = 3/2
3D Ising: = 2
2D “BEC”: = 1
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Sapphire platform
C=Q/T C=/Quasi-Adiabatic Thermal Relaxation Time
Measuring Specific Heat
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C/T
(m
J/m
ol K
2 )Specific Heat
0
2
4
6
8
10
0 0.4 0.8 1.2 1.6T (K)
H = 10 T
T (
K)
Magnetocaloric Effect
0.39
0.4
0.41
0.42
0.43
0.44
10 11 12 13 14B(T)
inflec. point
increasing Hdecreasing H
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6 8 10 12 14
Magnetocaloric effect
Specific heat
H (T)
V. S. Zapf, D. Zocco, B. R. Hansen, M. Jaime, N. Harrison, C. D. Batista, M. Kenzelmann, C. Niedermayer, A. Lacerda, and A. Paduan-Filho, Phys. Rev. Lett., 96, 077204 (2006)
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0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6 8 10 12 14
Magnetocaloric effectSpecific heat
H (T)
H – Hc TN
H – Hc TN 2 (3D Ising
magnet)
3/2 (3D BEC)
1 (2D “BEC”)
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H-Hc1 = aT
= 1.47 ± 0.10
= 1.5 BEC)
Ising magnet
2D BEC
3D BEC
Windowing Technique: see
THH cc 1TMz
V. S. Zapf, et al, Phys. Rev. Lett., 96, 077204 (2006)
S. Sebastian et al, Phys. Rev. B 72, 100404(R) (2005)
0
0.5
1
1.5
2
2.5
0 0.2 0.4 0.6 0.8 1
Tmax/1.2 K A. Paduan Filho, unpublished
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Tc
(K)
TH
TH
c
c
8510
22
2
1
.
.
Predictions (3-level system):
KJ
KD
av 690
128
.
.
Inelastic Neutron Diffractionand magnetization :
C. D. Batista, M. Tsukamoto, N. Kawashima, in progress
V. S. Zapf et al, Phys. Rev. Lett. 96, 77204 (2006).
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6 8 10 12 14
Magnetocaloric effectSpecific heat
H (T)
predicted Hc1
predicted Hc2
Spin wave theory
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Magnetostriction
Capacitance
Titanium Dilatometer(design by G. Schmiedeshoff)
CuBe spring
V. Correa, V.S. Zapf, T. Murphy, E. Palm, S. Tozer, A. Lacerda, A. Paduan-Filho
-0.010
-0.005
0.000
0.005
0.010
0.015
0.020
0.025
0 2 4 6 8 10 12 14B (T)
L/L
(%
)Hc1
Hc2
T = 25 mK
H || c
Lc
La
Hc
a
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JJJJJJJJJ = 1.7 K
J = 0.17 K
-0.010
-0.005
0.000
0.005
0.010
0.015
0.020
0.025
0 2 4 6 8 10 12 14B (T)
L/L
(%
)
Magnetostriction
Hc1
Hc2
Lc
La
Ni++
c
a
H
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-0.010
-0.005
0.000
0.005
0.010
0.015
0.020
0.025
0 2 4 6 8 10 12 14B (T)
L/L
(%
)
Magnetostriction
Hc1
Hc2
Lc
La
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6 8 10 12 14
Magnetocaloric effectSpecific heat
H (T)
predicted Hc1
predicted Hc2
Tc
(K)
Summary
BEC confirmed experimentally via H-Hc1 ~ T and M ~ T
Magnetostriction effect distorts phase diagram with increasing magnetic field
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?
Future work:
Frustration-induced symmetry change?
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Acknowledgements
LANLCristian Batista (T-11 theory group)
NHMFL-LANLDiego Zocco Marcelo Jaime Neil HarrisonAlex Lacerda
NHMFL-TallahasseeVictor Correa (Magnetostriction)Tim Murphy Eric PalmStan Tozer
Universidade de Sao Paulo, Brazil
Armando Paduan-Filho (Crystal growth and Magnetization)
Paul Scherrer Institute and ETH, Zürich, Switzerland
B. R. Hansen
M. Kenzelmann (Neutron scattering)
University of Tokyo
Mitsuaki Tsukamoto
Naoki Kawashima (Monte Carlo Simulations)
Occidental College
George Schmiedeshoff (dilatometer design)
NSF NHMFL DOE