Pyrochlore Antiferromagnet Research Articles

Cooperative Paramagnetism in the Geometrically Frustrated Pyrochlore AntiferromagnetTb2Ti2O7

Neutron scattering, muon spin relaxation, and dc susceptibility studies have been carried out on polycrystalline ${\mathrm{Tb}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$, a pyrochlore antiferromagnet in which the ${\mathrm{Tb}}^{3+}$ moments reside on a network of corner-sharing tetrahedra. Unlike other geometrically frustrated systems, ${\mathrm{Tb}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ remains paramagnetic down to $\ensuremath{\sim}0.07\mathrm{K}$, rather than ordering into a conventional N\'eel or spin-glass-like state, despite the fact that short-range antiferromagnetic correlations (AFC) develop at $\ensuremath{\sim}50\mathrm{K}$. At the first AFC wave vector, its low-lying, relatively flat magnetic excitation spectrum softens partially below 30 K.

Low-temperature properties of classical geometrically frustrated antiferromagnets

We study the ground-state and low-energy properties of classical vector spin models with nearest-neighbour antiferromagnetic interactions on a class of geometrically frustrated lattices which includes the kagome and pyrochlore lattices. We explore the behaviour of these magnets that results from their large ground-state degeneracies, emphasising universal features and systematic differences between individual models. We investigate the circumstances under which thermal fluctuations select a particular subset of the ground states, and find that this happens only for the models with the smallest ground-state degeneracies. For the pyrochlore magnets, we give an explicit construction of all ground states, and show that they are not separated by internal energy barriers. We study the precessional spin dynamics of the Heisenberg pyrochlore antiferromagnet. There is no freezing transition or selection of preferred states. Instead, the relaxation time at low temperature, T, is of order hbar/(k_B T). We argue that this behaviour can also be expected in some other systems, including the Heisenberg model for the compound SrCr_8Ga_4O_{19}.

Single crystal growth by the floating-zone method of a geometrically frustrated pyrochlore antiferromagnet, Tb 2Ti 2O 7

Large, high quality, single crystals of Tb 2Ti 2O 7, have been successfully grown by the floating zone method under a controlled atmosphere. Crystals, approximately 3–5 mm in diameter and up to 20 mm in length, were grown from a small seed crystal. Several crystals have been characterised to determine their crystal quality, chemical structure and magnetic properties and these results were compared to those of sintered polycrystalline pellets. These materials were shown to have the face centred cubic structure, Fd–3m, with a room temperature lattice parameter a=10.12(7) Å, when grown in oxygen, and a=10.13(6) Å, when grown in argon. They are currently of interest as they are comprised of antiferromagnetically coupled magnetic moments residing on a network of corner-sharing tetrahedra, a system known to display the effects of geometrical frustration. Magnetic susceptibility measurements, with the applied field parallel to the growth direction were performed on both crystals. Both single crystal and polycrystalline samples showed very similar Curie-Weiss like behaviour down to 5 K, with Curie–Weiss temperatures, θ cw of approximately −19 K.

Pyrochlore Antiferromagnet: A Three-Dimensional Quantum Spin Liquid

The quantum pyrochlore antiferromagnet is studied by perturbative expansions and exact diagonalization of small clusters. We find that the ground state is a spin-liquid state: The spin-spin correlation functions decay exponentially with distance and the correlation length never exceeds the interatomic distance. The calculated magnetic neutron diffraction cross section is in very good agreement with experiments performed on $\mathrm{Y}(\mathrm{Sc}){\mathrm{Mn}}_{2}$. The low energy excitations are singlet-singlet ones, with a finite spin gap.

Neutron scattering studies of geometrically frustrated pyrochlore antiferromagnets

Elastic and inelastic neutron scattering work on the cubic pyrochlore antiferromagnets Y 2Mo 2O 7, Tb 2Ti 2O 7, and Tb 2Mo 2O 7 is reviewed. These materials are characterized by antiferromagnetically coupled moments residing on a network of corner-sharing tetrahedra. Geometrical frustration manifests itself strongly in such systems in that two of them display a spin-glass-like transition in the apparent absence of chemical disorder, while the other remains paramagnetic to at least 0.1 K, despite developing antiferromagnetic short-range order at 50 K.

Short-range magnetic order in the frustrated pyrochlore antiferromagnetCsNiCrF6

In the pyrochlore antiferromagnets, the magnetic ions are situated at the vertices of a framework of corner-sharing tetrahedra. The result is intense geometrical frustration of the magnetic interactions. We present the results of a single-crystal neutron-diffraction study of the pyrochlore ${\mathrm{CsNiCrF}}_{6}$ to investigate the development of magnetic order at low temperatures. We find that even at a temperature of 2 K (which is below the apparent spin-glass transition), the order does not extend further than two nearest neighbors, in spite of the strong antiferromagnetic interactions between spins. We also present the results of Monte Carlo calculations of the magnetic scattering utilizing a simple model Hamiltonian, and find good qualitative agreement with the experimental data.

Order by disorder in the pyrochlore antiferromagnets

We calculate the spin wave energies of the Heisenberg antiferromagnet in the Pyrochlore structure for several Néel states, which are degenerate for classical spins. In the harmonic approximation we show that the degeneracy is partially lifted leading to the stabilization of collinear structures.

Static Critical Behavior of the Spin-Freezing Transition in the Geometrically Frustrated Pyrochlore AntiferromagnetY2Mo2O7

Some frustrated pyrochlore antiferromagnets, such as ${\mathrm{Y}}_{2}$M${\mathrm{o}}_{2}$${\mathrm{O}}_{7}$, show a spin-freezing transition and magnetic irreversibilities below a temperature ${T}_{f}$ similar to what is observed in randomly frustrated spin-glasses. We present results of nonlinear dc magnetization measurements on ${\mathrm{Y}}_{2}$M${\mathrm{o}}_{2}$${\mathrm{O}}_{7}$ that provide strong evidence that there is an underlying thermodynamic phase transition at ${T}_{f}$, which is characterized by critical exponents $\ensuremath{\gamma}\ensuremath{\approx}2.8$ and $\ensuremath{\beta}\ensuremath{\approx}0.8$. These values are typical of those found in random spin-glasses, despite the fact that the level of random disorder in ${\mathrm{Y}}_{2}$M${\mathrm{o}}_{2}$${\mathrm{O}}_{7}$ is immeasurably small.

Muon spin relaxation investigation of frustrated antiferromagnetic pyrochlores A 2 B 2 O 7

In a system where magnetic ions occupy the vertices of edge or corner sharing triangular units, the natural antiferromagnetic coupling between ions is geometrically frustrated. A wide variety of interesting magnetic behaviour has been observed in pyrochlores, where magnetic ions form a network of corner sharing tetrahedra. The low temperature spin dynamics of a number of pyrochlores A2B2O7 have been investigated using the technique of μ SR. For example, Y2Mo2O7 shows a transition to a disordered magnetic state similar to a spin glass at TF=22 K. However, unlike conventional metallic spin glasses, a non‐zero muon spin depolarization rate is observed to persist well below 0.1\ TF. These results suggest that there is a finite density of states for magnetic excitations in this system near zero energy.

Muon spin relaxation investigation of the spin dynamics of geometrically frustrated antiferromagnets Y2Mo2O7 and Tb2Mo2O7.

The spin dynamics of geometrically frustrated pyrochlore antiferromagnets ${\mathrm{Y}}_{2}$${\mathrm{Mo}}_{2}$${\mathrm{O}}_{7}$ and ${\mathrm{Tb}}_{2}$${\mathrm{Mo}}_{2}$${\mathrm{O}}_{7}$ have been investigated using muon spin relaxation. A dramatic slowing down of the moment fluctuations occurs as one approaches the spin freezing temperatures (${\mathit{T}}_{\mathit{F}}$=22 and 25 K, respectively) from above. Below ${\mathit{T}}_{\mathit{F}}$ there is a disordered magnetic state similar to that found in a spin glass but with a residual muon spin relaxation rate at low temperatures. These results show that there is a large density of states for magnetic excitations in these systems near zero energy. \textcopyright{} 1996 The American Physical Society.

Low temperature spin dynamics of geometrically frustrated antiferromagnets Y2Mo2O7 and Y2Mo1.6Ti0.4O7 studied by muon spin relaxation

The spin dynamics of geometrically frustrated pyrochlore antiferromagnets Y2Mo2O7 and Y2Mo1.6Ti0.4O7 have been investigated using muon spin relaxation. In Y2Mo2O7 a dramatic slowing down of the Mo4+ spin fluctuations occurs as one approaches the spin freezing temperature TF of 22 K from above. At lower temperatures the spins freeze into a disordered magnetic state similar to that found in a spin glass but with a small residual muon spin relaxation rate at low temperatures. This residual relaxation rate is larger in Y2Mo1.6Ti0.4O7 where TF=15 K. These results suggest that there is a nonzero density of states for magnetic excitations in these systems near zero energy.

Magnetic excitations in a highly frustrated pyrochlore antiferromagnet.

Spins that are coupled antiferromagnetically on the pyrochlore lattice are exposed to a high degree of geometrical frustration, resulting in the general absence of long-range order at all temperatures. We have investigated the inelastic response of the pyrochlore ${\mathrm{CsNiCrF}}_{6}$ using neutron scattering. At positions where strong magnetic diffuse scattering has been observed we find a strong elastic signal, together with an unusual wing of inelastic scattering that is present even below the spin-glass transition of ${\mathrm{CsNiCrF}}_{6}$. This indicates that while some of the magnetic fluctuations are being frozen out, others persist on a scale well in excess of the apparent spin-freezing temperature.

A single crystal neutron scattering study of a highly frustrated pyrochlore

The antiferromagnetic pyrochlore structure contains a high degree of geometrical frustration. We present the results of single crystal neutron scattering experiments on the pyrochlore CsNiCrF6, and show that the elastic and inelastic scattering we observe is characteristic of magnetic order occurring only on an extremely short length scale.

Geometrically-frustrated magnetism on triangular and tetrahedral lattices

The combination of simple, nearest neighbor antiferromagnetic interactions and certain lattice symmetries leads to phenomena known broadly as frustration. In such systems, the formation of a collinear magnetic structure cannot occur at low temperature. The material may undergo a phase transition to an unusual magneticallyordered state, or it may not undergo a conventional transition at all-entering a glass-like state as the temperature is lowered. This paper will review recent work, mostly from neutron scattering studies, on three such magnetic materials. CsMnBr3 and CsCoBr3 are XY-like and Ising-like stacked-triangular lattice antiferromagnets, respectively. Both undergo magnetic phase transitions with interesting properties due to the presence of geometricalfrustration within the triangular layers. TD2Mo2O7 is a pyrochlore antiferromagnet, in which the magnetic moments reside on a network of corner-sharing tetrahedra. This material enters a magnetic glass-like state at low temperature.

Magnetic structure of the spin-liquid state in a frustrated pyrochlore.

The antiferromagnetic pyrochlores exhibit a high degree of frustration, resulting in a continuously disordered ground state. Neutron powder diffraction experiments have detected magnetic scattering similar in form to a liquid structure factor. We present a single crystal neutron scattering study of the pyrochlore ${\mathrm{CsNiCrF}}_{6}$ and quantify the anisotropy of the scattering. Using these data, we show that there are strong correlations between nearest-neighbor spins, and no significant longer correlations. This provides clear evidence for the liquidlike nature of the pyrochlore magnetic structure.

Comment on "Critical properties of highly frustrated pyrochlore antiferromagnets"

We argue that the analysis of Reimers et al. [Phys. Rev. B 45, 7295 (1992)] of their Monte Carlo data on the Heisenberg pyrochlore antiferromagnet, which suggests a new universality class, is not conclusive. By reanalysis of their data, we demonstrate asymptotic volume dependence in some thermodynamic quantities, which suggests the possibility that the transition may be first order.

Critical properties of highly frustrated pyrochlore antiferromagnets.

The pyrochlore form of ${\mathrm{FeF}}_{3}$ (pyr-${\mathrm{FeF}}_{3}$) exhibits an unusual noncoplanar form of long-range magnetic order below 16 K. This is a result of the topological frustration inherent in the lattice of corner-sharing tetrahedra formed by the iron atoms. Neutron-diffraction experiments fix the critical exponent \ensuremath{\beta} at 0.18(2), which does not correspond to any known universality class. Monte Carlo simulations on the same lattice with Heisenberg spins confirm this value of \ensuremath{\beta} and also determine that \ensuremath{\nu}=0.38(2), \ensuremath{\gamma}=1.1(1), and \ensuremath{\alpha}=0.6(1). The power of Ferrenberg and Swendsen's histogram method of Monte Carlo data analysis is discussed, as well as careful checks for weak first-order behavior in the transition. The recently discovered universality classes in triangular-lattice antiferromagnets are compared to the situation in pyr-${\mathrm{FeF}}_{3}$.