Two-dimensional Antiferromagnet Research Articles

Quasielastic neutron scattering from two-dimensional antiferromagnets at a finite temperature

We consider frequency dependence of the neutron scattering amplitude from a two-dimensional quantum antiferromagnet. It is well known that the long range order disappears at any finite temperature and hence the elastic neutron scattering Bragg peak is transformed to the quasielastic neutron scattering spectrum ~dw/w. We show that the widely known formula for the spectrum of an isotropic antiferromagnet derived by Auerbach and Arovas should be supplemented by a logarithmic term that changes the integrated intensity by two times. A similar formula for an easy-plane magnet is very much different because of the Berezinsky-Kosterlitz-Thouless physics. An external uniform magnetic field switches smoothly the isotropic magnet to the easy-plane magnet. We demonstrate that the quasielastic neutron scattering spectrum in the crossover regime combines properties of both limiting cases. We also consider a quantum antiferromagnet close to the O(3) quantum critical point and show that in an external uniform magnetic field the intensity of elastic (quasielastic) neutron scattering peak depends linearly and significantly on the applied field.

Collapse of Ferrimagnetism in Two-Dimensional Heisenberg Antiferromagnet due to Frustration

We study ferrimagnetism in the ground state of the antiferromagnetic Heisenberg model on the spatially anisotropic kagome lattice, in which ferrimagnetism of the conventional Lieb-Mattis type appears in the region of weak frustration whereas the ground state is nonmagnetic in the isotropic case. Numerical diagonalizations of small finite-size clusters are carried out to examine the spontaneous magnetization. We find that the spontaneous magnetization changes continuously in the intermediate region between conventional ferrimagnetism and the nonmagnetic phase. Local magnetization of the intermediate state shows strong dependence on the site position, which suggests non-Lieb-Mattis ferrimagnetism.

The magnetic order of two-dimensional anisotropic antiferromagnets

We study the two-dimensional quantum Heisenberg antiferromagnet on the square lattice with easy-axis exchange anisotropy by means of Green’s function approach within random phase and Callen’s approximations. The Néel temperature TN, energy gap w0 and staggered magnetization m are calculated. The theoretical predictions of TN and w0 for K2NiF4, Rb2MnF4, K2MnF4, Rb2MnCl4 and (CH3NH3)2MnCl4 fit well to the measured values. The power law behavior of w(T)w(0)=β[m(T)m(0)]ν is also investigated. The exponents β and ν for K2NiF4 are in excellent agreement with the experimental results.

Anisotropic spin dynamics in the frustrated chainCa3Co2O6detected by single-crystalC59oNMR

Static and dynamic magnetic properties are investigated by $^{59}\text{C}\text{o}$ NMR measurements on a single crystal of ${\text{Ca}}_{3}{\text{Co}}_{2}{\text{O}}_{6}$, a rare model of the ferromagnetic Ising chain coupled antiferromagnetically on a triangular lattice. Above a ferrimagnetic order transition temperature ${T}_{\text{N}}=25\text{ }\text{K}$, the static spin susceptibility probed by the $^{59}\text{C}\text{o}$ Knight shift shows anisotropic behavior in the temperature dependence, consistent with ferromagnetic interactions along the $c$-axis chain and antiferromagnetic interactions in the $ab$ plane. Correspondingly, the dynamical spin susceptibility obtained from the $^{59}\text{C}\text{o}$ nuclear spin-lattice relaxation rate is also highly anisotropic. The intrachain ferromagnetic correlation steeply develops below 300 K while the interchain antiferromagnetic one does below 120 K with the critical exponent expected in the two-dimensional Ising antiferromagnet. Below ${T}_{\text{N}}$, the low-energy excitation arising from the predominant spin-wave magnons has an anisotropic full gap, reflecting the strongly Ising nature. Clear microscopic evidence of the ferrimagnetic order is demonstrated in the $^{59}\text{C}\text{o}$ NMR spectra at 5 K. Rotation of the external magnetic field from the $ab$ plane to the $c$ axis shows the first-order transition from the ferrimagnetic to the fully polarized state. The ferrimagnetic state with the uniform magnitude of magnetic moment is observed even in the transverse field adjusted parallel to the $ab$ plane.

Emergence of robust gaps in two-dimensional antiferromagnets via additional spin-1/2 probes

We study the capacity of antiferromagnetic lattices of varying geometries to entangle two additional spin-$1/2$ probes. Analytical modeling of the quantum Monte Carlo data shows the appearance of a robust gap, allowing a description of entanglement in terms of probe-only states, even in cases where the coupling to the probes is larger than the gap of the spin lattice and cannot be treated perturbatively. We find a considerable enhancement of the temperature at which probe entanglement disappears as we vary the geometry of the bus and the coupling to the probes. In particular, the square Heisenberg antiferromagnet exhibits the best thermal robustness of all systems, whereas the three-leg ladder chain shows the best performance in the natural quantum ground state.

Magnetic order on a frustrated spin-12Heisenberg antiferromagnet on the Union Jack lattice

We use the coupled cluster method (CCM) to study the zero-temperature phase diagram of a two-dimensional frustrated spin-half antiferromagnet, the so-called Union Jack model. It is defined on a square lattice such that all nearest-neighbor pairs are connected by bonds with a strength ${J}_{1}>0$, but only half the next-nearest-neighbor pairs are connected by bonds with a strength ${J}_{2}\ensuremath{\equiv}\ensuremath{\kappa}{J}_{1}>0$. The bonds are arranged such that on the $2\ifmmode\times\else\texttimes\fi{}2$ unit cell they form the pattern of the Union Jack flag. Alternating sites on the square lattice are thus four-connected and eight-connected. We find strong evidence for a first phase transition between a N\'eel antiferromagnetic phase and a canted ferrimagnetic phase at a critical coupling ${\ensuremath{\kappa}}_{{c}_{1}}=0.66\ifmmode\pm\else\textpm\fi{}0.02$. The transition is an interesting one, at which the energy and its first derivative seem continuous, thus providing a typical scenario of a second-order transition (just as in the classical case for the model), although a weakly first-order transition cannot be excluded. By contrast, the average on-site magnetization approaches a nonzero value ${M}_{{c}_{1}}=0.195\ifmmode\pm\else\textpm\fi{}0.005$ on both sides of the transition, which is more typical of a first-order transition. The slope, $dM/d\ensuremath{\kappa}$, of the order parameter curve as a function of the coupling strength $\ensuremath{\kappa}$, also appears to be continuous, or very nearly so, at the critical point ${\ensuremath{\kappa}}_{{c}_{1}}$, thereby providing further evidence of the subtle nature of the transition between the N\'eel and canted phases. Our CCM calculations provide strong evidence that the canted ferrimagnetic phase becomes unstable at large values of $\ensuremath{\kappa}$, and hence we have also used the CCM with a model collinear semistripe-ordered ferrimagnetic state in which alternating rows (and columns) are ferromagnetically and antiferromagnetically ordered, and in which the spins connected by ${J}_{2}$ bonds are antiparallel to one another. We find tentative evidence, based on the relative energies of the two states, for a second zero-temperature phase transition between the canted and semistripe-ordered ferrimagnetic states at a large value of the coupling parameter around ${\ensuremath{\kappa}}_{{c}_{2}}\ensuremath{\approx}125\ifmmode\pm\else\textpm\fi{}5$. This prediction, however, is based on an extrapolation of the CCM results for the canted state into regimes where the solutions have already become unstable and the CCM equations based on the canted state at any level of approximation beyond the lowest have no solutions. Our prediction for ${\ensuremath{\kappa}}_{{c}_{2}}$ is hence less reliable than that for ${\ensuremath{\kappa}}_{{c}_{1}}$. Nevertheless, if this second transition at ${\ensuremath{\kappa}}_{{c}_{2}}$ does exist, our results clearly indicate it to be of first-order type.

C59oNMR shift anomalies and spin dynamics in the normal state of superconductingCeCoIn5: Verification of two-dimensional antiferromagnetic spin fluctuations

We have measured the Knight shifts $(K)$ and nuclear relaxation times $({T}_{1})$ for $^{59}\text{C}\text{o}$ in ${\text{CeCoIn}}_{5}$ under external fields along $a$ and $c$ axes with the goal of establishing the anisotropy of antiferromagnetic (AFM) spin fluctuations (SF). In our approach, we revisit the problem of interpreting anomalies in the relationship between Knight shift ${K}_{a,c}$ and static susceptibility ${\ensuremath{\chi}}_{a,c}$: assuming a single component susceptibility implies a temperature-dependent hyperfine coupling ${A}_{a,c}(T)$. Once adopted, a known discrepancy between the behaviors of ${T}_{1}^{\ensuremath{-}1}$ for $^{59}\text{C}\text{o}$ and $^{115}\text{I}\text{n}(1)$ sites is eliminated to within experimental uncertainties and the variation with temperature is analyzed within the framework of two-dimensional AFM SF in proximity to a quantum-critical point. Moreover, the ratio $[{T}_{1a}/{T}_{1c}]$ indicates easy-plane anisotropy for $Tl{T}^{\ensuremath{\ast}}\ensuremath{\sim}40\text{ }\text{K}$, for the heavy-fermion state.

Spectrum of short-wavelength magnons in a two-dimensional quantumHeisenberg antiferromagnet on a square lattice: third-order expansion in1/S

The spectrum of short-wavelength magnons in a two-dimensional quantumHeisenberg antiferromagnet on a square lattice is calculated to the third order in a1/S expansion. It isshown that a 1/S series for S = 1/2 converges quickly in the whole Brillouin zone except in the neighborhood of the pointk = (π, 0), at which absolute values of the third-and the second-order1/S-corrections are approximately equal to each other. It is shown that thethird-order corrections make deeper the roton-like local minimum atk = (π, 0), improving the agreement with recent experiments and numericalresults in the neighborhood of this point. It is suggested that the1/S series convergesslowly near k = (π, 0) also for S = 1 although the spectrum renormalization would be small in this case due to the very small values of high-order1/S corrections.

Reentrant enhancement of quantum fluctuations for symmetric environmental coupling

The system-plus-reservoir (SPR) model is the most common and effective approach to study quantum dissipative effects. Indeed, it makes quantization possible by considering the whole energy-conserving system, while the reservoir's degrees of freedom, assumed to be harmonic, can be traced out by the path-integral technique, leading to a formulation that only includes the system of interest. In the standard SPR model the environment is only coupled with the system's coordinate and turns out to quench its quantum fluctuations. However, there are physical systems coupled with an environment whose "coordinates" and "momenta" can be completely interchangeable (e.g., magnets), so an SPR coupling must symmetrically affect both canonical variables. In this paper such a general environmental coupling is studied in the case of a harmonic oscillator. It is found that quantum fluctuations are generally enhanced by environmental coupling with an unexpected nonmonotonic behavior. This leads one to speculate about the possibility that spin-lattice coupling could drive the two-dimensional Heisenberg antiferromagnet to reach its quantum-critical point.

Effective theory of Fermi pockets in fluctuating antiferromagnets

We describe fluctuating two-dimensional metallic antiferromagnets by transforming to a rotating reference frame in which the electron spin polarization is measured by its projections along the local antiferromagnetic order. This leads to a gauge-theoretic description of an ``algebraic charge liquid'' involving spinless fermions and a spin $S=1/2$ complex scalar. We propose a phenomenological effective lattice Hamiltonian which describes the binding of these particles into gauge-neutral, electronlike excitations, and describe its implications for the electron spectral function across the entire Brillouin zone. We discuss connections of our results to photoemission experiments in the pseudogap regime of the cuprate superconductors.

Instability of magnons in two-dimensional antiferromagnets at high magnetic fields

Spin dynamics of the square lattice Heisenberg antiferromagnet, \BaMnGeO, is studied by a combination of bulk measurements, neutron diffraction, and inelastic neutron scattering techniques. Easy plane type antiferromagnetic order is identified at $T \le 4.0$ K. The exchange interactions are estimated as $J_1$ = 27.8(3)${\mu}$eV and $J_2$ = 1.0(1) ${\mu}$eV, and the saturation field $H_{\rm C}$ is 9.75 T. Magnetic excitation measurements with high experimental resolution setup by triple axis neutron spectrometer reveals the instability of one magnon excitation in the field range of $0.7H_{\rm C} \lesssim H \lesssim 0.85H_{\rm C}$.

First-principles comparative study of multiferroic compound PbVO 3

We report a comprehensive first-principles investigation of the structural, electronic, magnetic and phase transition properties in multiferroic compound PbVO 3 with systematic comparisons of various exchange-correlation (XC) functionals. The antiferromagnetic (AFM) insulating ground state of tetragonal phase has been obtained in the framework of the band theory, which is characterized by C-type two-dimensional AFM magnetic ordering in the ab plane. A first-order structural transformation from tetragonal phase to idea cubic perovskite structure takes place at 1.75 GPa, corresponding to the ferroelectric to paraelectric phase transition. Electronic structure calculations suggest that the ground state of the cubic paraelectric phase is a nonmagnetic orbital-disorder metal.

High-Field and Multi-Frequency ESR in the Quasi Two-Dimensional Triangular-Lattice Antiferromagnet CuCrO2

We have performed high-field and multi-frequency electron spin resonance (ESR) and magnetization measurements in magnetic fields up to about 53 T on single crystals of a delafossite triangular-lattice antiferromagnet CuCrO2, which has been proposed to show an out-of-plane 120° spiral spin structure below about 24 K. We calculated ESR resonance modes and magnetization curves assuming an Ising-like Heisenberg Hamiltonian with a spiral spin structure by a mean-field theory. The experimental results can be well reproduced using the following parameters, the intralayer exchange constant J/kB=26.9 K, the easy-axis anisotropy D/kB=−0.47 K, and the in-plane g-factor gab=2.0.

Partially disordered antiferromagnetic state in two-dimensional triangular-lattice antiferromagnet

The partially disordered antiferromagnetic (PDA) state, as an exotic phase peculiar to the antiferromagnet with Ising spin in triangular lattice, is investigated by using Monte Carlo simulations of Wang–Landau algorithm and Glauber algorithm. It is revealed that PDA state, as the ground state of the triangular antiferromagnetic system, presents the complicated spin configuration due to geometrical frustration. The formation of multi-domain structure within the framework of honeycomb antiferromagnet results in the high degeneracy of PDA state. And this degeneracy of ground state can be lifted by a small magnetic field. Consequently the system shows the ferrimagnetic state, and the magnetization plateau of 1/3 saturate value ( M s ) is observed in many experiments. Moreover, due to the multi-domain structure of PDA state and those spins on domain walls, the metastable steps may manifest themselves superposed on the 1 / 3 M s plateau in some special cases.

Antiferromagnetic to valence-bond-solid transitions in two-dimensionalSU(N)Heisenberg models with multispin interactions

We study two-dimensional Heisenberg antiferromagnets with additional multi-spin interactions which can drive the system into a valence-bond solid state. For standard SU(2) spins, we consider both four- and six-spin interactions. We find continuous quantum phase transitions with the same critical exponents. Extending the symmetry to SU(N), we also find continuous transitions for N=3 and 4. In addition, we also study quantitatively the cross-over of the order-parameter symmetry from Z4 deep inside the valence-bond-solid phase to U(1) as the phase transition is approached.

Spin transport in the anisotropic easy-plane two-dimensional Heisenberg antiferromagnet

Spin transport in the easy-plane two-dimensional anisotropic Heisenberg antiferromagnet with S=1 is studied. Regular part of spin conductivity is calculated, at zero temperature, using a self-consistent harmonic approximation and the Kubo formalism. Three magnon processes provide the dominant contribution to the spin conductivity. Furthermore, the transport is ballistic and characterized by finite Drude weight.

Spontaneous trimerization in two-dimensional antiferromagnets

In this paper, we propose an exotic quantum paramagnetic state in two-dimensionalantiferromagnets—the spontaneous trimer state—which is the direct product state of thetrimers of spins. Each trimer is a singlet state formed by three neighboring spins withSU(3) symmetry. A frustrated spin-1 Heisenberg model in the kagome lattice is investigated. Byanalogy to the pseudo-potential approach in the fractional quantum Hall effect (FQHE), wefind that the trimer state provides a good description for the exact ground state of thismodel. Other interesting properties, such as the local excitations as well as magnetizationplateaus have also been investigated.

Vortex dynamics and frustration in two-dimensional triangular chromium lattices

The spin dynamics of the two-dimensional (2D) triangular lattice antiferromagnets ${\text{HCrO}}_{2}$, ${\text{LiCrO}}_{2}$, and ${\text{NaCrO}}_{2}$ is investigated by electron spin resonance. In these oxides, on approaching the N\'eel temperature ${T}_{\text{N}}$ from above, the divergence of the temperature dependent linewidth is well described in terms of a Berezinskii-Kosterlitz-Thouless scenario due to magnetic vortex-antivortex pairing. A refined analysis suggests analogies to the melting scenario of a 2D triangular lattice described by Nelson, Halperin, and Young.

Phason-disordered two-dimensional quantum antiferromagnets

We examine a novel type of disorder in quantum antiferromagnets. Our model consists of localized spins with antiferromagnetic exchanges on a bipartite quasiperiodic structure, which is geometrically disordered in such a way that no frustration is introduced. In the limit of zero disorder, the structure is the perfect Penrose rhombus tiling. This tiling is progressively disordered by augmenting the number of random "phason flips" or local tile-reshuffling operations. The ground state remains N\'eel ordered, and we have studied its properties as a function of increasing disorder using linear spin wave theory and quantum Monte Carlo. We find that the ground state energy decreases, indicating enhanced quantum fluctuations with increasing disorder. The magnon spectrum is progressively smoothed, and the effective spin wave velocity of low energy magnons increases with disorder. For large disorder, the ground state energy as well as the average staggered magnetization tend towards limiting values characteristic of this type of randomized tilings.

Hydrodynamic relation in a two-dimensional Heisenberg antiferromagnet in a field

The spin stiffness ${\ensuremath{\rho}}_{s}$ of a two-dimensional (2D) Heisenberg antiferromagnet depends nonanalytically on external magnetic field. We demonstrate that the hydrodynamic relation between ${\ensuremath{\rho}}_{s}$, the uniform susceptibility $\ensuremath{\chi}$, and the spin-wave velocity $c$ is not violated by such a behavior because similar nonanalytic terms from all three quantities mutually cancel out. In this work, explicit expressions for the field-dependent spin stiffness and for the magnon velocity of the 2D square-lattice antiferromagnet are obtained by direct calculation to order $1/S$ and in the whole range of magnetic fields.