Direct visualization of the Jahn Teller effect coupled to Na ordering in Na 5/8 MnO 2

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1 Direct visualization of the Jahn Teller effect coupled to Na ordering in Na 5/8 MnO 2 Xin Li 1, Xiaohua Ma 1, Dong Su 2, Lei Liu 1, Robin Chisnell 3, Shyue Ping Ong 1, Hailong Chen 1, Alexandra Toumar 1, Juan-Carlos Idrobo 5, Yuechuan Lei 1, Jianming Bai 6, Feng Wang 7, Jeffrey W. Lynn 4, Young S. Lee 3, Gerbrand Ceder 1* 1. Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA USA 2. Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, NY USA 3. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA USA 4. NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA 5. Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN USA 6. National Synchrotron Light Source, Brookhaven National Laboratory, Upton, NY Sustainable Energy Technologies Department, Brookhaven National Laboratory, Upton, NY Current address: Department of NanoEngineering, University of California, San Diego, La Jolla, CA, USA School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, USA *Corresponding author: gceder@mit.edu 1 NATURE MATERIALS 1

2 Figure S1 Rietveld refinement of the synchrotron XRD for Na 5/8 MnO 2 (space group C2/m) gives a satisfactory fit, with wrp = 2.34%, Rp=1.74%, R(F 2 )=5.5%. The refined lattice parameters, ion coordinates and main bond lengths between the ions are shown in Supplementary Table S2 and S3. For the readers convenience, the hkl labels are based on a conversion back to a supercell 4x4x4 times the conventional monoclinic unit cell of NaMnO 2, rather than directly from the primitive superstructure cell shown in Supplementary Table S NATURE MATERIALS

3 Figure S2 Calculated ground state phase diagram of Na x MnO 2 showing that the Na 5/8 MnO 2 superstructure is the lowest in energy at x=5/8. Several hundred Na x MnO 2 structures with both O3 and P3 oxygen stackings and different Na orderings up to 4 formula units at compositions x=0.25, 0.33, 0.5, 0.66, 0.75 were relaxed by DFT. Three hundred O3 structures were calculated at x=5/8. The diagram shows the lowest energy O3 and P3 structures at most Na compositions and the stable phases are marked by blue. At x = 5/8 the structure with the lowest electrostatic energy (Ewald_0) is also shown. The energy of Na 5/8 MnO 2 (O3 * ) is below the tie line connecting 3 NATURE MATERIALS 3

4 the two lowest energy structures at neighboring compositions of x = 0.5 and 0.75 (energy below the hull), indicating that it is stable and will appear in the electrochemical voltage profile. 4 4 NATURE MATERIALS

5 Figure S3 Relaxed superstructure model showing Mn charge ordering strongly correlated with CJTE and Na ordering. a) The 3D view of the superstructure with the labeled (202) planes. The Mn 3+ label indicates the plane that cuts only through those Mn 3+ stripes, while Mixed means the plane cuts through Mn 4+ and mixed valence Mn stripe. Disp means the plane also cuts through the displaced Na ions. b-c) The section of the two types of (202) planes. In the [(202), Mn 3+, Disp] plane the displaced half-full Na columns are marked by the red arrows. The original Na ion and vacancy NATURE MATERIALS 5

6 positions are marked by the dashed circle and dashed cross, respectively, while the displaced Na vacancy positions are marked by the solid cross. The symmetrical attraction of two neighboring -O-Mn 3+ -O-Na configurations drives the Na displacement. In the [(202),Mixed] plane there are no twoneighboring -O-Mn 3+ -O-Na configurations to provide the symmetrical attraction to displace the Na ions, as in the mixed valence stripe Mn 3+ and Mn 4+ always alternate. 6 NATURE MATERIALS

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8 Figure S4 a) The ZFC and FC magnetic susceptibility curves between 1.8K and 30K for chemically and electrochemically de-intercalated samples show the same magnetic behavior at 20 Oe. b) Field cooled magnetic susceptibility for 0.2 T shows a substantial difference between Na 5/8 MnO 2 and pristine NaMnO 2. The inset in 4b) shows that the 1/χ vs. temperature curve of Na 5/8 MnO 2 deviates from the Curie-Weiss law below 60K. Note: 1 Oe = (1000/4π) A/m 8 NATURE MATERIALS

9 Table S1. Magnetic exchange parameters!!"! (in Kelvin) calculated by mapping DFT+U total energies onto spin Hamiltonians and at different U values.!!"! are defined in Figure 3a, where i identifies the NN (1) or NNN (2) interaction, a and b identify the valence states of the two interacting Mn ions, IC represents the inter-chain (stripe) interaction. The ground states (GS) are also shown for each stripe at different U values. The resulting exchange NATURE MATERIALS 9

10 parameters and GS magnetic structures in Table S1 demonstrate that the Mn 3+ stripe is always strongly AF NN coupled (negative values indicate AF coupling) along the stripe for all values of the DFT Hubbard parameter U from 0 to 3.9 ev, which is consistent with the behavior of the Mn 3+ ions in pristine NaMnO Similarly, the mixed Mn valence stripe is also strongly AF NN coupled independent of U, and thus is a ferrimagnetic stripe with alternating spin 2 for the Mn 3+ ion, and spin -3/2 for the Mn 4+ ion. The GS of the Mn 4+ stripe is sensitive to U, which can change from AF at U = 0 ev to ferrimagnetic at U = 2.47 ev (competing NN FM coupling of positive value with NNN AF coupling of negative value) and to FM at U > 2.83 ev (dominated by large NN FM coupling of positive value). Previous studies show that U around 2.5 ev in GGA+U predicts the closest intra- and interchain (stripe) exchange parameters to the neutron diffraction experiments for pristine NaMnO 1-3 2, thus we show the GS spin ordering on the Mn 4+ stripe at U = 2.47 ev in Figure 3a. 10 NATURE MATERIALS

11 Table S2. The SXRD refinement result (space group C2/m). U iso is the isotropic thermal parameter. The ion coordinates are only allowed for less than 2% deviation in the refinement from the DFT relaxed input positions. The different sites of Mn(α-δ) and Na(Disp, 2, 3) are labelled in Figure 3. NATURE MATERIALS 11

12 Table S3. Main atomic distance calculated from the O3-Na 5/8 MnO 2 structure after Rietveld refinement. The different sites of Mn(α-δ) and Na(Disp, 2, 3) are labelled in Figure 3. References: 1. Stock, C. et al. One-Dimensional Magnetic Fluctuations in the Spin-2 Triangular Lattice α- NaMnO 2. Phys. Rev. Lett. 103, (2009). 2. Wu, F., Yu, G., Xu, D. & Kan, E. First-principles investigations on the magnetic structure of α- NaMnO 2. J. Phys. Condens. Matter 24, (2012). 12 NATURE MATERIALS

13 3. Giot, M. et al. Magnetoelastic Coupling and Symmetry Breaking in the Frustrated Antiferromagnet α-namno 2. Phys. Rev. Lett. 99, (2007). NATURE MATERIALS 13