Coulomb interactions in two-dimensional lattice structures

Розенбаум, В. М.

doi:10.1103/physrevb.53.6240

Cited by 46 publications

(40 citation statements)

References 43 publications

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“…1. For sufficiently small separations z a, where a is lattice constant, we reproduce the earlier predicted [20,21] canted antiferromagnetic phase, AFM K , with the ordering vector K. For z > a, we find an antiferromagnetic phase, AFM M , with a larger unit cell and ordering wave vector at the M point of the Brillouin zone of the bipartite lattice. For intermediate interlayer distances, we find a stable ferromagnetic phase (FM), separated from the antiferromagnetic ones by incommensurate spin-wave states (ISW).…”

supporting

confidence: 82%

“…Finally, for z z 4 , q 0 lies at the point, which corresponds to an easy-plane ferromagnetic state. In the limit z → ∞, this coincides with the ground state calculated for a dipolar magnet on a plane triangular lattice [20]. The above analysis of magnetic phases of dipolar gases on square and triangular bipartite lattices, limited to the quadratic terms in the Landau theory, is formally valid at T → T c .…”

supporting

confidence: 75%

“…2. For z a, we find a helical phase with the ordering vector K (H K ), which is specific for dipoles on a two-dimensional (2D) honeycomb lattice [20]. A large vertical displacement of the two sublattices of the honeycomb lattice results in two weakly coupled triangular lattices, for which the ground state is ferromagnetic (FM) [20].…”

mentioning

confidence: 92%

“…For z a, we find a helical phase with the ordering vector K (H K ), which is specific for dipoles on a two-dimensional (2D) honeycomb lattice [20]. A large vertical displacement of the two sublattices of the honeycomb lattice results in two weakly coupled triangular lattices, for which the ground state is ferromagnetic (FM) [20]. In between those two extremes lies an antiferromagnetic phase AFM M with the ordering vector M [22], separated from the helical and ferromagnetic phases by parametric intervals, where the magnetization texture is incommensurate with the lattice.…”

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confidence: 93%

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Phase transitions in dipolar gases in optical lattices

2012

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We investigate the phase diagrams of two-dimensional lattice dipole systems with variable geometry. For bipartite square and triangular lattices with tunable vertical sublattice separation, we find rich phase diagrams featuring a sequence of easy-plane magnetically ordered phases separated by incommensurate spin-wave states. A recent breakthrough in the cooling of dipolar gases in optical lattices [1], following a decade of intensive research [2][3][4][5][6][7][8][9], has opened a door into the earlier inaccessible manybody physics of lattice systems with anisotropic long-range interaction. Although bulk crystalline dipolar systems are abundant in nature [10,11], their experimental investigation has been hindered by the extremely low temperatures required for the observation of ordering transitions [12] and the absence of continuously variable parameters. Recently, artificial twodimensional dipolar systems, such as lithographically created nanomagnet arrays, have been realized [13,14]. However, it is the advent of optical lattices with tunable lattice structure containing ultracold dipolar gases that has created numerous possibilities for studies of previously unexplored phase transitions-both classical and quantum-between ordered and disordered phases of this fundamental many-body system.In this paper, we analyze a series of magnetic phase transitions in a classical dipolar gas in deep optical lattices (square, Fig. 1 and triangular, Fig. 2) obtained from bipartite monolayer lattices by vertical separation, z, of the two sublattices. One way to realize such systems would be loading the ferromagnetic spinor Bose-Einstein minicondensates in the nodes [15] of a deep bilayer optical lattice created with the help of a painted potential technique [16], which would allow for a high degree of control over the shapes of optical lattices and interlayer separation.We find that, upon the variation of z, each system experiences a sequence of easy-plane magnetically ordered phases separated by incommensurate spin-wave states, which could be detected with the help of Bragg diffraction of light [17][18][19]. The phase diagram for the square lattice on the z-T plane is shown in Fig. 1. For sufficiently small separations z a, where a is lattice constant, we reproduce the earlier predicted [20,21] canted antiferromagnetic phase, AFM K , with the ordering vector K. For z > a, we find an antiferromagnetic phase, AFM M , with a larger unit cell and ordering wave vector at the M point of the Brillouin zone of the bipartite lattice. For intermediate interlayer distances, we find a stable ferromagnetic phase (FM), separated from the antiferromagnetic ones by incommensurate spin-wave states (ISW). At the critical temperature T c , all of the ordered phases feature a degeneracy in the orientation of magnetization, characterized in Fig. 1 by angle θ , or θ A and θ B for AFM M . Away from T c , such a degeneracy is lifted, and Fig. 1 shows the optimal orientation of the order parameter for the low-temperature states. The structure of the i...

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supporting

confidence: 82%

supporting

confidence: 75%

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confidence: 92%

mentioning

confidence: 93%

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Phase transitions in dipolar gases in optical lattices

2012

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“…To meet this goal, theory (2) suggests that the rotors should be assembled in a trigonal lattice. The surface assembly is expected to be ferroelectric between the Debye temperature T D , below which rotational barriers prevent the rotors from turning, and the Curie temperature T C , above which thermal disorder dominates.…”

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confidence: 99%

Structure of a monolayer of molecular rotors on aqueous subphase from grazing-incidence X-ray diffraction

Kaleta

Wen

Magnera

et al. 2018

Proc. Natl. Acad. Sci. U.S.A.

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In situ grazing-incidence X-ray scattering shows that a monolayer of artificial rod-shaped dipolar molecular rotors produced on the surface of an aqueous subphase in a Langmuir trough has a structure conducive to a 2D ferroelectric phase. The axes of the rotors stand an average of 0.83 nm apart in a triangular grid, perpendicular to the surface within experimental error. They carry 2,3-dichlorophenylene rotators near rod centers, between two decks of interlocked triptycenes installed axially on the rotor axle. The analysis is based first on simultaneous fitting of observed Bragg rods and second on fitting the reflectivity curve with only three adjustable parameters and the calculated rotor electron density, which also revealed the presence of about seven molecules of water near each rotator. Dependent on preparation conditions, a minor and variable amount of a different crystal phase may also be present in the monolayer.grazing-incidence X-ray scattering | X-ray reflectivity | molecular rotors | aqueous-surface monolayer | synchrotron radiation W e have been examining 2D assemblies of dipolar molecular rotors in an effort to detect collective behavior (1). Ultimately, we hope to produce an artificial 2D ferroelectric phase of dipolar azimuthal molecular rotors located on a flat electrical insulator, both for fundamental investigations and for its possible applications in nanoscience.To meet this goal, theory (2) suggests that the rotors should be assembled in a trigonal lattice. The surface assembly is expected to be ferroelectric between the Debye temperature T D , below which rotational barriers prevent the rotors from turning, and the Curie temperature T C , above which thermal disorder dominates. The former condition calls for small rotational barriers, no higher than 1-2 kcal/mol [in 3D assemblies, rotational barriers as low as 0.7 kcal/mol have been achieved (3)]. The latter condition requires large rotatable dipoles μ spaced a small distance a apart, since T C is expected to be proportional to μ 2 /a 3 . After dealing with surface inclusions, in which molecular rotors were contained on the surface of a host crystal, and detecting ferroelectric interactions but no ferroelectric phase in bulk inclusions (4), we are now also exploring monolayers produced on aqueous surfaces using a Langmuir-Blodgett (LB) trough (5) and molecular rotors designed to assemble into a trigonal lattice (6). The hope is that the rotor axes will be perpendicular to the surface and separated by a small lattice constant (a < 1 nm) and that large monocrystalline domains can be produced. Ultimately, a monolayer of a suitable structure is to be transferred from the aqueous surface to a solid substrate for further study, possibly only after cross-linking for increased sturdiness.Many organic materials pack closely at the air-water interface. Their unit cells tend to be tilted and distorted (7-19), but some nearly perfectly straight structures have also been observed (20). We were inspired by close-packed LB films of fatty acids, which hav...

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