Quantum Tunneling Of The Magnetization Research Articles

Elucidation of Dual Magnetic Relaxation Processes in Dinuclear Dysprosium(III) Phthalocyaninato Triple-Decker Single-Molecule Magnets Depending on the Octacoordination Geometry.

When applying single-molecule magnets (SMMs) to spintronic devices, control of the quantum tunneling of the magnetization (QTM) as well as a spin-lattice interactions are important. Attempts have been made to use not only coordination geometry but also magnetic interactions between SMMs as an exchange bias. In this manuscript, dinuclear dysprosium(III) (DyIII ) SMMs with the same octacoordination geometry undergo dual magnetic relaxation processes at low temperature. In the dinuclear DyIII phthalocyaninato (Pc2- ) triple-decker type complex [(Pc)Dy(ooPc)Dy(Pc)] (1) (ooPc2- =2,3,9,10,16,17,23,24-octakis(octyloxy)phthalocyaninato) with a square-antiprismatic (SAP) geometry, the ground state is divided by the Zeeman effect, and level intersection occurs when a magnetic field is applied. Due to the ground state properties of 1, since the Zeeman diagram where the levels intersect in an Hdc of 2500 Oe, two kinds of QTM and direct processes occur. However, dinuclear DyIII -Pc systems with C4 geometry, which have a twist angle (ϕ) of less than 45° do not undergo dual magnetic relaxation processes. From magnetic field and temperature dependences, the dual magnetic relaxation processes were clarified.

Nuclear Spin Isomers: Engineering a Et4N[DyPc2] Spin Qudit

Two dysprosium isotopic isomers were synthesized: Et4 N[163 DyPc2 ] (1) with I=5/2 and Et4 N[164 DyPc2 ] (2) with I=0 (where Pc=phthalocyaninato). Both isotopologues are single-molecule magnets (SMMs); however, their relaxation times as well as their magnetic hystereses differ considerably. Quantum tunneling of the magnetization (QTM) at the energy level crossings is found for both systems via ac-susceptibility and μ-SQUID measurements. μ-SQUID studies of 1(I=5/2) reveal several nuclear-spin-driven QTM events; hence determination of the hyperfine coupling and the nuclear quadrupole splitting is possible. Compound 2(I=0) shows only strongly reduced QTM at zero magnetic field. 1(I=5/2) could be used as a multilevel nuclear spin qubit, namely qudit (d=6), for quantum information processing (QIP) schemes and provides an example of novel coordination-chemistry-discriminating nuclear spin isotopes. Our results show that the nuclear spin of the lanthanide must be included in the design principles of molecular qubits and SMMs.

Nuclear Spin Isomers: Engineering a Et4N[DyPc2] Spin Qudit

AbstractTwo dysprosium isotopic isomers were synthesized: Et4N[163DyPc2] (1) with I=5/2 and Et4N[164DyPc2] (2) with I=0 (where Pc=phthalocyaninato). Both isotopologues are single‐molecule magnets (SMMs); however, their relaxation times as well as their magnetic hystereses differ considerably. Quantum tunneling of the magnetization (QTM) at the energy level crossings is found for both systems via ac‐susceptibility and μ‐SQUID measurements. μ‐SQUID studies of 1(I=5/2) reveal several nuclear‐spin‐driven QTM events; hence determination of the hyperfine coupling and the nuclear quadrupole splitting is possible. Compound 2(I=0) shows only strongly reduced QTM at zero magnetic field. 1(I=5/2) could be used as a multilevel nuclear spin qubit, namely qudit (d=6), for quantum information processing (QIP) schemes and provides an example of novel coordination‐chemistry‐discriminating nuclear spin isotopes. Our results show that the nuclear spin of the lanthanide must be included in the design principles of molecular qubits and SMMs.

Molecular Orientation of a Terbium(III)-Phthalocyaninato Double-Decker Complex for Effective Suppression of Quantum Tunneling of the Magnetization.

Single-molecule magnet (SMM) properties of crystals of a terbium(III)-phthalocyaninato double-decker complex with different molecular packings (1: TbPc2, 2: TbPc2·CH2Cl2) were studied to elucidate the relationship between the molecular packing and SMM properties. From single crystal X-ray analyses, the high symmetry of the coordination environment of 2 suggested that the SMM properties were improved. Furthermore, the shorter intermolecular Tb–Tb distance and relative collinear alignment of the magnetic dipole in 2 indicated that the magnetic dipole–dipole interactions were stronger than those in 1. This was confirmed by using direct current magnetic measurements. From alternating current magnetic measurements, the activation energy for spin reversal for 1 and 2 were similar. However, the relaxation time for 2 is three orders of magnitude slower than that for 1 in the low-T region due to effective suppression of the quantum tunneling of the magnetization. These results suggest that the SMM properties of TbPc2 highly depend on the molecular packing.

Conducting Molecular Nanomagnet of DyIII with Partially Charged TCNQ Radicals

Bifunctional electrically conducting single-molecule magnets are highly promising platforms for non-volatile memory devices and quantum computing applications. The development of these molecular materials, however, has largely been hindered by the lack of straightforward synthetic methods. Herein a facile and modular approach is demonstrated for the realization of bifunctional materials that does not require electrochemical or chemical oxidation to obtain partially charged organic radicals. Magnetic and electrical conductivity studies reveal that the DyIII compound exhibits slow relaxation of the magnetization between 5.0-8.0 K and semiconducting behavior over the range 180-350 K. DC magnetic fields have been found to suppress the quantum tunneling of the magnetization and affect the spin-canted antiferromagnetic interactions.

Investigation of thermalization in giant-spin models by different Lindblad schemes

The theoretical understanding of time-dependence in magnetic quantum systems is of great importance in particular for cases where a unitary time evolution is accompanied by relaxation processes. A key example is given by the dynamics of single-molecule magnets where quantum tunneling of the magnetization competes with thermal relaxation over the anisotropy barrier. In this article we investigate how good a Lindblad approach describes the relaxation in giant spin models and how the result depends on the employed operator that transmits the action of the thermal bath.

Homometallic DyIII Complexes of Varying Nuclearity from 2 to 21: Synthesis, Structure, and Magnetism

The synthesis, structure, and magnetic properties of four DyIII coordination compounds isolated as [Dy2 (LH2 )2 (μ2 -η1 :η1 -Piv)]Cl⋅2 MeOH⋅H2 O (1), [Dy4 (LH)2 (μ3 -OH)2 (Piv)4 (MeOH)2 ]⋅4 MeOH⋅2 H2 O (2), [Dy6 (LH2 )3 (tfa)3 (O3 PtBu)(Cl)3 ]Cl4 ⋅15.5 H2 O⋅4 MeOH⋅5 CHCl3 (3) and [Dy21 (L)7 (LH)7 (tfa)7 ]Cl7 ⋅15 H2 O⋅7 MeOH⋅12 CHCl3 (4) are reported (Piv=pivalate, tfa=1,1,1-trifluoroacetylacetone, O3 PtBu=tert-butylphosphonate). Among these, 3 displays an equilateral triangle topology with a side length of 9.541 Å and a rare pentagonal-bipyramidal Dy3+ environment, whereas complex 4 exhibits a single-stranded nanowheel structure with the highest nuclearity known for a homometallic lanthanide cluster structure. A tentative model of the dc magnetic susceptibility and the low-temperature magnetization of compounds 1 and 2 indicates that the former exhibits weak ferromagnetic intramolecular exchange interaction between the Dy3+ ions, whereas in the latter both intramolecular ferromagnetic and antiferromagnetic magnetic exchange interactions are present. Compounds 1, 3, and 4 exhibit frequency-dependent ac signals below 15 K at zero bias field, but without exhibiting any maximum above 2 K at frequencies up to 1400 Hz. The observed slow relaxation of the magnetization suggests that these compounds could exhibit single molecule magnet (SMM) behavior with either a thermal energy barrier for the reversal of the magnetization that is not high enough to block the magnetization above 2 K, or there exists quantum tunneling of the magnetization (QTM).

An air stable radical-bridged dysprosium single molecule magnet and its neutral counterpart: redox switching of magnetic relaxation dynamics.

A pair of related dinuclear lanthanide compounds, viz., [Dy(tmhd)3]2(bptz) (1) and {Cp2Co}{[Dy(tmhd)3]2(bptz)} (2) (tmhd = 2,2,6,6-tetramethyl-3,5-heptane dionate; bptz = 3,6-bis(2-pyridyl)-1,2,4,5-tetrazine) are reported. These molecules represent the first study of rare earth ions in which an organic ligand bridged species is isolated in both the neutral and radical anion forms. Both compounds exhibit out-of-phase signals below 4 K. The radical compound is highly air stable, with minimal changes in magnetic behavior after exposure to the atmosphere for two weeks.

Slow magnetisation relaxation in tetraoxolene-bridged rare earth complexes.

Three families of tetraoxolene-bridged dinuclear rare earth (RE) complexes have been synthesised and characterised, with general formula [((HB(pz)3)2RE)2(μ-tetraoxolene)] (HB(pz)3- = hydrotris(pyrazolyl)borate; tetraoxolene = chloranilate (1-RE), the dianionic form of 2,5-dihydroxy-1,4-benzoquinone (2-RE), or its 3,6-dimethyl analogue (3-RE)). In each case, the bridging tetraoxolene ligand is in the diamagnetic dianionic form and species with selected lanthanoid(iii) ions from Eu(iii) to Yb(iii) have been obtained, as well as the diamagnetic Y(iii) analogues. Use of the 3,6-dimethyl substituted tetraoxolene ligand (Me2-dhbq2-) has also afforded the two byproducts [((HB(pz)3)(MeOH)(B(OMe)4)Y)2(μ-Me2dhbq)] (4-Y) and [{((HB(pz)3)(MeOH)Y)2(μ-B(OMe)4)}2(μ-Me2dhbq)2]Cl2 (5-Y), with the B(OMe)4- ligands arising from partial decomposition of HB(pz)3-. Electrochemical studies on the soluble 1-RE and 3-RE families indicate multiple tetraoxolene-based redox processes. Magnetochemical and EPR studies of 3-Gd indicate the negligible magnetic coupling between the two Gd(iii) centres through the diamagnetic tetraoxolene bridge. Alternating current magnetic susceptibility studies of 1-Dy and 3-Dy reveal slow magnetic relaxation, with quantum tunnelling of the magnetisation (QTM) dominant in the absence of an applied dc field. The application of a dc field suppresses the QTM and relaxation data are consistent with an Orbach relaxation mechanism playing a major role in both cases, with effective energy barriers to magnetisation reversal determined as 47 and 24 K for 1-Dy and 3-Dy, respectively. The different dynamic magnetic behaviour evident for 1-Dy and 3-Dy arises from small differences in the local Dy(iii) coordination environments, highlighting the subtle structural effects responsible for the electronic structure and resulting magnetic behaviour.

Lanthanide Tetrazolate Complexes Combining Single-Molecule Magnet and Luminescence Properties: The Effect of the Replacement of Tetrazolate N3 by β-Diketonate Ligands on the Anisotropy Energy Barrier.

Three new sets of mononuclear Ln(III) complexes of general formulas [LnL3 ]⋅CH3 OH [Ln(III) =Yb (1), Er (2), Dy (3), Gd (4), and Eu (5)], [LnL2 (tmh)(CH3 OH)]⋅n H2 O⋅m CH3 OH [Ln(III) =Yb (1 b), Er (2 b), Dy (3 b), Gd (4 b)], and [LnL2 (tta)(CH3 OH)]⋅CH3 OH [Ln(III) =Yb (1 c), Er (2 c), Dy (3 c), Gd (4 c)] were prepared by the reaction of Ln(CF3 SO3 )⋅n H2 O salts with the tridentate ligand 2-(tetrazol-5-yl)-1,10-phenanthroline (HL) and, for the last two sets, additionally with the β-diketonate ligands 2,2,6,6-tetramethylheptanoate (tmh) and 2-thenoyltrifluoroacetonate (tta), respectively. In the [LnL3 ]⋅CH3 OH complexes the Ln(III) ions are coordinated to three phenanthroline tetrazolate ligands with an LnN9 coordination sphere. Dynamic ac magnetic measurements on 1-3 reveal that these complexes only exhibit single-molecule magnet (SMM) behavior when an external dc magnetic field is applied, with Ueff values of 11.7 K (1), 16.0 K (2), and 20.2 K (3). When the tridentate phenanthroline tetrazolate ligand is replaced by one molecule of methanol and the β-diketonate ligand tmh (1 b-3 b) or tta (1 c-3 c), a significant increase in Ueff occurs and, in the case of the Dy(III) complexes 3 b and 3 c, out-of-phase χ'' signals below 15 and 10 K, respectively, are observed in zero dc magnetic field. CASSCF+RASSI ab initio calculations performed on the Dy(III) complexes support the experimental results. Thus, for 3 the ground Kramers' doublet is far from being axial and the first excited state is found to be very close in energy to the ground state, so the relaxation barrier in this case is almost negligible. Conversely, for 3 b and 3 c, the ground Kramers' doublet is axial with a small quantum tunneling of the magnetization, and the energy difference between the ground and first Kramers' doublets is much higher, which allows these compounds to behave as SMMs at zero field. Moreover, these calculations support the larger Ueff observed for 3 b compared to 3 c. Additionally, the solid-state photophysical properties of 1, 2, 4, and 5 show that the phenanthroline tetrazolate ligand can act as an effective antenna to sensitize the characteristic Yb(III) , Er(III) , and Eu(III) emissions through an energy-transfer process.

The Frontier of Molecular Spintronics Based on Multiple-Decker Phthalocyaninato Tb(III) Single-Molecule Magnets.

Ever since the first example of a double-decker complex (SnPc2) was discovered in 1936, MPc2 complexes with π systems and chemical and physical stabilities have been used as components in molecular electronic devices. More recently, in 2003, TbPc2 complexes were shown to be single-molecule magnets (SMMs), and researchers have utilized their quantum tunneling of the magnetization (QTM) and magnetic relaxation behavior in spintronic devices. Herein, recent developments in Ln(III)-Pc-based multiple-decker SMMs on surfaces for molecular spintronic devices are presented. In this account, we discuss how dinuclear Tb(III)-Pc multiple-decker complexes can be used to elucidate the relationship between magnetic dipole interactions and SMM properties, because these complexes contain two TbPc2 units in one molecule and their intramolecular Tb(III)-Tb(III) distances can be controlled by changing the number of stacks. Next, we focus on the switching of the Kondo signal of Tb(III)-Pc-based multiple-decker SMMs that are adsorbed onto surfaces, their characterization using STM and STS, and the relationship between the molecular structure, the electronic structure, and the Kondo resonance of Tb(III)-Pc multiple-decker complexes.

Record High Single-Ion Magnetic Moments Through 4f(n)5d(1) Electron Configurations in the Divalent Lanthanide Complexes [(C5H4SiMe3)3Ln]⁻.

The recently reported series of divalent lanthanide complex salts, namely [K(2.2.2-cryptand)][Cp'3Ln] (Ln = Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm; Cp' = C5H4SiMe3) and the analogous trivalent complexes, Cp'3Ln, have been characterized via dc and ac magnetic susceptibility measurements. The salts of the complexes [Cp'3Dy](-) and [Cp'3Ho](-) exhibit magnetic moments of 11.3 and 11.4 μB, respectively, which are the highest moments reported to date for any monometallic molecular species. The magnetic moments measured at room temperature support the assignments of a 4f(n+1) configuration for Ln = Sm, Eu, Tm and a 4f(n)5d(1) configuration for Ln = Y, La, Gd, Tb, Dy, Ho, Er. In the cases of Ln = Ce, Pr, Nd, simple models do not accurately predict the experimental room temperature magnetic moments. Although an LS coupling scheme is a useful starting point, it is not sufficient to describe the complex magnetic behavior and electronic structure of these intriguing molecules. While no slow magnetic relaxation was observed for any member of the series under zero applied dc field, the large moments accessible with such mixed configurations present important case studies in the pursuit of magnetic materials with inherently larger magnetic moments. This is essential for the design of new bulk magnetic materials and for diminishing processes such as quantum tunneling of the magnetization in single-molecule magnets.

Influence of Guest Exchange on the Magnetization Dynamics of Dilanthanide Single-Molecule-Magnet Nodes within a Metal-Organic Framework.

Multitopic organic linkers can provide a means to organize metal cluster nodes in a regular three-dimensional array. Herein, we show that isonicotinic acid N-oxide (HINO) serves as the linker in the formation of a metal-organic framework featuring Dy2 single-molecule magnets as nodes. Importantly, guest solvent exchange induces a reversible single-crystal to single-crystal transformation between the phases Dy2(INO)4(NO3)2⋅2 solvent (solvent=DMF (Dy2-DMF), CH3CN (Dy2-CH3CN)), thereby switching the effective magnetic relaxation barrier (determined by ac magnetic susceptibility measurements) between a negligible value for Dy2-DMF and 76 cm(-1) for Dy2-CH3CN. Ab initio calculations indicate that this difference arises not from a significant change in the intrinsic relaxation barrier of the Dy2 nodes, but rather from a slowing of the relaxation rate of incoherent quantum tunneling of the magnetization by two orders of magnitude.

Influence of Guest Exchange on the Magnetization Dynamics of Dilanthanide Single‐Molecule‐Magnet Nodes within a Metal–Organic Framework

AbstractMultitopic organic linkers can provide a means to organize metal cluster nodes in a regular three‐dimensional array. Herein, we show that isonicotinic acid N‐oxide (HINO) serves as the linker in the formation of a metal–organic framework featuring Dy2 single‐molecule magnets as nodes. Importantly, guest solvent exchange induces a reversible single‐crystal to single‐crystal transformation between the phases Dy2(INO)4(NO3)2⋅2 solvent (solvent=DMF (Dy2‐DMF), CH3CN (Dy2‐CH3CN)), thereby switching the effective magnetic relaxation barrier (determined by ac magnetic susceptibility measurements) between a negligible value for Dy2‐DMF and 76 cm−1 for Dy2‐CH3CN. Ab initio calculations indicate that this difference arises not from a significant change in the intrinsic relaxation barrier of the Dy2 nodes, but rather from a slowing of the relaxation rate of incoherent quantum tunneling of the magnetization by two orders of magnitude.

Six-coordinate lanthanide complexes: slow relaxation of magnetization in the dysprosium(III) complex.

A series of six-coordinate lanthanide complexes {(H3O)[Ln(NA)2]⋅H2O}n (H2NA=5-hydroxynicotinic acid; Ln=Gd(III) (1⋅Gd); Tb(III) (2⋅Tb); Dy(III) (3⋅Dy); Ho(III) (4⋅Ho)) have been synthesized from aqueous solution and fully characterized. Slow relaxation of the magnetization was observed in 3⋅Dy. To suppress the quantum tunneling of the magnetization, 3⋅Dy diluted by diamagnetic Y(III) ions was also synthesized and magnetically studied. Interesting butterfly-like hysteresis loops and an enhanced energy barrier for the slow relaxation of magnetization were observed in diluted 3⋅Dy. The energy barrier (Δ(τ)) and pre-exponential factor (τ0) of the diluted 3⋅Dy are 75 K and 4.21×10(-5) s, respectively. This work illustrates a successful way to obtain low-coordination-number lanthanide complexes by a framework approach to show single-ion-magnet-like behavior.

ChemInform Abstract: Magnetic Cluster Excitations

AbstractReview: 354 refs.

Field‐Induced Hysteresis and Quantum Tunneling of the Magnetization in a Mononuclear Manganese(III) Complex

There is plenty of room at the bottom: A gap in the literature of molecular nanomagnets has been filled with the preparation of the first mononuclear manganese(III) complex exhibiting a slow relaxation of the magnetization, that is, a species with a single slow-relaxing, highly anisotropic MnIII ion, as confirmed by very low-temperature micro-SQUID magnetization and high-field EPR spectroscopic measurements (N blue, O red, Mn purple, Cl green).

Field‐Induced Hysteresis and Quantum Tunneling of the Magnetization in a Mononuclear Manganese(III) Complex

Field‐Induced Hysteresis and Quantum Tunneling of the Magnetization in a Mononuclear Manganese(III) Complex

Tuning Transverse Anisotropy in CoIII–CoII–CoIII Mixed-Valence Complex toward Slow Magnetic Relaxation

Two cobalt mixed-valence complexes with different substituents have been prepared and structurally characterized by single-crystal X-ray diffraction to alter slow magnetic relaxation by tailoring the transverse anisotropy. The trinuclear complexes [(L(1))4Co3(H2O)2](NO3)4·CH3OH·5H2O (1-NO3) and [(L(2))4Co3(H2O)2](NO3)4·6H2O (2-NO3) feature a distorted octahedral Co(II) strongly hindered in a trinuclear Co(III)-Co(II)-Co(III) mixed-valence array. Detailed magnetic studies of 1-NO3 and 2-NO3 have been conducted using direct- and alternating-current magnetic susceptibility data. In accordance with variable-field magnetic susceptibility data at low temperatures, high-field electron paramagnetic resonance (HF-EPR) spectroscopy reveals the presence of an easy-plane anisotropy (D > 0) with a significant transverse component, E, in complexes 1-NO3 and 2-NO3. These findings indicate that the onset of the variation of distortion within complex 2-NO3 leads to a suppression of quantum tunneling of the magnetization within the easy plane, resulting in magnetic bistability and slow relaxation behavior. Consequently, the anisotropy energy scale associated with the relaxation barrier, 5.46 cm(-1) (τo = 1.03 × 10(-5) s), is determined by the transverse E term. The results demonstrate that slow magnetic relaxation can be switched through optimization of the transverse anisotropy associated with magnetic ions that possess easy-plane anisotropy.

Quantum fluctuations and long-range order in molecular magnets

We review our studies of the effect of transverse fields on the susceptibility and magnetization of single crystals of the prototype single molecule magnet (SMM), Mn12-acetate, and of a new high-symmetry variant, Mn12-acetate–MeOH. SMM single crystals can exhibit long range ferromagnetic order associated with intermolecular dipole interactions. Transverse fields increase quantum spin fluctuation and quantum tunneling of the magnetization suppressing long range order. However, we have found that suppression of the Curie temperature by a transverse field in Mn12-acetate is far more rapid than predicted by the Transverse-Field Ising Ferromagnetic Model (TFIFM). It appears that solvent disorder in Mn12-acetate that results in an intrinsic distribution of small discrete tilts of the molecular magnetic easy axis from the global easy axis of the crystal (≈±1°) gives rise to a distribution of random-fields that further suppresses long-range order. Semiquantitative agreement with the predictions of a Random-Field Ising Ferromagnet Model is found. Subsequent susceptibility studies we have conducted of the high symmetry Mn12 variant, Mn12-acetate–MeOH, with the same spin structure and similar lattice constants but without the same solvent disorder as Mn12-acetate, agrees with the TFIFM. An important implication of our studies is that long-range order in these two chemically very similar SMMs are described by distinct physical models.