We have determined the spatial distribution of the magnetisation induced by a field of 9 T in the tetragonal phase of BaFe2As2 using polarised neutron diffraction. Magnetic structure factors derived from the polarisation dependence of the intensities of Bragg reflections were used to make a maximum entropy reconstruction of the distribution projected on the 110 plane. The reconstruction shows clearly that the magnetisation is confined to the region around the iron atoms and that there is no significant magnetisation associated with either the As or Ba atoms. The distribution of magnetisation around the Fe atom is significantly non-spherical with a shape which is extended in the <111> directions in the projection. These results show that the electrons which give rise to the paramagnetic susceptibility are confined to the Fe atoms their distribution suggests that they occupy 3d t_2g type orbitals with about 60% in those of xy symmetry.
This paper provides an analysis of neutron inelastic scattering experiments on single crystals of UPd2Al3. The emphasis is on establishing robust, general, inferences on the joint antiferromagnetic-superconducting state which characterises UPd2Al3 at low temperatures. A distinction is drawn between these conclusions and various theoretical perspectives of a more model sensitive nature that have been raised in the literature.
The ground state of the ring-shape magnetic nanoparticle is studied. Depending on the geometrical and magnetic parameters of the nanoring, there exist different magnetisation configurations (magnetic phases): two phases with homogeneous magnetisation (easy-axis and easy-plane phases) and two inhomogeneous (planar vortex phase and out-of-plane one). The existence of a new intermediate out-of-plane vortex phase, where the inner magnetisation is not strongly parallel to the easy axis, is predicted. Possible transitions between different phases are analysed using the combination of analytical calc…
Recently, KFe$_2$As$_2$ was shown to exhibit a structural phase transition from a tetragonal to a collapsed tetragonal phase under applied pressure of about $15~\mathrm{GPa}$. Surprisingly, the collapsed tetragonal phase hosts a superconducting state with $T_c \sim 12~\mathrm{K}$, while the tetragonal phase is a $T_c \leq 3.4~\mathrm{K}$ superconductor. We show that the key difference between the previously known non-superconducting collapsed tetragonal phase in AFe$_2$As$_2$ (A= Ba, Ca, Eu, Sr) and the superconducting collapsed tetragonal phase in KFe$_2$As$_2$ is the qualitatively distinct e…
This paper, I, presents new results from neutron inelastic scattering experiments on single crystals of UPd2Al3. The focus is on the experimental position whilst the sequel, II, advances theoretical perspectives. We present a detailed and complete characterisation of the wavevector- and energy-dependent magnetisation dynamics in UPd2Al3 as measured by neutron inelastic scattering primarily in the form of extensive surveys in energy-momentum space under a wide range of experimental conditions, and put our observations in context with data that has been previously published by two independent gr…
We present a study of the tetragonal to collapsed-tetragonal transition of CaFe2As2 using angle-resolved photoemission experiments and dynamical mean field theory-based electronic structure calculations. We observe that the collapsed-tetragonal phase exhibits reduced correlations and a higher coherence temperature due to the stronger Fe-As hybridization. Furthermore, a comparison of measured photoemission spectra and theoretical spectral functions shows that momentum-dependent corrections to the density functional band structure are essential for the description of low-energy quasiparticle dis…
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 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…
Inelastic neutron scattering measurements of CaFe2As2 under applied hydrostatic pressure show that the antiferromagnetic spin fluctuations observed in the ambient pressure, paramagnetic, tetragonal (T) phase are strongly suppressed, if not absent, in the collapsed tetragonal (cT) phase. These results are consistent with a quenched Fe moment in the cT phase and the strong decrease in resistivity observed upon crossing the boundary from the T to cT phase. The suppression or absence of static antiferromagnetic order and dynamic spin fluctuations in the non-superconducting cT phase supports the no…
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 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…
Temperature dependent measurements of 57Fe Mossbauer spectra on CaFe2As2 single crystals in the tetragonal and collapsed tetragonal phases are reported. Clear features in the temperature dependencies of the isomer shift, relative spectra area and quadrupole splitting are observed at the transition from the tetragonal to the collapsed tetragonal phase. From the temperature dependent isomer shift and spectral area data, an average stiffening of the phonon modes in the collapsed tetragonal phase is inferred. The quadrupole splitting increases by ~25% on cooling from room temperature to ~100 K in …
A large part of the interest in magnets with frustrated antiferromagnetic interactions comes from the many new phases found in applied magnetic field. In this Article, we explore some of the new phases which arise in a model with frustrated ferromagnetic interactions, the $J_1-J_2-J_3$ Heisenberg model on a square lattice. Using a combination of classical Monte-Carlo simulation and spin-wave theory, we uncover behaviour reminiscent of some widely-studied frustrated antiferromagnets, but with a number of new twists. We first demonstrate that, for a suitable choice of parameters, the phase diagr…
In the temperature-concentration phase diagram of most iron-based superconductors, antiferromagnetic order is gradually suppressed to zero at a critical point, and a dome of superconductivity forms around that point. The nature of the magnetic phase and its fluctuations is of fundamental importance for elucidating the pairing mechanism. In Ba{1-x}KxFe2As2 and Ba{1-x}NaxFe2As2, it has recently become clear that the usual stripe-like magnetic phase, of orthorhombic symmetry, gives way to a second magnetic phase, of tetragonal symmetry, near the critical point, between x = 0.24 and x = 0.28. Here…
We investigate the role of correlations in the tetragonal and collapsed tetragonal phases of CaFe2As2 by performing charge self-consistent DFT+DMFT (density functional theory combined with dynamical mean-field theory) calculations. While the topology of the Fermi surface is basically unaffected by the inclusion of correlation effects, we find important orbital-dependent mass renormalizations which show good agreement with recent angle-resolved photoemission (ARPES) experiments. Moreover, we observe a markedly different behavior of these quantities between the low-pressure tetragonal and the hi…
An existence of predominant symmetrical spin configuration (spin polarised phase) and "diluted" density of states (pseudo-gap) in a layer under the Fermi level in a quantum wire is predicted. The condition of cross-over from non-polarised phase to polarised one was derived. The transition occurs for sufficiently low electron density in a wire and is accompanied by an acute decrease of electron density of states near the Fermi level.It may result in a corresponding decrease of conductance. A similar effect may exist in a two-dimensional electron gas.
We have determined the superconducting and magnetic properties of a hydrothermally synthesized powder sample of tetragonal FeS using muon spin rotation (μSR). The superconducting properties are entirely consistent with those of a recently published study, showing fully gapped behavior and giving a penetration depth of λ_{ab} = 204(3) nm. However, our zero-field μSR data are rather different and indicate the presence of a small, non-superconducting magnetic phase within the sample. These results highlight that sample-to-sample variations in magnetism can arise in hydrothermally prepared phases,…
Recent investigations of the superconducting iron-arsenide families have highlighted the role of pressure, be it chemical or mechanical, in fostering superconductivity. Here we report that CaFe2As2 undergoes a pressure-induced transition to a non-magnetic, volume "collapsed" tetragonal phase, which becomes superconducting at lower temperature. Spin-polarized total-energy calculations on the collapsed structure reveal that the magnetic Fe moment itself collapses, consistent with the absence of magnetic order in neutron diffraction.
FeSe has a unique ground state in which superconductivity coexists with a nematic order without long-range magnetic ordering at ambient pressure. Here, to study how the pairing interaction evolves with nematicity, we measured the thermal conductivity and specific heat of FeSe$_{1-x}$S$_x$, where the nematicity is suppressed by isoelectronic sulfur substitution. We find that in the whole nematic ($0\leq x \leq 0.17$) and tetragonal ($x=0.20$) regimes, the application of small magnetic field causes a steep increase of both quantities. This indicates the existence of deep minima or line nodes in …
Measurements of the static magnetization, susceptibility and ESR of Gd spin probes have been performed to study the properties of antiferromagnetically ordered La_{2-x-y}Eu_ySr_xCuO_4 (x less or equal 0.02) with the low temperature tetragonal structure. According to the static magnetic measurements the CuO_2 planes are magnetically decoupled in this structural phase. The ESR study reveals strong magnetic fluctuations at the ESR frequency which are not present in the orthorhombic phase. It is argued that this drastic enhancement of the spin fluctuations is due to a considerable weakening of the…
Single crystals of Ca(Fe1-xRux)2As2 (0<x<0.065) and Ca1-yLay(Fe0.973Ru0.027)2As2 (0<y<0.2) have been synthesized and studied with respect to their structural, electronic and magnetic properties. The partial substitution of Fe by Ru induces a decrease of the c-axis constant leading for x<0.023 to a suppression of the coupled magnetic and structural (tetragonal to orthorhombic) transitions. At x_cr=0.023 a first order transition to a collapsed tetragonal (CT) phase is found, which behaves like a Fermi liquid and which is stabilized by further increase of x. The absence of superconductivity near …
At ambient pressure CaFe2As2 has been found to undergo a first order phase transition from a high temperature, tetragonal phase to a low temperature orthorhombic / antiferromagnetic phase upon cooling through T ~ 170 K. With the application of pressure this phase transition is rapidly suppressed and by ~ 0.35 GPa it is replaced by a first order phase transition to a low temperature collapsed tetragonal, non-magnetic phase. Further application of pressure leads to an increase of the tetragonal to collapsed tetragonal phase transition temperature, with it crossing room temperature by ~ 1.7 GPa. …
In copper-oxide and iron-based high temperature (high-$T_{\rm c}$) superconductors, many physical properties exhibit in-plane anisotropy, which is believed to be caused by a rotational symmetry-breaking nematic order, whose origin and its relationship to superconductivity remain elusive. In many iron-pnictides, a tetragonal-to-orthorhombic structural transition temperature $T_{\rm s}$ coincides with the magnetic transition temperature $T_{\rm N}$, making the orbital and spin degrees of freedom highly entangled. NaFeAs is a system where $T_{\rm s}$ = 54 K is well separated from $T_{\rm N}$ = 42…
Realisation of the tetragonal phase of $Cs_2CuCl_4$ is possible using specific crystal growth conditions at a temperature below $281K$. This work deals with the comparison of the magnetic susceptibility and the magnetization of this new tetragonal compound with the magnetic behaviour of tetragonal $Cs_2CuCl_{2.9}Br_{1.1}$, $Cs_2CuCl_{2.5}Br_{1.5}$, $Cs_2CuCl_{2.2}Br_{1.8}$ and presents consistent results for such quasi $2-D$ antiferromagnets. Structural investigation at low temperature for $Cs_2CuCl_{2.2}Br_{1.8}$ shows no phase transition. The structure remains in the tetragonal symmetry $I4/…
We present high-energy x-ray diffraction data under applied pressures up to p = 29 GPa, neutron diffraction measurements up to p = 1.1 GPa, and electrical resistance measurements up to p = 5.9 GPa, on SrCo2As2. Our x-ray diffraction data demonstrate that there is a first-order transition between the tetragonal (T) and collapsed-tetragonal (cT) phases, with an onset above approximately 6 GPa at T = 7 K. The pressure for the onset of the cT phase and the range of coexistence between the T and cT phases appears to be nearly temperature independent. The compressibility along the a-axis is the same…
Synchrotron x-ray diffraction experiments were performed on BaFe$_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$_{1-x…
We report a high-pressure study of simultaneous low-temperature electrical resistivity and Hall effect measurements on high quality single-crystalline KFe2As2 using designer diamond anvil cell techniques with applied pressures up to 33 GPa. In the low pressure regime, we show that the superconducting transition temperature T_c finds a maximum onset value of 7 K near 2 GPa, in contrast to previous reports that find a minimum T_c and reversal of pressure dependence at this pressure. Upon applying higher pressures, this T_c is diminished until a sudden drastic enhancement occurs coincident with a…
We calculate the influence of transverse fluctuations on the longitudinal dynamics in the striped phase of cuprates by using the bosonization technique. We find that a charge density wave instability can arise if the stripe is quarter filled and the underlying lattice potential has a zigzag symmetry. Our results explain why static stripes are experimentally observed in underdoped La_{2-x-y}Nd_ySr_xCuO_4 exactly at the onset of the low-temperature-tetragonal transition.
The majority of magnetic materials possess some degree of magnetic anisotropy, either at the level of a single ion, or in the exchange interactions between different magnetic ions. Where these exchange interactions are also frustrated, the competition between them and anisotropy can stabilize a wide variety of new phases in applied magnetic field. Motivated by the hexagonal delafossite 2H-AgNiO 2, we study the Heisenberg antiferromagnet on a layered triangular lattice with competing first- and second-neighbour interactions and single-ion easy-axis anisotropy. Using a combination of classical M…
The surprising discovery of tripling the superconducting critical temperature of KFe$_2$As$_2$ at high pressures issued an intriguing question of how the superconductivity in the collapsed tetragonal phase differs from that in the non-collapsed phases of Fe-based superconductors. Here we report $^{89}$Y nuclear magnetic resonance study of YFe$_2$Ge$_{x}$Si$_{2-x}$ compounds whose electronic structure is similar to that of iron-pnictide collapsed tetragonal phases already at ambient pressure. Fe(Ge,Si) layers show strong ferromagnetic spin fluctuations whereas layers are coupled antiferromagnet…
As the simplest iron-based superconductor, FeSe forms a tetragonal structure with transition temperature Tc ~ 8 K. With assistance of pressure, or other techniques, Tc can be greatly enhanced, even to above liquid nitrogen temperature. The newly discovered superconducting tetragonal FeS (Tc ~ 4.5 K), a sulfide counterpart of FeSe, promotes us on its high pressure investigation. The transport and structure evolution of FeS with pressure have been studied. A rapid suppression of Tc and vanishing of superconductivity at 4.0 GPa are observed, followed by a second superconducting dome with a 30% en…
A well-known feature of CaFe$_{2}$As$_{2}$-based superconductors is the pressure-induced collapsed tetragonal phase that is commonly ascribed to the formation of an interlayer As-As bond. Using detailed X-ray scattering and spectroscopy, we find that Rh-doped Ca$_{0.8}$Sr$_{0.2}$Fe$_{2}$As$_{2}$ does not undergo a first-order phase transition and that local Fe moments persist despite the formation of interlayer As-As bonds. Our density functional theory calculations reveal that the Fe-As bond geometry is critical for stabilizing magnetism and that the pressure-induced drop in the $c$ lattice p…
Highly-strained BiFeO3 exhibits a "tetragonal-like, monoclinic" crystal structure found only in epitaxial films (with an out-of-plane lattice parameter exceeding the in-plane value by >20%). Previous work has shown that this phase is properly described as a M$_{C}$ monoclinic structure at room temperature [with a (010)$_{pc}$ symmetry plane, which contains the ferroelectric polarization]. Here we show detailed temperature-dependent x-ray diffraction data that evidence a structural phase transition at ~100C to a high-temperature M$_{A}$ phase ["tetragonal-like" but with a (1-10)$_{pc}$ symmetry…
We investigate the stability of the multipolar orderings in $f$-electron material CeCoSi based on a self-consistent mean-field calculation for the effective localized model. This material has two ordered phases in the temperature-pressure phase diagram: the antiferromagnetic phase and the nonmagnetic phase, the latter of which has been suggested to be an antiferroquadrupolar phase. Meanwhile, the origin of the antiferroquadrupolar phase has been unclear, since a quadrupole degree of freedom is present only between the ground-state level and highly separated excited-state level under a tetragon…
We present uniaxial pressure structural relaxations for CaFe2As2 and BaFe2Ase2 within density functional theory and compare them with calculations under hydrostatic pressure conditions as well as available experimental results. We find that CaFe2As2 shows a unique phase transition from a magnetic orthorhombic phase to a nonmagnetic collapsed tetragonal phase for both pressure conditions and no indication of a tetragonal phase is observed at intermediate uniaxial pressures. In contrast, BaFe2As2 shows for both pressure conditions two phase transitions from a magnetic orthorhombic to a collapsed…
Formation of the triangular skyrmion-lattice is found in a tetragonal polar magnet VOSe$_2$O$_5$. By magnetization and small-angle neutron scattering measurements on the single crystals, we identify a cycloidal spin state at zero field and a Néel-type skyrmion-lattice phase under a magnetic field along the polar axis. Adjacent to this phase, another magnetic phase of an incommensurate spin texture is identified at lower temperatures, tentatively assigned to a square skyrmion-lattice phase. These findings exemplify the versatile features of Néel-type skyrmions in bulk materials, and provide a u…
A skyrmion crystal (SkX) expressed as a multiple number of spiral modulations manifests itself not only in its peculiar magnetic texture but also in nontrivial transport properties originating from an emergent magnetic field. We here report our numerical results for multiple SkXs in a centrosymmetric tetragonal crystal system. By performing simulated annealing for an effective spin model for itinerant magnets, we find that three types of the SkXs with the skyrmion numbers of one and two, which are characterized by different superpositions of helices, are stabilized in the ground state, and are…
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…
Polar materials can host a variety of topologically significant magnetic phases, which often emerge from a modulated magnetic ground state. Relatively few noncentrosymmetric tetragonal materials have been shown to host topological spin textures and new candidate materials are necessary to expand the current theoretical models. This manuscript reports on the anisotropic magnetism in the polar, tetragonal material NdCoGe$_3$ via thermodynamic and neutron diffraction measurements. The previously reported $H$-$T$ phase diagram is updated to include several additional phases, which exist for both $…
To gain insights into the fundamental and characteristic features of the surface of doped manganites, we constructed a general magnetic phase diagram of La$_{1-x}$Sr$_{x}$MnO$_3$ (001) surfaces in the plane spanned by $x$ and the bulk tetragonal distortion $c/a$, from the first-principles calculations. We found that the surfaces are quite different from the bulk in the sense that both the (La, Sr)O and MnO$_2$ terminated surfaces show strong tendency toward antiferromagnetism (A-type and C-type respectively). The basic physics governing the phase diagram can be understood in terms of the surfa…
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 …
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…
BiFeO$_3$ thin films can be epitaxially stabilized in a nearly-tetragonal phase under a high biaxial compressive strain. Here we investigate the polarized Raman spectra of constrained BiFeO$_3$ films with tetragonal-like (BFO-T), rhombohedral-like (BFO-R) and multiphase (BFO-T+R) structure. Based on analysis of the number and symmetry of the Raman lines, we provide strong experimental evidence that the nearly-tetragonal films are monoclinic ($Cc$ symmetry) and not tetragonal $(P4mm)$. Through the Raman mapping technique we show localized coexistence of BFO-T and BFO-R phases with the relative …
We study the origin of the cubic to tetragonal and tetragonal to monoclinic structural transitions in KCrF3, and the associated change in orbital order, paying particular attention to the relevance of super-exchange in both phases. We show that super-exchange is not the main mechanism driving these transitions. Specifically, it is not strong enough to be responsible for the high-temperature cubic to tetragonal transition and does not yield the type of orbital order observed in the monoclinic phase. The energy difference between the tetragonal and the monoclinic structure is tiny, and most like…
