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Atomically thin films of layered chromium triiodide (CrI$_3$) have recently been regarded as suitable candidates to a wide spectrum of technologically relevant applications, mainly owing to the opportunity they offer to achieve a reversible transition between coexisting in-plane ferro- and out-of-plane antiferro-magnetic orders. However, no routes for inducing such a transition have been designed down to the single-layer limit. Here, we address the magnetic response of monolayer CrI$_3$ to in-plane lattice deformations through a combination of isotropic Heisenberg spin Hamiltonians and first-principles calculations. Depending on the magnitude and orientation of the lattice strain exerted, we unveil a series of direction-dependent parallel-to-antiparallel spins crossovers, which yield the emergence of ferromagnetic, Neel antiferromagnetic, zigzag and stripy antiferromagnetic ground states. Additionally, we identify a critical point in the magnetic phase diagram whereby the exchange couplings vanish and the magnetism is quenched. Our work establishes guidelines for extensively tailoring the spin interactions in monolayer CrI$_3$ via strain engineering, and further expands the magnetically ordered phases which can be hosted in a two-dimensional crystal.
The marked interplay between the crystalline, electronic, and magnetic structure of atomically thin magnets has been regarded as the key feature for designing next-generation magneto-optoelectronic devices. In this respect, a detailed understanding o
Few-layer CrI$_3$ is the most known example among two-dimensional (2D) ferromagnets, which have attracted growing interest in recent years. Despite considerable efforts and progress in understanding the properties of 2D magnets both from theory and e
The magnetic structures and the magnetic phase transitions in the Mn-doped orthoferrite TbFeO$_3$ studied using neutron powder diffraction are reported. Magnetic phase transitions are identified at $T^mathrm{Fe/Mn}_N approx$ 295~K where a paramagneti
We have performed Raman scattering investigations on the high energy magnetic excitations in a BiFeO$_3$ single crystal as a function of both temperature and laser excitation energy. A strong feature observed at 1250 cm$^{-1}$ in the Raman spectra ha
Bilayer ruthenate Ca$_3$(Ru$_{1-x}$Fe$_x$)$_2$O$_7$ ($x$ = 0.05) exhibits an incommensurate magnetic soliton lattice driven by the Dzyaloshinskii-Moriya interaction. Here we report complex field-induced magnetic phase transitions and memory effect in