Temperature‐dependent Raman scattering studies of the geometrically frustrated pyrochlores Dy2Ti2O7, Gd2Ti2O7 and Er2Ti2O7

The temperature‐dependent Raman studies of A₂Ti₂O₇(A = Dy, Er, Gd) were performed on single crystals and polycrystalline samples in the 4.2–295 K temperature range. The Raman spectra showed softening of the majority of phonon modes upon cooling in the whole temperature range studied and large decrease of linewidths. These changes have been analyzed in terms of strong third‐order phonon–phonon anharmonic interactions. Moreover, the 312 and 330 cm⁻¹ modes of Er₂Ti₂O₇(Gd₂Ti₂O₇) showed hardening upon cooling down to about 130 K (100 K) and then anomalous softening below this temperature. The observed anomalous behavior of the Raman modes indicates that some important changes occur in these materials at low temperatures. However, the origin of this behavior is still not clear. Copyright © 2008 John Wiley & Sons, Ltd.     

Statics and dynamics of incommensurate spin order in a geometrically frustrated antiferromagnet CdCr2O4

Using elastic and inelastic neutron scattering we show that a cubic spinel, CdCr2O4, undergoes an elongation along the c axis (c > a = b) at its spin-Peierls-like phase transition at T(N) = 7.8 K. The Néel phase (T < T(N)) has an incommensurate spin structure with a characteristic wave vector Q(M) = (0, delta,1) with delta approximately 0.09 and with spins lying on the ac plane. This is in stark contrast to another well-known Cr-based spinel, ZnCr2O4, that undergoes a c-axis contraction and a commensurate spin order. The magnetic excitation of the incommensurate Néel state has a weak anisotropy gap of 0.6 meV and it consists of at least three bands extending up to 5 meV.     

Spin dynamics of geometrically frustrated spin systems observed by muon spin relaxation

μSR is shown to be a sensitive probe of fluctuating internal magnetic fields in geometrically frustrated magnets. The usefulness of μSR in these systems is illustrated in the case of pyrochlores, in which the antiferromagnetically coupled ions occupy a lattice of corner sharing tetrahedra. Remarkably, one observes a type of spin freezing in Y₂Mo₂O₇ and Tb₂Mo₂O₇ which is similar to that seen in conventional spin glasses, even though there is no detectable structural disorder. Unlike ordinary spin glasses these geometrically frustrated antiferromagnets display unusual low temperature spin dynamics which persist down to the lowest accessible temperatures.     

Low temperature spin dynamics of the geometrically frustrated antiferromagnetic garnet Gd3Ga5O12

The low temperature spin dynamics of the geometrically frustrated antiferromagnet Gd 3Ga 5O (12) (GGG) have been investigated using muon spin relaxation. No evidence for static order is seen down to a temperature of 25 mK or a few percent of the Curie-Weiss temperature. Instead there is a linear decrease in the Gd spin fluctuation rate below 1 K which extrapolates to a small but finite value of 2 GHz at zero temperature. In terms of the spin fluctuations the system appears essentially to remain dynamic at low temperatures (T>0.02 K) and magnetic fields up to 1.8 T.     

Local spin resonance and spin-peierls-like phase transition in a geometrically frustrated antiferromagnet

Inelastic magnetic neutron scattering reveals a localized spin resonance at 4.5 meV in the ordered phase of the geometrically frustrated cubic antiferromagnet ZnCr2O4. The resonance develops abruptly from quantum critical fluctuations upon cooling through a first order transition to a co-planar antiferromagnet at T(c) = 12. 5(5) K. We argue that this transition is a three dimensional analog of the spin-Peierls transition.     

Molecular spin resonance in the geometrically frustrated magnet MgCr2O4 by inelastic neutron scattering

We measured two magnetic modes with finite and discrete energies in an antiferromagnetic ordered phase of a geometrically frustrated magnet MgCr2O4 by single-crystal inelastic neutron scattering, and clarified the spatial spin correlations of the two levels: one is an antiferromagnetic hexamer and the other is an antiferromagnetic heptamer. Since these correlation types are emblematic of quasielastic scattering with geometric frustration, our results indicate instantaneous suppression of lattice distortion in an ordered phase by spin-lattice coupling, probably also supported by orbital and charge. The common features in the two levels, intermolecular independence and discreteness of energy, suggest that the spin molecules are interpreted as quasiparticles (elementary excitations with energy quantum) of highly frustrated spins, in analogy with the Fermi liquid approximation.     

Microscopic study of a pressure-induced ferromagnetic-spin-glass transition in the geometrically frustrated pyrochlore (Tb1-xLax)2Mo2O7

We have studied (Tb1-xLax)2Mo2O7 pyrochlores by neutron diffraction and muSR at ambient and under applied pressure. (Tb,La) substitution expands the lattice and induces a change from a spin-glass-like state (x=0) to a noncollinear ferromagnet (x=0.2). In the ferromagnetic structure, the Tb moments orient close to their local anisotropy axes as for an ordered spin ice, while the Mo ones orient close to the net moment. The temperature dependence of the muSR relaxation rates and static local fields suggests a second transition of dynamical nature below the Curie transition. Under pressure, the long range order breaks down and a spin-glass-like state is recovered. The whole set of data provides a microscopic picture of the spin correlations and fluctuations in the region of the ferromagnetic-spin-glass threshold.     

Dy2Ti2O7 spin ice: a test case for emergent clusters in a frustrated magnet

Dy2Ti2O7 is a geometrically frustrated magnetic material with a strongly correlated spin ice regime that extends from 1 K down to as low as 60 mK. The diffuse elastic neutron scattering intensities in the spin ice regime can be remarkably well described by a phenomenological model of weakly interacting hexagonal spin clusters, as invoked in other geometrically frustrated magnets. We present a highly refined microscopic theory of Dy2Ti2O7 that includes long-range dipolar and exchange interactions to third nearest neighbors and which demonstrates that the clusters are purely fictitious in this material. The seeming emergence of composite spin clusters and their associated scattering pattern is instead an indicator of fine-tuning of ancillary correlations within a strongly correlated state.     

Competing spin phases in geometrically frustrated magnetic molecules

We identify a class of zero-dimensional classical and quantum Heisenberg spin systems exhibiting anomalous behavior in an external magnetic field B similar to that found for the geometrically frustrated kagome lattice of classical spins. Our calculations for the isotropic Heisenberg model show the emergence of a pronounced minimum in the differential susceptibility dM/dB at B(sat)/3 as the temperature T is raised from 0 K for structures based on corner-sharing triangles, specifically the octahedron, cuboctahedron, and icosidodecahedron. As the first experimental evidence we note that the giant Keplerate magnetic molecule {Mo(72)Fe(30)} (Fe(3+) ions on the 30 vertices of an icosidodecahedron) exhibits this behavior. For low T when B approximately B(sat)/3 two competing families of spin configurations exist of which one behaves magnetically "stiff" leading to a reduction of dM/dB.     

Multiple field-induced phase transitions in the geometrically frustrated dipolar magnet: Gd(2) Ti(2)O(7)

Field-driven phase transitions generally arise from competition between Zeeman energy and exchange or crystal-field anisotropy. Here we present the phase diagram of a frustrated pyrochlore magnet Gd(2)Ti(2)O(7), where crystal-field splitting is small compared to the dipolar energy. We find good agreement between zero-temperature critical fields and those obtained from a mean-field model. Here, dipolar interactions couple real space and spin space, so the transitions in Gd(2)Ti(2)O(7) arise from field-induced "cooperative anisotropy," reflecting the broken spatial symmetries of the pyrochlore lattice.     

Absence of magnetic order in Yb3Ga5O12: relation between phase transition and entropy in geometrically frustrated materials

From muon spin relaxation spectroscopy experiments, we show that the sharp peak (lambda-type anomaly) detected by specific heat measurements at 54 mK for the ytterbium gallium garnet compound, Yb3Ga5O12, does not correspond to the onset of a magnetic phase transition, but to a pronounced building up of dynamical magnetic pair correlations. Beside the lambda anomaly, a broad hump is observed at higher temperature in the specific heat of this garnet and other geometrically frustrated compounds. Comparing with other frustrated magnetic systems we infer that a ground state with long-range order is reached only when at least 1/4-1/3 of the magnetic entropy is released at the lambda transition.     

Magnetic-field induced transition to the 1/2 magnetization plateau state in the geometrically frustrated magnet CdCr2O4

The magnetization of the geometrically frustrated spinel CdCr2O4 was measured in pulsed fields of up to 47 T. We found a metamagnetic transition to a very wide magnetization plateau state with one half of the full moment of S=3/2 Cr3+ at 28 T, independent of the field direction. This is the first observation of magnetization plateau state realized in Heisenberg pyrochlore magnet. The plateau state can be ascribed to a collinear spin configuration with three-up and one-down spins out of four spins of each Cr tetrahedron. A large magnetostriction is observed at the transition in spite of the negligible spin-orbit couplings. We argue that spin frustration plays a vital role in this large spin-lattice coupling.     

Low energy spin dynamics in the spin ice Ho2Sn2O7

The magnetic properties of Ho(2)Sn(2)O(7) have been investigated and compared to other spin ice compounds. Although the lattice has expanded by 3% relative to the better studied Ho(2)Ti(2)O(7) spin ice, no significant changes were observed in the high temperature properties, T is more or approximately equal to 20 K. As the temperature is lowered and correlations develop, Ho(2)Sn(2)O(7) enters its quantum phase at a slightly higher temperature than Ho(2)Ti(2)O(7) and is more antiferromagnetic in character. Below 80 K a weak inelastic mode associated with the holmium nuclear spin system has been measured. The hyperfine field at the holmium nucleus was found to be ≈700 T.     

Muon spin relaxation investigation of frustrated antiferromagnetic pyrochlores A2B2O7

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 T_F=22 K. However, unlike conventional metallic spin glasses, a non‐zero muon spin depolarization rate is observed to persist well below 0.1\ T_F. These results suggest that there is a finite density of states for magnetic excitations in this system near zero energy. This revised version was published online in July 2006 with corrections to the Cover Date.     

Competing ferri- and antiferromagnetic phases in geometrically frustrated LuFe2O4

We present a detailed study of magnetism in LuFe(2)O(4), combining magnetization measurements with neutron and soft x-ray diffraction. The magnetic phase diagram in the vicinity of T(N) involves a metamagnetic transition separating an antiferro- and a ferrimagnetic phase. For both phases the spin structure is refined by neutron diffraction. Observed diffuse magnetic scattering far above T(N) is explained in terms of near degeneracy of the magnetic phases.     

Spin dynamics and magnetic order in magnetically frustrated Tb2Sn2O7

We report a study of the geometrically frustrated magnetic material Tb2Sn2O7 by the positive muon-spin relaxation technique. No signature of a static magnetically ordered state is detected while neutron magnetic reflections are observed in agreement with a published report. This is explained by the dynamical nature of the ground state of Tb2Sn2O7: the Tb3+ magnetic moment characteristic fluctuation time is approximately 10(-10) s. The strong effect of the magnetic field on the muon-spin-lattice relaxation rate at low fields indicates a large field-induced increase of the magnetic density of states of the collective excitations at low energy.     

Observation of a liquid-gas-type transition in the pyrochlore spin ice compound Dy2Ti2O7 in a magnetic field

Low temperature magnetization measurements on the pyrochlore spin ice compound Dy2Ti2O7 reveal that the ice-rule breaking spin flip, appearing at H approximately 0.9 T applied parallel to the [111] direction, turns into a novel first-order transition for T<0.36 K which is most probably of a liquid-gas type. T-linear variation of the critical field observed down to 0.03 K suggests the unusual situation that the entropy release across the transition remains finite [approximately 0.5 (J/K) x mol-Dy] as T-->0, in accordance with a breaking of the macroscopic degeneracy in the intermediate "kagomé ice" state.     

Spin waves and quantum criticality in the frustrated XY pyrochlore antiferromagnet Er2Ti2O7

We report detailed measurements of the low temperature magnetic phase diagram of Er2Ti2O7. Heat capacity and time-of-flight neutron scattering studies of single crystals reveal unconventional low-energy states. Er3+ magnetic ions reside on a pyrochlore lattice in Er2Ti2O7, where local XY anisotropy and antiferromagnetic interactions give rise to a unique frustrated system. In zero field, the ground state exhibits coexisting short and long-range order, accompanied by soft collective spin excitations previously believed to be absent. The application of finite magnetic fields tunes the ground state continuously through a landscape of noncollinear phases, divided by a zero temperature phase transition at micro{0}H{c} approximately 1.5 T. The characteristic energy scale for spin fluctuations is seen to vanish at the critical point, as expected for a second order quantum phase transition driven by quantum fluctuations.