Workshop on current trends in frustrated magnetism, 9-13 Feb 2015, JNU Spin-liquid Behaviour in Sc 2 Ga 2 CuO 7 Avinash V. Mahajan IIT Bombay
GENERAL THEME OF OUR WORK • Explore systems for novel magnetism • Low dimensional, frustrated magnets and spin- liquid behaviour • 3 d /4 d /5 d systems... strong spin-orbit coupling • Characterisation…structure, χ (T), C P (T), NMR • Here, I will focus on Sc 2 Ga 2 CuO 7
Magnetic Frustration Balents, KITP Few examples: Triangular: NiGa 2 S 4 , Ba 3 CuSb 2 O 9 Kagome: ZnCu 3 (OH) 6 Cl 2 , SrCr 9p Ga 12 − 9p O 19 Hyperkagome: Na 4 Ir 3 O 8 Pyrochlore: Y 2 Mo 2 O 7 , Ho 2 Ti 2 O 7
STRUCTURE OF Sc 2 Ga 2 CuO 7 Triangular Cu planes Triangular Ga bi-planes 14 Å Triangular Cu planes
Cu PLANE AND Ga BI-PLANE
X-RAY AND NEUTRON DIFFRACTION (PSI) Ò Small amts of impurities….Sc 2 O 3 ~1.2 %, CuGa 2 O 4 ~0.5% Ò Cu-Ga antisite disorder expected due to their similar ionic sizes. Ò Due to similar scattering lengths of Cu and Ga (in both XRD and ND), refinements are very similar for various occupancies Ò The (0, 0, 0.25) planes are nearly fully Ga (10-15% Cu). The biplanes are an equal mix.
ACTUAL STRUCTURE Triangular Cu Ga planes Triangular Ga-Cu bi-planes 14 Å Triangular Cu Ga planes
MAGNETIC SUSCEPTIBILITY ¡ 3.0 12 − 1 ¡ Z F C 0.03 ( χ−χ 0 ) µ eff = 1.79 µ B ¡ χ ( cm 3 /mol ) 2.5 ¡F C θ ~ -50 K 0.02 10 χ−χ 0 ) -‑1 (10 2 ¡m ol/C m 3 ) H= ¡25 ¡Oe No ZFC/FC bifurcation 0.01 χ ( 10 -‑2 ¡ cm 3 /mol ) 2.0 8 0.00 1 10 100 T (K ) 1.5 6 Z F C 1.0 ( χ−χ 4 ¡C urie-‑Weis s ¡F it 0.5 H ¡= ¡5 ¡kO e 2 0.0 0 0 100 200 300 400 T (K )
MAGNETISATION ISOTHERMS ¡ ¡ 1000 g=2.0 g=2.1 800 M (H, T) = χ H + Brillouin fcn ¡1.8K ¡1.8K 600 consistent with about 12% free spins ¡2.5K ¡2.5K ¡ ¡ ¡ ¡3.0K 3.0K 400 3 /mol) ¡3.6K ¡3.6K (b) 200 (a) ¡4.5K ¡4.5K ¡ ¡F IT ¡ ¡F IT 0 ¡ ¡ M ¡(G ¡cm ¡ ¡ ¡ 1000 ¡g=2.2 g=2.3 800 ¡1.8K ¡1.8K 600 ¡2.5K ¡2.5K ¡ ¡ ¡ ¡ ¡3.0K ¡3.0K 400 ¡3.6K ¡3.6K 200 (c) ¡4.5K ¡4.5K (d) ¡ ¡F IT ¡ ¡F IT 0 0 20 40 60 80 0 20 40 60 80 ¡ H (kO e)
71 Ga NMR (AMES LAB) NMR susceptibility shows a broad max around 50 K Above 30K consistent with HTSE of triangular Heisenberg Two Ga lines originate from the Ga in the two planes
71 Ga AND 45 Sc SPIN-LATTICE RELAXATION RATE 1/KT 1 T α A Γ /( Γ 2 + ω N 2 ) Γ is the inverse of the correlation time of 1/T 1 α T 3.2 fluctuating hyperfine fields at the nucleus
Slowing down of fluctuation frequency of Cu spins
HEAT CAPACITY (MPICPfS DRESDEN) 100 Schottky anomaly 10 C p ¡(J /mol ¡K ) 1 10kO e Schottky 0kO e + 0.1 40kO e Lattice 70kO e + 90kO e “intrinsic” 0.01 120kO e 140kO e 1 10 100 T (K )
ANALYSIS OF HEAT CAPACITY Ò Subtract data at different fields from each other (removes the lattice and any field independent contribution) Ò Fit such data to a combination of two Schottky terms Ò Obtain (i) the Schottky gap for various fields and the (ii) fraction of spins which contribute (fixed to 10% in our case) Ò Fit high-T data to a combination of Einstein and Debye terms… extrapolate to low-T Ò Subtract Schottky and lattice part from the measured data to obtain the magnetic contribution C m .
LATTICE HEAT CAPACITY 350 ¡ 8 ¡C p(T ) ¡(0 ¡O e) ¡C p ¡(0 ¡O e) 300 ¡ ¡F it ¡(20-‑90K ) 6 1 Debye + 3 Einstein with C p ¡(J /mol ¡K ) ¡F IT ¡ ¡F it ¡(0.35-‑300K ) weights 1:1:4:6 4 250 ¡ Entropy change only about 20% 2 (a) C p ¡(J /mol ¡K ) of the value for ordered S = ½ system 200 0 Even lower at higher fields. 9 18 27 ¡ T (K ) 150 1.2 Δ S ¡(J /mol ¡K ) 100 0.8 ¡ 0.4 50 (b) 0.0 0 20 40 60 80 0 T (K ) 0 50 100 150 200 250 300 350 T ¡(K )
MAGNETIC HEAT CAPACITY ¡ Broad max around 2-4 K 0.4 Similar max seen in other frustrated systems NiGa 2 S 4 , Na 4 Ir 3 O 8 , Ba 3 CuSb 2 O 9 , Ba 3 NiSb 2 O 9 C m ¡(J /mol ¡K ) 0kO e 40kO e 0.2 ¡ 70kO e 90kO e 120kO e 140kO e 0.0 0 2 4 6 T (K )
POWER LAW BEHAVIOUR ¡ 0.31 C m ¡(J /mol ¡K ) Note that in high field data below 1K 1.5 0.92 ¡0kO e There is negligible Schottky as also 0.100 lattice contribution. ¡40kO e Exponent is more robust. 1.0 ¡70kO e In any case, there is a field induced ¡ 1.5 suppression of C m at low-T. ¡90kO e (b) 1.9 0.010 120kO e 140kO e 1.9 1 10 T (K )
Conclusion § Sc 2 Ga 2 CuO 7 has “triangular” Cu planes with some Ga/Cu disorder § Large Curie-Weiss θ = -50K but no ordering/freezing down to 50mK § NMR susceptibility follows HTSE for a Heisenberg triangular system with J ~ 40 K § Slowing down of Cu spin fluctuations below 2 K as T 2.2 § Magnetic heat capacity follows power law (T 2 ) at low-T for H > 90 kOe § Field induced suppression of the magnetic excitations at low-T at lower fields § We suggest a quantum spin liquid ground state for Sc 2 Ga 2 CuO 7
Collaboration and Funding IIT Bombay:Ramender Kumar, B. Koteswararao MPICPfS Dresden: P. Khuntia, M. Baenitz Ames Lab ISU: P. Khuntia, Yuji Furukawa EPFL/PSI: P. Freeman, H. Ronnow, Denis Sheptyakov Indian Institute of Technology Bombay Department of Science and Technology, India Indo-Swiss Joint Research Programme
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