EuAl4 possesses the BaAl4 crystal structure type with tetragonal symmetry I4/mmm. It undergoes a charge-density-wave (CDW) transition at TCDW = 145 K and it features four consecutive antiferromagnetic phase transitions below 16 K. Here, we use single-crystal x-ray diffraction to determine incommensurately modulated crystal structure of EuAl4 in its CDW state. The CDW is shown to be incommensurate with modulation wave vector q = (0, 0, 0.1781(3)) at 70 K. The symmetry of the incommensurately modulated crystal structure is orthorhombic with superspace group Fmmm(00σ)s00, where Fmmm is a subgroup of I4/mmm of index 2. Both the lattice and the atomic coordinates of the basic structure remain tetragonal. Symmetry breaking is entirely due to the modulation wave, where atoms Eu and Al1 have displacements exclusively along a, while the fourfold rotation would require equal displacement amplitudes along a and b. The calculated band structure of the basic structure and interatomic distances in the modulated crystal structure both indicate the aluminum atoms as location of the CDW. The temperature dependence of the specific heat reveals an anomaly at TCDW = 145 K of a magnitude similar to canonical CDW systems. The present discovery of orthorhombic symmetry for the CDW state of EuAl4 leads to the suggestion of monoclinic instead of orthorhombic symmetry for the third AFM state.
High-quality Pr0.7Ca0.3MnO3/SrRuO3 superlattices with ultrathin layers were fabricated by pulsed laser deposition on SrTiO3 substrates. The superlattices were studied by atomically resolved scanning transmission electron microscopy, high-resolution transmission electron microscopy, resistivity and magnetoresistance measurements. The superlattices grew coherently without growth defects. Viewed along the growth direction, SrRuO3 and Pr0.7Ca0.3MnO3 layers were terminated by RuO2 and MnO2, respectively, which imposes a unique structure to their interfaces. Superlattices with a constant thickness o…
A-122 pnictides (A an alkaline earth element) possess striped antiferromagnetic states of orthorhombic (OR) symmetry and nonmagnetic states of tetragonal (T) symmetry. Based on total energy calculations, we show that the T = 0K pressure-driven transition from OR to T states occurs at a pressure, $P_H$, where the tetragonal enthalpy drops below the orthorhombic. The OR state remains metastable up to a higher pressure, $P_M$ > $P_H$. We find anomalies in magnetism and orthorhombicity as $P \rightarrow P_M$, and a trend towards elastic instability.
Using high resolution X-Ray diffraction (XRD) on high purity powders, we resolved the structure and $ab$ symmetry of the intriguing compound \svo$ $ from room temperature down to 20 K to an unprecedented level of accuracy. Upon cooling, this new set of data unambiguously reveals a second order phase transition lowering the symmetry from tetragonal to orthorhombic at a temperature $T_{c2}=136$ K. The observation of an orthorhombic distortion of the $ab$-plane is attributed to nematic phase formation supported by local Jahn-Teller (JT) dynamical instability. At $T_{N}=105$ K, spins order and at …
It is shown that a quasi two dimensional (layered) Heisenberg antiferromagnet with fully frustrated interplane couplings ({\it e.g.} on a body-centered tetragonal lattice) generically exhibits two thermal phase transitions with lowering temperature -- an upper transition at $T_{TO}$ (``order from disorder without order'') in which the lattice point-group symmetry is spontaneously broken, and a lower Néel transition at $T_{N}$ at which spin-rotation symmetry is broken. Although this is the same sequence of transitions observed in La$_2$CuO$_4$, in the Heisenberg model (without additional lattic…
Synchrotron x-ray diffraction experiments were performed on BaFe$_2$As$_2$ and Sr(Fe$_{1-x}$Co$_{x}$)$_2$As$_2$ single crystals as a function of temperature and applied magnetic field along the tetragonal $[1 \bar{1} 0]$ direction, complemented by electrical resistivity and specific heat experiments. For a BaFe$_2$As$_2$ crystal with spin-density-wave antiferromagnetic ordering temperature $T_{AF}=132.5$ K and onset of the orthorhombic phase at $T_{o}=137$ K, the magnetic field favors the growth of tetragonal domains that compete with orthorhombic ones for $T \gtrsim T_{AF}$. For a Sr(Fe$_{1-x…
$^{75}$As and $^{139}$La NMR results of LaFeAs(O$_{1-x}$F$_x$) ($x$=0, 0.025, and 0.04) were reported. Upon F-doping, the tetragonal-to-orthorhombic structural phase transition temperature $T_S$, antiferromagnetic transition temperature $T_N$ and internal magnetic field $μ_0H_{\rm int}$ are gradually reduced for $x<0.04$. However, at $x=0.04$, $T_N$ is abruptly suppressed to be 30 K along with a tiny $μ_0H_{\rm int}$, which is distinct from the continuous disappearance of the ordered phases in the Ba122 systems of Ba(Fe,Co)$_2$As$_2$ and BaFe$_2$(As,P)$_2$. The anisotropy of the spin-lattice r…
Understanding the interplay between nematicity, magnetism and superconductivity is pivotal for elucidating the physics of iron-based superconductors. Here we use neutron scattering to probe magnetic and nematic orders throughout the phase diagram of NaFe$_{1-x}$Ni$_x$As, finding that while both static antiferromagnetic and nematic orders compete with superconductivity, the onset temperatures for these two orders remain well-separated approaching the putative quantum critical points. We uncover local orthorhombic distortions that persist well above the tetragonal-to-orthorhombic structural tran…
Results of in situ high pressure x-ray powder diffraction on the mixed valence compound Cs2Au(I)Au(III)I6 (CsAuI3) are reported, for pressures up to 21 GPa in a diamond anvil cell under hydrostatic conditions. We find a reversible pressure-induced tetragonal to orthorhombic structural transition at 5.5-6 GPa, and reversible amorphization at 12-14 GPa. Two alternative structures are proposed for the high-pressure orthorhombic phase, and are discussed in the context of a possible Au valence transition.
We report detailed thermal expansion and magnetostriction experiments on GdCoIn$_5$ and GdRhIn$_5$ single crystal samples that show a sudden change in the dilation at a field B$^\ast$ for temperatures below the Néel transition temperature TN. We present a first-principles model including crystal-field effects, dipolar and exchange interactions, and the dependence of the exchange couplings with lattice distortions in order to fully account for the magnetostriction and magnetic susceptibility data. The mean-field solution of the model shows that a transition between metastable states occurs at t…
We use neutron polarization analysis to study temperature dependence of the spin excitation anisotropy in BaFe$_2$As$_2$, which has a tetragonal-to-orthorhombic structural distortion at $T_s$ and antiferromagnetic (AF) phase transition at $T_N$ with ordered moments along the orthorhombic $a$-axis below $T_s\approx T_N\approx 136$ K. In the paramagnetic tetragonal state at 160 K, spin excitations are isotropic in spin space with $M_a=M_b=M_c$, where $M_a$, $M_b$, and $M_c$ are spin excitations polarized along the $a$, $b$, and $c$-axis directions of the orthorhombic lattice, respectively. On co…
We use polarized neutron scattering to demonstrate that in-plane spin excitations in electron doped superconducting BaFe1.904Ni0.096As2 (Tc=19.8 K) change from isotropic to anisotropic in the tetragonal phase well above the antiferromagnetic (AF) ordering and tetragonal-to-orthorhombic lattice distortion temperatures (Tn=Ts=33 K) without an uniaxial pressure. While the anisotropic spin excitations are not sensitive to the AF order and tetragonal-to-orthorhombic lattice distortion, superconductivity induces further anisotropy for spin excitations along the [1,1,0] and [1,-1,0] directions. These…
We use inelastic light scattering to study Sr$_{1-x}$Na$_x$Fe$_2$As$_2$ ($x\approx0.34$), which exhibits a robust tetragonal magnetic phase that restores the four-fold rotation symmetry inside the orthorhombic magnetic phase. With cooling, we observe splitting and recombination of an $E_g$ phonon peak upon entering the orthorhombic and tetragonal magnetic phases, respectively, consistent with the reentrant phase behavior. Our electronic Raman data reveal a pronounced feature that is clearly associated with the tetragonal magnetic phase, suggesting the opening of an electronic gap. No phonon ba…
We undertake a detailed high-resolution diffraction study of a novel plain band insulator, La$_2$MgO$_4$, which may be viewed as a structural surrogate system of the undoped end-member of the high-T$_c$ superconductors, La$_{2-x-y}$A$^{2+}_x$RE$^{3+}_y$CuO$_{4}$ (A = Ba, Sr, RE= Rare Earth). We find that La$_2$MgO$_4$ exhibits the infamous low-temperature orthorhombic (LTO) to low-temperature tetragonal (LTT) phase transition that has been linked to the suppression of superconductivity in a variety of underdoped cuprates, including the well known La$_{2-x}$Ba$_{x}$CuO$_4$ ($x=0.125$). Furtherm…
The experimental study of the modulation of the envelope of spin-echo signals due to internal and external fields is an important spectroscopic tool to detect very small internal magnetic fields. We derive the free induction decay and the frequency spectrum and amplitude of spin-echo signals for arbitrary orientation of fields with respect to crystalline axis for nuclei in a crystal of orthorhombic symmetry. Results reproduce the results that no modulation should be observed in tetragonal crystals for fields either along the c-axis or any direction in the basal plane and give details of the si…
Magnetic interactions are generally believed to play a key role in mediating electron pairing for superconductivity in iron arsenides; yet their character is only partially understood. Experimentally, the antiferromagnetic (AF) transition is always preceded by or coincident with a tetragonal to orthorhombic structural distortion. Although it has been suggested that this lattice distortion is driven by an electronic nematic phase, where a spontaneously generated electronic liquid crystal state breaks the C4 rotational symmetry of the paramagnetic state, experimental evidence for electronic anis…
We report on the different roles of two orbital-active Fe$^{2+}$ at the A site and V$^{3+}$ at the B site in the magnetic excitations and on the anomalous spin wave broadening in FeV$_{2}$O$_{4}$. FeV$_{2}$O$_{4}$ exhibits three structural transitions and successive paramagnetic (PM)-collinear ferrimagnetic (CFI)-noncollinear ferrimagnetic (NCFI) transitions. The high-temperature tetragonal/PM -orthorhombic/CFI transition is accompanied by the appearance of an energy gap with a high magnitude in the magnetic excitations due to strong spin-orbit coupling induced anisotropy at the Fe$^{2+}$ site…
We present detailed electronic structure calculations for CaFe2As2. We investigate in particular the `collapsed' tetragonal and orthorhombic regions of the temperature-pressure phase diagram and find properties that distinguish CaFe2As2 from other Fe-pnictide compounds. In contrast to the tetragonal phase of other Fe-pnictides the electronic structure in the `collapsed' tetragonal phase of CaFe2As2 is found to be strongly 3D. We discuss the influence of these properties on the formation of superconductivity and in particular we find evidence that both magnetic and lattice interactions may be i…
We study the order parameter for mixed-symmetry states involving a major $d_{x^2-y^2}$ state and various minor s-wave states ($s$, $s_{xy}$, and $s_{x^2+y^2}$) for different filling and temperature for mixing angles 0 and $π/2$. We employ a two-dimensional tight-binding model incorporating second-neighbor hopping for tetragonal and orthorhombic lattice. There is mixing for the symmetric $s$ state both on tetragonal and orthorhombic lattice. The $s_{xy}$ state mixes with the $d_{x^2-y^2}$ state only on orthorhombic lattice. The $s_{x^2+y^2}$ state never mixes with the $d_{x^2-y^2}$ state. The t…
The symmetry of the Bloch functions in the conduction band of tetragonal and orthorhombic La_2CuO_4 is examined for the existence of symmetry-adapted and optimally localizable (usual or spin-dependent) Wannier functions. It turns out that such Wannier functions do not exist in the tetragonal phase. In the orthorhombic phase, on the other hand, the Bloch functions can be unitarily transformed in three different ways into optimally localizable Wannier functions: they can be chosen to be adapted to each of the three phases observed in the pure or doped material, that is, to the antiferromagnetic …
Depending on the crystal growth conditions, an orthorhombic (O-type) or a tetragonal (T-type) structure can be found in the solid solution Cs2CuCl4-xBrx (0 < x < 4). Here we present measurements of the temperature-dependent magnetic susceptibility and isothermal magnetization on the T-type compounds x = 1.6 and 1.8 and compare these results with the magnetic properties recently derived for the O-type variant by Cong et al., Phys. Rev. B 83, 064425 (2011). The systems were found to exhibit quite dissimilar magnetic properties which can be assigned to differences in the Cu coordination in these …
High-resolution x-ray diffraction measurements reveal an unusually strong response of the lattice to superconductivity in Ba[Fe(1-x)Cox]2As2. The orthorhombic distortion of the lattice is suppressed and, for Co-doping near x = 0.063, the orthorhombic structure evolves smoothly back to a tetragonal structure. We propose that the coupling between orthorhombicity and superconductivity is indirect and arises due to the magneto-elastic coupling, in the form of emergent nematic order, and the strong competition between magnetism and superconductivity.
We present a structural analysis of the substituted system (Ba$_{1-x}$Sr$_{x}$)CuSi$_{2}$O$_{6}$, which reveals a stable tetragonal crystal structure down to 1.5 K. We explore the structural details with lowtemperature neutron and synchrotron powder diffraction, room-temperature and cryogenic highresolution NMR, as well as magnetic- and specific-heat measurements and verify that a structural phase transition into the orthorhombic structure which occurs in the parent compound BaCuSi2O6, is absent for the x = 0.1 sample. Furthermore, synchrotron powder-diffraction patterns show a reduction of th…
With decreasing temperature Sr$_2$VO$_4$ undergoes two structural phase transitions, tetragonal-to-orthorhombic-to-tetragonal, without long-range magnetic order. Recent experiments suggest, that only at very low temperature Sr$_{2}$VO$_{4}$ might enter some, yet unknown, phase with long-range magnetic order, but without orthorhombic distortion. By combining relativistic density functional theory with an extended spin-1/2 compass-Heisenberg model we find an antiferromagnetic single-stripe ground state with highly competing exchange interactions, involving a non negligible inter-layer coupling, …
We calculate the influence of transverse fluctuations on the longitudinal dynamics in the striped phase of cuprates by using the bosonization technique. We find that a charge density wave instability can arise if the stripe is quarter filled and the underlying lattice potential has a zigzag symmetry. Our results explain why static stripes are experimentally observed in underdoped La_{2-x-y}Nd_ySr_xCuO_4 exactly at the onset of the low-temperature-tetragonal transition.
We study magnetism on the fcc lattice with tetragonal distortions, with general exotic directional magnetic interactions allowed by symmetry. We consider two models, corresponding to a uniform tetragonal distortion, or a two-sublattice model with a tetragonal screw axis. We establish their low temperature phase diagrams in the semi-classical limit using classical optimization and consideration of fluctuations both analytically and by Monte Carlo simulation. Both order by disorder and exchange anisotropy mechanisms favor a $\langle 110\rangle$ easy axis for magnetization. We also show that spin…
We report the magnetization, ac susceptibility, and specific heat of optically float-zoned single crystals of CePdAl$_{3}$. In comparison to the properties of polycrystalline CePdAl$_{3}$ reported in the literature, which displays a tetragonal crystal structure and no long-range magnetic order, our single crystals exhibit an orthorhombic structure ($Cmcm$) and order antiferromagnetically below a Néel temperature $T_{\rm N}$ = 5.6 K. The specific heat at zero-field shows a clear $λ$-type anomaly with a broad shoulder at $T_{\rm N}$. A conservative estimate of the Sommerfeld coefficient of the e…
The Sr concentration dependence of the structural transition from the orthorhombic into the tetragonal low-temperature phase in rare-earth-doped (R = Nd, Eu) La_{2-x-y}Sr_xR_yCuO_4 has been studied in detail. Independently of the rare earth concentration the transition temperature is strongly reduced at x ~ 0.05. We give a qualitative argument that the effect can be attributed to the Coulomb repulsion between doped carriers. We find the enthalpy jump at the low-temperature transition to scale transition temperature between the high-temperature tetragonal and the orthorhombic phase. This effect…
We use density-functional theory with the local-density approximation to study the structural and ferroelectric properties of SrTiO$_3$ under misfit strains. Both the antiferrodistortive (AFD) and ferroelectric (FE) instabilities are considered. The rotation of the oxygen octahedra and the movement of the atoms are fully relaxed within the constraint of a fixed in-plane lattice constant. We find a rich misfit strain-induced phase transition sequence and is obtained only when the AFD distortion is taken into account. We also find that compressive misfit strains induce ferroelectricity in the te…
We found, using density-functional theory calculations within the generalized gradient approximation, that Cs$_2$AgF$_4$ is stabilized in the insulating orthorhombic phase rather than in the metallic tetragonal phase. The lattice distortion present in the orthorhombic phase corresponds to the $x^2-z^2$/$y^2-z^2$ hole-orbital ordering of the Ag$^{2+}$ $4d^9$ ions, and this orbital ordering leads to the observed ferromagnetism, as confirmed by the present total-energy calculations. This picture holds in the presence of moderate 4d-electron correlation. The results are compared with the picture o…
We consider p-wave pairing of single hyperfine state and s-wave pairing of two hyperfine states ultracold atomic gases trapped in quasi-two-dimensional optical lattices. First, we analyse superfluid properties of p-wave and s-wave symmetries in the strictly weak coupling BCS regime where we discuss the order parameter, chemical potential, critical temperature, atomic compressibility and superfluid density as a function of filling factor for tetragonal and orthorhombic optical lattices. Second, we analyse superfluid properties of p-wave and s-wave superfluids in the evolution from BCS to BEC re…
The interplay between magnetism and crystal structures in three CaFe$_{2}$As$_{2}$ samples is studied. For the nonmagnetic quenched crystals, different crystalline domains with varying lattice parameters are found, and three phases (orthorhombic, tetragonal, and collapsed tetragonal) coexist between T$_{S}$ = 95 K and 45 K. Annealing of the quenched crystals at 350°C leads to a strain relief through a large (~1.3 %) expansion of the c-parameter and a small (~0.2 %) contraction of the a-parameter, and to local ~0.2 Å displacements at the atomic-level. This annealing procedure results in the mos…
FeSe undergoes a transition from a tetragonal to a slightly orthorhombic phase at 90\,K, and becomes a superconductor below 8\,K. The orthorhombic phase is sometimes called a nematic phase because quantum oscillation, neutron, and other measurements detect a significant asymmetry in $x$ and $y$. How nematicity affects superconductivity has recently become a matter of intense speculation. Here we employ an advanced \emph{ab-initio} Green's function description of superconductivity and show that bulk tetragonal FeSe would, in principle, superconduct with almost the same T$_{c}$ as the nematic ph…
The centrosymmetric tetragonal itinerant magnet EuAl$_{4}$ exhibits an intricate magnetic phase diagram including rhombic and square skyrmion-lattice (SkL) phases in the external magnetic field. Here, we report a multi-axis dilatometric investigation of EuAl$_{4}$ by means of a newly designed fiber-Bragg-grating technique complemented by a resonant x-ray scattering experiment, revealing anisotropic magnetostriction and magnetovolume effect associated with successive phase transitions. The rhombic and square SkL phases are found to possess $\sim$0.10% and $\sim$0.03% orthorhombic structural dis…
We study the crystal structure of the tetragonal iron selenide FeSe and its nematic phase transition to the low-temperature orthorhombic structure using synchrotron x-ray and neutron scattering analyzed in both real and reciprocal space. We show that in the local structure the orthorhombic distortion associated with the electronically driven nematic order is more pronounced at short length scales. It also survives up to temperatures above 90 K where reciprocal-space analysis suggests tetragonal symmetry. Additionally, the real-space pair distribution function analysis of the synchrotron x-ray …
Room temperature charge density wave in a tetragonal polymorph of Gd2Os3Si5 and study of its origin in the RE2T3X5 (RE = Rare earth, T = transition metal, X = Si, Ge) series
TThe parent compounds of iron-arsenide superconductors, $A$Fe$_{2}$As$_{2}$ ($A$=Ca, Sr, Ba), undergo a tetragonal to orthorhombic structural transition at a temperature $T_{\mathrm{TO}}$ in the range 135 to 205K depending on the alkaline earth element. Below $T_{\mathrm{TO}}$ the free standing crystals split into equally populated structural domains, which mask intrinsic, in-plane, anisotropic properties of the materials. Here we demonstrate a way of mechanically detwinning CaFe$_{2}$As$_{2}$ and BaFe$_{2}$As$_{2}$. The detwinning is nearly complete, as demonstrated by polarized light imaging…
Magneto-structural phase transitions in Ba1-xAxFe2As2 (A = K, Na) materials are discussed for both magnetically and orbitally driven mechanisms, using a symmetry analysis formulated within the Landau theory of phase transitions. Both mechanisms predict identical orthorhombic space-group symmetries for the nematic and magnetic phases observed over much of the phase diagram, but they predict different tetragonal space-group symmetries for the newly discovered re-entrant tetragonal phase in Ba1-xNaxFe2As2 (x ~ 0.24-0.28). In a magnetic scenario, magnetic order with moments along the c-axis, as fo…
We report a 75-As single crystal NMR investigation of LaFeAsO, the parent phase of a pnictide high Tc superconductor. We demonstrate that spin dynamics develop a strong two-fold anisotropy within each orthorhombic domain below the tetragonal-orthorhombic structural phase transition at T[TO]~156 K. This intermediate state with a dynamical breaking of the rotational symmetry freezes progressively into a spin density wave (SDW) below T[SDW]~142 K. Our findings are consistent with the presence of a spin nematic state below T[TO] with an incipient magnetic order.
Diminishing in the concentration of quenching defects during thermocycling of orthorhombic TaS$_3$ samples in the temperature range below the Peierls transition temperature $T <T_P$ is observed. It makes it possible to study the character of pinning of the charge density wave (CDW) by these defects. A number of fundamental differences from pinning by ordinary local pinning centers - impurities and point defects - have been found. We conclude that quenching defects are extended (non-local) objects (presumably, dislocations) that can diffuse from the crystal during low-temperature termocycling d…
We report the reflectivity and the resistivity measurement of Ca_{2-x}Na_{x}CuO_{2}Cl_{2} (CNCOC), which has a single-CuO2-plane lattice with no orthorhombic distortion. The doping dependence of the in-plane optical conductivity spectra for CNCOC is qualitatively the same to those of other cuprates, but a slight difference between CNCOC and LSCO, i.e., the absence of the 1.5 eV peak in CNCOC, can be attributed to the smaller charge-stripe instability in CNCOC. The temperature dependence of the optical onductivity spectra of CNCOC has been analyzed both by the two-component model (Drude+Lorentz…
