Kramers Doublet Research Articles

Luminescence and Single‐Molecule Magnet Properties in Ideal Symmetry Compounds: Example of a Near‐Planar Tricoordinate Ytterbium(III) Amide

AbstractWe are reporting on the use of a low‐coordinate YbIII amide with near‐ideal planar trigonal [Yb{N(SiMe3)2}3] (1) and on a bipyramidal trigonal derivative [Yb{N(SiMe2H)2}3 ⋅ (thf)2] (2) that constitute quintessential cases to investigate luminescent and magnetic properties otherwise usually blurred on less symmetrical compounds. These compounds represent the first experimental objects that allow for the confirmation of the recent conjecture about best‐performing SMM built on the archetypal prolate lanthanide ion. We have performed a combined theoretical, luminescent, and magnetic study on these molecules. For 1, a spectacular split of the 2F7/2 ground state of 1312 cm−1 is measured by low‐temperature near‐infra‐red luminescence as well as the calculated pure wavefunction composition of the low‐lying Kramers doublets, making this complex a textbook example of a prolate SMM. These results are corroborated by comparison with 2, that exhibits as expected a 50 % decrease of the ground state splitting compared to 1. Yet, we show that these remarkable features are insufficient to promote SMM behavior, and Orbach relaxation is unlikely to occur even on such an ideal low‐coordinate SMM without control of spin‐phonon coupling.

THz-EPR-based Magneto-Structural Correlations for Cobalt(II) Single-Ion Magnets With Bis-Chelate Coordination.

New cobalt(II)-based complexes with [N2O2] coordination formed by two bis-chelate ligands were synthesized and characterized by a multi-technique approach. The complexes possess an easy-axis anisotropy (D<0) and magnetic measurements show a field-induced slow relaxation of magnetization. The spin-reversal barriers, i. e., the splitting of the two lowest Kramers doublets (UZFS), have been measured by THz-EPR spectroscopy, which allows to distinguish the two crystallographically independent species present in one of the complexes. Based on these experimental UZFS energies together with those for related complexes reported in literature, it was possible to establish magneto-structural correlations. UZFS linearly depends on the elongation parameter ϵT of the (pseudo-)tetrahedral coordination, which is given by the ratio between the average obtuse and acute angles at the cobalt(II) ion, while UZFS was found to be virtually independent of the twist angle of the chelate planes. With increasing deviation from the orthogonality of the latter, the rhombicity (|E/D|) increases.

Exploring rare-earth Kitaev magnets by massive-scale computational analysis

The Kitaev honeycomb model plays a pivotal role in the quest for quantum spin liquids, in which fractional quasiparticles would provide applications in decoherence-free topological quantum computing. The key ingredient is the bond-dependent Ising-type interactions, dubbed the Kitaev interactions, which require strong entanglement between spin and orbital degrees of freedom. Here we investigate the identification and design of rare-earth materials displaying robust Kitaev interactions. We scrutinize all possible 4f electron configurations, which require up to 6+ million intermediate states in the perturbation processes, by developing a parallel computational program designed for massive-scale calculations. Our analysis reveals a predominant interplay between the isotropic Heisenberg J and anisotropic Kitaev K interactions across all realizations of the Kramers doublets. Remarkably, instances featuring 4f3 and 4f11 configurations showcase the prevalence of K over J, presenting unexpected prospects for exploring the Kitaev quantum spin liquids in compounds, including Nd3+ and Er3+, respectively.

Anisotropic magnetic and quadrupolar H−T phase diagram of CeRh2As2

The tetragonal heavy-fermion compound CeRh2As2 has intriguing low-temperature symmetry-breaking phases whose nature is unclear. The unconventional superconducting phase is complemented by other normal-state phases which presumably involve ordering of 4f electron multipoles supported by the Kramers doublets split by the tetragonal crystal electric field (CEF). The most striking aspect is the pronounced anisotropic H−T phase boundary for in-plane and out-of plane field directions. Using a localized 4f CEF model we demonstrate that its essential features can be understood as the result of competing low-field easy-plane magnetic order and field-induced quadrupolar order of xy type. We present calculations based on coupled multipole random phase approximation response function approach as well as molecular field treatment in the ordered regime. We use an analytical approach for a reduced quasiquartet model and numerical calculations for the complete CEF level scheme. We discuss the quantum critical properties as function of multipolar control parameters and explain the origin of a pronounced ac anisotropy of the H−T phase diagram. Finally, the field and temperature evolution of multipolar order parameters is derived and the high-field phase diagram is predicted. Published by the American Physical Society 2024

Syntheses, crystal structures, and magnetic properties of three cyclic dimeric M2L2 complexes constructed from a nitronyl nitroxide ligand and M(hfac)2 (M = Ni2+, Co2+, and Cu2+)

Three complexes derived from a new functional nitronyl nitroxide ligand, [Ni(hfac)2(NIT-3-OMe-4PhPy)]2 (1), [Co(hfac)2(NIT-3-OMe-4PhPy)]2 (2), and [Cu(hfac)2(NIT-3-OMe-4PhPy)]2 (3) were synthesized and characterized structurally and magnetically, where NIT-3-OMe-4PhPy stands for 2-[3-methoxy-4-(4-pyridinylmethoxy)phenyl]-4,4,5,5-tetramethyl-imidazolyl-1-oxyl-3-oxide and hfac is hexafluoroacetylacetonate anion (hfac). Complexes 1–3 are isomorphous in which the NIT-3-OMe-4PhPy molecule acts as a bridging ligand linking two M(II) ions (M = Ni2+, Co2+, and Cu2+) through the nitrogen of pyridine and the oxygen of the nitroxide unit to form a rectangle-like centrosymmetric dimer. The magnetic behaviors of 1–3 were investigated. For 1, the nitronyl nitroxides and Ni(II) ions are strongly antiferromagnetically (AFM) coupled, yielding the intradimer magnetic exchange constant of J = −87.3 cm−1. The temperature dependence of the magnetic susceptibility for 2 in the T > 30 K region was simulated with a two-spin model with S1 = 3/2 and S2 = 1/2 because of depopulation of the higher energy Kramers doublets of the Co(II) centers and the interaction of Co(II)…O coordination bonding, leading to J = −18.6 cm−1, g = 2.16, and zj′ = −2.94 cm−1 for the magnetic interactions between Co(II) ions and nitronyl nitroxides through pyridine rings. The ferromagnetic interaction between Cu(II) ions and nitronyl nitroxide radicals was observed in 3 with J = 68.9 cm−1 and θ = 0.51 k.

Slow magnetic relaxation in a europium(II) complex.

Single-ion anisotropy is vital for the observation of Single-Molecule Magnet (SMM) properties (i.e., a slow dynamics of the magnetization) in lanthanide-based systems. In the case of europium, the occurrence of this phenomenon has been inhibited by the spin and orbital quantum numbers that give way to J = 0 in the trivalent state and the half-filled population of the 4f orbitals in the divalent state. Herein, by optimizing the local crystal field of a quasi-linear bis(silylamido) EuII complex, the [EuII(N{SiMePh2}2)2] SMM is described, providing an example of a europium complex exhibiting slow relaxation of its magnetization. This behavior is dominated by a thermally activated (Orbach-like) mechanism, with an effective energy barrier of approximately 8 K, determined by bulk magnetometry and electron paramagnetic resonance. Ab initio calculations confirm second-order spin-orbit coupling effects lead to non-negligible axial magnetic anisotropy, splitting the ground state multiplet into four Kramers doublets, thereby allowing for the observation of an Orbach-like relaxation at low temperatures.

Magneto-optical and high-frequency electron paramagnetic resonance spectroscopy of Er3+ ions in CaMoO4 single crystal

We present the optical and magneto-optical spectroscopy and electron paramagnetic resonance (EPR) investigations of CaMoO4 single crystals doped with the erbium ions. Telecom-wavelength resonance transition inhomogeneous line width of Er3+ is relatively narrow for oxide crystals which makes this material promising for quantum technologies applications. The hyperfine structure in optical spectra of 167Er3+ isotope is well resolved. Energies and symmetries of wavefunctions of 39 energy levels of Er3+ ions in the crystal-field (CF) of S4 symmetry and g-factors of some CF Kramers doublets were measured and successfully simulated on the basis of CF calculations. The obtained set of CF parameters was used for modeling the hyperfine structure profiles observed in the optical absorption spectra.

Bimetallic Synergy Enables Silole Insertion into THF and the Synthesis of Erbium Single‐Molecule Magnets

AbstractThe potassium silole K2[SiC4‐2,5‐(SiMe3)2‐3,4‐Ph2] reacts with [M(η8‐COT)(THF)4][BPh4] (M=Er, Y; COT=cyclo‐octatetraenyl) in THF to give products that feature unprecedented insertion of the nucleophilic silicon centre into a carbon‐oxygen bond of THF. The structure of the major product, [(μ‐η8 : η8‐COT)M(μ‐L1)K]∞ (1M), consists of polymeric chains of sandwich complexes, where the spiro‐bicyclic silapyran ligand [C4H8OSiC4(SiMe3)2Ph2]2− (L1) coordinates to potassium via the oxygen. The minor product [(μ‐η8 : η8‐COT)M(μ‐L1)K(THF)]2 (2M) features coordination of the silapyran to the rare‐earth metal. In forming 1M and 2M, silole insertion into THF only occurs in the presence of potassium and the rare‐earth metal, highlighting the importance of bimetallic synergy. The lower nucleophilicity of germanium(II) leads to contrasting reactivity of the potassium germole K2[GeC4‐2,5‐(SiMe3)2‐3,4‐Me2] towards [M(η8‐COT)(THF)4][BPh4], with intact transfer of the germole occurring to give the coordination polymers [{η5‐GeC4(SiMe3)2Me2}M(η8‐COT)K]∞ (3M). Despite the differences in reactivity induced by the group 14 heteroatom, the single‐molecule magnet properties of 1Er, 2Er and 3Er are similar, with thermally activated relaxation occurring via the first‐excited Kramers doublet, subject to effective energy barriers of 122, 80 and 91 cm−1, respectively. Compound 1Er is also analysed by high‐frequency dynamic magnetic susceptibility measurements up to 106 Hz.

Bimetallic Synergy Enables Silole Insertion into THF and the Synthesis of Erbium Single-Molecule Magnets.

The potassium silole K2 [SiC4 -2,5-(SiMe3 )2 -3,4-Ph2 ] reacts with [M(η8 -COT)(THF)4 ][BPh4 ] (M=Er, Y; COT=cyclo-octatetraenyl) in THF to give products that feature unprecedented insertion of the nucleophilic silicon centre into a carbon-oxygen bond of THF. The structure of the major product, [(μ-η8 : η8 -COT)M(μ-L1 )K]∞ (1M ), consists of polymeric chains of sandwich complexes, where the spiro-bicyclic silapyran ligand [C4 H8 OSiC4 (SiMe3 )2 Ph2 ]2- (L1 ) coordinates to potassium via the oxygen. The minor product [(μ-η8 : η8 -COT)M(μ-L1 )K(THF)]2 (2M ) features coordination of the silapyran to the rare-earth metal. In forming 1M and 2M , silole insertion into THF only occurs in the presence of potassium and the rare-earth metal, highlighting the importance of bimetallic synergy. The lower nucleophilicity of germanium(II) leads to contrasting reactivity of the potassium germole K2 [GeC4 -2,5-(SiMe3 )2 -3,4-Me2 ] towards [M(η8 -COT)(THF)4 ][BPh4 ], with intact transfer of the germole occurring to give the coordination polymers [{η5 -GeC4 (SiMe3 )2 Me2 }M(η8 -COT)K]∞ (3M ). Despite the differences in reactivity induced by the group 14 heteroatom, the single-molecule magnet properties of 1Er , 2Er and 3Er are similar, with thermally activated relaxation occurring via the first-excited Kramers doublet, subject to effective energy barriers of 122, 80 and 91 cm-1 , respectively. Compound 1Er is also analysed by high-frequency dynamic magnetic susceptibility measurements up to 106 Hz.

Total angular momentum conservation in Ehrenfest dynamics with a truncated basis of adiabatic states.

We show that standard Ehrenfest dynamics does not conserve linear and angular momentum when using a basis of truncated adiabatic states. However, we also show that previously proposed effective Ehrenfest equations of motion [M. Amano and K. Takatsuka, "Quantum fluctuation of electronic wave-packet dynamics coupled with classical nuclear motions," J. Chem. Phys. 122, 084113 (2005) and V. Krishna, "Path integral formulation for quantum nonadiabatic dynamics and the mixed quantum classical limit," J. Chem. Phys. 126, 134107 (2007)] involving the non-Abelian Berry force do maintain momentum conservation. As a numerical example, we investigate the Kramers doublet of the methoxy radical using generalized Hartree-Fock with spin-orbit coupling and confirm that angular momentum is conserved with the proper equations of motion. Our work makes clear some of the limitations of the Born-Oppenheimer approximation when using abinitio electronic structure theory to treat systems with unpaired electronic spin degrees of freedom, and we demonstrate that Ehrenfest dynamics can offer much improved, qualitatively correct results.

Tailoring single-ion magnet properties of coordination polymer C11H18DyN3O9 (Dy-CP) using the radial effective charge model (RECM) and superposition model (SPM).

We investigate Dy-based coordination polymer C11H18DyN3O9 (Dy-CP) exhibiting single-ion magnet (SIM) properties, e.g., quantum tunnelling of magnetization (QTM), magnetic anisotropy, magnetic relaxation, and effective energy barrier (Ueff). To elucidate the underlying mechanisms, crystal field parameters (CFPs) for Dy3+ ions were modelled using the radial effective charge model (RECM) and superposition model (SPM), and the computational packages SIMPRE and SPECTRE. The modelled CFPs enable the prediction of the energy levels and associated wave functions, which successfully explain the field-induced Dy-CP SIM properties. The so-calculated magnetic susceptibility and isothermal magnetization match the experimental data reasonably well. The smaller energy separations of the first (Δ0-1 ∼ 31 cm-1) and the second (Δ0-2 = 74 cm-1) excited Kramers doublets suggest small Ueff = 65 cm-1 for Dy-CP. The magnetic moments of Dy3+ ions exhibit an easy-axis type magnetic anisotropy in the ground state, but change orientation in the excited states due to mixing of states from different Kramers doublets. Low-symmetry CF components play a crucial role in connecting different |±MJ〉 states within the ground multiplet, resulting in QTM and magnetic relaxation to the ground state occurring via the excited states. The RECM and SPM calculated CFP sets are standardized employing the 3DD package to enable meaningful comparison and assessing their mutual equivalence. The results demonstrate the correlation between structural and electronic features of the molecule and site symmetry and distortion of the local coordination polyhedra with SIM properties, offering insights for rational design of new SIMs. The importance of considering low-symmetry aspects in CFP modelling for accurate predictions of magnetic properties is highlighted. This study provides deeper understanding of field-induced behaviour in rare-earth-based SIMs and approaches for rationalization of experimentally measured SIMs' properties.

From field-induced to zero-field SMMs associated with open/closed structures of bis(ZnDy) tetranuclear complexes: a combined magnetic, theoretical and optical study.

We have prepared a bis(compartmental) Mannich base ligand H4L (1,4,8,11-tetraaza-1,4,8,11-tetrakis(2-hydroxy-3-methoxy-5-methylbenzyl)cyclotetradecane) specifically designed to obtain bis(TMIILnIII) tetranuclear complexes (TM = transition metal). In this regard, we have succeeded in obtaining three new complexes of the formula [Zn2(μ-L)(μ-OAc)Dy2(NO3)2]·[Zn2(μ-L)(μ-OAc)Dy2(NO3)(OAc)]·4CHCl3·2MeOH (1) and [TM2(μ-H2L)2(μ-succinate)Ln2(NO3)2] (NO3)2·2H2O·6MeOH (TMII = Zn, LnIII = Dy (2); TMII = Co, LnIII = Dy (3)). Compound 1 contains two different bis(ZnDy) tetranuclear molecules that cocrystallize in the structure, in which acetato bridging ligands connect the ZnII and DyIII ions within each ZnDy subunit. This compound does not exhibit slow magnetic relaxation at zero field, but it is activated in the presence of an applied dc magnetic field and/or by Dy/Y magnetic dilution, showing two relaxation processes corresponding to each of the two different bis(ZnDy) units found in the structure. As revealed by the theoretical calculations, magnetic relaxation in 1 is single-ion in origin and takes place through the first excited state of each DyIII ion. When using the succinato dicarboxylate bridging ligand instead of acetate, compounds 2 and 3 were serendipitously formed, which have a closed structure with the succinate anion bridging two ZnDy subunits belonging to two different ligands. It should be noted that only compound 2 exhibits slow relaxation of magnetization in the absence of an external magnetic field. According to experimental and theoretical data, 2 relaxes through the second excited Kramers doublet (Ueff = 342 K). In contrast, 3 displays field-induced SMM behaviour (Ueff = 203 K). However, the Co/Zn diluted version of this compound 3Zn shows slow relaxation at zero field (Ueff = 347 K). Ab initio theoretical calculations clearly show that the weak ferromagnetic coupling between CoII and DyIII ions is at the origin of the lack of slow relaxation of this compound at zero field. Compound 2 and its diluted analogues 2Y and 3Zn show hysteresis loops at very low temperature, thus confirming their SMM behaviour. Finally, compounds 1 and 2 show DyIII based emission even at room temperature that, in the case of 2, allows us to extract the splitting of the ground 6H15/2 term, which matches reasonably well with theoretical calculations.

Intramolecular bridging strategies to suppress two-phonon Raman spin relaxation in dysprosocenium single-molecule magnets.

Dy(III) bis-cyclopentadienyl (Cp) sandwich compounds exhibit extremely strong single-ion magnetic anisotropy which imbues them with magnetic memory effects such as magnetic hysteresis, and has put them at the forefront of high-performance single-molecule magnets (SMMs). Owing to the great success of design principles focused on maximising the anisotropy barrier, ever higher Ueff values have been reported leading to significant slow down of single-phonon Orbach spin relaxation. However, anisotropy-based SMM design has largely ignored two-phonon Raman spin relaxation, which is still limiting the temperatures at which a memory effect can be observed. In this work, we study the suppression of Raman relaxation through covalent bridging of the Cp ligands by alkyl chains, testing the hypothesis that increasing the rigidity of the ligand framework results in a blue shift of low frequency vibrations in the first coordination sphere of the Dy(III) ion. This reshaping of the vibrational low-energy density of states (DOS) results in lower occupation of pseudo-acoustic phonons available to drive Raman relaxation at low temperatures. We simulate Orbach and Raman spin relaxation in a series of zero-, mono-, di- and tri-bridged [Dy(Cpttt)2]+ analogues fully ab initio, using a quantum mechanics (QM)/molecular mechanics (MM) condensed phase embedding protocol in a periodic solvent matrix as a generic and experimentally testable environment model that can include (pseudo-)acoustic phononic degrees of freedom. We show that this approach can simulate magnetic relaxation dynamics in the condensed phase for the existing non-bridged [Dy(Cpttt)2]+ compound with quantitative experimental accuracy. Subsequently, we find a significant slowing down of Raman relaxation can be achieved for the singly-bridged SMM, while the introduction of further bridges leads to faster relaxation. A key result being that we find the two-phonon Raman rates correlate with the purity of the first-excited Kramers doublet in terms of its mJ = ±13/2 content. Even though the bridging design principle is successful at progressively reshaping the low-energy DOS, the introduction of linker atoms in the equatorial plane successively degrades magnetic anisotropy, suggesting the importance of refined design of the linker chemistry. The accuracy of our results emphasises the value of a generic periodic solvent embedding model, such that it permits the modelling of molecular spin dynamics in the condensed phase without knowledge of a crystal structure. This allows the study of hypothetical molecules or aggregates under real-world conditions, which we expect to have utility beyond the field of molecular magnetism.

Geometry and electronic structure of Yb(III)[CH(SiMe3)2]3 from EPR and solid-state NMR augmented by computations.

Characterization of paramagnetic compounds, in particular regarding the detailed conformation and electronic structure, remains a challenge, and - still today it often relies solely on the use of X-ray crystallography, thus limiting the access to electronic structure information. This is particularly true for lanthanide elements that are often associated with peculiar structural and electronic features in relation to their partially filled f-shell. Here, we develop a methodology based on the combined use of state-of-the-art magnetic resonance spectroscopies (EPR and solid-state NMR) and computational approaches as well as magnetic susceptibility measurements to determine the electronic structure and geometry of a paramagnetic Yb(III) alkyl complex, Yb(III)[CH(SiMe3)2]3, a prototypical example, which contains notable structural features according to X-ray crystallography. Each of these techniques revealed specific information about the geometry and electronic structure of the complex. Taken together, both EPR and NMR, augmented by quantum chemical calculations, provide a detailed and complementary understanding of such paramagnetic compounds. In particular, the EPR and NMR signatures point to the presence of three-centre-two-electron Yb-γ-Me-β-Si secondary metal-ligand interactions in this otherwise tri-coordinate metal complex, similarly to its diamagnetic Lu analogues. The electronic structure of Yb(III) can be described as a single 4f13 configuration, while an unusually large crystal-field splitting results in a thermally isolated ground Kramers doublet. Furthermore, the computational data indicate that the Yb-carbon bond contains some π-character, reminiscent of the so-called α-H agostic interaction.

Slow magnetic relaxation behaviors and diamagnetic dilution studies of a carboxyl bridged dinuclear dysprosium(III) complex

By using a rigid bulky carboxylic ligand α-cyanocinnamic acid (CCA), a dinuclear dysprosium (III) complex [Dy2(CCA)6 (MeOH)4] (1) was synthesized. Single crystal X-ray crystallography reveals that the two eight-coordinate dysprosium ions are bridged by four deprotonated carboxyl groups, forming a centrosymmetric paddle-wheel-like structure. Dynamic magnetic property measurements indicate that complex 1 displays field-induced slow magnetic relaxation. The temperature-dependent relaxation times can be fitted using Orbach and Raman processes with parameters of n = 2.8 (2), C = 27 (8) s−1/Kn, τ0 = 5 (2) × 10−10 s and Ueff = 40 (3) cm−1. Magnetic studies on the diamagnetic YIII-diluted analogue [Dy0.206Y1.794(CCA)6 (MeOH)4] (2) reveal its slow magnetic relaxation behavior without external dc field and the antiferromagnetic coupling between the DyIII ions in 1. Fits on the obtained relaxation times of 2 lead to the parameters of n = 4.5 (3), C = 0.7 (2) s−1/Kn, τ0 = 2.8 (2) × 10−9 s and Ueff = 38 (2) cm−1. The results suggest that slow magnetic relaxation originates from the single-ion relaxation of DyIII ions. Moreover, the diamagnetic dilution can suppress other fast relaxation pathways at low temperature, on account of the elimination of magnetic coupling and dipolar interaction. Ab initio calculations were then performed on the single DyIII ion species {YDy} and indicate that the first excited Kramers doublets (KDs) lie at ca. 76 cm−1, which is slightly higher than the experimental Ueff value. The intramolecular magnetic interactions were also calculated and indicate a weak ferromagnetic dipole-diploe magnetic interaction and an antiferromagnetic exchange coupling.

Structural and Magnetization Dynamics of Borohydride-Bridged Rare-Earth Metallocenium Cations.

The structure and magnetic properties of the bimetallic borohydride-bridged dysprosocenium compound [{(η5-Cpttt)(η5-CpMe4t)Dy}2(μ:κ2:κ2-BH4)]+[B(C6F5)4]- ([3Dy][B(C6F5)4]) are reported along with the solution-phase dynamics of the isostructural yttrium and lutetium analogues (Cpttt is 1,2,4-tri(tert-butyl)cyclopentadienyl, CpMe4t is tetramethyl(tert-butyl)cyclopentadienyl). The synthesis of [3M][B(C6F5)4] was accomplished in the 2:1 stoichiometric reactions of [(η5-Cpttt)(η5-CpMe4t)Dy(BH4)] (2M) with [CPh3][B(C6F5)4], with the metallocenes 2M obtained from reactions of the half-sandwich complexes [(η5-Cpttt)M(BH4)2(THF)] (1M) (M = Y, Dy, Lu) with NaCpMe4t. Crystallographic studies show significant lengthening of the M···B distance on moving through the series 1M, 2M, and 3M, with essentially linear {M···B···M} bridges in 3M. Multinuclear NMR spectroscopy indicates restricted rotation of the Cpttt ligands in 3Y and 3Lu in solution. The single-molecule magnet (SMM) properties of [3M][B(C6F5)4] are characterized by Raman and Orbach processes, with an effective barrier of 533(18) cm-1 and relaxation via the second-excited Kramers doublet. Although quantum tunneling of the magnetization (QTM) was not observed for [3M][B(C6F5)4], it was, surprisingly, found in its magnetically dilute version, which has a very similar barrier of Ueff = 499(21) cm-1. Consistent with this observation, slightly wider openings of the magnetic hysteresis loop at 2 K are found for [3M][B(C6F5)4] but not for the diluted analogue. The dynamic magnetic properties of the dysprosium SMMs and the role of exchange interactions in 3Dy are interpreted with the aid of multireference ab initio calculations.

Magnetism in frustrated Kondo and non-Kondo intermetallics: CeInCu2 versus NdInCu2

Single crystalline intermetallics ${\mathrm{CeInCu}}_{2}$ and ${\mathrm{NdInCu}}_{2}$, where the rare earth ions occupy geometrically frustrated fcc lattice of Heusler-type structure, have been studied comparatively to shed light on the ground-state magnetism derived from Kondo physics and/or spin frustration competing with the Ruderman-Kittel-Kasuya-Yosida interaction. ${\mathrm{CeInCu}}_{2}$ is distinct from ${\mathrm{NdInCu}}_{2}$ due to the significant Kondo effect that is absent in the latter. They order antiferromagnetically at ${T}_{N}\phantom{\rule{0.16em}{0ex}}\ensuremath{\approx}\phantom{\rule{0.16em}{0ex}}1.4$ and 2.0 K with large paramagnetic Curie-Weiss temperature of $\ensuremath{-}35.4$ K and $\ensuremath{-}41.1$ K, respectively. The electronic specific-heat coefficient $\ensuremath{\gamma}$ = $C/T$ ($T\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightarrow}\phantom{\rule{0.16em}{0ex}}0$) = 870 mJ ${\mathrm{mol}}^{\ensuremath{-}1}\phantom{\rule{4pt}{0ex}}{\mathrm{K}}^{\ensuremath{-}2}$ in ${\mathrm{CeInCu}}_{2}$ is significantly enhanced, much larger than 180 mJ ${\mathrm{mol}}^{\ensuremath{-}1}\phantom{\rule{4pt}{0ex}}{\mathrm{K}}^{\ensuremath{-}2}$ of the latter that is also enhanced albeit its non-Kondo nature. For both compounds, the Kadowaki-Woods ratio deviates greatly from the standard value expected from a Kramers doublet ground state, which, however, can be restored if one considers a smaller but still sizable $\ensuremath{\gamma}$ estimated from the paramagnetic state. Likewise, the Kondo temperature of ${\mathrm{CeInCu}}_{2}$ is revised to be ${T}_{K}\phantom{\rule{4pt}{0ex}}\ensuremath{\approx}$ 13 K that is double the literature values, manifesting a major effect of spin frustration to low-temperature thermodynamics beyond the Kondo physics. Similarities between the two compounds is also noticed in their temperature-field phase diagrams in spite of their thermodynamic distinctions in the thermal expansion and the Gr\"uneisen ratio, which are much more sensitive to Kondo hybridization than to geometrical frustration.

Triangular Kondo lattice in YbV6Sn6 and its quantum critical behavior in a magnetic field

We report on the magnetization, specific heat, and electrical resistivity for a newly discovered heavy-fermion (HF) compound, ${\mathrm{YbV}}_{6}{\mathrm{Sn}}_{6}$, which is crystallized in a hexagonal ${\mathrm{HfFe}}_{6}{\mathrm{Ge}}_{6}$-type structure, highlighted by the stacking of the triangular ytterbium sublattice and kagome vanadium sublattice. Above 2 K, ${\mathrm{YbV}}_{6}{\mathrm{Sn}}_{6}$ shows typical HF properties due to the Kondo effect on the Kramers doublet of ${\mathrm{Yb}}^{3+}$ ions in the crystalline electric field. A remarkable magnetic ordering occurs at ${T}_{\mathrm{N}}=0.40$ K in zero field, while a weak external field suppresses the ordering and induces non-Fermi-liquid behavior. In strong magnetic field, the compound shows a heavy Fermi-liquid state. ${\mathrm{YbV}}_{6}{\mathrm{Sn}}_{6}$ is represented as one of the few examples of Yb-based HF compounds hosting a triangular Kondo lattice on which a magnetic field induces quantum criticality near zero temperature.

Zero-Field Splitting in Hexacoordinate Co(II) Complexes

A collection of 24 hexacoordinate Co(II) complexes was investigated by ab initio CASSCF + NEVPT2 + SOC calculations. In addition to the energies of spin–orbit multiplets (Kramers doublets, KD) their composition of the spins is also analyzed, along with the projection norm to the effective Hamiltonian. The latter served as the evaluation of the axial and rhombic zero-field splitting parameters and the g-tensor components. The fulfilment of spin-Hamiltonian (SH) formalism was assessed by critical indicators: the projection norm for the first Kramers doublet N(KD1) &gt; 0.7, the lowest g-tensor component g1 &gt; 1.9, the composition of KDs from the spin states |±1/2&gt; and |±3/2&gt; with the dominating percentage p &gt; 70%, and the first transition energy at the NEVPT2 level 4Δ1. Just the latter quantity causes a possible divergence of the second-order perturbation theory and a failure of the spin Hamiltonian. The data set was enriched by the structural axiality Dstr and rhombicity Estr, respectively, evaluated from the metal–ligand distances Co-O, Co-N and Co-Cl corrected to the mean values. The magnetic data (temperature dependence of the molar magnetic susceptibility, and the field dependence of the magnetization per formula unit) were fitted simultaneously, either to the Griffith–Figgis model working with 12 spin–orbit kets, or the SH-zero field splitting model that utilizes only four (fictitious) spin functions. The calculated data were analyzed using statistical methods such as Cluster Analysis and the Principal Component Analysis.

ВЛИЯНИЕ ВНЕШНЕГО МАГНИТНОГО ПОЛЯ НА МАГНИТНЫЕ СВОЙСТВА КВАЗИОДНОМЕРНЫХ ХАЛДЕЙНОВСКИХ МАГНЕТИКОВ (Y1-XNDX)2BANIO5 (X = 0.25 И 0.04)

In the compounds of the (Y1-xNdx)2BaNiO5 family, the paradoxical coexistence of the Haldane phase and spin waves is realized. The magnetic ordering in the system is caused by the interaction of Nd3+ ions through spin fluctuations of a nickel chain, which remains internally disordered. Nd3+ magnetic moments do not deviate from the c axis of the crystal even in the presence of an external magnetic field. In this paper, for compounds (Y1-xNdx)2BaNiO5 with x = 0.25 and x = 0.04, an experimental study of the field dependence of the magnetization M(B) and the temperature dependence of the heat capacity C( T ), measured in fields B = 0; 2 and 5 T. For compounds with x = 0.25 on the dependence M(B) measured at T = 4.2 K, an anomaly was detected indicating a metamagnetic transition. Changes in the parameters of the magnetic interaction between the magnetic moments Nd along the c axis of the crystal leads to the periorientation of the magnetic moments of all Nd3+ ions along the direction of the external field B||c. For the connection with x = 0.04, no anomalies were detected on the dependence M(B), the magnetic moments of both neodymium sublattices lie along the direction of the applied magnetic field. The presence of a Schottky anomaly on the dependence C( T ) at B =0 indicates the existence of an internal magnetic field acting on the Nd3+ ion from the side of the nickel subsystem, and leading to the splitting of the main Kramers doublet of the Nd3+ ion. For a connection with x = 0.04, the Schottky anomaly shifts towards higher temperatures with an increase in the external magnetic field, and for a connection with x = 0.25, the Schottky anomaly shifts towards low temperatures only in the field B = 5 T. The displacement of the Schottky anomaly in the presence of a field is due to the ratio between the magnitude of the applied magnetic field and the component of the internal magnetic field fields с along the c axis of the crystal. For connection with x = 0.25 , the magnetic moments of the two neodymium sublattices are oppositely directed, and the Schottky anomaly of the 1st sublattice shifts towards higher temperatures, and the Schottky anomaly of the 2nd sublattice shifts towards lower temperatures. For connection with x = 0.04 с The magnetic moments of the two neodymium sublattices are directed towards the applied field, and the Schottky anomaly of both sublattices shifts towards higher temperatures, which is consistent with the experimen