Static Antiferromagnetic Order Research Articles

Quantum anomalous hall effect in collinear antiferromagnetism

The two-dimensional Quantum Hall effect with no external magnetic field is called the Quantum anomalous Hall (QAH) effect. So far, experimentally realized QAH insulators all exhibit ferromagnetic order and the QAH effect only occurs at very low temperatures. On the other hand, up to now the QAH effect in collinear antiferromagnetic (AFM) materials has never been reported and the corresponding mechanism has never been proposed. In this work, we realize the QAH effect by proposing a four-band lattice model with static AFM order, which indicates that the QAH effect can be found in AFM materials. Then, as a prototype, we demonstrate that a monolayer CrO can be switched from an AFM Weyl semimetal to an AFM QAH insulator by applying strain, based on symmetry analysis and the first-principles electronic structure calculations. Our work not only proposes a scenario to search for QAH insulators in materials, but also reveals a way to considerably increase the critical temperature of the QAH phase.

Unusual suppression of a spin resonance mode by magnetic field in underdoped NaFe1−xCoxAs : Evidence for orbital-selective pairing

We use inelastic neutron scattering to study the fate of the two spin resonance modes in underdoped superconducting NaFe$_{1-x}$Co$_x$As ($x=0.0175$) under applied magnetic fields. While an applied in-plane magnetic field of $B=12$ T only modestly suppresses superconductivity and enhances static antiferromagnetic order, the two spin resonance modes display disparate responses. The spin resonance mode at higher energy is mildly suppressed, consistent with the field effect in other unconventional superconductors. The spin resonance mode at lower energy, on the other hand, is almost completely suppressed. Such dramatically different responses to applied magnetic field indicate distinct origins of the two spin resonance modes, resulting from the strongly orbital-selective nature of spin excitations and Cooper-pairing in iron-based superconductors.

Magnetism of the A -site ordered perovskites CaCu3Cr4O12 and LaCu3Cr4O12

The microscopic magnetic nature of the $A$-site ordered chromium perovskites ${\mathrm{CaCu}}_{3}{\mathrm{Cr}}_{4}{\mathrm{O}}_{12}$ and ${\mathrm{LaCu}}_{3}{\mathrm{Cr}}_{4}{\mathrm{O}}_{12}$ and their solid-solution system, ${\mathrm{Ca}}_{1\ensuremath{-}x}{\mathrm{La}}_{x}{\mathrm{Cu}}_{3}{\mathrm{Cr}}_{4}{\mathrm{O}}_{12}$, with $x=0.2$, 0.4, and 0.8, has been studied with muon spin rotation and relaxation (${\ensuremath{\mu}}^{+}\mathrm{SR}$) measurements down to 2 K using a powder sample. For ${\mathrm{CaCu}}_{3}{\mathrm{Cr}}_{4}{\mathrm{O}}_{12}$, ${\ensuremath{\mu}}^{+}\mathrm{SR}$ revealed the formation of static antiferromagnetic (AF) order below 122 K ($={T}_{\mathrm{N}}$), although magnetization measurements showed a very small change at ${T}_{\mathrm{N}}$. Analyses of the internal magnetic field ${H}_{\mathrm{int}}$ at the muon sites, predicted with first-principles calculations, suggested $G$-type AF order as a ground state. For ${\mathrm{LaCu}}_{3}{\mathrm{Cr}}_{4}{\mathrm{O}}_{12}$ with ${T}_{\mathrm{N}}=225$ K, ${\ensuremath{\mu}}^{+}\mathrm{SR}$ also supported the presence of a $G$-type AF ordered state, which was recently proposed based on neutron diffraction measurements. However, the ordered Cr moments were found to change the direction at around 10 K. For ${\mathrm{Ca}}_{1\ensuremath{-}x}{\mathrm{La}}_{x}{\mathrm{Cu}}_{3}{\mathrm{Cr}}_{4}{\mathrm{O}}_{12}$, both ${T}_{\mathrm{N}}$ and ${H}_{\mathrm{int}}$ at 2 K increase monotonically with $x$.

Antiferromagnetic order and spin dynamics in iron-based superconductors

Like the superconductivities in other unconventional superconductors, high-temperature superconductivity in the iron pnictide often emerges after the static antiferromagnetic order has been suppressed, and is always accompanied by strong spin fluctuations. Therefore, understanding the magnetism and its origin could be an important premise for ascertaining the microscopic mechanism of iron-based superconductivity. Neutron scattering, as a powerful tool for studying magnetic ordering and spin dynamics in condensed matters, plays an essential role in understanding the relationship between magnetism and superconductivity in iron-based superconductors. In this paper, we review the neutron scattering results for iron pnictides, including static magnetic structures, magnetic phase transitions, spin excitations and electronic nematicity, and discuss their relationship with superconductivity.

Magnetic structure for NaCr2O4 analyzed by neutron diffraction and muon spin-rotation

We have investigated the magnetic ground state of a novel one-dimensional compound, NaCr2O4, in which Cr2O4 double chains, i.e. zig-zag chains are aligned parallel to the b-axis, by means of both muon-spin rotation and relaxation (μ+SR) and neutron diffraction (ND) measurements. The μ+SR results reveal the formation of static antiferromagnetic order below Néel temperature (TN=124K). The ND measurements also demonstrate the appearance of magnetic Bragg peaks with the propagation vector k→=(1, 0, 1) below TN. Combined analyses of the μ+SR and ND data clarify that the Cr moments in each zig-zag chain are aligned ferromagnetically along the c-axis, whereas antiferromagnetically along the a-axis between the adjacent zig-zag chains.

Orbital selective neutron spin resonance in underdoped superconducting NaFe0.985Co0.015As

We use neutron scattering to study the electron-doped superconducting NaFe$_{0.985}$Co$_{0.015}$As ($T_c=14$ K), which has co-existing static antiferromagnetic (AF) order ($T_N=31$ K) and exhibits two neutron spin resonances ($E_{r1}\approx 3.5$ meV and $E_{r2}\approx 6$ meV) at the in-plane AF ordering wave vector ${\bf Q}_{\rm AF}={\bf Q}_{1}=(1,0)$ in reciprocal space. In the twinned state below the tetragonal-to-orthorhombic structural transition $T_s$, both resonance modes appear at ${\bf Q}_{1}$ but cannot be distinguished from ${\bf Q}_{2}=(0,1)$. By detwinning the single crystal with uniaxial pressure along the orthorhombic $b$-axis, we find that both resonances appear only at ${\bf Q}_{1}$ with vanishing intensity at ${\bf Q}_{2}$. Since electronic bands of the orbital $d_{xz}$ and $d_{yz}$ characters split below $T_s$ with the $d_{xz}$ band sinking $\sim10$ meV below the Fermi surface, our results indicate that the neutron spin resonances in NaFe$_{0.985}$Co$_{0.015}$As arise mostly from quasi-particle excitations between the hole and electron Fermi surfaces with the $d_{yz}$ orbital character.

Vehement Competition of Multiple Superexchange Interactions and Peculiar Magnetically Disordered State in Cu(OH)F

The mixed anion copper compound Cu(OH)F was studied in measurements of dc- and ac-magnetic susceptibility, static and pulsed field magnetization, specific heat, X-band electron magnetic resonance and muon-spin spectroscopy. In variance with its layered structure, the magnetic behavior shows no evidence of low-dimensionality. Cu(OH)F reaches short range static antiferromagnetic order at TN = 9.5–11.5 K and experiences the spin-flop transition at B ∼ 3.5 T. This behavior is in a sharp contrast with physical properties of earlier reported isostructural compound Cu(OH)Cl. The first principle calculations reveal highly competitive nature of ferromagnetic and antiferromagnetic superexchange interactions, the details being rather sensitive to choice of magnetic structure employed in the extraction of magnetic interaction. Rather broad anomaly in Cp(T) dependence at phase transition and smeared magnetization curve M(B) at low temperatures suggest static disorder at low temperatures however no frequency dependence...

Antiferromagnetic order and spin dynamics in iron-based superconductors

High-transition temperature (high-$T_c$) superconductivity in the iron pnictides/chalcogenides emerges from the suppression of the static antiferromagnetic order in their parent compounds, similar to copper oxides superconductors. This raises a fundamental question concerning the role of magnetism in the superconductivity of these materials. Neutron scattering, a powerful probe to study the magnetic order and spin dynamics, plays an essential role in determining the relationship between magnetism and superconductivity in high-$T_c$ superconductors. The rapid development of modern neutron time-of-flight spectrometers allows a direct determination of the spin dynamical properties of iron-based superconductors throughout the entire Brillouin zone. In this review, we present an overview of the neutron scattering results on iron-based superconductors, focusing on the evolution of spin excitation spectra as a function of electron/hole-doping and isoelectronic substitution. We compare spin dynamical properties of iron-based superconductors with those of copper oxide and heavy fermion superconductors, and discuss the common features of spin excitations in these three families of unconventional superconductors and their relationship with superconductivity.

Neutron spin resonance as a probe of superconducting gap anisotropy in partially detwinned electron underdopedNaFe0.985Co0.015As

We use inelastic neutron scattering (INS) to study the spin excitations in partially detwinned NaFe$_{0.985}$Co$_{0.015}$As which has coexisting static antiferromagnetic (AF) order and superconductivity ($T_c=15$ K, $T_N=30$ K). In previous INS work on a twinned sample, spin excitations form a dispersive sharp resonance near $E_{r1}=3.25$ meV and a broad dispersionless mode at $E_{r1}=6$ meV at the AF ordering wave vector ${\bf Q}_{\rm AF}={\bf Q}_1=(1,0)$ and its twinned domain ${\bf Q}_2=(0,1)$. For partially detwinned NaFe$_{0.985}$Co$_{0.015}$As with the static AF order mostly occurring at ${\bf Q}_{\rm AF}=(1,0)$, we still find a double resonance at both wave vectors with similar intensity. Since ${\bf Q}_1=(1,0)$ characterizes the explicit breaking of the spin rotational symmetry associated with the AF order, these results indicate that the double resonance cannot be due to the static and fluctuating AF orders, but originate from the superconducting gap anisotropy.

Doping evolution of antiferromagnetism and transport properties in nonsuperconductingBaFe2−2xNixCrxAs2

We report elastic neutron scattering and transport measurements on the Ni and Cr equivalently doped iron pnictide BaFe$_{2-2x}$Ni$_{x}$Cr$_{x}$As$_{2}$. Compared with the electron-doped BaFe$_{2-x}$Ni$_{x}$As$_{2}$, the long-range antiferromagnetic (AF) order in BaFe$_{2-2x}$Ni$_{x}$Cr$_{x}$As$_{2}$ is gradually suppressed with vanishing ordered moment and N\'{e}el temperature near $x= 0.20$ without the appearance of superconductivity. A detailed analysis on the transport properties of BaFe$_{2-x}$Ni$_{x}$As and BaFe$_{2-2x}$Ni$_{x}$Cr$_{x}$As$_{2}$ suggests that the non-Fermi-liquid behavior associated with the linear resistivity as a function of temperature may not correspond to the disappearance of the static AF order. From the temperature dependence of the resistivity in overdoped compounds without static AF order, we find that the transport properties are actually affected by Cr impurity scattering, which may induce a metal-to-insulator crossover in highly doped BaFe$_{1.7-y}$Ni$_{0.3}$Cr$_{y}$As$_{2}$.

Static Magnetic Order in A-site Ordered Perovskite, LaCu3Cr4O12, Probed with Muon Spin Spectroscopy

The microscopic magnetic nature of a novel A-site ordered chromium perovskite, LaCu3Cr4O12, has been studied with muon spin rotation and relaxation (μ+SR) measurements down to 2K using a powder sample. Magnetization and resistivity measurements indicated the presence of a magnetic transition at TM = 225K together with a metal-to-metal transition. Moreover, since the magnetization versus temperature curve showed a step-like decrease at TM with de- creasing temperature, LaCu3Cr4O12 was thought to enter into a spin-singlet like state below TM. However, μ+SR together with magnetization measurements demonstrate the appearance of static antiferromagnetic (AF) order below TM, i.e. TM = TN. Furthermore, the AF order was assigned to be incommensurate (IC) to the lattice and such IC-AF phase was most likely to change to a commensurate-AF phase below 25K.

Internal magnetic field in the zigzag-chain family (Na,Ca)Cr2O4

In order to elucidate the magnetic nature for a novel one-dimensional zigzag chain compound, NaCr2O4, we have measured μ+SR spectra using a powder sample in the temperature range between 2 and 200 K. Weak transverse field (wTF-) μ+SR measurements indicated that the whole volume of the sample enters into an antiferromagnetic (AF) phase below TN = 125 K. The zero field (ZF-) μ+SR spectrum obtained below TN exhibits a clear oscillation with a single muon-spin precession frequency (fμ). This suggests that static AF order is formed below TN and that all the implanted muons sense the same internal magnetic field. The temperature dependence of fμ was found to be very similar to that for the intensity of the magnetic Bragg peak in neutron diffraction (ND) measurements. On the other hand, the ZF-μ+SR spectrum for the isostructural compound, β-CaCr2O4, showed a rapidly damped oscillation below TN = 21 K, supporting the formation of incommensurate AF order, as proposed by ND.

Microscopic magnetic nature of K2NiF4-type 3d transition metal oxides

In order to elucidate the magnetic nature of K2NiF4-type 3d transition metal oxides, we have measured μ+SR spectra for Sr2VO4, LaSrVO4, and Sr2CrO4 using powder samples. ZF- and wTF-μ+SR measurements propose that Sr2VO4 enters into the static antiferromagnetic (AF) order phase below 8 K. In addition, TF-μ+SR measurements evidence that the transition at 105 K is not magnetic but structural and/or electronic in origin. For LaSrVO4, static long-range order has not been observed down to 20 K, while, as T decreases from 145 K, wTF asymmetry starts to decrease below 60 K, suggesting the appearance and evolution of localized magnetic moments below 60 K. For Sr2CrO4, by contrast, both ZF- and wTF-μ+SR have confirmed the presence of antiferromagnetic order below 117 K, as predicted in the χ(T) curve.

Anisotropic neutron spin resonance in underdoped superconductingNaFe1−xCoxAs

We use polarized inelastic neutron scattering (INS) to study spin excitations in superconducting NaFe0.985Co0.015As (C15) with static antiferromagnetic (AF) order along the a-axis of the orthorhombic structure and NaFe0.935Co0.045As (C45) without AF order. In previous unpolarized INS work, spin excitations in C15 were found to have a dispersive sharp resonance near Er1=3.25 meV and a broad dispersionless mode at Er2=6 meV. Our neutron polarization analysis reveals that the dispersive resonance in C15 is highly anisotropic and polarized along the a- and c-axis, while the dispersionless mode is isotropic similar to that of C45. Since the a-axis polarized spin excitations of the anisotropic resonance appear below Tc, our data suggests that the itinerant electrons contributing to the magnetism are also coupled to the superconductivity.

Hidden magnetic order in Sr2VO4clarified withμ+SR

In order to elucidate the magnetic ground state of Sr2VO4, we have measured muon spin rotation and relaxation (mu+SR) spectra of a powder sample in the temperature range between 1.8 and 140 K. As a result, we have clarified that the transition at 105 K is not magnetic but structural and/or electric in origin and found the appearance of static antiferromagnetic (AF) order below 8 K. Moreover, the distribution of the internal AF field was found to be very broad, even at the lowest temperature measured. These results are consistent with the formation of an orbital-stripe order with collinear AF order for the magnetic ground state of Sr2VO4.

Partially disordered spin structure in Ag2CrO2studied withμ+SR

The magnetism of a metallic two-dimensional triangular antiferromagnetic (AF) compound, Ag${}_{2}$CrO${}_{2}$, has been investigated by muon-spin rotation and relaxation (${\ensuremath{\mu}}^{+}$SR) using a powder sample in the temperature range between 1.8 and 40 K. Below ${T}_{\mathrm{N}}=24$ K, a muon-spin precession signal was clearly observed in the zero-field spectrum, indicating the formation of static AF order. It was also found that the internal field is temperature independent except for in the vicinity of ${T}_{\mathrm{N}}$, as in the case for the susceptibility versus temperature curve. This suggests that the AF transition is induced by a first-order structural phase transition at ${T}_{\mathrm{N}}$. Combining the ${\ensuremath{\mu}}^{+}$SR result with the prediction for muon sites in the lattice by first-principles calculations, a partially disordered AF state was found to be the most reasonable spin structure for Ag${}_{2}$CrO${}_{2}$.

Electron doping evolution of the magnetic excitations in BaFe2−xNixAs2

We use inelastic neutron scattering (INS) spectroscopy to study the magnetic excitations spectra throughout the Brillouin zone in electron-doped iron pnictide superconductors BaFe${}_{2\ensuremath{-}x}$Ni${}_{x}$As${}_{2}$ with $x=0.096,0.15,0.18$. While the $x=0.096$ sample is near optimal superconductivity with ${T}_{c}=20$ K and has coexisting static incommensurate magnetic order, the $x=0.15,0.18$ samples are electron overdoped with reduced ${T}_{c}$ of 14 and 8 K, respectively, and have no static antiferromagnetic (AF) order. In previous INS work on undoped ($x=0$) and electron optimally doped ($x=0.1$) samples, the effect of electron doping was found to modify spin waves in the parent compound BaFe${}_{2}$As${}_{2}$ below $\ensuremath{\sim}$100 meV and induce a neutron spin resonance at the commensurate AF ordering wave vector that couples with superconductivity. While the new data collected on the $x=0.096$ sample confirm the overall features of the earlier work, our careful temperature dependent study of the resonance reveals that the resonance suddenly changes its $Q$ width below ${T}_{c}$ similar to that of the optimally hole-doped iron pnictides Ba${}_{0.67}$K${}_{0.33}$Fe${}_{2}$As${}_{2}$. In addition, we establish the dispersion of the resonance and find it to change from commensurate to transversely incommensurate with increasing energy. Upon further electron doping to overdoped iron pnictides with $x=0.15$ and 0.18, the resonance becomes weaker and transversely incommensurate at all energies, while spin excitations above $\ensuremath{\sim}$100 meV are still not much affected. Our absolute spin excitation intensity measurements throughout the Brillouin zone for $x=0.096,0.15,0.18$ confirm the notion that the low-energy spin excitation coupling with itinerant electron is important for superconductivity in these materials, even though the high-energy spin excitations are weakly doping dependent.

Impact of Local Lattice Disorder on Spin and Orbital Orders in Ca2-xSrxRuO4

We have studied relationship between local lattice disorder, Ru 4$d$ spin-orbit interaction, and global spin/orbital orders of Ca$_{2-x}$Sr$_x$RuO$_4$ in the Sr-rich and Ca-rich regions of its phase diagram by using unrestricted Hartree-Fock calculation on a $8\times8$ RuO$_4$ lattice model. The calculations show that the local elongation of RuO$_6$ octahedron in an antiferromagnetic insulator Ca$_2$RuO$_4$ induces local orbital change with making the Mott gap narrower. On the other hand, local compression of RuO$_6$ octahedron in a paramagnetic metal Sr$_2$RuO$_4$ induces global antiferromagnetic or ferromagnetic states. This result is consistent with a recent systematic $\mu$SR study by Carlo {\it et al.} which has revealed the static antiferromagnetic order at low temperature in the Sr-rich region.

Electron doping evolution of the anisotropic spin excitations in BaFe2−xNixAs2

We use inelastic neutron scattering to systematically investigate the Ni-doping evolution of the low-energy spin excitations in BaFe${}_{2\ensuremath{-}x}$Ni${}_{x}$As${}_{2}$ spanning from underdoped antiferromagnet to overdoped superconductor ($0.03\ensuremath{\le}x\ensuremath{\le}0.18$). In the undoped state, BaFe${}_{2}$As${}_{2}$ changes from paramagnetic tetragonal phase to orthorhombic antiferromagnetic (AF) phase below about 138 K, where the low-energy ($\ensuremath{\le}\ensuremath{\sim}80$ meV) spin waves form transversely elongated ellipses in the $[H,K]$ plane of the reciprocal space. Upon Ni doping to suppress the static AF order and induce superconductivity, the $c$-axis magnetic exchange coupling is rapidly suppressed and the momentum distribution of spin excitations in the $[H,K]$ plane is enlarged in both the transverse and longitudinal directions with respect to the in-plane AF ordering wave vector of the parent compound. As a function of increasing Ni-doping $x$, the spin excitation widths increase linearly but with a larger rate along the transverse direction. These results are in general agreement with calculations of dynamic susceptibility based on the random phase approximation (RPA) in an itinerant electron picture. For samples near optimal superconductivity at $x\ensuremath{\approx}0.1$, a neutron spin resonance appears in the superconducting state. Upon further increasing the electron doping to decrease the superconducting transition temperature ${T}_{c}$, the intensity of the low-energy magnetic scattering decreases and vanishes concurrently with vanishing superconductivity in the overdoped side of the superconducting dome. Comparing with the low-energy spin excitations centered at commensurate AF positions for underdoped and optimally doped materials ($x\ensuremath{\le}0.1$), spin excitations in the overdoped side ($x=0.15$) form transversely incommensurate spin excitations, consistent with the RPA calculation. Therefore, the itinerant electron approach provides a reasonable description to the low-energy AF spin excitations in BaFe${}_{2\ensuremath{-}x}$Ni${}_{x}$As${}_{2}$.

Unconventional magnetic phase diagram of cuprate superconductor La2−xSrxCuO4 at quantum critical point x=1/9

We propose a new magnetic phase diagram of La2−xSrxCuO4 around a quantum critical point x=1/9 based on field-cooled magnetization measurements and critical fittings. A new phase boundary Tm2(H) is discovered which buries deeply below the first order vortex melting line in the vortex solid phase. The coupling between superconductivity and antiferromagnetism is found to be attractive below Tm2(H) while repulsive above. The attractive coupling between superconducting order and static antiferromagnetic order provides compelling experimental evidence that the antiferromagnetism microscopically coexists and collaborates with the high temperature superconductivity in cuprates.