Decoupling Lattice and Magnetic Instabilities in Frustrated CuMnO2.

The AMnO2 delafossites (A = Na, Cu) are model frustrated antiferromagnets, with triangular layers of Mn3+ spins. At low temperatures (TN = 65 K), a C2/m → P1̅ transition is found in CuMnO2, which breaks frustration and establishes magnetic order. In contrast to this clean transition, A = Na only shows short-range distortions at TN. Here, we report a systematic crystallographic, spectroscopic, and theoretical investigation of CuMnO2. We show that, even in stoichiometric samples, nonzero anisotropic Cu displacements coexist with magnetic order. Using X-ray/neutron diffraction and Raman scattering, we show that high pressures act to decouple these degrees of freedom. This manifests as an isostuctural phase transition at ∼10 GPa, with a reversible collapse of the c-axis. This is shown to be the high-pressure analogue of the c-axis negative thermal expansion seen at ambient pressure. Density functional theory (DFT) simulations confirm that dynamical instabilities of the Cu+ cations and edge-shared MnO6 layers are intertwined at ambient pressure. However, high pressure selectively activates the former, before an eventual predicted reemergence of magnetism at the highest pressures. Our results show that the lattice dynamics and local structure of CuMnO2 are quantitatively different from nonmagnetic Cu delafossites and raise questions about the role of intrinsic inhomogeneity in frustrated antiferromagnets.

Magnetic Structure and Excitations in CeCuxAl4-x System.

CeCuAl3 crystallizing in the tetragonal BaNiSn3-type structure and CeCuxAl4-x solid solutions were investigated by means of elastic and inelastic neutron scattering. Powder neutron diffraction brought information on both temperature evolution of crystallographic parameters and magnetic order at low temperatures. No structural change was observed in the investigated temperature range from 1.5 to 300 K. Weak magnetic peaks outside nuclear Bragg positions observed in solid solutions with 0.90 ≤ x ≤ 1.10 were described by the propagation vector k = (0.40 + δx, 0.60 + δy, 0), where δx ≈ 0.02 and δy ≈ 0.01. The magnetic structure of CeCu0.75Al3.25 consists of two components: an anti-ferromagnetic one described by the same k and a ferromagnetic one with k0 = (0, 0, 0) and magnetic moments lying within the tetragonal basal plane. The evolution of magnetic excitations as a function of Cu-Al concentration in CeCuxAl4-x was studied by inelastic neutron scattering. The measured spectra of CeCuAl3 and the solution with x = 0.95 point to a three-magnetic-peak energy scheme, while only two excitations are expected from the local symmetry conditions on Ce atoms. The standard two-peak spectrum of crystal electric field excitations was observed for Cu-Al substitutions further from the 1:1:3 stoichiometry (x = 0.75 and 1.10). The intermediate concentrations (x = 0.90 and 1.05) exhibit spectra on the border between the former cases with a less clear pronounced first inelastic magnetic peak. The observed behavior is discussed considering the evolution of structural parameters in the CeCuxAl4-x system and the coupling between the lattice vibrations and the crystal electric field excitations.

Studies of a Large Odd-Numbered Odd-Electron Metal Ring: Inelastic Neutron Scattering and Muon Spin Relaxation Spectroscopy of Cr8 Mn.

The spin dynamics of Cr8 Mn, a nine-membered antiferromagnetic (AF) molecular nanomagnet, are investigated. Cr8 Mn is a rare example of a large odd-membered AF ring, and has an odd-number of 3d-electrons present. Odd-membered AF rings are unusual and of interest due to the presence of competing exchange interactions that result in frustrated-spin ground states. The chemical synthesis and structures of two Cr8 Mn variants that differ only in their crystal packing are reported. Evidence of spin frustration is investigated by inelastic neutron scattering (INS) and muon spin relaxation spectroscopy (µSR). From INS studies we accurately determine an appropriate microscopic spin Hamiltonian and we show that µSR is sensitive to the ground-spin-state crossing from S=1/2 to S=3/2 in Cr8 Mn. The estimated width of the muon asymmetry resonance is consistent with the presence of an avoided crossing. The investigation of the internal spin structure of the ground state, through the analysis of spin-pair correlations and scalar-spin chirality, shows a non-collinear spin structure that fluctuates between non-planar states of opposite chiralities.

Design of Single-Molecule Magnets: Insufficiency of the Anisotropy Barrier as the Sole Criterion.

Determination of the electronic energy spectrum of a trigonal-symmetry mononuclear Yb(3+) single-molecule magnet (SMM) by high-resolution absorption and luminescence spectroscopies reveals that the first excited electronic doublet is placed nearly 500 cm(-1) above the ground one. Fitting of the paramagnetic relaxation times of this SMM to a thermally activated (Orbach) model {τ = τ0 × exp[ΔOrbach/(kBT)]} affords an activation barrier, ΔOrbach, of only 38 cm(-1). This result is incompatible with the spectroscopic observations. Thus, we unambiguously demonstrate, solely on the basis of experimental data, that Orbach relaxation cannot a priori be considered as the main mechanism determining the spin dynamics of SMMs. This study highlights the fact that the general synthetic approach of optimizing SMM behavior by maximization of the anisotropy barrier, intimately linked to the ligand field, as the sole parameter to be tuned, is insufficient because of the complete neglect of the interaction of the magnetic moment of the molecule with its environment. The Orbach mechanism is expected dominant only in the cases in which the energy of the excited ligand field state is below the Debye temperature, which is typically low for molecular crystals and, thus, prevents the use of the anisotropy barrier as a design criterion for the realization of high-temperature SMMs. Therefore, consideration of additional design criteria that address the presence of alternative relaxation processes beyond the traditional double-well picture is required.

On the microscopic dynamics of the 'Einstein solids' AlV2Al20 and GaV2Al20, and of YV2Al20: a benchmark system for 'rattling' excitations.

The inelastic response of AV2Al20 (with A = Al, Ga and Y) was probed by high-resolution inelastic neutron scattering experiments and density functional theory (DFT) based lattice dynamics calculations (LDC). Features characteristic of the dynamics of Al, Ga and Y are established experimentally in the low-energy range of the compounds. In the stereotype 'Einstein-solid' compound AlV2Al20 we identify a unique spectral density extending up to 10 meV at 1.6 K. Its dominating feature is a peak centred at 2 meV at the base temperature. A very similar spectral distribution is established in GaV2Al20 albeit the strong peak is located at 1 meV at 1.6 K. In YV2Al20 signals characteristic of Y dynamics are located above 8 meV. The spectral distributions are reproduced by the DFT-based LDC and identified as a set of phonons. The response to temperature changes between 1.6 and ∼300 K is studied experimentally and the exceptionally vivid renormalization of the A characteristic modes in AlV2Al20 and GaV2Al20 is quantified by following the energy of the strong peak. At about 300 K it is shifted to higher energies by 300% for A = Al and 450% for A = Ga. The dynamics of A = Y in YV2Al20 show a minor temperature effect. This holds in general for modes located above 10 meV in any of the compounds. They are associated with vibrations of the V2Al20 matrix. Atomic potentials derived through DFT calculations indicate the propensity of A = Al and Ga to a strong positive energy shift upon temperature increase by a high quartic component. The effect of the strong phonon renormalization on thermodynamic observables is computed on grounds of the LDC results. It is shown that through the hybridization of A = Al and Ga with the V2Al20 dynamics the matrix vibrations in the low-energy range follow this renormalization.

A classification of spin frustration in molecular magnets from a physical study of large odd-numbered-metal, odd electron rings.

The term "frustration" in the context of magnetism was originally used by P. W. Anderson and quickly adopted for application to the description of spin glasses and later to very special lattice types, such as the kagomé. The original use of the term was to describe systems with competing antiferromagnetic interactions and is important in current condensed matter physics in areas such as the description of emergent magnetic monopoles in spin ice. Within molecular magnetism, at least two very different definitions of frustration are used. Here we report the synthesis and characterization of unusual nine-metal rings, using magnetic measurements and inelastic neutron scattering, supported by density functional theory calculations. These compounds show different electronic/magnetic structures caused by frustration, and the findings lead us to propose a classification for frustration within molecular magnets that encompasses and clarifies all previous definitions.

A detailed study of the magnetism of chiral {Cr7M} rings: an investigation into parametrization and transferability of parameters.

Compounds of general formula [Cr7MF3(Etglu)(O2C(t)Bu)15(Phpy)] [H5Etglu = N-ethyl-d-glucamine; Phpy = 4-phenylpyridine; M = Zn (1), Mn (2), Ni (3)] have been prepared. The structures contain an irregular octagon of metal sites formed around the penta-deprotonated Etglu(5-) ligand; the chirality of N-ethyl-d-glucamine is retained in the final product. The seven Cr(III) sites have a range of coordination environments, and the divalent metal site is crystallographically identified and has a Phpy ligand attached to it. By using complementary experimental techniques, including magnetization and specific heat measurements, inelastic neutron scattering, and electron paramagnetic resonance spectroscopy, we have investigated the magnetic features of this family of {Cr7M} rings. Microscopic parameters of the spin Hamiltonian have been determined as a result of best fits of the different experimental data, allowing a direct comparison with corresponding parameters found in the parent compounds. We examine whether these parameters can be transferred between compounds and compare them with those of an earlier family of heterometallic rings.

Magnetic interactions through fluoride: magnetic and spectroscopic characterization of discrete, linearly bridged [Mn(III)2(µ-F)F4(Me3tacn)2](PF6).

The nature of the magnetic interaction through fluoride in a simple, dinuclear manganese(III) complex (1), bridged by a single fluoride ion in a perfectly linear fashion, is established by experiment and density functional theory. The magnitude of the antiferromagnetic exchange interaction and the manganese(III) zero-field-splitting parameters are unambiguously determined by inelastic neutron scattering to yield J = 33.0(2) cm(-1) (H = JS1·S2 Hamiltonian definition) and single-ion D = -4.0(1) cm(-1). Additionally, high-field, high-frequency electron paramagnetic resonance and magnetic measurements support the parameter values and resolve |E| ≈ 0.04 cm(-1). The exchange coupling constant (J) is 1 order of magnitude smaller than that found in comparable systems with linear oxide bridging but comparable to typical magnitudes through cyanide, thus underlining the potential of fluoride complexes as promising building blocks for novel magnetic systems.

Effect of the electropositive elements A = Sc, La, and Ce on the microscopic dynamics of AV2Al20.

We report on the inelastic response of AV2Al20 (with A = Sc, La and Ce) probed by high-resolution inelastic neutron scattering experiments. Intense signals associated with the dynamics of Sc, La and Ce are identified in the low-energy range at 6-14 meV in ScV2Al20 and at 8-16 meV in LaV2Al20 and CeV2Al20. Their response to temperature changes between 2 and 300 K reveals a very weak softening of the modes upon heating in LaV2Al20 and CeV2Al20 and a distinguished blue shift by about 2 meV in ScV2Al20. By means of density functional theory (DFT) and lattice dynamics calculations (LDC) we show that the unusual anharmonicity of the Sc-dominated modes is due to the local potential of Sc featured by a strong quartic term. The vibrational dynamics of ScV2Al20 as well as of LaV2Al20 and CeV2Al20 is reproduced by a set of eigenmodes. To screen the validity of the DFT and LDC results they are confronted with data from X-ray diffraction measurements. The effect of the strong phonon renormalization in ScV2Al20 on thermodynamic observables is computed on grounds of the LDC derived inelastic response. To set the data in a general context of AV2Al20 compounds and their physical properties we report in addition computer and experimental results of the binary V2Al20 compound.

Magnetic properties of nano-scale hematite, α-Fe2O3, studied by time-of-flight inelastic neutron spectroscopy.

Samples of nanoscale hematite, α-Fe2O3, with different surface geometries and properties have been studied with inelastic time-of-flight neutron scattering. The 15 nm diameter nanoparticles previously shown to have two collective magnetic excitation modes in separate triple-axis neutron scattering studies have been studied in further detail using the advantage of a large detector area, high resolution, and large energy transfer range of the IN5 TOF spectrometer. A mesoporous hematite sample has also been studied, showing similarities to that of the nanoparticle sample and bulk α-Fe2O3. Analysis of these modes provides temperature dependence of the magnetic anisotropy coefficient along the c-axis, κ1. This is shown to remain negative throughout the temperature range studied in both samples, providing an explanation for the previously observed suppression of the Morin transition in the mesoporous material. The values of this anisotropy coefficient are found to lie between those of bulk and nano-particulate samples, showing the hybrid nature of the mesoporous 3-dimensional structure.

[ReF(6)](2-) : a robust module for the design of molecule-based magnetic materials.

A facile synthesis of the [ReF6 ](2-) ion and its use as a building block to synthesize magnetic systems are reported. Using dc and ac magnetic susceptibility measurements, INS and EPR spectroscopies, the magnetic properties of the isolated [ReF6 ](2-) unit in (PPh4 )2 [ReF6 ]⋅2 H2 O (1) have been fully studied including the slow relaxation of the magnetization observed below ca. 4 K. This slow dynamic is preserved for the one-dimensional coordination polymer [Zn(viz)4 (ReF6 )]∞ (2, viz=1-vinylimidazole), demonstrating the irrelevance of low symmetry for such magnetization dynamics in systems with easy-plane-type anisotropy. The ability of fluoride to mediate significant exchange interactions is exemplified by the isostructural [Ni(viz)4 (ReF6 )]∞ (3) analogue in which the ferromagnetic Ni(II) -Re(IV) interaction (+10.8 cm(-1) ) dwarfs the coupling present in related cyanide-bridged systems. These results reveal [ReF6 ](2-) to be an unique new module for the design of molecule-based magnetic materials.

Anisotropic propagating excitations and quadrupolar effects in Tb2Ti2O7.

The dynamical magnetic correlations in Tb2Ti2O7 have been investigated using polarized inelastic neutron scattering. Dispersive excitations are observed, emerging from pinch points in reciprocal space and characterized by an anisotropic spectral weight. Anomalies in the crystal field and phonon excitation spectrum at Brillouin zone centers are also reported. These findings suggest that Coulomb phases, although they present a disordered ground state with dipolar correlations, allow the propagation of collective excitations. They also point out a strong spin-lattice coupling, which likely drives effective interactions between the 4f quadrupolar moments.

Three-axis anisotropic exchange coupling in the single-molecule magnets NEt4[Mn(III)2(5-Brsalen)2(MeOH)2M(III)(CN)6] (M=Ru, Os).

We have investigated the single-molecule magnets [Mn(III)2 (5-Brsalen)2 (MeOH)2 M(III) (CN)6 ]NEt4 (M=Os (1) and Ru (2); 5-Brsalen=N,N'-ethylenebis(5-bromosalicylidene)iminate) by frequency-domain Fourier-transform terahertz electron paramagnetic resonance (THz-EPR), inelastic neutron scattering, and superconducting quantum interference device (SQUID) magnetometry. The combination of all three techniques allows for the unambiguous experimental determination of the three-axis anisotropic magnetic exchange coupling between Mn(III) and Ru(III) or Os(III) ions, respectively. Analysis by means of a spin-Hamiltonian parameterization yields excellent agreement with all experimental data. Furthermore, analytical calculations show that the observed exchange anisotropy is due to the bent geometry encountered in both 1 and 2, whereas a linear geometry would lead to an Ising-type exchange coupling.

Frequency-domain Fourier-transform terahertz spectroscopy of the single-molecule magnet (NEt4)[Mn2(5-Brsalen)2(MeOH)2Cr(CN)6].

We have investigated the novel single-molecule magnet (NEt(4))[Mn(2)(5-Brsalen)(2)(MeOH)(2)Cr(CN)(6)] (1; 5-Brsalen = N,N'-ethylenebis(5-bromosalicylidene)iminato anion) using spectroscopic as well as magnetization and susceptibility measurements. Frequency-domain Fourier-transform terahertz electron paramagnetic resonance (FDFT THz-EPR) based on the generation of THz radiation from a synchrotron in combination with inelastic neutron scattering (INS) allows for the discrimination between intermultiplet and intramultiplet transitions. Together with ac/dc magnetic susceptibility measurements the obtained set of data provides a complete characterization of the lowest energetic magnetic excitations. We find that the new compound 1 exhibits much weaker intermolecular interactions than found in the closely related compound: K[Mn(2)(5-Brsalen)(2)(H(2)O)(2)Cr(CN)(6)] (2). Furthermore, two phonon lines in the vicinity of the magnetic excitations are detected.

Enhancing the blocking temperature in single-molecule magnets by incorporating 3d-5d exchange interactions.

We report the first single-molecule magnet (SMM) to incorporate the [Os(CN)(6)](3-) moiety. The compound (1) has a trimeric, cyanide-bridged Mn(III)-Os(III)-Mn(III) skeleton in which Mn(III) designates a [Mn(5-Brsalen)(MeOH)](+) unit (5-Brsalen=N,N'-ethylenebis(5-bromosalicylideneiminato)). X-ray crystallographic experiments reveal that 1 is isostructural with the Mn(III)-Fe(III)-Mn(III) analogue (2). Both compounds exhibit a frequency-dependent out-of-phase χ''(T) alternating current (ac) susceptibility signal that is suggestive of SMM behaviour. From the Arrhenius expression, the effective barrier for 1 is found to be Δ(eff)/k(B)=19 K (τ(0)=5.0×10(-7) s; k(B)=Boltzmann constant), whereas only the onset (1.5 kHz, 1.8 K) of χ''(T) is observed for 2, thus indicating a higher blocking temperature for 1. The strong spin-orbit coupling present in Os(III) isolates the E'(1g(1/2))(O(h)*) Kramers doublet that exhibits orbital contributions to the single-ion anisotropy. Magnetic susceptibility and inelastic neutron-scattering measurements reveal that substitution of [Fe(CN)(6)](3-) by the [Os(CN)(6)](3-) anion results in larger ferromagnetic, anisotropic exchange interactions going from quasi-Ising exchange interactions in 2 to pure Ising exchange for 1 with J(parallel)(MnOs)=-30.6 cm(-1). The combination of diffuse magnetic orbitals and the Ising-type exchange interaction effectively contributes to a higher blocking temperature. This result is in accordance with theoretical predictions and paves the way for the design of a new generation of SMMs with enhanced SMM properties.

Spin-chain correlations in the frustrated triangular lattice material CuMnO2.

The Ising triangular lattice remains the classic test-case for frustrated magnetism. Here we report neutron scattering measurements of short range magnetic order in CuMnO2, which consists of a distorted lattice of Mn3+ spins with single-ion anisotropy. Physical property measurements on CuMnO2 are consistent with 1D correlations caused by anisotropic orbital occupation. However the diffuse magnetic neutron scattering seen in powder measurements has previously been fitted by 2D Warren-type correlations. Using neutron spectroscopy, we show that paramagnetic fluctuations persist up to ∼25 meV above T N = 65 K. This is comparable to the incident energy of typical diffractometers, and results in a smearing of the energy integrated signal, which hence cannot be analysed in the quasi-static approximation. We use low energy XYZ polarised neutron scattering to extract the purely magnetic (quasi)-static signal. This is fitted by reverse Monte Carlo analysis, which reveals that two directions in the triangular layers are perfectly frustrated in the classical spin-liquid phase at 75 K. Strong antiferromagnetic correlations are only found along the b-axis, and our results hence unify the pictures seen by neutron scattering and macroscopic physical property measurements.

Breakdown of phonon glass paradigm in La- and Ce-filled Fe4Sb12 skutterudites.

The material class of skutterudites is believed to have strong potential for thermoelectric application due to the very low thermal conductivity of the filled structures. It is generally assumed that the atoms filling the skutterudite cages act as 'rattlers' and essentially induce a disordered lattice dynamics referred to as 'phonon glass'. Here, we present neutron spectroscopy experiments and ab initio computational work on phonons in LaFe(4)Sb(12) and CeFe(4)Sb(12). Our results give unequivocal evidence of essentially temperature-independent lattice dynamics with well-defined phase relations between guest and host dynamics, indicative of a quasi-harmonic coupling between the guests and the host lattice. These conclusions are in disagreement with the 'phonon glass' paradigm based on individual 'rattling' of the guest atoms. These findings should have an essential impact on the design and improvement of thermoelectric materials and on the development of microscopic models needed for these efforts.

Single-ion anisotropy and exchange interactions in the cyano-bridged trimers MnIII2MIII(CN)6 (MIII = Co, Cr, Fe) species incorporating [Mn(5-Brsalen)]+ units: an inelastic neutron scattering and magnetic susceptibility study.

The electronic structures of the compounds K[(5-Brsalen)(2)(H(2)O)(2)-Mn(2)M(III)(CN)(6)].2H(2)O (M(III) = Co(III), Cr(III), Fe(III)) have been determined by inelastic neutron scattering (INS) and magnetic susceptibility studies, revealing the manganese(III) single-ion anisotropy and exchange interactions that define the low-lying states of the Mn-M(III)-Mn trimeric units. Despite the presence of an antiferromagnetic intertrimer interaction, the experimental evidence supports the classification of both the Cr(III) and Fe(III) compounds as single-molecule magnets. The value of 17(2) cm(-1) established from AC susceptibility measurements for a spin-reversal barrier of K[(5-Brsalen)(2)(H(2)O)(2)-Mn(2)Cr(CN)(6)].2H(2)O may be readily rationalized in terms of the energy level diagram determined directly by INS. AC susceptibility measurements on samples of K[(5-Brsalen)(2)(H(2)O)(2)-Mn(2)Fe(CN)(6)].2H(2)O are contrary to those previously reported, exhibiting but the onset of peaks below temperatures of 1.8 K at oscillating frequencies in the range of 100-800 Hz. INS measurements reveal an anisotropic ferromagnetic manganese(III)-iron(III) exchange interaction, in accordance with theoretical expectations based on the unquenched orbital angular momentum of the [Fe(CN)(6)](3-) anion, giving rise to an M(s) approximately +/-9/2 ground state, isolated by approximately 11.5 cm(-1) from the higher-lying levels. The reported INS and magnetic data should now serve as a benchmark against which theoretical models that aim to inter-relate the electronic and molecular structure of molecular magnets should be tested.

High-energy spin fluctuation in low-Tc iron-based superconductor LaFePO0.9.

Spin fluctuations are widely believed to play an important role in the superconducting mechanisms of unconventional high temperature superconductors. Spin fluctuations have been observed in iron-based superconductors as well. However, in some iron-based superconductors such as LaFePO0.9, they have not been observed by inelastic neutron scattering (INS). LaFePO0.9 is an iron-based superconductor with a low superconducting transition temperature (Tc = 5 K), where line nodes are observed in the superconducting gap function. The line-node symmetry typically originates from sign reversal of the order parameter in spin-fluctuation-mediated superconductivity. This contradiction has been a long-standing mystery of this superconductor. Herein, spin fluctuations were found at high energies such as 30-50 meV with comparable intensities to an optimally doped LaFeAs(O, F). Based on this finding, the line-node symmetry can be explained naturally as spin-fluctuation-mediated superconductivity.

Magnetic properties of transition metal dimers probed by inelastic neutron scattering.

The physical characterisation and understanding of molecular magnetic materials is one of the most important steps towards the integration of such systems in hybrid spintronic devices. Amongst the many characterisation techniques employed in such a task, Inelastic Neutron Scattering (INS) stands as one of the most powerful and sensitive tools to investigate their spin dynamics. Herein, the magnetic properties and spin dynamics of two dinuclear complexes, namely [(M(hfacac)2)2(bpym)] (where M = Ni2+, Co2+, abbreviated in the following as Ni2, Co2) are reported. These are model systems that could constitute fundamental units of future spintronic devices. By exploiting the highly sensitive IN5 Cold INS spectrometer, we are able to gain a deep insight into the spin dynamics of Ni2 and to fully obtain the microscopic spin Hamiltonian parameters; while for Co2, a multitude of INS transitions are observed demonstrating the complexity of the magnetic properties of octahedral cobalt-based systems.