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Register a new userSpin dynamics and magnetic correlation length in two-dimensional quantum Heisenberg antiferromagnets
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The correlated spin dynamics and the temperature dependence of the correlation length $xi(T)$ in two-dimensional quantum ($S=1/2$) Heisenberg antiferromagnets (2DQHAF) on square lattice are discussed in the light of experimental results of proton spin lattice relaxation in copper formiate tetradeuterate (CFTD). In this compound the exchange constant is much smaller than the one in recently studied 2DQHAF, such as La$_2$CuO$_4$ and Sr$_2$CuO$_2$Cl$_2$. Thus the spin dynamics can be probed in detail over a wider temperature range. The NMR relaxation rates turn out in excellent agreement with a theoretical mode-coupling calculation. The deduced temperature behavior of $xi(T)$ is in agreement with high-temperature expansions, quantum Monte Carlo simulations and the pure quantum self-consistent harmonic approximation. Contrary to the predictions of the theories based on the Non-Linear $sigma$ Model, no evidence of crossover between different quantum regimes is observed.
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Counterintuitive order-disorder phenomena emerging in antiferromagnetically coupled spin systems have been reported in various studies. Here we perform a systematic effective field theory analysis of two-dimensional bipartite quantum Heisenberg antiferromagnets subjected to either mutually aligned -- or mutually orthogonal -- magnetic and staggered fields. Remarkably, in the aligned configuration, the finite-temperature uniform magnetization $M_T$ grows as temperature rises. Even more intriguing, in the orthogonal configuration, $M_T$ first drops, goes through a minimum, and then increases as temperature rises. Unmasking the effect of the magnetic field, we furthermore demonstrate that the finite-temperature staggered magnetization $M^H_s$ and entropy density -- both exhibiting non-monotonic temperature dependence -- are correlated. Interestingly, in the orthogonal case, $M^H_s$ presents a maximum, whereas in mutually aligned magnetic and staggered fields, $M^H_s$ goes through a minimum. The different behavior can be traced back to the existence of an easy XY-plane that is induced by the magnetic field in the orthogonal configuration.
A perturbation spin-wave theory for the quantum Heisenberg antiferromagnets on a square lattice is proposed to calculate the uniform static magnetic susceptibility at finite temperatures, where a divergence in the previous theories due to an artificial phase transition has been removed. To the zeroth order, the main features of the uniform static susceptibility are produced: a linear temperature dependence at low temperatures and a smooth crossover in the intermediate range and the Curie law at high temperatures. When the leading corrections from the spin-wave interactions are included, the resulting spin susceptibility in the full temperature range is in agreement with the numerical quantum Monte Carlo simulations and high-temperature series expansions.
Pulsed-field magnetization experiments (fields $B$ of up to 85 T and temperatures $T$ down to 0.4 K) are reported on nine organic Cu-based two-dimensional (2D) Heisenberg magnets. All compounds show a low-$T$ magnetization that is concave as a function of $B$, with a sharp ``elbow transition to a constant value at a field $B_{rm c}$. Monte-Carlo simulations including a finite interlayer exchange energy $J_{perp}$ quantitatively reproduce the data; the concavity indicates the effective dimensionality and $B_{rm c}$ is an accurate measure of the in-plane exchange energy $J$. Using these values and Neel temperatures measured by muon-spin rotation, it is also possible to obtain a quantitative estimate of $|J_{perp}/J|$. In the light of these results, it is suggested that in magnets of the form [Cu(HF$_2$)(pyz)$_2$]X, where X is an anion, the sizes of $J$ and $J_{perp}$ are controlled by the tilting of the pyrazine (pyz) molecule with respect to the 2D planes.
By means of nuclear spin-lattice relaxation rate 1/T1, we follow the spin dynamics as a function of the applied magnetic field in two gapped one-dimensional quantum antiferromagnets: the anisotropic spin-chain system NiCl2-4SC(NH2)2 and the spin-ladder system (C5H12N)2CuBr4. In both systems, spin excitations are confirmed to evolve from magnons in the gapped state to spinons in the gapples Tomonaga-Luttinger-liquid state. In between, 1/T1 exhibits a pronounced, continuous variation, which is shown to scale in accordance with quantum criticality. We extract the critical exponent for 1/T1, compare it to the theory, and show that this behavior is identical in both studied systems, thus demonstrating the universality of quantum critical behavior.
Every singlet state of a quantum spin 1/2 system can be decomposed into a linear combination of valence bond basis states. The range of valence bonds within this linear combination as well as the correlations between them can reveal the nature of the singlet state, and are key ingredients in variational calculations. In this work, we study the bipartite valence bond distributions and their correlations within the ground state of the Heisenberg antiferromagnet on bipartite lattices. In terms of field theory, this problem can be mapped to correlation functions near a boundary. In dimension d >= 2, a non-linear sigma model analysis reveals that at long distances the probability distribution P(r) of valence bond lengths decays as |r|^(-d-1) and that valence bonds are uncorrelated. By a bosonization analysis, we also obtain P(r) proportional to |r|^(-d-1) in d=1 despite the different mechanism. On the other hand, we find that correlations between valence bonds are important even at large distances in d=1, in stark contrast to d >= 2. The analytical results are confirmed by high-precision quantum Monte Carlo simulations in d=1, 2, and 3. We develop a single-projection loop variant of the valence bond projection algorithm, which is well-designed to compute valence bond probabilities and for which we provide algorithmic details.
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