We investigate the metal-insulator transition (MIT) of the osmium pyrochlore oxide Cd2Os2O7 through transport and magnetization measurements. The MIT and a magnetic transition to the all-in/all-out (AIAO) order occur simultaneously at 227 K. We propose a mechanism based on a Lifshitz transition induced by the AIAO magnetic order probably via strong spin-orbit couplings in the specific semimetallic band structure. It is suggested, moreover, that two observed puzzles, a finite conductivity near T = 0 and an emergence of weak ferromagnetic moments, are not bulk properties but originate at magnetic domain walls between two kinds of AIAO domains.
We investigate the ultrafast dynamics of Cd$_2$Os$_2$O$_7$, a prototype material showing a Lifshitz-type transition as a function of temperature. In the paramagnetic metallic state, the photo-reflectivity shows a sub-picosecond relaxation, followed by a featureless small offset. In the antiferromagnetic state slightly below $T_N$, however, the photo-reflectivity resurges over hundreds of picoseconds, which goes beyond the usual realm of the effective-temperature model. Our observations are consistent with the Lifshitz phase transition of Cd$_2$Os$_2$O$_7$ driven by the evolution of the local m…
The pyrochlore oxides $A_2B_2$O$_7$ exhibit a complex interplay between geometrical frustration, electronic correlations, and spin-orbit coupling, due to the lattice structure and active charge, spin, and orbital degrees of freedom. Understanding the properties of these materials is a theoretical chalenge, because their intricate nature depends on material-specific details and quantum many-body effects. Here we review our recent studies based on first-principles calculations and quantum many-body theories for 4$d$ and 5$d$ pyrochlore oxides with $B$=Mo, Os, and Ir. In these studies, the spin-o…
Spontaneous symmetry breakings, metal-insulator transitions, and transport properties of magnetic-domain-wall states in pyrochlore iridium oxides are studied by employing a symmetry adapted effective hamiltonian with a slab perpendicular to the (111) direction of the pyrochlore lattice. Emergent metallic domain wall, which has unconventional topological nature with a controllable and mobile metallic layer, is shown to host Fermi surfaces with modulated helical spin textures resembling Rashba metals. The helical nature of the domain-wall Fermi surfaces is experimentally detectable by anomalous …
Motivated by recent observation of a new high field phase near saturation in chromium spinels $A$Cr$_2$O$_4$ ($A=$ Zn, Cd, Hg), we study the $S = 3/2$ pyrochlore Heisenberg antiferromagnet with biquadratic interactions. Magnon instability analysis at the saturation field reveals that a very small biquadratic interaction can induce magnon pairing in pyrochlore antiferromagnets, which leads to the emergence of a ferro-quadrupolar phase, or equivalently a spin nematic phase, below the saturation field. We present the magnetic phase diagram in an applied field, studying both $S=3/2$ and $S=1$ spin…
The superconducting pyrochlore oxide Cd2Re2O7 (Tc = 1 K), which is now considered as a candidate of the spin-orbit-coupled metal, shows an inversion-symmetry-breaking structural transition at Ts1 = 200 K. Ts1 decreases with increasing pressure and disappears at around Pc = 4:2GPa, where at least four high-pressure phases with tiny structural distortions are suggested by means of powder X-ray diffraction [Yamaura PRB 2017]. We have carried out Raman scattering experiments to investigate changes in the crystal symmetry under high pressures up to 4.8 GPa. A structural transition at 1.9-3.0 GPa an…
Semimetallic osmium pyrochlore oxide Cd2Os2O7 undergoes a magnetic transition to an all-in-all-out (AIAO)-type order at 227 K, followed by a crossover to an AIAO insulator at around 210 K. Here, we studied the isostructural and isoelectronic compound Hg2Os2O7 through thermodynamic measurements, muSR spectroscopy and neutron diffraction experiments. A similar magnetic transition, probably to an AIAO-type order, was observed at 88 K, while the resistivity showed a decrease at the transition and remained metallic down to 2 K. Thus, the ground state of Hg2Os2O7 is most likely an AIAO semimetal, wh…
In frustrated systems, some or many states are competed due to frustration of exchange interactions, and this competition often results in exotic states, such as spin liquid and chiral orders. We consider a pyrochlore oxide, a three-dimensional frustrated system, and study its $S=\frac{1}{2}$ effective model, consisting of the Heisenberg-type and Dzyaloshinsky-Moriya-type superexchange interactions between the nearest-neighbor transition-metal ions. We show that by using new multiorbital effects of the $t_{2g}$ orbitals on coefficients of those interactions, we can change the effective dimensi…
Topological phases in layered pyrochlore oxide thin films along the [111] direction
本文从理论上研究了烧绿石氧化物A $_2$ B $_2$ O $_7$的多带哈伯德模型，其中B是具有强自旋轨道耦合的重过渡金属离子，在沿[111]方向取向的薄膜几何结构中.沿着这个方向，烧绿石晶格由B离子的交替的kagome和三角形晶格平面组成。我们考虑一个单一的可果美层，双层，和两个不同的三层。作为一个函数的自旋-轨道耦合，直接和间接的$d$ -轨道跳跃，和频带填充的强度，我们确定了一些情况下，一个非相互作用的时间反演不变的Z $_2$拓扑相位是预期的，我们建议一些候选材料。我们在Hatree-Fock理论下研究了半填充$d$壳层中的相互作用，并确定了可以找到零磁场Chern绝缘体的参数区域，其中Chern数为$\pm1$.最有希望的拓扑相的几何结构似乎是既支持Z $_2$拓扑绝缘体又支持Chern绝缘体的双层结构，以及三角形-kagome-三角形三层，其支持相对稳健的Chern绝缘体相。
Magnetism of ruthernium pyrochlore oxides A2Ru2O7 (A = Hg, Cd, Ca), whose electronic properties within a localized ion picture are characterized by non-degenerate t2g orbitals (Ru5+, 4d3) and thereby subject to geometrical frustration, has been investigated by muon spin rotation/relaxation (muSR) technique. The A cation (mostly divalent) was varied to examine the effect of covalency (Hg > Cd > Ca) on their electronic property. In a sample with A = Hg that exhibits a clear metal-insulator (MI) transition below >> 100 K (which is associated with a weak structural transition), a nearly commensura…
Pyrochlore lattices, which are found in two important classes of materials -- the $A_2B_2X_7$ pyrochlore family and the $AB_2X_4$ spinel family -- are the quintessential 3-dimensional frustrated lattice architecture. While historically oxides ($X =$~O) have played the starring role in this field, the past decade has seen materials synthesis breakthroughs that have lead to the emergence of fluoride ($X =$~F) and chalcogenide ($X =$~S, Se) pyrochlore lattice materials. In this Research Update, we summarize recent progress in understanding the magnetically frustrated ground states in three famili…
Breathing Pyrochlore Lattice Realized in A-Site Ordered Spinel Oxides LiGaCr4O8 and LiInCr4O8
在两种A位有序尖晶石氧化物LiGaCr 4 O 8和LiInCr 4 O 8中发现了一种独特的阻挫晶格。由于Li+和Ga 3 +/In 3+离子在A位处的大尺寸失配，由携带自旋3/2的Cr 3+离子组成的烧绿石晶格变成小四面体和大四面体的交替阵列，即，“呼吸”烧绿石晶格。我们引入了一个参数，呼吸因子Bf，它量化了烧绿石晶格中的挫折程度：Bf被定义为J '/J，其中J'和J是最近邻的磁相互作用在大，小四面体，分别。具有Bf ~ 0.6的LiGaCr 4 O 8显示出与常规Cr尖晶石氧化物如ZnCr 2 O 4类似的磁化率。与此相反，LiInCr 4 O 8与一个小的Bf ~ 0.1的磁化率表现出自旋带隙的行为，表明接近一个奇特的单重基态。磁长程序发生在13.8和15.9 K的LiGaCr 4 O 8和LiInCr 4 O 8，分别，在这两种情况下可能是由于耦合到结构扭曲。
Pyrochlore FeF$_{3}$ (pyr-FeF$_{3}$) is a Heisenberg anti-ferromagnetic (AF) with a magnetic susceptibility deviating from the Curie-Weiss law, even at the room temperature. This compound shows a transition to a long-range ordered state with all-in all-out (AIAO) spin configuration. The critical properties of this transition have remained a matter of dispute. In this work, to gain more insight into the critical properties of pyr-FeF$_{3}$, using ab initio density functional theory (DFT), we obtain spin Hamiltonian of this material under the relative volume change with respect to the experiment…
The Bragg diffraction of neutrons and x-rays are well-suited to the task of determining the distribution of magnetization in crystals. Applications of the two techniques proceed by contrasting observed intensities with intensities calculated with a specific model, and changing the model as need be to achieve satisfactory agreement. An all-in-all-out (AIAO) magnetic configuration of magnetic dipoles on a cubic face-centred lattice with networks of corner-sharing tetrahedra is often mentioned in the context of pyrochlore oxides, for example, but the corresponding neutron and x-ray diffraction pa…
In this study, we have performed the magnetocaloric effect and the specific heat measurements of chromium spinel oxide HgCr$_2$O$_4$, wherein the magnetic Cr$^{3+}$ ions form a highly frustrated pyrochlore lattice with significant spin-lattice coupling. In addition to the known magnetic-field-induced phases, our thermodynamic measurements detect a novel quantum phase just before the saturation of the magnetization, which has not been expected from the classical theories of the pyrochlore lattice antiferromagnet with spin-lattice coupling. Based on recent theoretical model calculation, we discu…
Pyrochlore oxides show several fascinating phenomena, such as the formation of heavy fermions and the thermal Hall effect. Although a key to understanding some phenomena may be the Dzyaloshinsky-Moriya (DM) interaction, its microscopic origin is unclear. To clarify the microscopic origin, we constructed a $t_{2g}$-orbital model with the kinetic energy, the trigonal-distortion potential, the multiorbital Hubbard interactions, and the $LS$ coupling, and derived the low-energy effective Hamiltonian for a $d^{1}$ Mott insulator with the weak $LS$ coupling. We first show that lack of the inversion …
Noncollinear magnetism and spin-orbit coupling in 5d pyrochlore oxide Cd2Os2O7
采用密度泛函理论加在位排斥（$U$）方法研究了焦绿石氧化物Cd $_2$ Os $_2$ O $_7$的电子和磁性，绘制了$U$的基态相图.我们得出结论：在很宽的$U$范围内，全进/全出非共线磁序是稳定的.我们还表明，易轴各向异性所产生的自旋轨道（SO）耦合起着重要的作用，在稳定的全进/全出磁秩序。一个\textit{pseudo gap}附近的反铁磁金属和绝缘相之间的过渡观察。最后，我们讨论了在实验中观察到的奇特的低温（$T$）性能的可能来源。
Evolution of the electronic structure across the filling-control and bandwidth-control metal-insulator transitions in pyrochlore-type Ru oxides
我们已经进行了光电子发射和软X射线吸收的研究，即填充控制系统Sm $_{2-x}$ Ca $_x$ Ru $_2$ O $_7$和带宽控制系统Sm $_{2-x}$ Bi $_x$ Ru $_2$ O $_7$，这表明绝缘体到金属的转变，随着钙和铋浓度的增加，分别。Sm $_{2-x}$ Ca $_x$ Ru $_2$ O $_7$中的芯能级和O 2 $p$价带随Ca浓度的变化呈现出几乎相同的单调向上的能量移动，这表明空穴掺杂导致化学势向下移动。Sm $_{2-x}$ Ca $_x$ Ru $_2$ O $_7$中的Ru 4 $d$带也随着空穴掺杂而向费米能级（$E_F$）移动，并且$E_F$处的态密度（DOS）增加.另一方面，Sm $_{2-x}$ Bi $_x$ Ru $_2$ O $_7$中的芯能级除了Ru 3 $d$芯能级之外没有显示出明显的能量移动，其线形变化也反映了金属屏蔽随Bi浓度的增加。我们观察到明显的光谱重量转移从非相干的Ru 4d $t_{2g}$带与Bi浓度，这是预期的带宽控制莫特-哈伯德系统的相干部分。根据最近的理论预测，在$E_F$下，在带宽控制Sm $_{2-x}$ Bi $_x$ Ru $_2$ O $_7$中的DOS增加比在填充控制Sm $_{2-x}$ Ca $_x$ Ru $_2$ O $_7$中的DOS增加更突然。讨论了Bi 6 $sp$带和R…
Magnetic pyrochlore oxides, including the spin ice materials, have proved to be a rich field for the study of geometrical frustration in 3 dimensions. Recently, a new family of magnetic oxides has been synthesised in which the half of the tetrahedra in the pyrochlore lattice are inflated relative to the other half, making an alternating array of small and large tetrahedra. These "breathing pyrochlore" materials such as LiGaCr4O8, LiInCr4O8 and Ba3Yb2Zn5O11 provide new opportunities in the study of frustrated magnetism. Here we provide an analytic theory for the ground state phase diagram and s…
From Spin Glass to Quantum Spin Liquid Ground States in Molybdate Pyrochlores
本文给出了两种磁阻挫高温超导体：$S=1$氧化物Lu $_2$ Mo $_2$ O $_7$和$S={\frac{1}{2}}$氧氮化物Lu $_2$ Mo $_2$ O $_5$ N $_2$的新的磁热容和中子散射结果. Lu $_2$ Mo $_2$ O $_7$在$T_f {\sim} 16$ K下经历到非常规自旋玻璃基态的转变。然而，相应的氧氮化物的制备将基态的性质从自旋玻璃调谐到量子自旋液体。这里介绍的氧化物和氧氮化物相内的静态和动态自旋相关性的比较揭示了量子涨落在选择基态中所起的关键作用。此外，我们估计了$Δ {\sim} 0.05$ meV或${\fracΔ{|θ|}}\sim0.004$的氮氧化物的量子自旋液体态的自旋激发谱中的间隙的上限，以其反铁磁外斯常数$θ {\sim}-121$ K为单位。
We report neutron scattering measurements of the spinel oxide LiGaCr$_{4}$O$_{8}$, in which magnetic ions Cr$^{3+}$ form a breathing pyrochlore lattice. Our experiments reveal the coexistence of a nearly dispersionless resonance mode and dispersive spin wave excitations in the magnetically ordered state, which can be quantitatively described by a quantum spin model of hexagonal loops and linear spin wave theory with the same set of exchange parameters, respectively. Comparison to other Cr spinel oxides reveals a linear relationship between the resonance energy and lattice constant across all t…
Spin ice materials are the model systems that have a zero-point entropy as \textit{T} $\rightarrow$ 0 K, owing to the frozen disordered states. Here, we chemically alter the well-known spin ice Ho$_{2}$Ti$_{2}$O$_{7}$ by replacing Ti sites with isovalent but larger Zr ion. Unlike the Ho$_{2}$Ti$_{2}$O$_{7}$ which is a pyrochlore material, Ho$_{2}$Zr$_{2}$O$_{7}$ crystallizes in disordered pyrochlore structure. We have performed detailed structural, ac magnetic susceptibility and heat capacity studies on Ho$_{2}$Zr$_{2}$O$_{7}$ to investigate the interplay of structural disorder and frustrated …
The family of magnetic rare-earth pyrochlore oxides R2M2O7 plays host to a diverse array of exotic phenomena, driven by the interplay between geometrical frustration and spin-orbit interaction, which leads to anisotropy in both magnetic moments and their interactions. In this article we establish a general, symmetry--based theory of pyrochlore magnets with anisotropic exchange interactions. Starting from a very general model of nearest-neighbour exchange between Kramers ions, we find four distinct classical ordered states, all with q=0, competing with a variety of spin-liquids and unconvention…
This study reports atomic-scale characterization of structural defects in Yb2Ti2O7, a pyrochlore oxide whose subtle magnetic interactions is prone to small perturbations. Due to discrepancies in the reported magnetic ground states, it has become a pressing issue to determine the nature of defects in this system. In the present study, we use atomic resolution scanning transmission electron microscopy techniques to identify the type of defects in the ytterbium titanate single crystals grown by the conventional optical floating zone (FZ) method. In addition to the known point defects of substitut…
Geometrical frustration and spin-orbit coupling effect together play vital role to influence properties in pyrochlore based iridium oxides. Here we have investigated detailed structural, magnetic, thermodynamic and transport properties of pyrochlore iridate Y$_2$Ir$_2$O$_7$. Magnetization data show onset of magnetic irreversibility around temperature $T_{irr}$ $\sim$ 160 K, however, no sign of long-range type ferromagnetic ordering is observed below $T_{irr}$. Specific heat data show no visible anomaly across $T_{irr}$, and the analysis of data indicate sizable density of states across Fermi l…
Since the discovery of the Verwey transition in magnetite, transition metal compounds with pyrochlore structures have been intensively studied as a platform for realizing remarkable electronic phase transitions. We report the discovery of a unique phase transition that preserves the cubic symmetry of the beta-pyrochlore oxide CsW$_2$O$_6$, where each of W 5d electrons are confined in regular-triangle W3 trimers. This trimer formation is an unprecedented self-organization of d electrons, which can be resolved into a charge order satisfying the Anderson condition in a nontrivial way, orbital ord…
