Magnetic Properties Research Articles

Temperature dependence of spin transport behavior in Heusler alloy CPP-GMR

In this study, we investigate the effect of temperature on the performance of a read sensor by utilizing an atomistic model coupled with a spin transport model. Specifically, we study the temperature dependence of spin transport behavior and MR outputs in a Co2FeAl0.5Si0.5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {Co}_2\ ext {FeAl}_{0.5}\ ext {Si}_{0.5}$$\\end{document} (CFAS)(5nm)/Cu(5nm)/CFAS(5nm) trilayer with diffusive interfaces. Initially, the two-channel model of spin-dependent resistivity is used to calculate the temperature dependence of spin transport parameters which serves as essential input for the spin accumulation model. Our findings demonstrate that as the temperature increases, the spin transport parameters and magnetic properties decrease due to the influence of thermal fluctuation. At a critical temperature, where the ferromagnet transitions to a paramagnetic state, we observe zero spin polarization. Furthermore, at elevated temperatures, the spin accumulation deviates from the equilibrium value, leading to a reduction in the magnitude of spin current and spin transport parameters due to thermal effects. As a consequence, the MR ratio decreases from 65% to 20% with increasing temperature from 0 to 400 K. Our results are consistent with previous experimental measurements. This study allows to deeply understand the physical mechanism in the reader stack which can significantly benefit reader design.

Recovering MRI magnetic field strength properties using machine learning based on image compression quality scores

AbstractOver the years, significant hardware advancements have led to higher magnetic field MRI (Magnetic Resonance Imaging) acquisitions, providing improved diagnostic image quality at a higher cost. While higher image quality is desired, the investment required for high-field MRI imaging systems remains a significant consideration. Furthermore, historical patient records may still contain low-field magnetic strength MRI data. In this work, we present how image compression quality scores of MRI images could be used to recover their magnetic field strength properties. This work presents an interesting inverse problem scenario where output properties are used to recover an input property of an image. We implemented supervised machine learning models that utilize compressed image quality scores - based on Mean Squared Error (MSE), Structural Similarity Index (SSIM), Visual Information Fidelity (VIF), and Earth Movers Distance (EM) metrics - as inputs. These models classify images into specific classes of magnetic field strength at which they were acquired (Low, Medium, and High) based solely on the quality scores of their compressed copies. The trained machine learning models (Support Vector Machine (SVM), Logistic Regression, K-nearest Neighbours (KNN), Decision Tree and Random Forest) achieved nearly 100% performance efficiency based on accuracy and F-1 score for all considered quality measures. This comprehensive evaluation offers insights into how compression techniques and quality factors impact image fidelity across various MRI magnetic field strengths. The findings of this study may prove valuable in recovering missing meta-tag information in historical image DICOM records and Context-Based Retrieval Systems (CBRS). The approach of using quality scores as features in training machine learning models, as demonstrated in this work, can be extended to other image groups where input parameters create statistically significant distinctions or are challenging to extract from images.

Multiprogrammable Anisotropic Soft Material via Magneto‐Orientation of Ferromagnetic Nanoplates

AbstractAnisotropic materials featured with ordered arrangement of sub‐structures are ubiquitous in living organisms, and possess rapidly increasing relevance to emerging technologies in smart materials, soft robotics, flexible displays, and biomedicines. However, the integration and programming of multiple properties into anisotropic materials, which endow themselves with extended intrinsic capabilities and utilities, still remain a challenge. Herein, we report a multi‐programmable anisotropic material by embedding ferromagnetic two‐dimensional nanoplates into hydrogel matrix. The nanoplate exhibits not only a disc‐like non‐isotropic shape, but also an intrinsic easy magnetization axis perpendicular to its basal plane. Using a directional external magnetic field, we can precisely control the orientation of nanoplates inside hydrogel precursor solution and then fix them via photolithographic polymerization, leading to the fabrication of anisotropic hydrogel with on‐demand ordered alignment of nanoplates. Such deliberate arrangement of nanoplates brings in extraordinary optical properties due to birefringence, enabling us to encrypt pattern information into hydrogel materials that is only visible under polarized light. Soft actuators with programmable optical, mechanical and magnetic properties are engineered, which allow to encode diverse deformation and locomotion modes, determine the actuation sites, and monitor the sub‐structural anisotropy all simultaneously, opening new avenues for the design of anisotropic soft materials.

Low temperature machining advantages for sintered NdFeB magnets: A comparative experimental study of WAWJ with laser and WEDM

Sintered NdFeB magnets exhibit excellent magnetic properties and high reliability, making them widely used in fields such as new energy vehicles and electronic communications. However, NdFeB magnets have a low Curie temperature and poor thermal stability. Common machining methods such as laser cutting and EDM (Electrical Discharge Machining) often involve cutting temperatures in the hundreds or even thousands of degrees Celsius, leading to defects such as melting and cracks on the magnet surface. These defects degrade the surface quality and magnetic properties of the magnet. To avoid thermal damage to the magnet during processing, WAWJ (Wet Abrasive Waterjet) cutting was employed on sintered NdFeB. Experimental results indicate that at an ambient temperature of 4.5 °C, the maximum cutting temperature remains below 50 °C, with an average cutting temperature below 25 °C. No heat-affected zones or oxidation layers are exhibited on the cutting surface of the magnet. Jet pressure is identified as the primary factor influencing the maximum cutting temperature, accounting for 96.13 %. With jet pressure increasing from 200 MPa to 280 MPa, the maximum cutting temperature rises from 38.7 °C to 47.9 °C. Furthermore, to validate the necessity of low-temperature cutting for NdFeB magnets, WEDM (Wire Electrical Discharge Machining) and laser cutting were employed on sintered NdFeB magnets. The cutting surfaces of both methods exhibit defects such as cracks, craters, and melting. Compared to the original magnet surface, no significant changes in elemental content were observed on the WAWJ-cut surface. Under high-temperature conditions, the oxidation rate increased, leading to a 18.9 % and 19.8 % increase in oxygen content on the WEDM and laser machined surfaces, respectively. Some neodymium (Nd) and iron (Fe) elements exist in the form of oxides such as FeO and Nd2O3, resulting in loss of magnetism. Moreover, the presence of oxides reduces the continuity of magnetic phases, adversely affecting the magnetic properties of the magnet.

Development of highly oriented crystals in the magnetoplumbite structure of metal (Sr, Cr, Sc) doped M-type BaFe12O19 hexaferrite films with improved optical and magnetic properties

We have deposited magnetoplumbite (P63/mmc) structured Ba-hexaferrite (BaFe12O19) and its metal (T: Sc and Cr) doped (Ba0.7Sr0.3Fe12O19 and BaFe11.5T0.5O19) films on Si substrate using the Pulsed Laser Deposition technique. The as-grown films showed preferential orientation of the crystals along (2 0 3), (2 0 7), (1 1 14), and (4 0 5) directions. The post-heat treatment oriented the crystals only along (2 0 7) direction. The Fe ions varied it charge state from +3 at the surface of the films to a mixed charge state in the interior, which promoted a local clustering of Fe3O4-like phase. Ferrimagnetic properties of the hexaferrite films have been modified due to metal doping. The bi-phased magnetic structure, arising from clustering of the soft ferrimagnetic Fe3O4 phase in the matrix of hard ferrimagnetic hexaferrite films, is suitable for tuning the magnetic coercivity and moment over a wide range of temperatures. The optical band gap in the range of 3.40–3.50 eV and a strong magneto-optical Kerr signal are promising for potential applications of the films in magneto-optical devices working in UV regime of radiation.

Structural, electronic, magnetic and optical properties of GdCuX2 (X = S, Se and Te) compounds

Structural, electronic, magnetic and optical properties of GdCuX2 (X = S, Se and Te) compounds

Transition-Metal-Related Quantum Emitters in Wurtzite AlN and GaN.

Transition-metal centers exhibit a paramagnetic ground state in wide-bandgap semiconductors and are promising for nanophotonics and quantum information processing. Specifically, there is a growing interest in discovering prominent paramagnetic spin defects that can be manipulated using optical methods. Here, we investigate the electronic structure and magneto-optical properties of Cr and Mn substitutional centers in wurtzite AlN and GaN. We use state-of-the-art hybrid density functional theory calculations to determine level structure, stability, optical signatures, and magnetic properties of these centers. The excitation energies are calculated using the constrained occupation approach and rigorously verified with the complete active space configuration interaction approach. Our simulations of the photoluminescence spectra indicate that in AlN and in GaN are responsible for the observed narrow quantum emission near 1.2 eV. We compute the zero-field splitting (ZFS) parameters and outline an optical spin polarization protocol for and . Our results demonstrate that these centers are promising candidates for spin qubits.

Studying the Defects in Spinel Compounds: Discovery, Formation Mechanisms, Classification, and Influence on Catalytic Properties.

Spinel ferrites demonstrate extensive applications in different areas, like electrodes for electrochemical devices, gas sensors, catalysts, and magnetic adsorbents for environmentally important processes. However, defects in the real spinel structure can change the many physical and chemical properties of spinel ferrites. Although the number of defects in a crystal spinel lattice is small, their influence on the vast majority of physical properties could be really decisive. This review provides an overview of the structural characteristics of spinel compounds (e.g., CoFe2O4, NiFe2O4, ZnFe2O4, Fe3O4, γ-Fe2O3, Co3O4, Mn3O4, NiCo2O4, ZnCo2O4, Co2MnO4, etc.) and examines the influence of defects on their properties. Attention was paid to the classification (0D, 1D, 2D, and 3D defects), nomenclature, and the formation of point and surface defects in ferrites. An in-depth description of the defects responsible for the physicochemical properties and the methodologies employed for their determination are presented. DFT as the most common simulation approach is described in relation to modeling the point defects in spinel compounds. The significant influence of defect distribution on the magnetic interactions between cations, enhancing magnetic properties, is highlighted. The main defect-engineering strategies (direct synthesis and post-treatment) are described. An antistructural notation of active centers in spinel cobalt ferrite is presented. It is shown that the introduction of cations with different charges (e.g., Cu(I), Mn(II), Ce(III), or Ce(IV)) into the cobalt ferrite spinel matrix results in the formation of various point defects. The ability to predict the type of defects and their impact on material properties is the basis of defect engineering, which is currently an extremely promising direction in modern materials science.

The effect of Mn doping on the electrical and magnetic properties of Cr2Te3 thin films

Mn doped Cr2-xMnxTe3 thin films were prepared by molecular beam epitaxy technology. The effect of Mn doping concentration on the structural, morphological, electrical and magnetic performance of Cr2Te3 thin films were detailed analyzed. By varying the beam current of the Mn source, it is found that Mn can be doped into the Cr2Te3 thin film when the Mn source temperature is lower than 700 ℃, while the Mn tends to bind with Te as MnTe crystal for Mn source temperature higher than 700 ℃. Cr2-xMnxTe3 films all exhibt strong ferromagnetism with a Curie temperature of around 175 K. The magnetization of the films decreases with increasing Mn doping concentration. A notable negative magnetoresistance effect is observed with the highest MR ratio about −60 % in the vicinity of the Curie temperature. A clear topological Hall signal was observed in the sample with a Mn source temperature of 700 ℃ at low temperature (2 K). These results imply that the electrical and magnetic properties of Cr2Te3 materials can be effectively controlled by doping to meet the practical needs of different fields.

Effect of transition metals (Fe, Ru and Os) on the elastic, thermodynamic, electronic, magnetic and thermoelectric properties of three Nd-filled arsenide skutterudites based on first-principles computations

Elastic, electronic, magnetic, thermodynamic, and thermoelectric properties of three neodymium-filled skutterudites NdT4As12 (T = Fe, Ru and Os) have been investigated using density functional theory. The bulk moduli increase with the atomic numbers of the transition metals. All materials are stiff, while the Os compound is the stiffest. A considerable ionic contribution is seen in their inter-atomic bonding. The Fe compound possesses the highest Debye temperature, while the Os compound has the highest melting temperature. GGA+U formalism predicts the semimetallic nature of all the compounds, but their total DOS differs near the Fermi level in both spin channels. The contributions of the Nd-f and T-d electrons differ in the three compounds and two methods. GGA+U predicts the highest magnetic moment in the Fe compound, followed by the Ru and Os compounds. The thermoelectric figure of merit shows no systematic variation with z of the transition metals and in the high temperature region it increases with temperature pretty fast. The highest value of ZT is 0.32 in the Ru compound in the spin-down channel while it is 0.24 in the spin-up channel in the Fe compound, both at 1000 K.

Structural, electronic and dielectric properties of carbon nanotubes interacting with Co nanoclusters

A new frontier in tuning the electromagnetic response of carbon-based materials, particularly carbon nanotubes, consists in adding metallic clusters or nanoparticles at their external surface. This allows to change optical, dielectric and magnetic properties with potential applications in electronics and telecommunications for aeronautics. By resorting to first principles dynamical simulations, we provide a microscopic picture of the interaction at finite temperature between a carbon nanotube and Co aggregates mimicking the experimental coverage. The electronic structure evolution provides the absorption spectrum and the dielectric function for comparison with experiments and guidelines for tuning these composite systems.

Early diagenesis, sedimentary dynamics and metal enrichment reveal deep-sea ventilation in Magellan Seamounts during the middle Pleistocene

Seamounts are ubiquitous topographic units in the global oceans, and the Caiwei Guyot in the Magellan Seamounts of the western Pacific is a prime example. In this study, we analyzed a well-dated sediment core using magnetic properties, sediment grain size, and metal enrichment to uncover regional ventilation history during the middle Pleistocene and explore potential linkages to global climate changes. Our principal findings are as follows: (1) The median grain size is 3.3 ± 0.2 μm, and clay and silt particles exhibit minimal variation, with average values of 52.8 ± 1.8% and 38.2 ± 1.6%, respectively, indicating a low-dynamic process; (2) Three grain-size components are identified, characterized by modal patterns of ~3 μm (major one), ~40 μm, and 400–500 μm, respectively; (3) Magnetic coercivity of the deep-sea sediments can be classified into three subgroups, and their coercivity values are 6.1 ± 0.5 mT, 25.7 ± 1.0 mT, and 65.2 ± 2.1 mT. Based on these results, we propose a close linkage between magnetic coercivity and metal enrichment, correlating with changes in deep-sea circulation intensity. Conversely, sediment grain-size changes seem to be more strongly influenced by eolian inputs. Consequently, we suggest that regional ventilation has weakened since ~430 ka, likely linked to a reduction in Antarctic bottom water formation.

Advanced Anti-icing and Deicing Strategies for Overhead Power Transmission Lines Based on Giant Magnetocaloric Effect of La0.7Ca0.254Sr0.046MnO3.

Perovskite manganates (AMnO3) exhibit diverse structural, thermal, electrical, and magnetic properties. Their strong magnetocaloric effect (MCE) near the Curie temperature (TC) makes them ideal for magnetic-thermal anti-icing and deicing in power transmission lines. Below TC, ferromagnetic AMnO3 produces heat through multiple mechanisms, with the changing magnetic field induced by the strong AC current, causing heat through magnetic hysteresis and eddy currents, alongside the direct MCE. Above TC, no heating is generated, as MCE is unfavorable, thus preventing additional energy loss at elevated temperatures. In this work, La0.7Ca0.254Sr0.046MnO3 with TC close to 0 °C were synthesized by solid-state reaction. It is found that particle size >10 μm is beneficial for a large MCE, based on the results of particle size dependence of MCE. The resulting maximum magnetic entropy change at 277 K is 7.69 J·kg-1·K-1, and an adiabatic temperature change of 3.87 K at 277 K is achieved under 5 T. The prototype cable is fabricated using a well-established wire drawing process. A climate-simulation chamber is employed for the anti-icing and deicing experiments. The prototype cables demonstrated a strong capability for deicing and anti-icing. This simple and cost-effective prototype cable shows significant potential for mitigating the icing problem of overhead high-voltage power transmission lines.

Magnetoelectric Tuning of 2D Ferromagnetism in 1T-CrTe2 through In2Se3 Substrate.

Electric field control of two-dimensional (2D) materials with optimized magnetic properties is not only of scientific interest but also of technological importance in terms of the functionality of various nanoscale devices. Here, we report the multiferroic control of the 2D ferromagnetism in 1T-CrTe2 monolayer through a ferroelectric In2Se3 sublayer. Our results reveal the effect of polarization switching on the electronic structures and magnetic properties of 1T-CrTe2/In2Se3 heterostructures, enabling effective manipulation of their magnetic anisotropy energy (MAE) and magnetization orientation. Additionally, we also demonstrate the strong dependence of their MAE and switching effect on the external strain and surface hydrogenation. Notably, polarization switching exhibits a reversal modification in the hydrogenated multiferroic structures. These tunable behaviors are primarily attributed to the alteration of p-orbitals near the Fermi level of the interfacial Te atoms due to magnetoelectric coupling. Our findings suggest the potential of 1T-CrTe2/In2Se3 heterojunctions for the practical application of 2D multiferroic spintronic devices.

Effect of the Dispersion Medium on NMR Relaxation Properties of Superparamagnetic Iron Oxide Nanoparticles between 0.24 mT and 14.1 T.

Due to weak exchange interactions, magnetite particles at a critical diameter of about 20 nm are considered monodomain. At this size, they exhibit a phenomenological magnetic property called superparamagnetism, making them useful as magnetic resonance imaging contrast agents, or MRI CAs. However, questions persist regarding the impact of using different physiological solvents and varying the environment in which these particles are dispersed on their performance, determined by their relaxivity. A colloidal suspension of superparamagnetic iron oxide nanoparticles (SPIONs) electrostatically stabilized by citrate ligand was synthesized using a fast, reliable, and reproducible developed microwave approach, ensuring high stability over time at pH 7. We studied the effects of three physiological media on these MRI CAs. Ultrapure water was used for the synthesis, while phosphate-buffered saline and physiological liquid were used to disperse the nanoparticles, as these media contain essential electrolytes for the functioning of the human body. The SPIONs underwent systematic characterizations to determine their physicochemical and magnetic properties. This study reports the longitudinal relaxivities of SPIONs at medically relevant magnetic field strengths. Field dependence of their relaxivity (efficacy) was evaluated using a nuclear magnetic resonance dispersion (NMRD) profile measured over a wide range of proton resonance frequencies between 5 kHz and 600 MHz. The Roch et al. model (Roch, A.; et al. J. Chem. Phys., 1999, 110, 5403-5411) was used to analyze the NMRD profile and evaluate the impact of SPIONs on water proton relaxation in the different redispersion media. It was observed in this study that the dynamics of water protons are not influenced by the redispersion media of these citrate-coated SPIONs. However, the presence of salt ions notably reduces their relaxivities by lowering the saturation magnetization of SPIONs.

The incorporation of armchair and zigzag boron nitride nanoribbons in graphene monolayers: An examination of the structural, electronic, and magnetic properties

The opening of an energy gap and generating magnetism in graphene are certainly the most significant and urgent topics in your current research. The majority of proposed applications for it require the ability to modify its electronic structure and induce magnetism in it. Here, using first-principles calculations utilizing the PBE and HSE06 functionals, we examine the structural, energetic, electronic, magnetic, and phonon transport characteristics of armchair graphene and boron nitride nanoribbons (aGNRs and aBNNRs), and zigzag graphene and boron nitride nanoribbons (zGNRs and zBNNRs) with varying widths. We shall emphasize the impact of incorporating aBNNRs and zBNNRs of varying widths into graphene monolayers (GMLs). The findings suggest that zBNNRs are easier to insert into GMLs than aBNNRs. A study of the average formation energies of graphene and boron nitride nanoribbons reveals that BNNRs have a formation energy that is at least twenty times greater than GNRs. We have observed energy gaps that can be classified into three distinct families in aGNRs, aBNNRs, and aBNNRs inserted into GML. In the zGNRs and zBNNRs inserted in GML, depending on the width, different magnetic orderings (antiferromagnetic, ferrimagnetic, and ferromagnetic), and electronic behaviors are observed (metallic, semimetallic, semiconductor, and topological insulator).

Magnetostrictive Behavior of Severe Plastically Deformed Nanocrystalline Fe-Cu Materials

Reducing the saturation magnetostriction is an effective way to improve the performance of soft magnetic materials and reduce core losses in present and future applications. The magnetostrictive properties of binary Fe-based alloys are investigated for a broad variety of alloying elements. Although several studies on the influence of Cu-alloying on the magnetic properties of Fe are reported, few studies have focused on the effect on its magnetostrictive behavior. High pressure torsion deformation is a promising fabrication route to produce metastable, single-phase Fe-Cu alloys. In this study, the influence of Cu-content and the chosen deformation parameters on the microstructural and phase evolution in the Fe-Cu system is investigated by scanning electron microscopy and synchrotron X-ray diffraction. Magnetic properties and magnetostrictive behavior are measured as well. While a reduction in the saturation magnetostriction λs is present for all Cu-contents, two trends are noticeable. λs decreases linearly with decreasing Fe-content in Fe-Cu nanocomposites, which is accompanied by an increasing coercivity. In contrast, both the saturation magnetostriction as well as the coercivity strongly decrease in metastable, single-phase Fe-Cu alloys after HPT-deformation.

Role of biquadratic exchange on thermodynamic quantities in anisotropic Heisenberg model

The magnetic and thermodynamic properties of the spin-1 anisotropic Heisenberg system are studied within Oguchi approximation. The system contains both the bilinear and biquadratic exchange interactions between the nearest neighboring spins located on a centered honeycomb lattice. For the positive biquadratic exchange interaction parameters, the phase transition in the Heisenberg case is of both second and first order where there is a discontinuity in the thermodynamic properties at this transition temperature. For some negative biquadratic exchange interaction parameters, in both the Heisenberg and Ising cases, the ferromagnetic state changes in favor of the antiferromagnetic state. The frustrated antiferromagnetic structure created by the biquadratic exchange parameter with negative sign was shown significantly influence the magnetization, quadrupolar moment, internal energy, heat capacity, entropy and free energy of the system, where the system has an oscillating chaotic phase regime. A double peak behavior was observed in the specific heat, with one at the critical temperature and another at a low temperature.

Uncovering efficient sensing properties of vanadium disulfide (VS2) nanosheets towards specific neurotransmitters: A DFT prospective

Designing efficient nanosensors based on ultrathin materials for the detection of neurotransmitters is crucial for biosensing applications. In this work, using spin-polarized density functional theory (DFT) calculations, structural, electronic, magnetic, and adsorption of the selected neurotransmitters, such as dopamine (DA) and histamine (HA), were investigated using light transition metals dichalcogenides, vanadium disulfide (VS2) nanosheets. It was revealed that DA and HA adsorbed relatively weakly on pristine (p-VS2) as well as single sulfur (S) Vacancy-induced (SV-VS2). However, the introduction of selected transition metals (TMs) dopants, such as cobalt (Co), iron (Fe), and nickel (Ni), significantly improved the adsorption of DA and HA. Among the studied systems, Ni-doped VS2 (Fe-doped VS2) exhibited the strongest adsorption toward DA (HA) with an adsorption energy of −2.00 (−1.28) eV, which is promising for practical sensing applications. Charge analysis revealed that both DA and HA acted as charge donors to the TMs-doped VS2. Upon DA/HA adsorptions, quantifiable variations were observed in the electronic structures and magnetic properties of TMs-doped VS2, which were studied through band structures, spin-polarized density of states, and work function calculations. Lastly, for the practical detection capabilities at diverse pressure and temperature settings, we employed the Langmuir adsorption model. It was found that TMs-doped VS2 detected DA and HA at concentrations ranging from tens of ppt to ppm levels, respectively. We strongly believe that our findings will contribute towards the development of highly effective nanosensors based on TMs-doped VS2 nanosheets for the detection of DA, and HA.

Crystal structure and magnetic properties of Yb2Pt2Pb under multi-extreme conditions

ABSTRACT Structural and magnetic properties of the Shastry-Sutherland material Yb2Pt2Pb were studied in single-crystalline form under pressures up to 10 GPa, magnetic fields up to 17 T, and temperatures down to 0.3 K. Surprisingly robust magnetic order is observed with the Néel temperature T N = 2.1 K stable up to 8.1 GPa. Indication of an additional magnetic phase formation can be traced in resistivity data for magnetic field along the c-axis exceeding the (pressure-dependent) metamagnetic transition. The related anomaly shifts to higher temperatures with increasing field, merging T N at the tricritical point. Experiments with μ0 H // [110] revealed the pressure stabilization of observed magnetic phases with respect to the magnetic field. The crystal-structure type is stable up to 10 GPa, without any sign of symmetry change, exhibiting moderate volume compressibility with bulk modulus B = 116(13) GPa, in good agreement with B = 118 GPa provided by the density functional theory.