Three-dimensional Heisenberg Antiferromagnet Research Articles

Precise spin-wave model for one-, two-, and three-dimensional Heisenberg antiferromagnets inclusive of dipolar interactions

Precise spin-wave model for one-, two-, and three-dimensional Heisenberg antiferromagnets inclusive of dipolar interactions

Nonuniversal critical aging scaling in three-dimensional Heisenberg antiferromagnets

We numerically investigate the stationary and non-equilibrium critical dynamics in three-dimensional isotropic Heisenberg antiferromagnets. Since the non-conserved staggered magnetization couples dynamically to the conserved magnetization density, we employ a hybrid simulation algorithm that combines reversible spin precession with relaxational Kawasaki spin exchange processes. We measure the dynamic critical exponent and identify a suitable intermediate time window to obtain the aging scaling exponents. Our results support an earlier renormalization group prediction: While the critical aging collapse exponent assumes a universal value, the associated temporal decay exponent in the two-time spin autocorrelation function depends on the initial distribution of the conserved fields; here, specifically on the width of the initial spin orientation distribution.

Phase transition induced by an external field in a three-dimensional isotropic Heisenberg antiferromagnet

The critical frontier of the isotropic antiferromagnetic Heisenberg model in a magnetic field along the z-axis has been studied by mean-field and effective-field renormalization group calculations. These methods, abbreviated as MFRG and EFRG, are based on the comparison of two clusters of different sizes, each of them trying to mimic a specific Bravais lattice. The frontier line in the plane of temperature versus magnetic field was obtained for the simple cubic and the body-centered cubic lattices. Spin clusters with sizes N = 1, 2, 4 were used so as to implement MFRG-12, EFRG-12 and EFRG-24 numerical equations. For the simple cubic lattice, the MFRG frontier exhibits a notorious re-entrant behavior. This problem is improved by the EFRG technique. However, both methods agree at lower fields. For the body-centered cubic lattice, the MFRG method did not work. As in the cubic lattice, all the EFRG results agree at lower fields. Nevertheless, the EFRG-12 approach gave no solution for very low temperatures. Comparisons with other methods have been discussed.

Signatures of a gearwheel quantum spin liquid in a spin- 12 pyrochlore molybdate Heisenberg antiferromagnet

We theoretically investigate the low-temperature phase of the recently synthesized Lu$_2$Mo$_2$O$_5$N$_2$ material, an extraordinarily rare realization of a $S=1/2$ three-dimensional pyrochlore Heisenberg antiferromagnet in which Mo$^{5+}$ are the $S=1/2$ magnetic species. Despite a Curie-Weiss temperature ($\Theta_{\rm CW}$) of $-121(1)$ K, experiments have found no signature of magnetic ordering $or$ spin freezing down to $T^*\approx0.5$ K. Using density functional theory, we find that the compound is well described by a Heisenberg model with exchange parameters up to third nearest neighbors. The analysis of this model via the pseudofermion functional renormalization group method reveals paramagnetic behavior down to a temperature of at least $T=|\Theta_{\rm CW}|/100$, in agreement with the experimental findings hinting at a possible three-dimensional quantum spin liquid. The spin susceptibility profile in reciprocal space shows momentum-dependent features forming a "gearwheel" pattern, characterizing what may be viewed as a molten version of a chiral noncoplanar incommensurate spiral order under the action of quantum fluctuations. Our calculated reciprocal space susceptibility maps provide benchmarks for future neutron scattering experiments on single crystals of Lu$_2$Mo$_2$O$_5$N$_2$.

Coexistence of localized and collective magnetism in the coupled-spin-tetrahedra systemCu4Te5O12Cl4

We report high-field magnetization, electron spin resonance (ESR), and Raman scattering measurements of the coupled spin-tetrahedra system ${\mathrm{Cu}}_{4}{\mathrm{Te}}_{5}{\mathrm{O}}_{12}{\mathrm{Cl}}_{4}$ with magnetic ordering at ${T}_{N}=13.6$ K. We find thermodynamic and spectroscopic signatures for the concomitant occurrence of localized and collective magnetism. Magnetization measurements up to 60 T exhibit a spin-flop transition at ${\ensuremath{\mu}}_{0}{H}_{\mathrm{SF}}=16$ T only for $H\ensuremath{\parallel}c$ as well as periodic magnetization steps at ${\ensuremath{\mu}}_{0}H=16.5,\phantom{\rule{0.28em}{0ex}}24.8,\phantom{\rule{0.28em}{0ex}}33.8,\phantom{\rule{0.28em}{0ex}}42.3,\phantom{\rule{0.16em}{0ex}}\text{and}\phantom{\rule{0.16em}{0ex}}49.7$ T, which are independent of the crystallographic orientations. For $T>{T}_{N}$, the temperature dependence of ESR linewidth is described by a critical power law, $\ensuremath{\Delta}{B}_{pp}(T)\ensuremath{\propto}{(T\ensuremath{-}{T}_{N})}^{\ensuremath{-}0.56\ifmmode\pm\else\textpm\fi{}0.02}$. For $T<{T}_{N}$, an antiferromagnetic resonance mode is observed for $H\ensuremath{\parallel}c$, and its linewidth is given by $\ensuremath{\Delta}{B}_{pp}(T)\ensuremath{\propto}{T}^{3.13\ifmmode\pm\else\textpm\fi{}0.04}$, being close to ${T}^{4}$ expected for a classical magnet. Raman spectra show three one-magnon-like excitations superimposed on a broad two-magnon continuum. While the two higher frequency modes show an intensity variation in accordance to a three-dimensional Heisenberg antiferromagnet, the lower frequency mode clearly deviates. These results suggest that ${\mathrm{Cu}}_{4}{\mathrm{Te}}_{5}{\mathrm{O}}_{12}{\mathrm{Cl}}_{4}$ is a unique material which shows a dual character of zero-dimensional, localized and three-dimensional, collective magnetic behaviors.

High-resolution Monte Carlo study of the multicritical point in the three-dimensional XXZ Heisenberg antiferromagnet.

We use Monte Carlo simulations to study the XXZ Heisenberg antiferromagnet in a field in order to clearly determine the nature of the multicritical point. We use a hybrid sampling method with Metropolis and Wolff-cluster algorithms, along with histogram reweighting techniques. Staggered magnetization susceptibilities, Binder cumulants, and finite-size scaling are considered in an effort to detect a possible biconical phase. An analysis of the probability distribution of the magnetization allowed us to conclude that the multicritical point is bicritical and it is in the three-dimensional Heisenberg universality class.

Critical phenomena at the antiferromagnetic phase transition of azurite

We report on high-resolution acoustic, specific-heat and thermal expansion measurements in the vicinity of the antiferromagnetic phase transition at T_N = 1.88 K on a high-quality single crystal of the natural mineral azurite. A detailed investigation of the critical contribution to the various quantities at T_N is presented. The set of critical exponents and amplitude ratios of the singular contributions above and below the transition indicate that the system can be reasonably well described by a three-dimensional Heisenberg antiferromagnet.

Excitations and spin correlations near the interface of two three-dimensional Heisenberg antiferromagnets

Magnetic excitations and spin correlations near the interface of two spin-12 Heisenberg antiferromagnets are considered using the spin-wave approximation. When the interaction between boundary spins differs essentially from exchange constants inside the antiferromagnets, quasi-two-dimensional spin waves appear in the near-boundary region. They eject bulk magnons from this region, thereby dividing the antiferromagnets into areas with different magnetic excitations. The decreased dimensionality of the near-boundary modes leads to amplified nearest-neighbor spin correlations in the interface area.

Spin correlations near the surface of a three-dimensional Heisenberg antiferromagnet

Nearest-neighbor spin correlations are considered near the surface of a semi-infinite spin- 1 2 Heisenberg antiferromagnet on a simple cubic lattice. In the spin-wave approximation, the excitation spectrum of this model involves bulk modes – standing spin waves and a quasi-two-dimensional mode of surface spin waves. These latter excitations eject the bulk excitations from the surface region thus dividing the antiferromagnet into two parts with different excitations. As a result absolute values of the spin correlations near the surface exceed the bulk value. In the surface region, the pattern of spin correlations resembles the comb structure recently obtained for the two-dimensional case.

The effect of magnetic field on the susceptibility maximum in the spatially anisotropic Heisenberg antiferromagnet

The effect of magnetic field h on the longitudinal susceptibility in a spin S = 1 / 2 exchange anisotropic three-dimensional Heisenberg antiferromagnet, is studied by the double-time Green’s function method within Tyablikov approximation. The calculation results indicated that the height χ ( T m ) and position T m of the maximum of the longitudinal susceptibility display different behaviors related to the magnetic fields and exchange anisotropic parameters. These behaviors are very different from that in the exchange anisotropic Heisenberg ferromagnet in the magnetic field. The results are: (1) When the field h is weak, in a antiferromagnet, the height χ ( T m ) is a constant χ 0 which is independent of field and exchange anisotropy, but the position T m is only a function of the exchange anisotropy. While in a ferromagnet, both χ ( T m ) and T m are a function of field and the exchange anisotropy. (2) When the field h is strong, in a antiferromagnet, χ ( T m ) becomes dependent of field and the exchange anisotropy, and χ ( T m ) and T m are fitted satisfactory to power laws: χ ( T m ) − χ 0 ∝ h d and T N − T m ∝ h c , respectively. Here T N is the Neel temperature. On the contrary, in a ferromagnet, χ ( T m ) and T m are fitted to power laws: χ ( T m ) ∝ h − d ′ and T m − T c ∝ h c ′ , where T c is the Curie temperature. The above results are very useful in studying the magnetic property of coordination polymers.

Static magnetic properties and magnetic phase diagram of Mn 1−xNi xCl 2·2H 2O

The magnetic properties of Mn 1− x Ni x Cl 2·2H 2O are examined by DC magnetization and susceptibility measurements on a wide range of compositions. The pure components are three-dimensional Heisenberg antiferromagnets, ordering at 6.7 K (MnCl 2·2H 2O) and at 7.2 5 K (NiCl 2·2H 2O). Each contains MC1 2MC1 2M… chemical (and structural) chains, with intrachain exchange ferromagnetic and antiferromagnetic in the Ni and Mn materials, respectively. Interchain exchange is predominantly antiferromagnetic in each. The Curie and Weiss constants, in χ M = C / ( T – θ ) fits to high temperature data, vary regularly with composition. C( x) is essentially linear, and θ ( x ) exhibits systematic curvature which is analyzed to show that unlike-ion exchange is antiferromagnetic and weaker than like-ion interactions. The form of the susceptibility evolves with composition: maxima in χ ( T ) broaden and shift to lower temperature with admixture of either component, but beyond about 20% minority component such maxima are absent, with upturns appearing instead. T c descends rapidly with admixture from either composition extreme, but varies only weakly between x = 0.30 and 0.70. Magnetization isotherms display a subtle composition dependence which suggests that the ordered state differs for intermediate compositions from those for the composition extremes. Although frustration in mixtures is likely, from competing (sign) intrachain interactions, it is not strong enough to yield magnetic irreversibilities or time dependences signaling a spin glass phase.

High-Energy Resolution Inelastic Neutron Scattering Experiment on Magnetic Fracton Dispersion in Near-Percolating Three-Dimensional Heisenberg Antiferromagnet, RbMn0.4Mg0.6F3

Magnetic fractons in the near-percolating three-dimensional (3D) Heisenberg antiferromagnet, RbMn 0.4 Mg 0.6 F 3 , were studied using inelastic neutron scattering with a high energy resolution (Δ E =17.5 µeV) and at low temperature ( T =1.5 K). It was demonstrated that the fractons follow the dispersion relation of q z ( q being the wave number). The observed exponent, z =2.5, was in good agreement with the fractal dimension of the 3D system ( D f =2.48), as predicted by theory.

Magnetic structures of the B and C type Cr(PO3)3metaphosphates

The B and C type Cr(PO3)3 metaphosphates were synthesised by ceramic methods with control of the Cr/P ratio in the reaction medium. Neutron powder diffraction experiments and heat-capacity measurements were carried out on polycrystalline samples. The C-type [Cr(PO3)3] compound is ordered as a three-dimensional Heisenberg antiferromagnet with a J/k value of 0.3 K whereas the B-type [Cr2P6O18] phase shows that the magnetic susceptibility depends strongly on the magnetic field at temperatures less than 4 K suggesting the presence of some ferromagnetic contributions in the ordered state. The heat-capacity measurements of C-type Cr(PO3)3 exhibit a three-dimensional magnetic ordering (λ-type) peak at 4.2 K. The absence of an appreciable anomaly in the magnetic heat capacity obtained above TN suggests a small short-range order in this Cr(PO3)3 metaphosphate. The magnetic structures of both compounds are consistent with the existence of predominant antiferromagnetic superexchange interactions via |PO4| tetrahedra between the Cr(III) ions. In the C-type phase, the magnetic moments arranged in (100) ferromagnetic layers are antiparallel with those of the neighbouring layers stabilising an antiferromagnetic structure. The magnetic moments lie in the xz plane pointing 13° out of the x axis. In the B-type phase, the presence of a weak ferromagnetic component is observed. Magnetostructural correlations in both chromium compounds indicate that only super-superexchange interactions via one or two phosphate groups are present. The [Cr–O–P and O–P–O] angles of the magnetic exchange pathways show typical values of antiferromagnetic couplings. The competition between different magnetic interactions in Cr(PO3)3 through super-superexchange pathways is not strong enough to cause magnetic frustration as observed in other metaphosphates.

Magnetic properties of M(PO3)3(M = Fe, Mo). A comparative neutron diffraction study

The isostructural M(PO3)3 (M = Fe, Mo) metaphosphates were synthesised by ceramic methods with control of the M/P ratio in the reaction medium. Neutron powder diffraction experiments, heat capacity measurements and Mossbauer spectrometry were carried out on polycrystalline samples. Both compounds are ordered as three-dimensional Heisenberg antiferromagnets with J/k values of ca. 0.3 K. The magnetic susceptibility in the Fe(PO3)3 phase depends strongly on the magnetic field at temperatures less than 10 K suggesting the presence of some ferromagnetic contributions in the ordered state whereas in the Mo(PO3)3 metaphosphate field dependence of the magnetic susceptibility even at 10 mT was not detected. The heat-capacity measurements exhibit three-dimensional magnetic ordering (λ-type) peaks at 4 and 7.8 K for the molybdenum and iron phases respectively. The measurements above TN suggest the presence of a small short-range order in both phases. However, it is worth mentioning that Fe(PO3)3 shows the presence of a significant magnetic anomaly below the ordering temperature. The Mossbauer measurements in the iron metaphosphate indicate the presence of three different high-spin Fe(III) ions in the structure. The magnetic structures of both compounds are consistent with the existence of predominant antiferromagnetic superexchange interactions via |PO4| tetrahedra between the metal(III) ions. The magnetic moments are arranged in (100) and (001) ferromagnetic layers for the molybdenum and iron metaphosphate respectively. The neighbouring layers are disposed antiparallel cancelling their components and stabilising the antiferromagnetic structure in both compounds. Magnetostructural correlations indicate that only super-superexchange interactions via one or two phosphate groups are present in both Fe and Mo compounds. The values of the magnetic exchange pathways [M–O–P and O–P–O] are characteristic of antiferromagnetic couplings. Notwithstanding this, the existence of competition between different magnetic interactions through super-superexchange pathways can cause magnetic frustration giving rise to the presence of a weak ferromagnetic component in Fe(PO3)3.

Composition induced lowering of metamagnetic critical field and static magnetic properties of Co1-xNixCl2⋅2H2O

The magnetic behavior of ${\mathrm{Co}}_{1\ensuremath{-}x}{\mathrm{Ni}}_{x}{\mathrm{Cl}}_{2}\ensuremath{\cdot}{2\mathrm{H}}_{2}\mathrm{O}$ has been studied by dc magnetization and susceptibility measurements on mixtures spanning the entire composition range. The pure components are three-dimensional Ising (Co) and Heisenberg (Ni) antiferromagnets, ordering at 17.2 K and at 7.25 K (with a 6.31 K spin reorientation transition), respectively. Each contains ${\mathrm{MCl}}_{2}{\mathrm{MCl}}_{2}\mathrm{M}\dots{}$ chemical (and structural) chains, with ferromagnetic intrachain exchange and weaker but significant antiferromagnetic interchain exchange. Curie-Weiss fits, ${\ensuremath{\chi}}_{M}=C/(T\ensuremath{-}\ensuremath{\theta}),$ to high-temperature powder susceptibilities of mixtures yield Curie and Weiss constants that vary regularly with composition. C vs x is close to linear. The $\ensuremath{\theta}(x)$ dependence is less conventional, exhibiting only weak variation for small x, a marked increase between $x>~0.2$ and $x<~0.4,$ and a steady increase from $x>0.4$ to 1. In the susceptibilities of all mixtures below 20 K antiferromagnetic maxima appear. For Ni-rich mixtures only one maximum occurs, with ${T}_{\mathrm{max}}$ increasing weakly but uniformly from $x=1$ ${(7.4}_{7}\mathrm{K})$ to ${x=0.56}_{4}{(8.8}_{3}\mathrm{K}).$ A maximum in this region persists even down to ${x=0.27}_{2}$ ${(9.1}_{5}\mathrm{K});$ for ${x=0.21}_{0}$ only a shoulder in $\ensuremath{\chi}(T)$ near 9 K appears. For Co-rich mixtures a maximum near 18 K occurs, becoming merely incipient for $x\ensuremath{\sim}0.4;$ its location varies weakly between ${17.9}_{5}$ and ${18.2}_{5}\mathrm{K}.$ Transition temperatures, slightly lower than the associated ${T}_{\mathrm{max}},$ can often be estimated; these display a weak but regular composition dependence as well. Magnetization vs field isotherms evolve with composition. For high x the appearance of $M(H)$ is similar to that of ${\mathrm{NiCl}}_{2}\ensuremath{\cdot}{2\mathrm{H}}_{2}\mathrm{O}.$ For low x somewhat more curvature in $M(H)$ occurs than for ${\mathrm{CoCl}}_{2}\ensuremath{\cdot}{2\mathrm{H}}_{2}\mathrm{O},$ and there is a suggestion of qualitatively different behavior, though hysteresis effects are very small. Dramatically different properties are observed for ${x=0.27}_{2}$ and ${0.40}_{9},$ where field induced transitions in the 6 to 10 kG range occur for temperatures below 7 K. Major hysteretic effects, especially below 2 K, also appear. The overall behavior is reminiscent of metamagnets, and since the inferred transition fields are two or more times smaller than those previously determined for the pure components, this is a composition induced effect. A mean-field theory analysis of the temperature dependence of the hysteresis is made, suggesting that the ratio of interchain to intrachain exchange is somewhat larger in the ${x=0.27}_{2}$ and ${0.40}_{9}$ mixtures than in the pure components. The temperature dependence of the hysteresis loop area suggests the presence of an activation process with a characteristic temperature of the order of 1 K.

Néel temperature and sublattice magnetiztion of a three-dimensional classical and quantum Heisenberg antiferromagnet

The effective-field theory (EFT) of a two-spin cluster is applied to study the critical behavior of a three-dimensional classical and quantum Heisenberg antiferromagnet (AF). Néel temperature ( T N ) and sublattice magnetization are calculated numerically and compared with the results of these models with ferromagnetic (F) interaction. We find that our results, for the quantum model T N is higher than T c (Curie temperature, F case) but for the classical model T N = T c . The difference between F and AF results for the quantum model obtained here by EFT is in accordance with Monte Carlo simulation and high-temperature expansion.

Critical Temperature and the Transition from Quantum to Classical Order Parameter Fluctuations in the Three-Dimensional Heisenberg Antiferromagnet

We present results of extensive quantum Monte Carlo simulations of the three-dimensional (3D) S=1/2 Heisenberg antiferromagnet. Finite-size scaling of the spin stiffness and the sublattice magnetization gives the critical temperature Tc/J = 0.946 +/- 0.001. The critical behavior is consistent with the classical 3D Heisenberg universality class, as expected. We discuss the general nature of the transition from quantum mechanical to classical (thermal) order parameter fluctuations at a continuous Tc > 0 phase transition.

Critical behavior of the three-dimensional Heisenberg antiferromagnetRbMnF3

The magnetic critical scattering of the near-ideal three-dimensional Heisenberg antiferromagnet (AF) ${\mathrm{RbMnF}}_{3}$ has been remeasured using neutron scattering. The critical dynamics has been studied in detail in the temperature range ${0.77T}_{N}<T<{1.11T}_{N},$ where ${T}_{N}$ is the N\'eel temperature. In agreement with previous measurements, at ${T}_{N}$ and for wave vectors away from the AF zone center, the scattering has a quasielastic component in addition to the inelastic response predicted by renormalization-group and mode-coupling theories. Both components scale with the dynamic exponent $z=1.43\ifmmode\pm\else\textpm\fi{}0.04$, in agreement with dynamic scaling. On cooling below ${T}_{N}$ the inelastic peaks transform into the transverse spin waves and a crossover has been observed in the dispersion from a power-law relation ${\ensuremath{\omega}}_{q}{=Aq}^{z}$ at ${T}_{N}$ to a linear behavior ${\ensuremath{\omega}}_{q}=cq$ in the hydrodynamic region below ${T}_{N}.$ The quasielastic component evolves below ${T}_{N}$ into the longitudinal susceptibility identified in an earlier polarized neutron experiment. The intensity and energy width of the longitudinal scattering decrease on cooling below ${T}_{N}.$ Down to the lowest temperatures where the longitudinal susceptibility could be measured the leading term in the scaling behavior of the energy width was ${\ensuremath{\gamma}}_{q}\ensuremath{\approx}{q}^{1.58\ifmmode\pm\else\textpm\fi{}0.03}$ (hydrodynamic theory predicts a ${q}^{2}$ law). Possible explanations for the observed behavior of the longitudinal susceptibility are discussed.

Paramagnetic phase of the infinite-layer antiferromagnet Ca0.85Sr0.15CuO2as seen by Cu NMR

We report a nuclear magnetic resonance study of the Cu nuclei in the paramagnetic phase of Ca${}_{0.85}$Sr${}_{0.15}$CuO${}_{2}$. By measuring the temperature dependence of the magnetic and quadrupolar shift and of the spin-lattice relaxation rate, we have obtained the following major results. With decreasing temperature, Ca${}_{0.85}$Sr${}_{0.15}$CuO${}_{2}$ undergoes two successive crossovers: a dimensionality crossover from a two-dimensional to a three-dimensional (3D) Heisenberg antiferromagnet followed, very close to ${T}_{N},$ by a spin-degree crossover from a 3D Heisenberg to a 3D $\mathrm{XY}$ antiferromagnet. There is no evidence for any structural changes accompanying the magnetic phase transition. The values of the hyperfine coupling constants ${A}_{c},$ ${A}_{\mathrm{ab}},$ and $B$ have been determined.

Spin waves in the antiferromagnet perovskite LaMnO3: A neutron-scattering study.

As part of a general work on doped manganese perovskites, we have carried out detailed neutron-scattering experiments on powder and single crystals of the othorhombic phase of undoped LaMn${\mathrm{O}}_{3}$. The temperature dependence of the sublattice magnetization has been determined in the antiferromagnetic phase (${T}_{N}=139.5$ K), and the critical exponent is $\ensuremath{\beta}=0.28$, well below that corresponding to a pure three-dimensional Heisenberg antiferromagnet. We have measured the dispersion of the spin waves propagating in the highest symmetry directions solving the problems related to twinning. The whole spin wave spectrum is well accounted for with a Heisenberg Hamiltonian and a single ion anisotropy term responsible for the easy magnetization direction (b axis). This term induces a gap of 2.7 meV at low temperature in the spin wave dispersion curve. An important result is that the ferromagnetic exchange integral (${J}_{1}\ensuremath{\approx}0.83$ meV), coupling the spins within the ferromagnetic basal plane (a,b), is larger by a factor 1.4 than the antiferromagnetic exchange integral (${J}_{2}\ensuremath{\approx}\ensuremath{-}0.58$ meV) coupling spins belonging to adjacent Mn${\mathrm{O}}_{2}$ planes along c.