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Phenomenological phase diagram for the spin-orbital model. The exchange energy scale in the problem sets the transition temperature TO for orbital order, which in turn drives the structural transition. ǫ0 is the energy scale below which long wavelength fluctuations are suppressed. There are two separate continuous orbital and magnetic transitions for ǫ ≪ ǫ0 (shown as dotted and dashd lines respectively) and one simultaneous first order transition for ǫ ≫ ǫ0 (shown as a solid line). Near the region ǫ ≃ ǫ0 (segment AB in the figure), the two transition temperatures can be very close and can be continuous or first order. In iron pnictides, ǫ would refer to the larger of the spin anisotropies or 3D couplings.
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The common phase diagrams of superconducting iron pnictides show interesting
material specificities in the structural and magnetic phase transitions. In
some cases the two transitions are separate and second order, while in others
they appear to happen concomitantly as a single first order transition. We
explore these differences using Monte Carlo...
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Citations
... Meanwhile, the opposite resistivity anisotropy of FeSe in comparison to pnictides can be explained by reversed orbital occupation imbalance. The preferred resistivity direction can be determined on the understanding that the d xz and d yz orbitals at E F favor conduction along the a-axis and b-axis, respectively 30,31 . Therefore, the resistivity along the a-axis is larger than that along the b-axis in FeSe, which is the opposite of the case of pnictide (because the d yz orbital is more occupied than d xz ). ...
The FeSe nematic phase has been the focus of recent research on iron-based superconductors (IBSs) due to its unusual properties, which are distinct from those of the pnictides. A series of theoretical/experimental studies were performed to determine the origin of the nematic phase. However, they yielded conflicting results and caused additional controversies. Here, we report the results of angle-resolved photoemission and X-ray absorption spectroscopy studies on FeSe detwinned by a piezo stack. We fully resolved band dispersions with orbital characters near the Brillouin zone (BZ) corner, and revealed an absence of any Fermi pocket at the Y point in the 1-Fe BZ. In addition, the occupation imbalance between \({d}_{{xz}}\) and \({d}_{{yz}}\) orbitals was the opposite of that of iron pnictides, consistent with the identified band characters. These results resolve issues associated with the FeSe nematic phase and shed light on the origin of the nematic phase in IBSs.
... In addition to its impact on the Fermi surface and electronic band dispersions, SOC also brings lattice anisotropies into anisotropies of magnetic fluctuations [20,21], as seen from nuclear magnetic resonance [22] and polarized inelastic neutron scattering (INS) experiments on different iron-based superconductors [23][24][25][26][27][28][29][30][31][32][33][34]. Compared with ARPES measurements, polarized INS measurements have much better energy and momentum resolution, and can directly probe the energy, wave vector, and temperature dependence of the spin excitation anisotropy and determine its relationship with T c , T N , T s , and nematic phase. ...
... In general, the symmetries of the crystallographic lattice can induce anisotropies in spin space that can determine the magnetic ordered moment direction. For iron pnictides that display a tetragonal-to-orthorhombic lattice distortion at T s , orbital ordering in the low-temperature orthorhombic phase is believed to play an important role in determining the a-axis moment direction of the collinear AF ordered phase [21]. When BaFe 2 As 2 is doped with P to form superconducting BaFe 2 (As 0.7 P 0.3 ) 2 , the static AF order and orthorhombic lattice distortion of the parent compounds are completely suppressed, similar to optimally hole-doped Ba 0.67 K 0.33 Fe 2 As 2 [49]. ...
... When BaFe 2 As 2 is doped with P to form superconducting BaFe 2 (As 0.7 P 0.3 ) 2 , the static AF order and orthorhombic lattice distortion of the parent compounds are completely suppressed, similar to optimally hole-doped Ba 0.67 K 0.33 Fe 2 As 2 [49]. Given that both pnictides are near optimal superconductivity with no orthorhombic lattice distortion and static AF order, orbital or nematic ordering associated with lattice distortion cannot play a direct role for the observed spin excitation anisotropy [21]. However, if we assume that the resonance arises from hole and electron Fermi surface nesting [8], the presence of SOC [13] may induce hole-and electron-doping asymmetry, giving rise to a double-Q tetragonal AF structure with ordered moments along the c axis near optimally hole-doped Ba 1−x K x Fe 2 As 2 and a simple collinear AF structure for electron-doped iron pnictides [18]. ...
We use neutron polarization analysis to study spin excitation anisotropy in the optimal-isovalent-doped superconductor BaFe2(As0.7P0.3)2 (Tc = 30 K). Different from optimally hole and electron-doped BaFe2As2, where there is a clear spin excitation anisotropy in the paramagnetic tetragonal state well above Tc, we find no spin excitation anisotropy for energies above 2 meV in the normal state of BaFe2(As0.7P0.3)2. Upon entering the superconducting state, significant spin excitation anisotropy develops at the antiferromagnetic (AF) zone center QAF = (1, 0, L = odd), while magnetic spectrum is isotropy at the zone boundary Q = (1, 0, L = even). By comparing temperature, wave vector, and polarization dependence of the spin excitation anisotropy in BaFe2(As0.7P0.3)2 and hole-doped Ba0.67K0.33Fe2As2 (Tc = 38 K), we conclude that such anisotropy arises from spin-orbit coupling and is associated with the nearby AF order and superconductivity.
... While in most cases the magnetic ground state corresponds to spin stripes with either one of these two ordering vectors [4], several hole-doped systems display double-Q magnetic order consisting of a linear combination of the two possi- ble types of order [5][6][7][8]. Orbital order is also found in the phase diagram below the nematic transition temperature, and is characterized by an unequal occupation between the Fe d xz and d yz orbitals, which breaks the tetrago- nal symmetry of the system [9][10][11]. At least in the iron pnictides, the evidence points to a magnetic origin of this orbital order [12], unveiling the close interaction between these two distinct degrees of freedom. ...
We show that the stripe spin-density wave state commonly observed in the phase diagrams of the iron-based superconductors necessarily triggers loop currents characterized by charge transfer between different Fe 3d orbitals. This effect is rooted on the glide-plane symmetry of these materials and on the existence of an atomic spin-orbit coupling that couples states at the $X$ and $Y$ points of the 1-Fe Brillouin zone. In the particular case in which the spins are aligned parallel to the magnetic ordering vector direction which is the spin configuration most commonly found in the iron-based superconductors these loop currents involve the $d_{xy}$ orbital and either the $d_{yz}$ orbital (if the spins point along the $y$ axis) or the $d_{xz}$ orbitals (if the spins point along the $x$ axis). We show that the two main manifestations of the orbital loop currents are the emergence of magnetic moments in the pnictide/chalcogen site and an orbital-selective band splitting in the magnetically ordered state, both of which could be detected experimentally. Our results highlight the unique intertwining between orbital and spin degrees of freedom in the iron-based superconductors, and reveal the emergence of an unusual correlated phase that may impact the normal state and superconducting properties of these materials.
... In the orbital scenario, the orbital ordering gives rise to the structural transition and then triggers the magnetic transition at the same or lower temperature [2][3][4][5]. In the spin scenario, on the other hand, it has been argued that magnetic fluctuations are of primary responsibility for triggering the nematic instability, although it is still not clear whether a correct microscopic theory should be built solely on a local spin model or the itinerant characteristic of the Fe 3d electrons should be taken into full account [6][7][8][9][10][11][12][13][14]. ...
... The rich behaviors of the magnetic and nematic transitions in Sr 1−x Ba x Ni 0.03 Fe 1.97 As 2 suggest that the intermediate phase with magnetic and nematic tricritical points is crucial to distinguishing various theories [2][3][4][5][6][7][8][9][10][11][12][13][14]. To our knowledge, our results can only be explained by Ref. [11]. ...
We have systematically studied the antiferromagnetic and nematic transitions in Sr$_{1-x}$Ba$_x$Fe$_{1.97}$Ni$_{0.03}$As$_2$ by magnetic susceptibility and uniaxial-pressure resistivity measurements, respectively. The derivatives of the temperature dependence of both magnetic and nematic susceptibilities show clearly sharp peak when the transitions are first-order. Accordingly, we show that while both of the magnetic and nematic transitions change from first-order to second-order with increasing Barium doping level, there is a narrow doping range where the former becomes second-order but the latter remains first-order, which has never been realized before in other systems. Moreover, the antiferromagnetic and nematic transition temperatures become different and the jump of nematic susceptibility becomes small in this intermediate doping range. Our results provide key information on the interplay between magnetic and nematic transitions. Concerning the current debate on the microscopic models for nematicity in iron-based superconductors, these observations agree with the magnetic scenario for an itinerant fermionic model in excellent details.
... Alternative low-energy models have been proposed based on Heisenberg or Kugel-Khomskii type Hamiltonians [20][21][22][23], which effectively assume that the system is an insulator. The argument here is that, while FeSC do display the metallic behavior at low temperatures, some orbitals may be either localized or near localization [24][25][26][27]. ...
The development of sensible microscopic models is essential to elucidate the normal-state and superconducting properties of the iron-based superconductors. Because these materials are mostly metallic, a good starting point is an effective low-energy model that captures the electronic states near the Fermi level and their interactions. However, in contrast to cuprates, iron-based high-$T_{c}$ compounds are multi-orbital systems with Hubbard and Hund interactions, resulting in a rather involved 10-orbital lattice model. Here we review different minimal models that have been proposed to unveil the universal features of these systems. We first review minimal models defined solely in the orbital basis, which focus on a particular subspace of orbitals, or solely in the band basis, which rely only on the geometry of the Fermi surface. The former, while providing important qualitative insight into the role of the orbital degrees of freedom, do not distinguish between high-energy and low-energy sectors and, for this reason, generally do not go beyond mean-field. The latter allow one to go beyond mean-field and investigate the interplay between superconducting and magnetic orders as well as Ising-nematic order. However, they cannot capture orbital-dependent features like spontaneous orbital order. We then review recent proposals for a minimal model that operates in the band basis but fully incorporates the orbital composition and symmetries of the low-energy excitations. We discuss the results of the renormalization group study of such a model, particularly of the interplay between superconductivity, magnetism, and spontaneous orbital order, and compare theoretical predictions with experiments on iron pnictides and chalcogenides. We also discuss the impact of the glide-plane symmetry on the low-energy models, highlighting the key role played by the spin-orbit coupling.
... Both orbital and magnetic fluctuations have been proposed as the glue that binds electrons together for superconductivity, yielding different pairing states [1][2][3][4][5][6][7][8]. However, which of the two degrees of freedom, orbital or spin, is the driving force, is a hotly debated topic [9][10][11][12][13][14][15][16][17][18][19][20][21][22]. ...
... are the Green functions for the xz and yz electrons with dispersions (15). The integration over frequency and over directions of k yield ...
... The band dispersions c(d) (k) are given in Eq. (15). The Eq. (34) is illustrated in Fig. 8. ...
Magnetism and nematic order are the two non-superconducting orders observed in iron-based superconductors. To elucidate the interplay between them and ultimately unveil the pairing mechanism, several models have been investigated. In models with quenched orbital degrees of freedom, magnetic fluctuations promote stripe magnetism which induces orbital order. In models with quenched spin degrees of freedom, charge fluctuations promote spontaneous orbital order which induces stripe magnetism. Here we develop an unbiased approach, in which we treat magnetic and orbital fluctuations on equal footing. Key to our approach is the inclusion of the orbital character of the low-energy electronic states into renormalization group analysis. Our results show that in systems with large Fermi energies, such as BaFe2As2, LaFeAsO, and NaFeAs, orbital order is induced by stripe magnetism. However, in systems with small Fermi energies, such as FeSe, the system develops a spontaneous orbital order, while magnetic order does not develop. Our results provide a unifying description of different iron-based materials.
... Studies of models with both localized and itinerant orbitals also found [37][38][39] that the proximity to magnetism is an important ingredient for orbital order. In purely localized-spin models the interplay between magnetism and ferro-orbital order is blurred by the complicated form of the effective Hamiltonian, which deviates from a simpler Kugel-Khomskii type [35,36]. ...
Although the existence of nematic order in iron-based superconductors is now
a well-established experimental fact, its origin remains controversial. Nematic
order breaks the discrete lattice rotational symmetry by making the $x$ and $y$
directions in the Fe plane non-equivalent. This can happen because of (i) a
tetragonal to orthorhombic structural transition, (ii) a spontaneous breaking
of an orbital symmetry, or (iii) a spontaneous development of an Ising-type
spin-nematic order - a magnetic state that breaks rotational symmetry but
preserves time-reversal symmetry. The Landau theory of phase transitions
dictates that the development of one of these orders should immediately induce
the other two, making the origin of nematicity a physics realization of a
"chicken and egg problem". The three scenarios are, however, quite different
from a microscopic perspective. While in the structural scenario lattice
vibrations (phonons) play the dominant role, in the other two scenarios
electronic correlations are responsible for the nematic order. In this review,
we argue that experimental and theoretical evidence strongly points to the
electronic rather than phononic mechanism, placing the nematic order in the
class of correlation-driven electronic instabilities, like superconductivity
and density-wave transitions. We discuss different microscopic models for
nematicity in the iron pnictides, and link nematicity to other ordered states
of the global phase diagram of these materials -- magnetism and
superconductivity. In the magnetic model nematic order pre-empts stripe-type
magnetic order, and the same interaction which favors nematicity also gives
rise to an unconventional $s^{+-}$ superconductivity. In the charge/orbital
model magnetism appears as a secondary effect of ferro-orbital order, and the
interaction which favors nematicity gives rise to a conventional $s^{++}$
superconductivity.
Iron‐based superconductors are well‐known for their intriguing phase diagrams, which manifest a complex interplay of electronic, magnetic, and structural degrees of freedom. Among the phase transitions observed are superconducting, magnetic, and several types of structural transitions, including a tetragonal‐to‐orthorhombic and a collapsed‐tetragonal transition. In particular, the widely observed tetragonal‐to‐orthorhombic transition is believed to be a result of an electronic order that is coupled to the crystalline lattice and is, thus, referred to as nematic transition. Nematicity is therefore a prominent feature of these materials, which signals the importance of the coupling of electronic and lattice properties. Correspondingly, these systems are particularly susceptible to tuning via pressure (hydrostatic, uniaxial, or some combination). Efforts to probe the phase diagrams of pressure‐tuned iron‐based superconductors are reviewed with a strong focus on recent insights into the phase diagrams of several members of this material class under hydrostatic pressure. These studies on FeSe, Ba(Fe 1 − x Cox)2As2, Ca(Fe 1 − x Cox)2As2, and CaK(Fe 1 − x Nix)4As4 are, to a significant extent, made possible by advances of what measurements can be adapted to their use under differing pressure environments. The potential impact of these tools for the study of the wider class of strongly correlated electron systems is pointed out.
The tetragonal-to-orthorhombic phase transition at Ts, which precedes the antiferromagnetic phase transition at TN in many iron-based superconductors, is considered one of the manifestations of electronic nematic order. By constructing temperature-pressure phase diagrams of pure and Co-doped BaFe2As2, we study the relation of Ts and TN under pressure p. Our data disclose two qualitatively different regimes in which ΔT=Ts−TN either increases or decreases with p. We provide experimental evidence that the transition between the two regimes may be associated with sudden changes of the Fermi surface topology. Therefore, our results not only support the electronic origin of the structural order, but also emphasize the importance of details of the Fermi surface for the evolution of nematic order under pressure.
We use neutron polarization analysis to study spin excitation anisotropy in the optimally isovalent-doped superconductor BaFe2(As0.7P0.3)2 (Tc=30 K). Different from optimally hole- and electron-doped BaFe2As2, where there is a clear spin excitation anisotropy in the paramagnetic tetragonal state well above Tc, we find no spin excitation anisotropy for energies above 2 meV in the normal state of BaFe2(As0.7P0.3)2. Upon entering the superconducting state, significant spin excitation anisotropy develops at the antiferromagnetic (AF) zone center QAF=(1,0,L=odd), while the magnetic spectrum is isotropic at the zone boundary Q=(1,0,L=even). By comparing the temperature, wave vector, and polarization dependence of the spin excitation anisotropy in BaFe2(As0.7P0.3)2 and hole-doped Ba0.67K0.33Fe2As2 (Tc=38 K), we conclude that such anisotropy arises from spin-orbit coupling and is associated with the nearby AF order and superconductivity.
