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تسجيل مستخدم جديدGapless spin liquids on the three dimensional hyper-kagome lattice of Na$_4$Ir$_3$O$_8$
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Michael Lawler
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Recent experiments indicate that Na$_4$Ir$_3$O$_8$, a material in which s=1/2 iridium local moments form a three dimensional network of corner-sharing triangles, may have a quantum spin liquid ground state with gapless spin excitations. Using a combination of exact diagonalization, symmetry analysis of fermionic mean field ground states and Gutzwiller projected variational wavefunction studies, we propose a quantum spin liquid with spinon Fermi surfaces as a favorable candidate for the ground state of the Heisenberg model on the hyper-kagome lattice of Na$_4$Ir$_3$O$_8$. We present a renormalized mean field theory of the specific heat of this spin liquid and also discuss possible low temperature instabilities of the spinon Fermi surfaces.
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We report on the effects of introducing magnetic and non-magnetic disorder in the hyperkagome iridate quantum spin liquid (QSL) candidate Na$_4$Ir$_3$O$_8$ by partially replacing Ir$^{4+}$ ($S = 1/2$) with Ru$^{4+}$ ($S = 1$) or Ti$^{4+}$ ($S = 0$).
Specifically, we synthesized Na$_4$(Ir$_{1-x}$Ru$_x$)$_3$O$_8 (x = 0.05, 0.10, 0.2, 0.3)$ and Na$_4$Ir$_{2.7}$Ti$_{0.3}$O$_8$ samples and measured electrical transport, AC and DC magnetization, and heat capacity down to $T = 1.8$ K. Na$_4$Ir$_3$O$_8$ is associated with a large Weiss temperature $theta = -650$ K, a broad anomaly in magnetic heat capacity C$_{mag}$ at T $approx25$ K, low temperature power-law heat capacity, and spin glass freezing below $T_f approx 6$ K. We track the change in these characteristic features as Ir is partially substituted by Ru or Ti. We find that for Ru substitution, $theta$ increases and stays negative, the anomaly in C$_{mag}$ is suppressed in magnitude and pushed to lower temperatures, low temperature $C sim T^alpha$ with $alpha$ between $2$ and $3$ and decreasing towards $2$ with increasing $x$, and $T_f$ increases with increase in Ru concentration $x$. For Ti substitution we find that $theta$ and T$_f$ become smaller and the anomaly in $C_{mag}$ is completely suppressed. In addition, introducing non-magnetic Ti leads to the creation of orphan spins which show up in the low temperature magnetic susceptibility.
We develop high temperature series expansions for $ln{Z}$ and the uniform structure factor of the spin-half Heisenberg model on the hyperkagome lattice to order $beta^{16}$. These expansions are used to calculate the uniform susceptibility ($chi$), t
he entropy ($S$), and the heat capacity ($C$) of the model as a function of temperature. Series extrapolations of the expansions converge well down to a temperature of approximately $J/4$. A comparison with the experimental data for Na$_4$Ir$_3$O$_8$ shows that its magnetic susceptibility is reasonably well described by the model with an exchange constant $Japprox 300 K$, but there are also additional smaller terms present in the system. The specific heat of the model has two peaks. The lower temperature peak, which is just below our range of convergence contains about 40 percent of the total entropy. Despite being a 3-dimensional lattice, this model shares many features with the kagome lattice Heisenberg model and the material must be considered a strong candidate for a quantum spin-liquid.
We study the nearest neighbor $XXZ$ Heisenberg quantum antiferromagnet on the kagome lattice. Here we consider the effects of several perturbations: a) a chirality term, b) a Dzyaloshinski-Moriya term, and c) a ring-exchange type term on the bowties
of the kagome lattice, and inquire if they can suppport chiral spin liquids as ground states. The method used to study these Hamiltonians is a flux attachment transformation that maps the spins on the lattice to fermions coupled to a Chern-Simons gauge field on the kagome lattice. This transformation requires us to consistently define a Chern-Simons term on the kagome lattice. We find that the chirality term leads to a chiral spin liquid even in the absence of an uniform magnetic field, with an effective spin Hall conductance of $sxy = frac{1}{2}$ in the regime of $XY$ anisotropy. The Dzyaloshinkii-Moriya term also leads a similar chiral spin liquid but only when this term is not too strong. An external magnetic field also has the possibility of giving rise to additional plateaus which also behave like chiral spin liquids in the $XY$ regime. Finally, we consider the effects of a ring-exchange term and find that, provided its coupling constant is large enough, it may trigger a phase transition into a chiral spin liquid by the spontaneous breaking of time-reversal invariance.
We review recent density-matrix renormalization group (DMRG) studies of lightly doped quantum spin liquids (QSLs) on the kagome lattice. While a number of distinct conducting phases, including high-temperature superconductivity, have been theoretical
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