Breathing Pyrochlore Research Articles

Evolution of ferromagnetism and electrical resistivity in Sb-doped Cr4PtGa17

We describe the doping effects on a metallic breathing pyrochlore compound, Cr4PtGa17. Upon doping with Sb, i.e., Cr4Pt(Ga1-xSbx)17, it was found that a selective doping on one of the seven Ga sites occurs. With increasing dopant level, the ferromagnetism in the parent compound is gradually suppressed, along with a decrease in fitted Curie-Weiss temperature (from 61 (1) K to −1.8 (1) K) and effective moment (from ∼2.26 μB/f.u. to ∼0.68 μB/f.u.). Low-temperature heat capacity measurements confirm the absence of magnetic ordering above 0.4 K for the three most doped samples. Meanwhile, electrical resistivity measurements display a metal-semiconductor transition with increasing Sb contents, which is attributed to an increase of Fermi energy based on the calculations of electronic band structure and density of states. Moreover, we have speculated that the ferromagnetism in Cr4PtGa17 is governed by itinerant electrons according to our observations. This study of Sb-doping effect on Cr4PtGa17 provides deeper understanding of magnetism of this system and possibilities for future modifications.

Disclosing magnetic clusters in the metallic half-Heusler ferromagnet Cr4PtGa17 with a breathing pyrochlore lattice

We report a ferromagnetic resonance (FMR) study of a single crystal of Cr4PtGa17, the first material of a half-Heusler (HH) type with a metallic ferromagnetic breathing pyrochlore structure. The spatial distribution of the magnetic free energy density derived from the FMR data appears to be of a cubic symmetry despite the lower symmetry coordination of magnetic Cr ions. This surprising finding strongly suggests that the Cr4Ga14 structural unit at the Y site of the HH general XYZ formula forms an octahedrally shaped integral magnetic cluster, likely due to strong exchange interaction between the Cr ions via covalent Cr-Ga-Cr bonds. The presence of magnetic clusters within a regular metallic lattice appears to be a new intriguing characteristics of these novel types of HH compounds whereas Cr4PtGa17, at the same time, constitutes the rare example of such metallic pyrochlore-type material.

Dynamics of the antiferromagnetic spin ice phase in pyrochlore spinels

Motivated by the classical spin-nematic state observed in the breathing pyrochlore spinel LiGa0.95In0.05Cr4O8, we theoretically discuss spin dynamics in models of spin-lattice coupling in these materials. Semiclassical dynamical simulations successfully recover the key features of inelastic neutron-scattering experiments on LiGa0.95In0.05Cr4O8: a broad finite-energy peak alongside a continuum of scattering near the (200) wave vector that extends from the elastic line to high energies. To interpret this result, we generalize linear-spin-wave theory for conventionally ordered magnets to the disordered spin-ice-like ground states expected for moderate spin-lattice coupling, which reproduces the numerical simulation results quantitatively. In particular, we find that the inelastic peak is well explained by collective modes confined to ferromagnetic loops of the underlying nematic order. In addition, we find a sharp, linearly dispersing mode in the dynamic structure factor, which originates in long-wavelength fluctuations of the nematic director. We believe identifying this mode will be an interesting target for future experiments on these materials. We also outline potential future applications of our methods to both pyrochlore spinels and other spin-nematic systems. Published by the American Physical Society 2024

Vison crystal in quantum spin ice on the breathing pyrochlore lattice

Recent excitement in the quantum spin ice (QSI) community has come from the experimental discovery of pseudospin-12 breathing pyrochlores, including Ba3Yb2Zn5O11, in which inversion symmetry is broken by the “up” and “down” tetrahedra taking different physical sizes. We show here that the often-neglected Jz± coupling between Kramers ions, in combination with the breathing nature of the lattice, can produce an imaginary ring flip term. This can lead to an unconventional “U(1)π/2 phase”, corresponding to a maximally dense packing of visons on the lattice. The coherent, emergent QED dynamics of conventional QSI persist in this phase, in a manner reminiscent of fragmentation in spinon crystals. We characterize the excitations of the system within the enlarged QSI phase diagram, showing that the imaginary ring flip acts both as a chemical potential for visons and as an effective three-photon vertex akin to strong light-matter coupling. The coupling causes a structured high-energy continuum to emerge above the photon dispersion, which is naturally interpreted as three photon up-conversion in a nonlinear optical crystal. Published by the American Physical Society 2024

Three-dimensional checkerboard spin structure on a breathing pyrochlore lattice

The standard approach to realize a spin-liquid state is through magnetically frustrated states, relying on ingredients such as the lattice geometry, dimensionality, and magnetic interaction type of the spins. While Heisenberg spins on a pyrochlore lattice with only antiferromagnetic nearest-neighbor interactions are theoretically proven disordered, spins in real systems generally include longer-range interactions. The spatial correlations at longer distances typically stabilize a long-range order rather than enhancing a spin-liquid state. Both states can, however, be destroyed by short-range static correlations introduced by chemical disorder. Here, using disorder-free specimens with a clear long-range antiferromagnetic order, we refine the spin structure of the Heisenberg spinel ZnFe2O4 through neutron magnetic diffraction. The unique wave vector (1,0,12) leads to a spin structure that can be viewed as alternatively stacked ferromagnetic and antiferromagnetic tetrahedra in a three-dimensional checkerboard form. Stable coexistence of these opposing types of clusters is enabled by the bipartite breathing pyrochlore crystal structure, leading to a second-order phase transition at 10 K. The diffraction intensity of ZnFe2O4 is an exact complement to the inelastic scattering intensity of several chromate spinel systems which are regarded as model classical spin liquids. Our results challenge this attribution, and suggest instead of the six-spin ring mode, spin excitations in chromate spinels are closely related to the (1,0,12) type of spin order and the four-spin ferromagnetic cluster locally at one tetrahedron. Published by the American Physical Society 2024

Crystal structural, magnetic, and dielectric properties of Cobalt−doped breathing pyrochlore LiInCr4−xCoxO8

Here, the structural, magnetic, and dielectric features of breathing pyrochlore LiInCr4−xCoxO8 were investigated. The XRD analysis showed changes in Cr–Cr length and distorted CrO6 octahedral as Co ion doping level rises. The x-ray photoemission spectroscopy measurements showed that there are both Co2+ and Co3+ ions in the LiInCr4−xCoxO8 compounds. The difference between temperature-dependent magnetization curves during field cooling and zero-field cooling suggested that there is a spin-glass state, which was verified by the heat capacity measurement. Doping affects the bond length, which affects the magnetic properties and electronic properties. The dielectric characteristics were systematically studied, and the temperature dependence of the dielectric loss and dielectric constant was examined in the temperature range of 323−573 K at various frequencies. The dielectric behavior strongly changes with the change in temperature and/or frequency. The activation energies of grain boundary resistance of doped samples show a decreasing trend with increasing doping.

Signatures of a magnetic superstructure phase induced by ultrahigh magnetic fields in a breathing pyrochlore antiferromagnet

The mutual coupling of spin and lattice degrees of freedom is ubiquitous in magnetic materials and potentially creates exotic magnetic states in response to the external magnetic field. Particularly, geometrically frustrated magnets serve as a fertile playground for realizing magnetic superstructure phases. Here, we observe an unconventional two-step magnetostructural transition prior to a half-magnetization plateau in a breathing pyrochlore chromium spinel by means of state-of-the-art magnetization and magnetostriction measurements in ultrahigh magnetic fields available up to 600 T. Considering a microscopic magnetoelastic theory, the intermediate-field phase can be assigned to a magnetic superstructure with a three-dimensional periodic array of 3-up-1-down and canted 2-up-2-down spin molecules. We attribute the emergence of the magnetic superstructure to a unique combination of the strong spin-lattice coupling and large breathing anisotropy.

Beyond single tetrahedron physics of the breathing pyrochlore compound Ba3Yb2Zn5O11

Recently, a new class of quantum magnets, the so-called breathing pyrochlore spin systems, have attracted much attention due to their potential to host exotic emergent phenomena. Here, we present magnetometry, heat capacity, thermal conductivity, muon-spin relaxation, and polarized inelastic neutron scattering measurements performed on high-quality single crystal samples of the breathing pyrochlore compound ${\mathrm{Ba}}_{3}{\mathrm{Yb}}_{2}{\mathrm{Zn}}_{5}{\mathrm{O}}_{11}$. We interpret these results using a simplified toy model and provide insight into the low-energy physics of this system beyond the single tetrahedron physics proposed previously.

Pressure-Induced Structural Phase Transitions in the Chromium Spinel LiInCr4O8 with Breathing Pyrochlore Lattice

This study reports high-pressure structural and spectroscopic studies on polycrystalline cubic chromium spinel compound LiInCr4O8. According to pressure-dependent X-ray diffraction measurements, three structural phase transitions occur at ∼14 GPa, ∼19 GPa, and ∼36 GPa. The first high-pressure phase is indexed to the low-temperature tetragonal phase of the system which coexists with the ambient phase before transforming to the second high-pressure phase at ∼19 GPa. The pressure-dependent Raman and infrared spectroscopic measurements show a blue-shift of the phonon modes and the crystal field excitations and an increase in the bandgap under compression. During pressure release, the sample reverts to its ambient cubic phase, even after undergoing multiple structural transitions at high pressures. The experimental findings are compared to the results of first principles based structural and phonon calculations.

Competing quantum spin liquids, gauge fluctuations, and anisotropic interactions in a breathing pyrochlore lattice

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 analytical solution to the parton mean field theory for each of these two $U(1)$ spin liquids. It is revealed that one of them has gapless, while the other one has gapped, spinon excitations. The two $U(1)$ spin liquids are equal in energy regardless of the degree of breathing anisotropy, and they can be differentiated by the low-temperature heat capacity contribution from the quadratically-dispersing gapless spinons. We further show that the latter is unaffected by fluctuations of the $U(1)$ gauge field within the random phase approximation. Finally, we demonstrate that a small Dzyaloshinskii-Moriya interaction lifts the degeneracy between the two $U(1)$ spin liquids, and it eventually causes the lattice to decouple into independent tetrahedra at strong coupling. While current model parameters for Ba$_3$Yb$_2$Zn$_5$O$_{11}$ place it indeed in the decoupled regime, other candidate materials may be synthesised in the near future that realize the spin liquid states discussed in our work.

Complex magnetic phase diagram with a small phase pocket in a three-dimensional frustrated magnet CuInCr4S8

Frustrated magnets with a strong spin-lattice coupling can show rich magnetic phases and the associated fascinating phenomena. A promising platform is the breathing pyrochlore magnet ${\mathrm{CuInCr}}_{4}{\mathrm{S}}_{8}$ with localized $S=3/2\phantom{\rule{4pt}{0ex}}{\mathrm{Cr}}^{3+}$ ions, which is proposed to be effectively viewed as an $S=6$ Heisenberg antiferromagnet on the face-centered-cubic lattice. Here we unveil that ${\mathrm{CuInCr}}_{4}{\mathrm{S}}_{8}$ exhibits a complex magnetic phase diagram with a small phase pocket ($A$ phase) by means of magnetization, magnetostriction, magnetocapacitance, and magnetocaloric-effect measurements in pulsed high magnetic fields of up to 60 T. Remarkably, the appearance of $A$ phase is accompanied by anomalous magnetostrictive and magnetocapacitive responses, suggesting the emergence of helimagnetism in contrast to the neighboring commensurate magnetic phases. Besides, the high-entropy nature is confirmed in the high-temperature side of $A$ phase. These features are potentially related to a thermal fluctuation-driven multiple-$q$ state caused by the magnetic frustration, which has been theoretically predicted but yet experimentally undiscovered in insulating magnets.

Towards understanding the magnetic properties of the breathing pyrochlore compound Ba3Yb2Zn5O11through single-crystal studies

Ba3Yb2Zn5O11 is exceptional 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 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 magnitude and direction) down to a temperature of 70 mK, where inelastic scattering reveals dispersionless bands of excitations as found in earlier powder sample studies, in good agreement with a single-tetrahedron model. However, diffuse neutron scattering at zero field and dc-susceptibility at finite field exhibit features suggesting the presence of excitations at low-energy that are not captured by the single tetrahedron model. Analysis of the local structure down to 2 K via pair distribution function analysis finds no evidence of structural disorder. We conclude that effects beyond the single tetrahedron model are important in describing the low-energy, low-temperature physics of Ba3Yb2Zn5O11, but their nature remains undetermined.

Hedgehog lattice and field-induced chirality in breathing-pyrochlore Heisenberg antiferromagnets

We theoretically investigate a ${J}_{1}\text{\ensuremath{-}}{J}_{3}$ classical Heisenberg model on the breathing pyrochlore lattice, where the nearest-neighbor (NN) exchange interactions for small and large tetrahedra, ${J}_{1}$ and ${J}_{1}^{\ensuremath{'}}$, 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-$\mathbf{Q}$ state characterized by the ordering vector of $\mathbf{Q}=(\ifmmode\pm\else\textpm\fi{}\frac{1}{2},\ifmmode\pm\else\textpm\fi{}\frac{1}{2},\ifmmode\pm\else\textpm\fi{}\frac{1}{2})$, being irrespective of the signs of ${J}_{1}$ and/or ${J}_{1}^{\ensuremath{'}}$ as long as ${J}_{1}\ensuremath{\ne}{J}_{1}^{\ensuremath{'}}$. It is also found that in an applied magnetic field, there appear six quadruple-$\mathbf{Q}$ states depending on the values of ${J}_{1}$ and ${J}_{1}^{\ensuremath{'}}$, among which three phases including the in-field hedgehog-lattice state exhibit nonzero total chirality ${\mathbit{\ensuremath{\chi}}}^{\mathrm{T}}$ associated with the anomalous Hall effect of chirality origin. In the remaining two chiral phases, which are realized in the presence of ferromagnetic ${J}_{1}$ and/or ${J}_{1}^{\ensuremath{'}}$, the spin structure is not topologically nontrivial, in spite of the fact that ${\mathbit{\ensuremath{\chi}}}^{\mathrm{T}}\ensuremath{\ne}0$. The role of the topological objects of the monopoles in ${\mathbit{\ensuremath{\chi}}}^{\mathrm{T}}$ is also discussed.

Synthesis and physical and magnetic properties of CuAlCr4S8 : A Cr-based breathing pyrochlore

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 ($\mu$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 breathing pyrochlores can be an important parameter to tune the magnetic ground states of the pyrochlore lattice. The breathing factor can be modulated through breathing ratio, the ratio of sizes of the two tetrahedra, by using different elements at A and A' sites in the breathing pyrochlore structure. We find that CuAlCr$_4$S$_8$ has a breathing ratio of 1.0663(8), which is comparable to other sulfur breathing pyrochlores.

Realization of fractonic quantum phases in the breathing pyrochlore lattice

Fractonic phases of matter are novel quantum ground states supporting subdimensional emergent excitations with mobility restrictions. Due to a subextensive 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 breathing pyrochlore lattice of existing materials. We show that the emergent ``cluster charge'' excitations arise as vacuum fluctuations residing on the boundary of membrane objects, and move in a subdimensional space. Using the membrane operators, we demonstrate the existence of a subextensive ground state degeneracy explicitly depending on the lattice geometry, which is a useful resource for novel quantum memory.

Structural, magnetic and dielectric properties of Ni doped LiInCr4O8 breathing pyrochlore

Herein, polycrystalline compounds of breathing pyrochlore LiInCr4-xNixO8 (x = 0, 0.1, 0.2, 0.4) were synthesized by the solid state method. Structure, magnetism, and dielectric properties have been investigated with x-ray diffraction, Raman spectroscopy, magnetic susceptibility, isothermal magnetization, AC impedance, and heat capacity measurements. The mean particle size of the Ni substituted samples decreased from 1.95 μm to 1.22 μm, which is larger than the size determined by the Scherrer formula and the Williamson-Hall method. Raman scattering revealed slightly red-shifted modes Eg, F2g(2), F2g(3), and A1g, which were caused by higher effective atomic mass and increased bond strength. At low temperatures, field cooled and zero field cooled susceptibility measurements, as well as frequency dependent χac data, show a spin-glass type freezing. The resulting Mydosh parameter p of x = 0.4 is 0.01, suggesting the spin glass state. Magnetic measurements exhibit a large negative CW temperature (|θCW| > 290 K), initially decreasing and then increasing at high Ni concentration, in support of the relationship between magnetic interactions and the structural parameters of Cr–Cr spins. Despite the large negative θCW in substituted samples, long-range magnetic order was suppressed at high Ni contents. With increasing nickel concentration, the spin gap gradually vanished, indicating a significant reduction in breathing distortion. The isothermal magnetization at 2 K confirms antiferromagnetic characteristics and weak ferromagnetic components in the substituted samples. When the frequency is increased at room temperature, the dielectric data shows a drop in dielectric constant as well as lower dielectric loss. At low frequencies, interfacial polarization mechanisms play a crucial role. In contrast, at high frequencies, the dielectric constant becomes frequency independent up to ∼ 105 Hz, due to reverse electron motion. The low temperature specific heat behavior implies the good insulator characteristic of LiInCr3.6Ni0.4O8 and a residual entropy feature related to spin-glass type freezing.

Dynamical signatures of rank-2 U(1) spin liquids

Emergent $U(1)$ gauge theories and artificial photons in frustrated magnets are outstanding examples of many-body collective phenomena. The classical and quantum regimes of these systems provide platforms for classical and quantum spin liquids, and are the subject of current active theoretical and experimental investigations. Recently, realizations of rank-2 $U(1)$ (R2-U1) gauge theories in three-dimensional frustrated magnets have been proposed. Such systems in the quantum regime may lead to the so-called fracton ordered phases---a new class of topological order that has been associated with quantum stabilizer codes and holography. However, there exist few distinguishing characteristics of these states for their detection in real materials. Here we focus on the classical limit and present the dynamical spin structure factor for a R2-U1 spin liquid state on a breathing pyrochlore lattice. Remarkably, we find unique signatures of the R2-U1 state, and we contrast them with the results obtained from a more conventional $U(1)$ spin liquid. These results provide a path of investigation for future inelastic neutron scattering experiments on candidate materials.

Effects of spin-lattice coupling and a magnetic field in classical Heisenberg antiferromagnets on the breathing pyrochlore lattice

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 realized only in the site-phonon model. In the bond-phonon model, additional further neighbor interactions are necessary to induce a magnetic LRO. In the site-phonon model, it is also found that in addition to the low-field, middle-field $\frac{1}{2}$ plateau, and high-field phases appearing on both the uniform and breathing pyrochlore lattices, various types of unconventional phases which can be viewed as LRO's in units of tetrahedron are induced by the breathing bond alternation just below the $\frac{1}{2}$ plateau and the saturation field. The occurrence of these tetrahedron-based orders could be attributed to the nature characteristic of the breathing pyrochlore lattice, i.e., the existence of the nonequivalent small and large tetrahedra. Experimental implications of our result are also discussed.

Neutron Scattering Studies of the Breathing Pyrochlore Antiferromagnet LiGaCr_{4}O_{8}.

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 these materials, which is in agreement with our hexagonal loop calculations. Our results suggest a unified picture for spin resonances in Cr spinel oxides.

The effect of manganese doping on the structural, magnetic and dielectric properties of breathing pyrochlore LiInCr4-xMnxO8

In the present paper, polycrystalline samples of LiInCr4-xMnxO8 varying from 0.0 to 0.5 were synthesized by the solid state method. In order to explore the effect of substitution Cr by Mn in LiInCr4O8, the structural, magnetic and dielectric properties are studied. The result of XRD patterns show that there is a nonmonotonic expansion in the lattice parameter, which may be due to ions disorder or/and partial exchange between A- and B-atoms. The SEM micrographs show that the Mn substituted samples are smaller in the average crystallite size and more agglomerated than the parent material. Magnetization data show the nonmonotonic variation of the effective magnetic moment and Curie-Weiss temperature, the suppressed long-range antiferromagnetic (AFM) order and spin gap, and occurrence of a spin glasslike state. Although the breathing pyrochlore lattice is robust against doping, only 5% doping concentration (x = 0.2) makes the spin gap vanish absolutely. The increased Bf makes the pyrochlore lattice more uniform, leading to the disappearance of the spin gap. The dielectric data show that Mn doping increases the dielectric constant and decreases dielectric loss at room temperature, thus these compounds should be satisfactory to the possible application in microelectronics. The result of heat capacity also verifies glass-type insulator state.