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Metallization of vanadium dioxide driven by large phonon entropy

Nature volume 515, pages 535–539 (2014)Cite this article

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Abstract

Phase competition underlies many remarkable and technologically important phenomena in transition metal oxides. Vanadium dioxide (VO2) exhibits a first-order metal–insulator transition (MIT) near room temperature, where conductivity is suppressed and the lattice changes from tetragonal to monoclinic on cooling. Ongoing attempts to explain this coupled structural and electronic transition begin with two alternative starting points: a Peierls MIT driven by instabilities in electron–lattice dynamics and a Mott MIT where strong electron–electron correlations drive charge localization1,2,3,4,5,6,7,8,9,10. A key missing piece of the VO2 puzzle is the role of lattice vibrations. Moreover, a comprehensive thermodynamic treatment must integrate both entropic and energetic aspects of the transition. Here we report that the entropy driving the MIT in VO2 is dominated by strongly anharmonic phonons rather than electronic contributions, and provide a direct determination of phonon dispersions. Our ab initio calculations identify softer bonding in the tetragonal phase, relative to the monoclinic phase, as the origin of the large vibrational entropy stabilizing the metallic rutile phase. They further reveal how a balance between higher entropy in the metal and orbital-driven lower energy in the insulator fully describes the thermodynamic forces controlling the MIT. Our study illustrates the critical role of anharmonic lattice dynamics in metal oxide phase competition, and provides guidance for the predictive design of new materials.

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Figure 1: PDOS spectra of rutile and M1 phases in VO2 showing phonon stiffening in the M1 phase.
Figure 2: Comparison of experimental and calculated X-ray TDS.
Figure 3: Phonon dispersions in rutile VO2.
Figure 4: Simulations of VO2 phases.

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Acknowledgements

Research by J.D.B., O.D., M.E.M., E.D.S., L.A.B. and R.J.M. was supported by the US Department of Energy (DOE), Basic Energy Sciences (BES), Materials Sciences and Engineering Division (MSED). Research by J.H. was supported by the Center for Accelerating Materials Modeling, funded by the US DOE, BES, MSED. Experimental work by C.W.L. was sponsored by the Laboratory Directed Research and Development Program of ORNL (Principal Investigator, O.D.). Research by D.L.A. at the Spallation Neutron Source and J.Z.T., A.H.S. and B.M.L. at the Advanced Photon Source (APS), Argonne National Laboratory (ANL), was supported by the US DOE, BES, Scientific User Facilities Division. We thank A. Tselev, S. Nagler, A. Banerjee, H. Krakauer and V. Cooper for interesting discussions on VO2. Inelastic neutron scattering measurements were performed using the ARCS facility at the ORNL Spallation Neutron Source, which is sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, US Department of Energy. We thank J. Niedziela for help with the sample environment at ARCS. IXS measurements were performed using the X-ray Operations and Research (XOR) beamline 30-ID (HERIX) at the APS. Diffuse X-ray scattering measurements were performed using the XOR beamline 33-BM-C at the APS. We thank J. Karapetrova and C. Schleputz for assistance in setting up experiments at UNICAT. Use of the APS, an Office of Science User Facility operated for the US DOE Office of Science by ANL, was supported by the US DOE under contract no. DE-AC02-06CH11357. Theoretical calculations were performed using resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the US Department of Energy under contract no. DE-AC02-05CH11231. We thank O. Hellman for providing the temperature-dependent effective potential software and assistance.

Author information

Author notes

  1. John D. Budai and Jiawang Hong: These authors contributed equally to this work.

Authors and Affiliations

  1. Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, 37831, Tennessee, USA

    John D. Budai, Jiawang Hong, Michael E. Manley, Eliot D. Specht, Chen W. Li, Lynn A. Boatner & Olivier Delaire

  2. Advanced Photon Source, Argonne National Laboratory, Argonne, 60439, Illinois, USA

    Jonathan Z. Tischler, Ayman H. Said & Bogdan M. Leu

  3. Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, 37831, Tennessee, USA

    Douglas L. Abernathy

  4. Neutron Sciences Directorate, Oak Ridge National Laboratory, Oak Ridge, 37831, Tennessee, USA

    Robert J. McQueeney

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  1. John D. Budai
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Contributions

This project included significant contributions from many researchers and all authors participated in scientific discussions. J.D.B. (experiment) and O.D. (experiment and calculations) designed this research project. L.A.B. synthesized single-crystal samples. J.H. and O.D. performed the theoretical calculations with analysis. M.E.M., C.W.L., J.D.B., O.D. and D.L.A. performed the INS measurements and analysis. E.D.S., J.D.B., O.D., C.W.L. and J.Z.T. performed the diffuse X-ray scattering measurements and analysis. J.D.B., M.E.M., O.D., C.W.L., A.H.S., B.M.L., J.Z.T. and R.J.M. performed the IXS measurements and analysis. O.D., J.D.B., M.E.M., E.D.S. and J.H. wrote the manuscript with assistance from C.W.L.

Corresponding authors

Correspondence to John D. Budai or Olivier Delaire.

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Extended data figures and tables

Extended Data Figure 1 Temperature-dependent scattering function S(E).

Data come from inelastic powder neutron scattering measurements integrated over Q values up to ∼6 Å−1, obtained using an incident neutron energy of 30 meV, and show gradual softening of the low-energy phonons and abrupt disappearance of these modes across the transition at temperature Tc.

Extended Data Figure 2 Optical photograph of rectangular VO2 single crystal mounted on copper post.

Crystal dimensions are 0.25 mm × 0.25 mm × ∼4 mm. Unlike larger crystals, small crystals such as this did not show sample cracking while thermally cycling through the MIT.

Extended Data Figure 3 Integrated first-order TDS intensity for a H + K + L = 8 sheet near (4.5 0 3.5) using diffuse X-ray scattering measurements from the APS-33BM beamline, compared with the thermal occupation factor for phonons.

Extended Data Figure 4 IXS energy scan.

Data (filled blue circles) are for a transverse acoustic phonon in the rutile phase measured at an M point in reciprocal space, q = (0.5, 3.5, 0), at a temperature of 810 K. The solid red line is a fit using the expression for a damped harmonic oscillator.

Extended Data Figure 5 IXS measurements for individual phonon branches.

Schematic at left shows total scattering vectors, QLA and QTA, for separate measurements of longitudinal and transverse phonons with wavevector q = (0, 0, ζ) (ζ ≈ 0.3) along the Γ–Z symmetry direction. Plot at right shows experimental energy scan at QTA = (0, 4, 0.3) corresponding to the transverse acoustic branch. The line shape is well fitted by a strongly damped harmonic model, and the large anharmonic linewidth corresponds to a very short phonon lifetime.

Extended Data Figure 6 Calculated phonon dispersions with harmonic approximations.

Data calculated at 0 K with PBE (a) and PBE+U (b). Negative energies correspond to unstable modes with imaginary frequencies which are unphysical.

Extended Data Figure 7 DFT frozen-phonon potential energy curves (per atom).

Blue curves are parabolic fits and magenta fits include quadratic as well as quartic terms. Insets show the displacement patterns of the modes. Black dots represent DFT total energy as a function of uVmax, the maximum displacement of a V atom in the phonon mode. Vanadium and oxygen atoms are depicted by green and red, respectively.

Extended Data Table 1 Mean squared atomic displacements
Full size table

Supplementary information

Three-Dimensional Thermal Diffuse Scattering (TDS) X-ray Measurements

Temperature-dependent x-ray diffuse scattering measurements from VO2 single crystals were measured using an area detector as the sample was rotated. The reciprocal lattice vector was calculated for each pixel of the detector at each angle setting. Two-dimensional and three dimensional diffuse scattering maps were calculated by averaging the counts of all pixels contained in each voxel of a regular 0.05 x 0.05 x 0.025 rutile reciprocal-lattice grid. The Supplementary Video illustrates that, as discussed in the article, the 3-D thermal diffuse H+K+L=2n, n≠0) in reciprocal space. (MOV 1675 kb)

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Budai, J., Hong, J., Manley, M. et al. Metallization of vanadium dioxide driven by large phonon entropy. Nature 515, 535–539 (2014). https://doi.org/10.1038/nature13865

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