Mott criticality studied by dilatometry under 4 He-gas pressure on - PowerPoint PPT Presentation

Mott criticality studied by dilatometry under 4 He-gas pressure on the quasi-2D organic charge-transfer salts κ -(BEDT-TTF) 2 X Rudra Sekhar Manna Augsburg University, Germany Goethe University Frankfurt, Germany κ -(ET) 2 X (P 0 ,T 0 ) param . ins. T MI metal T N ICTP-New-Delhi AFM supercon 12.02.2015 sc ins. ductor 40 20 60 P (MPa) 1 1 SFB/TR 49

acknowledgement M. Lang L. Bartosch Goethe University Frankfurt, Germany E. Gati U. Tutsch Tohoku University, Japan T. Sasaki J. A. Schlueter Argonne National Laboratory, USA R. Kato RIKEN, Japan 2

outline - organic charge-transfer salts - phase diagrams - spin-liquid: κ -(ET) 2 Cu 2 (CN) 3 - Mott criticality in κ -(ET) 2 X - valence-bond-solid: EtMe 3 P[Pd(dmit) 2 ] 2 - summary and outlook 3

κ -(BEDT-TTF) 2 X: charge-transfer salts [(BEDT-TTF) 2 ] + X - Anion (insulating ) ET (conducting) Anion (insulating) t t ET (BEDT-TTF) t' • κ -phase: “effective dimer model”: 1 hole/ dimer ⇒ half-filled conduction band • W ~ U eff : correlated π electrons 4 4

Mott criticality at the 2 nd -order end-point (P 0 , T 0 ) κ -(ET) 2 X (P 0 ,T 0 ) param . insulator T MI metal T N AFM superconductor superconductor insulator 20 40 60 P (MPa) U/W X = Cu[N(CN) 2 ]Cl Cu[N(CN) 2 ]Br κ -d8-Br CH 2 ⇒ CD 2 Lefebvre et al. , PRL 85 , 5420 (00) 5 5

effect-of-frustration t t t' t ʹ″ ʹ″ /t κ -(ET) 2 Cu[N(CN) 2 ]Cl κ -(ET) 2 Cu 2 (CN) 3 ext. Hückel calc. Mori et al. , 0.72 Chem. Soc. Jpn. 72 , 179 (99) 1.06 Komatsu et al. , JPSJ 65 , 1340 (96) ab initio calc. Kandpal et al. , 0.44 ~ 0.8 PRL 103 , 067004 (09) Nakamura et al. , 6 JPSJ 78 , 083710 (09)

spin-liquid - κ -(ET) 2 Cu 2 (CN) 3 T t t t' c Mott insulator b metal T c = 4.5 K spin liquid sc !? P 100 MPa X = Cu 2 (CN) 3 t ʹ″ /t ~ 0.8 no long-range magnetic order down to 32 mK ( J = 250 K) R. S. Manna et al. , PRL 104 , 016403 (10) Kitaev spin-liquid Kurosaki et al. , PRL 95 , 177001 (05) Shimizu et al. , PRL 91 , 107001 (03) A 2 IrO 3 (A = Na, Li) 7

Mott universality (V 1-x Cr x ) 2 O 3 crossover: δ , β , γ = 3, 0.5, 1 (mean field values) δ , β , γ = 4.81, 0.34, 1 (3D Ising) ⇒ liquid-gas universality (3D Ising) Limelette et al ., Science 302 , 89 (03) DMFT of the Hubbard model: an order parameter for the finite temperature Mott end point ⇒ Ising universality class, similar to the liquid-vapor transition Castellani et al. , PRL 43 , 1957 (79) Kotliar et al. , PRL 84 , 5180 (00) 8 8

controversy : κ -(ET) 2 Cu[N(CN) 2 ]Cl conductivity 13 C-NMR Δ 1/T 1 T ∝ | P-P c | 1/2 ⇒ δ = 2 unconventional δ , β , γ = 2, 1, 1 unconventional Mott criticality Kagawa et al. , Nature Physics 5 , 880 (09) Kagawa et al ., Nature 436 , 534 (05) conductivity data of κ -(ET) 2 Cu[N(CN) 2 ]Cl: coupling to the energy density dominates ⇒ consistent with 2D Ising universality class 9 9 Papanikolaou et al. , PRL 100 , 026408 (08)

Mott criticality at the 2 nd -order end-point (P 0 , T 0 ) D8-Br κ -(ET) 2 X D8-Br (P 0 ,T 0 ) h D8-Br sample 1 param . α s insulator T MI metal T MI T * T N sample 2 AFM T g superconductor t insulator superconductor 40 20 60 P (MPa) assumption: Grüneisen scaling - breakdown of Grüneisen scaling in the vicinity an an C δ ∝ δα i of a finite-temp. critical end point D8-Br ∼ - consistent with 2D Ising universality class critical exponent α = (0.8 ± 0.15)?! CH 2 ⇒ CD 2 - large anomaly in alpha and sign change at the Souza et al. , PRL 99 , 037003 (07) critical end-point (P 0 , T 0 ) Souza et al. , PRL 99 , 037003 (07) Bartosch et al. , PRL 104 , 245701 (10) 10 10 Lefebvre et al. , PRL 85 , 5420 (00)

thermal expansion measurements under He-gas pressure experimental specifications - high-resolution capacitive dilatometer (5 × 10 -2 Å) - temperature range 1.4 - 293 K - hydrostatic pressure range 0 - 250 MPa (helium as a pressure transmitting medium) - magnetic field range 0 - 14 T 11 11

pressure cell and dilatometer 1 dilatometer cell 2 n-InSb pressure gauge ( Δ P = ± 0.1 MPa) ⇒ p = p 0 ≈ const. V p-cell ≈ 80 cm 3 3 seal 4 plug with electrical feed-throughs 5 retaining screw 22 mm Thermal expansion coefficient, 1 2 - constant-pressure condition 3 - 4 He (pressure-transmitting medium): gas/ liquid phase 4 V = 50.000 cm 3 - pressure reservoirs: gas bottle/ compressor with micropump 4 He P ≤ 300 bar 5 R. S. Manna, PhD thesis (12) 12 12 R. S. Manna et al. , Rev. Sci. Instrum. 83 , 085111 (12)

Mott criticality at the 2 nd -order end-point (P 0 , T 0 ) κ -(ET) 2 X (P 0 ,T 0 ) param . insulator T MI metal T N AFM superconductor superconductor insulator 20 40 60 P (MPa) U/W X = Cu[N(CN) 2 ]Cl Cu[N(CN) 2 ]Br κ -d8-Br CH 2 ⇒ CD 2 Lefebvre et al. , PRL 85 , 5420 (00) 13 13

κ -D8-Br at finite pressure p α s T * T * T MI T g T g Bartosch et al. , PRL 104 , 245701 (10) α T max T MI - T g pressure independent, cf. Müller et al. , PRB (02) - T MI (1 st -order) consistent with literature 14 14 - effect of pressure on T * (2 nd -order)

κ -D8-Br at finite pressure after subtracting a T-linear background 1 β α sgn (h)( t) − + ∞ − scaling theory: sing and consistent with 2D Ising universality class 15 15

Mott criticality at the 2 nd -order end-point (P 0 , T 0 ) κ -(ET) 2 X (P 0 ,T 0 ) param . insulator T MI metal T N AFM superconductor superconductor insulator 20 40 60 P (MPa) U/W X = Cu[N(CN) 2 ]Cl Cu[N(CN) 2 ]Br κ -d8-Br CH 2 ⇒ CD 2 Lefebvre et al. , PRL 85 , 5420 (00) 16 16

κ -Cl at finite pressure Δ α max “ κ -Cl“ 0 background 17 17

κ -Cl at finite pressure Δα max ∝ ( P – P c ) - κ Scaling theory: Bartosch et al. , PRL 104 , 245701 (10) 1 - β 0 for “unconventional criticality“ ( β = 1) ?! κ = = 7/15 for 2D Ising β + γ ( ) determination of κ requires precise knowledge of P c ! crossover from 2D Ising ( κ ≈ 0.5) to mean-field ( κ ≈ 0.3) criticality? 18 18 Zacharias et al. , PRL 109 , 176401 (12)

summary • Thermal expansion measurements under 4 He-gas pressure have been performed on κ -(ET) 2 X for probing critical fluctuations. • data of κ -D8-Br and κ -Cl: - Mott critical end point is consistent with 2D Ising universality class. outlook • sample-to-sample variations • determination of P c ⇒ κ = (1 - β )/( β + γ ) • measurement in the insulating (low-P) regime ⇒ sign change in α ! • role of lattice degrees of freedom 19 19

EtMe 3 X[Pd(dmit) 2 ] 2 (X = P/Sb) X = P uniform stacking (one type of [Pd(dmit) 2 ] layer) Tamura et al. , JPSJ 75 , 093701 (06) Itou et al. , Nat. Phys. 6 , 673 (10) K. Kanoda and R. Kato, Annu. Rev. Condens. Matter Phys. 2 , 167 (11) 20

EtMe 3 X[Pd(dmit) 2 ] 2 – ground state properties X = Sb ⇒ spin-liquid X = P ⇒ valence-bond-solid J = 240 K J = 250 K J = 260 K similar to κ -(ET) 2 Cu 2 (CN) 3 Tamura et al. , JPSJ 75 , 093701 (06) Itou et al. , PRB 77 , 104413 (08) Shimizu et al. , PRL 99 , 256403 (07) 21

b - strongly anisotropic lattice distortions accompanying the formation of VBS - weak in-plane α a vs α c anisotropy for T > T VBS suggests dominant contribution from EtMe 3 P cations 22 R. S. Manna et al. , PRB 89, 045113 (14)

anomalous thermal expansion in the paramagnetic region Assumptions: α a = α lat a + α mag a α c = α lat c + α mag c α lat c = A α lat a α mag c = B α mag a α b α mag c – 1.15 α mag a anomalous contribution at T α max ≈ 40 K due to the short-range afm correlation, cf. T χ max = 70 K 23 χ -data: Tamura et al. , JPSJ 75 , 093701 (06) R. S. Manna et al. , PRB 89, 045113 (14)

variation of T χ max / T α max = T χ max /T C max for low-D quantum magnets with different degree of frustration • for 2D triangular lattice S = ½ Heisenberg afm ~ 1 T χ max - for Cs 2 CuBr 4 : J'/J = 0.74 - for κ -(ET) 2 Cu 2 (CN) 3 : J'/J = 0.64 - 0.74 T α max Shimizu et al. , PRL 91 , 107001 (03) R. S. Manna et al. , PRL 104 , 016403 (10) κ -(ET) 2 Cu 2 (CN) 3 • for 1D uniform S = ½ Heisenberg chain ~ 1.34, T χ for alternating exchange variant ~ 3 and max including next-nearest-neighbor interactions ~ 3.6 T C Klümper, Eur. Phys. J. B 5 , 677 (98) max Bühler et al. , PRB 64 , 024428 (01) present case:T χ max / T α max ≈ 1.7 - 2.3 t' t ⇒ suggests a more anisotropic (quasi-1D) scenario t'' 24 R. S. Manna et al. , PRB 89, 045113 (14)

lattice distortion at VBS transition R. S. Manna et al. , PRB 89, 045113 (14) - distinct and strongly anisotropic second-order phase transition into the low-T VBS phase at 25 K - upon cooling c -axis (in-plane) contracts, a -axis (in-plane) expands while the dominant effect is along the b -axis (out-of-plane) which expands ⇒ pressure dependency comes from the out-of-plane component as the in-plane pressure effects cancel each other out (- 4.2 K/100 MPa) 25

summary • valence-bond-solid, EtMe 3 P[Pd(dmit) 2 ] 2 - An anomalous contribution at T α max ≈ 40 K is found and assigned to the short- range afm correlations. - T χ max / T α max ≈ 1.7 - 2.3 seems incompatible with quasi-2D triangular lattice (~ 1), rather compatible with a quasi-1D more anisotropic scenario. outlook • perform similar experiments for the spin-liquid (dmit-Sb) compound • study the Mott criticality in dmit-salts vs ET-based compounds ?! Thank you for your attention ! 26