Pure Heisenberg Model Research Articles

Frustrated Heisenberg model within the stretched diamond lattice of LiYbO2.

We investigate the magnetic properties of LiYbO2, containing a three-dimensionally frustrated, diamond-like lattice via neutron scattering, magnetization, and heat capacity measurements. The stretched diamond network of Yb3+ ions in LiYbO2 enters a long-range incommensurate, helical state with an ordering wave vector that "locks-in" to a commensurate phase under the application of a magnetic field. The spiral magnetic ground state of LiYbO2 can be understood in the framework of a Heisenberg Hamiltonian on a stretched diamond lattice, where the propagation vector of the spiral is uniquely determined by the ratio of . The pure Heisenberg model, however, fails to account for the relative phasing between the Yb moments on the two sites of the bipartite lattice, and this detail as well as the presence of an intermediate, partially disordered, magnetic state below 1 K suggests interactions beyond the classical Heisenberg description of this material.

Spin liquids and state selection in the Kitaev-Heisenberg model in corner sharing lattices

Abstract In the last ten years, the Kitaev-Heisenberg model has attracted much attention since the work by G. Jackeli and G. Khaliullin [1], where they showed that Kitaev interactions are relevant in iridate materials. Experimental results in honeycomb iridates are not consistent with a pure Kitaev model, and exchange couplings may play an important role in the low temperature behavior of these materials [2]. In this work, we present a study of the classical Kitaev-Heisenberg model in the pyrochlore and kagome lattices in the highly frustrated regime. Previous works have studied this model with the Luttinger-Tisza approximation, indicating frustrated phases and highly degenerate points [3,4]. Here, we focus on the highly degenerate points. We explore their magnetic properties at low temperature by means of Monte-Carlo Simulations. We compare the specific heat and the structure factors with their dual counterpart, the antiferromagnetic pure Heisenberg model. This allows us to identify order-by-disorder state selection in the kagome lattice, and spin liquid behavior in the pyrochlore case.

Thermal Hall effect of spins in a paramagnet

Theory of Hall transport of spins in a correlated paramagnetic phase is developed. By identifying the thermal Hall current operator in the spin language, which turns out to equal the spin chirality in the pure Heisenberg model, various response functions can be derived straightforwardly. Subsequent reduction to the Schwinger boson representation of spins allows a convenient calculation of thermal and spin Hall coefficients in the paramagnetic regime using self-consistent mean-field theory. Com- parison is made to results from the Holstein-Primakoff reduction of spin operators appropriate for ordered phases.

Critical behaviour of magnetic transitions in KCoF3 and KNiF3 perovskites

KAF3 (A=Mn, Co, Ni) are considered as perfect 3-D Heisenberg antiferromagnets though there are scarce experimental evidences of that behaviour in the case of the last two perovskites. In this work, a high resolution photopyroelectric technique has been used to study the critical behaviour of the antiferromagnetic transition in KCoF3 and KNiF3 measuring specific heat, thermal diffusivity and thermal conductivity. The critical behaviour of KNiF3 slightly deviates from the perfect Heisenberg universality class (the retrieved parameters are α=−0.110, A+/A−=1.30), due to its small uniaxial anisotropy; this behaviour has been confirmed by the critical parameters of both the specific heat and the thermal diffusivity. In opposition to what is assumed in literature, the critical behaviour of KCoF3 cannot be simply described by the Heisenberg universality class (α=−0.081, A+/A−=1.19) due to the spin–orbit interaction at the magnetic transition, which introduces a perturbation in the Hamiltonian and makes the pure Heisenberg model incomplete for this case. The results for both materials disagree with and correct previous works on them.

Study of critical properties of the frustrated antiferromagnetic Heisenberg model on a triangular lattice

The replica Monte Carlo method has been applied to study critical properties of the three-dimensional frustrated antiferromagnetic Heisenberg model on a layered triangular lattice. Magnetic and chiral critical exponents for this model have been calculated within the finite-size scaling theory. The data for this model have been analyzed for the first time taking into account corrections to scaling. It has been shown that the critical behavior of the frustrated antiferromagnetic Heisenberg model on the triangular lattice differs from the critical behavior of the pure Heisenberg model and is independent of the type of interlayer exchange interaction.

Critical behavior of diluted magnetic semiconductors: Apparent violation and eventual restoration of the Harris criterion for all regimes of disorder

Using large-scale Monte Carlo calculations, we consider strongly disordered Heisenberg models on a cubic lattice with missing sites (as in diluted magnetic semiconductors such as ${\text{Ga}}_{1\ensuremath{-}x}{\text{Mn}}_{x}\text{As}$). For disorder ranging from weak to strong levels of dilution, we identify Curie temperatures and calculate the critical exponents $\ensuremath{\nu}$, $\ensuremath{\gamma}$, $\ensuremath{\eta}$, and $\ensuremath{\beta}$; we find, per the Harris criterion, good agreement with critical indices of the pure Heisenberg model where there is no disorder component. Moreover, we find that thermodynamic quantities (e.g., the second moment of the magnetization per spin) self-average at the ferromagnetic transition temperature with relative fluctuations tending to zero with increasing system size. We directly calculate effective critical exponents for $T>{T}_{c}$, yielding values which may differ significantly from the critical indices for the pure system, especially in the presence of strong disorder. Ultimately, the difference is only apparent, and eventually disappears when $T$ is very close to ${T}_{c}$.

Incoherent transport induced by a single static impurity in a Heisenberg chain

The effect of a single static impurity on the many-body states and on the spin and thermal transport in the one-dimensional anisotropic Heisenberg chain at finite temperatures is studied. Whereas the pure Heisenberg model reveals Poisson level statistics and dissipationless transport due to integrability, we show using the numerical approach that a single impurity induces Wigner-Dyson level statistics and at high enough temperature incoherent transport within the chain, whereby the relaxation time and dc conductivity scale linearly with length.

Magnetic Susceptibility of the Kagome AntiferromagnetZnCu3(OH)6Cl2

We analyze the experimental data for the magnetic susceptibility of the material ZnCu3(OH)6Cl2 in terms of the Kagome Lattice Heisenberg model (KLHM), discussing possible role of impurity spins, dilution, exchange anisotropy, and both out-of-plane and in-plane Dzyloshinski-Moriya (DM) anisotropies, with explicit theoretical calculations using the numerical linked cluster method and exact diagonalization. The high-temperature experimental data are well described by the pure Heisenberg model with J=170 K. We show that the sudden upturn in the susceptibility around T=75 K is due to DM interactions. We also observe that at intermediate temperatures, below T=J, our calculated susceptibility for KLHM fits well with a power law T(-0.25).

Antiferromagnetic order and phase transitions in GdS as studied with X-ray resonance-exchange scattering

We report on X-ray resonance exchange and neutron scattering of metallic GdS. At the LII and L III absorption edges of Gd, resonance enhancements of more than two orders of magnitude over the non-resonant magnetic scattering are observed. Polarisation analysis proves that these enhancements are due to dipolar transitions from the 2p to the 5d states. The branching ratio between the LII and L III edges of 2.5 suggests a polarisation of the 5d electrons in the ground state. The antiferromagnetic order is of type II in the fcc lattice. Single crystal diffraction of hot neutrons suggests that the spin direction lies within the (111) planes with a value for the sublattice magnetisation of 6.51(3) . The critical exponent for the sublattice magnetisation has a value of β = 0.38(2) in agreement with a pure Heisenberg model. Above T N, a sharp component persists in the critical diffuse scattering. Lattice distortions give indications for two additional low-temperature phase transitions at about 49 K and 32 K. We argue that these transitions are not connected to spin reorientations and discuss the possible influence of fourth-order exchange interactions.

Surface Phase Transition in Anisotropic Heisenberg Models

The behavior of an anisotropic Heisenberg model on a semi-infinite cubic lattice is studied. We employ the Green's function formalism and the random-phase approximation in our analysis. We consider different possible configurations for the anisotropy parameters of the surface and bulk. We determine the profile of the magnetization and the renormalized magnon energy spectrum as a function of temperature and of the anisotropy parameters of the surface and bulk. We also find the complete phase diagram for the multicritical points which is in agreement with the real-space renormalization group calculations. The onset of surface ordering takes place when the surface magnons become more energetic than the bulk modes. In the limit where bulk and surface are both described by a pure Heisenberg model, there is no long-range surface magnetic order over the paramagnetic bulk, whatever the values of the exchange couplings are. We relate this result with the Mermin-Wagner theorem. We show that the slope of the surface magnetization is discontinuous at the bulk critical temperature and that the discontinuity increases when the model on the surface varies from Ising to Heisenberg. In the particular case when the exchange couplings become antiferromagnetic, we have found the canted-paramagnetic critical field at the surface which is larger than that of the bulk. At very low temperatures, the critical field at the surface does not follow a T3/2 Bloch law, but instead decreases linearly with temperature.

Magnetic Raman Scattering in Undoped and Doped Antiferromagnets

Magnetic Raman scattering of doped and undoped high-Tc (HTc) cuprates is presented in comparison with the conventional antiferromagnet NiO. In both classes of materials the strong magnetic Raman response is caused by a Me–O superexchange mechanism. The difference in the absolute Raman cross-sections of 90×10−5 sr−1 cm−1 (YBa2Cu3O6.3) and 1.6×10−5 sr−1 cm−1 (NiO) is explained by the different strengths of the exchange energies. The magnetic scattering signal of NiO is explainable by the pure Heisenberg model, whereas the zone edge magnons of the HTc cuprates show additional damping due to magnon phonon interaction. On doping, the damping of the zone-edge magnons increases by a factor of 4 more than the decrease of magnon energy. This is characteristic of the interaction of the spin system with the charge carriers. The absolute Raman cross-section is reduced owing to the interruption of antiferromagnetic spin correlations on doping.

Magnetic Raman Scattering in Undoped and Doped Antiferromagnets

Magnetic Raman scattering of doped and undoped high-Tc (HTc) cuprates is presented in comparison with the conventional antiferromagnet NiO. In both classes of materials the strong magnetic Raman response is caused by a Me–O superexchange mechanism. The difference in the absolute Raman cross-sections of 90×10−5 sr−1 cm−1 (YBa2Cu3O6.3) and 1.6×10−5 sr−1 cm−1 (NiO) is explained by the different strengths of the exchange energies. The magnetic scattering signal of NiO is explainable by the pure Heisenberg model, whereas the zone edge magnons of the HTc cuprates show additional damping due to magnon phonon interaction. On doping, the damping of the zone-edge magnons increases by a factor of 4 more than the decrease of magnon energy. This is characteristic of the interaction of the spin system with the charge carriers. The absolute Raman cross-section is reduced owing to the interruption of antiferromagnetic spin correlations on doping.

Singularity of the surface magnetization in anisotropic Heisenberg ferromagnets.

The surface-magnetization singularity at the bulk critical temperature is studied within the context of the Green-function formalism. We take a pure Heisenberg model on the bulk of a semi-infinite lattice and the surface is described by an anisotropic Heisenberg model, whose anisotropy parameter ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{s}}$ permits us to consider a sequence of models from pure Heisenberg to Ising. We show that the slope of the surface magnetization is discontinuous at the bulk critical temperature and that the discontinuity increases when the model on the surface varies from Ising to Heisenberg. This result could indicate that the exchange coupling on the surface of Gd is highly anisotropic.

Anisotropic Heisenberg ferromagnet on a semi-infinite lattice

The behavior of an anisotropic Heisenberg ferromagnet on a semi-infinite cubic lattice is studied within the context of the Green function formalism. The bulk is described by a pure Heisenberg model while on the surface an exchange anisotropy parameter permits to consider a sequence of models from pure Heisenberg to Ising. We show that in the limit where bulk and surface are both described by a pure Heisenberg model, there is no long range surface magnetic order over a paramagnetic bulk, whatever the values of the exchange couplings are. We relate our results with the Mermin-Wagner theorem.

The S=1 quantum spin chain with equal Heisenberg and biquadratic exchange in a magnetic field

The S=1 quantum spin chain with equal Heisenberg and biquadratic exchange was shown by Sutherland to be integrable. In this paper the equations obtained by Sutherland are solved numerically to obtain the behaviour at zero temperature in a magnetic field. It is found that there is an additional phase change at a lower field than the spin flop field. This new phase change marks the boundary between a regime in which the ground state contains only atoms with Sz=1, 0 and one in which 1, 0 and -1 are present. The form of the elementary excitations in the two regimes is discussed and the possibility of a similar phase change in the pure Heisenberg model is considered.

Analysis of the migdal transformation for models with Heisenberg spins on a d-dimensional lattice

We show for classical Heisenberg spins, with a general nearest neighbour interaction, that in the Migdal approximation the only low-temperature phase transitions are Ising ones (ferror antiferromagnetic). For d=2 neither the pure Heisenberg model nor the Lebwohl-Lasher model show a phase transition at a finite temperature. For d>2 transitions do exist at intermediate temperature and the complete flow diagram together with a two-parameter phase diagram is obtained numerically for d=3. Apart from critical temperatures and thermal exponents, also the magnetic exponents (for both Heisenberg and XY spins) are calculated. The latter are in very good agreement with exact results.