NMR and field-induced magnetic ordered phases in the S =1 spin dimer system Ba 3 Mn 2 O 8
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NMR and field-induced magnetic ordered phases in the S=1 spin dimer system Ba3Mn2O8
UCLAS. SuhSB
StanfordE. SamulonI. R. Fisher
FSU/NHMFLL. LumataJ. S. BrooksP. KuhnsA. Reyes
LANLC. Batista
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Ba3Mn2O8
c
Magnetic properties:
spin gap =12.3K
M. Uchida, et al. PRB 66 054429 (2002).
powder samples
Trigonal structure→S=1 dimers arranged in layers with hexagonal coordination, oriented vertically in layers
single layer coordination
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S=1 spin dimer compound with spin gap
Electron counting→3d2, S=1 for Mn5+ ions
given by form for S=1 with dominant J0+interdimer interactions
B closes spin gap. Two plateaus for T→0 corresp. to Sz=1,2 T=650mK
Uchida, et al., 2002
From M(B)-plateau separation a result of dispersive excitations linked to interdimer coupling
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BaCuSi2O6
Jaime, et al., PRL (2004)
In applying a magnetic field H>Hc1, possibility for various magnetic phases, qu. criticality-e.g., Magnetization plateaus in isolated dimers →spin liquid states=no broken symmetry coupled dimers
Interdimer AF exchange→LRMO between the plateaus (order is in component transverse to field), finite T phase transitions and possibility for QCP
→phase transition sometimes described as condensation of hard-core (no double occupancy) bosons.
→ BEC if rotational symmetry spontaneously broken
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H/T phase diagram established by specific heat-several phases evident:At least 3 phases for H<Hc2 [Tsujii, et al., PRB 72 214434 (2005)]
Ba3Mn2O8--this time S=1, with single-ion anisotropy D<>0, intralayer frustration…
→S=1 dimers: model Hamiltonians allow for possibility of broken translational symmetry (fractional plateaus), and nearby supersolid phase(s). See, e.g., Sengupta and Batista, PRL (2007).
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Broken symmetry phases between the plateaus from Cp, magnetocaloric effect[(Samulon, et al., Phys. Rev. B 77, 214441 (2008)]
3 phases identified by Tsujii, et al., PRB 72 214434 (2005)
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I. A little more about Ba3Mn2O8
II. Basic 135,137Ba NMR observations for B(||,)c
III. B||c
IV. Bc
What is to be learned from NMR?
1. Nature of broken symmetry phases I, II from spectra
2. Critical behavior in physical properties, such as: Tc(H-Hc1), order parameter Mt(H-Hc1), M(T,Hc1)
3. Correlations/fluctuations, characteristic of broken symmetries, near quantum phase transitions from relaxation
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Phase I, B//c
AF J1→intralayer FM order, interlayer AF order
AF J2 →=120° state (total spin zero in the plane)
Compromise result:Spiral w/ <>120 ° (Uchida, et al.)
3
111
120
jljli SSJH ,,'
:exchange (NN) interlayer on turns
…frustration…?
BaCuSi2O6: interlayer frustration→2D Qu. Cr.
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Cristian Batista’s model of phases I, II
321
1
/
/
)(
)(~
c
dzcc
HH
HHT
23
1
/
/
~
~),(
T
TTHHM zdc
211 /(~
parameter order
llt MMM
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Cristian Batista’s model of phases I, II
211
/)(~ cc HHT
21 TTHHM c ~),(
211 /(~
parameter order
llt MMM
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• 135,137Ba NMR, I=3/2------2 isotopes
• 135=432Hz/G, 135Q=0.18(10-24)cm2
• 137=472Hz/G, 137Q=0.28(10-24)cm2
• uniaxial point group symmetry for Ba(1,2)
• 12 transitions total m=1: 2 isotopesx 2 sitesx 3 transitions
(I=3/2)
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•Ba(1) consistent with sinusoidal modulation of hyperfine field•Ba(2) symmetry breaking; 2 different field modulations
(+)
(-)
I
T=1.5KEvidence for incommensurate phase
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•Ba(1) consistent with sinusoidal modulation of hyperfine field
I
Evidence for incommensurate phase
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Relevance of the hyperfine couplings
jiA
AAAijA
AAA
AAA
AAA
A
IASH
ij
zzyyxxij
zzzyzx
yzyyyx
xzxyxx
hf
for
ninteractio Dipolar :2 Ex.
and, for
ninteractio contact Fermi :1 Ex.
with
0
0
order transverse to ysensitivit NO
Ba(2) (intra-layer)
Acc=1.8T/B
Aaa=2.8T/ B
Ba(1) (inter-layer)
Acc=4.8T/B
Aaa=5.8T/ B
non-zero anisotropic part…values way too big for direct dipolar
BaH0
Mn Mn
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Mn layer above Mn layer below
Chirality of triangles is relevant to spectrum seen by Ba(2)-situated in the middle of each but offset vertically
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Ba(2)+
Ba(2)-
Couple dipole fields of 3 nearest Mn spins to Ba(2)
Sinusoidal variation of longitudinal field for 120° state, + chirality
No variation of longitudinal field for 120° state, - chirality
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With anisotropic coupling,
introduces linewidth to the Ba(2-) site
120
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Samulon, et al., PRB (2008)
Phase II,Phase I near phase II
…and maybe in REALLYHigh field range phase I?
Goal: interpretation of spectra, phases
Approach: Use Heff from (Cristian B.) and dipole couplings to Mn-spins to model spectral features from perspective of symmetry
-0.5 0 0.5 1 1.50
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
=0-(h) (MHz)
inte
nsity
(a.
u.)
H0(T)
10.0
9.75
9.50
9.25
9.00
8.90
8.80
8.75
137Ba(2) satellite T=100mK
phase IIH
0(T)
10.0
9.75
9.50
9.25
9.00
8.90
8.80
8.75
137Ba(2) satellite T=100mK
phase IIH
0(T)
10.0
9.75
9.50
9.25
9.00
8.90
8.80
8.75
137Ba(2) satellite T=100mK
phase IIH
0(T)
10.0
9.75
9.50
9.25
9.00
8.90
8.80
8.75
137Ba(2) satellite T=100mK
phase IIH
0(T)
10.0
9.75
9.50
9.25
9.00
8.90
8.80
8.75
137Ba(2) satellite T=100mK
phase IIH
0(T)
10.0
9.75
9.50
9.25
9.00
8.90
8.80
8.75
137Ba(2) satellite T=100mK
phase IIH
0(T)
10.0
9.75
9.50
9.25
9.00
8.90
8.80
8.75
Spectra, (B>Bc) c, entering phase II:(incommensurate)
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Dipolar interaction only
ml=0.0
ml=0.025
ml=0.050
ml=0.075
ml=0.10
ml=0.0
ml=0.025
ml=0.050
ml=0.075
ml=0.10
Dipolar+contact interaction
-0.5 0 0.5 1 1.50
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
=0-(h) (MHz)
inte
nsity
(a.
u.)
H0(T)
10.0
9.75
9.50
9.25
9.00
8.90
8.80
8.75
137Ba(2) satellite T=100mK
phase IIH
0(T)
10.0
9.75
9.50
9.25
9.00
8.90
8.80
8.75
137Ba(2) satellite T=100mK
phase IIH
0(T)
10.0
9.75
9.50
9.25
9.00
8.90
8.80
8.75
137Ba(2) satellite T=100mK
phase IIH
0(T)
10.0
9.75
9.50
9.25
9.00
8.90
8.80
8.75
137Ba(2) satellite T=100mK
phase IIH
0(T)
10.0
9.75
9.50
9.25
9.00
8.90
8.80
8.75
137Ba(2) satellite T=100mK
phase IIH
0(T)
10.0
9.75
9.50
9.25
9.00
8.90
8.80
8.75
137Ba(2) satellite T=100mK
phase IIH
0(T)
10.0
9.75
9.50
9.25
9.00
8.90
8.80
8.75
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8.5 9 9.5 10 10.50
0.2
0.4
0.6
0.8
1
1.2
1.4
field (T)
linew
idth
(M
Hz)
spectral widths Ba(2)T=100mK Bc
full width[H-H
c]1/2
2nd feature[H-H
c]
-0.5 0 0.5 1 1.50
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
=0-(h) (MHz)
inte
nsity
(a.
u.)
H0(T)
10.0
9.75
9.50
9.25
9.00
8.90
8.80
8.75
137Ba(2) satellite T=100mK
phase IIH
0(T)
10.0
9.75
9.50
9.25
9.00
8.90
8.80
8.75
137Ba(2) satellite T=100mK
phase IIH
0(T)
10.0
9.75
9.50
9.25
9.00
8.90
8.80
8.75
137Ba(2) satellite T=100mK
phase IIH
0(T)
10.0
9.75
9.50
9.25
9.00
8.90
8.80
8.75
137Ba(2) satellite T=100mK
phase IIH
0(T)
10.0
9.75
9.50
9.25
9.00
8.90
8.80
8.75
137Ba(2) satellite T=100mK
phase IIH
0(T)
10.0
9.75
9.50
9.25
9.00
8.90
8.80
8.75
137Ba(2) satellite T=100mK
phase IIH
0(T)
10.0
9.75
9.50
9.25
9.00
8.90
8.80
8.75
Samulon, et al.
Transverse mag.mT~[mL(1-mL)]1/2
Modulation of longitud.mL~mL
2nd featurefull width
Order parameter near QCP at edge of phase II:
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Samulon, et al.
Transverse mag.mT~[mL(1-mL)]1/2
Modulation of longitud.mL~mL
Order parameter near QCP at edge of phase I:
B//c
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At the critical field, H=Hc1
M(H~Hc1)~Td/z
1. B//c: d=3, z=2
M~T3/2
2. Bc:
M~?…to be determined
B//c
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At the critical field, H=Hc1
B//c: d=3, z=2
T1-1~T3/4
Variety of dynamical behavior in neighborhood of BEC QCPOrignac, Citro, Giamarchi, PRB 75, 140403 (2007)
BEC case
?
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1. Ba3Mn2O8 is an S=1 spin dimer compound where frustration, AF exchange interactions, and single-ion anisotropy each play a role in establishing field-induced quantum phases
2. By rotating the field, possibility for changing character of QCP from BEC (B//c) to Ising or… XY (?).
3. NMR is sensitive to transverse components of magnetization. I, II are incommensurate phases. NMR spectroscopy is consistent with phase II as easy-plane phase.
4. Order parameter follows expected form for QCP for both phases. mT~[H-Hc1]1/2. More complicated structure near boundary of I/II.
5. M(Hc1,T) for B//c consistent with BEC univerality class.
6. Dynamics on approach, as probed by T1-1, is not behaving in a
simple way-a result of incommensurability?
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-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
30
35
40
45
50
frequency (Mhz)
Inte
nsity
(A
.U.)
137Ba(2)sat at 100mK between phase?
11T
10.5T
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
30
35
40
frequency (Mhz)
Inte
nsity
(A
.U.)
137Ba(2)sat at 100mK, phase I
12T
11.5T
11.5T
12T
10.5T
11T
-0.5 0 0.5 1 1.50
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
=0-(h) (MHz)
inte
nsity
(a.
u.)
H0(T)
10.0
9.75
9.50
9.25
9.00
8.90
8.80
8.75
137Ba(2) satellite T=100mK
phase IIH
0(T)
10.0
9.75
9.50
9.25
9.00
8.90
8.80
8.75
137Ba(2) satellite T=100mK
phase IIH
0(T)
10.0
9.75
9.50
9.25
9.00
8.90
8.80
8.75
137Ba(2) satellite T=100mK
phase IIH
0(T)
10.0
9.75
9.50
9.25
9.00
8.90
8.80
8.75
137Ba(2) satellite T=100mK
phase IIH
0(T)
10.0
9.75
9.50
9.25
9.00
8.90
8.80
8.75
137Ba(2) satellite T=100mK
phase IIH
0(T)
10.0
9.75
9.50
9.25
9.00
8.90
8.80
8.75
137Ba(2) satellite T=100mK
phase IIH
0(T)
10.0
9.75
9.50
9.25
9.00
8.90
8.80
8.75
“Complicated” spectra moving from II into I
Spectra going into phase I for Bc