The ordering of the Ising model on a pyrochlore lattice interacting via the long-range RKKY interaction, which models a metallic pyrochlore magnet such as Pr_2Ir_2O_7, is studied by Monte Carlo simulations. Depending on the parameter k_F representing the Fermi wavevector, the model exhibits rich ordering behaviors.
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.
The standard Metropolis algorithm and the parallel tempering method are used to examine magnetization processes in the Ising model with the long-range RKKY interaction on the Shastry-Sutherland lattice. It is shown that the Ising model with RKKY interaction exhibits, depending on the value of the Fermi wave vector $k_F$, the reach spectrum of magnetic solutions, which is manifested in the appearance of new magnetization plateaus on the magnetization curve. In particular, we have found the following set of individual magnetization plateaus with fractional magnetization $m/m_s$=1/18, 1/9, 1/8, 1…
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…
We use Monte Carlo simulations to evaluate the feasibility of detecting thermal order by disorder in real antiferromagnetic Ising pyrochlores, frustrated by a magnetic field applied in the $[110]$ direction. Building on an ideal system with only nearest-neighbour exchange interactions and a perfectly oriented field, we consider the effects of dipolar interactions and field misalignment. Our approach is special in that it relies more in the possibility to switch on and off the entropic drive towards order than in the absence of (or immunity to) a particular perturbation. It can then be applied,…
A phase transition of a model compound of the long-range Ising spin glass (SG) Dy$_{x}$Y$_{1-x}$Ru$_{2}$Si$_{2}$, where spins interact via the RKKY interaction, has been investigated. The static and the dynamic scaling analyses reveal that the SG phase transition in the model magnet belongs to the mean-field universality class. Moreover, the characteristic relaxation time in finite magnetic fields exhibits a critical divergent behavior as well as in zero field, indicating a stability of the SG phase in finite fields. The presence of the SG phase transition in field in the model magnet strongly…
Ising pyrochlore magnets: Low temperature properties, ice rules and beyond
烧绿石磁铁是自旋冰行为的候选者。我们提出了相关的烧绿石家族R2 Ti 2 O 7（R=稀土）的理论模拟支持选定的系统上的磁热测量。通过考虑长程偶极-偶极以及短程超交换相互作用，我们得到了三种不同的行为：（i）有序的双简并态，（ii）高度无序的状态与广泛的过渡到顺磁性，（iii）部分有序的状态与急剧过渡到顺磁性。因此，这些相互竞争的相互作用可以引起与传统的“自旋冰”非常不同的行为。在实际化合物中可以看到密切对应的行为-特别是Ho 2 Ti 2 O 7对应于以前没有讨论过的情况（iii），而不是前面建议的情况（ii）。
Ising models on a pyrochlore oxide lattice are usually associated with spin ice materials and "magnetic monopoles". Ever more often effects connecting magnetic and elastic degrees of freedom are reported on these and other related frustrated materials. Here we extend a spin-ice Hamiltonian to include coupling between spins and the O$^{-2}$ ions mediating superexchange; we call it the Magnetoelastic Spin Ice model (MeSI). There has been a long search for a model in which monopoles would spontaneously become the building blocks of new ground-states: the MeSI Hamiltonian is such a model. In spite…
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…
Comment on `Ising Pyrochlore Magnets: Low Temperature Properties, ``Ice Rules,'' and Beyond' by R. Siddharthan et al., Phys. Rev. Lett. 83, 1854 (1999)
在这篇评论中，我们认为Ho $_2$ Ti $_2$ O $_7$没有表现出向部分有序态的转变，这与PRL 83，1854（1999）中所讨论的不同，它表现出自旋冰行为，Siddharthan等人的实验比热数据可以用“偶极自旋冰”来解释。模型包括一个预期的贡献从核何自旋适当的长程治疗的偶极-偶极相互作用。
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…
We study magnetism in simple models for rare earth quasicrystals by means of a two-step theoretical approach. First, we compute RKKY interactions from a tight-binding Hamiltonian defined on a two-dimensional quasiperiodic tiling. Second, we examine the statistical mechanics of Ising spins coupled via these interactions using Monte Carlo simulations. We find the emergence of strongly coupled spin clusters with significantly weaker inter-cluster coupling, and a transition to a low-temperature phase that has long-range order evidenced by a finite domain wall tension.
We perform the high-performance computation of the ferromagnetic Ising model on the pyrochlore lattice. We determine the critical temperature accurately based on the finite-size scaling of the Binder ratio. Comparing with the data on the simple cubic lattice, we argue the universal finite-size scaling. We also calculate the classical XY model and the classical Heisenberg model on the pyrochlore lattice.
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+。
From a microscopic model for the pyrochlore antiferromagnet Tb2Sn2O7, including the crystal field Hamiltonian and interactions between the angular momenta, we compute an effective pseudospin-1/2 Hamiltonian Heff$ that incorporates perturbatively in the effective interactions the effect of excited crystal field levels. We obtain the semiclassical ground states of Heff and find a region of parameter space with a two-in/two-out spin ice configuration on each tetrahedron with ordering wavevector q=0 and with spins canted away from the local Ising axes as found in Tb2Sn2O7. This ground state can al…
We demonstrate the appearance of thermal order by disorder in Ising pyrochlores with staggered antiferromagnetic order frustrated by an applied magnetic field. We use a mean-field cluster variational method, a low-temperature expansion and Monte Carlo simulations to characterise the order-by-disorder transition. By direct evaluation of the density of states we quantitatively show how a symmetry-broken state is selected by thermal excitations. We discuss the relevance of our results to experiments in $2d$ and $3d$ samples, and evaluate how anomalous finite-size effects could be exploited to det…
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…
An effective Ising model for the spin-ice type Kondo lattice model is investigated by the classical Monte Carlo simulation. We clarify the magnetic phase diagram with four phases: ice-ferro, ice-(0,0,2π), 32-sublattice, and all-in/all-out ordered states. The result well reproduces the phase diagram of the Kondo lattice model studied previously [H. Ishizuka et al.: J. Phys. Soc. Jpn. 81 (2012) 113706], which suggests that the RKKY interactions up to third neighbors are sufficient to describe the magnetic properties of the itinerant electron model. We discuss the peculiar nature of phase transit…
We study diluted antiferromagnetic Ising models on triangular and kagome lattices in a magnetic field, using the replica-exchange Monte Carlo method. We observe seven and five plateaus in the magnetization curve of the diluted antiferromagnetic Ising model on the triangular and kagome lattices, respectively, when a magnetic field is applied. These observations contrast with the two plateaus observed in the pure model. The origin of multiple plateaus is investigated by considering the spin configuration of triangles in the diluted models. We compare these results with those of a diluted antifer…
We have investigated a phase transition of a long-range RKKY Ising spin glass \dyyrusi by means of the dc and the ac magnetization measurements. The static nonlinear susceptibility $χ_{2}$ exhibits a divergent behavior toward $\Tg$ $=$ 1.925 K with the exponent of $γ$ $=$ 1.08. The characteristic relaxation time $τ$ obtained from the ac magnetization measurements also diverges to the same $\Tg$ with the exponent of $zν$ $=$ 1.9 in zero static field . These results indicate the spin glass phase transition belonging to the mean-field universality class, in which the exponents of $\gammaMF$ and $…
Ill-Behaved Convergence of a Model of the Gd3Ga5O12 Garnet Antiferromagnet with Truncated Magnetic Dipole-Dipole Interactions
以前的研究已经发现，计算认为远程磁偶极相互作用截断在一个有限的截止距离Rc预测假的（非物理的）远程有序相伊辛和海森堡系统的烧绿石晶格。在本文中，我们表明，类似于这两种情况下，使用截断偶极相互作用模型的Gd 3Ga 5 O 12石榴石反铁磁体的计算也预测非物理相位与无公度有序波矢量q_ord是非常敏感的偶极截止距离Rc。
