Magnetic susceptibility, specific heat, and muon spin relaxation ($μ$SR) measurements have been performed on a newly synthesized three-dimensional sandglass-type lattice Tm$_3$SbO$_7$, where two inequivalent sets of non-Kramers Tm$^{3+}$ ions (Tm$^{3+}_1$ and Tm$^{3+}_2)$ show crystal electrical field effect at different temperature ranges. The existence of an ordered or a glassy state down to 0.1~K in zero field is excluded. The low-energy properties of Tm$_3$SbO$_7$ are dominated by the lowest non-Kramers quasi-doublet of $\rm Tm^{3+}_1$, and the energy splitting is regarded as an intrinsic transverse field. Therefore, the low-temperature paramagnetic phenomenon in Tm$_3$SbO$_7$ is explained by a transverse field Ising model, which is supported by the quantitative simulation of specific heat data. In addition, the perturbation from Tm$^{3+}_2$ may play an important role in accounting for the low temperature spin dynamics behavior observed by $μ$SR.
Localized magnetic moments with crystal-field doublet or pseudo-spin 1/2 may arise in correlated insulators with even number of electrons and strong spin-orbit coupling. Such a non-Kramers pseudo-spin 1/2 is the consequence of crystalline symmetries as opposed to the Kramers doublet arising from time-reversal invariance, and is necessarily a composite of spin and orbital degrees of freedom. We investigate possible spin-orbital liquids with fermionic spinons for such non-Kramers pseudo-spin 1/2 systems on the Kagome lattice. Using the projective symmetry group analysis, we find {\it ten} new ph…
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 report magnetic properties of a 4f-honeycomb iodide SmI3 made up of edge-shared network of SmI6 octahedra. High temperature magnetic susceptibility indicates Γ7 Kramers doublet ground state of Sm3+ (4f5) ions stabilized by the spin-orbit coupling and octahedral crystal electric field, which interact with Sm-I-Sm bond angle nearly 90 degree. Magnetization measurements down to 0.1 K detected antiferromagnetic correlations and an anomaly in the magnetization curve before saturation without a sign of long-range order. Relevance between SmI3 and the antiferromagnetic Kitaev material proposed in …
We discuss possible competition between magnetic and quadrupole Kondo effects in non-Kramers doublet systems under cubic symmetry. The quadrupole Kondo effect leads to non-Fermi-liquid (NFL) ground state, while the magnetic one favors ordinary Fermi liquid (FL). In terms of the $j$-$j$ coupling scheme, we emphasize that the orbital fluctuation must develop in the vicinity of the NFL-FL boundary. We demonstrate a change of behavior in the f-electron entropy by the Wilson's numerical renormalization-group (NRG) method on the basis of the extended two-channel Kondo exchange model. We present impl…
Praseodymium-based 1-2-20 cage compounds Pr$T_2X_{20}$ ($T$ is generally Ti, V, Nb, Ru, Rh, Ir; and $X$ is either Al, Zn or Cd) provide yet another platform to study non-trivial electronic states of matter ranging from topological and magnetic orders to unconventional multipolar orders and superconductivity. In this paper, we report measurements of the electronic heat capacity in two Pr-based 1-2-20 materials: PrNi$_2$Cd$_{20}$ and PrPd$_2$Cd$_{20}$. We find that the lowest energy multiplet of the Pr $4f^2$ valence configuration is a $Γ_3$ non-Kramers doublet and the first excited triplet is a…
In this article, I study magnetic response of electron wavefunctions in a commensurate collinear antiferromagnet. I show that, at a special set of momenta, hidden anti-unitary symmetry protects Kramers degeneracy of Bloch eigenstates against a magnetic field, pointing transversely to staggered magnetization. Hence a substantial momentum dependence of the transverse g-factor in the Zeeman term, turning the latter into a spin-orbit coupling, that may be present in materials from chromium to borocarbides, cuprates, pnictides, as well as organic and heavy fermion conductors.
In non-Kramers Kondo systems with a quadrupolar degrees of freedom, an ordinary magnetic Kondo effect can compete with the quadrupolar Kondo effect. We discuss such competition keeping Pr$T_{2}$Zn$_{20}$ ($T$=Ir, Rh) and Pr$T_{2}$Al$_{20}$ ($T$=V, Ti) in mind, where the $Γ_{3}$ non-Kramers crystalline-electric-field (CEF) doublet ground state is realized in Pr$^{3+}$ ion with $(4f)^{2}$ configuration under cubic symmetry. The quadrupolar Kondo effect can be described by the two-channel Kondo model, which leads to the local non-Fermi-liquid (NFL) ground state, while the magnetic Kondo effect fa…
In this study, ultrasonic measurements were performed on a single crystal of cubic PrNi$_2$Cd$_{20}$, down to a temperature of 0.02 K, to investigate the crystalline electric field ground state and search for possible phase transitions at low temperatures. The elastic constant $(C_{11}-C_{12})/2$, which is related to the $Γ_3$-symmetry quadrupolar response, exhibits the Curie-type softening at temperatures below $\sim$30 K, which indicates that the present system has a $Γ_3$ non-Kramers doublet ground state. A leveling-off of the elastic response appears below $\sim$0.1 K toward the lowest tem…
We have investigated the low temperature quadrupolar phenomena of the non-Kramers system PrRh2Zn20 under magnetic fields in the [100] and [110] directions. Our experiments reveal the B-T phase diagram of PrRh2Zn20 involving four electronic states regardless of the field direction, namely, a non-Fermi liquid (NFL) state, an antiferro-quadrupolar (AFQ) ordered state, a novel heavy-fermion (HF) state, and a field-induced singlet (FIS) state. In the wide range of the NFL state, the resistivity can be well scaled by a characteristic temperature, suggesting the realization of the quadrupole Kondo ef…
Cubic Pr-based compounds with $Γ_3$ non-Kramers doublet ground states can realize a novel heavy Fermi liquid with spinorial hybridization ('hastatic' order) that breaks time reversal symmetry. Several Pr-"1-2-20" materials exhibit a suggestive heavy Fermi liquid stabilized in intermediate magnetic fields; these provide key insight into the quadrupolar Kondo lattice. We develop a simple, yet realistic microscopic model of ferrohastatic order, and elaborate its experimental signatures and behavior in field, where it is a good candidate to explain the observed heavy Fermi liquids at intermediate …
Crystal-Field--Driven Magnetoelectric Coupling in the Non-Kramers Hexaaluminate PrMgAl11O19
Charles University（查理大学）；Adam Mickiewicz University（亚当·密茨凯维奇大学）；Institute of Physics, Czech Academy of Sciences（捷克科学院物理研究所）；Institute of Molecular Physics, Polish Academy of Sciences（波兰科学院分子物理研究所）
Induced quantum magnetism on a triangular lattice of non-Kramers ions in PrMgAl11O19
Charles University, Faculty of Mathematics and Physics（查理大学数学物理学院）；Adam Mickiewicz University, Faculty of Physics and Astronomy（亚当·密茨凯维奇大学物理与天文学学院）；Institute of Physics of the Czech Academy of Sciences（捷克科学院物理研究所）；Adam Mickiewicz University, NanoBioMedical Centre（亚当·密茨凯维奇大学纳米生物医学中心）
We investigate antiferro quadrupole orders in systems with non-Kramers doublet ground state with total angular momentum J=4 in T_d point group symmetry. We demonstrate that a pure O_2^2 antiferro quadrupole order is impossible in general crystalline-electric field potential and should be accompanied by ferro O_2^0 quadrupole moment. The temperature and magnetic-field phase diagram is obtained by mean-field approximation of intersite quadrupole interactions and the excitation spectrum is analyzed by "spin"-wave approximations. Gapless excitations emerge at the boader of antiferro O_2^2 quadrupo…
Multipolar magnetism is an emerging field of quantum materials research. The building blocks of multipolar phenomena are magnetic ions with a non-Kramers doublet, where the orbital and spin degrees of freedom are inextricably intertwined, leading to unusual spin-orbital entangled states. The detection of such subtle forms of matter has, however, been difficult due to a limited number of appropriate experimental tools. In this work, motivated by a recent magnetostriction experiment on Pr$_2$Zr$_2$O$_7$, we theoretically investigate how multipolar quantum spin ice, an elusive three dimensional q…
In this article, I analyze the symmetries and degeneracies of electron eigenstates in a commensurate collinear antiferromagnet. In a magnetic field transverse to the staggered magnetization, a hidden anti-unitary symmetry protects double degeneracy of the Bloch eigenstates at a special set of momenta. In addition to this `Kramers degeneracy' subset, the manifold of momenta, labeling the doubly degenerate Bloch states in the Brillouin zone, may also contain an `accidental degeneracy' subset, that is not protected by symmetry and that may change its shape under perturbation. These degeneracies g…
Motivated by the rapid experimental progress on the spin-orbit-coupled Mott insulators, we propose and study a generic spin model that describes the interaction between the non-Kramers doublets on a triangular lattice and is relevant for triangular lattice rare-earth magnets. We predict that the system supports both pure quadrupolar orders and intertwined multipolar orders in the phase diagram. Besides the multipolar orders, we explore the magnetic excitations to reveal the dynamic properties of the systems. Due to the peculiar properties of the non-Kramers doublets and the selective coupling …
The exact diagonalization and the variational cluster approximation (VCA) are used to study the nature of a novel Mott insulator induced by a strong spin-orbit coupling for a two-dimensional three-band Hubbard model consisting of the $t_{2g}$ manifold of $5d$ orbitals. To characterize the ground state, we introduce a local Kramer's doublet which can represent a state with effective angular momentum $J_{\rm eff}=|{\bm S}-{\bm L}|=1/2$ as well as spin $S=1/2$. Our systematic study of the pseudo-spin structure factor defined by the Kramer's doublet shows that the $J_{\rm eff}=1/2$ Mott insulator …
Strongly Quenched Kramers Doublet Magnetism in SmMgAl11O19
Charles University, Faculty of Mathematics and Physics（查理大学数学物理学院）；Adam Mickiewicz University, Faculty of Physics and Astronomy（亚当·密茨凯维奇大学物理与天文学学院）；Institute of Physics of the Czech Academy of Sciences（捷克科学院物理研究所）
Acoustic signatures of the single-site quadrupolar Kondo effect in Y$_{0.966}$Pr$_{0.034}$Ir$_2$Zn$_{20}$ are presented. The elastic constant ($C_{11}-C_{12}$)/2, corresponding to the $Γ_3$(E)-symmetry electric-quadrupolar response, reveals a logarithmic temperature dependence of the quadrupolar susceptibility in the low-magnetic-field region below $\sim$0.3 K. Furthermore, the Curie-type divergence of the elastic constant down to $\sim$1 K indicates that the Pr ions in this diluted system have a non-Kramers ground-state doublet. These observations evidence the single-site quadrupolar Kondo ef…
Zeeman split Kramers doublets in spin-supersolid candidate Na$_{2}$BaCo(PO$_{4}$)$_{2}$
School of Physics and Astronomy, University of Edinburgh（爱丁堡大学物理与天文学院）；ISIS Pulsed Neutron and Muon Source, STFC Rutherford Appleton Laboratory（STFC卢瑟福阿普尔顿实验室ISIS脉冲中子与缪子源）；NIST Center for Neutron Research（美国国家标准与技术研究院中子研究中心）；Department of Chemistry, Princeton University（普林斯顿大学化学系）
We performed ultrasonic measurement on the rare-earth intermetallic compound PrInAg_2 to examine the quadrupolar Kondo effect associated with the non-Kramers Gamma_3 doublet ground state. The characteristic softening of the elastic constant (c_{11}-c_{12})/2 below 10 K in PrInAg_2 is attributed to a Curie term in quadrupolar susceptibility for the quadrupole O_2^2=J_x^2-J_y^2 of the stable Gamma_3 ground state. (c_{11}-c_{12})/2 turns to a slight increase with the -lnT dependence below 0.1 K, which suggests the quenching of the quadrupolar moment in the quadrupolar Kondo state. Under applied m…
Goldstone modes emerge associated with spontaneous breakdown of the continuous symmetry in the two-channel Kondo lattice, which describes strongly correlated f-electron systems with a non-Kramers doublet at each site. This paper derives the spectra of these collective modes by the equation of motion method together with the random phase approximation. The diagonal composite order breaks the SU(2) channel symmetry, and the symmetry-restoring collective mode couples with magnetic field. On the other hand, the off-diagonal or superconducting composite order breaks the gauge symmetry of conduction…
We study the spin-phonon relaxation rate of both Kramers and non-Kramers molecular magnets in strongly diluted samples at low temperature. Using the "rotational" contribution to the spin-phonon Hamiltonian, universal formulae for the relaxation rate are obtained. Intriguingly, these formulae are all entirely expressed via measurable or \emph{ab initio} computable physical quantities. Moreover, they are also independent of the energy gaps to excited states involved in the relaxation process. These obtained expressions for direct and Raman processes offer an easy way to determine the lowest limi…
Field-Induced Up-Up-Down State and Frustrated Magnetism in a Non-Kramers Triangular Antiferromagnet
Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology（南方科技大学量子科学和工程研究院）；International Quantum Academy（国际量子学院）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）；School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院）；School of Physics and Electronics, Henan University（河南大学物理与电子学院）
Quantum magnets with spin $J=2$, which arise in spin-orbit coupled Mott insulators, can potentially display multipolar orders. We carry out an exact diagonalization study of a simple octahedral crystal field Hamiltonian for two electrons, incorporating spin-orbit coupling (SOC) and interactions, finding that either explicitly including the $e_g$ orbitals, or going beyond the rotationally invariant Coulomb interaction within the $t_{2g}$ sector, causes a degeneracy breaking of the $J\!=\!2$ level degeneracy. This can lead to a low-lying non-Kramers doublet carrying quadrupolar and octupolar mom…
"Magnetic monopole" is an exotic quantum excitation in pyrochlore U(1) spin liquid, and its emergence is purely of quantum origin and has no classical analogue. We predict topological thermal Hall effect (TTHE) of "magnetic monopoles" and present this prediction through non-Kramers doublets. We observe that, when the external magnetic field polarizes the Ising component of the local moment, internally this corresponds to the induction of emergent dual U(1) gauge flux for the "magnetic monopoles". The motion of "magnetic monopoles" is then twisted by the induced dual gauge flux. This emergent L…
The orthoperovskites TbCoO$_3$ and DyCoO$_3$ with Co$^{3+}$ in a non-magnetic low-spin state have been investigated by neutron diffraction down to 0.25 K. Magnetic ordering is evidenced below $T_N=3.3$ K and 3.6 K, respectively, and the ordered arrangements are of canted type, A$_x$G$_y$ for TbCoO$_3$ and G$_x$A$_y$ for DyCoO$_3$ in Bertaut's notation. The experiments are confronted with the first-principle calculations of the crystal field and magnetism of Tb$^{3+}$ and Dy$^{3+}$ ions, located in the $Pbnm$ structure on sites of $C_s$ point symmetry. Both these ions exhibit an Ising behavior,…
Materials with non-Kramers doublet ground states naturally manifest the two-channel Kondo effect, as the valence fluctuations are from a non-Kramers doublet ground state to an excited Kramers doublet. Here, the development of a heavy Fermi liquid requires a channel symmetry breaking spinorial hybridization that breaks both single and double time-reversal symmetry, and is known as hastatic order. Motivated by cubic Pr-based materials with $Γ_3$ non-Kramers ground state doublets, this paper provides a survey of cubic hastatic order using the simple two-channel Kondo-Heisenberg model. Hastatic or…
We report thermal expansion and magnetostriction of the cubic non-Kramers system PrIr$_2$Zn$_{20}$ with a non-magnetic $\varGamma_{3}$ ground state doublet. In previous experiments, antiferroquadrupolar order at \hbox{$T_{\mathrm{Q}}=0.11$\,K} and a Fermi liquid state around $B_{\mathrm{c}}\approx5$\,T for \hbox{$\boldsymbol{B}\parallel[001]$}, indicative of possible ferrohastatic order, were discovered. For magnetic fields \hbox{$\boldsymbol{B}\parallel[001]$}, the low temperature longitudinal and transverse thermal expansion and magnetostriction are highly anisotropic. The resulting volume s…
We study the U(1) quantum spin liquid on the pyrochlore spin ice systems. For the non-Kramers doublets such as Pr$^{3+}$ and Tb$^{3+}$, we point out that the inelastic neutron scattering not only detects the low-energy gauge photon, but also contains the continuum of the "magnetic monopole" excitations. Unlike the spinons, these "magnetic monopoles" are purely of quantum origin and have no classical analogue. We further point out that the "magnetic monopole" experiences a background dual "$π$" flux due to the spin-1/2 nature of the local moment when the "monopole" hops on the dual diamond latt…
CeRhSi$_{3}$ is a superconductor under pressure coexisting with a weakly antiferromagnetic phase characterized by a Bragg peak at $\vec{q}_{0}$=($\sim$ 0.2, 0, 0.5) (N. Aso et al. J. Magn. Magn. Mater. 310, 602 (2007)). The compound is also a heavy fermion material with a large specific heat coefficient $γ$=110 mJ $\cdot$ mol$^{-1}$ $\cdot$ K$^{-2}$ and a high Kondo temperature of $T_{K}$=50 K indicative that CeRhSi$_{3}$ is in a strongly Kondo screened state. We apply high resolution neutron spectroscopy to investigate the magnetic fluctuations in the normal phase, at ambient pressures, and a…
Quantum spin liquids (QSLs) are exotic phases of matter exhibiting long-range entanglement and supporting emergent gauge fields. A vigorous search for experimental realizations of these states has identified several materials with properties hinting at QSL physics. A key issue in understanding these QSL candidates is often the interplay of weak disorder of the crystal structure with the spin liquid state. It has recently been pointed out that in at least one important class of candidate QSLs - pyrochlore magnets based on non-Kramers ions such as Pr$^{3+}$ or Tb$^{3+}$- structural disorder can …
Loss of altermagnetic order and smooth restoration of Kramers' spin degeneracy with increasing temperature in CrSb and MnTe
H.H. Wills Physics Laboratory, University of Bristol（布里斯托大学 H.H. 威尔斯物理实验室）；Department of Physics, University of Warwick（华威大学物理系）；Institute for Theoretical Physics, Johannes Keppler University Linz（林茨约翰内斯·开普勒大学理论物理研究所）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）；Max-Planck-Institut für Mikrostrukturphysik（马克斯·普朗克微结构物理研究所）
The so-called V15 molecule is formed of 15 spins 1/2 antiferromagnetically coupled. The resultant spin is equal to 1/2. Contrary to what is expected at first sight, this half-integer spin is gapped. We show that this is a consequence of the multi-spin character of the molecule. Time reversal symmetry (Kramers theorem) is preserved due to the existence of a groundstate degeneracy larger than 2. Magnetization experiments have been performed at different temperatures, sweeping-field rates and couplings with the cryostat. Their interpretation in terms of the Landau-Zener-Stuckelberg model gives ev…
Magnetization measurements and time-of-flight neutron powder-diffraction studies on the high-temperature (300--980 K) magnetism and crystal structure (321--1200 K) of a pulverized YCrO$_3$ single crystal have been performed. Temperature-dependent inverse magnetic susceptibility coincides with a piecewise linear function with five regimes, with which we fit a Curie-Weiss law and calculate the frustration factor $f$. The fit results indicate a formation of magnetic polarons between 300 and 540 K and a very strong magnetic frustration. By including one factor $η$ that represents the degree of spi…
Ultrasonic investigations of the single-site quadrupolar Kondo effect in diluted Pr system Y$_{0.966}$Pr$_{0.034}$Ir$_2$Zn$_{20}$ are reported. The elastic constant $(C_{11}-C_{12})/2$ is measured down to ~40 mK using ultrasound for the dilute system Y$_{0.966}$Pr$_{0.034}$Ir$_2$Zn$_{20}$ and the pure compound YIr$_2$Zn$_{20}$. We found that the elastic constant $(C_{11}-C_{12})/2$ of the Pr-dilute system exhibits a logarithmic temperature dependence below $T_0$ ~0.3 K, where non-Fermi-liquid (NFL) behavior in the specific heat and electrical resistivity is observed. This logarithmic temperatu…
Orbital degrees of freedom in condensed matters could play important roles in forming a variety of exotic electronic states by interacting with conduction electrons. In 4f electron systems, because of strong intra-atomic spin-orbit coupling, an orbitally degenerate state inherently carries quadrupolar degrees of freedom. The present work has focussed on a purely quadrupole-active system PrIr2Zn20 showing superconductivity in the presence of an antiferroquadrupole order at TQ = 0.11 K. We observed non-Fermi liquid (NFL) behaviors emerging in the electrical resistivity and the 4f contribution to…
The low-temperature spin dynamics of the orthorhombic TbFeO$_3$ perovskite has been studied. It has been found that the inelastic neutron scattering (INS) spectrum contains two modes corresponding to different sublattices in the compound. The iron subsystem orders antiferromagnetically at T$_N$ = 632 K and exhibits the high-energy magnon dispersion. Magnetic dynamics of this subsystem has been described using the linear spin wave theory and our solution yields sizable anisotropy between in-plane and out-of-plane exchange interactions. This approach was previously used to describe the magnon di…
Spin reorientation is an important phenomenon of rare-earth perovskites, orthoferrites and orthochromites. In this study, we consider a simple but realistic microscopic theory of the spontaneous spin-reorientation transitions induced by the 4f-3d interaction, more specifically, the interaction of the main Kramers doublet or non-Kramers quasi-doublet of the 4f ion with an effective magnetic field induced by the 3d sublattice. The obtained results indicate that the cause of both the temperature and the character of the spin-reorientation transition is a competition between the second and fourth …
Motivated by its role as a central pillar of current theories of dynamics of spin ice in and out of equilibrium, we study the single-ion dynamics of the magnetic rare earth ions in their local environments, subject to the effective fields set up by the magnetic moments they interact with. This effective field has a transverse component with respect to the local easy-axis of the crystal electric field, which can induce quantum tunnelling. We go beyond the projective spin-1/2 picture and use instead the full crystal-field Hamiltonian. We find that the Kramers vs non-Kramers nature, as well as th…
The existence of CEF states and the magnetism in conducting compounds NdAl2, UPd2Al3 and YbRh2Si2 is discussed. We point out that in metallic compounds localized crystal-field states coexist with conduction electrons. These compounds are physical realization of an anisotropic spin liquid, which in case of the atomic-like configuration with an odd number of f electrons, is unstable with respect to spin fluctuations for T->0K. YbRh2Si2 is discussed as a compound with the Kramers doublet ground state with a very low magnetic ordering temperature being a reason for the quantum critical point pheno…
A quantum melting of the spin ice is proposed for pyrochlore-lattice magnets Pr$_2TM_2$O$_7$ ($TM=$Ir, Zr, and Sn). The quantum superexchange Hamiltonian having a nontrivial magnetic anisotropy is derived in the basis of atomic non-Kramers magnetic doublets. The ground states exhibit a cooperative ferroquadrupole and pseudospin chirality, forming a magnetic analog of smectic liquid crystals. Our theory accounts for dynamic spin-ice behaviors experimentally observed in Pr$_2TM_2$O$_7$.
