We present a general framework for deriving effective spin Hamiltonians of correlated magnetic systems based on a combination of relativistic ab initio density functional theory calculations (DFT), exact diagonalization of a generalized Hubbard Hamiltonian on finite clusters and spin projections onto the low-energy subspace. A key motivation is to determine anisotropic bilinear exchange couplings in materials of interest. As an example, we apply this method to the pyrochlore Lu$_2$V$_2$O$_7$ where the vanadium ions form a lattice of corner-sharing spin-1/2 tetrahedra. In this compound, anisotropic Dzyaloshinskii-Moriya interactions (DMI) play an essential role in inducing a magnon Hall effect. We obtain quantitative estimates of the nearest-neighbor Heisenberg exchange, the DMI, and the symmetric part of the anisotropic exchange tensor. Finally, we compare our results with experimental ones on the Lu$_2$V$_2$O$_7$ compound.
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 Green's function technique within the random-phase (or Tyablikov) approximation as well as the linear spin-wave theory and quantum Monte Carlo simulations. We compare our results to the ones obtained recently by other methods to corroborate our findings. Finally, we contrast our results with the ones for the simple-cubic-lattice case: both lattices are identical at the mean-field level. We demonstrate that thermal fluctuations are mo…
We use the rotation-invariant Green's 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. W…
Motivated by recent experiments and computational results on pyrochlore iridates, we compare single-particle properties of Y2Ir2O7 obtained from single-site dynamical mean-field calculations with results within the TRILEX approximation, where the latter takes non-local correlations into account. Our calculations are all based on ab-initio calculations within density-functional theory, and take spin-orbit coupling into account. In order to make the treatment within TRILEX feasible, we first define a single-band jeff = 1/2 model, by comparing its spectral features within DMFT to a three-band mod…
Two Dimensional Kagome Correlations and Field Induced Order in the Ferromagnetic XY Pyrochlore Yb2Ti2O7
中子散射测量表明，铁磁XY烧绿石Yb 2 Ti 2 O 7在低温下表现出很强的准二维（2D）自旋关联，在适当的磁场作用下，这种关联让位于长程序（LRO）.由于< 111 >这些2D自旋相关性沿方向的散射棒意味着立方烧绿石系统的磁分解成解耦的可果美平面。沿[1-10]方向施加约0.5 T的磁场，诱导向3D LRO状态的转变，其特征在于长寿命的色散自旋波。我们的测量绘制出一个复杂的低温场相图，这种异国情调的烧绿石磁铁。
The nontrivial topology of quasiparticle wavefunctions can manifest themselves in the form of observable surface states. This is now well established in electronic systems, with Dirac and Weyl semimetals bringing to fore the exotic nature of these topologically protected entities. Magnons - which refer to collective excitations of localized spins - offer another sector where many of these concepts could be realized. Here, we report magneto-thermal measurements on a pyrochlore ferromagnet which is theoretically predicted to host such topological magnons. It is demonstrated that the thermoelectr…
Ferromagnetic - spin glass transition induced by pressure in the geometrically frustrated pyrochlore (Tb$_{1-x}$La$_x$)$_2$Mo$_2$O$_7$
本文用中子衍射和$μ$ SR研究了（Tb $_{1-x}$ La $_x$）$_2$ Mo $_2$ O $_7$高温超导体。Tb取代La使晶格膨胀，并引起从自旋玻璃状状态（{ \itshape x}=0）到非共线铁磁体（{ \itshape x}=0.2）的变化。在铁磁结构中，Tb矩的取向接近于它们的局部各向异性轴，而Mo矩的取向接近于净矩。$μ$ SR动力学弛豫速率在居里温度T $_C$处显示尖状峰，在T $^\star$ $<$ T $_C$处显示宽异常，表明局部或动力学性质的第二次转变。在压力下，长程有序被破坏，恢复到类似自旋玻璃的状态。这组数据提供了铁磁-自旋玻璃阈值区自旋关联和涨落的微观图像。
Nonconventional Spin Glass Transition in a Chemically Ordered Pyrochlore
本文报道了几何阻挫烧绿石Tb $_{2}$ Mo $_{2}$ O $_{7}$，$T$ $_{g}$ $\simeq$ 24 K中不寻常的自旋玻璃性质的研究。分析的非线性部分的直流和复杂的磁化率，附近的玻璃化转变制度，表明存在一个统计分布的弛豫时间在短程有序铁磁簇。此外，磁自旋在低于玻璃化转变温度时没有被充分冻结;显然，这是非线性磁化率的静态临界指数的非平衡标度行为的原因。我们的报告有望为理解具有短程铁磁相互作用的挫火辉石的冻结特性提供新的思路。
Ferromagnetic fragmented state in the pyrochlore Ho$_2$Ru$_2$O$_7$
Paul Scherrer Institut（保罗谢尔研究所）；ETH Zurich（苏黎世联邦理工学院）；Institut Néel, CNRS & Univ. Grenoble Alpes（内尔研究所，法国国家科学研究中心与格勒诺布尔阿尔卑斯大学）；ENS de Lyon, CNRS, Laboratoire de Physique（里昂高等师范学院，法国国家科学研究中心，物理实验室）；Institut Laue Langevin（劳厄-朗之万研究所）；ISIS Facility, Rutherford Appleton Laboratory-STFC（中子源设施，鲁瑟福阿普尔顿实验室-STFC）；French American Center for Theoretical Science, CNRS, KITP, Santa Barbara（法美理论科学中心，法国国家科学研究中心，加州大学圣塔芭芭拉分校卡弗里理论物理研究所）
Pyrochlore iridates have recently attracted growing interest in condensed matter physics because of their potential for realizing new topological states. In order to achieve such quantum states, it is essential to understand themagnetic properties of these compounds, as their electronic structures are strongly coupled with theirmagnetic ground states. In this work, we report a systematic study of the magnetic properties of pyrochlore Y2Ir2O7 and its hole-doped compounds by performing magnetic, electron spin resonance, electrical transport, and x-ray photoelectron spectroscopy (XPS) measurement…
Amorphous ferromagnetism and re-entrant magnetic glassiness in Sm$_{2}$Mo$_{2}$O$_{7}$: new insights into the electronic phase diagram of pyrochlore molybdates
本文讨论了Sm $_{2}$ Mo $_{2}$ O $_{7}$单晶的磁性。在文献中，一个传统的巡游铁磁态的钼$^{4+}$亚晶格低于$\sim 78$ K的报道。然而，我们的直流磁强计，μ子自旋谱（$μ^{+}$ SR）和高次谐波交流磁化率的结果毫不含糊地证明在这个阶段的高度无序的条件下，尽管结晶和化学顺序。这种无序的磁性状态与非晶铁磁合金有几个共同的特征。Sm $_{2}$ Mo $_{2}$ O $_{7}$的这种情况是支持的临界指数，主要是由我们的直流磁化数据的标度分析推导和确认的其他技术的过高的值。此外，$μ^{+}$ SR在微观尺度上检测到显著的静态磁无序。同时，交流磁化率的三次谐波分量在$\sim 78$ K附近的临界发散导致该磁相的玻璃性质的额外证据。最后，纵向弛豫的$μ^{+}$自旋极化（也支持交流磁化率的结果）的证据再入玻璃的功能类似于非晶铁磁体。
We report a comprehensive study on the magnetic and structural properties of the spinel sulfides LiInCr4S8, LiGaCr4S8, and CuInCr4S8, where Li+/Cu+ and Ga3+/In3+ ions form a zinc-blende-type order. On the basis of synchrotron X-ray diffraction and magnetization data obtained using polycrystalline samples, these three sulfides are suggested to be breathing pyrochlore magnets with alternating antiferromagnetic and ferromagnetic interactions on the small and large tetrahedra, respectively. The measured magnetization processes of the three sulfides up to 72 T are significantly different. The magne…
There are two discrepant experimental results on the magnetic ground state of Y$_{2}$Mn$_{2}$O$_{7}$, one study proposes a spin glass state, while another introduces the material as a ferromagnet. In this study, we attempt to resolve this issue by employing density functional theory and Monte Carlo simulations. We derive different spin models by varying the Hubbard $U$ parameter in ab initio GGA+$U$ calculations. For the most range of Hubbard $U$, We obtain that the leading terms in the spin Hamiltonian are bi-quadratic and the nearest neighbor Heisenberg exchange interactions. By comparing Mo…
We describe the crystal structure and elementary magnetic properties of a previously unreported ternary intermetallic compound, Cr4PtGa17, which crystallizes in a rhombohedral unit cell in the noncentrosymmetric space group R3m. The crystal structure is closely related to those of XYZ half-Heusler compounds, where X, Y and Z are reported to be single elements only, occupying three different face-centered cubic sublattices. The new material, Cr4PtGa17, can be most straightforwardly illustrated by writing the formula as (PtGa2)(Cr4Ga14)Ga (X=PtGa2, Y = Cr4Ga14, Z = Ga), that is, the X and Y site…
The two orbital Hubbard model, with the electrons additionally coupled to a complex magnetic background, arises in the pyrochlore molybdates. The background involves local moments Hund's coupled to the electrons, driving double exchange ferromagnetism, and antiferromagnetic (AF) tendency arising from competing superexchange. The key scales include the Hubbard repulsion and the superexchange, both of which can be tuned in these materials. They control the phase transition from a ferromagnetic metal to a spin glass metal and then to a spin glass (Mott) insulator. We provide a comprehensive descr…
The frustrated rare-earth pyrochlore Yb$_2$Ti$_2$O$_7$ is remarkable among magnetic materials: despite a ferromagnetically ordered ground state it exhibits a broad, nearly gapless, continuum of excitations. This broad continuum connects smoothly to the sharp one-magnon excitations expected, and indeed observed, at high magnetic fields, raising the question: how does this picture of sharp magnons break down as the field is lowered? In this paper, we consider the effects of magnon interactions in Yb$_2$Ti$_2$O$_7$, showing that their inclusion greatly extends the reach of spin-wave theory. First…
Pyrochlore iridates and pyrochlore ices are two families of materials where novel quantum phenomena are intertwined with strong spin-orbit coupling, substantial electron correlation and geometrical frustration. Motivated by the puzzling experiments on two pyrochlore systems Pr2Ir2O7 and Yb2Ti2O7, we study the proximate Ising orders and the quantum phase transition out of quantum spin ice U(1) quantum spin liquid (QSL). We apply the electromagnetic duality of the compact quantum electrodynamics to analyze the "magnetic monopoles" condensation for U(1) QSL. The monopole condensation transition r…
The ytterbium pyrochlore magnets, Yb2B2O7 (B = Sn, Ti, Ge) are well described by S_eff = 1/2 quantum spins decorating a network of corner-sharing tetrahedra and interacting via anisotropic exchange. Structurally, only the non-magnetic B-site cation, and hence, primarily the lattice parameter, is changing across the series. Nonetheless, a range of magnetic behaviors are observed: the low temperature magnetism in Yb2Ti2O7 and Yb2Sn2O7 has ferromagnetic character, while Yb2Ge2O7 displays an antiferromagnetically ordered Neel state at low temperatures. While the static properties of the ytterbium …
Critical phenomenon at the phase transition reveals the universal and long-distance properties of the criticality. We study the ferromagnetic criticality of the pyrochlore magnet Lu$_2$V$_2$O$_7$ at the ferromagnetic transition ${T_\text{c}\approx 70\, \text{K}}$ from the isotherms of magnetization $M(H)$ via an iteration process and the Kouvel-Fisher method. The critical exponents associated with the transition are determined as ${β= 0.32(1)}$, ${γ= 1.41(1)}$, and ${δ= 5.38}$. The validity of these critical exponents is further verified by scaling all the $M(H)$ data in the vicinity of $T_\te…
Tenth-order high-temperature expansion for the susceptibility and the specific heat of spin-s Heisenberg models with arbitrary exchange patterns: Application to pyrochlore and kagome magnets
Direct evidence for a dynamical ground state in the highly frustrated Tb$_2$Sn$_2$O$_7$ pyrochlore
对“有序自旋冰”Tb $_2$ Sn $_2$ O $_7$烧绿石化合物的粉末样品进行了MuSR实验。在基温（T=35mK），μ子弛豫具有动力学性质，表明在铁磁相变（T_C=0.87K）以下仍存在强涨落。长程序的暗示表现为μ子极化在外场作用下的振荡和T_C以下的滞后行为。我们提出了一个动态的和强相关的情况下，动力学的结果从大自旋团簇的波动与“有序自旋冰”的结构。
Materials with strong spin-orbit interactions are presently a main target in the search for systems with novel magnetic properties. Magnetic anisotropies can be very large in such compounds, ranging from strongly frustrated Kitaev exchange in honeycomb iridates and the associated spin-liquid states to robust antisymmetric couplings in square-lattice Sr_2IrO_4 . Here we predict from ab initio quantum chemistry calculations that another highly unusual regime is realized in pyrochlore iridium oxides: the nearest-neighbor Heisenberg interaction can vanish whilst the antisymmetric Dzyaloshinskii- M…
The consequences of nonmagnetic-ion dilution for the pyrochlore family Y$_{2}$($M_{1-x}N_{x}$)$_{2}$O$_{7}$ ($M$ = magnetic ion, $N$ = nonmagnetic ion) have been investigated. As a first step, we experimentally examine the magnetic properties of Y$_{2}$CrSbO$_{7}$ ($x$ = 0.5), in which the magnetic sites (Cr$^{3+}$) are percolative. Although the effective Cr-Cr spin exchange is ferromagnetic, as evidenced by a positive Curie-Weiss temperature, $Θ_\mathrm{CW}$ = 20.1(6) K, our high-resolution neutron powder diffraction measurements detect no sign of magnetic long range order down to 2 K. In ord…
We report the low temperature magnetic properties of the pyrochlore Pr$_2$Hf$_2$O$_7$. Polycrystalline and single-crystal samples are investigated using time-of-flight neutron spectroscopy and macroscopic measurements, respectively. The crystal-field splitting produces a non-Kramers doublet ground state for Pr$^{3+}$, with Ising-like anisotropy. Below 0.5 K ferromagnetic correlations develop, which suggests that the system enters a spin ice-like state associated with the metamagnetic behavior observed at $μ_0H_c\sim2.4$~T. In this regime, the development of a discrete inelastic excitation in t…
We study the ground state and thermodynamic properties of the spin-half XXZ model, with an Ising interaction $J_z$ and a transverse exchange interaction $J_{x}$, on a pyrochlore tube obtained by joining together elementary cubes in a one-dimensional array. Periodic boundary conditions in the transverse directions ensure that the bulk of the system consists of corner-sharing tetrahedra, with the same local geometry as the pyrochlore lattice. We use exact diagonalization, the density matrix renormalization group (DMRG), and minimally entangled typical thermal states (METTS) methods to study the …
In a ferromagnet, the spin excitations are the well-studied magnons. In frustrated quantum magnets, long-range magnetic order fails to develop despite a large exchange coupling between the spins. In contrast to the magnons in conventional magnets, their spin excitations are poorly understood. Are they itinerant or localized? Here we show that the thermal Hall conductivity $κ_{xy}$ provides a powerful probe of spin excitations in the "quantum spin ice" pyrochlore Tb$_2$Ti$_2$O$_7$. The thermal Hall response is large even though the material is transparent. The Hall response arises from spin exc…
This work aims to present a representation for the Kagomé and pyrochlore lattices for Monte Carlo simulation and some results of the critical properties. These geometric frustrated lattices are composed of corner sharing triangles and tetrahedrons respectively. The simulation was performed with the Cluster Wollf Algorithm for the spins updates using the standard ferromagnetic Ising Model. The determination of the critical temperature and exponents was done through the Histogram Technique and the Finite-Size Scalling Theory.
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…
We present a comprehensive neutron scattering study of the breathing pyrochlore magnet LiGaCr4S8. We observe an unconventional magnetic excitation spectrum with a separation of high and low-energy spin dynamics in the correlated paramagnetic regime above a spin-freezing transition at 12(2) K. By fitting to magnetic diffuse-scattering data, we parameterize the spin Hamiltonian. We find that interactions are ferromagnetic within the large and small tetrahedra of the breathing pyrochlore lattice, but antiferromagnetic further-neighbor interactions are also essential to explain our data, in qualit…
We present a comprehensive experimental and theoretical study of the pyrochlore Tb$_2$Ge$_2$O$_7$, an exemplary realization of a material whose properties are dominated by competition between magnetic dipolar and electric quadrupolar correlations. The dipolar and quadrupolar correlations evolve over three distinct regimes that we characterize via heat capacity, elastic and inelastic neutron scattering. In the first regime, above $T^*=1.1$ K, significant quadrupolar correlations lead to an intense inelastic mode that cannot be accounted for within a scenario with solely magnetic dipole-dipole c…
We predict magnetisation plateaux ground states for $S=1/2$ Heisenberg antiferromagnets on pyrochlore lattices by formulating arguments based on gauge and spin-parity transformations. We derive a twist operator appropriate to the pyrochlore lattice, and show that it is equivalent to a large gauge transformation. Invariance under this large gauge transformation indicates the sensitivity of the ground state to changes in boundary conditions. This leads to the formulation of an Oshikawa-Yamanaka-Affleck (OYA)-like criterion at finite external magnetic field, enabling the prediction of plateaux in…
Valence-Bond Crystal, and Lattice Distortions in a Pyrochlore Antiferromagnet with Orbital Degeneracy
讨论了高阻挫烧绿石晶格上自旋为1/2的三重$t_{2g}$轨道简并磁性离子的基态性质，如B-尖晶石MgTi $_2$ O $_4$中的Ti $^{3+}$离子.在Hund耦合为零的情况下，我们构造了一个有效的自旋轨道哈密顿量，并通过构造几个精确的本征态研究了它的低能区。我们发现，轨道自由度调制的自旋交换能，释放烧绿石结构的无限自旋简并，并驱动系统到一个非磁性的自旋单重态流形。后者是自旋单重态二聚体的集合，然而，相对于二聚体取向高度简并。这种"定向“简并性随后被磁弹性相互作用提升，磁弹性相互作用通过在合适的方向上扭曲键并导致四元相来优化先前的能量增益。以这种方式，通过二聚体沿着围绕四角轴延伸的螺旋链的缩合形成价键晶体状态，如在MgTi $_2$ O $_4$中实际观察到的。在二聚相的轨道有序模式被预测为铁型沿螺旋和反铁型之间。最后，通过分析的考虑以及数值从头算模拟，我们预测一个可能的实验工具，通过共振X射线散射观察这样的轨道排序。
We report inelastic neutron scattering measurements from our newly synthesized single crystals of the structurally metastable antiferromagnetic pyrochlore Yb$_{2}$Ge$_{2}$O$_{7}$. We determine the four symmetry-allowed nearest-neighbor anisotropic exchange parameters via fits to linear spin wave theory supplemented by fits of the high-temperature specific heat. The exchange parameters so-determined are strongly correlated to the values determined for the $g$-tensor components, as previously observed for the related Yb pyrochlore Yb$_{2}$Ti$_{2}$O$_{7}$. To address this issue, we directly deter…
Ordered spin-ice state in the geometrically frustrated metallic-ferromagnet Sm2Mo2O7
最近发现的自旋冰是一个壮观的例子，非共面自旋安排，可以出现在烧绿石A2 B2 O 7结构。我们对金属铁磁烧绿石Sm 2 Mo 2 O 7进行了磁性和热力学研究。我们的研究，进行了定向晶体，表明Sm自旋有一个有序的自旋冰基态低于约T* = 15 K。有序自旋冰态的温度和场演化受Sm和Mo自旋之间的反铁磁耦合的支配。我们建议，作为一个强大的功能，这种耦合的结果，四面体与外部场对齐，采用“1-在，3-出”自旋结构，而不是“3-在，1-出”在偶极自旋冰，因为字段超过一个临界值。
A quantum spin liquid is a novel state of matter characterized by quantum entanglement and the absence of any broken symmetry. In condensed matter, the frustrated rare-earth pyrochlore magnets Ho$_2$Ti$_2$O$_7$ and Dy$_2$Ti$_2$O$_7$, so-called spin ices, exhibit a classical spin liquid state with fractionalized thermal excitations (magnetic monopoles). Evidence for a quantum spin ice, in which the magnetic monopoles become long range entangled and an emergent quantum electrodynamics arises, seems within reach. The magnetic properties of the quantum spin ice candidate Yb$_2$Ti$_2$O$_7$ have elu…
采用完全相对论密度泛函理论结合在位排斥（U）方法研究了钼系高温超导体A2 Mo 2 O 7的电子和磁性，重点研究了自旋玻璃绝缘材料Y2 Mo 2 O 7.我们发现在大U绝缘区，系统的不同磁态之间存在着特殊的能量竞争。传统的海森堡反铁磁交换作用的几何阻挫模型不能解释这种磁竞争。通过对广义自旋模型的分析，我们发现有效自旋相互作用不同于简单的海森堡形式，在自旋空间中具有强的各向异性。我们还发现，它们引起激烈的竞争之间的反铁磁态和铁磁态。磁相互作用的复杂形式表明了轨道自由度的关键作用。通过对一个三轨道哈伯德模型的分析，阐明了在4d 2电子组态中，磁竞争通过自旋-轨道相互作用与轨道阻挫密切相关.结果挑战了传统的自旋玻璃行为的图片，属性的起源纯粹的反铁磁交换相互作用的几何挫折。
In the search for topological phases in correlated electron systems, iridium-based pyrochlores A2Ir2O7 -- materials with 5d transition-metal ions -- provide fertile grounds. Several novel topological states have been predicted but the actual realization of such states is believed to critically depend on the strength of local potentials arising from distortions of IrO6-cages. We test this hypothesis by measuring with resonant x-ray scattering the electronic level splittings in the A= Y, Eu systems, which we show to agree very well with ab initio electronic structure calculations. We find, howev…
