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Accurate knowledge of the heating performance of magnetic nanoparticles (MNPs) under AC magnetic fields is critical for the development of hyperthermia-mediated applications. Usually reported in terms of the specific loss power (SLP) obtained from the temperature variation (Δ T ) vs. time ( t ) curve, such an estimate is subjected to a huge uncertainty. Thus, very different SLP values are reported for the same particles when measured on different equipment/in different laboratories. This lack of control clearly hampers the further development of nanoparticle-mediated heat-triggered technologies. Here, we report a device-independent approach to calculate the SLP value of a suspension of magnetic nanoparticles: the SLP is obtained from the analysis of the peak at the AC magnetic field on/off switch of the Δ T (time) curve. The measurement procedure, which itself constitutes a change of paradigm within the field, is based on the heat diffusion equation, which is still valid when the assumptions of Newton's law of cooling are not applicable, as (i) it corresponds to the ideal scenario in which the temperature profiles of the system during heating and cooling are the same; and (ii) it diminishes the role of coexistence of various heat dissipation channels. Such an approach is supported by theoretical and computational calculations to increase the reliability and reproducibility of SLP determination. Furthermore, the new methodological approach is experimentally confirmed, by magnetic hyperthermia experiments performed using 3 different devices located in 3 different laboratories. Furthermore, the application of this peak analysis method (PAM) to a rapid succession of stimulus on/off switches which results in a zigzag-like Δ T ( t ), which we term the zigzag protocol, allows evaluation of possible variations of the SLP values with time or temperature., Competing Interests: C. Jones works for Nanotherics, a company that produces devices to characterize the heating performance of magnetic nanoparticles., (This journal is © The Royal Society of Chemistry.)

An antiferromagnet emits spin currents when time-reversal symmetry is broken. This is typically achieved by applying an external magnetic field below and above the spin-flop transition or by optical pumping. In this work we apply optical pump-THz emission spectroscopy to study picosecond spin pumping from metallic FeRh as a function of temperature. Intriguingly we find that in the low-temperature antiferromagnetic phase the laser pulse induces a large and coherent spin pumping, while not crossing into the ferromagnetic phase. With temperature and magnetic field dependent measurements combined with atomistic spin dynamics simulations we show that the antiferromagnetic spin-lattice is destabilised by the combined action of optical pumping and picosecond spin-biasing by the conduction electron population, which results in spin accumulation. We propose that the amplitude of the effect is inherent to the nature of FeRh, particularly the Rh atoms and their high spin susceptibility. We believe that the principles shown here could be used to produce more effective spin current emitters. Our results also corroborate the work of others showing that the magnetic phase transition begins on a very fast picosecond timescale, but this timescale is often hidden by measurements which are confounded by the slower domain dynamics., (© 2024. The Author(s).)

We present an experimental and computational investigation the Neodymium thickness dependence of the effective damping constant (αeff) in Ni 80 Fe 20 /Neodymium (Py/Nd) bilayers. The computational results show that the magnetic damping is strongly dependent on the thickness of Nd, which is in agreement with experimental data. Self consistent solutions of the spin accumulation model and the local magnetisation were used in the simulations. It was not possible to obtain agreement with experiment under the assumption of an enhanced damping in a single Py monolayer. Instead, it was found that the enhanced damping due to spin pumping needed to be spread across two monolayers of Py. This is suggested to arise from interface mixing. Subsequently, the temperature dependence of the effective damping was investigated. It is found that, with increasing temperature, the influence of thermally-induced spin fluctuations on magnetic damping becomes stronger with increasing Nd thickness., (Creative Commons Attribution license.)

Ultrafast manipulation of magnetic order has challenged the understanding of the fundamental and dynamic properties of magnetic materials. So far single-shot magnetic switching has been limited to ferrimagnetic alloys, multilayers, and designed ferromagnetic (FM) heterostructures. In FM/antiferromagnetic (AFM) bilayers, exchange bias (H e ) arises from the interfacial exchange coupling between the two layers and reflects the microscopic orientation of the antiferromagnet. Here the possibility of single-shot switching of the antiferromagnet (change of the sign and amplitude of H e ) with a single femtosecond laser pulse in IrMn/CoGd bilayers is demonstrated. The manipulation is demonstrated in a wide range of fluences for different layer thicknesses and compositions. Atomistic simulations predict ultrafast switching and recovery of the AFM magnetization on a timescale of 2 ps. The results provide the fastest and the most energy-efficient method to set the exchange bias and pave the way to potential applications for ultrafast spintronic devices., (© 2024 Wiley‐VCH GmbH.)

The power consumption of modern random access memory (RAM) has been a motivation for the development of low-power non-volatile magnetic RAM (MRAM). Based on a CoFeB/MgO magnetic tunnel junction, MRAM must satisfy high thermal stability and a low writing current while being scaled down to a sub-20 nm size to compete with the densities of current RAM technology. A recent development has been to exploit perpendicular shape anisotropy along the easy axis by creating tower structures, with the free layers' thickness (along the easy axis) being larger than its width. Here we use an atomistic model to explore the temperature dependent properties of thin cylindrical MRAM towers of 5 nm diameter while scaling down the free layer from 48 to 8 nm thick. We find thermal fluctuations are a significant driving force for the switching mechanism at operational temperatures by analysing the switching field distribution from hysteresis data. We find that a reduction of the free layer thickness below 18 nm rapidly loses shape anisotropy, and consequently stability, even at 0 K. Additionally, there is a change in the switching mechanism as the free layer is reduced to 8 nm. Coherent rotation is observed for the 8 nm free layer, while all taller towers demonstrate incoherent rotation via a propagated domain wall., (Creative Commons Attribution license.)

The discovery of magnetization switching via spin transfer torque (STT) in PMA-based MTJs has led to the development of next-generation magnetic memory technology with high operating speed, low power consumption and high scalability. In this work, we theoretically investigate the influence of finite size and temperature on the mechanism of magnetization switching in CoFeB-MgO based MTJ to get better understanding of STT-MRAM fundamentals and design. An atomistic model coupled with simultaneous solution of the spin accumulation is employed. The results reveal that the incoherent switching process in MTJ strongly depends on the system size and temperature. At 0 K, the coherent switching mode can only be observed in MTJs with the diameter less than 20 nm. However, at any finite temperature, incoherent magnetization switching is thermally excited. Furthermore, increasing temperature results in decreasing switching time of the magnetization. We conclude that temperature dependent properties and thermally driven reversal are important considerations for the design and development of advanced MRAM systems., (© 2023. The Author(s).)

Understanding formation of metastable phases by rapid energy pumping and quenching has been intriguing scientists for a long time. This issue is crucial for technologically relevant systems such as magnetic skyrmions which are frequently metastable at zero field. Using Atomistic Spin Dynamics simulations, we show the possibility of creating metastable skyrmion lattices in cobalt-based trilayers by femtosecond laser heating. Similar to the formation of supercooled ice droplets in the gas phase, high temperature ultrafast excitation creates magnon drops and their fast relaxation leads to acquisition and quenching of the skyrmion topological protection. The interplay between different processes corresponds to a specific excitation window which can be additionally controlled by external fields. The results are contrasted with longer-scale heating leading to a phase transition to the stable states. Our results provide insight into the dynamics of the highly non-equilibrium pathway for spin excitations and pave additional routes for skyrmion-based information technologies.

We present a theoretical investigation of the magnetisation reversal process in CoFeB-based magnetic tunnel junctions (MTJs). We perform atomistic spin simulations of magnetisation dynamics induced by combination of spin orbit torque (SOT) and spin transfer torque (STT). Within the model the effect of SOT is introduced as a Slonczewski formalism, whereas the effect of STT is included via a spin accumulation model. We investigate a system of CoFeB/MgO/CoFeB coupled with a heavy metal layer where the charge current is injected into the plane of the heavy metal meanwhile the other charge current flows perpendicular into the MTJ structure. Our results reveal that SOT can assist the precessional switching induced by spin polarised current within a certain range of injected current densities yielding an efficient and fast reversal on the sub-nanosecond timescale. The combination of STT and SOT gives a promising pathway to improve high performance CoFeB-based devices with high speed and low power consumption., (© 2022. The Author(s).)

Magnetic hyperthermia (MHT) is a therapeutic modality for the treatment of solid tumors that has now accumulated more than 30 years of experience. In the ongoing MHT clinical trials for the treatment of brain and prostate tumors, iron oxide nanoparticles are employed as intra-tumoral MHT agents under a patient-safe 100 kHz alternating magnetic field (AMF) applicator. Although iron oxide nanoparticles are currently approved by FDA for imaging purposes and for the treatment of anemia, magnetic nanoparticles (MNPs) designed for the efficient treatment of MHT must respond to specific physical-chemical properties in terms of magneto-energy conversion, heat dose production, surface chemistry and aggregation state. Accordingly, in the past few decades, these requirements have boosted the development of a new generation of MNPs specifically aimed for MHT. In this review, we present an overview on MNPs and their assemblies produced via different synthetic routes, focusing on which MNP features have allowed unprecedented heating efficiency levels to be achieved in MHT and highlighting nanoplatforms that prevent magnetic heat loss in the intracellular environment. Moreover, we review the advances on MNP-based nanoplatforms that embrace the concept of multimodal therapy, which aims to combine MHT with chemotherapy, radiotherapy, immunotherapy, photodynamic or phototherapy. Next, for a better control of the therapeutic temperature at the tumor, we focus on the studies that have optimized MNPs to maintain gold-standard MHT performance and are also tackling MNP imaging with the aim to quantitatively assess the amount of nanoparticles accumulated at the tumor site and regulate the MHT field conditions. To conclude, future perspectives with guidance on how to advance MHT therapy will be provided.

Nanoparticle-based magnetic hyperthermia is a well-known thermal therapy platform studied to treat solid tumors, but its use for monotherapy is limited due to incomplete tumor eradication at hyperthermia temperature (45 °C). It is often combined with chemotherapy for obtaining a more effective therapeutic outcome. Cubic-shaped cobalt ferrite nanoparticles (Co-Fe NCs) serve as magnetic hyperthermia agents and as a cytotoxic agent due to the known cobalt ion toxicity, allowing the achievement of both heat and cytotoxic effects from a single platform. In addition to this advantage, Co-Fe NCs have the unique ability to form growing chains under an alternating magnetic field (AMF). This unique chain formation, along with the mild hyperthermia and intrinsic cobalt toxicity, leads to complete tumor regression and improved overall survival in an in vivo murine xenograft model, all under clinically approved AMF conditions. Numerical calculations identify magnetic anisotropy as the main Co-Fe NCs' feature to generate such chain formations. This novel combination therapy can improve the effects of magnetic hyperthermia, inaugurating investigation of mechanical behaviors of nanoparticles under AMF, as a new avenue for cancer therapy., (© 2020 The Authors. Published by Wiley-VCH GmbH.)

Magnetic hyperthermia is a cancer treatment based on the exposure of magnetic nanoparticles to an alternating magnetic field in order to generate local heat. In this work, 3D cell culture models were prepared to observe the effect that a different number of internalized particles had on the mechanisms of cell death triggered upon the magnetic hyperthermia treatment. Macrophages were selected by their high capacity to uptake nanoparticles. Intracellular nanoparticle concentrations up to 7.5 pg Fe/cell were measured both by elemental analysis and magnetic characterization techniques. Cell viability after the magnetic hyperthermia treatment was decreased to <25% for intracellular iron contents above 1 pg per cell. Theoretical calculations of the intracellular thermal effects that occurred during the alternating magnetic field application indicated a very low increase in the global cell temperature. Different apoptotic routes were triggered depending on the number of internalized particles. At low intracellular magnetic nanoparticle amounts (below 1 pg Fe/cell), the intrinsic route was the main mechanism to induce apoptosis, as observed by the high Bax / Bcl-2 mRNA ratio and low caspase-8 activity. In contrast, at higher concentrations of internalized magnetic nanoparticles (1-7.5 pg Fe/cell), the extrinsic route was observed through the increased activity of caspase-8. Nevertheless, both mechanisms may coexist at intermediate iron concentrations. Knowledge on the different mechanisms of cell death triggered after the magnetic hyperthermia treatment is fundamental to understand the biological events activated by this procedure and their role in its effectiveness.

The controlled assembly of colloidal magnetic nanocrystals is key to many applications such as nanoelectronics, storage memory devices, and nanomedicine. Here, the motion and ordering of ferrimagnetic nanocubes in water via liquid-cell transmission electron microscopy is directly imaged in situ. Through the experimental analysis, combined with molecular dynamics simulations and theoretical considerations, it is shown that the presence of highly competitive interactions leads to the formation of stable monomers and dimers, acting as nuclei, followed by a dynamic growth of zig-zag chain-like assemblies. It is demonstrated that such arrays can be explained by first, a maximization of short-range electrostatic interactions, which at a later stage become surpassed by magnetic forces acting through the easy magnetic axes of the nanocubes, causing their tilted orientation within the arrays. Moreover, in the confined volume of liquid in the experiments, interactions of the nanocube surfaces with the cell membranes, when irradiated at relatively low electron dose, slow down the kinetics of their self-assembly, facilitating the identification of different stages in the process. The study provides crucial insights for the formation of unconventional linear arrays made of ferrimagnetic nanocubes that are essential for their further exploitation in, for example, magnetic hyperthermia, magneto-transport devices, and nanotheranostic tools., (© 2020 The Authors. Published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

Magnetic nanoparticles (MNPs) constitute promising nanomedicine tools based on the possibility of obtaining different actuations (for example, heating or mechanical response) triggered by safe remote stimuli. Particularly, the possibility of performing different tasks using the same entity constitutes a main research target towards optimizing the treatment. But such a goal represents, in general, a very difficult step because the requisites for achieving efficient responses for separate actuations are often disparate - if not completely incompatible. An example of this is the response of MNPs to external AC fields, which could in principle be exploited for either magneto-mechanical actuation (MMA) at low frequencies (tens of Hz); or heat release at high frequency (0.1-1 MHz range) for magnetic fluid hyperthermia (MFH). The problem is that efficient MMA involves large torque, the required material parameters for which are detrimental to high heating, thus hindering the possibility of effective alternation between both responses. To overcome such apparent incompatibility, we propose a simple approach based on the use of anisotropic MNPs. The key idea is that the AC-frequency change must be concurrent with a field-amplitude variation able to promote - or impede - the reversal over the shape-determined anisotropy energy barrier. This way it is possible to switch the particle response between an efficient (magnetically dissipationless) rotation regime at low-f, for MMA, and a "frozen" (non-rotatable) high-energy-dissipation regime at high-f, for MFH. Furthermore, we show that such an alternation can also be achieved within the same high-f MFH regime. We use combined Brownian dynamics and micromagnetic simulations, based on real experimental samples, to show how such a field threshold can be tuned to working conditions with hexagonal-disk shape anisotropy.

The controlled size and surface treatment of magnetic nanoparticles (NPs) make one-stage combination feasible for enhanced magnetic resonance imaging (MRI) contrast and effective hyperthermia. However, superparamagnetic behavior, essential for avoiding the aggregation of magnetic NPs, substantially limits their performance. Here, a superparamagnetic core-shell structure is developed, which promotes the formation of vortex-like intraparticle magnetization structures in the remanent state, leading to reduced dipolar interactions between two neighboring NPs, while during an MRI scan, the presence of a DC magnetic field induces the formation of NP chains, introducing increased local inhomogeneous dipole fields that enhance relaxivity. The core-shell NPs also reveal an augmented anisotropy, due to exchange coupling to the high anisotropy core, which enhances the specific absorption rate. This in vivo tumor study reveals that the tumor cells can be clearly diagnosed during an MRI scan and the tumor size is substantially reduced through hyperthermia therapy by using the same FePt@iron oxide nanoparticles, realizing the concept of theranostics., (© 2018 The Authors. Published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

The complex magnetic properties of Fe/Ir/Fe sandwiches are studied using a hierarchical multi-scale model. The approach uses first principles calculations and thermodynamic models to reveal the equilibrium spinwave, magnetization and dynamic demagnetisation properties. Finite temperature calculations show a complex spinwave dispersion and an initially counter-intuitive, increasing exchange stiffness with temperature (a key quantity for device applications) due to the effects of frustration at the interface, which then decreases due to magnon softening. Finally, the demagnetisation process in these structures is shown to be much slower at the interface as compared with the bulk, a key insight to interpret ultrafast laser-induced demagnetization processes in layered or interface materials.

Rate (master) equations are ubiquitous in statistical physics, yet, to the best of our knowledge, a rate equation with memory has previously never been considered. We write down an integro-differential rate equation for the evolution of a thermally relaxing system with memory. For concreteness we adopt as a model a single-domain magnetic particle driven by a small ac field and derive the modified Debye formulas. For any memory time Θ the in-phase component of the resultant ac susceptibility is positive at small probing frequencies ω, but becomes negative at large ω. The system thus exhibits frequency induced diamagnetism. For comparison we also consider particle pairs with dipolar coupling. The memory effect is found to be enhanced by ferromagnetic coupling and suppressed by antiferromagnetic coupling. Numerical calculations support the prediction of a negative susceptibility which arises from a phase shift induced by the memory effect. It is proposed that the onset of frequency induced diamagnetism represents a viable experimental signature of correlated noise.

Magnetic hyperthermia (MH) based on magnetic nanoparticles (MNPs) is a promising adjuvant therapy for cancer treatment. Particle clustering leading to complex magnetic interactions affects the heat generated by MNPs during MH. The heat efficiencies, theoretically predicted, are still poorly understood because of a lack of control of the fabrication of such clusters with defined geometries and thus their functionality. This study aims to correlate the heating efficiency under MH of individually coated iron oxide nanocubes (IONCs) versus soft colloidal nanoclusters made of small groupings of nanocubes arranged in different geometries. The controlled clustering of alkyl-stabilized IONCs is achieved here during the water transfer procedure by tuning the fraction of the amphiphilic copolymer, poly(styrene-co-maleic anhydride) cumene-terminated, to the nanoparticle surface. It is found that increasing the polymer-to-nanoparticle surface ratio leads to the formation of increasingly large nanoclusters with defined geometries. When compared to the individual nanocubes, we show here that controlled grouping of nanoparticles-so-called "dimers" and "trimers" composed of two and three nanocubes, respectively-increases specific absorption rate (SAR) values, while conversely, forming centrosymmetric clusters having more than four nanocubes leads to lower SAR values. Magnetization measurements and Monte Carlo-based simulations support the observed SAR trend and reveal the importance of the dipolar interaction effect and its dependence on the details of the particle arrangements within the different clusters.

Power consumption is the main limitation in the development of new high performance random access memory for portable electronic devices. Magnetic RAM (MRAM) with CoFeB/MgO based magnetic tunnel junctions (MTJs) is a promising candidate for reducing the power consumption given its non-volatile nature while achieving high performance. The dynamic properties and switching mechanisms of MTJs are critical to understanding device operation and to enable scaling of devices below 30 nm in diameter. Here we show that the magnetic reversal mechanism is incoherent and that the switching is thermally nucleated at device operating temperatures. Moreover, we find an intrinsic thermal switching field distribution arising on the sub-nanosecond time-scale even in the absence of size and anisotropy distributions or material defects. These features represent the characteristic signature of the dynamic properties in MTJs and give an intrinsic limit to reversal reliability in small magnetic nanodevices.

The generic problem of extracting information on intrinsic particle properties from the whole class of interacting magnetic fine particle systems is a long standing and difficult inverse problem. As an example, the Switching Field Distribution (SFD) is an important quantity in the characterization of magnetic systems, and its determination in many technological applications, such as recording media, is especially challenging. Techniques such as the first order reversal curve (FORC) methods, were developed to extract the SFD from macroscopic measurements. However, all methods rely on separating the contributions to the measurements of the intrinsic SFD and the extrinsic effects of magnetostatic and exchange interactions. We investigate the underlying physics of the FORC method by applying it to the output predictions of a kinetic Monte-Carlo model with known input parameters. We show that the FORC method is valid only in cases of weak spatial correlation of the magnetisation and suggest a more general approach.

In the magnetic fluid hyperthermia (MFH) research field, it is usually assumed that achieving a uniform temperature enhancement (ΔT) of the entire tumour is a key-point for treatment. However, various experimental works reported successful cell apoptosis via MFH without a noticeable ΔT of the system. A possible explanation of the success of these negligible-ΔT experiments is that a local ΔT restricted to the particle nanoenvironment (i.e. with no significant effect on the global temperature T) could be enough to trigger cell death. Shedding light on such a possibility requires accurate knowledge of heat dissipation at the local level in relation to the usually investigated global (average) one. Since size polydispersity is inherent to all synthesis techniques and the heat released is proportional to the particle size, heat dissipation spots with different performances - and thus different effects on the cells - will likely exist in every sample. In this work we aim for a double objective: (1) to emphasize the necessity to distinguish between the total dissipated heat and hyperthermia effectiveness, and (2) to suggest a theoretical approach on how to select, for a given size polydispersity, a more adequate average size so that most of the particles dissipate within a desired heating power range. The results are reported in terms of Fe 3 O 4 nanoparticles as a representative example.

We present a newtype 2-dimensional (2D) magnetic semiconductor based on transition-metal dichalcogenides VX2 (X = S, Se and Te) via first-principles calculations. The obtained indirect band gaps of monolayer VS2, VSe2, and VTe2 given from the generalized gradient approximation (GGA) are respectively 0.05, 0.22, and 0.20 eV, all with integer magnetic moments of 1.0 μB. The GGA plus on-site Coulomb interaction U (GGA + U) enhances the exchange splittings and raises the energy gap up to 0.38~0.65 eV. By adopting the GW approximation, we obtain converged G0W0 gaps of 1.3, 1.2, and 0.7 eV for VS2, VSe2, and VTe2 monolayers, respectively. They agree very well with our calculated HSE gaps of 1.1, 1.2, and 0.6 eV, respectively. The gap sizes as well as the metal-insulator transitions are tunable by applying the in-plane strain and/or changing the number of stacking layers. The Monte Carlo simulations illustrate very high Curie-temperatures of 292, 472, and 553 K for VS2, VSe2, and VTe2 monolayers, respectively. They are nearly or well beyond the room temperature. Combining the semiconducting energy gap, the 100% spin polarized valence and conduction bands, the room temperature TC, and the in-plane magnetic anisotropy together in a single layer VX2, this newtype 2D magnetic semiconductor shows great potential in future spintronics.

Magnetic recording using circularly polarised femto-second laser pulses is an emerging technology that would allow write speeds much faster than existing field driven methods. However, the mechanism that drives the magnetisation switching in ferromagnets is unclear. Recent theories suggest that the interaction of the light with the magnetised media induces an opto-magnetic field within the media, known as the inverse Faraday effect. Here we show that an alternative mechanism, driven by thermal excitation over the anisotropy energy barrier and a difference in the energy absorption depending on polarisation, can create a net magnetisation over a series of laser pulses in an ensemble of single domain grains. Only a small difference in the absorption is required to reach magnetisation levels observed experimentally and the model does not preclude the role of the inverse Faraday effect but removes the necessity that the opto-magnetic field is 10 s of Tesla in strength.

We present a systematic first-principles study of Fe | MgO bilayer systems emphasizing the influence of the iron layer thickness on the geometry, the electronic structure and the magnetic properties. Our calculations ensure the unconstrained structural relaxation at scalar relativistic level for various numbers of iron layers placed on the magnesium oxide substrate. Our results show that due to the formation of the interface the electronic structure of the interface iron atoms is significantly modified involving charge transfer within the iron subsystem. In addition, we find that the magnetic anisotropy energy increases from 1.9 mJ m(-2) for 3 Fe layers up to 3.0 mJ m(-2) for 11 Fe layers.

We study spin relaxation in n-type bulk GaAs, due to the Dyakonov-Perel mechanism, using ensemble Monte Carlo methods. Our results confirm that spin relaxation time increases with the electronic density in the regime of moderate electronic concentrations and high temperature. We show that the electron-electron scattering in the non-degenerate regime significantly slows down spin relaxation. This result supports predictions by Glazov and Ivchenko. Most importantly, our findings highlight the importance of many-body interactions for spin dynamics: we show that only by properly taking into account electron-electron interactions within the simulations, results for the spin relaxation time-with respect to both electron density and temperature-will reach good quantitative agreement with corresponding experimental data. Our calculations contain no fitting parameters.

We investigated the influences of the magnetic field strength and particle areal density on the microstructure of a quasi-two-dimensional monolayer composed of ferromagnetic particles by means of a Monte Carlo simulation. The magnetic field was applied along a direction perpendicular to the plane of the monolayer. Microstructures of the monolayer obtained in the simulations were analyzed in terms of radial distribution and orientational distribution functions. Formation of the microstructures is discussed from the perspective of particle-particle interaction energy and the perpendicular magnetic susceptibility of the monolayer was calculated from simulated magnetization curves. The obtained results are summarized as follows. For small areal density of particles, formation of chain-like structures is prevented by the repulsive magnetic interaction between particles due to orientations of the magnetic moments in the particles along the magnetic field direction. For intermediate areal density of particles, the chain-like structures remain even when a relatively strong magnetic field is applied, because contributions of the attractive magnetic interactions increase. For large areal density of particles, mixtures of chain-like and locally ordered structures appear due to the anisotropic attractive magnetic interactions in the absence of the magnetic field. However, when a sufficiently strong magnetic field is applied, the magnetic interactions between particles change to isotropic repulsive interactions, which results in the short-range repulsive steric interactions between particles becoming dominant with the appearance of hexagonal close packed structures.

We have investigated the orientational distributions and rheological properties of dilute colloidal dispersions, which consist of ferromagnetic spherocylinder particles. First, the governing equation of the orientational distribution function has been derived for the typical two cases of magnetic field directions: the direction parallel to the shear flow and the direction parallel to the angular velocity vector of the shear flow. The equation has been solved approximately by Galerkin's method. With these numerical solutions we have obtained the results of the orientational distribution and viscosity. The results obtained for the magnetic field in the shear flow direction are summarized as follows. In the case of a weak magnetic field, the particle tends to orient nearly toward the shear flow direction and its opposite direction. As the magnetic field increases, the orientation of the particle is restricted and the viscosity increases significantly. As the influence of the magnetic field becomes dominant, an overshoot in the viscosity curve appears. This is due to the fact that there is a maximum deviation of the averaged particle direction from the magnetic field direction. When the strength of the magnetic field increases significantly, the particle inclines close to the magnetic field direction and the viscosity converges to a constant value. Particles with a larger aspect ratio give rise to a larger increment in the viscosity since such elongated particles induce larger resistance in a flow field. We also have obtained results for the case of the magnetic field in the direction parallel to the angular velocity vector of the shear flow. When the flow field is dominant over both the rotational Brownian motion and the magnetic interaction, the particle rotates in the plane nearly perpendicular to the magnetic field direction. As the magnetic field increases, the particle inclines toward the magnetic direction. For this direction of field, the viscosity is independent of the magnetic field and is always zero.