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Geometrically frustrated magnetism Geometrically frustrated magnetism Geometrically frustrated magnetism Geometrically frustrated magnetism

in in in in

spin spin-

• chain oxides,

chain oxides, (Ca,Sr) (Ca,Sr)3

3MXO

MXO6

6

( (K

K4

4CdCl

CdCl6

6-

• type

type rhombohedral rhombohedral structure) structure)

Tata Institute of Fundamental Research, Mumbai, India

E.V. Sampathkumaran

HVAR2005: Unusual transport anomalies in some rare- earth compounds, RCuAs2

100 200 300 0.5 1.0 1.5 2.0

YCuAs2 LuCuAs2 LaCuAs2 CeCuAs2

ρ(T)/ρ(300 K)

T (K)

Negative for Ce only!

dT d ρ

Change in the sign of T-coefficient at high P. Increase in TK and/or pseudo-gap closure?

5.6 6.0

H = 50 kOe H = 0

R = Pr 5.10 5.25 Tb 1.26 1.35 Nd 1.95 2.10 Dy 3.3 3.6

T (K)

ρ (mΩ cm)

Sm 1.8 2.7 Yb 25 50 4.4 4.6 Gd 25 50 0.90 0.99 Y

PRL, PRB, SCES, JPSJ 2003-2004

In addition, 25 years ago – our exhaustive work on pnictides

• EuNi2P2, an exotic fluctuating valent

compound (PRB 1980-85), CeNi2P2, YbNi2P2,

• EuPd2P2, an unusual magnetic compound

(PRL 1985)

• EuCo2As2 (1986)
• EuCu2As2 (PRB 2005)

Our interest

• Explore geometrical frustration effects on magnetism

in spin-chain oxides of the type: A3MXO6 – Wide possibilities at M and X sites, both non- magnetic and magnetic. {Li/Ru compound orders near 110K} – Offers tunability of interchain versus intrachain coupling strengths (?) – Insulators

Initial magnetic properties: Groups of Zur Loye (USA), H. Kagayama (Kyoto), Raveau, Maignan (France), Battle (UK)

Study of ‘geometrically frustrated magnetic effects’ in Kagome lattices and pyrochlores is a current topic

Ca3CoIrO6 Figure of merit, Z= S2/ρk. Possible thermoelectric applications? Maignan et al, Mat. Sci. Eng. 2003 Large S and low k favorable, but large resistivity!

Acknowledgements

• M. Mahesh Kumar, Asad Niazi, Sudhindra

Rayaprol, Kausik Sengupta, Subham Majumdar, Kartik K Iyer, Niharika Mohapatra, Suryanarayana (Samples & bulk studies in TIFR)

• P.L. Paulose
• M. Loewenhaupt’s group (TU Dresden; neutron)
• K.H. Mueller’s group (IFW Dresden, some M studies)
• Fujimori, DDSarma (Univ. Tokyo, IISc;

Spectroscopy)

• N. Fujiwara, Y. Uwatoko (ISSP, Tokyo for NMR)
• Z. Hiroi (ISSP)
• W. Jeitschko (Muenster, Crystal analysis)

During last 10 years

A3MXO6 - Structure

–

K4CdCl6 type derived Rhombohedral structure – Face sharing MO3 (trigonal prisms) and XO3 octahedra – M, X are transition metal ion, generally M ≠ X, except for Co

Viewing along b-axis

e.g., Sr3ZnIrO6

Zn Ir Rhombohedral ( ) system

c R3

Different types of crystal structures of A3MXO6

Triclinic (P –1) K4CdCl6 Rhombhohedral Rhombhohedral (Hexagonal expression)

(R –3c)

Monoclinic (C 2/c)

Ca3Co2O6 Ca3CoRhO6 Ca3CoIrO6 Ca3CoMnO6

Sr3ZnRhO6 Sr3ZnIrO6 etc

Sr3CuPtO6 Sr3CuIrO6 Ca3CuIrO6 Ca3CuRhO6 Ca3CuMnO6

Ca3CoXO6 (X = Co, Rh, Ir, Mn ) Sr3NiRhO6, Sr3NiPtO6,

Compare and contrast

• Two magnetic transitions observed in

susceptibility around 10 K and 24 K.

Niitaka et al, PRL 2001;

1 0 2 0 3 0 0 .5 1 .0 1 .5

χ (emu/mol)

T ( K ) H = 1 0 0 O e 5 k O e Z F C F C

Ca3Co2O6

Partially disordered AF structure ? ←

?

Neutron paper in favor of ‘ferri’ Kageyama, JPCM 1997, 1998 Co is trivalent at both sites, High spin at trigonal prismatic site Low-spin at octahedral site

• C vs. T exhibits a well defined peak at 24 K, but no such

peak around 10 K

10 20 30 5 10

C (J/mol K) T (K)

?

C/T vs T2 is linear below 6 K γ= 1 to 10 mJ/mol K2 Irreversibility at 5 K = Spin glass like

Magnetic phase diagram proposed for Ca3Co2O6

Complex magnetic phase?

Large frequency dependence at 12 K (To) peak No frequency dependence – 24 K (To) prominent peak, long range ordering?

20 40

1 kHz 1 Hz

1 Hz 10 100 1000

H = 0 Oe

χ

'' (x10

• 4 emu/gm)

χ

' (x10

• 4emu/gm)

Ca3Co2O6 H = 10 kOe

100 Hz 10 Hz 1 Hz

H = 50 kOe 20 8 20 40 20

T (K)

The frequency dependence of 12 K peak reappears!!

Ca3Co2O6

Rayaprol et.al, Solid State Comm. (2003)

0.05 0.06 0.07 0.08 0.09 10 12 14 16

ω = ω0exp[-Ea/kB(Tf-Ta)]

Tf = Ta+ (Ea/kB)*(1/ln{ω0/ω})

Ta = 3 (±1) Ea/kB = 143 (±21)

ω0 = 10

8 Hz

Tf (K) 1/ln (ω0/ω)

Ac susceptibility

Vogel-Fulcher relationship obeyed

.

1 2 Ca3Co2O6

T= 1.8 K

40 80 120 1 2

30 K

M (μB/formula unit) H (kOe) 1 2

8 K

1 2

5 K

1 2

20 K

Steps

Ca3Co2O6

H = 5 kOe θp = 30 K μeff = 5.1 μB/fu

Steps in M in equal intervals

(Molecular magnets? Maignan et al 2004)? Single crystals (Maignan et al 2000) Polycrystals

100 200 300 0.0 0.2 0.4

T1 T2

ZFC

FC FC FC

T (K)

χ

• 1 (mol/emu)

50 kOe 30 kOe 1 kOe

χ (emu/mol)

T (K)

100 200 300 40 H = 50 kOe

Ferromagnetic coupling: θp = 160 K

Ca3CoRhO6

Sampathkumaran et al. Phys. Rev. B 65 180401(R), 2002 μeff = 5.06μB Co2+: High spin, d7 Rh4+: Low spin, d5 (present status) Different from Ca3Co2O6

Multiple steps absent

PDA structure of Ca3CoRhO6

CoO6

(trigonal prism)

RhO6

(octahedra)

Ca3CoRhO6

• S. Niitaka et al. PRL 2001

Ca3CoRhO6

ω = 2πν; ν = frequency (Hz) Tf = peak temperature in ac χ Ta = ideal glass temperature for real glasses

0.05 0.06 0.07 0.08 0.09 50 52 54 56 58 60 62 64 66 68 70

Observed data V-F fitting

ω = ω0exp[-Ea/kB(Tf-Ta)]

Ta 21 (±1) Ea/kB 550 (±25)

ω0 = 10

8 Hz

Tf (K) 1/ln(ω0/ω)

0.0 0.1 0.2 40 80 120 160

H = 0 kOe

1 Hz 10 Hz 100 Hz 1 kHz

χ'' (emu/mol) χ' (emu/mol)

40 80 120

• 0.02

0.00 0.02 0.04

T (K)

1 Hz, 30 kOe 1 kHz 5 kOe 1 Hz, 5 kOe 1 Hz, 30 kOe 1 Hz,5 kOe 1 kHz, 5 kOe

Large frequency dependence Disappears under field

• E. V. Sampathkumaran et al. Phys. Rev. B 65 180401(R), 2002

Ca3CoIrO6

100 200 300 0.08 0.16 0.24

θp = 168 K μeff = 4.40 μB

FC (40 kOe) FC (100 Oe)

χ (emu/mol)

T (K)

100 Oe ZFC 5 kOe ZFC 40 kOe ZFC

100 200 30 60 90

H = 5 kOe

χ

• 1 (mol/emu)

Rayaprol et al. Phys. Rev. B (2003) Rapid Comm Co2+: High spin, d7 Ir4+: Low spin, d5 Θp, inverse χ behavior above 100 K Same as Rh sample, But no well-defined transition above 30 K, However a frustrated system

Ca3CoIrO6

Large frequency dependence – Robust to the applied field

2 4

H = 0 Oe 1 kHz 1 Hz H = 5 kOe

30 60 10 20

χ' (10

• 4 emu/g)

χ'' (10

• 5 emu/g)

30 60

T (K)

H = 40 kOe

30 60

60 120 180

2 4

1 Hz

Rayaprol et al. Phys. Rev. B, (2003)

20 40 20 40

C (J/mol K) T (K)

No peak !!

20 40 60 0.01 0.02 0.03 T = 5 K MIRM = 0.0269 - (0.0123 logt) MIRM (emu/g) time (min)

Slow relaxation of M

Spin glass like behavior??

Ca3CoIrO6

Rayaprol et al. Phys. Rev. B, (2003) No relaxation above 30 K, unlike in Rh case. Coefficient of logT is 5 times larger compared to Rh case

• All three Ca3CoXO6 compounds an ‘exotic’

geometrical frustration – of an unusual type, but with subtle differences, despite differences in valence and spin at M and X sites.

• c/a ratios difference possibly controls interchain

vs intrachain interaction? X= Co: 1.143 = Rh: 1.166 = Ir: 1.189

100 200 30 60 (a)

H= 5 kOe

χ-1 (mol/emu)

1.5

(d) 1.6 K

10 20 30 0.08 0.10

T (K) H (kOe) M (μB/formula unit)

(b)

H= 100 Oe ZFC FC

χ (emu/mol)

1.5

5 K

10 20 30 2 3

(c)

1 H z 10 100 1000

χ' (x10-4emu/g)

1.5

10 K

50 100 0.0 1.5

30 K

Ca3CoMnO6

20 40 60 10 20 30 40

Cp (J/mol K) T (K )

θp = - 45 K; μeff = 6 μB Long range order

Long range antiferromagnetic ordering ! Frustration reflected marginally in θp/TN

Hysteretic, metamagnetic like transition 13 K No frequency dependence !

Rayaprol et al. Solid State Commun, (2003) Frustration effect Also Ferroelectricity! Rutger’s group, PRL2008

Neutron results on Ca3CoRhO6 Loewenhaupt et al, EuroPhys Lett 2003

• Magnetic Bragg peaks appear below 100 K
• A diffuse peak superimposed over strongest

magnetic peak = Coexistence of low-dimensional features with long range ordering. Moment on Co: 3.7μB/Co, parallel to c-axis No moment on Rh detected! Inverse relation between FWHM and cluster size: correlation of ‘diffused’ peak is 16 Å above 100 K; increased to 23 Å at much low T. Nano spin-glass?

Do spin-chains order? “Line-width behavior of Eu-based systems”

(Paulose et al PRB 2008)

Intriguing relationship between spectral broadening and the paramagnetic Curie temperature representing intra-chain coupling

• The values of T* are: 80 K for Ca2.9Eu0.1Co2O6
• 150, 130 and 110 K for x= 0.1, 0.3 and 0.5 of Ca3-xEuxCoRhO6.
• These values follow the trends in θp.

Inset: The universal curve of the normalized data: (W-W300K)/(W4.2K--W300K) versus T/T*

• A microscopic experimental indication

for the existence of incipient magnetic

• rder of spin-chains through (doped)

151Eu Mössbauer spectroscopic studies

in the spin-chain systems, Ca3Co2O6 and Ca3CoRhO6.

• The present results bring out the need

to recognize a new characteristic temperature in future theoretical formulation of these ‘exotic’ systems.

H-dependence of M/H vanishes in 30-90 K range even for x= 0.15 PDA structural instability! Θp decreases Intrachain ferromag. strength decreases

Co/Rh moment changes Step vanishes! = PDA structure destroyed.

Huge frequency dependence persists even at high fields with Y substitution, despite a significant change in magnetic moment

No influence of lattice expansion by Sr substitution

Ca3-xSrxCoRhO6

χ' (emu/mol)

χ'' (emu/mol)

T (K)

No influence of external pressure

Above 150 K, μeff = 3.3 μB per formula unit. = spin-only moment for Rh4+ (4d5, low-spin) and Ni2+ (3d8; high spin)

PDA-features like in Co systems

Low moment at high fields Ni and Rh AF coupled Evidence from: LSDA calculations by Maiti et al, PRB2008 Moment on Ni: 1.3 μB

• n Rh: 0.36 μB

Unlike in Co systems

Sr3NiPtO6

Lattice compression does not influence Non-magnetic ground state The value of μeff and θp (above 200 K) are found to be nearly 3.4 μB and -25 K No magnetic ordering spin-liquid? Pt has no moment. Ni has 1.5 μB (LSDA calculations by Maiti et al, unpubished)

Zero field and in 50 kOe Finite linear term insensitive field, despite these are insulators Spin-liquid property not affected By lattice expansion

Major points made:

• A class of oxides, containing spin-chains +

triangular lattice

• Features due to geometrical frustration:

High θp/TN, spin-glass-like features. Release of frustration by lowering symmetry

• r disorder.
• In some Co/Ni systems, unusually large

frequency dependence of ac χ (interesting spin dynamics, different from Cu systems); PDA magnetic structure (uncommon); irrespective of magnetic moment and valence at both sites. Exception Mn compound

• Multiple steps in M(H) in Ca3Co2O6 only!

• A Ni compound also exhibits PDA features, behaving

like Co systems, despite intrachain AF interaction!

• A new S=1 (Ni) spin-liquid?
• Extreme insensitivity to pressure
• Signals of intra-chain ordering
• Jahn-Teller effect in Cu systems
• Griffiths phase in a Cu system
• Anomalous NMR
• A nice playground