superconductivity with t c up to 4.5 k

Magnetic order and spin state transition in

NaxCoO2 at 0.75x1.

C. Bernhard

University of Fribourg, Department of Physics, CH-1700 Fribourg, Switzerland

christian.bernhard@unifr.ch

Collaborators Muons: Ch. Niedermayer (PSI, CH)

Ellipsometry: Li Yu (UniFr), A. Boris, and

B. Keimer (MPI-FKF, D)

Synchrotron: Y.-L. Mathis (ANKA, FZ Karlsruhe, D)

Crystals: C.T. Lin, D.P. Chen (MPI-FKF, D),

D. Argyriou (HMI, D)

Theory: G. Khaliullin (MPI-FKF, D)

Outline

What is the nature of the magnetic state at high Na content?

Superconductivity with Tc up to 4.5 K

3d6 3d5

Crystal field splitting

Low-spin state:

Co3+Co4+

x=0.82

Muon Spin Rotation establishes:

- bulk magnetic order

- commensurate order (guess A-type AF)

-the moment is about 0.3 B.

Meanwhile confirmed by neutrons: S. Bayrakci et al, PRL 94, 157205 (2005); L.M. Helme et al., PRL 94, 157206 (2005).

Ist not likely to be a spin density wave (SDW) state !

-Strictly commensurate magnetic order.

- Nearly doping independent transition temperature

-Almost isotropic exchange coupling despite of large FS anisotropy.

μSRS. Bayrakci et al., Phys. Rev. B 69, 100410 (2004),

P. Mendels et al., Phys. Rev. Lett. 94, 136403 (2005).

Neutrons S. Bayrakci et al., Phys. Rev. Lett. 94, 157205 (2005)L.M. Helme et al., Phys. Rev. Lett. 94, 157206 (2005)

Idea of Giniyat Khaliullin:

Hole doping induced Co spin-state transition.

ReducedSymmetry

May sound like a wear idea

but its actually realized in the isoelectronic compoundLa1-xSrxCoO3

New buzz-word“Spin-state degree of freedom”

>Antiferromagnetic clusters with small total spin of S=1/2.

> Strong geometrical frustration!

G. Khaliullin, Prog. Theor. Phys. 160, 155 (2005). M. Daghofer, P. Horsch, and HG. Khaliullin, cond-mat/0605334.

Important differences to La1-xSrxCoO3

Bulk magnetic state @ x=0.75

LS, S=1/2

IS, S=1@ x=0.75

Ellipsometry on Na0.82(2)CoO2

C. Bernhard et al., PRL 93, 167003 (2004).

8066 cm-1 = 1 eVC. Bernhard et al., PRL 93, 167003 (2004).

Co3+Co4+

x=0.97

0.00

0.25

0.50

0.75

1.00

0 2 4 6 0 2 4

0.00

0.25

0.50

0.75

1.00

0 2 40.00

0.25

0.50

0.75

1.00

0 100 200 3000

3

6

18

20

22

24

time (s)

300K; 200K 100K; 25K

5 K

P(t

)/P

(0)

a)

1 kOe 50 Oe 0 Oe

time (s-1)

P(t)/P

(0)

T=30 Kb)

1 kOe 50 Oe 0 Oe

time (s-1)

P(t)/P

(0)

T=15 Kc)

T (K)

T

F (s

-1) T

f

d) tranverse field 6 kOe

Muon Spin Rotation (SR) on Na0.97CoO2

μSR data on Na0.97CoO2 establish:

Magnetic volume fraction of 40% with sizeable magnetic moments.

Glassy freezing transition around Tf20-50 K

Evidence for nanoscopic clusters.

Na-content from EDX and ICPS analysisConsistent with c-axis parameters from x-ray

Q. Huang et al., Phys. Rev. B 70, 184110 (2004).

Chemical phase separation due to segregation of Na vacancies?

C. de Vaulx et al., Phys. Rev. Lett. 95, 186405 (2005); G. Lang et al., Phys. Rev. B 72, 094404 (2005).

We investigated two growth batches with x=0.97- one is pure -phase

- other has a minor phase with lower Na content Both give virtually identical μSR results!

Chemical segregation is NOT the primary mechanism!

Optics shows that the x=0.97 sample is on the verge of percolation !

Consistent with 40% volume fraction from μSR

Na0.97CoO2

0 100 200 3000

50

100

150

200

250

3000 100 200 300

12 K 50 K 100 K 200 K 300 K

1a

b(

-1cm

-1)

(cm-1)

0 100 200 3000

1

2

x=0.97: H c; H//c

T (K)

(e

mu/

mol

* 1

04 )

dc-suszeptibility small moment of J1/2 per cluster.

0 2 40 2 40.00

0.25

0.50

0.75

1.00

0 2 4 6

-0.5

0.0

0.5

1.0

300 K; 200 K 25 K; 5 K

x=0.87

P(t

)/P

(0)

x=0.94?

time (s)

P(t

)/P

(0)

x=0.78

Evolution with hole doping, 1-x.

x A1 [%] 1 [MHz] 1 [μs-1] A2 [%] 2 [MHz] 2 [μs-1] Adis [%] 0.97 40 - >20 - - - 40 0.94 15 - >20 23 1.2 3.0 38 0.87 10 - >20 31 1.2 2.7 41 0.82 - - - 14 1.2 2.8 14 0.78 - - - - - - 0 x A3 [%] 3 [MHz] 3 [μs-1] A4 [%] 4 [MHz] 4 [μs-1] A5 [%] 5 [MHz] 5 [μs-1] A6 [%] 6 [MHz] 6 [μs-1] Aord. [%] 0.97 - - - - - - - - - - - - 0 0.94 17 2.5 2.4 - - - - - - - - - 17 0.87 26 2.5 1.0 - - - - - - - - - 26 0.82 32 2.6 1.2 - - - 43 3.2 0.8 - - - 75 0.78 14 2.2 0.3 13 2.6 0.2 31 3.1 0.5 39 3.3 0.45 >95

Evolution of magnetic signal with hole doping, 1-x

x=0.75

Na0.78CoO2; TN=22 K

Evidence for geometrical frustrationfrom μSR data at T>TN,Tf

Very fast spin fluctuations for bulk magnetic state at x=0.78 (<10-9 s at T>TN)

Very slow spin fluctuations for nanoscopic clusters at x=0.97(>10-9 s up to 250 K>>Tf=20 K)

0.00

0.25

0.50

0.75

1.00

0 2 4 6

0 2 4 6

-0.5

0.0

0.5

1.0

5 K; 40 K 100 K; 200 K

300 K

P(t

)/P

(0)

x=0.97

5 K 25 K>T

N=22 K

time (s)

x=0.78

0 50 100 150 200 250 3000.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

H // c H c

mo

l

T (K)

Na0.78

CoO2, H = 1 Tesla

Inconsistent with chemical phase separationsince fluctuations should be enhanced for finite size clusters!

Evidence for frustrated magnetic interaction in ordered state! SST model gives a Kagome lattice geometry.

Degeneracy is lifted for isolated clusters.- Disorder due to interaction with Na vacancies.

- Single, double and triple hole clusters.- Weak dipolar interaction between clusters.

Remember this is just a naive model that neglects all additional complexities of NaxCoO2!

The IS Co3+ ions (S=1) form a Kagome lattice withgeometrical frustration and thus strong fluctuations.

The amplitude of the charge modulation may be smaller.

Charge order may not be static.

This is the end of the talk

but not the end of the story !