By phenomenological Landau analysis, it is shown that a scalar order parameter with the point-group symmetry $Γ_{1g}$ explains most properties associated with the phase transition in PrFe$_4$P$_{12}$ at 6.5 K. The scalar-order model reproduces magnetic and elastic properties in PrFe$_4$P$_{12}$ consistently such as (i) the anomaly of the magnetic susceptibility and elastic constant at the transition temperature, (ii) anisotropy of the magnetic susceptibility in the presence of uniaxial pressure, and (iii) the anomaly in the elastic constant in magnetic field. An Ehrenfest relation is derived which relates the anomaly of the magnetic susceptibility to that of the elastic constant at the transition.
In order to clarify exotic multipole properties of filled skutterudites, we evaluate multipole susceptibility for $n$=1$\sim$5, where $n$ is the local $f$-electron number, on the basis of a multiorbital Anderson model constructed using the $j$-$j$ coupling scheme. For $n$=1, magnetic fluctuations dominate over low-temperature electronic properties, while for $n$=2 and 4, electronic states are dominated by both magnetic and quadrupole fluctuations. For $n$=3 and 5, octupole fluctuations are found to be significant, depending on the crystalline electric field potential. We discuss possible relev…
Current status is described toward identifying unconventional order parameters in filled skutterudites with unique ordering phenomena. The order parameters in PrFe$_4$P$_{12}$ and PrRu$_4$P$_{12}$ are discussed in relation to associated crystalline electric field (CEF) states and angular form factors. By phenomenological Landau analysis, it is shown that a scalar order model explains most properties in both PrFe$_4$P$_{12}$ and PrRu$_4$P$_{12}$ with very different magnetic properties. In particular, the highly anisotropic susceptibility induced by uniaxial pressure in PrFe$_4$P$_{12}$ is expla…
PrCo$_2$Ga$_8$ is an orthorhombic quasi-skutterudite type compound which crystallizes in the CaCo$_2$Al$_8$ structure type, with space group $Pbam$ (No. 55). The Pr$^{3+}$ ion has a site symmetry of $C_s$ which predicts a crystal electric field (CEF) level splitting into 9 singlets for $J$ = 4. However, a phase transition at $T_m$ = 1.28~K is observed in electrical resistivity and specific heat results and is reported in this paper. The electrical resistivity shows an upturn below $T_m$ due to the superzone-gap formation. This transition is tuneable in fields and is suppressed to lower tempera…
Experiments on rare-earth filled skutterudites demonstrate an intriguing array of thermodynamic, transport and superconducting properties, and bring to fore theoretical challenges posed by f-electron systems. First principle calculations based density functional theory and its extensions for strongly correlated systems such as the Hubbard U correction, provide valuable information about electronic structure that can be used to understand experiments. We present a comprehensive study of the electronic structure and Fermi surface of a series of rare earth filled skutterudites, RPt4Ge12 (where R …
Phenomenological Landau analysis shows that the properties of ordered phases in some skutterudites are consistently accounted for by a scalar order parameter which preserves the cubic symmetry, even in the ordered phase. A universal value is found for the anisotropy ratio of the transition temperature in a magnetic field, homogeneous magnetization, and induced staggered magnetization. The difference in magnetic behavior between PrFe$_4$P$_{12}$ and PrRu$_4$P$_{12}$ near their phase transitions is explained within a single framework. For the low-field phase of PrFe$_4$P$_{12}$, the scalar order…
The optical conductivity [$σ(ω)$] spectra of alkaline-earth-filled skutterudites with the chemical formula $A^{2+}M_{4}$Sb$_{12}$ ($A$ = Sr, Ba, $M$ = Fe, Ru, Os) and a reference material La$^{3+}$Fe$_{4}$Sb$_{12}$ were obtained and compared with the corresponding band structure calculations and with calculated $σ(ω)$ spectra to investigate their electronic structures. At high temperatures, the energy of the plasma edge decreased with the increasing valence of the guest atoms $A$ in the Fe$_{4}$Sb$_{12}$ cage indicating hole-type conduction. A narrow peak with a pseudogap of 25 meV was observe…
Thermal conductivity measurements were performed on single crystal samples of the superconducting filled skutterudite compounds PrOs$_4$Sb$_{12}$ and PrRu$_4$Sb$_{12}$ both as a function of temperature and magnetic field applied perpendicular to the heat current. In zero magnetic field, the low temperature electronic thermal conductivity of PrRu$_4$Sb$_{12}$ is vanishingly small, consistent with a fully-gapped Fermi surface. For PrOs$_4$Sb$_{12}$, however, we find clear evidence for residual electronic conduction as the temperature tends to zero Kelvin which is consistent with the presence of …
Motivated by current research efforts towards exploring the interplay between magnetism and superconductivity in multiband electronic systems, we have investigated the effects of Eu substitution through thermodynamic measurements on the superconducting filled skutterudite alloys Pr$_{1-x}$Eu$_x$Pt$_4$Ge$_{12}$. An increase in Eu concentration leads to a suppression of the superconducting transition temperature consistent with an increase of magnetic entropy due to Eu local moments. While the low-temperature heat capacity anomaly is present over the whole doping range, we find that in alloys wi…
$^{75}$As nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) measurements have been carried out to investigate the magnetic and electronic properties of the filled skutterudite metallic compound SrFe$_4$As$_{12}$. The temperature dependence of Knight shift $K$ determined by the NQR spectrum under a small magnetic field ($\le$ 0.5 T) shows the similar temperature dependence of the magnetic susceptibility $χ$ which exhibits a broad maximum at $T^\ast$ $\sim$ 50 K. The nuclear spin-lattice relaxation rate divided by temperature, 1/$T_1T$, increases with decreasing temperature…
The magnetic, thermodynamic and electrical/thermal transport properties of the caged-structure quasi-skutterudite Gd$_3$Ir$_4$Sn$_{13}$ are re-investigated. The magnetization $M(T)$, specific heat $C_p(T)$ and the resistivity $ρ(T)$ reveal a double-phase transition -- at $T_{N1}\sim$ 10~K and at $T_{N2}\sim$ 8.8~K -- which was not observed in the previous report on this compound. The antiferromagnetic transition is also visible in the thermal transport data, thereby suggesting a close connection between the electronic and lattice degrees of freedom in this Sn-based quasi-skutterudite. The temp…
We report the electronic and superconducting properties in the Pr-based filled-skutterudite superconductor PrRu$_4$Sb$_{12}$ with $T_c = 1.3$ K via the measurements of nuclear-quadrupole-resonance (NQR) frequency $ν_Q$ and nuclear-spin-lattice-relaxation time $T_1$ of Sb nuclei. The temperature dependence of $ν_Q$ has revealed the energy scheme of Pr$^{3+}$ crystal electric field (CEF) that is consistent with an energy separation $Δ_{CEF}\sim 70$K between the ground state and the first-excited state. In the normal state, the Korringa relation of $(1/T_1T)_{Pr}$=const. is valid, with [$(1/T_{1}…
Results of a phenomenological Monte carlo calculation for a 2D electron-phonon Holstein model near a Peierls-CDW transition are presented. Here the zero Matsubara frequency part of the phonon action is dominant and we approximated it by a phenomenological form that as an Ising-like Peierls-CDW transition. The resulting model is studied on a 32 by 32 lattice. The single particle spectral weight A(k,ω), the density of states N(ω), and the real part of the conductivity σ_1(ω) all show evidence of a pseudogap which develops in the low-energy electronic degrees of freedom as the Peierls-CDW transit…
The classification of structural phase transitions as displacive or order-disorder in character is usually based on spectroscopic data above the transition. We use single crystal x-ray diffraction to investigate structural correlations in the quasi-skutterudites, (Ca$_x$Sr$_{1-x}$)$_3$Rh$_4$Sn$_{13}$, which have a quantum phase transition at $x\sim0.9$. Three-dimensional pair distribution functions show that the amplitudes of local atomic displacements are temperature-independent below the transition and persist to well above the transition, a signature of order-disorder behavior. The implicat…
Ordered states in itinerant magnets may be related to magnetic moments displaying some weak local moment characteristics, as in intermetallic compounds hosting transition metal coordination complexes. In this paper, we report on the Fe $K$-edge X-ray absorption spectroscopy (XAS) of the itinerant magnets $R$Fe$_{4}$Sb$_{12}$ ($R=$ Na, K, Ca, Sr, Ba), aiming at exploring the electronic and structural properties of the octahedral building block formed by Fe and the Sb ligands. We find evidence for strong hybridization between the Fe $3d$ and Sb $5p$ states at the Fermi level, giving experimental…
In the study of oscillatory electron transport in high-mobility Si MOSFETs at low temperatures we observed two correlated effects in weak in-plane magnetic fields: a steep decrease of the renormalized magnetic susceptibility $χ^*(H)$ and an increase of the concentration of mobile carriers $n(H)$. We suggest a phenomenological model of the magnetic field driven redistribution between the extended and localized electronic states that qualitatively explains both effects. We argue that the redistribution is mainly caused by magnetization of the large-spin localized states with energies close to th…
We address the fundamental question of crossover from localized to itinerant state of a paradigmatic heavy fermionmaterial CeIrIn5. The temperature evolution of the one electron spectra and the optical conductivity is predicted from first principles calculation. The buildup of coherence in the form of a dispersive many body feature is followed in detail and its effects on the conduction electrons and optical conductivity of the material is revealed. We find multiple hybridization gaps and link them to the crystal structure of the material. Our theoretical approach explains the multiple peak st…
The heavy fermion properties are reviewed on selected examples often studied in Grenoble. The physical problems are presented as example of exotic matter at low temperature with three major insights: the localisation of the 4f electrons, the collapse of the long range magnetic order and the entrance in an intermediate valence regime. The question on the first or second order nature of the quantum phase transition will be discussed. In the first example, the Ising Kondo lattice of CeRu2Si2, experiments seem to be described with the picture of 4f itinerant electron dominated by their spin fluctu…
This paper clarifies the microscopic nature of the staggered scalar order, which is specific to even number of f electrons per site. In such systems, crystalline electric field (CEF) can make a singlet ground state. As exchange interaction with conduction electrons increases, the CEF singlet at each site gives way to Kondo singlets. The collective Kondo singlets are identified with itinerant states that form energy bands. Near the boundary of itinerant and localized states, a new type of electronic order appears with staggered Kondo and CEF singlets. We present a phenomenological three-state m…
Inverse melting refers to the rare thermodynamic phenomenon in which a solid melts into a liquid upon cooling, a transition that can occur only when the ordered (solid) phase has more entropy than the disordered (liquid) phase, and that has so far only been observed in a handful of systems. Here we report the first experimental observation for the inverse melting of an electronic liquid crystalline order in strontium-doped lanthanum nickelate, a compound isostructural with the superconducting cuprates, with a hole doping concentration of 1/3. Using x-ray scattering, we demonstrate that the iso…
Many recent experiments addressed manifestations of electronic crystals, particularly the charge density waves, in nano-junctions, under electric field effect, at high magnetic fields, together with real space visualizations by STM and micro X-ray diffraction. This activity returns the interest to stationary or transient states with static and dynamic topologically nontrivial configurations: electronic vortices as dislocations, instantons as phase slip centers, and ensembles of microscopic solitons. Describing and modeling these states and processes calls for an efficient phenomenological theo…
The phenomenon of colossal magnetoresistance in manganites is generally agreed to be a result of competition between crystal phases with different electronic, magnetic, and structural order; a competition which can be strong enough to cause phase separation between metallic ferromagnet and insulating charge modulated states. Nevertheless, closer inspection of phase diagrams in many manganites reveals complex phases where the two order parameters of magnetism and charge modulation unexpectedly coexist. Here we show that such experiments can be naturally explained within a phenomenological Ginzb…
The quasi-skutterudite superconductor La$_3$Co$_4$Sn$_{13}$ undergoes a phase transition at $T^*=152$ K. By measuring the temperature dependence of heat capacity, electrical resistivity, and the superlattice reflection intensity using X-ray, we explore the character of the phase transition at $T^*$. Our lattice dynamic calculations found imaginary phonon frequencies around the ${\bf M}$ point, when the high temperature structure is used in the calculations, indicating that the structure is unstable at the zero temperature limit. The combined experimental and computational results establish tha…
Based on the microscopic model introduced previously the observed specific heat and ac-susceptibility data in the superconducting phase in Sr_2RuO_4 with applied magnetic fields are described consistently within a phenomenological approach. Discussed in detail are the temperature dependence of the upper critical fields H_{c2} and H_2, the dependence of the upper critical fields on the field direction, the linear specific heat below the superconducting phase transition as a function of field or temperature, the anisotropy of the two spatial components of the order parameter, and the fluctuation…
A semi-phenomenological approach to describe the evolution of Fermi surface (FS) and electronic structure with doping is presented which is based on the spin-fermion model. The doping is simulated by a frustration term in the spin Hamiltonian and the complex internal structure of the spin-polaron quasiparticle is taken into account by a superposition of spin-polaron states with different radii. By calculating the spectrum, the spectral weights and the FS we find a rather drastic change of the electronic structure with doping which explains many photoemission data, i.e. the isotropic band botto…
We compare the pole structure of the electronic Green's function obtained by Cluster Dynamical Mean Field Theory to the results from the fractionalized Pair Density Wave idea. In the superconducting phase, we can consider the system in a state with coexistence of Superconducting and Charge order. Writing the Green's function in a way analogous to the previously proposed "hidden-fermions" model from S. Sakai et al (2016) leads to a similar pole structure for the self-energy. The fractionalization of the Pair Density Wave order also describes the pseudogap phase as a superposition of superconduc…
Phase transitions induced by short optical pulses is a new mainstream in studies of cooperative electronic states. Its special realization in systems with neutral-ionic transformations stands out in a way that the optical pumping goes to excitons rather than to electronic bands. We present a semi-phenomenological modeling of spacio-temporal effects applicable to any system where the optical excitons are coupled to a symmetry breaking order parameter. In our scenario, after a short initial pulse of photons, a quasi-condensate of excitons appears as a macroscopic quantum state which then evolves…
We present a phenomenological model that describes the low energy electronic structure of the cuprate high temperature superconductor Bi2Sr2CaCu2O8+x as observed by Spectroscopic Imagining Scanning Tunneling Microscopy (SI-STM). Our model is based on observations from Quasiparticle Interference (QPI) measurements and Local Density of States (LDOS) measurements that span a range of hole densities from critical doping, p~0.19, to extremely underdoped, p~0.06. The model presented below unifies the spectral density of states observed in QPI studies with that of the LDOS. In unifying these two sepa…
Recent observations of broken symmetries have partly demystified the pseudogap phase. Here we review evidence for long-range intra-unit-cell(IUC) nematic order and its unexpectedly strong coupling to the phase of the fluctuating stripes in the pseudogap states of underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$. In particular, we focus on the analysis techniques that reveal this evidence in scanning tunneling spectroscopy data, the definition of the extracted IUC nematic order parameter, and a phenomenological theory of the coupling between the IUC nematic order and the previously reported coexisting …
We propose a Ginzburg-Landau phenomenological model for the dependence of the critical temperature on microscopic strain in tetragonal high-Tc cuprates. Such a model is in agreement with the experimental results for LSCO under epitaxial strain, as well as with the hydrostatic pressure dependence of Tc in most cuprates. In particular, a nonmonotonic dependence of Tc on hydrostatic pressure, as well as on in-plane or apical microstrain, is derived. From a microscopic point of view, such results can be understood as due to the proximity to an electronic topological transition (ETT). In the case o…
We study the superconducting properties of a two-dimensional superconductor in the proximity to an electronic topological transition (ETT). In contrast to the 3D case, we find that the superconducting gap at T=0, the critical temperature Tc, and the impurity scattering rate are characterized by a nonmonotonic behavior, with maxima occurring close to the ETT. We derive analytical expressions for the value of such maxima both in the s-wave and in the d-wave case. Such expressions are in good qualitative agreement with the phenomenological trend recently observed for Tc^max as a function of the h…
First-principles calculations are performed to investigate f magnetism in A$_2$Ti$_2$O$_7$ (A=Eu, Gd, Tb, Dy, Ho, Er, Yb) magnetic pyrochlore oxides. The Hubbard U parameter and the relativistic spin orbit correction is applied for more accurate description of the electronic structure of the systems. It is argued that the main obstacle for first-principles study of these systems is the multi-minima solutions of their electronic configuration. Among the studied pyrochlores, Gd$_2$Ti$_2$O$_7$ shows the least multi-minima problem. The crystal electric field theory is applied for phenomenological …
We perform a phenomenological analysis of the problem of the electronic doping of a graphene sheet by deposited transition metal atoms, which aggregate in clusters. The sample is placed in a capacitor device such that the electronic doping of graphene can be varied by the application of a gate voltage and such that transport measurements can be performed via the application of a (much smaller) voltage along the graphene sample, as reported in the work of Pi et al. [Phys. Rev. B 80, 075406 (2009)]. The analysis allows us to explain the thermodynamic properties of the device, such as the level o…
A detailed high pressure investigation is carried out using x-ray diffraction, Raman spectroscopy and low temperature resistivity measurements on hexagonal ZrSe$_{2}$ having an excess of 3 at.\% Zr. Structural studies show that the sample goes through a gradual structural transition from hexagonal to monoclinic phase, with a mixed phase in the pressure range 5.9 GPa to 14.8 GPa. Presence of a minimum in the $c/a$ ratio in the hexagonal phase and a minimum in the full width half maximum of the $A_{1g}$ mode at about the same pressure indicates an electronic phase transition. The sample shows a …
Nuclear magnetic resonance (NMR) and transport measurements have been performed at high magnetic fields and low temperatures in a series of $n$-type Bi$_{2}$Se$_{3}$ crystals. In low density samples, a complete spin polarization of the electronic system is achieved, as observed from the saturation of the isotropic component of the $^{209}$Bi NMR shift above a certain magnetic field. The corresponding spin splitting, defined in the phenomenological approach of a 3D electron gas with a large (spin-orbit-induced) effective $g$-factor, scales as expected with the Fermi energy independently determi…
We present evidence for the existence of magnetic clusters of approximately 20 Åin the strongly correlated alloy system CeNi$_{1-x}$Cu$_{x}$ (0.7 $\le$ x $\le$ 0.2) based on small angle neutron scattering experiments as well as the occurrence of staircase-like hysteresis cycles during very low temperature (100 mK) magnetization measurements. An unusual feature is the observation of long-range ferromagnetic order below the cluster-glass transition without any indication of a sharp transition at a Curie temperature. These observations strongly support a phenomenological model where a percolative…
Logical devices based on spin waves offer the potential to avoid dissipation mechanisms that limit devices based on either the charge or spin of mobile electrons. Multiferroic magnetoelectrics, which are materials that combine ferroelectric and magnetic order, allow direct switching of magnetic order and thence of spin-wave properties using an applied electric field. The intrinsic coupling between polarization and magnetic moments, generated by strong electronic correlations in these multiferroic materials, is argued to provide new approaches to spin-wave injection and spin-wave switching usin…
The random substitutional solid solution between the antiferromagnetic (AFM) full-Heusler alloy Ru$_2$MnSn and the ferromagnetic (FM) full-Heusler alloy Ru$_2$FeSn provides a rare opportunity to study FM-AFM phase competition in a near-lattice-matched, cubic system, with full solubility. At intermediate $x$ in Ru$_2$Mn$_{1-x}$Fe$_x$Sn this system displays suppressed magnetic ordering temperatures, spatially coexisting FM and AFM order, and strong coercivity enhancement, despite rigorous chemical homogeneity. Here, we construct the most detailed temperature- and $x$-dependent understanding of t…
We present an atomic scale theory of lattice distortions using strain related variables and their constraint equations. Our approach connects constrained atomic length scale variations to continuum elasticity and describes elasticity at all length scales. We apply the general approach to a two-dimensional square lattice with a monatomic basis, and find the atomic scale elastic textures around a structural domain wall and a single defect, as exemplary textures. We clarify the microscopic origin of gradient terms, some of which are included phenomenologically in Landau-Ginzburg theory. The obtai…
