Cluster Frustration in the Breathing Pyrochlore Magnet LiGaCr4S8
Ganesh Pokharel, Hasitha Suriya Arachchige, Travis J. Williams, Andrew F. May, Randy S. Fishman, Gabriele Sala, Stuart Calder, Georg Ehlers, David S. Parker, Ta… 展开作者
Ganesh Pokharel, Hasitha Suriya Arachchige, Travis J. Williams, Andrew F. May, Randy S. Fishman, Gabriele Sala, Stuart Calder, Georg Ehlers, David S. Parker, Tao Hong, Andrew Wildes, David Mandrus, Joseph A. M. Paddison, Andrew D. Christianson
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 qualitative agreement with density-functional theory predictions [Ghoshet al.,npj Quantum Mater.4, 63 (2019)]. We explain the origin of geometrical frustration in LiGaCr4S8 interms of net antiferromagnetic coupling between emergent tetrahedral spin clusters that occupy a face-centered lattice. Our results provide insight into the emergence of frustration in the presence of strong further-neighbor couplings, and a blueprint for the determination of magnetic interactions in classical spin liquids.
The Coulombic quantum spin liquid in quantum spin ice is an exotic quantum phase of matter that emerges on the pyrochlore lattice and is currently actively searched for. Motivated by recent experiments on the Yb-based breathing pyrochlore material Ba$_3$Yb$_2$Zn$_5$O$_{11}$, we theoretically study the phase diagram and magnetic properties of the relevant spin model. The latter takes the form of a quantum spin ice Hamiltonian on a breathing pyrochlore lattice, and we analyze the stability of the quantum spin liquid phase in the absence of the inversion symmetry which the lattice breaks explicit…
Higher-rank generalisations of electrodynamics have recently attracted considerable attention because of their ability to host "fracton" excitations, with connections to both quantum stabilizer codes and holography. However, the search for higher-rank gauge theories in experiment has been greatly hindered by the lack of materially-relevant microscopic models. Here we show how a spin liquid described by rank-2 $U(1)$ gauge theory can arise in a magnet on the breathing pyrochlore lattice. We identify Yb-based breathing pyrochlores as candidate systems, and make explicit predictions for how the r…
The synthesis and characterization of a new Yb-based material Ba3Yb2Zn5O11 are reported. This material is identified as the first model system of a pseudospin-1/2 quantum antiferromagnet on "breathing" pyrochlore lattice characterized by an alternating array of small and large Yb tetrahedra. Despite dominant antiferromagnetic interactions J ~ 7 K, a large amount of magnetic entropy (25%) remains at 0.38 K, indicating that each small Yb tetrahedron forms a unique doubly degenerate singlet state. These results are well described by the Heisenberg pseudospin-1/2 single tetrahedron model.
We theoretically investigate spin-lattice coupling (SLC) effects on the in-field ordering properties of classical Heisenberg antiferromagnets on the breathing pyrochlore lattice. Here, we use the two possible simplified models describing the effect of local lattice distortions on the spin ordering via the SLC, the bond-phonon and site-phonon models. It is found by means of Monte Carlo simulations that in both models, the $\frac{1}{2}$ plateau shows up in the magnetization curve being relatively robust against the breathing bond-alternation, although magnetic long-range orders (LRO's) are reali…
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 study a spin-ice Kondo lattice model on a breathing pyrochlore lattice with classical localized spins. The highly efficient kernel polynomial expansion method, together with a classical Monte Carlo method, is employed in order to study the magnetic phase diagram at four representative values of the number density of itinerant electrons. We tune the breathing mode by varying the hopping ratio -- the ratio of hopping parameters for itinerant electrons along inequivalent paths. Several interesting magnetic phases are stabilized in the phase diagram parameterized by the hopping ratio, Kondo cou…
Frustrated quantum magnets not only provide exotic ground states and unusual magnetic structures, but also support unconventional excitations in many cases. Using a physically relevant spin model for a breathing pyrochlore lattice, we discuss the presence of topological linear band crossings of magnons in antiferromagnets. These are the analogs of Weyl fermions in electronic systems, which we dub Weyl magnons. The bulk Weyl magnon implies the presence of chiral magnon surface states forming arcs at finite energy. We argue that such antiferromagnets present a unique example in which Weyl points…
The hierarchy of the coupling strengths in a physical system often engenders an effective model at low energies where the decoupled high-energy modes are integrated out. Here, using neutron scattering, we show that the spin excitations in the breathing pyrochlore lattice compound CuInCr$_4$S$_8$ are hierarchical and can be approximated by an effective model of correlated tetrahedra at low energies. At higher energies, intra-tetrahedron excitations together with strong magnon-phonon couplings are observed, which suggests the possible role of the lattice degree of freedom in stabilizing the spin…
The magnetization processes of the spin-3/2 antiferromagnet LiInCr4O8 comprising a "breathing" pyrochlore lattice, which is an alternating array of small and large tetrahedra, are studied under ultrahigh magnetic fields of up to 130 T using state-of-the-art pulsed magnets. A half magnetization plateau is observed above 90 T to 130 T, suggesting that LiInCr4O8 has a strong spin-lattice coupling, similar to conventional chromium spinel oxides. The magnetization of LiGa0.125In0.875Cr4O8, in which the structural and magnetic transitions at low temperatures have been completely suppressed, shows a …
The low energy spin excitation spectrum of the breathing pyrochlore Ba3Yb2Zn5O11 has been investigated with inelastic neutron scattering. Several nearly resolution limited modes with no observable dispersion are observed at 250 mK while, at elevated temperatures, transitions between excited levels become visible. To gain deeper insight, a theoretical model of isolated Yb3+ tetrahedra parametrized by four anisotropic exchange constants is constructed. The model reproduces the inelastic neutron scattering data, specific heat, and magnetic susceptibility with high fidelity. The fitted exchange pa…
We present the synthesis and physical properties of a new breathing pyrochlore magnet CuAlCr$_4$S$_8$ with the help of synchrotron x-ray diffraction (XRD), magnetization under ambient and applied hydrostatic pressure, heat capacity, and muon spin relaxation/rotation ($μ$SR) measurements. CuAlCr$_4$S$_8$ exhibits positive thermal expansion with concave upward temperature dependence. We observed a sharp antiferromagnetic ordering transition of a purely magnetic nature at 20 K, which shifts by as much as 3.2 K on the application of 600 MPa pressure. The breathing factor (B$_f$ = $J'/J$) in breath…
To search for novel spin-charge coupled phenomena in the strongly correlated electron system on a frustration lattice, charge transport and dynamics have been investigated for the hole-doped spin-glass (Mott) insulator (Y$_{1-x}$Cd$_{x}$)$_{2}$Mo$_{2}$O$_{7}$ with pyrochlore structure. Coincident with the disappearance of spin-glass state by hole doping, a diffusive metallic transport with strongly renormalized electron mass shows up with no long range spin order, which is caused by strong antiferromagnetic spin fluctuation due to the geometrical frustration.
We report on the muon spin rotation/relaxation study of a pyrochlore oxide, Cd2Os2O7, which exhibits a metal-insulator (MI) transition at T_{MI}~225 K without structural phase transition. It reveals strong spin fluctuation (>10^8/s) below the MI transition, suggesting a predominant role of geometrical spin frustration amongst Os^{5+} ions. Meanwhile, upon further cooling, a static spin density wave discontinuously develops below T_{SDW}~150 K. These observations strongly suggest the occurrence of an anomalous magnetic transition and associated change in the local spin dynamics in undistorted p…
We address the long-standing problem of the microscopic origin of the richly diverse phenomena in the chromium breathing pyrochlore material family. Combining electronic structure and renormalization group techniques we resolve the magnetic interactions and analyze their reciprocal-space susceptibility. We show that the physics of these materials is principally governed by long-range Heisenberg Hamiltonian interactions, a hitherto unappreciated fact. Our calculations uncover that in these isostructural compounds, the choice of chalcogen triggers a proximity of the materials to classical spin l…
We report 7Li-NMR studies on LiInCr4O8 and LiGaCr4O8, in which Cr3+ ions with spin 3/2 form a breathing pyrochlore lattice, a network of tetrahedra with alternating sizes. In LiInCr4O8 with large alternation, the nuclear relaxation rate 1/T1 shows an activated temperature (T) dependence down to 18 K, indicating a singlet ground state with a spin gap. This behavior, however, is disrupted by an antiferromagnetic (AF) transition at 13 K, which is preceded by another, most likely structural, transition at 16 K. In contrast, LiGaCr4O8 with small alternation shows no spin gap but exhibits a first-or…
CeFe$_2$ is a geometrically frustrated ferromagnet that lies close to an instability at which a subtle change in the lattice symmetry couples to a transition to antiferromagnetism. We use x-ray diffraction, diamond-anvil-cell techniques, and numerical simulation to identify the ground states and to quantitatively illustrate effects of competing magnetic energy scales and geometrical frustration on the magnetic phase diagram. Comparison of phase transitions under both chemical substitution and applied pressure suggests a general solution to the physics of pyrochlore rare earth inter-metallic ma…
We study low energy excitations in the quantum breathing pyrochlore antiferromagnet Ba$_3$Yb$_2$Zn$_5$O$_{11}$ by combination of inelastic neutron scattering (INS) and thermodynamical properties measurements. The INS spectra are quantitatively explained by spin-1/2 single-tetrahedron model having $XXZ$ anisotropy and Dzyaloshinskii-Moriya interaction. This model has a two-fold degeneracy of the lowest-energy state per tetrahedron and well reproduces the magnetization curve at 0.5 K and heat capacity above 1.5 K. At lower temperatures, however, we observe a broad maximum in the heat capacity ar…
The A-site ordered chromate spinels LiGa1-xInxCr4O8 host a network of size-alternating spin-3/2 Cr3+ tetrahedra known as a 'breathing' pyrochlore lattice. For the x=0.05 composition, the complex magneto-structural ordering observed in the parent x=0 material is replaced by a single transition at Tf=11 K, ascribed to the collinear nematic order caused by strong spin-lattice coupling. We present here an inelastic neutron scattering study of the spin dynamics in this composition. Above Tf , the dynamical scattering function S(Q,E) is ungapped and quasi-elastic, similar to undoped LiGaCr4O8. Below…
Fractonic phases of matter are novel quantum ground states supporting sub-dimensional emergent excitations with mobility restrictions. Due to a sub-extensive ground state degeneracy that is dependent on the geometry of the underlying lattice, fractonic phases are considered as models for quantum memory or quantum glass. While there exist a number of exactly solvable models with interactions between multiple particles/spins, the realization of such models in real materials is extremely challenging. In this work, we provide a realistic quantum model of quadratic spin interactions on the breathin…
Inelastic neutron scattering measurement is performed on a breathing pyrochlore antiferromagnet Ba3Yb2Zn5O11. The observed dispersionless excitations are explained by a crystalline electric field (CEF) Hamiltonian of Kramers ion Yb3+ of which the local symmetry exhibits C3v point group symmetry. The magnetic susceptibility previously reported is consistently reproduced by the energy scheme of the CEF excitations. The obtained wave functions of the ground state Kramers doublet exhibit the planer-type anisotropy. The result demonstrates that Ba3Yb2Zn5O11 is an experimental realization of breathi…
We derive analytic forms for spin waves in pyrochlore magnets with dipolar-octupolar interactions, such as ${\rm Nd}_2{\rm Zr}_2{\rm O}_7$. We obtain full knowledge of the diagonalized magnonic Hamiltonian within the linear spin wave approximation. We also consider the effect of a "breathing mode" as a perturbation of this system. The breathing mode lifts the degeneracy of the upper band of the spin wave dispersion along the direction $X\to W$ in $k$-space.
The spinel oxides LiGaCr4O8 and LiInCr4O8 contain size-alternating pyrochlore lattices of spin-3/2 Cr3+ tetrahedra with different magnitudes of alternation. We show here that the solid solutions LiGa1-xInxCr4O8 between these two 'breathing' pyrochlore compounds display (i) rapid suppression of magnetic and structural transitions upon doping the end members, (ii) spin-glass-like freezing above 2 K in the range 0.1 $\lesssim$ x $\lesssim$ 0.6, and (iii) apparent spin-gap behavior for x $\gtrsim$ 0.7. Furthermore, no transitions are observed above 2 K at x ~ 0.9, where magnetic susceptibility rem…
The breathing pyrochlore lattice material Ba$_3$Yb$_2$Zn$_5$O$_{11}$ exists in the nearly decoupled limit, in contrast to most other well-studied breathing pyrochlore compounds. As a result, it constitutes a useful platform to benchmark theoretical calculations of exchange interactions in insulating Yb$^{3+}$ magnets. Here we study Ba$_3$Yb$_2$Zn$_5$O$_{11}$ at low temperatures in applied magnetic fields as a further probe of the physics of this model system. Experimentally, we consider the behavior of polycrystalline samples of Ba$_3$Yb$_2$Zn$_5$O$_{11}$ with a combination of inelastic neutro…
We investigate the effect of partial replacement of extended 5d Ir4+ sites by localized 3d Cr3+ moments on the magnetocaloric properties of Y2Ir2O7 (YIO) pyrochlore iridates. We find that Y2Ir2-xCrxO7 (YICO) undergoes cluster glass transition, possibly due to RKKY like interaction between localized Cr3+ moments occupying random sites in the pyrochlore network, mediated by 5d Ir conduction electrons. The coexistence of ferromagnetic and antiferromagnetic clusters give rise to the conventional and inverse magnetocaloric effect (MCE). We observe significant enhancement of conventional as well as …
Spin-singlet orders are studied for the antiferromagnetic Heisenberg model with spin $S$>1/2 on a breathing pyrochlore lattice, where tetrahedron units are weakly coupled and exchange constants have two values $0<J' \ll J$. The ground state has a thermodynamic degeneracy at $J'$=0, and I have studied lattice symmetry breaking associated to lifting this degeneracy. Third-order perturbation in $J'$ for general spin $S$ shows that the effective Hamiltonian has a form of three-tetrahedron interactions of pseudospins $τ$, which is identical to that previously derived for $S$=1/2, and I have calcula…
Tetrahedrally ferromagnetic correlations and a glassy-freezing anomaly in the breathing pyrochlore magnet $\mathrm{AgInCr_4S_8}$ with partial $A$-site disorder
Tokyo University of Agriculture and Technology（东京农工大学）；The Institute for Solid State Physics, The University of Tokyo（东京大学固体物理研究所）；Kyoto University（京都大学）
We have performed a detailed investigation of the new `breathing' pyrochlore compound LiInCr$_4$O$_8$ through Rh substitution with measurements of magnetic susceptibility, specific heat, and x-ray powder diffraction. The antiferromagnetic phase of LiInCr$_4$O$_8$ is found to be slowly suppressed with increasing Rh, up to the critical concentration of $x$ = 0.1 where the antiferromagnetic phase is still observed with the peak in specific heat $T_p$ = 12.5 K, slightly lower than $T_p$ = 14.3 K for the $x$ = 0 compound. From the measurements of magnetization we also uncover evidence that substitu…
Electronic and magnetic properties of molybdenum pyrochlores A2Mo2O7 are studied by the fully relativistic density-functional theory plus on-site repulsion (U) method, with focusing on the spin-glass insulating material Y2Mo2O7. We find that the system exhibits peculiar competition in energy between different magnetic states in the large-U insulating region. The magnetic competition cannot be explained by the conventional picture based on the geometrical frustration of isotropic Heisenberg antiferromagnetic exchange interactions. Through an analysis by using a generalized spin model, we find t…
A unique type of frustrated lattice is found in two A-site ordered spinel oxides, LiGaCr4O8 and LiInCr4O8. Because of the large size mismatch between Li+ and Ga3+/In3+ ions at the A site, the pyrochlore lattice, made up of Cr3+ ions carrying spin 3/2, becomes an alternating array of small and large tetrahedra, i.e., a "breathing" pyrochlore lattice. We introduce a parameter, the breathing factor Bf, which quantifies the degree of frustration in the pyrochlore lattice: Bf is defined as J'/J, where J' and J are nearest-neighbor magnetic interactions in the large and small tetrahedra, respectivel…
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…
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…
A second-order topological insulator in $d$ dimensions is an insulator which has no $d-1$ dimensional topological boundary states but has $d-2$ dimensional topological boundary states. It is an extended notion of the conventional topological insulator. Higher-order topological insulators have been investigated in square and cubic lattices. In this paper, we generalize them to breathing Kagome and pyrochlore lattices. First, we construct a second-order topological insulator on the breathing Kagome lattice. Three topological boundary states emerge at the corner of the triangle, realizing a 1/3 f…
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…
We use the projective symmetry group analysis to classify the quantum spin liquids on the $S=1/2$ pyrochlore magnet with a breathing anisotropy. We find 40 $\mathbb{Z}_2$ spin liquids and 16 $U(1)$ spin liquids that respect the $F\bar{4}3m$ space group and the time reversal symmetry. As an application, we consider the antiferromagnetic Heisenberg model, which is proposed to be the dominant interaction in the candidate material Ba$_3$Yb$_2$Zn$_5$O$_{11}$. Focusing on the $U(1)$ spin liquid ansatze, we find that only two of them are physical when restricted to this model. We present an analytica…
The gadolinium pyrochlores, Gd$_2B_2$O$_7$, are amongst the best realizations of antiferromagnetically coupled Heisenberg spins on a pyrochlore lattice. We present a magnetic characterization of Gd$_2$Pt$_2$O$_7$, a unique member of this family. Magnetic susceptibility, heat capacity, and muon spin relaxation measurements show that Gd$_2$Pt$_2$O$_7$ undergoes an antiferromagnetic ordering transition at $T_N = 1.6$ K. This transition is strongly first order, as indicated by the sharpness of the heat capacity anomaly, thermal hysteresis in the magnetic susceptibility, and a non-divergent relaxat…
We theoretically investigate effects of lattice distortions on the spin ordering of classical Heisenberg antiferromagnets on the breathing pyrochlore lattice. In the model, local lattice distortions originating from the site vibration are taken into account to yield effective spin interactions via the spin-lattice coupling (SLC). The breathing lattice-alternation is characterized by the ratio of the nearest-neighbor interaction for large tetrahedra to that for small ones, J'/J. It is found by Monte Carlo simulations that the system exhibits a first-order transition into four different types of…
We study the effects of a uniform electric field on the the ground state and excitations of the three-dimensional U(1) spin liquid phase of a breathing pyrochlore lattice, arising due to the coupling between the conventional (Maxwell) electric field and the emergent electrodynamics of the quantum spin ice material. This is an extension of the studies for isotropic pyrochlores in Phys. Rev. B 96, 125145 (2017) to the anisotropic case, as the lattice inversion symmetry is broken in breathing pyrochlores. The emergent photons are found to exhibit birefringence, analogous to the isotropic case. Ho…
The highly frustrated Heisenberg antiferromagnet on Checkerboard and Pyrochlore lattices is subject to strong quantum fluctuations. This problem is amenable to the Contractor Renormalization (CORE) algorithm, which systematically computes the effective interactions in a basis of local cluster eigenstates. CORE was recently used to derive the Plaquette Boson-Fermion model for the square lattice Hubbard model (cond-mat/0108087). For the spin half Checkerboard and Pyrochlore cases, we find singlet ground states which break lattice symmetry, and a gap to spin one excitations. The low excitations a…
The hedgehog lattice, a three-dimensional periodic array of magnetic monopoles and antimonopoles, is known to be realized in the presence of the Dzyaloshinskii-Moriya (DM) interaction. Here, we demonstrate by means of Monte Carlo simulations that the hedgehog lattice is induced by not the DM interaction but frustration in classical Heisenberg antiferromagnets on the breathing pyrochlore lattice. In the model, the breathing bond-alternation is characterized by the ratio of the nearest-neighbor (NN) antiferromagnetic exchange interaction for large tetrahedra to that for small ones, J1'/J1. A qua…
Ba3Yb2Zn5O11 is unique among breathing pyrochlore compounds for being in the nearly decoupled limit where inter-tetrahedron interactions are weak, hosting isolated clusters or "molecular magnet" like tetrahedra of magnetic ytterbium (Yb3+) ions. In this work, we present the first study carried out on single-crystal samples of the breathing pyrochlore Ba3Yb2Zn5O11, using a variety of magnetometry and neutron scattering techniques along with theoretical modeling. We employ inelastic neutron scattering to investigate the magnetic dynamics as a function of applied field (with respect to both magni…
The rich phase diagrams of magnetically frustrated pyrochlores have maintained a high level of interest over the past 20 years. To experimentally explore these phase diagrams requires a means of tuning the relevant interactions. One approach to achieve this is chemical pressure, that is, varying the size of the non-magnetic cation. Here, we report on a new family of lead-based pyrochlores A$_2$Pb$_2$O$_7$ (A = Pr, Nd, Gd), which we have characterized with magnetic susceptibility and specific heat. Lead is the largest known possible B-site cation for the pyrochlore lattice. Thus, these material…
Reproducing the electronic structure of AM$_4$X$_8$ lacunar spinels with a breathing pyrochlore lattice is a great theoretical challenge due to the interplay of various factors. The character of the M$_4$X$_4$ cluster orbitals is critically influenced by the Jahn-Teller instability, the spin-orbit interaction, and also by the magnetic state of the clusters. Consequently, to reproduce the narrow-gap semiconducting nature of these moderately correlated materials requires advanced approaches, since the strength of the inter-cluster hopping is strongly affected by the character of the cluster orbi…
Competition between the ferromagnetic double-exchange interaction and the super-exchange antiferromagnetic interaction is theoretically studied in the presence of geometrical frustration. As increasing the super-exchange interaction, the ferromagnetic metal becomes unstable, and is taken over by a cooperative paramagnetic metal, in sharp contrast with a discontinuous transition to the antiferromagnetic insulator in the absence of frustration. In the critical region, the system exhibits a peculiar temperature-independent behavior with highly incoherent transport, suggesting a large residual ent…
We study the low-energy properties of the geometrically frustrated Hubbard model on a three-dimensional pyrochlore lattice and a two-dimensional checkerboard lattice on the basis of the renormalization group method and mean field analysis. It is found that in the half-filling case, a (semi-)metal to insulator transition (MIT) occurs. Also, in the insulating phase, which has a spin gap, the spin rotational symmetry is not broken, while charge ordering exists. The results are applied to the description of the MIT observed in the pyrochlore system ${\rm Tl_2Ru_2O_7}$.
We investigate the quantum Heisenberg model on the pyrochlore lattice for a generic spin $S$ in the presence of nearest-neighbor $J_{1}$ and second-nearest-neighbor $J_{2}$ exchange interactions. By employing the pseudofermion functional renormalization group method, we find, for $S=1/2$ and $S=1$, an extended quantum-spin-liquid phase centered around $J_{2}=0$, which is shown to be robust against the introduction of breathing anisotropy. The effects of temperature, quantum fluctuations, breathing anisotropies, and a $J_{2}$ coupling on the nature of the scattering profile, and the pinch point…
The magnetization process of the breathing pyrochlore magnet CuInCr4S8 has been investigated in ultra-high magnetic fields up to 150 T. Successive phase transitions characterized with a substantially wide 1/2-plateau from 55 T to 110 T are observed in this system, resembling those reported in chromium spinel oxides. In addition to the 1/2-plateau phase, the magnetization is found to exhibit two inherent behaviors: a slight change in the slope of the M-H curve at ~ 85 T and a shoulder-like shape at ~ 130 T prior to the saturation. Both of them are accompanied by a hysteresis, suggesting first-o…
We theoretically investigate a $J_1$-$J_3$ classical Heisenberg model on the breathing pyrochlore lattice, where the nearest-neighbor (NN) exchange interactions for small and large tetrahedra, $J_1$ and $J_1'$, take different values due to the breathing bond-alternation and $J_3$ is the third NN antiferromagnetic interaction along the bond direction. It is found by means of Monte Carlo simulations that for large $J_3$, a hedgehog lattice, a three-dimensional periodic array of magnetic monopoles and antimonopoles, emerges in the form of a quadruple-${\bf Q}$ state characterized by the ordering …
The crystal structures and magnetic properties of three previously unreported A2B2F7 pyrochlore materials, NaSrMn2F7, NaCaFe2F7, and NaSrFe2F7 are presented. In these compounds, either S=2 Fe2+ or S=5/2 Mn2+ is on the B site, while nonmagnetic Na and Ca (Na and Sr) are disordered on the A site. The materials, which were grown as crystals via the floating zone method, display high effective magnetic moments and large Curie-Weiss thetas. Despite these characteristics, freezing of the magnetic spins, characterized by peaks in the susceptibility or specific heat, is not observed until low temperat…
Cobalt pyrochlore fluoride NaCaCo$_2$F$_7$ is a disordered frustrated magnet composed of Co$^{2+}$ ions with an effective spin-$\frac{1}{2}$ magnetic moment and exhibits spin freezing below $T_f \sim$2.4 K. We perform ultrasound velocity measurements on a single crystal of the cubic NaCaCo$_2$F$_7$. The temperature dependence of the bulk modulus (the breathing elastic mode) exhibits Curie-type softening upon cooling below $\sim$20 K down to $T_f$, which is suppressed by the magnetic field. This Curie-type softening should be a precursor to the enhancement of the strength of exchange disorder v…
In breathing pyrochlores and kagomes, couplings between neighbouring tetrahedra and triangles are free to differ. Breathing lattices thus offer the possibility to explore a different facet of the rich physics of these systems. Here we consider nearest-neighbour classical Heisenberg interactions, both ferromagnetic and antiferromagnetic, and study how the anisotropy of breathing lattices modifies the mode spectrum of pyrochlore and kagome systems. The nature and degeneracy of the flat bands are shown to be preserved for any value of the anisotropy. These flat bands can coexist with Dirac nodes …
