Large spin–orbit coupling in combination with circular dichroism allows access to spin-polarized and valley-polarized states in a controlled way in transition metal dichalcogenides. The promising application in spin-valleytronics devices requires a thorough understanding of intervalley coupling mechanisms, which determine the lifetime of spin and valley polarizations. Here we present a joint theory–experiment study shedding light on the Dexter-like intervalley coupling. We reveal that this mechanism couples A and B excitonic states in different valleys, giving rise to an efficient intervalley transfer of coherent exciton populations. We demonstrate that the valley polarization vanishes and is even inverted for A excitons, when the B exciton is resonantly excited and vice versa. Our theoretical findings are supported by energy-resolved and valley-resolved pump-probe experiments and also provide an explanation for the recently measured up-conversion in photoluminescence. The gained insights might help to develop strategies to overcome the intrinsic limit for spin and valley polarizations.

A remarkable property of atomically thin transition metal dichalcogenides (TMDs) is the possibility to selectively address single valleys by circularly polarized light. In the context of technological applications, it is very important to understand possible intervalley coupling mechanisms. Here, we show how the Dexter-like intervalley coupling mixes A and B states from opposite valleys leading to a significant broadening of the B1s exciton. The effect is much more pronounced in tungsten-based TMDs, where the coupling excitonic states are quasi-resonant. We calculate a ratio , which is in good agreement with the experimentally measured value of . In addition to the broadening effect, the Dexter-like intervalley coupling also leads to a considerable energy renormalization resulting in an increased energetic distance between A1s and B1s states.

Using low-energy electron diffraction, we show that the room-temperature ( √ 2 × √ 2)R45 • reconstruction of Fe 3 O 4 (100) reversibly disorders at ∼450 • 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. Metal oxides are often useful because of their stability at high temperatures. An example is magnetite, Fe 3 O 4 . In catalytic applications such as the water-gas shift reaction, 1 magnetite is used at temperatures between 300 and 500 • C. Furthermore, magnetite's high Curie temperature of 580 • C allows spintronic applications. 2 Since such applications frequently depend on surface properties, a natural question arises-how does the surface structure change with temperature?The room-temperature properties of magnetite's surfaces are complex. Its (100) surface has been extensively studied. [3][4][5][6][7][8][9][10][11][12][13][14][15] Instead of the (1 × 1) bulklike termination, it reconstructs into a structure with a larger ( √ 2 × √ 2)R45 • unit cell. The atomic structure of this reconstruction has been painstakingly unraveled by density functional theory (DFT), low-energy electron diffraction (LEED), and scanning tunneling microscopy (STM) 4 -the surface is terminated by octahedrally coordinated iron atoms arranged in rows, as shown in Fig. 1(a). The observed periodicity results from small displacements of the iron atoms perpendicular to the rows [see Fig. 1(b)]. The driving force for the reconstruction is believed to be ordering of the charge state of the iron in octahedral sites beneath the surface. 15,16 In bulk magnetite at room temperature the average charge state of octahedral iron is +2.5e. The subsurface charge ordering involves disproportionation of this charge into more positively and negatively charged sites. It has been proposed 15,16 that the disproportionation is greatest in the plane of octahedral iron beneath the top layer. Figure 1(c) sketches the proposed charge order in this subsurface layer. In Fig. 1(c), and in our discussion below, the two charge states in the second layer are labeled by their nominal oxidation state Fe 3+ and Fe 2+ , although the charges are estimated to only differ by 0.2-0.4 e rather than e. 15,17 The top layer octahedral iron is displaced in the surface plane to decrease the distance to the nearest subsurface Fe 2+ , giving the undulating rows of surface octahedral iron observed by LEED and STM.What might happen to such a structure when the temperature is raised? One possibility is that the high-temperature, high-entropy surface differs significantly in stoichiometry and termination from the charge ordered ( √...

FeO(111) films have been synthesized by PLD revealing unexpected properties explained by a wurtzite-like environment at the surface.

At ambient conditions, the Fe3O4(001) surface shows a ( √ 2 × √ 2)R45 o reconstruction that has been proposed as the surface analog of the bulk phase below the Verwey transition temperature, TV . The reconstruction disappears at a high temperature, TS, through a second order transition. We calculate the temperature evolution of the surface electronic structure based on a reduced bulk unit cell of P 2/m symmetry that contains the main features of the bulk charge distribution. We demonstrate that the insulating surface gap arises from the large demand of charge of the surface O, at difference with that of the bulk. Furthermore, it is coupled to a significant restructuration that inhibits the formation of trimerons at the surface. An alternative bipolaronic charge distribution emerges below TS, introducing a competition between surface and bulk charge orders below TV .

Magnetite (Fe3O4) shows singular electronic and magnetic properties, resulting from complex electron-electron and electron-phonon interactions that involve the interplay of charge, orbital and spin degrees of freedom. The Verwey transition is a manifestation of these interactions, with a puzzling connection between the low temperature charge ordered state and the dynamic charge fluctuations still present above the transition temperature. Here we explore how these rich physical phenomena are affected by thin film geometries, particularly focusing on the ultimate size limit defined by thicknesses below the minimum bulk unit cell. On one hand, we address the influence of extended defects, such as surfaces or antiphase domains, on the novel features exhibited by thin films. On the other, we try to isolate the effect of the reduced thickness on the electronic and magnetic properties. We will show that a distinct phase diagram and novel charge distributions emerge under reduced dimensions, while holding the local high magnetic moments. Altogether, thin film geometries offer unique possibilities to understand the complex interplay of short- and long-range orders in the Verwey transition. Furthermore, they arise as interesting candidates for the exploitation of the rich physics of magnetite in devices that demand nanoscale geometries, additionally offering novel functionalities based on their distinct properties with respect to the bulk form.

We perform a detailed study of the electronic structure of Fe 1−x O at moderate values of x. Our results evidence that the Fe vacancies introduce significant local modifications of the structural, electronic, and magnetic features, which serve to explain the origin of the measured dependencies of the physical properties on x. The final properties are determined by a complex interplay of the charge demand from O, the magnetic interactions, and the charge order at the Fe sublattice. Furthermore, polaronic distributions of charge resembling those at magnetite, Fe 3 O 4 , emerge for the most stable defect structures. This defines a unique scenario to understand the nature of the short-range correlations in Fe 3 O 4 , and unveils their intimate connection to the long-range charge order developed below the Verwey transition temperature.

Based on ab initio calculations we determine the features and relative stability of different models proposed to describe the (2 × 2)-FeO(111) reconstruction. Our results suggest that both wurtzite and spinel-like environments are possible, and their coexistence explains phenomena of biphase ordering. The surface phase diagram reflects a competition of charge and magnetic compensation effects, and reveals the important influence of the substrate on the final surface structure. Though antiferromagnetic couplings are dominant, frustration and the delicate balance of surface and bulk exchange interactions lead to a net surface magnetization that accounts for the large measured values.