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Advances in relaxation and memory effects of magnetic nanoparticles for biomedical applications

Functionalized magnetic nanoparticles are pivotal in magnetic resonance imaging, computed tomography, controlled drug delivery, and hyperthermia treatments due to their exceptional magnetic relaxation and functional properties. The magnetic core composition and structure significantly affects the complex magnetic properties of these nanoparticles necessitating a thorough examination of magnetism fundamentals related to these systems. One important aspect is the ability of magnetic nanoparticles to retain previous magnetic state configurations known as memory effect, primarily governed by domain structure and magnetic anisotropy. Despite its relevance to advanced applications, comprehensive studies on magnetic relaxation and memory effects remain limited. Here, the present review aims to bridge this gap by investigating relaxation mechanisms, synthesis strategies, and applications, fostering further innovation. It investigates the memory effects and their dependence on particle composition and morphology along with key synthesis techniques for large-scale production in industrial adoption. Structured into focused sections on magnetic properties and their influence on biomedical and technological applications, this review provides essential insights into memory effects, magneto-relaxation mechanisms, influencing factors, and both experimental and theoretical methodologies. It also delves into computational modelling and AI-driven design, which are revolutionizing the prediction, discovery, and optimization of materials with tailored properties.

36 MATERIALS SCIENCE↗

Magnetic flux relaxation in YBa2Cu3O(7-x) thin film: Thermal or athermal

The magnetic flux relaxation behavior of YBa2Cu3O(7-x) thin film on LaAlO3 for H parallel c was studied in the range of 4.2-40 k and 0.2-1.0 T. Both the normalized flux relaxation rate (S) and the net flux pinning energy (U) increase continuously from 1.3 x 10 exp -2 to 3.0 x 10 exp -2 and from 70-240 meV respectively, as the temperature (T) increases from 10 to 40 K. This behavior is consistent with the thermally activated flux motion model. At low temperatures, however, S is found to decrease much more slowly as compared with kT, in contradiction to the thermal activation model. This behavior is discussed in terms of the athermal quantum tunneling of flux lines. The magnetic field dependence of U, however, is not completely understood.

Vitta, Satish↗

Magnetic flux relaxation in YBa2Cu3)(7-x) thin film: Thermal or athermal

The magnetic flux relaxation behavior of YBa2Cu3O(7-x) thin film on LaAlO3 for H is parallel to c was studied in the range 4.2 - 40 K and 0.2 - 1.0 T. Both the normalized flux relaxation rate S and the net flux pinning energy U increase continuously from 1.3 x 10(exp -2) to 3.0 x 10(exp -2) and from 70 to 240 meV respectively, as the temperature T increases from 10 to 40 K. This behavior is consistent with the thermally activated flux motion model. At low temperatures, however, S is found to decrease much more slowly as compared with kT, in contradiction to the thermal activation model. This behavior is discussed in terms of the athermal quantum tunneling of flux lines. The magnetic field dependence of U, however, is not completely understood.

Vitta, Satish↗

Strong Ferromagnetic Exchange Coupling and Single-Molecule Magnetism in MoS 4 3– -Bridged Dilanthanide Complexes

We report the synthesis and characterization of the trinuclear 4d-4f compounds [Co(C 5 Me 5 ) 2 ][(C 5 Me 5 ) 2 Ln(μ-S) 2 Mo(μ-S) 2 Ln(C 5 Me 5 ) 2 ], 1-Ln (Ln = Y, Gd, Tb, Dy), containing the highly polarizable MoS 4 3 - bridging unit. UV-Vis-NIR diffuse reflectance spectra and DFT calculations of 1-Ln reveal a low-energy metal-to-metal charge transfer transition assigned to charge transfer from the singly occupied 4d z 2 orbital of Mo V to the empty 5d orbitals of the lanthanides (4d in the case of 1-Y ), mediated by sulfur-based 3p orbitals. Electron paramagnetic resonance spectra collected for 1-Y in a tetrahydrofuran solution show large 89 Y hyperfine coupling constants of A ⊥ = 23 MHz and A || = 26 MHz, indicating the presence of significant yttrium-localized unpaired electron density. Magnetic susceptibility data support similar electron delocalization and ferromagnetic Ln-Mo exchange for 1-Gd , 1-Tb , and 1-Dy . This ferromagnetic exchange gives rise to an S = 15/2 ground state for 1-Gd and one of the largest magnetic exchange constants involving Gd III observed to date, with J Gd-Mo = +16.1(2) cm -1 . Additional characterization of 1-Tb and 1-Dy by ac magnetic susceptibility measurements reveals that both compounds exhibit slow magnetic relaxation. Although a Raman magnetic relaxation process is dominant for both 1-Tb and 1-Dy , an extracted thermal relaxation barrier of U eff = 68 cm -1 for 1-Dy is the largest yet reported for a complex containing a paramagnetic 4d metal center. Furthermore, these results provide a potentially generalizable route to enhanced n d-4f magnetic exchange, revealing opportunities for the design of new n d-4f single-molecule magnets and bulk magnetic materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Nuclear Magnetic Resonance Relaxation Pathways in Electrolytes for Energy Storage

Nuclear Magnetic Resonance (NMR) spin relaxation times have been an instrumental tool in deciphering the local environment of ionic species, the various interactions they engender and the effect of these interactions on their dynamics in conducting media. Of particular importance has been their application in studying the wide range of electrolytes for energy storage, on which this review is based. Here we highlight some of the research carried out on electrolytes in recent years using NMR relaxometry techniques. Specifically, we highlight studies on liquid electrolytes, such as ionic liquids and organic solvents; on semi-solid-state electrolytes, such as ionogels and polymer gels; and on solid electrolytes such as glasses, glass ceramics and polymers. Although this review focuses on a small selection of materials, we believe they demonstrate the breadth of application and the invaluable nature of NMR relaxometry.

25 ENERGY STORAGE↗

Magnetic field dependence of low-energy magnons, anisotropic heat conduction, and spontaneous relaxation of magnetic domains in the cubic helimagnet ZnCr 2 Se 4

Here, anisotropic low-temperature properties of the cubic spinel helimagnet ZnCr 2 Se 4 in the single-domain spin-spiral state are investigated by a combination of neutron scattering, thermal conductivity, ultrasound velocity, and dilatometry measurements. In an applied magnetic field, neutron spectroscopy shows a complex and nonmonotonic evolution of the spin-wave spectrum across the quantum-critical point that separates the spin-spiral phase from the field-polarized ferromagnetic phase at high fields. A tiny spin gap of the pseudo-Goldstone magnon mode, observed at wave vectors that are structurally equivalent but orthogonal to the propagation vector of the spin helix, vanishes at this quantum critical point, restoring the cubic symmetry in the magnetic subsystem. The anisotropy imposed by the spin helix has only a minor influence on the lattice structure and sound velocity but has a much stronger effect on the heat conductivities measured parallel and perpendicular to the magnetic propagation vector. The thermal transport is anisotropic at T≲ 2K, highly sensitive to an external magnetic field, and likely results directly from magnonic heat conduction. We also report long-time thermal relaxation phenomena, revealed by capacitive dilatometry, which are due to magnetic domain motion related to the destruction of the single-domain magnetic state, initially stabilized in the sample by the application and removal of magnetic field. Our results can be generalized to a broad class of helimagnetic materials in which a discrete lattice symmetry is spontaneously broken by the magnetic order.

36 MATERIALS SCIENCE↗

Coexistence of metamagnetism and slow relaxation of magnetization in ammonium hexafluoridorhenate

The (NH 4 ) 2 [ReF 6 ] (1) salt was studied by X-ray diffraction, Raman spectroscopy, theoretical calculations, and magnetic measurements. 1 crystallizes in the trigonal space group P$\overline{3}$m1 (Re–F = 1.958(5) Å). In the Raman spectrum of 1, splitting of the observed peaks was observed and correlated to the valence frequencies of vibration of the [ReF 6 ] 2– anion. The study of the magnetic properties of 1, through DC and AC magnetic susceptibility measurements, reveals the coexistence of metamagnetism and slow relaxation of magnetization at low temperature, which is unusual in the molecular systems based on the paramagnetic 5d metal ions reported so far.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Molecular Modes Elucidate the Nuclear Magnetic Resonance Relaxation of Viscous Fluids

The Bloembergen, Purcell, and Pound (BPP) theory of nuclear magnetic resonance (NMR) relaxation in fluids dating back to 1948 continues to be the linchpin in interpreting NMR relaxation data in applications ranging from characterizing fluids in porous media to medical imaging (MRI). The BPP theory is founded on assuming molecules are hard spheres with 1 H– 1 H dipole pairs reorienting randomly; assumptions that are severe in light of modern understanding of liquids. Nevertheless, it is intriguing to this day that the BPP theory was consistent with the original experimental data for glycerol, a hydrogen-bonding molecular fluid for which the hard-sphere-rigid-dipole assumption is inapplicable. To better understand this incongruity, atomistic molecular simulations are used to compute 1 H NMR T 1 relaxation dispersion (i.e., frequency dependence) in two contrasting cases: glycerol, and a (non hydrogen-bonding) viscosity standard. At high viscosities, simulations predict distinct functional forms of T 1 for glycerol compared to the viscosity standard, in agreement with modern measurements, yet both in contrast to BPP theory. The cause of these departures from BPP theory is elucidated, without assuming any relaxation models and without any free parameters, by decomposing the simulated T 1 response into dynamic molecular modes for both intramolecular and intermolecular interactions. The decomposition into dynamic molecular modes provides an alternative framework to understand the physics of NMR relaxation for viscous fluids.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Reconsidering spin-phonon relaxation in magnetic molecules

Because of the larger intra-molecular distortion, optical phonons usually have stronger spin-phonon coupling than acoustic phonons in molecular magnets. This property may pose problems to the theory of spin relaxation in ordinary paramagnetic materials, which have served as the basis for the understanding of spin dynamics in molecular magnets for decades. In this review, we explain why the Raman processes driven by optical phonons can play a dominant role at low temperature and provide unconventional dependence between relaxation time and temperature. Especially, we emphasize that the sub-barrier relaxation and anomalously low Raman exponents are two common signatures of the dominance. Here, we also present the algorithm and implementation for calculating spin-phonon relaxation in molecular solids with density functional theory codes.

36 MATERIALS SCIENCE↗

Strong Electronic and Magnetic Coupling in M 4 (M = Ni, Cu) Clusters via Direct Orbital Interactions between Low-Coordinate Metal Centers

In this report we present an extensive study of tetranuclear transition-metal cluster compounds M 4 (NP t Bu 3 ) 4 and [M 4 (NP t Bu 3 ) 4 ][B(C 6 F 5 ) 4 ] (M = Ni, Cu; t Bu = tert -butyl), which feature low-coordinate metal centers and direct metal-metal orbital overlap. X-ray diffraction, electrochemical, magnetic, spectroscopic, and computational analysis elucidate the nature of the bonding interactions in these clusters and the impact of these interactions on the electronic and magnetic properties. Direct orbital overlap results in strongly coupled, large-spin ground states in the [Ni 4 (NP t Bu 3 ) 4 ] +/0 clusters and fully delocalized, spin-correlated electrons. Correlated electronic structure calculations confirm the presence of ferromagnetic ground states that arise from direct exchange between magnetic orbitals, and, in the case of the neutral cluster, itinerant electron magnetism similar to that in metallic ferromagnets. The cationic nickel cluster also possesses large magnetic anisotropy exemplified by a large, positive axial zero-field splitting parameter of D = +7.95 or +9.2 cm -1 , as determined by magnetometry or electron paramagnetic resonance spectroscopy, respectively. The [Ni 4 (NP t Bu 3 ) 4 ] + cluster is also the first molecule with easy-plane magnetic anisotropy to exhibit zero-field slow magnetic relaxation, and under a small applied field, it exhibits relaxation exclusively through an Orbach mechanism with a spin relaxation barrier of 16 cm -1 . The S = 1 / 2 complex [Cu 4 (NP t Bu 3 ) 4 ] + exhibits slow magnetic relaxation via a Raman process on the millisecond time scale, supporting the presence of slow relaxation via an Orbach process in the nickel analogue. Overall, this work highlights the unique electronic and magnetic properties that can be realized in metal clusters featuring direct metal-metal orbital interactions between low-coordinate metal centers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Non-Equilibrium Effects in Quantum Magnets

While most often the state of a material will tend toward an equilibrium determined by its environment, there are many cases of scientific and technological interest where materials are manipulated to be or are found in non-equilibrium configurations. For example, data can be stored in hard drives by deliberately altering the magnetic orientation in a material to store information in non-equilibrium pattern. In this project, the main goals were studies of non-equilibrium properties of quantum magnets using neutron scattering as the primary experimental method. Neutron scattering allows characterization of magnetic correlation lengths sensitive to the presence of defects. It can also be used to distinguish equilibrium from non-equilibrium states via energy transfer rates. Typical bulk state magnetization relaxation times are too short to perform many neutron scattering measurements of interest. To enable the study of non-equilibrium conditions, materials with longer magnetic relaxation times were targeted. CoNb 2 O 6 was used in two experiments related to non-equilibrium physics. In the first, evidence for defects created via the Kibble-Zurek mechanism (KZM) was sought by quenching across a magnetic field-dependent phase transition. Somewhat unexpectedly, clear evidence for KZM-induced defects was absent. Additional measurements of CoNb 2 O 6 were made to better characterize its crystal field and other properties to provide a better theoretical understanding to enable more effective non-equilibrium physics measurements. In another project, LiHo 0.45 Y 0.55 F 4 was used to compare a quantum annealing protocol to a thermal annealing one since magnetic fields can be used to control the thermal fluctuations in LiHo 0.45 Y 0.55 F 4 . In addition, a new pulsed magnet power supply and new techniques were developed suitable for neutron scattering experimental environments to enable faster magnetic field changes for producing non-equilibrium conditions. The power supply developed for this project has wider technological applications in addition to faster magnetic field ramps.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Origin of the anomalously low Raman exponents in single molecule magnets

The Raman exponent of single molecular magnetic relaxation may take various unexpected values because of rich phonon spectra and spin-phonon coupling of molecular crystals. Here, we systematically examine the origins of different abnormalities and clarify misunderstandings of the past, particularly the appropriateness of the fitting procedures for the exponents. We find that exponential laws raised by optical phonons can yield spurious power laws with low exponents. This observation indicates long-standing misunderstandings of the origins of low Raman exponents in a large bulk of single molecule magnets. Resulting from spin-lattice coupling with optical modes, the presence of these exponents suggests the importance of the local dynamical environment for the magnetic relaxation in this regime.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Magnetic frustration driven by conduction carrier blocking in Nd 2 Co 0.85 Si 2.88

The intermetallic compound Nd 2 Co 0.85 Si 2.88 having a triangular lattice could be synthesized in single phase only with defect crystal structure. Investigation through different experimental techniques indicate the presence of two magnetic transitions in the system. As verified experimentally and theoretically, the high-temperature transition $T_H$ ~ 140 K is associated with the development of ferromagnetic interaction between itinerant Co moments, whereas the low-temperature transition at $T_L$ ~ 6.5 K is due to the coupling among Nd–4$\textit{f}$ and Co–3$\textit{d}$ moments, which is antiferromagnetic in nature. Detailed studies of temperature-dependent dc magnetic susceptibility, field dependence of isothermal magnetization, nonequilibrium dynamical behavior, viz., magnetic relaxation, aging effect, magnetic-memory effect, and temperature dependence of heat capacity, along with density functional theory (DFT) calculations, suggest that the ground state is magnetically frustrated spin glass in nature, having competing magnetic interactions of equivalent energies. DFT results further reveal that the 3$\textit{d}$/5$\textit{d}$-conduction carriers are blocked in the system and act as a barrier for the 4$\textit{f}$–4$\textit{f}$ RKKY interactions, resulting in spin frustration. Presence of vacancy defects in the crystal are also conducive to the spin frustration. This is an unique mechanism of magnetic frustration, not emphasized so far in any of the ternary $R_2TX_3$ ($\textit{R}$ = rare earth, $\textit{T}$ = transition elements, and $\textit{X}$ = Si, Ge, In) type compounds. Due to the competing character of the itinerant 3$\textit{d}$ and localized 4$\textit{f}$ moments, the compound exhibits anomalous field dependence of magnetic coercivity. Further, the system also exhibits a considerable magnetic entropy change of –Δ$S_M$ ~ 13.3 J/kg K with a relative cooling power (RCP) of 220 J/kg and adiabatic temperature change $ΔT_{\text{ad}}$ of 6 K for magnetic field change of 70 kOe.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Coercive Fields Exceeding 30 T in the Mixed-Valence Single-Molecule Magnet (Cp iPr5 ) 2 Ho 2 I 3

Mixed-valence dilanthanide complexes of the type (Cp iPr5 ) 2 Ln 2 I 3 (Cp iPr5 = pentaisopropylcyclopentadienyl; Ln = Gd, Tb, Dy) featuring a direct Ln–Ln σ-bonding interaction have been shown to exhibit well-isolated high-spin ground states and, in the case of the Tb and Dy variants, a strong axial magnetic anisotropy that gives rise to a large magnetic coercivity. Here, we report the synthesis and characterization of two new mixed-valence dilanthanide compounds in this series, (Cp iPr5 ) 2 Ln 2 I 3 (1-Ln; Ln = Ho, Er). Both compounds feature a Ln–Ln bonding interaction, the first such interaction in any molecular compounds of Ho or Er. Like the Tb and Dy congeners, both complexes exhibit high-spin ground states arising from strong spin–spin coupling between the lanthanide 4f electrons and a single σ-type lanthanide–lanthanide bonding electron. Beyond these similarities, however, the magnetic properties of the two compounds diverge. In particular, 1-Er does not exhibit observable magnetic blocking or slow magnetic relaxation, while 1-Ho exhibits magnetic blocking below 28 K, which is the highest temperature among Ho-based single-molecule magnets, and a spin reversal barrier of 556(4) cm –1 . Additionally, variable-field magnetization data collected for 1-Ho reveal a coercive field of greater than 32 T below 8 K, more than 6-fold higher than observed for the bulk magnets SmCo 5 and Nd 2 Fe 14 B, and the highest coercive field reported to date for any single-molecule magnet or molecule-based magnetic material. Multiconfigurational calculations, supported by far-infrared magnetospectroscopy data, reveal that the stark differences in magnetic properties of 1-Ho and 1-Er arise from differences in the local magnetic anisotropy of the lanthanide centers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Analysis of vibronic coupling in a 4f molecular magnet with FIRMS

Vibronic coupling, the interaction between molecular vibrations and electronic states, is a fundamental effect that profoundly affects chemical processes. In the case of molecular magnetic materials, vibronic, or spin-phonon, coupling leads to magnetic relaxation, which equates to loss of magnetic memory and loss of phase coherence in molecular magnets and qubits, respectively. The study of vibronic coupling is challenging, and most experimental evidence is indirect. Here we employ far-infrared magnetospectroscopy to directly probe vibronic transitions in [Yb(trensal)] (where H 3 trensal = 2,2,2-tris(salicylideneimino)trimethylamine). We find intense signals near electronic states, which we show arise due to an “envelope effect” in the vibronic coupling Hamiltonian, which we calculate fully ab initio to simulate the spectra. We subsequently show that vibronic coupling is strongest for vibrational modes that simultaneously distort the first coordination sphere and break the C 3 symmetry of the molecule. With this knowledge, vibrational modes could be identified and engineered to shift their energy towards or away from particular electronic states to alter their impact. Hence, these findings provide new insights towards developing general guidelines for the control of vibronic coupling in molecules.

36 MATERIALS SCIENCE↗