IMSS-Symposium, October 17, 2008

Magnetization “steps” in the spin-1/2
kagome lattice of volborthite
H. Yoshida

Y. Okamoto

RVB state, spin liquid or what?
long-standing issue on the frustrated latticeOutline
General aspects on the kagome AF magnets
Volborthite vs Herbertsmithitecommon features of the S-1/2 kagome
GS of volborthite: spin glass and liquids
Magnetization “steps”
Materials: H. Yoshida, Y. Okamoto
NMR: M. Yoshida and M. Takigawa
LT Mag.: T. Tayama and T. Sakakibara
HF Mag.: M. Tokunaga and K. Kindo (ISSP)
ESR: S. Okubo and H. Ohta (Kobe Univ.)mSR: A. Fukaya and Y.J. Uemura (Columbia Univ.)GS of the S-1/2 kagome: theory
Very small magnetic gap filled up with singlet states?
One expects a gap in c ,but not in Cp.
EDS = 0E=0

DS = 1

D0More, S = ½ excitations
for odd-number clusters.

singlet-triplet gap
D ~ J / 20

Waldtmann, et al., EPB 2, 501 (1998)

singletcontinuumClassically degeneratestates spread over into
the singlet continuum!

Materials: can we obtain a perfect frustrated latticein a real material?

Many obstacles:•interlayer coupling → 3D long-range order
Jarosite,...
•disorder
SCGO, Herbertsmithite, LiNiO2, ...
•distortion
Volborthite, organics, ...
•long-range interactions•coupling to the lattice → local singlet stateS-3/2 kagome lattice in SrCr8Ga4O19 (SCGO)No LRO, but SGKagome

Tf
C ~T2

magnetoplumbite structure~90% coverage in the kagome layer
extra Cr ions exist
A. P. Ramirez, et al., PRL 64, 2070 (1990)

S-5/2 Kagome latticein Jarosite
AFe3(SO4)2(OH)6: Fe3+, 3d5
A = Na, K → LRO (q = 0)
A = H2O → spin glass

Tf(D3O)Fe3(SO4)2(OD)697% coverage
QCW = -700 K: J = 50 K
Tf = 13.8 K
x = 19 Ａ at 2 K
small x, but no gap, why?
A. Harrison, et al., Europhys. Lett.
42, 325 (1998)~T2

S-1 kagome found in organics

N. Wada, et al., JPSJ 66, 961 (1997)
K. Hida, JPSJ 69, 4003 (2000)

S=1

D = 0.25 K~1/12J

S=0
hexagon singlet

S-1/2 “imPerfect” kagome ZnCu3(OH)6Cl2
ND diffraction by S.-H. Lee& A. Harrison
KagomeZn0.3Cu2.7
Zn0.7Cu0.3

G. Nocera, MIT, JACS 127, 13462 (2005)

10% “free” spins!
∠Cu-O-Zn = 96.9°: J ~ 0

Absence of~6% by NMR (Olariu)
LRO~3% in a better sample
gaps
ZnxCu3-x(OH)6Cl2
A. Harrison
x = 0: clinoatacamite
spin freezing
0.33 ≤ x <1:
down to 50 mK
Zn-paratacamite
by NMR, mSR, ac-c, ...
x = 1: herbertsmithiteS-1/2 kagome-like lattice
volborthite: Cu3V2O7(OH)2·2H2O
V5+

Cu2+
Cu2
Cu1

V5+

J2
J1
Monoclinic, C2/m
a = 10.607Åb = 5.864Å
c = 7.214Å
b = 94.90°

J23.03Å

2.94Å

J1 – J2 kagome
No exchange, Cu2+ / V5+~3%

Lafontaine et al., J. Solid State Chem. 85, 220 (1990)

ZH et al., JPSJ 70, 3377 (2001)

Volborthite vs Herbertsmithite

Isotropic kagome

Anisotropic kagome

Monoclinic, C2/md(Cu1-Cu2) = 3.031 Åd(Cu2-Cu2) = 2.937 Å∠Cu1-O-Cu2 = 105.6° (82.7°): J1∠Cu2-O-Cu2 = 101.1° (91.5°): J2
Jav = (2J1 + J2) / 3

Rhombohedral, R-3m
d(Cu-Cu) = 3.414 Å∠Cu-O-Cu = 119°: J∠Cu-O-Zn = 96.9°: J ~ 0DJ20%? cf. Sindzingre

Volborthite vs Herbertsmithite: c bulk
22 K ~J/4
D= J / 4
JCW = 115 K
H = J ! Si • S ji, j

J = 199 K
JBF = 136 K
Jav = 86 K

crystalline
defects?

Jav = 86 K
ximp = 0.5%

J = 199 K cf. J = 170 ~ 190 K
from Cu spins
ximp = 10%
at the Zn siteVolborthite vs Herbertsmithite: c loc
c loc from NMR Knight shift K: K = Ac loc / NA
22 K~J/4

Olariu et al., PRL 100, 087202 (2008)

A = 6.6 kOe / mB for volborthite and 35 kOe / mB for herbertsmithiteVolborthite vs Herbertsmithite: defects
Volborthite
crystalline defects near surfaces?

Herbertsmithite3 – 10% Zn

0.7% defects
2 of ~300

10% Znx0 can be limited by 1 / ximp in the dirty milit.

• The number of intact spins decreases rapidly with ximp.
• Even for small ximp, a defect may influence the surroundings.

Higher-quality sample: c down to 60 mK

by annealing inhydrothermalconditions

Tg

Gapless, or D < J / 1500

ximp = 0.5%
↓ximp = 0.07%
or smaller

T. Tayama & T. Sakakibara

Field-induced moments near a defectPrevious V NMR spectrum at 1.7 K

The line width increases with H.
cf. HAF chains in Sr2CuO3
chain ends or defects
induce staggered moments.

Sharp peak
Broad humpx
ZH et al., JPSJ 70, 3377 (2001)

No more broad component in a clean sample.

Impurity-induced spin-glass on frustrated lattices
Gapless ora very tiny gap
means large x!

xMaybe,x becomes verylarge as T → 0,close to thequantum critical
Even a small ximp
can cause SG.
A spin glass transition
may occur, when domains
with staggered moments
induced by defects
overlap with each other.

Recent 51V NMR results ona sample with ximp < 0.1%

0.28 K
1.4 K

LRO at T ~ 0.9 K?

4TNo hump, but only asharp peak at 1.4 K.
1T
1/T1 seems to diverge
at T ~ 0.9 K!
M. Yoshida & M. Takigawa

Slowing down toward T ~ 0.9K, but may not go to LRO!
dynamic spin fluctuations
persist below 1 K

Slow spin dynamics
No anomalies in c and C
C/TmSRH = 0, 1 T

Uemura et al.

1 / T1H=3TTg

H=1TcYoshida & Takigawa

Bert et al.

Hs1 = 4.3 T ~ (1/30)J

A “step” in M under a magnetic
field

Nothing before;
free spins masked.
with less ximp,
after SG,Anomaly at
Hs1 = 4.3 T,
M = 0.022Ms
M = 0.022 ~ (1/45)Ms

J = 86 K

Spin flop?
Metamagnetic?
but no LRO.

Tayama & Sakakibara

~ J / 30~21 T~21 T ~ J / 6 !

More anomalies athigher fields!!
Not plateaus, but ?

Hs3 = 46 T
Hs2 = 25.5 T

4 states, at least
Ms / 3

Hint = 21 T ~ 14 K~J/6

1.4 K
Hs1 = 4.3 T

4K

Ms / 6

Ms / 3, 6, ~45
mean what?
No change at 0.1 K
a powder average

Ms / 45

Tokunaga, Matsuo,
Narumi and Kindo

Phase diagram of volborthite: Summary
Spin liquids• D < J / 1500
• large x• extremely slow
spin dynamics?

Paramagnetic

SROmSRSG

1/T1

Impurity effects• SG due to largex• suppressed by H

SL1

Mag. steps???
SL3 SL4
a lot of mysteries
remain for future!

SL2