We analyzed the magnetic susceptibilities of several Cr spinels using two recent models for the geometrically frustrated pyrochlore lattice, the Quantum Tetrahedral Mean Field model and a Generalized Constant Coupling model. Both models can describe the experimental data for ACr2 O4 (with A = Zn, Mg, and Cd) satisfactorily, with the former yielding a somewhat better agreement with experiment for A = Zn, Mg. The obtained exchange constants for nearest and next-nearest neighbors are discussed.
We performed nuclear magnetic resonance (NMR) and muon spin relaxation (μSR) experiments to identify the magnetic ground state of the frustrated quantum A-site spinel, CuAl2O4. Our results verify that the ground state does not exhibit a long-range magnetic ordering, but a glass-like transition manifests at T*=2.3 K. However, the Gaussian shape and the weak longitudinal field dependence of μSR spectra below T* show that the ground state has dynamic spin fluctuations, distinct from those of conventional spin-glasses.
Different from other magnetically frustrated spinel systems, GeCu$_{2}$O$_{4}$ is a strongly tetragonal distorted spinel cuprate in which edge-sharing CuO$_{2}$ ribbons are running along alternating directions perpendicular to the $c$-axis. Here, GeCu$_{2}$O$_{4}$ samples of high quality were prepared via high pressure synthesis (at 4 GPa) and the corresponding magnetic and dielectric properties were investigated. For the first time, we observed a ferroelectric polarization emerging at T$_{N}$ $\sim$ 33~K. Although the ferroelectric polarization is weak in GeCu$_{2}$O$_{4}$ ($P$ $\sim$ 0.2$μ$C…
Frustrated magnets can host numerous exotic many-body quantum and topological phenomena. GeNi$_2$O$_4$ is a three dimensional $S=1$ frustrated magnet with an unusual two-stage transition to the two-dimensional antiferromagnetic ground state, while GeCu$_2$O$_4$ is a high-pressure phase with a strongly tetragonally elongated spinel structure and magnetic lattice formed by $S=1/2$ CuO$_2$ linear chains with frustrated exchange interactions and exotic magnetic behavior. Here we report on the first thin-film epitaxial stabilization of these two compounds. Developed growth mode, surface morphology,…
Molecular spin-liquid state in spin-3/2 frustrated spinel HgCr$_2$O$_4$
在尖晶石铬酸盐$A$ Cr $_2$ O $_4$（$A$ = Mg、Zn或Cd）中看到的六聚体型自旋激发是由几何挫折引起的典型的类自旋液体状态。为了澄清状态的起源，我们比较研究自旋激发在同构材料HgCr $_2$ O $_4$的非弹性中子散射，并观察到不同的分子类型的激发。使用模型哈密顿进行的数值分析表明，这两种类型的自旋激发起源于自旋3/2分子单线隐藏在磁有序相。分子类型之间的差异是由铬酸盐中发生的交换相互作用的种类的差异来解释的。
We report on negative thermal expansion (NTE) in the high-field, half-magnetization plateau phase of the frustrated magnetic insulator CdCr2O4. Using dilatometry, we precisely map the phase diagram at fields of up to 30T, and identify a strong NTE associated with the collinear half-magnetization plateau for B > 27T. The resulting phase diagram is compared with a microscopic theory for spin-lattice coupling, and the origin of the NTE is identified as a large negative change in magnetization with temperature, coming from a nearly-localised band of spin excitations in the plateau phase. These res…
The ground state of the frustrated A-site magnetic spinel CoAl2O4 has been a controversial issue whether it is a collinear antiferromagnetic ordering or a spiral spin - liquid state, as the ratio of the two competing interactions, J2/J1 lies close to the boundary between these two ground states. Here, we address the magnetic ground state in CoAl2O4 with different amount of Co2+/Al3+ site disorder from the study of magnetoelectric effect and Monte Carlo simulations. CoAl2O4 with low site disorder exhibits linear magnetoelectric effect below the magnetic ordering temperature. With increasing dis…
The crossover from localized- to itinerant-electron behavior is associated with many intriguing phenomena in condensed-matter physics. In this paper, we investigate the crossover from localized to itinerant regimes in the spinel system Mn$_{1-x}$Co$_x$V$_2$O$_4$. At low Co doping, orbital order (OO) of the localized electrons on the V3+ ions suppresses magnetic frustration by triggering a tetragonal distortion. With Co doping, electronic itinerancy melts the OO and suppresses the structural phase transition while the reduced spin-lattice coupling produces magnetic frustration. Neutron scatteri…
Electronic structure of spin frustrated magnets: Mn$_3$O$_4$ spinel and postspinel
Mn $_3$ O $_4$是自旋受抑磁体，其在环境条件下采用四方扭曲尖晶石结构，在高压下采用CaMn $_2$ O $_4$型后尖晶石结构。我们进行了光学测量和\emph{ab} \emph{initio}计算，并系统地研究了尖晶石和后尖晶石Mn $_3$ O $_4$相的电子能带结构。对于这两个阶段，理论电子结构是一致的光学吸收光谱，并显示特征带分裂的导带。从吸收光谱获得的带隙为1.91（6）eV的尖晶石相，和0.94（2）eV的后尖晶石相。两相都是电荷转移型绝缘体。Mn3 \emph{d} $t_2$ $_g$和O2 \emph{p}在导带形成能量较高的反键轨道.
Localized spins and itinerant electrons rarely coexist in geometrically-frustrated spinel lattices. We show that the spinel CoV2O4 stands at the crossover from insulating to itinerant behavior and exhibits a complex interplay between localized spins and itinerant electrons. In contrast to the expected paramagnetism, localized spins supported by enhanced exchange couplings are frustrated by the effects of delocalized electrons. This frustration produces a non-collinear spin state and may be responsible for macroscopic spin-glass behavior. Competing phases can be uncovered by external perturbati…
Multiple lattice instabilities resolved by magnetic-field and disorder sensitivities in cubic paramagnetic phase of the orbital-degenerate frustrated spinel MgV$_2$O$_4$
超声波速度测量的轨道简并沮丧尖晶石MgV $_2$ O $_4$中进行的高纯度的单晶，表现出连续的结构和反铁磁相变，并在无序引入的单晶，表现出自旋玻璃样的行为。测量结果表明，两种类型的不寻常的温度依赖性的弹性模量共存的立方顺磁相，这是解决了磁场和无序的敏感性：巨大的居里型软化与温度降低，和凹的温度依赖性的特征最小值。这些弹性异常表明晶格的耦合共存的轨道涨落和轨道自旋耦合激发。
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…
We investigate analytically and numerically the classical ground states of frustrated Heisenberg models on pyrochlore and kagome lattices in zero and finite magnetic fields. Each model has a wide region in the microscopic parameter space, where the propagation vector is turned to a commensurate position equal to a half of the reciprocal lattice vector with a nontrivial star. Within these regions the zero-field ground states for both models correspond to noncoplanar triple-k spin configurations. A universal appearance of the 3-k states can be related to the spin-space dimensionality. A strong m…
Approaching the Ground State of Frustrated A-site Spinels: A Combined Magnetization and Polarized Neutron Scattering Study
我们重新研究磁阻挫，{ \it金刚石晶格反铁磁体}尖晶石FeAl $_2$ O $_4$和MnAl $_2$ O $_4$使用磁化测量和极化中子的漫散射。在FeAl $_2$ O $_4$中，宏观测量证实了在13 K附近零场冷却磁化率的“尖点”。动态磁化率和{ \it记忆效应}实验提供的结果不符合该材料中的典型自旋玻璃情形。通过极化中子散射研究，证实了FeAl $_2$ O $_4$在低至4~K的温度范围内不存在长程磁序。通过模拟粉末平均微分磁中子散射截面，我们估计，在这种化合物中的自旋-自旋相关延伸到第三个最近邻壳。Landé $g$因子的估计值指向Fe $^{2+}$的轨道贡献。这也得到了居里-外斯磁化率分析的支持。而MnAl $_2$ O $_4$在低于$\approx$ 40~K时发生磁相变，进入长程有序态，这一点得到了宏观测量和极化中子衍射的证实。然而，极化中子研究揭示了显著的自旋涨落与长程反铁磁有序共存的存在。磁扩散强度表明与FeAl $_2$ O $_4$类似的短程有序。本工作的结果支持自旋自旋相关性的重要性，在理解磁响应的挫折磁铁一样，$A$网站尖晶石具有主导的短程自旋相关性，让人想起“自旋液体”状态。
Spin-lattice coupling in frustrated antiferromagnets
本文综述了自旋-晶格耦合在消除烧绿石反铁磁体，特别是尖晶石氧化物的几何阻挫中的作用机制。烧绿石晶格的组成单元四面体单元在晶格自由度与反铁磁性耦合时发生自旋驱动的Jahn-Teller不稳定性。通过限制我们的考虑，以保持平移对称性的晶格的扭曲，我们提出了一个一般的理论，集体自旋Jahn-Teller效应的烧绿石晶格。预测的晶格畸变之一打破了反转对称性，并产生了手性烧绿石晶格，其中受挫键形成具有一定手性的螺旋。手性通过自旋轨道耦合转移到自旋系统，导致长周期螺旋状态，如在尖晶石CdCr 2 O 4中观察到的。我们讨论了利用局域声子模的自旋-晶格耦合的显式模型，以及它们在其他阻挫磁体中的应用。
Massachusetts Institute of Technology（麻省理工学院）；Flatiron Institute（平顿研究所）；University of British Columbia（不列颠哥伦比亚大学）；Canadian Light Source, Inc.（加拿大光源公司）；Lund University（隆德大学）；Brookhaven National Laboratory（布鲁克海文国家实验室）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Max Planck Institute for Solid State Research（马克斯·普朗克固态研究所）；Universität Würzburg（维尔茨堡大学）；Ludwig- Maximilians-Universität München（慕尼黑路德维希-马克西米利安大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Université Paris-Saclay（巴黎萨克雷大学）；CNRS（法国国家科学研究中心）；CEA（法国原子能和替代能源委员会）；Institut de Physique Théorique（理论物理研究所）；University of Tokyo（东京大学）；University of Stuttgart（斯图加特大学）；Collège de France（法兰西公学院）；Université PSL（巴黎文理研究大学）；Ecole Polytechnique（巴黎综合理工学院）；IP Paris（巴黎理工学院）；Université de Genève（日内瓦大学）
The low temperature lattice structure and magnetic properties of Co$_{2.75}$Fe$_{0.25}$O$_4$ ferrite have been investigated using experimental results from synchrotron x-ray diffraction (SXRD), dc magnetization, ac susceptibility, neutron diffraction and neutron depolarization techniques. The samples have been prepared by chemical co-precipitation of the Fe and Co nitrates solution in high alkaline medium and subsequent thermal annealing of the precipitates in the temperature range of 200- 900 $^\circ$C. Rietveld refinement of the SXRD patterns at room temperature indicated two-phased cubic sp…
The inversion and volume effects on magnetism in a spinel-type magnetically frustrated compound, CoAl2O4, and its gallium-substituted system, CoAl2-xGaxO4, were investigated. Magnetically frustrated Co2+ with spin S = 3/2 on the tetrahedral site formed a diamond lattice in CoAl2O4 located in the vicinity of the magnetic phase boundary between Neel and spin-spiral states. In the Ga-substituted system, the number of Co ions, the so-called inversion h dominating the octahedral site, increased with increasing x. From comprehensive crystallographic, magnetic, and thermal measurements, increments of…
We report the magnetic properties of $A$-site spinel compound MnSc$_2$Se$_4$. The macroscopic magnetic measurements uncovers successive magnetic transitions at $T_{\rm{N1}}$= 2.04 K, followed by two further transitions at $T_{\rm{N2}}$=1.8 K and $T_{\rm{N3}}$=1.6 K. Neutron powder diffraction reveals that both, $T_{\rm{N2}} < T < T_{\rm{N1}}$ and $T <T_{\rm{N3}}$, orders are associated with the propagation vector $k$=(3/4 3/4 0), while the magnetic structures are collinear amplitude modulated and helical, respectively. Using neutron powder spectroscopy we demonstrated the effect of substitutio…
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…
The inconsistency about the degree of geometrical frustration has been a long issue in AV$_{2}$O$_{4}$ (A $\equiv$ Zn, Cd and Mg) compounds, which arises from the two experimental results: (i) frustration indices and (ii) magnetic moments. In the present study, we try to understand such inconsistency by using {\it ab initio} electronic structure calculations. The orbital degrees of freedom are found to play an important role in understanding the geometrically frustrated magnetic behaviour of these compounds. The inclusion of the orbital and spin angular momenta for calculating the frustration …
We report detailed dc and ac magnetic susceptibilities, specific heat, and thermal conductivity measurements on the frustrated magnet ZnCr$_2$Se$_4$. At low temperatures, with increasing magnetic field, this spinel material goes through a series of spin state transitions from the helix spin state to the spiral spin state and then to the fully polarized state. Our results indicate a direct quantum phase transition from the spiral spin state to the fully polarized state. As the system approaches the quantum criticality, we find strong quantum fluctuations of the spins with the behaviors such as …
Orbital and magnetic transitions in geometrically-frustrated vanadium spinels -- Monte Carlo study of an effective spin-orbital-lattice coupled model --
我们提出了我们的理论和数值计算结果的热力学性质和微观机制的两个连续的转变钒尖晶石氧化物$A$ V $_2$ O $_4$（$A$ =Zn，Mg，或Cd）的Monte Carlo计算得到的有效自旋轨道晶格模型在强关联极限。在烧绿石晶格结构的V阳离子的几何挫折抑制自旋和轨道相关的发展，但是，我们发现，该模型在低温下表现出两个转变。第一，不连续的过渡发生与轨道排序的四重Jahn-Teller失真的帮助。轨道顺序减少了自旋交换相互作用的挫折，并诱导反铁磁相关的一维链躺在垂直平面的四重畸变。其次，在较低温度下，一维反铁磁链之间的第三近邻相互作用稳定了三维反铁磁有序。热涨落是通过有序-无序机制稳定共线磁态的关键。结果很好地再现了实验数据，如转变温度，磁化率的温度依赖性，在转变的熵的变化，以及在低温下的磁有序结构。用线性自旋波理论研究了零温下的量子涨落效应。发现在基态的交错矩从饱和值显著降低，并合理地与实验数据相吻合。
Our polycrystalline sample study on the Yb-based chalcogenide spinels $A$Yb$_2$$X_4$ ($A =$ Cd, Mg, $X =$ S, Se) has revealed frustrated magnetism due to the antiferromagnetically coupled Heisenberg spin on the pyrochlore lattice. Our crystal electric field analysis indicates the Yb ground state has nearly Heisenberg spins with a strong quantum character of the ground doublet. All the materials exhibit an antiferromagnetic order at 1.4-1.8 K, much lower temperature than the antiferromagnetic exchange coupling scale of $\sim 10$ K. The magnetic specific heat $C_{\rm M}$ shows a $T^{3}$ dependen…
Intrinsic susceptibility and bond defects in the novel 2D frustrated antiferromagnet Ba$_{2}$Sn$_{2}$ZnCr$_{7p}$Ga$_{10-7p}$O$_{22}$
本文报道了高阻挫反铁磁体Ba $_{2}$ Sn $_{2}$ ZnCr $_{7p}$ Ga $_{10-7p}$ O $_{22}$的微观和宏观磁性，分别用NMR和SQUID实验进行了探测. Cr $^{3+}$受抑kagomé双层的固有磁化率的$T$ -变化，$χ_{kag}$，在45 K附近显示最大值。详细研究了$0.29 \leq p \leq0.97$的磁晶格稀释。新的稀释无关的缺陷，可能与磁键无序，证明和讨论。我们将我们的结果与SrCr $_{9p}$ Ga $_{12-9p}$ O $_{19}$进行比较。键缺陷和自旋空位都不影响kagomé双层膜的平均磁化率。
Magnetic transition and orbital degrees of freedom in vanadium spinels
基于烧绿石晶格上的有效自旋轨道模型，提出了$A$ V $_2$ O $_4$（$A$ =Zn，Mg，Cd）中两个相变的方案.在高温下，由于晶格结构，自旋相关性强烈受挫，并且在$\sim$ 50 [K]处的跃迁是由Jahn-Teller晶格畸变支持的轨道级。这种轨道顺序引入了取决于键方向的自旋交换耦合的空间调制。这部分地释放了挫折，并导致$\sim$ 40 [K]的自旋顺序。我们还考虑了第三近邻交换耦合和量子涨落的影响，研究了稳定的自旋组态。计算结果与实验结果一致。
The crystal and magnetic structures of stoichiometric ZnCr2Se4 have been investigated using synchrotron X-ray and neutron powder diffraction, muon spin relaxation (muSR) and inelastic neutron scattering. Synchrotron X-ray diffraction shows a spin-lattice distortion from the cubic spinel to a tetragonal I41/amd lattice below TN = 21 K, where powder neutron diffraction confirms the formation of a helical magnetic structure with magnetic moment of 3.04(3) μB at 1.5 K; close to that expected for high-spin Cr3+. MuSR measurements show prominent local spin correlations that are established at temper…
Ga NMR study of the local susceptibility in SrCr8Ga4O19: pseudogap and paramagnetic defects
本文首次用Ga（4 f）NMR研究了Kagome基阻挫反铁磁体原型SrCr $_{8}$ Ga $_{4}$ O $_{19}$中Cr的磁化率.我们的主要发现是受抑晶格的磁化率在50 K附近经历一个最大值。我们的数据也支持存在顺磁性自旋“团簇”，这是在低温下宏观磁化率中观察到的居里行为的原因。这些结果为几何阻挫磁体的物理学争论不休提供了新的特征。
GeCu$_2$O$_4$ is a high-pressure recoverable cuprate with a strongly tetragonally elongated spinel structure and magnetic lattice formed by $S=1/2$ CuO$_2$ linear chains with frustrated exchange interactions and exotic magnetic behavior. Here we report on the first stabilization of epitaxial thin films of GeCu$_2$O$_4$ on (001)-oriented MgAl$_2$O$_4$ substrate. Developed growth mode, surface morphology, crystal structure and copper valence state were characterized by \emph{in-situ} reflection high-energy electron diffraction, atomic force microscopy, X-ray reflectivity, X-ray diffraction and X…
Mixed valence on a pyrochlore lattice - LiV2O4 as a geometrically frustrated magnet
在40 K以上，重费米子尖晶石LiV_2O_4的磁化率与几何阻挫磁绝缘体的磁化率具有许多共同特征，而其室温电阻率舒适地超过Mott-Regel极限。这表明，当地的磁矩，以及烧绿石晶格的基本几何形状，在确定其磁性能发挥了重要作用。我们最近推出的四面体平均场论绝缘烧绿石反铁磁体的情况下，其中个别四面体包含不同长度的自旋，并以此为出发点，讨论三种不同的情况下，在LiV 2 O 4的磁性和电子的转变。
