Hannu Mutka

Bose–Einstein condensation of the triplet states in the magnetic insulator TlCuCl3

Bose–Einstein condensation denotes the formation of a collective quantum ground state of identical particles with integer spin or intrinsic angular momentum. In magnetic insulators, the magnetic properties are due to the unpaired shell electrons that have half-integer spin. However, in some such compounds (KCuCl3 and TlCuCl3), two Cu2+ ions are antiferromagnetically coupled to form a dimer in a crystalline network: the dimer ground state is a spin singlet (total spin zero), separated by an energy gap from the excited triplet state (total spin one). In these dimer compounds, Bose–Einstein condensation becomes theoretically possible. At a critical external magnetic field, the energy of one of the Zeeman split triplet components (a type of boson) intersects the ground-state singlet, resulting in long-range magnetic order; this transition represents a quantum critical point at which Bose–Einstein condensation occurs. Here we report an experimental investigation of the excitation spectrum in such a field-induced magnetically ordered state, using inelastic neutron scattering measurements of TlCuCl3 single crystals. We verify unambiguously the theoretically predicted gapless Goldstone mode characteristic of the Bose–Einstein condensation of the triplet states.

Modifying the properties of 4f single-ion magnets by peripheral ligand functionalisation

We study the ligand-field splittings and magnetic properties of three ErIII single-ion magnets which differ in the peripheral ligand sphere but exhibit similar first coordination spheres by inelastic neutron scattering (INS) and SQUID magnetometry. The INS spectra of the three compounds are profoundly different pointing at a strong response of the magnetic behavior to minor structural changes, as they are e.g. encountered when depositing molecules on surfaces. The observation of several magnetic excitations within the J = 15/2 ground multiplet together with single-crystal magnetic measurements allows for the extraction of the sign and magnitude of all symmetry-allowed Stevens parameters. The parameter values and the energy spectrum derived from INS are compared to the results of state-of-the-art ab initio CASSCF calculations. Temperature-dependent alternating current (ac) susceptibility measurements suggest that the magnetisation relaxation in the investigated temperature range of 1.9 K < T < 5 K is dominated by quantum tunnelling of magnetisation and two-phonon Raman processes. The possibility of observing electron paramagnetic resonance transitions between the ground-state doublet states, which can be suppressed in perfectly axial single-ion magnets, renders the studied systems interesting as representations of quantum bits.

Quantum magnets under pressure: controlling elementary excitations in TlCuCl3.

We follow the evolution of the elementary excitations of the quantum antiferromagnet TlCuCl3 through the pressure-induced quantum critical point, which separates a dimer-based quantum disordered phase from a phase of long-ranged magnetic order. We demonstrate by neutron spectroscopy the continuous emergence in the weakly ordered state of a low-lying but massive excitation corresponding to longitudinal fluctuations of the magnetic moment. This mode is not present in a classical description of ordered magnets, but is a direct consequence of the quantum critical point.

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.

[ReF6]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.

Direct observation of a ferri-to-ferromagnetic transition in a fluoride-bridged 3d–4f molecular cluster

We report on the synthesis, crystal structure and magnetic characterisation of the trinuclear, fluoride-bridged, molecular nanomagnet [Dy(hfac)3(H2O)–CrF2(py)4–Dy(hfac)3(NO3)] (1) (hfacH = 1,1,1,5,5,5-hexafluoroacetylacetone, py = pyridine) and a closely related dinuclear species [Dy(hfac)4–CrF2(py)4]·½CHCl3 (2). Element-specific magnetisation curves obtained on 1 by X-ray magnetic circular dichroism (XMCD) allow us to directly observe the field-induced transition from a ferrimagnetic to a ferromagnetic arrangement of the Dy and Cr magnetic moments. By fitting a spin-Hamiltonian model to the XMCD data we extract a weak antiferromagnetic exchange coupling of j = −0.18 cm−1 between the DyIII and CrIII ions. The value found from XMCD is consistent with SQUID magnetometry and inelastic neutron scattering measurements. Furthermore, alternating current susceptibility and muon-spin relaxation measurements reveal that 1 shows thermally activated relaxation of magnetisation with a small effective barrier for magnetisation reversal of Δeff = 3 cm−1. Density-functional theory calculations show that the Dy–Cr couplings originate from superexchange via the fluoride bridges.

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.

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.

Mechanism of ground-state selection in the frustrated molecular spin cluster V15

We report an inelastic neutron scattering (INS) study under a magnetic field on the frustrated molecular spin cluster V15. Several field-dependent transitions are observed and provide a comprehensive understanding of the low-energy quantum spin states. The energy gap 2Δ0 ≈ 27(3) μeV between the two lowest S = 1/2 Kramers doublets is unambiguously attributed to a symmetry lowering of the cluster. The INS data are mapped onto an S = 1/2 Antiferromagnetic Heisenberg triangle with scalene distortion. A quantitative description of the wave function mixing within the ground state is derived.

Magnetism in Polyoxometalates: Anisotropic Exchange Interactions in the Co Moiety of [Co3W(D2O)2(ZnW9O34)2]12−—A Magnetic and Inelastic Neutron Scattering Study

The ground-state properties of a Co3II moiety encapsulated in a polyoxometalate anion were investigated by combining measurements of specific heat, magnetic susceptibility, and low-temperature magnetization with a detailed inelastic neutron scattering (INS) study on a fully deuterated polycrystalline sample of Na12[Co3W(D2O)2(ZnW9O34)2].40D2O (Co3). The ferromagnetic Co3O14 cluster core consists of three octahedrally oxo-coordinated CoII ions. According to the single-ion anisotropy and spin-orbit coupling of the octahedral CoII ions, the appropriate exchange Hamiltonian to describe the ground-state properties of the Co3 spin cluster is anisotropic and is expressed as H = -2 sigma a = x,y,z (Ja12 S1a S2a + Ja23 S2a S3a), where Ja are the components of the exchange interactions between the CoII ions. To reproduce the INS data, different orientations of the two anisotropic J tensors must be considered, and the following conditions had to be introduced: Jx12 = Jy23, Jy12 = Jx23, Jz12 = Jz23. This result was correlated with the molecular symmetry of the complex. The following set of parameters was obtained: Jx12 = Jy23 = 1.37, Jy12 = Jx23 = 0.218, and Jz12 = Jz23 = 1.24 meV. This set also reproduces in a satisfactory manner the specific heat, susceptibility, and magnetization properties of Co3.