I consider the class of "depleted pyrochlore" lattices of corner-sharing triangles, made by removing spins from a pyrochlore lattice such that every tetrahedron loses exactly one. Previously known examples are the "hyperkagome" and "kagome staircase". I give criteria in terms of loops for whether a given depleted lattice can order analogous to the kagome \sqrt{3} \times \sqrt{three} state, and also show how the pseudo-dipolar correlations (due to local constraints) generalize to even the random depleted case.
We numerically compute the temperature dependence of spin structure factor and thermodynamic quantities in the antiferromagnetic quantum Ising model in the pyrochlore lattice. This model exhibits spin disorder ground state with exponentially-decayed spin correlation. We reproduce the temperature dependence of the pinch point structure in the neutron scattering experiment and correct entropy obtained from the measurement of the specific heat.
We study corrections to single tetrahedron based approximations for the entropy, specific heat and uniform susceptibility of the pyrochlore lattice Ising antiferromagnet, by a Numerical Linked Cluster (NLC) expansion. In a tetrahedron based NLC, the first order gives the Pauling residual entropy of ${1\over 2}\log{3\over 2}\approx 0.20273$. A 16-th order NLC calculation changes the residual entropy to 0.205507 a correction of 1.37 percent over the Pauling value. At high temperatures, the accuracy of the calculations is verified by a high temperature series expansion. We find the corrections to…
For Ising spin models which bear the spin-ice type macroscopic (quasi-)degeneracy, conventional classical Monte Carlo (MC) simulation using single spin flips suffers from dynamical freezing at low temperatures ($T$). A similar difficulty is seen also in a family of Heisenberg spin models with easy-axis anisotropy or biquadratic interactions. In the Ising case, the difficulty is avoided by introducing a non-local update based on the loop algorithm. We present an extension of the loop algorithm to the Heisenberg case. As an example of its application, we review our recent study on spin-glass (SG…
We investigate the properties of the XY pyrochlore antiferromagnet with local <111> planar anisotropy. We find the ground states and show that the configurational ground state entropy is subextensive. By computing the free energy due to harmonic fluctuations and by carrying out Monte Carlo simulations, we confirm earlier work indicating that the model exhibits thermal order-by-disorder leading to low temperature long-range order consisting of discrete magnetic domains. We compute the spin wave spectrum and show that thermal and quantum fluctuations select the same magnetic structure. Using Mon…
The glassy behavior observed in the pyrochlore magnet Y2Mo2O7, where the magnetic Mo^{4+} ions interact predominantly via isotropic nearest neighbor antiferromagnetic exchange, possibly with additional weak disorder, is a distinct class of spin glass systems where frustration is mostly geometrical. A model proposed to describe such a spin glass behavior is the Heisenberg model on a pyrochlore lattice with random but strictly antiferromagnetic exchange disorder. In this paper, we provide compelling numerical evidence from extensive Monte Carlo simulations which show that the model exhibits a fi…
Effects of local lattice distortions on the spin ordering are investigated for the antiferromagnetic classical Heisenberg model on the pyrochlore lattice. It is found by Monte Carlo simulations that the spin-lattice coupling (SLC) originating from site phonons induces a first-order transition into two different types of collinear magnetic ordered states. The state realized at stronger SLC is cubic symmetric characterized by the magnetic (1/2,1/2,1/2) Bragg peaks, while that at weaker SLC is tetragonal symmetric characterized by the (1,1,0) ones, each accompanied by the commensurate local latti…
Effect of structural disorder is investigated for an $XY$ pyrochlore antiferromagnet with continuous degeneracy of classical ground states. Two types of disorder, vacancies and weakly fluctuating exchange bonds, lift degeneracy selecting the same subset of classical ground states. Analytic and numerical results demonstrate that such an "order by structural disorder" mechanism competes with the effect of thermal and quantum fluctuations. Our theory predicts that a small amount of nonmagnetic impurities in $\rm{Er_2Ti_2O_7}$ will stabilize the coplanar $ψ_3$ ($m_{x^2-y^2}$) magnetic structure as…
Using $\rm Er_2Ti_2O_7$ as a motivation, we investigate finite-field properties of $XY$ pyrochlore antiferromagnets. In addition to a fluctuation-induced six-fold anisotropy present in zero field, an external magnetic field induces a combination of two-, three-, and six-fold clock terms as a function of its orientation providing for a rich and controllable magnetothermodynamics. For $\rm Er_2Ti_2O_7$, we predict a new phase transition for ${\bf H}\parallel [001]$. Re-entrant transitions are also found for ${\bf H}\parallel [111]$. We extend these results to the whole family the $XY$ pyrochlore…
Theory of Two-Step Magnetic Ordering Phenomena in a Geometrically Frustrated Heisenberg Pyrochlore Antiferromagnet with Long Range Dipolar Interactions
利用平均场论研究了具有交换作用和偶极-偶极相互作用的烧绿石晶格上的海森堡反铁磁体模型。在处理偶极通过使用埃瓦尔德方法，一个软（临界）模式与一个独特的有序波矢量被选择为所有强度的偶极偶极耦合。对于弱偶极子，选择部分有序的三个子晶格自旋结构（P态），其中q_{ord} =（1/2 1/2 1/2）。一个完全有序的四个子晶格自旋结构（F态），q =（000），与P态竞争，并随着温度的降低而成为稳定的结构。我们的结果进行了比较，对其他的理论计算和连接到最近的实验结果Gd 2 Ti 2 O 7进行了讨论。
We investigate the nature of phase transitions induced by Dzyaloshinskii-Moriya (DM) interactions on a classical pyrochlore antiferromagnet. For both symmetry-allowed antisymmetric exchange interactions, the macroscopic degeneracy due to geometrical frustration is relieved and a long-range magnetic order appears in the ground state. We find an Ising-like phase transition in the case of direct DM interaction which selects a doubly degenerate all-in all-out magnetic order. In the presence of indirect DM coupling, the magnet undergoes an XY-like phase transition into a state with broken Z6 symmet…
We study the pyrochlore Heisenberg antiferromagnet with additional positive biquadratic interaction in the semiclassical limit. The classical ground state manifold of the model contains an extensively large family of non-coplanar spin states known as "color ice states". Starting from a color ice state, a subset of spins may rotate collectively at no energy cost. Such excitation may be viewed in this three-dimensional system as a "membrane-like" analog of the well-known weathervane modes in the classical kagome Heisenberg antiferromagnet. We investigate the weathervane modes in detail and eluci…
The classical bilinear-biquadratic nearest-neighbor Heisenberg antiferromagnet on the pyrochlore lattice does not exhibit conventional Neel-type magnetic order at any temperature or magnetic field. Instead spin correlations decay algebraically over length scales r ~ \sqrt{T}, behavior characteristic of a Coulomb phase arising from a strong local constraint. Despite this, its thermodynamic properties remain largely unchanged if Neel order is restored by the addition of a degeneracy-lifting perturbation, e.g., further neighbor interactions. Here we show how these apparent contradictions can be r…
The hedgehog lattice, a three-dimensional periodic array of magnetic monopoles and antimonopoles, is known to be realized in the presence of the Dzyaloshinskii-Moriya (DM) interaction. Here, we demonstrate by means of Monte Carlo simulations that the hedgehog lattice is induced by not the DM interaction but frustration in classical Heisenberg antiferromagnets on the breathing pyrochlore lattice. In the model, the breathing bond-alternation is characterized by the ratio of the nearest-neighbor (NN) antiferromagnetic exchange interaction for large tetrahedra to that for small ones, J1'/J1. A qua…
The ordering of the classical Heisenberg model on the pyrochlore lattice with the antiferromagnetic nearest-neighbor interaction J1 and the ferromagnetic next-nearest-neighbour interaction J2 is investigated by means of a mean-field analysis and a Monte Carlo simulation. For a moderate J2/J1-value, the model exhibits a first-order transition into an incommensurate multiple-q ordered state where multiple Bragg peaks coexist in the spin structure factor. We show that there are two types of metastable multiple-q states, a cubic symmetric sextuple-q state and a non-cubic symmetric quadruple-q stat…
We study Ising pyrochlores by means of Monte Carlo simulations. We cover a set of exchange constants ranging from the frustrated ferromagnetic case (spin-ice) to the fully-ordered "all-in--all-out" antiferromagnet in the dipolar model, reinterpreting the results --as in an ionic system-- in terms of a temperature vs. magnetic charge density phase diagram. In spite of its spin nature and the presence of both double and single non-conserved magnetic charges, the dipolar model gives place to a phase diagram which is quite comparable with those previously obtained for on-lattice systems of electri…
Theory of paramagnetic scattering in highly frustrated magnets with long-range dipole-dipole interactions: The case of the Tb2Ti2O7, pyrochlore antiferromagnet
由稀土磁矩组成的高阻挫反铁磁体是目前实验和理论研究的热点。稀土离子通常具有小的交换相互作用和大的磁矩。这使得有必要详细了解长程磁偶极-偶极相互作用在这些系统中的作用，特别是在顺磁相中发展的自旋-自旋相关性的背景下，但通常无法凝聚成常规的长程磁有序相。这种情况在受抑烧绿石反铁磁体材料Tb 2 Ti 2 O 7中得到最显著的强调，尽管反铁磁居里-外斯温度Tcw ~ -20 K，但Tb 2 Ti 2 O 7在低至50 mK时不有序。在本文中，我们报告的结果从平均场论计算的顺磁弹性中子散射的高度挫折的磁系统与长程偶极-偶极相互作用，重点是Tb 2 Ti 207系统。将Tb_2Ti_2O_7模拟为反铁磁<111>Ising烧绿石，发现平均场顺磁散射与实验观测结果不一致.通过简单的对称性参数，我们表明，所观察到的Tb 2 Ti 207中的顺磁相关被排除由任何自旋哈密顿量，认为只有伊辛自旋，但定性一致的海森堡矩。明确计算的顺磁散射模式的<111>伊辛和海森堡模型，其中包括有限的单离子各向异性，支持这些主张。我们提供的建议，调和需要恢复自旋各向同性与伊辛样结构所建议的单离子性质的Tb 3+。
Several rare earth magnetic pyrochlore materials are well modeled by a spin-1/2 quantum Hamiltonian with anisotropic exchange parameters Js. For the Er2Ti2O7 material, the Js were recently determined from high-field inelastic neutron scattering measurements. Here, we perform high-temperature (T) series expansions to compute the thermodynamic properties of this material using these Js. Comparison with experimental data show that the model describes the material very well including the finite temperature phase transition to an ordered phase at Tc~1.2 K. We show that high temperature expansions g…
Low temperature specific heat and possible gap to magnetic excitations in the Heisenberg pyrochlore antiferromagnet Gd2Sn207
Gd_2Sn_2O_7烧绿石海森堡反铁磁体在1 K附近出现了向四个亚晶格Neel有序态的相变。尽管有序状态的表面上是传统的性质，但比热在350-800 mK的温度范围内被发现由反常的T平方幂定律描述。另一种烧绿石海森堡材料Gd 2 Ti 2 O 7也有类似的温度依赖性。Cv中这种反常的T平方行为被认为与态密度的不寻常的能量依赖性有关，这种不寻常的能量依赖性似乎也表现在μ子自旋弛豫实验中发现的低温自旋涨落中。在本文中，我们报告的Cv的计算，考虑自旋波一样的激发的Neel秩序中观察到的Gd 2Sn 2 O 7，并认为参数的T平方行为并不反映真正的低能量激发的Gd 2Sn 2 O 7。相反，我们发现这种材料的低能量激发是由单离子和偶极各向异性效应间隙的反铁磁振子，并且在先前的比热测量中考虑的350 mK的最低温度偶然地与交叉温度相一致，低于该交叉温度，磁振子变得热激活，Cv呈指数形式。我们认为，进一步的比热测量，延伸到至少100 mK是必需的，以归因于一个非常规的描述磁激发的基态的Gd 2 Sn 2 O 7或无效的标准图片的间隙激发本文提出的。
We theoretically investigate effects of lattice distortions on the spin ordering of classical Heisenberg antiferromagnets on the breathing pyrochlore lattice. In the model, local lattice distortions originating from the site vibration are taken into account to yield effective spin interactions via the spin-lattice coupling (SLC). The breathing lattice-alternation is characterized by the ratio of the nearest-neighbor interaction for large tetrahedra to that for small ones, J'/J. It is found by Monte Carlo simulations that the system exhibits a first-order transition into four different types of…
We theoretically investigate a $J_1$-$J_3$ classical Heisenberg model on the breathing pyrochlore lattice, where the nearest-neighbor (NN) exchange interactions for small and large tetrahedra, $J_1$ and $J_1'$, take different values due to the breathing bond-alternation and $J_3$ is the third NN antiferromagnetic interaction along the bond direction. It is found by means of Monte Carlo simulations that for large $J_3$, a hedgehog lattice, a three-dimensional periodic array of magnetic monopoles and antimonopoles, emerges in the form of a quadruple-${\bf Q}$ state characterized by the ordering …
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}, 202-204 (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, th…
