Strip Lattice Research Articles

From kagome strip to kagome lattice: Realizations of frustrated S=12 antiferromagnets in Ti(III) fluorides

We investigate the connection between highly frustrated kagome based Hamiltonians and a recently synthesized family of materials containing ${\mathrm{Ti}}^{3+}\phantom{\rule{4pt}{0ex}}S=\frac{1}{2}$ ions. Employing a combination of all electron density functional theory and numerical diagonalization techniques, we establish the Heisenberg Hamiltonians for the distorted kagome antiferromagnets ${\mathrm{Rb}}_{2}{\mathrm{NaTi}}_{3}{\mathrm{F}}_{12},{\mathrm{Cs}}_{2}{\mathrm{NaTi}}_{3}{\mathrm{F}}_{12}$, and ${\mathrm{Cs}}_{2}{\mathrm{KTi}}_{3}{\mathrm{F}}_{12}$. We determine magnetization curves in excellent agreement with experimental observations. Our calculations successfully clarify the relationship between the experimental observations and the magnetization-plateau behavior at $\frac{1}{3}$ height of the saturation and predict characteristic behaviors under fields that are higher than the experimentally measured region. We demonstrate that the studied Ti(III) family of materials interpolates between the kagome strip and kagome lattice.

Scattering Control Using Nonlinear Smart Metasurface with Internal Feedback

The ideology of creation of a nonlinear smart metasurface with internal feedback for the adaptive control by spectral composition of scattered field is offered. The metasurface contains a lattice of strip elements with nonlinear loads-sensors. They are included in a circuit of internal feedback for the adaptive control of scattered field. Numerically it is shown that maximal levels of the second harmonic in the spectrum of scattered far field correspond to maximum of voltage rectified on metasurface. Experimentally the prototype of the plane smart covering on the basis of the metasurface in the form of strip lattice with controlled nonlinear loads-sensors is investigated for an idea confirmation.

ChemInform Abstract: Synthesis, Structure, and Magnetic Properties of A2Cu5(TeO3)(SO4)3 (OH)4 (A: Na, K): The First Compounds with a 1D Kagome Strip Lattice.

AbstractSingle crystals of the title compounds are prepared by hydrothermal reaction of 1.5:0.5:2 molar mixtures of CuSO4, TeO2, and NaOH or KOH (autoclave, 190 °C, 5 d; cooling rate of ≈3 °C/h).

Synthesis, Structure, and Magnetic Properties of A2Cu5(TeO3)(SO4)3(OH)4 (A = Na, K): The First Compounds with a 1D Kagomé Strip Lattice.

Two new tellurite-sulfates A2Cu5(TeO3)(SO4)3(OH)4 (A = Na, K) have been synthesized by a conventional hydrothermal method. Both compounds feature 1D kagomé strip structure built by distorted CuO6 octahedra, which can be regarded as the dimensional reduction of kagomé lattice. Magnetic measurements confirmed that the titled compounds possess antiferromagnetic ordering at low temperature, while a field-induced magnetic transition can be observed at critical field. To the best of our knowledge, this is the first time to obtain distorted kagomé strip compounds.

Nontrivial ferrimagnetism of the Heisenberg model on the Union Jack strip lattice

We study the ground-state properties of the S=1/2 antiferromagnetic Heisenberg model on the Union Jack strip lattice by using the exact-diagonalization and density matrix renormalization group methods. We confirm a region of the intermediate-magnetization state between the Neel-like spin liquid state and the conventional ferrimagnetic state of Lieb-Mattis type. In the intermediate-state, we find that the spontaneous magnetization changes gradually with respect to the strength of the inner interaction. In addition, the local magnetization clearly shows an incommensurate modulation with long-distance periodicity in the intermediate-magnetization state. These characteristic behaviors lead to the conclusion that the intermediate-magnetization state is the non-Lieb-Mattis ferrimagnetic one. We also discuss the relationship between the ground-state properties of the S=1/2 antiferromagnetic Heisenberg model on the original Union Jack lattice and those on our strip lattice.

Ferrimagnetism of the Heisenberg model on the Kagome strip lattice

We study ground-state properties of the S = 1/2 Heisenberg model on the Kagome strip lattice by using exact-diagonalization and density matrix renormalization group methods. When the strength of magnetic frustration is tuned, we find from our numerical calculations that there exists an intermediate phase between the non-magnetic phase and the ferrimagnetic phase of the well-known Lieb-Mattis type and that the local magnetization shows an inocommensurate modulation with long-distance periodicity in the intermediate phase. Since the present model shares the same lattice structure in its inner part with the spatially anisotropic two-dimensional Kagome lattice in which an intermediate phase with a similar behavior is certainly observed, the intermediate phases of these models are the ferrimagnetic one of the unconventional non-Lieb-Mattis type.

Complex quantum dynamics in the integer quantum Hall regime.

The scattering matrix for potential scattering of planar electrons in a perpendicular magnetic field is required to understand normal and Hall conductivity off of the quantum Hall plateaus, at nonzero temperature and frequency, and fluctuations and nonlinear transport. Little, however, was previously known about it. We have developed a method to calculate amplitudes and phases for impurity scattering in the quantum Hall regime, by classically evolving appropriate Wigner distribution functions and projecting them onto quantum states. To check the reliability of this approximate calculation, we have also developed a numerical method that solves exactly the quantum scattering problem for an infinitely long strip lattice. We consider mainly nonadiabatic scattering, in which the potential variation is rapid or moderate. Quantum scattering is shown to exhibit sharp resonances, even from repulsive potentials. The results of the two approaches are compared and the relation between quantum and complex classical scattering is made apparent. The existence of classical periodic orbits is demonstrated for general potentials, and the relation between classical periodic orbits and quantum resonances and phase shifts is analyzed. The possibility that breakdown in the quantum Hall effect is due to inter-Landau-level tunneling caused by rapidly varying impurity potentials is investigated. The prediction for the critical Hall field improves on previous explanations by about two orders of magnitude and is in reasonable agreement with experimental results.

Smoothness of the integrated density of states on strips

Smoothness of the integrated density of states, k( E), of random Schrödinger operators, i.i.d. and non-i.i.d. cases, on a discrete strip lattice is investigated. It is proven that k( E) is C ∞ if only the potentials on the top surface of the strip have distributions with compactly supported densities in some fractional Sobolev space. The C ∞-result for the case of the Anderson model, i.e., all potentials having a distribution with compactly supported density in some Sobolev space, is also recovered.

Comparison and Discussion of Some Periodic Domain Structures

The energy density of seven periodic domain structures in sheets of uniaxial magnetic materials placed in a magnetic field Hz perpendicular to the sheet is calculated.1 The following periodic structures are considered: I. A hexagonal bubble lattice; within the cylinders the magnetization Ms is reversed with respect to Hz. II. The negative of I; within the cylinders, Ms and Hz have the same directions. III. A similar but square lattice of bubbles and its ``negative'' (IV). V. A honeycomb structure where the prisms are the reversed domains. VI. The negative of V. VII. A strip lattice. The energy density is minimized with respect to two variables. Comparing the structures I-VII it is found that: (1) In a large field region a hexagonal bubble lattice (I) has the lowest energy. At low fields, VII has the lowest energy. (2) The structures where the reversed domains are connected with each other (II, IV, VI) have a higher energy than their negatives (I, III, V). (3) The radius of a bubble in a hexagonal lattice (I) differs at the same magnetic field considerably from the radius of an isolated bubble. (4) The energy of the honeycomb structure V is always higher than the energy of structure I. Comparing VI and II this is not the case: at higher field, structure VI has a lower energy than structure II. (5) Comparing the fields at which for I, III, V, and VII the lattice distance becomes infinite, we found the lowest field for VII and the highest for I and III. The occurrence of the different structures will of course not only be determined by the energy difference between them but also by the number of nucleation points and the possible energy barriers. The occurrence of I in zero field seems to be possible since the lattice distance for I is almost the same at zero field as at the lowest field for which I have the lowest energy. If I can occur at low fields the same holds for II, since it can be formed from I by reversing Hz. For higher fields, II will go over into VI. At a field where the lattice distance of VI becomes infinite, an isolated interconnected reversed domain will appear. This can be a hollow cylindrical domain. Changing the field in such a way that the well-known transitions occur: ring→bubble→strip→strip lattice, a transition from I→VII via different structures has been described above. Such a transition was also found experimentally. Detailed calculations will be published elsewhere.1