nmr and field-induced magnetic ordered phases in the s =1 spin dimer system ba 3 mn 2 o 8
DESCRIPTION
NMR and field-induced magnetic ordered phases in the S =1 spin dimer system Ba 3 Mn 2 O 8. Stanford E. Samulon I. R. Fisher. UCLA S. Suh SB. FSU/NHMFL L. Lumata J. S. Brooks P. Kuhns A. Reyes. LANL C. Batista. Ba 3 Mn 2 O 8. Magnetic properties: spin gap =12.3K. - PowerPoint PPT PresentationTRANSCRIPT
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
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
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
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
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).
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)
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
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.
Cristian Batista’s model of phases I, II
321
1
/
/
)(
)(~
c
dzcc
HH
HHT
23
1
/
/
~
~),(
T
TTHHM zdc
211 /(~
parameter order
llt MMM
Cristian Batista’s model of phases I, II
211
/)(~ cc HHT
21 TTHHM c ~),(
211 /(~
parameter order
llt MMM
• 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)
•Ba(1) consistent with sinusoidal modulation of hyperfine field•Ba(2) symmetry breaking; 2 different field modulations
(+)
(-)
I
T=1.5KEvidence for incommensurate phase
•Ba(1) consistent with sinusoidal modulation of hyperfine field
I
Evidence for incommensurate phase
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
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
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
With anisotropic coupling,
introduces linewidth to the Ba(2-) site
120
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)
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
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:
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
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
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
?
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?
-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