nmr and field-induced magnetic ordered phases in the s =1 spin dimer system ba 3 mn 2 o 8

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