Compressibility of BiCu 2 PO 6 : polymorphism against S=1/2 magnetic spin ladders

Transcription

1 Compressibility of BiCu 2 PO 6 : polymorphism against S=1/2 magnetic spin ladders Marie Colmont Céline Darie, Alexander A. Tsirlin,* Anton Jesche, Mentré* Claire Colin, and Olivier Univ. Lille, CNRS, Centrale Lille, ENSCL, Univ. Artois, UMR UCCS - Unité de Catalyse et Chimie du Solide, F Lille, France Université Grenoble Alpes et CNRS, Institut NEEL, F Grenoble, France Experimental Physics VI, Center for Correlations and Magnetism, Institute of Physics, University of Augsburg, Augsburg, Germany SUPPLEMENTARY INFORMATIONS S1: Synthesis, XRD and thermal analyzes Synthesis of the precursor: Single phase of BiCu 2 PO 6 was obtained from the stoichiometric mixture of Bi 2 O 3, NH 4 H 2 PO 4 and CuO heated successively at 150, 300 and 800 in an alumina crucible. Several intermediate grindings were necessary to obtain the pure phase. The obtained phase is named AP-BCPO which denotes the Ambient Pressure BiCu 2 PO 6. High Pressure - High Temperature (HP-HT): Pressure makes a significant difference to the reaction equilibria, which stabilizes metastable. The device employed in this study is the Belt system, see Figure S1.a, b. Compounds are placed into a capsule made of Pt. The capsule has a cross section diameter of 3 mm. The powder in the capsule is compressed before being encapsulated, more final product will be obtained if the starting powder is as compact as possible. The encapsulated capsule is surrounded by a pyrophyllite tube and covered by a pyrophyllite cap at each end. All of these can be well filled into a graphite furnace tube. The graphite tube acts as the heater and the heat is generated from the electric current flowing through it. Two pieces of pyrophyllite cell and Teflon gasket aid to fix the sample and the furnace at the center of the middle plate of the Belt system. The pyrophyllite cells also act as the media to transmit the hydrostatic pressure to the sample in all directions. The pyrophylite caps and tube electrically separate the graphite furnace and the inner capsule. S1

2 (b) (a) Figure S1 (a) A real picture of the Belt system, (b) a sketch of the cell to contain and fix the starting materials for synthesis in the Belt system, a real picture of different components in this cell is also shown. [@ Institut NEEL] Pressure is transmitted from the apparatus to the reaction unit by two tungsten carbide pistons in the shape of a cone in the directions of top-down and bottom-up, respectively. The program for the synthesis of HP-BiCu2PO6 powder starting from AP-BiCu 2 PO 6 runs in the following sequence. Pressure is slowly applied until the 5 GPa value is reached. Then the temperature is raised to 950 C where it is maintained for 30 minutes. This is followed by a rapid quench at room temperature and only after the quench the pressure is slowly released. S2: Crystal structure: Selected cation-anion distances for the refined vs relaxed models are given table S2. Table S2: Selected M-O distances for HP-BCPO. refined DFT-relaxed Bi O1 2x 2.247(1) Bi O1 2x O1 2x 2.360(1) O1 2x O4 1x 2.537(6) O4 1x Cu1 O1 2x 1.925(1) Cu1 O1 2x O2 2x 2.044(5) O2 2x O3 1x 2.348(7) O3 1x Cu2 O1 2x 1.924(1) Cu2 O1 2x O2 2x 2.084(5) O2 2x O4 1x 2.359(4) O4 1x P O4 1x 1.449(3) P O4 1x O2 2x 1.470(5) O2 2x O3 1x 1.526(7) O3 1x S2

3 S3: Magnetic fits and various calculations: χ X 10-3 (emu/mol Cu) Exp.(1T) QMC- frustrated ladder (J 1,J 4,J 2 ) Spingap ( ) Analytic. Coupled ladder (J 1,J 4,J 3 ) T/K Figure S3: Experimental magnetic susceptibility under 1T and its fits. A Reasonable fit of χ(t) was obtained in the full temperature range (red plot above) using the hightemperature series expansion for a simple S= 1/2 ladder χ L (g, J1, J4) as given in [3] and intensively discussed in [4]. It is detailed below. In view of the sizable inter-ladder coupling J3 the expression was modified taking into account the inter-ladder interactions on a mean-field level via an effective temperature θint. The Curie-type impurity term and the χ0 temperature-independent term were included as well: χ = χ 0 + x imp C/(T-θ imp ) + (1-x imp ) χl/[1-(θ int χl /C)] (1) with C = cm 3 K mol -1, θ int = z S(S+1) J 3 /3K b and z=4 surrounding ladders via J 3. After fixing g=2.2 and J 1 /J 4 = 1.8 (from DFT calculations below) we found antiferromagnetic J1/K b = 88.8(3)K (i.e. J 4 /K b =49K) and ferromagnetic J 3 /K b = -4.85(2) K, χ 0 = cm 3 mol -1 x imp = 1.75(2)% and θ imp = (6) K giving a rough approximation of the J s involved and the deduced gap of 22 K given by = [3]. Here we have used reduced susceptibility and temperature described as follows: Then the ladder susceptibility is given by : / 4 + / 8 + / 24 + S3

4 Where With = = = = /4 J : Nearest neighbor, leg (2 ) =J1= Jmax J : Nearest neighbor, rung (1 ) =J4 Jdiag : Second neighbor diagonal intraladder, (2 ) =0 J : Trellis layer, interladder (2 ) = 0 J Stacked ladder, interladder (2 ) =0 J3D : 3D interladder, (2 ) = J3, but not fitted since considered in the effective temperature θint, see above. Exact Diagonalization: In figure S3a, the green line was computed by an exact diagonalization for the one-dimensional J 1 -J 2 -J 2 -J 4 lattice comprising 16 spins with periodic boundary conditions using the relevant algorithm of the ALPS simulation package [4]. This leads to a very good fit above 100 K (g=2.15 and the approximation J1=200K, J2=J2 =J1/2 and J4 =140K) and compares favorably with the exchange couplings obtained from DFT. On the other hand, the low-temperature part is not reproduced, because the interladder coupling J3 is crucial for the size of the spin gap. The model without J3 overestimates the gap and, therefore, shifts the susceptibility maximum toward higher temperatures. References [1] F. Abraham, E. M. Ketatni, G. Mairesse, and B. Mernari, Crystal structure of a new bismuth copper oxyphosphate: BiCu 2 PO 6, Eur. J. Solid State Inorg. Chem., , 313. [2] S. Miyahara, M. Troyer, D. C. Johnston, and K. Ueda, Quantum Monte Carlo Simulation of the Trellis Lattice Heisenberg Model for SrCu 2 O 3 and CaV 2 O 5 J. Phys. Soc. Jpn.1998, 67, [3] D. C. Johnston et al., Magnetic Susceptibilities of Spin-1/2 Antiferromagnetic Heisenberg Ladders and Applications to Ladder Oxide Compounds, arxiv:cond-mat/ , [4] A. Albuquerque et al. " The alps project release 1.3: open source software for strongly correlated systems" J. Magn. Magn. Mater. 2007, 310, [5] H.J. Xiang, E.J. Kan, S.-H. Wei, M-.H. Whangbo, and X.G. Gong., Predicting the spin-lattice order of frustrated systems from first principles Phys. Rev. B 2011, 84, [6] A.A. Tsirlin., Spin-chain magnetism and uniform Dzyaloshinsky-Moriya anisotropy in BaV3O8 Phys. Rev. B 2014, 89, S4

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