GeCo$_2$O$_4$ is a unique system in the family of cobalt spinels ACo$_2$O$_4$ (A= Sn, Ti, Ru, Mn, Al, Zn, Fe, etc.) in which magnetic Co ions stabilize on the pyrochlore lattice exhibiting a large degree of orbital frustration. Due to the complexity of the low-temperature antiferromagnetic (AFM) ordering and long-range magnetic exchange interactions, the lattice dynamics and magnetic structure of GeCo$_2$O$_4$ spinel has remained puzzling. To address this issue, here we present theoretical and experimental investigations of the highly frustrated magnetic structure, and the infrared (IR) and Raman-active phonon modes in the spinel GeCo$_2$O$_4$, which exhibits an AFM ordering below the Néel temperature $T_N$ ~21 K, followed by a cubic ($Fd{\bar 3}m$) to tetragonal ($I4_{1}/amd$) structural phase transition at $T_S$ ~16 K. Our density-functional theory (DFT+U) calculations reveal that one needs to consider magnetic-exchange interactions up to the third nearest neighbors to get an accurate description of the low-temperature AFM order in GeCo$_2$O$_4$. At room temperature three distinct IR-active modes ($T_{1u}$) are observed at frequencies 680, 413, and 325 cm$^{-1}$ along with four Raman-active modes $A_{1g}$, $T_{2g}(1)$, $T_{2g}(2)$, and $E_{g}$ at frequencies 760, 647, 550, and 308 cm$^{-1}$, respectively, which match reasonably well with our DFT+U calculated values. All the IR-active and Raman-active phonon modes exhibit signatures of moderate spin-phonon coupling. The temperature dependence of various parameters, such as the shift, width, and intensity, of the Raman-active modes, is also discussed. Noticeable changes around $T_N$ and $T_S$ are observed in the Raman line parameters of the $E_{g}$ and $T_{2g}$ modes, which are associated with the modulation of the Co-O bonds in CoO$_6$ octahedra during the excitations of these modes.
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 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…
We study double-exchange models with itinerant t2g electrons in spinel and pyrochlore crystals. In both cases the localized spins form a network of corner-sharing tetrahedra. We show that the strong directional dependence of t2g orbitals leads to unusual Fermi surfaces that induce spin superstructures and noncoplanar orderings for a weak coupling between itinerant electrons and localized spins. Implications of our results to ZnV2O4 and Cd2Os2O7 are also discussed.
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.
Single-crystalline thin film of an iridium dioxide polymorph Ir2O4 has been fabricated by the pulsed laser deposition of LixIr2O4 precursor and the subsequent Li-deintercalation using soft chemistry. Ir2O4 crystallizes in a spinel (AB2O4) without A cations in the tetrahedral site, which is isostructural to lambda-MnO2. Ir ions form a pyrochlore sublattice, which is known to give rise to a strong geometrical frustration. This Ir spinel was found to be a narrow gap insulator, in remarkable contrast to the metallic ground state of rutile-type IrO2. We argue that an interplay of strong spin-orbit …
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…
We report measurements of magnon spin transport in a spinel ferrite, magnesium aluminum ferrite $\mathrm{MgAl_{0.5}Fe_{1.5}O_4}$ (MAFO), which has a substantial in-plane four-fold magnetic anisotropy. We observe spin diffusion lengths $> 0.8$ $\mathrm{μm}$ at room temperature in 6 nm films, with spin diffusion length 30% longer along the easy axes compared to the hard axes. The sign of this difference is opposite to the effects just of anisotropy in the magnetic energy for a uniform magnetic state. We suggest instead that accounting for anisotropy in exchange stiffness is necessary to explain …
Insulating magnetic rare-earth pyrochlores related to spin ice host emergent bosonic monopolar spinons, which obey a magnetic analogue of quantum electrodynamics and may open a route to a magnetic analogue of electronics. However, the energy scales of the interactions among rare-earth moments are so low as 1 K that the possible quantum coherence can only be achieved at a sub-Kelvin. Here, we desgin high-temperature quantum spin ice materials from first principles. It is shown that the A-site deintercalated spinel iridate Ir2O4, which has been experimentally grown as epitaxial thin films, is a …
We study the exchange constants of MnV$_2$O$_4$ using magnetic force theorem and local spin density approximation of density functional theory supplemented with a correction due to on-site Hubbard interaction U. We obtain the exchanges for three different orbital orderings of the Vanadium atoms of the spinel. We then map the exchange constants to a Heisenberg model with single-ion anisotropy and solve for the spin-wave excitations in the non-collinear, low temperature phase of the spinel. The single-ion anisotropy parameters are obtained from an atomic multiplet exact-diagonalization program, …
It is shown that both structural phase transitions in Cd2Re2O7, which occur at T_{s1}=200 K and T_{s2}=120 K, are due to an instability of the Re tetrahedral network with respect to the same doubly degenerate long-wavelength phonon mode. The primary structural order parameter transforms according to the irreducible representation E_u of the point group O_h. We argue that the transition at T_{s1} may be of second order, in accordance with experimental data. We obtain the phase diagram in the space of phenomenological parameters and propose a thermodynamic path that Cd2Re2O7 follows upon cooling…
The non-equilibrium cation site occupancy in nanosized zinc ferrites (6-13 nm) with different degree of inversion (0.2 to 0.4) was investigated using Fe and Zn K-edge x-ray absorption spectroscopy XANES and EXAFS, and magnetic measurements. The very good agreement between experimental and ab-initio calculations on the Zn K-edge XANES region clearly show the large Zn2+(A)--Zn2+[B] transference that takes place in addition to the well-identified Fe3+[B]--Fe3+(A) one, without altering the long-range structural order. XANES spectra features as a function of the spinel inversion were shown to depen…
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…
We investigate analytically and numerically the classical ground states of frustrated Heisenberg models on pyrochlore and kagome lattices in zero and finite magnetic fields. Each model has a wide region in the microscopic parameter space, where the propagation vector is turned to a commensurate position equal to a half of the reciprocal lattice vector with a nontrivial star. Within these regions the zero-field ground states for both models correspond to noncoplanar triple-k spin configurations. A universal appearance of the 3-k states can be related to the spin-space dimensionality. A strong m…
We present an analytical model of orbital ordering in vanadium spinel MnV2O4. The model is based on recent first-principles calculation indicating a strong trigonal distortion at the vanadium sites of this compound [Phys. Rev. Lett. 102, 216405 (2009)]. At the single-ion level, the trigonal crystal field leaves a doubly degenerate atomic ground state and breaks the approximate rotational symmetry of t2g orbitals. We find that the effective interaction between the low-energy doublets is described by a quantum antiferromagnetic 120-degree model on the pyrochlore lattice. We obtain the classical …
We present a first-principles investigation of the spin-ice state in Dy$_2$Ti$_2$O$_7$ using a magnetic source-free exchange and correlation functional, implemented in the Castep electronic-structure code. By comparing results from the conventional local spin-density approximation, we show that a spin-ice state in Dy$_2$Ti$_2$O$_7$ can be reliably obtained by removing the magnetic sources from the exchange and correlation contributions to the potential, and we contrast this against the computed ground states of other frustrated pyrochlore magnets.
We perform systematic density functional theory (DFT) calculations to assess the performance of various exchange-correlation potentials $V_{xc}$ in describing the chalcogenide GaM$_4$Q$_8$ lacunar spinels (M=Mo, V, Nb, Ta; Q=S, Se). We examine the dependency of crystal structure (in cubic and rhombohedral symmetries), electronic structure, magnetism, optical conductivity, and lattice dynamics in lacunar spinels at four different levels of $V_{xc}$: the local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA, and hybrid with fractional Fock exchange. We find that L…
Multiferroicity in the Presence of Exchange Bias: The Case of Spinel CoMn2O4
School of Physical Science, Jawaharlal Nehru University（贾瓦哈拉尔·尼赫鲁大学物理科学学院）；Special Centre for Nanoscience, Jawaharlal Nehru University（贾瓦哈拉尔·尼赫鲁大学纳米科学特别中心）
The rare earth pyrochlore magnet Yb2Ti2O7 is among a handful of materials that apparently exhibit no long range order down to the lowest explored temperatures and well below the Curie-Weiss temperature. Paramagnetic neutron scattering on a single crystal sample has revealed the presence of anisotropic correlations and recent work has led to the proposal of a detailed microscopic Hamiltonian for this material involving significantly anisotropic exchange. In this article, we compute the local sublattice susceptibility of Yb2Ti2O7 from the proposed model and compare with the measurements of Cao a…
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…
The origin of negative thermal expansion (NTE) in the bond frustrated ZnCr2Se4 has been explored. ESR and FTIR document an ideal paramagnetic state above 100 K, below which ferromagnetic clusters coexist with the paramagnetic state down to TN. By fitting the inverse susceptibility above 100 K using a modified paramagnetic Curie-Weiss law, an exponentially changeable exchange integral J is deduced. In the case of the variable J, magnetic exchange and lattice elastic energy couple with each other effectively via magnetoelastic interaction in the ferromagnetic clusters, where NTE occurs at a loss…
Recent experimental studies on Fe substituted spinel CoCr$_{2}$O$_{4}$ have discovered multiple functional properties in the system such as temperature and composition dependent magnetic compensation, tunable exchange bias and magnetostriction. These properties are attributed to the renormalisation of the inter-atomic magnetic exchange interactions arising due to the non-regular site occupancies of the magnetic cations in the system. In this work, we perform {\it ab initio} electronic structure calculations by DFT+U method and combine with a generalised thermodynamic model to compute the site …
We apply the self-interaction corrected local spin density %(SIC-LSD) approximation to study the electronic structure and magnetic properties of the spinel ferrites MnFe$_{2}$O$_{4}$, Fe$_{3}$O$_{4}$, CoFe$_{2}$O$_{4}$, and NiFe$_{2}$O$_{4}$. We concentrate on establishing the nominal valence of the transition metal elements and the ground state structure, based on the study of various valence scenarios for both the inverse and normal spinel structures for all the systems. For both structures we find all the studied compounds to be insulating, but with smaller gaps in the normal spinel scenari…
Spinel structured compounds, $AB_2O_4$, are special because of their exotic multiferroic properties. In $ACr_2O_4$ ($A$=$Co$, $Mn$,$Fe$), a switchable polarization has been observed experimentally due to a non-collinear magnetic spin order. In this article, we demonstrated the microscopic origin behind such magnetic spin order, hysteresis, polarisation and the so-called magnetic compensation effect in $ACr_2O_4$ ($A$=$Co$, $Mn$,$Fe$, $Ni$) using Monte Carlo simulation. With a careful choice of the exchange interaction, we were able to explain various experimental findings such as magnetization…
Disentangling the contributions of individual cations to magnetic order in a spinel high entropy oxide
University of British Columbia（不列颠哥伦比亚大学）；Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）；University of Saskatchewan（萨斯喀彻温大学）；Canadian Light Source（加拿大光源）
The symmetry of local moments plays a defining role in the nature of exotic grounds states stabilized in frustrated magnetic materials. We present inelastic neutron scattering (INS) measurements of the crystal electric field (CEF) excitations in the family of compounds MgRE$_2$Se$_4$ (RE $\in$ $\{$Ho, Tm, Er and Yb$\}$). These compounds form in the spinel structure, with the rare earth ions comprising a highly frustrated pyrochlore sublattice. Within the symmetry constraints of this lattice, we fit both the energies and intensities of observed modes in the INS spectra to determine the most lik…
In this paper we present a study of magnetic order of quantum Heisenberg spins on pyrochlore type lattices: a lattice of corner sharing tetrahedra. We use the Cluster Variation Approximation with the tetrahedron as basic cluster. We find that in case of anti-ferromagnetic nearest--neighbour exchange there is no long--range spin order at any finite temperature for any spin s. For ferromagnetic exchange and s=1/2 the spin system remains in a non-magnetic phase for all temperatures, while for s > 1/2 there is a finite order temperature. We derive the ground state phase diagram as a function of ex…
Spinel ferrites in general show a rich interplay of structural, electronic, and magnetic properties. Here, we particularly focus on zinc ferrite (ZFO), which has been observed experimentally to crystallise in the cubic $normal$ spinel structure. However, its magnetic ground state is still under dispute. In addition, some unusual magnetic properties in ZFO thin films or nanostructures have been explained by a possible partial cation inversion and a different magnetic interaction between the two cation sublattices of the spinel structure compared to the crystalline bulk material. Here, density f…
When a conduction electron couples with a non-coplanar localized magnetic moment, the realspace Berry curvature is exerted to cause the geometrical Hall effect, which is not simply proportional to the magnetization. So far, it has been identified in the case mostly where the non-coplanar magnetic order is present on the sublattice of conduction electrons. Here, we demonstrate that the geometrical Hall effect shows up even without long-range magnetic order of conduction electrons, as induced by non-coplanar exchange fields from the localized magnetic moments, in hole-doped phyrochlore molybdate…
Low-energy spin excitations in any long-range ordered magnetic system in the absence of magnetocrystalline anisotropy are gapless Goldstone modes emanating from the ordering wave vectors. In helimagnets, these modes hybridize into the so-called helimagnon excitations. Here we employ neutron spectroscopy supported by theoretical calculations to investigate the magnetic excitation spectrum of the isotropic Heisenberg helimagnet ZnCr2Se4 with a cubic spinel structure, in which spin-3/2 magnetic Cr3+ ions are arranged in a geometrically frustrated pyrochlore sublattice. Apart from the conventional…
Magnetic ordering in the geometrically frustrated magnetic oxide spinels MgCr_2O_4 and ZnCr_2O_4 is accompanied by a structural change that helps relieve the frustration. Analysis of high-resolution synchrotron X-ray scattering reveals that the low-temperature structures are well described by a two-phase model of tetragonal I4_1/amd and orthorhombic Fddd symmetries. The Cr_4 tetrahedra of the pyrochlore lattice are distorted at these low-temperatures, with the Fddd phase displaying larger distortions than the I4_1/amd phase. The spin-Jahn-Teller distortion is approximately one order of magnitu…
Magneto-Structural Coupling Enables Cryogenic Cation Redistribution in a Spinel Oxide
Hainan University（海南大学）；Arizona State University（亚利桑那州立大学）；Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；Spallation Neutron Source Science Center（散裂中子源科学中心）；University of Science and Technology Beijing（北京科技大学）；Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所北京凝聚态物理国家实验室）
We report on x-ray diffraction, magnetic susceptibility, electron- spin resonance and heat- capacity studies of Co[Al_1-xCo_x]_2O_4 for Co concentrations 0<x<1. In this spinel system only the A-site Co^2+ cation is magnetic, while the non-magnetic B-site Al^3+ is substituted by the low-spin non-magnetic Co^3+, and it is possible to investigate the complete phase diagram from Co^2+Al^3+_2O_4 to Co^2+Co^3+_2O_4. All samples reveal large negative Curie-Weiss temperatures Theta_CW of the order of -110 K independent of concentration, which is attributed to a high multiplicity of the superexchange i…
Classical symmetry enriched topological orders and distinct monopole charges for dipole-octupole spin ices
International Center for Quantum Materials, Peking University（北京大学量子材料中心）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）；Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）；The University of Hong Kong, Shenzhen Institute of Research and Innovation（香港大学深圳研究院）；Beijing Key Laboratory of Quantum Devices, Peking University（北京大学量子器件北京市重点实验室）
We present here magnetization, specific heat and Raman studies on single-crystalline specimens of the first pyrochlore member $Sm_2Ti_2O_7$ of the rare-earth titanate series. Its analogous compound $Sm_2Zr_2O_7$ in the rare-earth zirconate series is also investigated in the polycrystalline form. The Sm spins in $Sm_2Ti_2O_7$ remain unordered down to at least T = 0.5 K. The absence of magnetic ordering is attributed to very small values of exchange ($θ_{cw} ~ -0.26 K$) and dipolar interaction ($μ_{eff} ~ 0.15 μ_B$) between the $Sm^{3+}$ spins in this pyrochlore. In contrast, the pyrochlore $Sm_…
The normal spinel oxide MgCr2O4 is cubic at room temperature while the normal spinel CuCr2O4 is tetragonal as a consequence of the Jahn-Teller nature of Cu2+ on the tetrahedral sites. Despite different end-member structures, complete solid solutions of Mg_{1-x}Cu_xCr2O4 can be prepared that display a first-order structural transition with composition x = 0.43 at room temperature. Reverse Monte Carlo analysis of total neutron scattering on data acquired between 300 K and 15 K on samples with x = 0.10, 0.20, and 0.43 provides unbiased local and average structure descriptions of the samples, incl…
Neutron diffraction studies have been carried out in the applied magnetic field H(//[011]) on a single crystal of pyrochlore ferromagnet Nd2Mo2O7, whose Hall resistivity(r_H) has been reported to have quite unusual magnetic field (H)- and temperature (T)- dependences. The intensities of the observed magnetic reflections have been reproduced at 1.6 K as a function of H, by considering the change of the magnetic structure with H, where effects of the exchange fields at the Mo and Nd sites induced by the Mo-Mo and Mo-Nd exchange interactions and the single ion anisotropies of Mo- and Nd- moments …
The very low temperature properties of two pyrochlore compounds, Yb2Ti2O7 and Gd2Sn2O7, were investigated using an ensemble of microscopic and bulk techniques. In both compounds, a first order transition is evidenced, as well as spin dynamics persisting down to the 20mK range. The transition however has a quite different character in the two materials: whereas that in Gd2Sn2O7$ (at 1K) is a magnetic transition towards long range order, that in Yb2Ti2O7 (at 0.24K) is reminiscent of the liquid-gas transition, in the sense that it involves a 4 orders of magnitude drop of the spin fluctuation freq…
The Raman spectroscopy and AC and DC magnetization of Dy$_{2-x}$Eu$_x$Ti$_2$O$_7$ have been investigated. In Raman Spectroscopy, the systematic shift in all phonon modes with Eu content in Dy$_{2-x}$Eu$_x$Ti$_2$O$_7$ confirms that Dy$^{3+}$ ion is substituted by Eu3+ ions. High concentration of Eu induces the dipolar exchange interactions and crystal-field interactions in Dy$_{2-x}$Eu$_x$Ti$_2$O$_7$. Rich Eu content samples (x=1.8 and 1.9) show the existence of wasp-waisted hysteresis loop and that can be attributed to the coexistence of dipolar field and anisotropy exchange interaction. AC su…
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…
GeCu2O4 exhibits a tetragonal spinel structure due to the strong Jahn-Teller distortion associated with Cu2+ ions. We show that its magnetic structure can be described as slabs composed of a pair of layers with orthogonally oriented spin 1/2 Cu chains in the basal ab plane. The spins between the two layers within a slab are collinearly aligned while the spin directions of neighboring slabs are perpendicular to each other. Interestingly, we find that spins along each chain form an unusual up-up-down-down (UUDD) pattern, suggesting a non-negligible nearest-neighbor biquadratic exchange interacti…
