Geometrically frustrated magnetism Geometrically frustrated - PowerPoint PPT Presentation

Geometrically frustrated magnetism Geometrically frustrated magnetism Geometrically frustrated magnetism Geometrically frustrated magnetism in in in in spin- -chain oxides, chain oxides, spin (Ca,Sr) 3 MXO 6 (Ca,Sr) 3 MXO 6 K 4 CdCl 6 -type type rhombohedral rhombohedral structure) structure) ( K 4 CdCl 6 - ( E.V. Sampathkumaran Tata Institute of Fundamental Research, Mumbai, India

HVAR2005: Unusual transport anomalies in some rare- earth compounds, RCuAs 2 2.0 R = Pr Tb 6.0 d ρ H = 0 5.25 Negative H = 50 kOe 5.6 dT for Ce only! 5.10 1.5 Dy ρ (T)/ ρ (300 K) Nd 1.35 2.10 CeCuAs 2 1.26 1.95 ρ (m Ω cm) 1.0 Yb 2.7 Sm LaCuAs 2 3.6 1.8 3.3 YCuAs 2 LuCuAs 2 0.5 4.6 Gd Y 0.99 0 100 200 300 T (K) 4.4 0.90 PRL, PRB, SCES, JPSJ 0 25 50 25 50 T (K) 2003-2004 Change in the sign of T-coefficient at high P. Increase in T K and/or pseudo-gap closure?

In addition, 25 years ago – our exhaustive work on pnictides • EuNi 2 P 2 , an exotic fluctuating valent compound (PRB 1980-85), CeNi 2 P 2 , YbNi 2 P 2 , • EuPd 2 P 2 , an unusual magnetic compound (PRL 1985) • EuCo 2 As 2 (1986) • EuCu 2 As 2 (PRB 2005)

Study of ‘geometrically frustrated magnetic effects’ in Kagome lattices and pyrochlores is a current topic Our interest • Explore geometrical frustration effects on magnetism in spin-chain oxides of the type: A 3 MXO 6 – 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)

Possible thermoelectric applications? Maignan et al, Mat. Sci. Eng. 2003 Ca3CoIrO6 Large S and low k favorable, but large resistivity! Figure of merit, Z= S 2 / ρ k .

During last 10 years 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)

A 3 MXO 6 - Structure K 4 CdCl 6 type derived – Rhombohedral structure – Face sharing MO 3 (trigonal prisms) and XO 3 octahedra – M, X are transition metal ion, generally M ≠ X, except for Co

R 3 c Rhombohedral ( ) system Viewing along b-axis Ir Zn e.g., Sr 3 ZnIrO 6

Different types of crystal structures of A 3 MXO 6 K 4 CdCl 6 Rhombhohedral Rhombhohedral Monoclinic Triclinic (Hexagonal expression) (C 2/c) (P –1) (R –3c) Ca 3 Co 2 O 6 Sr 3 CuPtO 6 Ca 3 CuMnO 6 Ca 3 CoRhO 6 Sr 3 CuIrO 6 Ca 3 CoIrO 6 Ca 3 CuIrO 6 Ca 3 CoMnO 6 Ca 3 CuRhO 6 Sr 3 ZnRhO 6 Sr 3 ZnIrO 6 etc

Ca 3 CoXO 6 (X = Co, Rh, Ir, Mn ) Sr 3 NiRhO 6 , Sr 3 NiPtO 6 , Compare and contrast

Ca 3 Co 2 O 6 • Two magnetic transitions observed in susceptibility around 10 K and 24 K. Co is trivalent at both sites, 1 .5 H = 1 0 0 O e High spin at trigonal prismatic site Low-spin at octahedral site χ (emu/mol) 1 .0 F C 5 k O e 0 .5 Z F C 1 0 2 0 3 0 T ( K ) ? ? ← Partially disordered AF structure Neutron paper in favor of ‘ferri’ Kageyama, JPCM 1997, 1998 Niitaka et al, PRL 2001;

• C vs. T exhibits a well defined peak at 24 K, but no such peak around 10 K 10 C (J/mol K) 5 ? 10 20 30 T (K) C/T vs T 2 is linear below 6 K Irreversibility at 5 K γ = 1 to 10 mJ/mol K 2 = � Spin glass like

Magnetic phase diagram proposed for Ca 3 Co 2 O 6 Complex magnetic phase?

Ac susceptibility Ca 3 Co 2 O 6 H = 50 kOe H = 0 Oe Ca 3 Co 2 O 6 40 1 Hz H = 10 kOe -4 emu/gm) 10 100 1000 The frequency 1 kHz 1 Hz 20 dependence of 12 ' ( x 10 10 Hz K peak 100 Hz 1 Hz χ reappears !! 0 -4 emu/gm) ω = ω 0 exp[-E a /k B (T f -T a )] 8 16 '' ( x 10 T f = T a + (E a /k B )*(1/ln{ ω 0 / ω }) χ T a = 3 (±1) T f (K) 0 14 E a /k B = 143 (±21) 0 20 0 20 0 20 40 8 Hz ω 0 = 10 T (K) Large 12 No frequency dependence – frequency 24 K (T o ) prominent peak, dependence at long range ordering? 12 K (T o ) peak 10 0.05 0.06 0.07 0.08 0.09 1/ln ( ω 0 / ω ) Vogel-Fulcher relationship obeyed Rayaprol et.al, Solid State Comm. (2003)

Steps in M in equal intervals Ca 3 Co 2 O 6 (Molecular magnets? Maignan et al 2004)? . Single crystals 2 Ca 3 Co 2 O 6 (Maignan et al 2000) 1 T= 1.8 K Polycrystals 2 5 K 1 M ( μ B /formula unit) 2 8 K 1 2 20 K H = 5 kOe 1 θ p = 30 K μ eff = 5.1 μ B /fu 2 Steps 30 K 1 0 40 80 120 H (kOe)

Ca 3 CoRhO 6 μ eff = 5.06 μ B -1 (mol/emu) FC Co 2+: High spin, d 7 40 Rh 4+ : Low spin, d 5 H = 50 kOe 0.4 T 2 (present status) 1 kOe Ferromagnetic coupling: θ p = 160 K χ 0 χ (emu/mol) 100 200 300 T (K) 0.2 FC 30 kOe FC 50 kOe T 1 ZFC 0.0 100 200 300 T (K) Different from Ca 3 Co 2 O 6 Multiple steps absent Sampathkumaran et al. Phys. Rev. B 65 180401(R), 2002

Ca 3 CoRhO 6 PDA structure of Ca 3 CoRhO 6 CoO 6 (trigonal prism) RhO 6 (octahedra) S. Niitaka et al. PRL 2001

Ca 3 CoRhO 6 H = 0 kOe 1 Hz, 5 kOe 0.2 χ ' (emu/mol) 1 Hz 1 kHz 70 10 Hz 5 kOe ω = ω 0 exp[-E a /k B (T f -T a )] 100 Hz 68 T a 21 (±1) 1 kHz 66 0.1 1 Hz, 30 kOe E a /k B 550 (±25) 64 8 Hz ω 0 = 10 62 T f (K) 60 Observed data 0.0 58 V-F fitting 1 Hz,5 kOe 0.04 56 χ '' (emu/mol) 54 0.02 1 kHz, 5 kOe 52 50 0.00 0.05 0.06 0.07 0.08 0.09 1/ln( ω 0 / ω ) 1 Hz, 30 kOe -0.02 40 80 120 40 80 120 160 ω = 2 πν ; ν = frequency (Hz) T (K) T f = peak temperature in ac χ Large frequency T a = ideal glass temperature for real dependence glasses Disappears under field E. V. Sampathkumaran et al. Phys. Rev. B 65 180401(R), 2002

Ca 3 CoIrO 6 0.24 FC (100 Oe) 90 H = 5 kOe -1 (mol/emu) 60 FC 30 0.16 (40 kOe) χ (emu/mol) χ 0 100 200 Co2+: High spin, d7 Ir4+: Low spin, d5 θ p = 168 K 0.08 μ eff = 4.40 μ B 100 Oe ZFC 5 kOe ZFC Θ p , inverse χ behavior 40 kOe ZFC above 100 K 0 100 200 300 Same as Rh sample, T (K) But no well-defined transition above 30 K, However a frustrated system Rayaprol et al. Phys. Rev. B (2003) Rapid Comm

Ca 3 CoIrO 6 H = 40 kOe H = 0 Oe H = 5 kOe 4 4 -4 emu/g) Large frequency 2 1 Hz dependence – 60 120 180 Robust to the applied 2 χ ' (10 field 1 kHz 1 Hz 20 -5 emu/g) 10 χ '' (10 0 0 30 60 0 30 60 0 30 60 T (K) Rayaprol et al. Phys. Rev. B, (2003)

Ca 3 CoIrO 6 Spin glass like behavior?? No peak !! 40 Slow relaxation of M C (J/mol K) 20 M IRM = 0.0269 - (0.0123 logt) 0.03 T = 5 K 0 20 40 T (K) 0.02 M IRM (emu/g) Rayaprol et al. Phys. Rev. B, (2003) 0.01 0 20 40 60 No relaxation above 30 K, unlike in Rh case. time (min) Coefficient of logT is 5 times larger compared to Rh case

• All three Ca 3 CoXO 6 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

Long range antiferromagnetic ordering ! Frustration reflected marginally in θ p /T N Ca 3 CoMnO 6 1.6 K (d) χ -1 (mol/emu) 60 (a) Hysteretic, 1.5 metamagnetic like H= 5 kOe transition 30 5 K 0 100 200 M ( μ B /formula unit) 1.5 (b) H= 100 Oe 0.10 ZFC 40 χ (emu/mol) FC 30 10 K C p (J/mol K) 0.08 20 1.5 0 10 20 30 10 13 K (c) 3 30 K χ ' ( x 10 -4 emu/g) 0 20 40 60 T (K ) 1 H z 1.5 10 100 θ p = - 45 K; μ eff = 6 μ B 2 1000 Long range order 0.0 0 10 20 30 0 50 100 Frustration effect T (K) H (kOe) No frequency dependence Also Ferroelectricity! Rutger’s group, ! PRL2008 Rayaprol et al. Solid State Commun, (2003)

Neutron results on Ca 3 CoRhO 6 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: 3.7 μ B /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 Inset: The universal curve of the normalized data: (W-W 300K )/(W 4.2K --W 300K ) versus T/T* •The values of T* are: 80 K for Ca 2.9 Eu 0.1 Co 2 O 6 •150, 130 and 110 K for x = 0.1, 0.3 and 0.5 of Ca 3-x Eu x CoRhO 6 . •These values follow the trends in θ p .

• A microscopic experimental indication for the existence of incipient magnetic order of spin-chains through (doped) 151 Eu Mössbauer spectroscopic studies in the spin-chain systems, Ca 3 Co 2 O 6 and Ca 3 CoRhO 6 . • The present results bring out the need to recognize a new characteristic temperature in future theoretical formulation of these ‘exotic’ systems .