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تسجيل مستخدم جديدThermodynamics of the pyrochlore Heisenberg ferromagnet with arbitrary spin $S$
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We use the rotation-invariant Greens function method (RGM) and the high-temperature expansion (HTE) to study the thermodynamic properties of the spin-$S$ Heisenberg ferromagnet on the pyrochlore lattice. We examine the excitation spectra as well as various thermodynamic quantities, such as the order parameter (magnetization), the uniform static susceptibility, the correlation length, the spin-spin correlations, and the specific heat, as well as the static and dynamic structure factors. We discuss the influence of the spin quantum number $S$ on the temperature dependence of these quantities. We compare our results for the pyrochlore ferromagnet with the corresponding ones for the simple-cubic lattice both having the same coordination number $z=6$. We find a significant suppression of magnetic ordering for the pyrochlore lattice due to its geometry with corner-sharing tetrahedra.
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The thermodynamic properties (magnetization, magnetic susceptibility, transverse and longitudinal correlation lengths, specific heat) of one- and two-dimensional ferromagnets with arbitrary spin S in a magnetic field are investigated by a second-orde
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We use the rotation-invariant Greens function method (RGM) and the high-temperature expansion (HTE) to study the thermodynamic properties of the Heisenberg antiferromagnet on the pyrochlore lattice. We discuss the excitation spectra as well as variou
s thermodynamic quantities, such as spin correlations, uniform susceptibility, specific heat and static and dynamical structure factors. For the ground state we present RGM data for arbitrary spin quantum numbers $S$. At finite temperatures we focus on the extreme quantum cases $S=1/2$ and $S=1$. We do not find indications for magnetic long-range order for any value of $S$. We discuss the width of the pinch point in the static structure factor in dependence on temperature and spin quantum number. We compare our data with experimental results for the pyrochlore compound NaCaNi$_2$F$_7$ ($S=1$). Thus, our results for the dynamical structure factor agree well with the experimentally observed features at 3 ldots 8~meV for NaCaNi$_2$F$_7$. We analyze the static structure factor ${S}_{bf q}$ to find regions of maximal ${S}_{bf q}$. The high-temperature series of the ${S}_{bf q}$ provide a fingerprint of weak {it order by disorder} selection of a collinear spin structure, where (classically) the total spin vanishes on each tetrahedron and neighboring tetrahedra are dephased by $pi$.
The spin-half pyrochlore Heisenberg antiferromagnet (PHAF) is one of the most challenging problems in the field of highly frustrated quantum magnetism. Stimulated by the seminal paper of M.~Planck [M.~Planck, Verhandl. Dtsch. phys. Ges. {bf 2}, 202-2
04 (1900)] we calculate thermodynamic properties of this model by interpolating between the low- and high-temperature behavior. For that we follow ideas developed in detail by B.~Bernu and G.~Misguich and use for the interpolation the entropy exploiting sum rules [the ``entropy method (EM)]. We complement the EM results for the specific heat, the entropy, and the susceptibility by corresponding results obtained by the finite-temperature Lanczos method (FTLM) for a finite lattice of $N=32$ sites as well as by the high-temperature expansion (HTE) data. We find that due to pronounced finite-size effects the FTLM data for $N=32$ are not representative for the infinite system below $T approx 0.7$. A similar restriction to $T gtrsim 0.7$ holds for the HTE designed for the infinite PHAF. By contrast, the EM provides reliable data for the whole temperature region for the infinite PHAF. We find evidence for a gapless spectrum leading to a power-law behavior of the specific heat at low $T$ and for a single maximum in $c(T)$ at $Tapprox 0.25$. For the susceptibility $chi(T)$ we find indications of a monotonous increase of $chi$ upon decreasing of $T$ reaching $chi_0 approx 0.1$ at $T=0$. Moreover, the EM allows to estimate the ground-state energy to $e_0approx -0.52$.
We consider the pyrochlore-lattice quantum Heisenberg ferromagnet and discuss the properties of this spin model at arbitrary temperatures. To this end, we use the Greens function technique within the random-phase (or Tyablikov) approximation as well
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