Order-disorder phase transition on the (100) surface of magnetite

Norman C. Bartelt, Shu Nie, Elena Starodub, Ivan Bernal-Villamil, Silvia Gallego, Lucia Vergara, Kevin F. McCarty, and Juan de la Figuera

Phys. Rev. B 88, 235436 – Published 30 December 2013

Abstract

Using low-energy electron diffraction, we show that the room-temperature $(\sqrt{2} \times \sqrt{2}) R 45^{\circ}$ reconstruction of Fe $_{3}$ O $_{4}$ (100) reversibly disorders at $\sim$ 450 $^{\circ}$ C. Short-range order persists above the transition, suggesting that the transition is second order and Ising-like. We interpret the transition in terms of a model in which subsurface Fe $^{3 +}$ is replaced by Fe $^{2 +}$ as the temperature is raised. This model reproduces the structure of antiphase boundaries previously observed with scanning tunneling microscopy, as well as the continuous nature of the transition. To account for the observed transition temperature, the energy cost of each charge rearrangement is 82 meV.

Received 9 October 2013

DOI:https://doi.org/10.1103/PhysRevB.88.235436

Authors & Affiliations

Norman C. Bartelt^1,*, Shu Nie¹, Elena Starodub¹, Ivan Bernal-Villamil², Silvia Gallego², Lucia Vergara³, Kevin F. McCarty¹, and Juan de la Figuera^3,†

¹Sandia National Laboratories, Livermore, California 94550, USA
²Instituto de Ciencia de Materiales de Madrid, CSIC, Madrid 28049, Spain
³Instituto de Química Física “Rocasolano,” CSIC, Madrid 28006, Spain

^*bartelt@sandia.gov
^†juan.delafiguera@iqfr.csic.es

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Issue

Vol. 88, Iss. 23 — 15 December 2013

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Images

Figure 1
(a) Side-view schematic of the magnetite (100) surface terminated by octahedrally coordinated iron. The oxygen atoms, octahedral iron atoms, and the tetrahedral iron atoms are colored red, yellow, and green, respectively. (b) Model of the $(\sqrt{2} \times \sqrt{2}) R 45^{\circ}$ reconstruction, where arrows indicate the displacements of the iron atoms perpendicular to their rows. (c) Top view of charge order in the subsurface octahedral Fe. The circles represent octahedral iron in the upper two layers. The top layer iron is colored yellow, as in (b). The black and open circles represent subsurface Fe $^{3 +}$ and Fe $^{2 +}$ iron, respectively. The $(\sqrt{2} \times \sqrt{2}) R 45^{\circ}$ cell is outlined by the dotted line.
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Figure 2
(a) Dark-field LEEM image acquired after several cleaning cycles. The field of view is 6.6 $μ$ m and the incident electron energy is 14 eV. Adjacent terraces appear either black and white, a result of alternating directions of the octahedral iron rows. (b) LEED pattern of Fe $_{3}$ O $_{4}$ (100) at room temperature. The center spot is the (0,0) beam. (c) LEED pattern at 488 $^{\circ}$ C, where the reconstruction spots have disappeared. Patterns obtained with 32 eV electrons.
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Figure 3
Profiles of the reconstruction diffraction spots at temperatures below and above the surface phase transition in 1 $\times$ 10 $^{- 6}$ Torr of oxygen. (a) Image and profile of a reconstruction diffraction beam at 448 $^{\circ}$ C. (b) Same except for 459 $^{\circ}$ C. (c) Same except for 465 $^{\circ}$ C. The experimental profiles, plotted versus the in-plane diffraction vector $k$ , are shown by filled circles. $k_{0}$ is the reciprocal lattice vector of the unreconstructed surface unit cell. Lorentzian fits are shown by continuous lines. The size of each image is 0.8 $k_{0}$ .
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Figure 4
Amplitude (circles) and FWHM (triangles) of a $(\sqrt{2} \times \sqrt{2}) R 45^{\circ}$ reconstruction diffraction spot through the phase transition extracted from fitting to Lorentzian line shapes. The fit to the square of the order parameter of the 2D Ising model is shown as a continuous line.
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Figure 5
(a) The structure of antiphase boundaries in the $(\sqrt{2} \times \sqrt{2}) R 45^{\circ}$ reconstruction reported in Ref. [16]. The configurations of subsurface Fe drawn in (b) and (c) were not observed.
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Figure 6
Mapping configurations of subsurface charges (left-hand panels) onto configurations of occupied sites of the hard square model (large circles in the right-hand panels). (a) Ground state. (b) The lowest-energy allowed excitation of the ground state that replaces a pair of Fe $^{3 +}$ with Fe $^{2 +}$ and corresponds to creating a vacancy in the ordered state of the hard square model. (c) An forbidden configuration in which Fe $^{3 +}$ replaces Fe $^{2 +}$ . In the hard square model this is not allowed because nearest neighbor sites in the square lattice are simultaneously occupied.
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