The heavy-fermion compound URu2Si2 exhibits a hidden-order phase below the temperature, ~ 17.5 K. In spite of intense research for past three decades, no consensus on the order parameter exists and the nature has posed a long-standing mystery. Here we report the discovery of a Griffiths phase within the hidden-order phase, characterized by residual short-range correlations on the collapse of long-range orders due to the dilution effects. In the Griffiths phase scenario, strong evidence are provided for those cluster-like spins, such as the unique power-law behavior of magnetic susceptibility and specific heat as well as the frequency dispersion of AC susceptibility. In this way, the existence of an order parameter is excluded, and the hidden order has a significant kinship with the long-range large-moment antiferromagnetism which is accessible by tuning the hydrostatic pressure or the chemical pressure (i.e., isoelectronic Fe doping). Moreover, an unidirectional anisotropy of resistivity measurements in rotating magnetic fields is observed in the hidden-order phase. The anisotropic magnetoresistance and the associated broken symmetries directly reflect the freezing behavior of at least part of magnetic clusters. Thus, the demonstrations of the Griffiths phase as an alternative proposal for the hidden-order phase of URu2Si2 are very promising, challenging the understanding of exotic electronic states in correlated matter and quantum materials.
We investigate the interplay between the Kondo effect and randomness in MxTiSe2 (M = Co, Ni, and Fe) single crystals. Although the typical low-T upturn of resistivity implies the Kondo effect around the single-ion Kondo temperature \overline{T}_{K}, positive magnetoresistance linearly proportional to the magnetic field and the power-law scaling of magnetization suggest the forbidden coexistence between Kondo effect and time reversal symmetry breaking. This puzzling result is resolved by the Griffiths scenario - disorder-induced distribution of the Kondo temperature produces an effective Kondo …
In this paper we provide the theoretical basis for the problem of Griffiths-McCoy singularities close to the quantum critical point for magnetic ordering in U and Ce intermetallics. We show that the competition between Kondo effect and RKKY interaction can be expressed in Hamiltonian form and the dilution effect due to alloying leads to a quantum percolation problem driven by the number of magnetically compensated moments. We argue that the exhaustion paradox proposed by Nozières is explained when the RKKY interaction is taken into account. We revisited the one impurity and two impurity Kondo …
Layered 5$d$ transition iridium oxides, Sr$_2$(Ir,Rh)O$_4$, are described as unconventional Mott insulators with strong spin-orbit coupling. The undoped compound, Sr$_2$IrO$_4$, is a nearly ideal two-dimensional pseudospin-$1/2$ Heisenberg antiferromagnet, similarly to the insulating parent compound of high-temperature superconducting copper oxides. Using polarized neutron diffraction, we here report a hidden magnetic order in pure and doped Sr$_2$(Ir,Rh)O$_4$, distinct from the usual antiferromagnetic pseudo-spin ordering. We find that time-reversal symmetry is broken while the lattice transl…
Since the 1985 discovery of the phase transition at $T_{\rm HO}=17.5$ K in the heavy-fermion metal URu$_2$Si$_2$, neither symmetry change in the crystal structure nor magnetic ordering have been observed, which makes this "hidden order" enigmatic. Some high-field experiments have suggested electronic nematicity which breaks fourfold rotational symmetry, but direct evidence has been lacking for its ground state at zero magnetic field. Here we report on the observation of lattice symmetry breaking from the fourfold tetragonal to twofold orthorhombic structure by high-resolution synchrotron X-ray…
Exploring the relationship between intriguing physical properties and structural complexity is a central topic in studying modern functional materials. Co$_{3}$Sn$_{2}$S$_{2}$, a new discovered kagome-lattice magnetic Weyl semimetal, has triggered intense interest owing to the intimate coupling between topological semimetallic states and peculiar magnetic properties. However, the origins of the magnetic phase separation and spin glass state below $T_{C}$ in this ordered compound are two unresolved yet important puzzles in understanding its magnetism. Here, we report the discovery of local symm…
We generalize the hidden symmetry-breaking picture of symmetry-protected topological (SPT) order developed by Kennedy and Tasaki in the context of the Haldane phase. Our generalization applies to a wide class of SPT phases in one-dimensional spin chains, protected by an on-site representation of a finite abelian group. This generalization takes the form of a non-local unitary map that relates local symmetry-respecting Hamiltonians in an SPT phase to local Hamiltonians in a symmetry-broken phase. Using this unitary, we establish a relation between the two-point correlation functions that charac…
A second-order phase transition is characterized by spontaneous symmetry breaking. The nature of the broken symmetry in the so-called "hidden order" phase transition in the heavy fermion compound URu2Si2, at transition temperature T_h=17.5 K, has posed a long-standing mystery. We report the emergence of an in-plane anisotropy of the magnetic susceptibility below T_h, which breaks the four-fold rotational symmetry of the tetragonal URu2Si2. Two-fold oscillations in the magnetic torque under in-plane field rotation were sensitively detected in small pure crystals. Our findings suggest that the h…
Hidden Magnetic Octupolar Order driven by Spin-Orbit coupling in KFeF$_3$
University of Warwick（华威大学）；Durham University（杜伦大学）；University of Edinburgh（爱丁堡大学）；European Synchrotron Radiation Facility（欧洲同步辐射装置）；Institut Laue-Langevin（朗之万研究所）
Spontaneous, collective ordering of electronic degrees of freedom leads to second-order phase transitions that are characterized by an order parameter. The notion "hidden order" (HO) has recently been used for a variety of materials where a clear phase transition occurs to a phase without a known order parameter. The prototype example is the heavy-fermion compound URu2Si2 where a mysterious HO transition occurs at 17.5K. For more than twenty years this system has been studied theoretically and experimentally without a firm grasp of the underlying physics. Using state-of-the-art density-functio…
Throughout the past three decades the hidden order (HO) problem in URu$_2$Si$_2$ has remained a "hot topic" in the physics of strongly correlated electron systems with well over 600 publications related to this subject. Presently in 2014 there has been significant progress in combining various experimental results embedded within electronic structure calculations using density functional theory (DFT) to give a consistent description of the itinerant behaviour of the HO transition and its low temperature state. Here we review six different experiments: ARPES, quantum oscillations, neutron scatt…
Despite decades of intense researches, the enigmatic pseudo-gap (PG) phase of superconducting cuprates remains an unsolved mystery. In the last 15 years, various symmetry breakings in the PG state have been discovered, spanning an intra-unit cell (IUC) magnetism, preserving the lattice translational (LT) symmetry but breaking time-reversal symmetry and parity, and an additional incipient charge density wave breaking the LT symmetry upon cooling. However, none of these states can (alone) account for the partial gapping of the Fermi surface. Here we report a hidden LT-breaking magnetism uisng po…
We formulate and study an effective Hamiltonian for low-energy Kramers doublets of $d^1$-ions on a square lattice. We find that the system exhibits a magnetically hidden order in which the expectation values of the local spin and orbital moments both vanish. The order parameter responsible for a time-reversal symmetry breaking has a composite nature and is a spin-orbital analog of a magnetic octupole. We argue that such a hidden order is realized in the layered perovskite Sr$_2$VO$_4$.
We discuss possible approaches to the problem of the URu2Si2 "Hidden Order" (HO) which remains unsolved after tremendous efforts of researches. Suppose there is no spatial symmetry breaking at the HO transition temperature and solely the time-reversal symmetry breaking emerges owing to some sort of magnetic order. As a result of its 4/mmm symmetry, each uranium atom is a three-dimensional magnetic vortex; its intra-atomic magnetization M(r) is intrinsically non-collinear, so that its dipole, quadrupole and toroidal moments vanish, thus making the vortex "hidden". The first non-zero magnetic mu…
We have introduced a class of exactly soluble Hamiltonian with either SO(2n+1) or SU(2) symmetry, whose ground states are the SO(2n+1) symmetric matrix product states. The hidden topological order in these states can be fully identified and characterized by a set of nonlocal string order parameters. The Hamiltonian possesses a hidden $(Z_{2}\times Z_{2})^{n} $ topological symmetry. The breaking of this hidden symmetry leads to $4^{n}$ degenerate ground states with disentangled edge states in an open chain system. Such matrix product states can be regarded as cluster states, applicable to measu…
Revealing Hidden Inversion Symmetry Breaking in ZrTe$_5$ via Phonon-Assisted Heterodyne Amplification
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理国家实验室）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料中心）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学汤川研究所）；Zhangjiang Institute for Advanced Study, Shanghai Jiao Tong University（上海交通大学张江高等研究院）
We demonstrate the existence of topologically nontrivial phase in a one-dimensional fermionic lattice system subjected to synthetic gauge fields, which is beyond the standard Altland-Zirnbauer classification of topological insulators. The topological phase can be characterized by the presence of degenerate zero-mode edge states or a quantized Berry phase of the occupied Bloch band. By analyzing symmetries of the system, we identify that the topological phase and zero-mode edge states are protected by two hidden symmetries. An extended model with hidden symmetry breaking is also studied in orde…
