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The strongly correlated system $\mathrm{Ho}^{11}\mathrm{B}_{12}$ with boron sublattice Jahn-Teller instability and nanoscale electronic phase separation (dynamic charge stripes) was studied in detail by inelastic neutron scattering (INS), magnetometry, and heat capacity measurements at temperatures in the range of 3--300 K. From the analysis of registered INS spectra, we determined parameters of the cubic crystal field (CF) at holmium sites ${B}_{4}=\ensuremath{-}0.333$ meV and ${B}_{6}=\ensuremath{-}2.003$ meV (in Stevens notations), with an unconventional large ratio ${B}_{6}/{B}_{4}$ pointing to the dominant role of conduction electrons in the formation of a CF potential. The molecular field in the antiferromagnetic (AFM) state ${B}_{\mathrm{loc}}=(1.75\ifmmode\pm\else\textpm\fi{}0.1)$ T has been directly determined from the INS spectra together with short-range order effects detected in the paramagnetic state. A comparison of measured magnetization in diluted ${\mathrm{Lu}}_{0.99}{\mathrm{Ho}}_{0.01}{\mathrm{B}}_{12}$ and concentrated ${\mathrm{HoB}}_{12}$ single crystals showed a strong suppression of Ho magnetic moments by AFM exchange interactions in holmium dodecaboride. To account explicitly for the short-range AFM correlations, a self-consistent holmium dimer model was developed that allowed us to reproduce successfully field and temperature variations of the magnetization and heat capacity in the cage-glass phase of ${\mathrm{HoB}}_{12}$ in external magnetic fields.

We have studied the normal and superconductive state characteristics (resistivity, Hall coefficient, heat capacity, and magnetization) of model strongly correlated electronic systems ${\mathrm{Lu}}_{x}{\mathrm{Zr}}_{1\ensuremath{-}x}{\mathrm{B}}_{12}$ with cooperative Jahn-Teller instability of the boron rigid cage and with dynamic charge stripes. It was found that these metals are s-wave dirty limit superconductors with a small mean free path of charge carriers $l=5--140\phantom{\rule{0.16em}{0ex}}\AA{}$ and with a Cooper pair size changing nonmonotonously in the range 450--4000 \AA{}. The parent ${\mathrm{ZrB}}_{12}$ and ${\mathrm{LuB}}_{12}$ borides are type-I superconductors, and Zr to Lu substitution induces a type-I to type-II phase transition providing a variation of the Ginzburg-Landau-Maki parameter in the limits $0.65\ensuremath{\le}{\ensuremath{\kappa}}_{1,2}\ensuremath{\le}6$. We argue in favor of the two-band scenario of superconductivity in ${\mathrm{Lu}}_{x}{\mathrm{Zr}}_{1\ensuremath{-}x}{\mathrm{B}}_{12}$ with gap values ${\mathrm{\ensuremath{\Delta}}}_{1}\ensuremath{\sim}14\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and ${\mathrm{\ensuremath{\Delta}}}_{2}\ensuremath{\sim}6--8\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, with pairing corresponding to strong coupling limit $({\ensuremath{\lambda}}_{\text{e-ph}}\ensuremath{\sim}1)$ in the upper band, and to weak coupling $({\ensuremath{\lambda}}_{\text{e-ph}}\ensuremath{\sim}0.1--0.4)$ in the lower one. A pseudogap ${\mathrm{\ensuremath{\Delta}}}_{\text{ps-gap}}\ensuremath{\sim}60--110\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ is observed in ${\mathrm{Lu}}_{x}{\mathrm{Zr}}_{1\ensuremath{-}x}{\mathrm{B}}_{12}$ above ${T}_{c}$. We discuss also the possibility of anisotropic single-band superconductivity with stripe-induced both pair breaking and anisotropy, and analyze the origin of a unique enhanced surface superconductivity detected in these model compounds.

A comprehensive study of magnetoresistance and Hall effect has been performed for the set of the single crystals of nonmagnetic metal $\mathrm{Lu}{\mathrm{B}}_{12}$ with the Jahn-Teller instability of the boron cage and dynamic charge stripes forming along $\ensuremath{\langle}110\ensuremath{\rangle}$ direction. An anomalous positive contribution to Hall effect for a particular direction of magnetic field $\mathbf{H}//[001]$ is found in the single crystals of $\mathrm{Lu}{\mathrm{B}}_{12}$ of the highest quality. This contribution arising at ${T}_{\mathrm{E}}\ensuremath{\sim}150\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ is shown to increase drastically when approaching the disordered ground state below ${T}^{*}\ensuremath{\sim}60\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. The Hall effect anomaly is shown to appear in combination with the peak of magnetoresistance. The various scenarios allowing for the topology of Fermi surface, anisotropy of relaxation time for charge carriers, and interaction of external magnetic field with the filamentary structure of fluctuating charge stripes are analyzed to explain the features of magnetotransport in this metal with inhomogeneous distribution of electron density. The origin of SdH oscillations, which are observed in this nonequilibrium metal with electron phase separation and strong charge carrier scattering, is discussed.

Precise angle-resolved magnetoresistance (ARM) measurements are applied to reveal the origin of symmetry lowering in electron transport and the emergence of a huge number of magnetic phases in the ground state of the antiferromagnetic metal ${\mathrm{HoB}}_{12}$ with fcc crystal structure. By analyzing the polar H-\ensuremath{\theta}-\ensuremath{\varphi} magnetic phase diagrams of this compound reconstructed from the experimental ARM data, we argue that nonequilibrium electron density oscillations (dynamic charge stripes) are responsible for the suppression of the indirect Ruderman-Kittel-Kasuya-Yosida exchange along the ⟨110⟩ directions between the nearest neighboring magnetic moments of ${\mathrm{Ho}}^{3+}$ ions in this strongly correlated electron system.

Based on accurate x-ray structure analysis of $\mathrm{Gd}{\mathrm{B}}_{6}$ over the temperature range 85--300 K it has been shown that anomalously strong charge carrier scattering in the quantum diffusion regime of charge transport in this compound arises due to the formation of (i) dynamically coupled $\mathrm{G}{\mathrm{d}}^{3+}$ pairs of about 3.3 \AA{} in size and with energy of quasilocal oscillations \ensuremath{\sim}7--8 meV, and due to (ii) dynamic charge stripes along the [001] direction of the cubic lattice. It has been shown that the anharmonic approximation is appropriate when analyzing the static and dynamic components of the atomic displacement parameters of gadolinium. The barrier height of double-well potential of $\mathrm{G}{\mathrm{d}}^{3+}$ ions was determined both from low-temperature heat capacity measurements and from the electron density distribution reconstructed from x-ray data.

Using Fourier-transform infrared spectroscopy and optical ellipsometry, room temperature spectra of complex conductivity of single crystals of hexaborides ${\mathrm{Gd}}_{x}{\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{B}}_{6},x(\text{Gd})=\text{0},0.01,0.1,0.78,1$, are determined in the frequency range $30--35000\phantom{\rule{4.pt}{0ex}}{\text{cm}}^{\ensuremath{-}1}$. In all compounds, in addition to the Drude free-carrier spectral component, broad excitations are discovered with unusually large dielectric contributions $\mathrm{\ensuremath{\Delta}}\ensuremath{\varepsilon}=7\phantom{\rule{0.16em}{0ex}}000--15\phantom{\rule{0.16em}{0ex}}000$ and non-Lorentzian line shapes. It is suggested that the origin of the excitations is connected with the dynamic cooperative Jahn-Teller effect of ${\mathrm{B}}_{6}$ clusters. Analysis of the spectra together with the results of dc and Hall resistivity measurements show that only $25--50%$ of the conduction band electrons are contributing to the free carrier ac conductivity, with the rest being involved in the formation of an overdamped excitation, thus providing a possible explanation, in terms of nonequilibrium (hot) electrons in these hexaborides, of both the remarkably low work function of thermoemission of ${\mathrm{Gd}}_{x}{\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{B}}_{6}$ and the non-Fermi-liquid behavior in ${\mathrm{GdB}}_{6}$ crystals.

The model strongly correlated electron system ${\mathrm{Ho}}_{0.8}{\mathrm{Lu}}_{0.2}{\mathrm{B}}_{12}$, which demonstrates a cooperative Jahn-Teller instability of the boron sublattice in combination with rattling modes of Ho(Lu) ions, dynamic charge stripes, and an unusual antiferromagnetic (AF) ground state, has been studied in detail at low temperatures by magnetoresistance (\ensuremath{\Delta}\ensuremath{\rho}/\ensuremath{\rho}), magnetization, and heat capacity measurements. Based on received results it turns out that the angular H-\ensuremath{\varphi}-T magnetic phase diagrams of this nonequilibrium AF metal can be reconstructed in the form of a ``Maltese cross''. The dramatic AF ground state symmetry lowering of this dodecaboride with fcc crystal structure can be attributed to the redistribution of conduction electrons. These leave the Ruderman-Kittel-Kasuya-Yosida oscillations of the electron spin density to participate in the dynamic charge stripes providing extraordinary changes in the indirect exchange interaction between magnetic moments of $\mathrm{H}{\mathrm{o}}^{3+}$ ions and resulting in the emergence of a number of various magnetic phases. It is also shown that the two main contributions to magnetoresistance in the complex AF phase, the (i) positive linear on magnetic field and the (ii) negative quadratic $\ensuremath{-}\mathrm{\ensuremath{\Delta}}\ensuremath{\rho}/\ensuremath{\rho}\ensuremath{\sim}{H}^{2}$ component can be separated and analyzed quantitatively, correspondingly, in terms of charge carrier scattering on the spin density wave ($5d$) component of the magnetic structure and on local $4f\ensuremath{-}5d$ spin fluctuations of holmium sites.

We investigate the doping-induced changes in the electronic structure of ${\mathrm{CeB}}_{6}$ on a series of substituted ${\mathrm{Ce}}_{1\ensuremath{-}x}{R}_{x}{\mathrm{B}}_{6}$ samples ($R=\mathrm{La}$, Nd) using diffuse neutron scattering. We observe a redistribution of magnetic spectral weight across the Brillouin zone, which we associate with the changes in the Fermi-surface nesting properties related to the modified charge carrier concentration. In particular, a strong diffuse peak at the corner of the Brillouin zone ($R$ point), which coincides with the propagation vector of the elusive antiferroquadrupolar (AFQ) order in ${\mathrm{CeB}}_{6}$, is rapidly suppressed by both La and Nd doping, like the AFQ order itself. The corresponding spectral weight is transferred to the $X(00\frac{1}{2})$ point, ultimately stabilizing a long-range AFM order at this wave vector at the Nd-rich side of the phase diagram. At an intermediate Nd concentration, a broad diffuse peak with multiple local maxima of intensity is observed around the $X$ point, evidencing itinerant frustration that gives rise to multiple ordered phases for which ${\mathrm{Ce}}_{1\ensuremath{-}x}{\mathrm{Nd}}_{x}{\mathrm{B}}_{6}$ is known. On the La-rich side of the phase diagram, however, dilution of the magnetic moments prevents the formation of a similar $(00\frac{1}{2})$-type order despite the presence of nesting. Our results demonstrate how diffuse neutron scattering can be used to probe the nesting vectors in complex $f$-electron systems directly, without reference to the single-particle band structure, and emphasize the role of Fermi surface geometry in stabilizing magnetic order in rare-earth hexaborides.

The dodecaboride ${\mathrm{LuB}}_{12}$ with cage-glass state and rattling modes has been studied to clarify the nature of the large amplitude vibrations of Lu ions. Discovered anisotropy of charge transport in conjunction with distortions of the conventional fcc symmetry of the crystal lattice may be attributed to coherent motion of Lu ions along a singular direction in the lattice. Arguments are presented in favor of cooperative dynamic Jahn-Teller effect in the boron sublattice to be the reason of the rattling mode, lattice distortion, and formation of the filamentary structure of the higher conducting channels---dynamic charge stripes.

The superconducting and normal state characteristics of yttrium hexaboride (YB$_6$) have been investigated for the single crystals with a transition temperatures $T_c$ ranging between 6 K and 7.6 K. The extracted set of microscopic parameters [the coherence length $\xi$(0) $\sim$ 320$\div$340 ${\AA}$, the penetration depth $\lambda$(0) $\sim$ 1100$\div$1600 ${\AA}$ and the mean free path of charge carriers $l$ = 31$\div$58 ${\AA}$, the Ginzburg-Landau-Maki parameters $\kappa$$_{1,2}$(0) $\sim$ 3.3$\div$4.8 and the superconducting gap $\Delta$(0) $\sim$ 10.3$\div$14.8 K] confirms the type II superconductivity in "dirty limit" ($\xi$$\gg$ $l$) with a medium to strong electron-phonon interaction (the electron-phonon interaction constant $\lambda_{e-ph}$ = 0.93$\div$0.96) and $s$-type pairing of charge carriers in this compound [2$\Delta$(0)$/k_BT_c$ $\approx$ 4]. The comparative analysis of charge transport (resistivity, Hall and Seebeck coefficients) and thermodynamic (heat capacity, magnetization) properties in the normal state in YB$_6$ allowed to detect a transition into the cage-glass state at $T^*$ $\sim$ 50 K with a static disorder in the arrangement of the Y$^{3+}$ ions. We argue that the significant $T_c$ variations in the YB$_6$ single crystals are determined by two main factors: (i) the superconductivity enhancement is related with the increase of the number of isolated vacancies, both at yttrium and boron sites, which leads to the development of an instability in the hexaboride lattice; (ii) the $T_c$ depression is additionally stimulated by the spin polarization of conduction electrons emerged and enhanced by the magnetic field in the vicinity of defect complexes in the YB$_6$ matrix., Comment: 17 pages, 15 figures, 5 tables

${\mathrm{CeB}}_{6}$ is a model compound exhibiting antiferroquadrupolar (AFQ) order, its magnetic properties being typically interpreted within localized models. More recently, the observation of strong and sharp magnetic exciton modes forming in its antiferromagnetic (AFM) state at both ferromagnetic and AFQ wave vectors suggested a significant contribution of itinerant electrons to the spin dynamics. Here we investigate the evolution of the AFQ excitation upon the application of an external magnetic field and the substitution of Ce with nonmagnetic La, both parameters known to suppress the AFM phase. We find that the exciton energy decreases proportionally to ${T}_{\text{N}}$ upon doping. In field, its intensity is suppressed, while its energy remains constant. Its disappearance above the critical field of the AFM phase is preceded by the formation of two modes, whose energies grow linearly with magnetic field upon entering the AFQ phase. These findings suggest a crossover from itinerant to localized spin dynamics between the two phases, the coupling to heavy-fermion quasiparticles being crucial for a comprehensive description of the magnon spectrum.

© 2014 American Physical Society. In nature, many systems exhibit modulated phases with periodic macroscopic patterns and textures mainly due to the competitive interactions of different phases. Vortex systems in superconductors, which are easy to access, offer the possibility of tuning the ratio between the competitive interactions, providing a unique tool to study the evolution and equilibrium of similar patterns. The κ-T phase diagram of clean superconductors shows the transition from type-I to type-II superconductivity via a narrow κ range near the dual point κ=1/2 where the vortices attract each other at long distances and repel each other at short distances. This κ range, which is termed the type-II/1 phase, becomes larger with decreasing temperature. The direct imaging at the scale of individual vortices of the vortex pattern transition would provide valuable information. Therefore, by using scanning Hall probe microscopy, we have performed direct visualization of the vortex pattern transition in a ZrB12 single crystal across the type-II and type-II/1 phases. By gradually lowering the temperature, and thereby tuning vortex interactions, a transition is observed from the ordered Abrikosov vortex lattice to a disordered vortex pattern with large areas of Meissner phase, vortex chains, and vortex clusters. The formation of vortex chains and clusters has been found to arise from the combined effect of quenched disorder and the attractive vortex-vortex interaction in the type-II/1 phase. The clusters and chains serve as the vortex reservoir to enable the formation of a triangular vortex lattice of the type-II phase at high temperatures. ispartof: Physical Review B, Condensed Matter and Materials Physics vol:90 issue:18 status: published

Line shape of magnetic spin resonance at 60 GHz specific to the phase II (so-called antiferroquadrupole phase) of ${\text{CeB}}_{6}$ was studied. The applied procedure of data analysis has allowed obtaining $g$ factor of the oscillating magnetic moments, line width, and oscillating magnetization. It is found that the approaching to the transition temperature ${T}_{\text{I-II}}$ from phase II to the paramagnetic phase I results in strong broadening of the resonance (the line width increases three times in the range $1.8\text{ }\text{K}\ensuremath{\le}T\ensuremath{\le}3.8\text{ }\text{K}$) whereas $g$ factor $g=1.59$ remains temperature independent. Magnetic-resonance data suggests that the magnetization of ${\text{CeB}}_{6}$ in the phase II consists of several contributions, one of which is responsible for the observed magnetic resonance. This term in magnetization is missing in the paramagnetic phase and corresponds to ferromagnetically interacting localized magnetic moments. The magnitude of the oscillating part of magnetization is less than total magnetization in the range ${T}^{\ensuremath{\ast}}\ensuremath{\le}T\ensuremath{\le}{T}_{\text{I-II}}$ and coincides with the total magnetization for $T\ensuremath{\le}{T}^{\ensuremath{\ast}}$, where ${T}^{\ensuremath{\ast}}\ensuremath{\sim}2\text{ }\text{K}$. We argue that ferromagnetic correlations play a key role in the observed phenomenon in analogy with the recent experimental and theoretical results on the magnetic resonance in the dense Kondo systems. At the same time the interpretation of the magnetic-resonance data in the framework of the existing models of magnetism in ${\text{CeB}}_{6}$ faces substantial difficulties, which demands further development of the theory of static and dynamic magnetic properties of this heavy fermion metal.