Antiferromagnetic Stripe Research Articles

The frustrated bilayer Ising model: A cluster mean-field approach

We investigate the Ising model on the bilayer square lattice with antiferromagnetic interactions between first-(J1) and second-neighbors (J2) inside each layer and a perpendicular antiferromagnetic interaction (Jp) between layers. The roles of frustration and interlayer interactions on the thermal phase transitions are described within a variational cluster mean-field (CMF) approach. For J2/J1<1/2, the model exhibits a Néel antiferromagnetic (AF) ground state and, for J2/J1>1/2, a stripe antiferromagnetic (SAF) ground state takes place. In the absence of interlayer interactions, a tricritical point is found in the phase boundary between SAF and paramagnetic (PM) phases. Our CMF calculations show that the ordering temperature of both AF and SAF phases is enhanced by the interlayer couplings. We also show that, at different levels of frustration, in the strong-interlayer-coupling limit, the ordering temperature is twice the one in the absence of interlayer interactions. At the weak-interlayer-coupling limit, a linear dependence of the ordering temperature with the interlayer interaction is observed, which indicates a shift exponent ϕ=1. Our investigation revealed that the model exhibits tricriticality at all strengths of the interlayer interactions, but the coupling coordinate of the tricritical point (J2/J1)t exhibits a minimum at a finite strength of Jp/J1. However, in the strong interlayer coupling limit, the coupling coordinate of the tricritical point is the same as in the decoupled (Jp=0) limit. Therefore, our CMF study reveals a persistent tricriticality in the frustrated bilayer Ising model.

Spin-selective tunneling from nanowires of the candidate topological Kondo insulator SmB6.

Incorporating relativistic physics into quantum tunneling can lead to exotic behavior such as perfect transmission through Klein tunneling. Here, we probed the tunneling properties of spin-momentum-locked relativistic fermions by designing and implementing a tunneling geometry that uses nanowires of the topological Kondo insulator candidate samarium hexaboride. The nanowires are attached to the end of scanning tunneling microscope tips and used to image the bicollinear stripe spin order in the antiferromagnet Fe1.03Te with a Neel temperature of about 50 kelvin. The antiferromagnetic stripes become invisible above 10 kelvin concomitant with the suppression of the topological surface states in the tip. We further demonstrate that the direction of spin polarization is tied to the tunneling direction. Our technique establishes samarium hexaboride nanowires as ideal conduits for spin-polarized currents.

Spin stripe fluctuations in antiferromagnetic Pr2−xSrxNiO4+δ

We report inelastic neutron scattering study of the antiferromagnetic spin stripe fluctuations above the spin stripe melting temperature ${\mathrm{T}}_{so}\ensuremath{\approx}190\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ in the hole doped ${\mathrm{Pr}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{NiO}}_{4+\ensuremath{\delta}}$ with stripe incommensurability $\ensuremath{\epsilon}=0.33$. The fluctuations are nondispersive and detected upto 10 meV at the incommensurate wave vector indicating a persisting instantaneous spin and charge stripe correlation above ${\mathrm{T}}_{so}$, while they are strongly diminished already below the charge stripe melting temperature ${\mathrm{T}}_{co}\ensuremath{\approx}255\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, which indicates that static charge stripe order is essential for the dynamical spin stripe correlation to exist. Furthermore, it also suggests that the presence of spin stripe fluctuations is not a prerequisite for the formation of static charge stripes.

Measuring a population of spin waves from the electrical noise of an inductively coupled antenna

We study how a population of spin waves can be characterized from the analysis of the electrical microwave noise delivered by an inductive antenna placed in its vicinity. The measurements are conducted on a synthetic antiferromagnetic thin stripe covered by a micron-sized antenna that feeds a spectrum analyzer after amplification. The antenna noise contains two contributions. The population of incoherent spin waves generates a fluctuating field that is sensed by the antenna: this is the ``magnon noise.'' The antenna noise also contains the contribution of the electronic fluctuations: the Johnson-Nyquist noise. The latter depends on all impedances within the measurement circuit, which includes the antenna self-inductance. As a result, the electronic noise contains information about the magnetic susceptibility of the stripe, though it does not inform on the absolute amplitude of the magnetic fluctuations. For micrometer-sized systems at thermal equilibrium, the electronic noise dominates and the pure magnon noise cannot be determined. If in contrast the spin wave bath is not at thermal equilibrium with the measurement circuit, and if the spin wave population can be changed then one could measure a mode-resolved effective magnon temperature provided specific precautions are implemented.

Topological Doping and Superconductivity in Cuprates: An Experimental Perspective

Hole doping into a correlated antiferromagnet leads to topological stripe correlations, involving charge stripes that separate antiferromagnetic spin stripes of opposite phases. The topological spin stripe order causes the spin degrees of freedom within the charge stripes to feel a geometric frustration with their environment. In the case of cuprates, where the charge stripes have the character of a hole-doped two-leg spin ladder, with corresponding pairing correlations, anti-phase Josephson coupling across the spin stripes can lead to a pair-density-wave order in which the broken translation symmetry of the superconducting wave function is accommodated by pairs with finite momentum. This scenario is now experimentally verified by recently reported measurements on La2−xBaxCuO4 with x=1/8. While pair-density-wave order is not common as a cuprate ground state, it provides a basis for understanding the uniform d-wave order that is more typical in superconducting cuprates.

Lattice symmetry and emergence of antiferromagnetic quantum Hall states

Strong local interaction in systems with non-trivial topological bands can stabilize quantum states such as magnetic topological insulators. We investigate the influence of the lattice symmetry on the possible emergence of antiferromagnetic quantum Hall states. We consider the spinful Harper-Hofstadter model extended by a next-nearest-neighbor (NNN) hopping which opens a gap at half-filling and allows for the realization of a quantum Hall insulator. The quantum Hall insulator has the Chern number $\mathcal{C}=2$ as both spin components are in the same quantum Hall state. We add to the system a staggered potential $\Delta$ along the $\hat{x}$-direction favoring a normal insulator and the Hubbard interaction $U$ favoring a Mott insulator. The Mott insulator is a N\'eel antiferromagnet for small and a stripe antiferromagnet for large NNN hopping. We investigate the $U$-$\Delta$ phase diagram of the model for both small and large NNN hoppings. We show that while for large NNN hopping there exists a $\mathcal{C}=1$ stripe antiferromagnetic quantum Hall insulator in the phase diagram, there is no equivalent $\mathcal{C}=1$ N\'eel antiferromagnetic quantum Hall insulator at the small NNN hopping. We discuss that a $\mathcal{C}=1$ antiferromagnetic quantum Hall insulator can emerge only if the effect of the spin-flip transformation cannot be compensated by a space group operation. Our findings can be used as a guideline in future investigations searching for antiferromagnetic quantum Hall states.

Spin dynamics in antiferromagnetic oxypnictides and fluoropnictides: LaMnAsO, LaMnSbO, and BaMnAsF

Inelastic neutron scattering (INS) from polycrystalline antiferromagnetic LaMnAsO, LaMnSbO, and BaMnAsF are analyzed using a ${J}_{1}\text{\ensuremath{-}}{J}_{2}\text{\ensuremath{-}}{J}_{c}$ Heisenberg model in the framework of the linear spin-wave theory. All three systems show clear evidence that the nearest- and next-nearest-neighbor interactions within the Mn square lattice layer (${J}_{1}$ and ${J}_{2}$) are both antiferromagnetic (AFM). However, for all compounds studied the competing interactions have a ratio of $2{J}_{2}/{J}_{1}&lt;1$, which favors the square lattice checkerboard AFM structure over the stripe AFM structure. The interplane coupling ${J}_{c}$ in all three systems is on the order of $\ensuremath{\sim}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}{J}_{1}$, rendering the magnetic properties of these systems with quasi-two-dimensional character. The substitution of Sb for As significantly lowers the in-plane exchange coupling, which is also reflected in the decrease of the N\'eel temperature, ${T}_{\mathrm{N}}$. Although BaMnAsF shares the same MnAs sheets as LaMnAsO, their ${J}_{1}$ and ${J}_{2}$ values are substantially different. Using density functional theory, we calculate exchange parameters ${J}_{ij}$ to rationalize the differences among these systems.

Collective in-plane magnetization in a two-dimensional XY macrospin system within the framework of generalized Ott-Antonsen theory.

The problem of magnetic transitions between the low-temperature (macrospin ordered) phases in two-dimensional XY arrays is addressed. The system is modelled as a plane structure of identical single-domain particles arranged in a square lattice and coupled by the magnetic dipole-dipole interaction; all the particles possess a strong easy-plane magnetic anisotropy. The basic state of the system in the considered temperature range is an antiferromagnetic (AF) stripe structure, where the macrospins (particle magnetic moments) are still involved in thermofluctuational motion: the superparamagnetic blocking Tb temperature is lower than that (Taf) of the AF transition. The description is based on the stochastic equations governing the dynamics of individual magnetic moments, where the interparticle interaction is added in the mean-field approximation. With the technique of a generalized Ott-Antonsen theory, the dynamics equations for the order parameters (including the macroscopic magnetization and the AF order parameter) and the partition function of the system are rigorously obtained and analysed. We show that inside the temperature interval of existence of the AF phase, a static external field tilted to the plane of the array is able to induce first-order phase transitions from AF to ferromagnetic state; the phase diagrams displaying stable and metastable regions of the system are presented. This article is part of the theme issue 'Patterns in soft and biological matters'.

Competing Electronic Phases near the Onset of Superconductivity in Hole-doped SrFe2As2

An intriguingly complex phase diagram of Na-doped SrFe2As2 is uncovered using high-resolution thermal-expansion, magnetization and heat-capacity measurements. The detailed temperature dependence of the orthorhombic distortion and the anisotropy of the uniform magnetic susceptibility provide evidence for nine distinct electronic phases near the transition region between stripe antiferromagnetism and unconventional superconductivity. In particular, we report the finding of a new magnetic phase which competes surprisingly strongly with superconductivity. From theoretical studies we propose that this phase is a double-Q phase consisting of a mixture of symmetry-distinct commensurate magnetic orders with a peculiar temperature-dependent magnetic moment reorientation.

Spin Stripe Order in a Square Planar Trilayer Nickelate.

Trilayer nickelates, which exhibit a high degree of orbital polarization combined with an electron count (d^{8.67}) corresponding to overdoped cuprates, have been identified as a promising candidate platform for achieving high-T_{c} superconductivity. One such material, La_{4}Ni_{3}O_{8}, undergoes a semiconductor-insulator transition at ∼105 K, which was recently shown to arise from the formation of charge stripes. However, an outstanding issue has been the origin of an anomaly in the magnetic susceptibility at the transition and whether it signifies the formation of spin stripes akin to single layer nickelates. Here we report single crystal neutron diffraction measurements (both polarized and unpolarized) that establish that the ground state is indeed magnetic. The ordering is modeled as antiferromagnetic spin stripes that are commensurate with the charge stripes, the magnetic ordering occurring in individual trilayers that are essentially uncorrelated along the crystallographic c axis. A comparison of the charge and spin stripe order parameters reveals that, in contrast to single-layer nickelates such as La_{2-x}Sr_{x}NiO_{4} as well as related quasi-2D oxides including manganites, cobaltates, and cuprates, these orders uniquely appear simultaneously, thus demonstrating a stronger coupling between spin and charge than in these related low-dimensional correlated oxides.

Toward the Mott state with magnetic cluster formation in heavily Cu-doped NaFe1−xCuxAs

Recent neutron scattering measurements indicate that NaFe$_{1-x}$Cu$_{x}$As forms an antiferromagnetic stripe phase near $x\approx 0.5$ in a Mott insulating state. This copper concentration is well in excess of that required for superconductivity, $x < 0.04$. We have investigated the development of magnetism in this compound using $^{23}$Na nuclear magnetic resonance (NMR) spectra and spin-lattice relaxation measurements performed on single crystals ($x$ = 0.13, 0.18, 0.24, and 0.39). We find multiple inequivalent Na sites, each of which is associated with a different number of nearest neighbor Fe sites occupied by a Cu dopant. We show that the distribution of Cu substituted for Fe is random in-plane for low concentrations ($x = 0.13$ and 0.18), but deviates from this with increasing Cu doping. As is characteristic of many pnictide compounds, there is a spin pseudo gap that increases in magnitude with dopant concentration. This is correlated with a corresponding increase in orbital NMR frequency shift indicating a change in valence from Cu$^{2+}$ to a Cu$^{1+}$ state as $x$ exceeds 0.18, concomitant with the change of Fe$^{2+}$ to Fe$^{3+}$ resulting in the formation of magnetic clusters. However, for $x\leq 0.39$ there is no evidence of long-range static magnetic order.

Possible superconductivity in chemically doped CrSb1 + δ

Antiferromagnetic system with stripe magnetic order provides a potential platform for the investigation of possible unconventional superconductivity. Here we report interesting new results that possibly indicate the development of superconductivity in chemically doped CrSb1 + δ. Electrical and magnetic measurements on CrSb1 + δ, with δ varying between 0.05 and 0.1, reveal field‐dependent properties that are usually observed in a superconductor. The transition to a possible superconducting state is found to occur at T = 8.8 K. The observation of possible superconducting state in CrSb1 + δ will shed new light on the origin of the unconventional superconductivity in magnetic material with long‐range antiferromagnetic stripe order.

Complex Three-Dimensional Magnetic Ordering in Segmented Nanowire Arrays.

A comprehensive three-dimensional picture of magnetic ordering in high-density arrays of segmented FeGa/Cu nanowires is experimentally realized through the application of polarized small-angle neutron scattering. The competing energetics of dipolar interactions, shape anisotropy, and Zeeman energy in concert stabilize a highly tunable spin structure that depends heavily on the applied field and sample geometry. Consequently, we observe ferromagnetic and antiferromagnetic interactions both among wires and between segments within individual wires. The resulting magnetic structure for our nanowire sample in a low field is a fan with magnetization perpendicular to the wire axis that aligns nearly antiparallel from one segment to the next along the wire axis. Additionally, while the low-field interwire coupling is ferromagnetic, application of a field tips the moments toward the nanowire axis, resulting in highly frustrated antiferromagnetic stripe patterns in the hexagonal nanowire lattice. Theoretical calculations confirm these observations, providing insight into the competing interactions and resulting stability windows for a variety of ordered magnetic structures. These results provide a roadmap for designing high-density magnetic nanowire arrays for spintronic device applications.

Stabilizing the spin vortex crystal phase in two-dimensional iron-based superconductors

We present an investigation of the magnetic structure for iron-based superconductors (FeSCs) when inversion symmetry is broken, such as in substrate-supported monolayers or in the presence of a $c$-axis electric field. We perform group-, mean-field-, and density-functional-theoretic analyses on a model system of monolayer iron selenide (FeSe) on a strontium titanate $[{\mathrm{SrTiO}}_{3}$(001)] substrate. Our group- and mean-field-theoretic calculations are more generally applicable to thin films of the rest of the 11 (e.g., FeSe) family of iron-based superconductors, as well as to thin films of the 111 (e.g., LiFeAs) and 1111 (e.g., LaOFeAs) families, as these all belong to the same space group. We find that in systems with a collinear antiferromagnetic phase in bulk, when inversion symmetry is broken, the transition is instead into a ``spin vortex crystal'' phase and that a further phase transition can occur at a lower temperature in some circumstances. The spin vortex crystal is a ${C}_{4}$-symmetric magnetic phase which is related to this parent ${C}_{2}$-symmetric collinear antiferromagnetic (stripe) phase which is ubiquitous among the iron-based superconductors.

Coexistence of localized and itinerant magnetism in intercalated iron-selenide (Li,Fe)OHFeSe

The electronic structure and magnetism of a new magnetic intercalation compound (Li0.8Fe0.2)OHFeSe are investigated theoretically. The electronic structure calculations predict that the Fe in the (Li,Fe)OH intercalated layer is in a +2 valence state, i.e. there is electron doping to the FeSe layer, resulting in the shrinking of the Fermi surface (FS) pocket around Γ and a strong suppression of dynamical spin susceptibility at M in comparison with the bulk FeSe compound. The ground state of the FeSe layer is a striped antiferromagnetic (SAFM) metal, while the (Li,Fe)OH layer displays a very weak localized magnetism, with an interlayer ferromagnetic (FM) coupling between the FeSe and intercalated (Li,Fe)OH layers. Moreover, the (Li,Fe)OH is more than a block layer; it is responsible for enhancing the antiferromagnetic (AFM) correlation in the FeSe layer through interlayer magnetic coupling. We propose that the magnetic spacer layer introduces a tuning mechanism for spin fluctuations associated with superconductivity in iron-based superconductors.

Fermionic Symmetry-Protected Topological Phase in a Two-Dimensional Hubbard Model.

We study the two-dimensional (2D) Hubbard model using exact diagonalization for spin-1/2 fermions on the triangular and honeycomb lattices decorated with a single hexagon per site. In certain parameter ranges, the Hubbard model maps to a quantum compass model on those lattices. On the triangular lattice, the compass model exhibits collinear stripe antiferromagnetism, implying d-density wave charge order in the original Hubbard model. On the honeycomb lattice, the compass model has a unique, quantum disordered ground state that transforms nontrivially under lattice reflection. The ground state of the Hubbard model on the decorated honeycomb lattice is thus a 2D fermionic symmetry-protected topological phase. This state-protected by time-reversal and reflection symmetries-cannot be connected adiabatically to a free-fermion topological phase.

Elucidating the magnetic and superconducting phases in the alkali metal intercalated iron chalcogenides

The complex interdigitated phases have greatly frustrated attempts to document the basic features of the superconductivity in the alkali metal intercalated iron chalcogenides. Here, using elastic neutron scattering, energy-dispersive x-ray spectroscopy, and resistivity measurements, we elucidate the relations of these phases in Rb$_{1-\delta}$Fe$_y$Se$_{2-z}$S$_z$. We find: i) the iron content is crucial in stabilizing the stripe antiferromagnetic (AF) phase with rhombic iron vacancy order ($y\approx1.5$), the block AF phase with $\sqrt{5}\times \sqrt{5}$ iron vacancy order ($y\approx1.6$), and the iron vacancy-free phase ($y\approx2$); ii) the superconducting phase ($z=0$) evolves into a metallic phase ($z>1.5$) with sulfur substitution due to the progressive decrease of the electronic correlation strength. Both the stripe AF phase and the block AF phase are Mott insulators. Our data suggest that there are miscibility gaps between these three phases. The existence of the miscibility gaps in the iron content is the key to understanding the relationship between these complicated phases.

Double-Q spin-density wave in iron arsenide superconductors

Elucidating the nature of the magnetic ground state of iron-based superconductors is of paramount importance in unveiling the mechanism behind their high temperature superconductivity. Until recently, it was thought that superconductivity emerges only from an orthorhombic antiferromagnetic stripe phase, which can in principle be described in terms of either localized or itinerant spins. However, we recently reported that tetragonal symmetry is restored inside the magnetically ordered state of a hole-doped BaFe2As2. This observation was interpreted as indirect evidence of a new double-Q magnetic structure, but alternative models of orbital order could not be ruled out. Here, we present Mossbauer data that show unambiguously that half of the iron sites in this tetragonal phase are non-magnetic, establishing conclusively the existence of a novel magnetic ground state with a non-uniform magnetization that is inconsistent with localized spins. We show that this state is naturally explained as the interference between two spin-density waves, demonstrating the itinerant character of the magnetism of these materials and the primary role played by magnetic over orbital degrees of freedom.

Magnetic order driven by orbital ordering in the semiconducting KFe1.5Se2

The two-orbital Hubbard model is studied numerically by using the Hartree-Fock approximation in both real space and momentum space, and the ground-state properties of the alkali metal iron selenide semiconducting KFe1.5Se2 are investigated. A rhombus-type Fe vacancy order with stripetype antiferromagnetic (AFM) order is found, as was observed in neutron scattering experiments [J. Zhao, et al., Phys. Rev. Lett. 109, 267003 (2012)]. Hopping parameters are obtained by fitting the experimentally observed stripe AFM phase in real space. These hopping parameters are then used to study the ground-state properties of the semiconductor in momentum space. It is found to be a strongly correlated system with a large on-site Coulomb repulsion U, similar to the AFM Mott insulator — the parent compound of copper oxide superconductors. We also find that the electronic occupation numbers and magnetizations in the dxz and dyz orbitals become different simultaneously when U > Uc (∼3.4 eV), indicating orbital ordering. These results imply that the rotational symmetry between the two orbitals is broken by orbital ordering and thus drives the strong anisotropy of the magnetic coupling that has been observed by experiments and that the stripe-type AFM order in this compound may be caused by orbital ordering together with the observed large anisotropy.

Mott localization in a pure stripe antiferromagnetRb1−δFe1.5−σS2

A combination of neutron diffraction and angle-resolved photoemission spectroscopy measurements on a pure antiferromagnetic stripe Rb$_{1-\delta}$Fe$_{1.5-\sigma}$S$_2$ is reported. A neutron diffraction experiment on a powder sample shows that a 98$\%$ volume fraction of the sample is in the antiferromagnetic stripe phase with rhombic iron vacancy order and a refined composition of Rb$_{0.66}$Fe$_{1.36}$S$_{2}$, and that only 2$\%$ of the sample is in the block antiferromagnetic phase with $\sqrt{5}\times \sqrt{5}$ iron vacancy order. Furthermore, a neutron diffraction experiment on a single crystal shows that there is only a single phase with the stripe antiferromagnetic order with the refined composition of Rb$_{0.78}$Fe$_{1.35}$S$_2$, while the phase with block antiferromagnetic order is absent. Angle-resolved photoemission spectroscopy measurements on the same crystal with the pure stripe phase reveal that the electronic structure is gapped at the Fermi level with a gap larger than 0.325 eV. The data collectively demonstrates that the extra 10$\%$ iron vacancies in addition to the rhombic iron vacancy order effectively impede the formation of the block antiferromagnetic phase; the data also suggest that the stripe antiferromagnetic phase with rhombic iron vacancy order is a Mott insulator.