Quantum Tunneling Of The Magnetization Research Articles

Exchange-biased quantum tunneling of magnetization in a nanomagnetic dimer via a Josephson current

We investigate a Josephson junction where the weak link consists of a nanomagnetic dimer, featuring two large, antiferromagnetically coupled spins under simple easy-axis anisotropy. In this setup, the exchange coupling constant serves as a transverse anisotropy constant, and the quantum tunneling of the magnetization is influenced by the supercurrent, which behaves like an external magnetic field applied along the hard axis. Our results demonstrate that the superconducting current induces non-Kramers freezing and unfreezing of the magnetic moment’s tunneling within a biaxial spin model driven by exchange interaction. We derive an exact expression for the quenching condition caused by the exchange coupling. Additionally, we extend our analysis to tunneling phenomena in two antiferromagnetically or ferromagnetically coupled spins biased by the anisotropic exchange interaction, revealing more varied cases of tunnel splitting.

Quantum Tunneling of the Magnetization in Systems with Anisotropic 4f Ion Pairs: Rates from Low-Temperature Zero-Field Relaxation.

Anisotropic open shell 4f ions have magnetic moments that can be read and written as atomic bits. If it comes to quantum applications where the phase of the wave function has to be written, controlled, and read, it is advantageous to rely on more than one atom that carries the quantum information on the system because states with different susceptibilities may be addressed. Such systems are realized for pairs of lanthanides in single-molecule magnets, where four pseudospin states are found and mixed in quantum tunneling processes. For the case of endohedral fullerenes like Dy2S@C82 or Tb2ScN@C80, the quantum tunneling of the magnetization is imprinted in the magnetization lifetimes at sub-Kelvin temperatures. A (4 × 4) Hamiltonian that includes quantum tunneling of the magnetization and the dipole and exchange interaction between the two lanthanide magnetic moments predicts the lifting of the zero-field ground state degeneracy and nonlinear coupling to magnetic fields in such systems.

Record Quantum Tunneling Time in an Air-Stable Exchange-Bias Dysprosium Macrocycle.

In recent years, dysprosium macrocycle single-molecule magnets (SMMs) have received increasing attention due to their excellent air/thermal stability, strong magnetic anisotropy, and rigid molecular skeleton. However, they usually display fast zero-field quantum tunneling of the magnetization (QTM) rate, severely hindering their data storage applications. Herein, we report the design, synthesis, and characterization of an air-stable monodecker didysprosium macrocycle integrating strong single-ion anisotropy, near-perfect local crystal field (CF) symmetry, and efficient exchange bias. These indispensable features enable clear-cut elucidation of the crucial role of very weak antiferromagnetic coupling on magnetization dynamics, creating a prominent SMM with a large effective energy barrier (Ueff) of 670 cm-1, open hysteresis loops at zero field up to 14.9 K, and a record relaxation time of QTM (τQTM), 24281 s, for all known nonradical-bridged lanthanide SMMs.

Modulating the Magnetic Dynamics of Five‐Coordinate DyIII Single‐Molecule Magnets by the Substitution Effect on the Axial Ligand

AbstractTwo five‐coordinate mononuclear DyIII single‐molecule magnets [(TrapenTMS)Dy(L)] (Trapen=tris(2‐aminobenzyl) amine; TMS=SiMe3; L=OPMe3 1, OPEt3 2) have been synthesized by the reaction of [(TrapenTMS)Dy(THF)] and OPMe3, OPEt3, respectively. The molecular structures of 1 and 2 were fully established by single crystal X‐ray diffraction. The centre DyIII ions of both complexes exhibit distorted triangular bipyramid geometries, varying with different neutral ligands L on the apex. The TrapenTMS ligand forms the pyramid base of the trigonal bipyramid. Subtle structural modifications of the axial O‐ligand terminal substituent result in different dynamic magnetic behaviors. Magnetic data analysis reveals that 1 and 2 exhibit the characteristic behavior of SMM without a dc field, accompanying an unambiguous quantum tunneling of the magnetization. Field‐induced slow magnetic relaxation was observed for 1 and 2 under an applied bias dc field of 1000 Oe, the relaxation energy barriers are 107 K and 88 K for 1 and 2, respectively. We have investigated the differences in magnetism and magnetic anisotropy between the two complexes by ab initio calculations.

Vibronic effects on the quantum tunnelling of magnetisation in Kramers single-molecule magnets

Single-molecule magnets are among the most promising platforms for achieving molecular-scale data storage and processing. Their magnetisation dynamics are determined by the interplay between electronic and vibrational degrees of freedom, which can couple coherently, leading to complex vibronic dynamics. Building on an ab initio description of the electronic and vibrational Hamiltonians, we formulate a non-perturbative vibronic model of the low-energy magnetic degrees of freedom in monometallic single-molecule magnets. Describing their low-temperature magnetism in terms of magnetic polarons, we are able to quantify the vibronic contribution to the quantum tunnelling of the magnetisation, a process that is commonly assumed to be independent of spin-phonon coupling. We find that the formation of magnetic polarons lowers the tunnelling probability in both amorphous and crystalline systems by stabilising the low-lying spin states. This work, thus, shows that spin-phonon coupling subtly influences magnetic relaxation in single-molecule magnets even at extremely low temperatures where no vibrational excitations are present.

Magnetic properties and magnetocaloric effect of Ln = Dy, Tb carborane-based metal-organic frameworks.

We present the synthesis and magneto-thermal properties of carborane-based lanthanide metal-organic frameworks (MOFs) with the formula {[(Ln)3(mCB-L)4(NO3)(DMF)n]·Solv}, where Ln = Dy or Tb, characterized by dc and ac susceptibility, X-ray absorption spectroscopy (XAS), X-ray magnetic circular dichroism (XMCD) and heat capacity measurements. The MOF structure is formed by polymeric 1D chains of Ln ions with three different coordination environments (Ln1, Ln2, Ln3) running along the b-axis, linked by carborane-based linkers thus to provide a 3D structure. Static magnetic measurements reveal that these MOFs behave at low temperature as a system of S* = 1/2 Ising spins, weakly interacting ferromagnetically along the 1D polymeric chain (J*/kB = +0.45 K (+0.5 K) interaction constant estimated for Dy-MOF (Tb-MOF)) and coupled to Ln ions in adjacent chains through dipolar antiferromagnetic interactions. The Dy MOF exhibits slow relaxation of magnetization through a thermally activated process, transitioning to quantum tunneling of the magnetization at low temperatures, while both compounds exhibit field-induced relaxation through a very slow, direct process. The maximum magnetic entropy changes (-ΔSmaxm) for an applied magnetic field change of 2-0 T are 5.71 J kg-1 K-1 and 4.78 J kg-1 K-1, for Dy and Tb MOFs, respectively, while the magnetocaloric effect (MCE) peak for both occurs at T ∼ 1.6 K, approximately double that for the Gd counterpart.

Proof-of-Concept Quantum Simulator Based on Molecular Spin Qudits.

The use of d-level qudits instead of two-level qubits can largely increase the power of quantum logic for many applications, ranging from quantum simulations to quantum error correction. Magnetic molecules are ideal spin systems to realize these large-dimensional qudits. Indeed, their Hamiltonian can be engineered to an unparalleled extent and can yield a spectrum with many low-energy states. In particular, in the past decade, intense theoretical, experimental, and synthesis efforts have been devoted to develop quantum simulators based on molecular qubits and qudits. However, this remarkable potential is practically unexpressed, because no quantum simulation has ever been experimentally demonstrated with these systems. Here, we show the first prototype quantum simulator based on an ensemble of molecular qudits and a radiofrequency broadband spectrometer. To demonstrate the operativity of the device, we have simulated quantum tunneling of the magnetization and the transverse-field Ising model, representative of two different classes of problems. These results represent an important step toward the actual use of molecular spin qudits in quantum technologies.

The slow magnetic relaxation in Dy-phthalocyanine single-molecule magnet induced by CH2Cl2 solvent molecules

DyPc2 and DyPc2•CH2Cl2 were prepared using the solvent thermal method. The x-ray diffractometer and the Fourier transform infrared spectrometer were used to explore the structure changes between DyPc2 and DyPc2•CH2Cl2. The results clearly demonstrate that the CH2Cl2 molecule can alter the crystal structures and, thus, change the molecular stacking structures of DyPc2 without destroying molecular integrity. Geometry optimization further proved that DyPc2 belongs to the space group P212121, while DyPc2•CH2Cl2 crystallizes in the space group Pnma. It is clearly demonstrated that the different molecular environment affects the structure of a single DyPc2 molecule to some extent, such as the twist angles of two Pc rings and the Pc−Dy−Pc angles. The molar magnetic susceptibility and hysteresis loops for DyPc2 and DyPc2•CH2Cl2 were also measured and compared. The negative Weiss constants were obtained by the Curie−Weiss law fitting above 50 K. The hysteresis loop for DyPc2•CH2Cl2 is wider than that of DyPc2, implying that the magnetic relaxation of DyPc2 slowed down, while quantum tunneling of the magnetization is prevented efficiently after absorbing CH2Cl2 molecules. This work clarifies the correlation between the molecular environment and magnetism of single-molecule magnets, which is helpful for their design guideline and future applications.

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.

Magnetic Anisotropy of Single-Ion Magnet (PPh4)2 [ReF6]·2H2O

Studying of single-molecule magnets has sprung many surprises such as, e.g., quantum tunneling of the magnetization, which is strongly related to the presence of a magnetic anisotropy. Electron spin resonance and inelastic neutron scattering measurements of (PPh4)2[ReF6]⋅2H2O complex evidence an unprecedented large single-site magnetic anisotropy of D sim 35 K in this material. Using state-of-the-art ab initio calculations we found that the single-ion anisotropy is indeed very large (but does not exceed 12 K) and revealed the physical mechanism lying behind this phenomenon.

Ligand Modulation of the Structures and Magnetic Relaxation in Triangular Dy3 Complexes Based on a Tricompartmental Scaffold.

Using a novel tricompartmental hydrazone ligand, a set of trinuclear Dy3 complexes has been isolated and structurally characterized. Complexes Dy3 ⋅ Cl, Dy3 ⋅ Br, and Dy3 ⋅ ClO4 feature a similar overall topology but different anions (Cl- , Br- , or ClO4 - ) in combination with exogenous OH- and solvent co-ligands, which is found to translate into very different magnetic properties. Complex Dy3 ⋅ Cl shows a double relaxation process with fast quantum tunneling of the magnetization, probably related to the structural disorder of μ2 -OH- and μ2 -Cl- co-ligands. Relaxation of the magnetization is slowed down for Dy3 ⋅ Br and Dy3 ⋅ ClO4 , which do not show any structural disorder. In particular, fast quantum tunneling is suppressed in case of Dy3 ⋅ ClO4 , resulting in an energy barrier of 341 K and magnetic hysteresis up to 3.5 K; this makes Dy3 ⋅ ClO4 one of the most robust air-stable trinuclear SMMs. Magneto-structural relationships of the three complexes are analyzed and rationalized with the help of CASSCF/RASSI-SO calculations.

Tuning Quantum Tunneling in Isomorphic {MII2DyIII2} “Butterfly” System via 3d-4f Magnetic Interaction

In order to probe the magnetic relaxation mechanism of 3d-4f complexes systematically, two “Butterfly” MII2DyIII2 complexes related to our previously reported butterfly compound, [Zn2Dy2(L)4(Ac)2(DMF)2]·4CH3CN (1), and formulated as [Co2Dy2(L)4(Ac)2(DMF)2]·3CH3CN (2) and [Ni2Dy2(L)4(Ac)2(DMF)2]·3CH3CN (3) are prepared and characterized. In comparison to complex 1, the replacement of CoII or NiII with ZnII led to the effective quenching of quantum tunneling of the magnetization (QTM) in complexes 2 and 3. Obviously, the introduction of 3d-4f spin–spin exchange can be important in determining the overall magnetic behaviors of 3d-4f {MII2DyIII2} “Butterfly” systems.

Strong Axiality in a Dysprosium(III) Bis(borolide) Complex Leads to Magnetic Blocking at 65 K.

Substituted dysprosocenium complexes of the type [Dy(CpR)2]+ exhibit slow magnetic relaxation at cryogenic temperatures and have emerged as top-performing single-molecule magnets. The remarkable properties of these compounds derive in part from the strong axial ligand field afforded by the cyclopentadiene anions, and the design of analogous compounds with even stronger ligand fields is one promising route toward identifying new single-molecule magnets that retain a magnetic memory at even higher temperatures. Here, we report the synthesis and characterization of a dysprosium bis(borolide) compound, [K(18-crown-6)][Dy(BC4Ph5)2] (1), featuring the dysprosocenate anion [Dy(BC4Ph5)2]- with a pseudoaxial coordination environment afforded by two dianionic pentaphenyl borolide ligands. Variable-field magnetization data reveal open magnetic hysteresis up to 66 K, establishing 1 as a top-performing single-molecule magnet among its dysprosocenium analogues. Ac magnetic susceptibility data indicate that 1 relaxes via an Orbach mechanism above ∼80 K with Ueff = 1500(100) cm-1 and τ0 = 10-12.0(9) s, whereas Raman relaxation and quantum tunneling of the magnetization dominate at lower temperatures. Compound 1 exhibits a 100 s blocking temperature of 65 K, among the highest reported for dysprosium-based single-molecule magnets. Ab initio spin dynamics calculations support the experimental Ueff and τ0 values and enable a quantitative comparison of the relaxation dynamics of 1 and two representative dysprosocenium cations, yielding additional insights into the impact of the crystal field splitting and vibronic coupling on the observed relaxation behavior. Importantly, compound 1 represents a step toward the development of alternatives to substituted dysprosocenium single-molecule magnets with increased axiality.

Single-Ion Magnets with Giant Magnetic Anisotropy and Zero-Field Splitting.

The design of mononuclear molecular nanomagnets exhibiting a huge energy barrier to the reversal of magnetization have seen a surge of interest during the last few decades due to their potential technological applications. More specifically, single-ion magnets are peculiarly attractive by virtue of their rich quantum behavior and distinct fine structure. These are viable candidates for implementation as single-molecule high-density information storage devices and other applications in future quantum technologies. The present review presents the comprehensive state of the art in the topic of single-ion magnets possessing an eminent magnetization-reversal barrier, very slow magnetic relaxation and high blocking temperature. We turn our attention to the achievements in the synthesis of 3d and 4f single-ion magnets during the last two decades and discuss the observed magnetostructural properties underlying the anisotropy behavior and the ensuing remanence. Furthermore, we highlight the fundamental theoretical aspects to shed light on the complex behavior of these nanosized magnetic entities. In particular, we focus on key notions, such as zero-field splitting, anisotropy energy and quantum tunneling of the magnetization and their interdependence.

Two monofluoride-bridged DyIII dimers with different magnetization dynamics

As a monoatomic bridge, fluoride ion can transmit efficient magnetic interaction between lanthanide ions but its effect on tuning the magnetization dynamics has not been well understood. Herein, two monofluoride-bridged dinuclear dysprosium complexes [Dy2F(bbpen)2(EtOH)2]Br·EtOH (1) and [Dy2F(bbppy)2]Br·2EtOH (2) with Dy-F-Dy angles of ∼178° and their diamagnetic-ion diluted analogues 1´ and 2´ were synthesized. Magnetic studies reveal that 1 and 1´ barely show any magnetization dynamics, but 2 and 2´ exhibit strong magnetization dynamics. Systematical experimental analysis combined with ab initio calculations reveals that the different magnetization dynamics between 1 and 2 mainly originate from the effect of magnetic anisotropy by terminal ligand and bridging group of the chelating ligand, and the fluoride bridge can effectively suppress the quantum tunneling of the magnetization and turn on Orbach process in 2.

Series of Benzoquinone-Bridged Dicobalt(II) Single-Molecule Magnets.

Mononuclear complexes within a particular coordination geometry have been well recognized for high-performance single-molecule magnets (SMMs), while the incorporation of such well-defined geometric ions into multinuclear complexes remains less explored. Using the rigid 2-(di(1H-pyrazol-1-yl)methyl)-6-(1H-pyrazol-1-yl)pyridine (PyPz3) ligand, here, we prepared a series of benzoquinone-bridged dicobalt(II) SMMs [{(PyPz3)Co}2(L)][PF6]2, (1, L = 2,5-dioxo-1,4-benzoquinone (dhbq2-); 2, L = chloranilate (CA2-); and 3, L = bromanilate (BA2-)), in which each Co(II) center adopts a distorted trigonal prismatic (TPR) geometry and the distortion increases with the sizes of 3,6-substituent groups (H (1) < Cl (2) < Br (3)). Accordingly, the magnetic study revealed that the axial anisotropy parameter (D) of the Co ions decreased from -78.5 to -56.5 cm-1 in 1-3, while the rhombic one (E) increased significantly. As a result, 1 exhibited slow relaxation of magnetization under a zero dc field, while both 2 and 3 showed only the field-induced SMM behaviors, likely due to the increased rhombic anisotropy that leads to the serious quantum tunneling of the magnetization. Our study demonstrated that the relaxation dynamics and performances of a multinuclear complex are strongly dependent on the coordination geometry of the local metal ions, which may be engineered by modifying the substituent groups.

Photophysical Properties and Single‐Molecule Magnet Behavior in Heterobimetallic 3d4 f Schiff Base Complexes

AbstractThree new heterobimetallic Schiff base complexes of formula [(LZnCl)2Gd(H2O)](ZnCl4)0.5 (2), [(LZn(OH))(LZnCl)Sm(H2O)](ZnCl4)0.5 (3) and [(LZnCl0.5(OH)0.5)(LZnCl)Dy(H2O)](ZnCl4)0.5 (4) were designed from the reaction of the metallo‐ligand ZnL (1) (H2L=N, N′‐bis(3‐methoxysalicylaldiimine)‐1,3‐propylene‐2‐ol) and lanthanide salt in a ratio 1 to 1. The crystallographic structures of 2–4 were resolved by single crystal X‐ray diffraction. Light irradiation allowed the observation of a broad emission centered on the organic ligand which is exalted upon Zn(II) coordination. 1 is able to act as a metallo‐organic chromophore for the sensitization of the Sm(III) luminescence. Finally the Dy(III) derivative displayed Single‐Molecule Magnet (SMM) behavior with an opening of the hysteresis loop up to 5 K and a magnetic relaxation operating through Orbach, Raman and Quantum Tunneling of the Magnetization (QTM) at 0 Oe while under an applied magnetic field the QTM is efficiently cancelled.

Luminescent and Sublimable Binaphthyl-Based Field-Induced Lanthanide Single-Molecule Magnets

The association of the [Ln(hfac)3(H2O)2] metallic building blocks with the new ligand [1,1’-binaphthalene]-8,8’-diylbis(diphenylphosphine oxide) (L) led to the formation of three mononuclear complexes of formula [Ln(hfac)3(L)] (LnIII = Eu (1), Dy (2) and Yb (3)). The mononuclear character of the compounds is due to the bidentate coordination mode adopted by L to link the metal. L allows the observation of the characteristic visible 5D0  7FJ (J = 0-4) EuIII- and near infrared 2F5/2  2F7/2 YbIII- emissions while 2 is only weakly emissive due to the mismatch between the energy positions of the triplet excited state of the ligand and DyIII emissive state. The magnetic data reveal a field-induced Single-Molecule Magnet (SMM) behavior for 2 and 3 with an efficient suppression of the Quantum Tunneling of the Magnetization (QTM). The slow magnetic relaxation occurs through a Raman process while the Orbach contribution is discarded as confirmed by the correlation with the MJ states energy splitting provided by the luminescence spectrum of 3.

Switching the coordination geometry to enhance erbium(III) single-molecule magnets

Two erbium(III) complexes [ErCl(OArAd)3][Na(THF)6] (1) and Er(OArAd)3 (2) are successfully prepared by using one variety of "hard" base ligand with large steric hindrance. The coordination geometry around the Er(III) site changes from distorted tetrahedral to flat trigonal pyramid geometry in different solvent environment due to the removal of the coordinated chloride. Such an alternation significantly enhances the single-molecule magnet (SMM) behavior and makes the field-induced effective energy barrier (Ueff) arrive at 43(1) cm−1 for the latter. Together with theoretical calculations, this study shows that strong equatorial ligand field and high local symmetry are critical to suppress the quantum tunneling of the magnetization (QTM) and achieve high-performance erbium(III) based SMMs.

Exchange-Bias Quantum Tunneling of the Magnetization in a Dysprosium Dimer.

Single-molecule magnets (SMMs) have been shown to possess bewildering phenomena leading to their proposal in several futuristic applications ranging from data storage devices to the basic unit of quantum computers. The main characteristic for the proposal of SMMs in such schemes is their inherent and intriguing quantum mechanical properties, which in turn, could be exploited in novel devices with larger capacities, such as for data storage or enhanced properties, such as quantum computers. In the quest of SMMs displaying such intriguing quantum effects, herein, we explore the synthesis, structural, and magnetic characterization of a dimeric dysprosium-based SMM composed of a tetradentate Schiff-base ligand with formula [Dy2(HL)2(benz)2(NO3)2]. Magnetic studies show that the complex is an SMM, while sub-Kelvin μ-SQUID studies revealed the exchange-bias characteristics of the system attributed to the presence of exchange interaction between the Dy3+ pair.