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Register a new userThermodynamics and spin mapping of quantum excitations in a Heisenberg spin heptamer
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Jason Haraldsen Ph.D
Publication date
2018
fields
Physics
and research's language is
English
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In this study, we examine the thermodynamics and spin dynamics of spin-1/2 and spin-3/2 heptamers. Through an exact diagonalization of the isotropic Heisenberg Hamiltonian, we find the closed-form, analytical representations for thermodynamic properties, spin excitations, and neutron scattering structure factors. Furthermore, we investigate the {cluster-like excitations of quantum spin heptamer} in the three-dimensional pyrochlore lattice material MgCr$_2$O$_4$. Using a spin mapping of the spin-1/2 heptamer excitations, the calculated structure factors of the spin-3/2 heptamer are be determined, which provides clarification for the spin excitations in MgCr$_2$O$_4$. Overall, this study demonstrates the ability to use the spin mapping of structure factors for small spin systems to analyze more complex structures.
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We report a comprehensive neutron scattering study on the spin excitations in the magnetic Weyl semimetal Co$_3$Sn$_2$S$_2$ with quasi-two-dimensional structure. Both in-plane and out-of-plane dispersions of the spin waves are revealed in the ferromagnetic state, similarly dispersive but damped spin excitations persist into the paramagnetic state. The effective exchange interactions have been estimated by a semi-classical Heisenberg model to consistently reproduce the experimental $T_C$ and spin stiffness. However, a full spin wave gap below $E_g=2.3$ meV is observed at $T=4$ K, much larger than the estimated magnetic anisotropy energy ($sim0.6$ meV), while its temperature dependence indicates a significant contribution from the Weyl fermions. These results suggest that Co$_3$Sn$_2$S$_2$ is a three-dimensional correlated system with large spin stiffness, and the low-energy spin dynamics could interplay with the topological electron states.
The $S$ = $frac{1}{2}$ kagome Heisenberg antiferromagnet (KHA) is a leading model hosting a quantum spin liquid (QSL), but the exact nature of its ground state remains a key issue under debate. In the previously well-studied candidate materials, magnetic defects always dominate the low-energy spectrum and hinder the detection of the intrinsic nature. We demonstrate that the new single crystal of YCu$_3$[OH(D)]$_{6.5}$Br$_{2.5}$ is a perfect KHA without evident magnetic defects ($ll$ 0.8%). Through fitting the magnetic susceptibilities of the orientated single crystals, we find the spin system with weak anisotropic interactions and with first-, second-, and third-neighbor couplings, $J_1$ $sim$ 56 K and $J_2$ $sim$ $J_3$ $sim$ 0.1$J_1$, belongs to the continuous family of fully frustrated KHAs. No conventional freezing is observed down to 0.36 K $sim$ 0.006$J_1$, and the raw specific heat exhibits a nearly quadratic temperature dependence below 1 K $sim$ 0.02$J_1$, well consistent with a gapless (spin gap $leq$ 0.025$J_1$) Dirac QSL.
We present a spin-rotation-invariant Green-function theory for the dynamic spin susceptibility in the spin-1/2 antiferromagnetic Heisenberg model on a stacked honeycomb lattice. Employing a generalized mean-field approximation for arbitrary temperatures, the thermodynamic quantities (two-spin correlation functions, internal energy, magnetic susceptibility, staggered magnetization, Neel temperature, correlation length) and the spin-excitation spectrum are calculated by solving a coupled system of self-consistency equations for the correlation functions. The temperature dependence of the magnetic (uniform static) susceptibility is ascribed to antiferromagnetic short-range order. The N{e}el temperature is calculated for arbitrary interlayer couplings. Our results are in a good agreement with numerical computations for finite clusters and with available experimental data on the beta-Cu2V2O2 compound.
Kagome antiferromagnets are known to be highly frustrated and degenerate when they possess simple, isotropic interactions. We consider the entire class of these magnets when their interactions are spatially anisotropic. We do so by identifying a certain class of systems whose degenerate ground states can be mapped onto the folding motions of a generalized spin origami two-dimensional mechanical sheet. Some such anisotropic spin systems, including Cs2ZrCu3F12, map onto flat origami sheets, possessing extensive degeneracy similar to isotropic systems. Others, such as Cs2CeCu3F12, can be mapped onto sheets with non-zero Gaussian curvature, leading to more mechanically stable corrugated surfaces. Remarkably, even such distortions do not always lift the entire degeneracy, instead permitting a large but sub-extensive space of zero-energy modes. We show that for Cs2CeCu3F12, due to an additional point group symmetry associated with structure, these modes are Dirac line nodes with a double degeneracy protected by a topological invariant. The existence of mechanical analogs thus serves to identify and explicate the robust degeneracy of the spin systems.
The dynamics of S=1/2 quantum spins on a 2D square lattice lie at the heart of the mystery of the cuprates cite{Hayden2004,Vignolle2007,Li2010,LeTacon2011,Coldea2001,Headings2010,Braicovich2010}. In bulk cuprates such as LCO{}, the presence of a weak interlayer coupling stabilizes 3D N{e}el order up to high temperatures. In a truly 2D system however, thermal spin fluctuations melt long range order at any finite temperature cite{Mermin1966}. Further, quantum spin fluctuations transfer magnetic spectral weight out of a well-defined magnon excitation into a magnetic continuum, the nature of which remains controversial cite{Sandvik2001,Ho2001,Christensen2007,Headings2010}. Here, we measure the spin response of emph{isolated one-unit-cell thick layers} of LCO{}. We show that coherent magnons persist even in a single layer of LCO{} despite the loss of magnetic order, with no evidence for resonating valence bond (RVB)-like spin correlations cite{Anderson1987,Hsu1990,Christensen2007}. Thus these excitations are well described by linear spin wave theory (LSWT). We also observe a high-energy magnetic continuum in the isotropic magnetic response. This high-energy continuum is not well described by 2 magnon LSWT, or indeed any existing theories.
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