field-induced magnetic behavior in quasi-1d ising-like ......synemag 2012 october 17-19 th, 2012,...

SYNEMAG 2012October 17-19th, 2012, Grenoble

Field-induced magnetic behavior in quasi-1D Ising-like antiferromagnet BaCo2V2O8:

a detailed single crystal neutron diffraction studya detailed single crystal neutron diffraction study

Béatrice GRENIER

UJF & CEA, INAC/SPSMS/MDNGrenoble, France

[email protected]

Outline

• Introduction on Ising-like quasi-1D systems

• The BaCo2V2O8 compound- crystallographic structure- previous results

• Single-crystal neutron diffraction results *- experimental- experimental- magnetic structure in the Néel phase- Néel-LSDW phase transition and (H, T ) phase diagram- magnetic structure in the LSDW phase

• Conclusion

* E. Canévet, B. Grenier, M. Klanjšek, C. Berthier, M. Horvatić, V. Simonet, and P. Lejay,

arXiv: 1210.3253 (2012); submitted to Phys. Rev. B

Introduction on Ising-like quasi-1D systemsHamiltonian of a S = ½ 1D XXZ AF chain system in a magnetic field:

Spin-spin correlation functions ofthe

Staggered transverse correlation:

4

3FM (gap)

HsatTomonaga-Luttinger liquid (TLL):

Workshop on Synchrotron and Neutron Applications of High Magnetic Fields, Grenoble, October 17-19th, 2012 – Béatrice Grenier

Incommensurate longitudinal correlation:

with

Staggered transverse correlation:

h= H/J

1

2

3

01 20-1 3-2

FM (gap)

AF (gap)

∆

TLL(no gap)

Heisenberg chainIsing chain

XY chain

Hc

1

Introduction on Ising-like quasi-1D systems

XXZ chain with weak 3D interaction

• Heisenberg chain (∆ = 1): η < 1 as soon as H ≠ 0 → transverse fluctuations dominate

• Ising-like chain (∆ > 1):

��H Ztransverse staggered

(XY Néel)

η > 1 at low H above Hc → longitudinal fluctuations dominate

H > H *: η < 1 → transverse staggered (XY Néel)

��H Z

Hc > H ≥ 0: gapped Néel

��H Z

Workshop on Synchrotron and Neutron Applications of High Magnetic Fields, Grenoble, October 17-19th, 2012 – Béatrice Grenier 2

• Ising-like chain (∆ > 1):

H * > H > Hc :longitudinal spin density wave(LSDW)

��H Z

η > 1 at low H above Hc → longitudinal fluctuations dominate

Introduction on Ising-like quasi-1D systems

h= H/J

4

2

3 FM (gap) TLL(no gap)

Hsat

Hc

BaCo2V2O8Néeltransverse staggered

LSDW


Hc H * Hsat

h

1

01 20-1 3-2

AF (gap)

∆

3.9 T 22.7 T~15 T

[1]

[1] Okunishi and Suzuki, PRB 76, 224411 (2007)

The BaCo2V2O8 compound: crystallographic structure

I 41/acd space group with a = 12.444 Å and c = 8.415 Å at T = 300 KR. Wichmann and Hk. Müller-Buschbaum, Z. Anorg. Allg. Chem. 532, 153 (1986)

4 screw chains ||c -axis per unit cell � 16 Co2+ with spin 3/2 (effective spin S = ½)


The BaCo2V2O8 compound: previous results

• H -T diagram from specific heat

• ”Discovery” of BaCo2V2O8: Crystal growth + Magnetic measurementsHe et al., Chem. Mater. 17, 2924 (2005)

Kimura et al., J. Phys.: Conf. Series 51, 99–102 (2006)

• Theoretical predictions applied to BaCo2V2O8Okunishi and Suzuki, PRB 76, 224411 (2007)


• H -T diagram from specific heat Kimura et al., PRL 100, 057202 (2008)

• First observation of IC satellites up to H = 5 Tby single-crystal neutron diffraction Kimura et al., PRL 101, 207201 (2008)

• Determination of the magnetic structure at H = 0by powder neutron diffraction Kawasaki et al., PRB 83, 064421 (2011)

Results: Experimental

•••• Crystal synthesis @ Institut Néel

•••• Specific heat measurements @ CEA


•••• Specific heat measurements @ CEA

•••• Magnetic structure in zero field(Néel phase) on D15 & D23 @ ILL

•••• Magnetic structure in the LSDW phase & incommensurability vs field on D23 @ ILLH || easy axis (chain c -axis)6 T / 12 T + dilutionVertical collimation 20'

6

D23

Results: Magnetic structure in the Néel phase

Propagation vector:

=�

(1,0,0)AFk

= +��

AF AFQ H k

=�

where ( , , )with 2

H h k lh k l n 1000

2000

30002 -3 0

Ne

utr

on

co

un

ts /

10

se

c.

Increasing T

Decreasing T

BaCo2V

2O

8


+ + =with 2h k l n

Critical exponent β = 0.32 ⇒ 3D Ising universality class

0 1 2 3 4 5 6 70

1000

Ne

utr

on

co

un

ts /

10

se

c.

T (K)

Results: Magnetic structure in the Néel phase

Nuclear structure:Same structure below TN as above

Magnetic structure:

313 reflections collected (113 independent)up to sinθ /λ = 0.55

Refinement with Fullprof

→ one of the four magnetic structures


→ one of the four magnetic structurespredicted by group theory with two magnetic domains of populations 49.5(4)% and 50.5(4)%

Results: Magnetic structure in the Néel phaseMagnetic domain #1

1

23

45

67

88'

5'

6'

7'

1'2'

3'

4'

a

c

Screw axis 41

4

a

c

1

2

3

5

67

88'

5'6'

7'

1'2'

3'

4'

Magnetic domain #2


a

c b

1 2

34 5 6

78

8'

5'6'

7' 1'2'

3' 4'

bScrew axis 41

a

c b

1 2

34 5 6

78

8'

5'6'

7' 1'2'

3' 4'

b

9

mx = my = 0mz = 2.267(3)µB /Co2+

3000

4000

5000

H = 0.0 T H = 1.0 T

H = 2.0 T H = 3.0 T

Ne

utr

on

co

nts

/ 2

0 s

ec.

(-2, -3, QL)

T = 50 mK

Results: Néel-LSDW phase transition

Hc

0 3.94 4.12 9.25H (T )

0 ≤ H ≤ 3.92 T:

Néel phase

=�

(1,0,0)AFk

-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15

0

1000

2000

3000

H = 3.4 T

QL (r.l.u.)

Ne

utr

on

co

nts

/ 2

0 s

ec.


= (1,0,0)AFk

10


HcH (T )

0 3.94 4.12 9.25

(-2, -3, QL)

T = 50 mK

1000

H = 3.98 TH = 4.00 T

Ne

utr

on

co

nts

/ 3

0 s

ec.

2000

1000

2000

3.94 ≤ H ≤ 4.12 T:

Coexistence betweenNéel & LSDW phases


-0.2 -0.1 0.0 0.1 0.2

1000

0

1000

0

QL (r.l.u.)

Ne

utr

on

co

nts

/ 3

0 s

ec.

1000

0

1000

0

Néel & LSDW phases

0.03 < δ < 0.07

=�

(1,0,0)AFk

δ=�

(1,0, )LSDWk

10

= ±��

LSDW LSDWQ H k

2000

3000

H = 4.1 T H = 5.0 T

H = 6.0 T H = 7.0 T

Ne

utr

on

co

nts

/ 1

min

.Results: Néel-LSDW phase transition

HcH (T )

0 3.94 4.12 9.25

(-2, -3, QL)

T = 50 mK

4.14 ≤ H ≤ 9.25 T:

LSDW phase

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4

0

1000

H = 8.0 T

QL (r.l.u.)

Ne

utr

on

co

nts

/ 1

min

.


0.07 ≤ δ ≤ 0.31δ=

�(1,0, )LSDWk

10


HcH (T )

0 3.94 4.12 9.25

1600

1800

2000

H = 8.75 T H = 9.00 T H = 9.25 T

Ne

utr

on

co

nts

/ 5

min

.

4.14 ≤ H ≤ 9.25 T:

LSDW phase

(-2, -3, QL)

T = 50 mK


0.1 0.2 0.3 0.4 0.5

1000

1200

1400

1600

QL (r.l.u.)

Ne

utr

on

co

nts

/ 5

min

.

0.07 ≤ δ ≤ 0.31

10

δ=�

(1,0, )LSDWk


HcH (T )

0 3.94 4.12 9.25

(-2, -3, QL)

T = 50 mK

1600

1800

2000

H = 8.75 T H = 9.00 T H = 9.25 T

Ne

utr

on

co

nts

/ 5

min

.

H ≥ 9.5 T:

I = 0


0.1 0.2 0.3 0.4 0.5

1000

1200

1400

1600

QL (r.l.u.)

Ne

utr

on

co

nts

/ 5

min

.

from NMR [1]: new phase

[1] M. Klanjšek et al.,

arXiv: 1202.6376 (2012)

10


Mz from Ref. [1] • Theory applies: Mz = 1/2 gµBS [2]

• Field hysteresis ~ 0.2 T

⇓

1st order transition


[1] Kimura et al., PRL 100, 057202 (2008)[2] Haldane, PRL 45, 1358 (1980)[3] Kimura et al., J. Phys.: Conf. Ser. 51, 9910 (2006)

Mz from Ref. [1]

scaled to our dataMz = 1/2 gµBS [2]

⇓

g = 7.2

(to be compared to g = 6.2 [3])

Results: H -T phase diagram


[1]

[1] Okunishi and Suzuki, PRB 76, 224411 (2007)

Results: Magnetic structure in the LSDW phase

H = 4.2 T coming down from 6 T

Nuclear structure:Same as in zero magnetic field

Magnetic structure:129 reflections collected (49 independent)

Continuity with that found in zero field


Continuity with that found in zero field

13

Two magnetic domains of populations 38.3(9)% and 61.7(9)%

⇑

small misalignment of the fieldHa = 0.11 T, Hb = 0.04 T

Results: Magnetic structure in the LSDW phase

Magnetic domain #1


Amplitude of the sine wave modulation = 1.398(6)µB /Co2+

Conclusion & perspectives

CONCLUSION

• Magnetic structures:- At H = 0: confirmation of the structure determined on powder

opportunity for a visualization of the magnetic domains- At H = 4.2 T: refined for the first time → continuity with zero field

first direct evidence of the LSDW phase in BaCo2V2O8

• Critical exponent β : BaCo2V2O8 belongs to the 3D Ising universality class


Critical exponent : BaCo2V2O8 belongs to the 3D Ising universality class

• δδδδ (H ) in perfect agreement with theory assuming g = 7.2

• H –T phase diagram in perfect agreement with theory up to ~9 T then not any more→ new phase seen by NMR [M. Klanjšek et al., arXiv: 1202.6376 (2012)]: ferromagnetic SDW

PERSPECTIVES

• Neutron diffraction: study of this new phase• Inelastic neutron scattering: study of the spin dynamics

15

Collaborations:

E. Canévet (ILL & UJF-Grenoble)

M. Klanjšek (Jozef Stefan Institute, Ljubljana, Slovenia)

C. Berthier and M. Horvatić (LNCMI-Grenoble)

V. Simonet and P. Lejay (Institut Néel, Grenoble)


V. Simonet and P. Lejay (Institut Néel, Grenoble)

Thank you

16

field-induced magnetic behavior in quasi-1d ising-like ......synemag 2012 october 17-19 th, 2012,...

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