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 remains finite at 2 K and magnetic heat capacity shows a quadratic temperature dependence at 1-5 K. Our work shows that breathing pyrochlore compounds provide a unique opportunity for studying both geometrical frustration and bond alternation.
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…
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 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…
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…
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…
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…
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…
We report thermal expansion and magnetostriction in breathing pyrochlore magnets LiACr$_4$X$_8$ (A = Ga, In, X = O, S) measured by a dilatometric method on sintered samples. All four of these compounds showed a large volume contraction associated with antiferromagnetic order with decreasing temperature. Above the Neél temperature, LiGaCr4S8 showed negative thermal expansion, LiInCr4O8 showed positive thermal expansion with concave-downward temperature dependence, and LiInCr4S8 showed positive forced volume magnetostriction. All these phenomena are likely caused by the complex structure-magneti…
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 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…
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…
Low-temperature powder neutron diffraction measurements are performed in the ordered magnetic state of the pyrochlore antiferromagnet Gd2Sn2O7. Symmetry analysis of the diffraction data indicates that this compound has the ground state predicted theoretically for a Heisenberg pyrochlore antiferromagnet with dipolar interactions. The difference in magnetic structures of Gd2Sn2O7 and of nominally analogous Gd2Ti2O7 is found to be determined by a specific type of third-neighbor superexchange interaction on the pyrochlore lattice between spins across empty hexagons.
Magnetization plateaus, visible as anomalies in magnetic susceptibility at low temperatures, are one of the hallmarks of frustrated magnetism. We show how an extremely robust half-magnetization plateau can arise from coupling between spin and lattice degrees of freedom in a pyrochlore antiferromagnet, and develop a detailed symmetry of analysis of the simplest possible scenario for such a plateau state. The application of this theory to the spinel oxides CdCr2O4 and HgCr2O4, where a robust half magnetization plateau has been observed, is discussed.
The physical properties of the spinel LiGaCr4S8 have been studied with neutron diffraction, X-ray diffraction, magnetic susceptibility and heat capacity measurements. The neutron diffraction and synchrotron X-ray diffraction data reveal negative thermal expansion (NTE) below 111(4) K. The magnetic susceptibility deviates from Curie-Weiss behavior with the onset of NTE. At low temperature a broad peak in the magnetic susceptibility at 10.3(3) K is accompanied by the return of normal thermal expansion. First principles calculations find a strong coupling between the lattice and the simulated mag…
Most works on pyrochlore magnets deal with the interacting spin-1/2 local moments. We here study the spin-one local moments on the pyrochlore lattice, and propose a generic interacting spin model on a pyrochlore lattice. Our spin model includes the antiferromagnetic Heisenberg interaction, the Dzyaloshinskii-Moriya interaction and the single-ion spin anisotropy. We develop a flavor wave theory and combine with a mean-field approach to study the global phase diagram of this model and establish the relation between different phases in the phase diagram. We find the regime of the quantum paramagn…
We report the magnetic characterization of the frustrated transition metal pyrochlore NaCaCo$_2$F$_7$. This material has high spin Co$^{2+}$ in CoF$_6$ octahedra in a pyrochlore lattice, and disordered non-magnetic Na and Ca on the large-atom sites in the structure. Large crystals grown by the floating zone method were studied. The magnetic susceptibility is isotropic, the Co moment is larger than the spin-only value, and in spite of the large Curie Weiss theta (-140 K), freezing of the spin system, as characterized by peaks in the ac and dc susceptibility and specific heat, does not occur unt…
From dimensional reduction to tetramerization in mixed ferro-antiferro breathing pyrochlores
Indian Institute of Technology Madras（印度理工学院马德拉斯分校）；CNRS, University of Bordeaux（法国国家科学研究中心，波尔多大学）；Ludwig-Maximilians-Universität München（慕尼黑路德维希-马克西米利安大学）；HUN-REN Wigner Research Centre for Physics（匈牙利研究与教育网络温格物理研究中心）；Helmholtz-Zentrum Berlin für Materialien und Energie（柏林亥姆霍兹材料能源中心）；Freie Universität Berlin（柏林自由大学）；University of Windsor（温莎大学）；Institute for Solid State Physics and Optics（凝聚态物理与光学研究所）
I study the structural and magnetic instabilities in LaNiO$_3$ using density functional theory calculations. From the non-spin-polarized structural relaxations, I find that several structures with different Glazer tilts lie close in energy. The $Pnma$ structure is marginally favored compared to the $R\overline{3}c$ structure in my calculations, suggesting the presence of finite-temperature structural fluctuations and a possible proximity to a structural quantum critical point. In the spin-polarized relaxations, both structures exhibit the $\uparrow\!\!0\!\!\downarrow\!\!0$ antiferromagnetic or…
We present synchrotron x-ray diffraction, neutron powder diffraction and time-of-flight inelastic neutron scattering measurements on the rare earth pyrochlore oxide Nd2Zr2O7 to study the ordered state magnetic structure and cystal field states. The structural characterization by high-resolution synchrotron x-ray diffraction confirms that the pyrochlore structure has no detectable O vacancies or Nd/Zr site mixing. The neutron diffraction reveals long range all-in/all-out antiferromagnetic order below T_N ~ 0.4 K with propagation vector k = (0 0 0) and an ordered moment of 1.26(2) μ_B/Nd at 0.1 …
We investigate novel topological magnon band crossings of pyrochlore antiferromagnets with all-in-all-out (AIAO) magnetic order. By general symmetry analysis and spin-wave theory, we show that pyrochlore materials with AIAO orders can host Weyl magnons under external magnetic fields or uniaxial strains. Under a small magnetic field, the magnon bands of the pyrochlore with AIAO background can feature two opposite-charged Weyl points, which is the minimal number of Weyl points realizable in quantum materials and has not be experimentally observed so far. We further show that breathing pyrochlore…
Using $\rm Er_2Ti_2O_7$ as a motivation, we investigate finite-field properties of $XY$ pyrochlore antiferromagnets. In addition to a fluctuation-induced six-fold anisotropy present in zero field, an external magnetic field induces a combination of two-, three-, and six-fold clock terms as a function of its orientation providing for a rich and controllable magnetothermodynamics. For $\rm Er_2Ti_2O_7$, we predict a new phase transition for ${\bf H}\parallel [001]$. Re-entrant transitions are also found for ${\bf H}\parallel [111]$. We extend these results to the whole family the $XY$ pyrochlore…
Unified Description of Spin-Lattice Coupling and Thermodynamics in the Pyrochlore Heisenberg Antiferromagnet
Institute for Solid State Physics, The University of Tokyo（东京大学固体物理研究所）；Department of Physics, The University of Tokyo（东京大学物理系）；Department of Chemistry, Graduate School of Science, Kyoto University（京都大学理学研究科化学系）；Research Center for Materials Nanoarchitectonics, National Institute for Materials Science（国立材料科学研究所材料纳米结构研究中心）；Department of Engineering Science, University of Electro-Communications（电气通信大学工学部）
We explore the field-temperature phase diagram of the XY pyrochlore antiferromagnet Er$_2$Ti$_2$O$_7$, by means of magnetization and neutron diffraction experiments. Depending on the field strength and direction relative to the high symmetry cubic directions $[001], [1\bar{1}0]$ and $[111]$, the refined field induced magnetic structures are derived from the zero field $ψ_2$ and $ψ_3$ states of the $Γ_5$ irreducible representation which describes the ground state of XY pyrochlore antiferromagnets. At low field, domain selection effects are systematically at play. In addition, for $[001]$, a pha…
FeF$_3$, with its half-filled Fe$^{3+}$ $3d$ orbital, hence zero orbital angular momentum and $S=5/2$, is often put forward as a prototypical highly-frustrated classical Heisenberg pyrochlore antiferromagnet. By employing {\it ab initio} density functional theory (DFT), we obtain an effective spin Hamiltonian for this material. This Hamiltonian contains nearest-neighbor antiferromagnetic Heisenberg, bi-quadratic and Dzyaloshinskii-Moriya interactions as dominant terms and we use Monte Carlo simulations to investigate the nonzero temperature properties of this minimal model. We find that upon d…
Rare-earth pyrochlores are known to exhibit exotic magnetic phenomena. We report a study of crystal growth and characterizations of a new rare-earth compound Er$_2$AlSbO$_7$, in which Al$^{3+}$ and Sb$^{5+}$ ions share the same positions with a random distribution. The magnetism are studied by magnetic susceptibility, specific heat and thermal conductivity measurements at low temperatures down to several tens of milli-kelvin. Different from the other reported Er-based pyrochlores exhibiting distinct magnetically ordered states, a spin-freezing transition is detected in Er$_2$AlSbO$_7$ below 0.…
We show that a continuous set of degenerate critical soft modes strongly enhances the first-order character of a fluctuation-induced first-order transition in the pyrochlore dipolar Heisenberg antiferromagnet. Such a degeneracy seems essential to explain the strong first-order transition recently observed in Gd(2)Sn(2)O(7). We present some evidence from Monte-Carlo simulations and a perturbative renormalization group expansion.
We report the crystal growth, crystal structure and basic magnetic properties of a new cobalt-based pyrochlore, NaSrCo$_2$F$_7$. Na and Sr are completely disordered on the non-magnetic large atom A sites, while magnetic S=3/2 Co$^{2+}$ fully occupies the pyrochlore lattice B sites. This system exhibits an isotropic magnetic susceptibility with strong antiferromagnetic interactions ($θ_{CW}$ = -127(1)), a large effective moment (${ρ_{eff}}$ = 5.9(1) ${μ_B}$/Co) and no spin freezing until 3 K. Thus NaSrCo$_2$F$_7$ is a geometrically frustrated antiferromagnet with a frustration index f = -${θ_{C…
The ordering of the classical Heisenberg model on the pyrochlore lattice with the antiferromagnetic nearest-neighbor interaction J1 and the ferromagnetic next-nearest-neighbour interaction J2 is investigated by means of a mean-field analysis and a Monte Carlo simulation. For a moderate J2/J1-value, the model exhibits a first-order transition into an incommensurate multiple-q ordered state where multiple Bragg peaks coexist in the spin structure factor. We show that there are two types of metastable multiple-q states, a cubic symmetric sextuple-q state and a non-cubic symmetric quadruple-q stat…
We investigate spin correlations in the dipolar Heisenberg antiferromagnet Gd2Sn2O7 using polarised neutron-scattering measurements in the correlated paramagnetic regime. Using Monte Carlo methods, we show that our data are sensitive to weak further-neighbour exchange interactions of magnitude ~0.5% of the nearest-neighbour interaction, and are compatible with either antiferromagnetic next-nearest neighbour interactions, or ferromagnetic third-neighbour interactions that connect spins across hexagonal loops. Calculations of the magnetic scattering intensity reveal rods of diffuse scattering al…
NaCaNi$_2$F$_7$ is an insulating, frustrated A$_2$B$_2$F$_7$ pyrochlore with magnetic S = 1 Ni$^{2+}$ on the pyrochlore B site. Non-magnetic Na and Ca are disordered on the A-site. Magnetic susceptibility measurements made on an oriented single crystal, grown in a floating zone furnace, show isotropic behavior at temperatures between 5 and 300 K, with an effective moment of 3.7 $μ_B$/Ni. Despite displaying a large Curie-Weiss theta (-129 K), spin-ordering-related features are not seen in the susceptibility or specific heat until a spin glass transition at 3.6 K. This yields an empirical frustr…
We investigate the magnetic susceptibility of the classical Heisenberg antiferromagnet with nearest-neighbour interactions on the geometrically frustrated pyrochlore lattice, for a pure system and in the presence of dilution with nonmagnetic ions. Using the fact that the correlation length in this system for small dilution is always short, we obtain an approximate but accurate expression for the magnetic susceptibility at all temperatures. We extend this theory to the compound SrCr_{9-9x}Ga_{3+9x}O_{19} (SCGO) and provide an explanation of the phenomenological model recently proposed by Schiff…
A model for a Heisenberg antiferromagnet on a pyrochlore lattice with exchange and dipole-dipole interactions is studied via mean-field theory. In treating the dipoles by use of the Ewald method, a soft (critical) mode with a unique ordering wave vector is selected for all strengths of the dipole-dipole coupling. For weak dipoles a partially ordered, three sublattice spin structure (P state), with q_{ord}= (1/2 1/2 1/2), is selected. A fully ordered, four sublattice spin structure (F state), with q = (000), competes with the P state and becomes the stable structure as the temperature is reduce…
We present micromagnetic simulations of the dynamic GHz-range resonance modes of skyrmions excited by either out-of-plane ac magnetic fields or spin torques in prototypical synthetic ferri- and antiferromagnetic trilayer structures. The observed features in the calculated power spectra exhibit a systematic dependence on the coupling strength between the individual magnetic layers and are related to pure in-phase and anti-phase breathing modes as well as to hybridizations of breathing and spin-wave modes that are characteristic for the considered circular-shaped geometry. The experimental detec…
Highly frustrated antiferromagnets composed of magnetic rare-earth moments are currently attracting much experimental and theoretical interest. Rare-earth ions generally have small exchange interactions and large magnetic moments. This makes it necessary to understand in detail the role of long-range magnetic dipole-dipole interactions in these systems, in particular in the context of spin-spin correlations that develop in the paramagnetic phase, but are often unable to condense into a conventional long-range magnetic ordered phase. This scenario is most dramatically emphasized in the frustrat…
The pyrochlore antiferromagnet Tb2Ti2O7 has proven to be an enigma to experimentalists and theorists working on frustrated magnetic systems. The experimentally determined energy level structure suggests a local <111> Ising antiferromagnet at low temperatures, T < 10 K. An appropriate model then predicts a long-range ordered Q = 0 state below approximately 2 K. However, muon spin resonance experiments reveal a paramagnetic structure down to tens of milli-Kelvin. The importance of fluctuations out of the ground state effective Ising doublet has been recently understood, for the measured paramagn…
The Gd2Sn2O7 pyrochlore Heisenberg antiferromagnet displays a phase transition to a four sublattice Neel ordered state at a temperature near 1 K. Despite the seemingly conventional nature of the ordered state, the specific heat has been found to be described in the temperature range 350-800 mK by an anomalous T-squared power law. A similar temperature dependence has also been reported for Gd2Ti2O7, another pyrochlore Heisenberg material. Such anomalous T-squared behavior in Cv has been argued to be correlated to an unusual energy-dependence of the density of states which also seemingly manifes…
