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The nonlocality of an entangled qubit pair can be recycled for several Bell experiments. Here, we go beyond standard Bell scenarios and investigate the recycling of nonlocal resources in a quantum network. First, we show that the ability to recycle nonlocality can be independent of the size of the network. Then, we realize a photonic quantum 3-branch star network in which three sources of entangled pairs independently connect three outer parties with a central node. After measuring, each outer party respectively relays their system to an independent secondary measuring party. We experimentally demonstrate that the outer parties can perform unsharp measurements that are strong enough to violate a network Bell inequality with the central party, but weak enough to maintain sufficient entanglement in the network to allow the three secondary parties to do the same. Moreover, the violations are strong enough to exclude any model based on standard projective measurements on the EPR pairs emitted in the network. Our experiment brings together the research program of recycling quantum resources with that of Bell nonlocality in networks.

Epitaxial strain has been extensively used to tailor the functionality of perovskite oxides, in which strain control of magnetism is highly desirable, especially for perovskite manganites. Here on the basis of the first-principles calculations we demonstrated the control of magnetic phase and orbital order in ${\mathrm{LuMnO}}_{3}$ film by epitaxial strain imposed by a square substrate and revealed the surface and interface effects by combining the strain-bulk and heterostructure models. The spiral and $E$ -type multiferroic phases present in perovskite manganites bulks can exist in the tensile strained films, while a ferromagnetic half-metal phase with high Curie temperature and an antiferromagnetic polar-metal phase arise in the range of compressive strain. Increasing compressive strain changes the sign of the ${Q}_{3}$ mode of Jahn-Teller distortion, resulting in the transition of the in-plane stagger orbital order to a uniform orbital order. The reconstruction of Jahn-Teller distortion and orbital order occur in the first two layers near the surface. The symmetry breaking of the crystal field at the surface leads to a uniform ${d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$ type orbital order and surface metallization. The electron accumulation at the interface with ${\mathrm{SrTiO}}_{3}$ substrate has been demonstrated and decreases dramatically with the increase in the number of ${\mathrm{LuMnO}}_{3}$ layers.

The effects of epitaxial strain on the structural, electronic, and magnetic properties in perovskite $R{\mathrm{MnO}}_{3}$ ($R=\mathrm{La}--\mathrm{Lu}$) films grown on (001) and (110) ${\mathrm{SrTiO}}_{3}$ substrates have been studied by density functional theory calculations. We demonstrate that the epitaxial strain causes the magnetic phase transitions from antiferromagnetic to ferromagnetic in most of the $R{\mathrm{MnO}}_{3}$ films, except those with smaller $R$ ions. These transitions can be attributed to the suppression of ${Q}_{3}$-type Jahn-Teller distortion caused by epitaxial strain, which significantly enhances the ferromagnetism in the nearest-neighbor exchange interactions. The strain gradient resulting from the strain relaxation provides the possibility to realize the coexistence of ferroelectricity and ferromagnetism, and a magnetoelectric coupling interface can be formed at the phase boundary between ferromagnetic and ferroelectric antiferromagnetic phases. Our results not only explain the observed ferromagnetism and the coexistence of multiple magnetic orders but also shed light on how to achieve the coexistence and coupling between ferroelectricity and ferromagnetism in $R{\mathrm{MnO}}_{3}$ films.