Inverse Susceptibility Research Articles

Interparticle interaction effect on superparamagnetic properties of ferrimagnetic particles

Uncoated and oleic acid coated ferrimagnetic particles are synthesized. Both samples contain similar magnetite particles. Structural characterization of these particles is performed using x-ray diffraction, Fourier transform infrared spectra, dynamic light scattering, transmission electron microscopy and thermogravimetric analysis. Average crystallite size of magnetite is 7 nm. Thickness of oleic acid layer on each magnetite particle is 1 nm. The oleic acid coated sample contains 23% oleic acid. Temperature dependence of the zero field cooled susceptibility curve of the uncoated magnetite particles peaks at 120 K. The zero field cooled and the field cooled susceptibility versus temperature curves bifurcate at 195 K. The peak temperature and the bifurcation temperature of the system decrease due to the oleic acid coating. The inverse susceptibility does not vary linearly with temperature in high temperature region. Magnetization versus applied magnetic field data at 250 K are analyzed in different ways to study the interparticle interaction effect on magnetization. We find that the interparticle interactions affect the magnetization process of ferrimagnetic nanoparticles.

Calculation of the order parameter and dielectric susceptibility under the electric field near the incommensurate phase in NaNO2 using Landau model

ABSTRACT Temperature dependences of the order parameters (P and Ψ) and inverse susceptibilities (χp −1 and χΨ -1 ) are calculated for the ferroelectric(FE)-incommensurate (INC) – paraelectric (PE) transitions in NaNO2 at zero (E = 0) and constant electric fields E by the Landau phenomenological model. For the calculation of the polarisation P and the order parameter Ψ, the phase line equations are fitted to the observed data (E = 0) from the literature. On this basis, E-T phase diagram including the ferroelectric, incommensurate and paraelectric phases is constructed using the observed (E-T) data for NaNO2 as reported in the literature. In the presence of the polarisation P (secondary order parameter), which has a biquadratic coupling with the Ψ (primary order parameter) in the incommensurate phase, the Landau model presented here describes the observed behaviour of the FE-INC and INC-PE transitions in NaNO2. Under constant electric fields, our predictions can be compared with the experiments. This method of calculation can be applied to some other crystals exhibiting the incommensurate phase between the FE and PE phases.

Magnetocaloric effect and critical exponents at near room temperature of CrTe

In this work, I investigated and studied the CrTe compound, which has a spin amplitude of about 2, to determine its critical behaviors at near room temperature, magnetocaloric cooling, and magnetic characteristics. For the purpose of this study, I used the Metropolis algorithm with the Monte Carlo approach. The Curie temperature of CrTe is around 326 K, which is determined through the magnetization M(T) and the inverse magnetic susceptibility (χ−1). The Arrott curves (H/M vs. M2) and the isothermal magnetization M(H) demonstrate a second-order ferromagnetic (FM) to paramagnetic (PM) state phase transition. The magnetic entropy change (-ΔSM), relative cooling power (RCP), and refrigeration capacity (Q) at 8 T are 1.31 J kg⁻1 K⁻1, 106 J kg⁻1, and 79 J kg⁻1, respectively. To calculate the critical exponents of CrTe, I used the Widom scaling relation and the modified Arrott plot (MAP). The critical exponent values were found to be in good agreement with those estimated using the renormalization group approach for a 3D-Ising model.

Evolution of ferromagnetic cluster in perovskite La0.88Sr0.12MnO3 nanocrystalline detected by EPR spectrum

Electron paramagnetic resonance (EPR) studies were performed on La0.88Sr0.12MnO3 (LSMO) nanocrystalline together with the measurement of its magnetization. Various spectrum parameters including line width, effective g-value and double-integrated intensities have been analyzed in detail. We found nonlinear behavior occurred in the inverse susceptibility far above the Curie temperature TC, indicating short-range ferromagnetic (FM) clusters and Griffiths-like phase behavior in the paramagnetic (PM) phase. Based on the variation of EPR spectra, except for a typical PM resonance peak, an extra resonance signal was observed in the lower field region and developed as temperature decreased from 320 K to 110 K, which gave a direct evidence of the existence of FM cluster in the PM region of LSMO nanocrystalline. We proposed that the appearance of the Griffiths phase was due to the short FM correlation in the PM regime enhanced by surface spin ordering.

Magnetic Single‐Ion Anisotropy and Curie‐Weiss Behaviour of Mg3V4(PO4)6

AbstractDirect current (DC) magnetometry data obtained for polycrystalline Mg3V4(PO4)6 were fitted by various magnetic models based on angular momentum basis states. As a result, single‐ion anisotropy of the magnetic V 3+ ions could be identified to decisively determine the magnetic properties of Mg3V4(PO4)6 and not antiferromagnetic exchange interaction between V ions as supposed in literature. It could be demonstrated analytically, by utilization of the Van Vleck equation, that also single‐ion anisotropy can lead to a linear and origin shifted inverse susceptibility curve in the high temperature region. The Weiss constant obtained from a Curie‐Weiss fit to such a susceptibility curve might falsely be ascribed to antiferromagnetic exchange interactions if additional low temperature magnetic properties are not considered for verification.

Effect of bismuth doping on structural, morphological, Griffiths-like phase, and magnetocaloric properties in La0.9−xBixBa0.1MnO3 (x = 0, 0.05, and 0.1)

In this recent work, we have carried out the structural, morphological, Griffiths-like phase, and magneto-caloric studies of sol–gel-synthesized, nanocrystalline manganite La0.9−xBixBa0.1MnO3 (x = 0, 0.05, and 0.1). The Rietveld analysis of X-ray diffraction patterns of nanocrystalline La0.9−xBixBa0.1MnO3 (x = 0, 0.05, and 0.1) confirm the single-phase nature and orthorhombic crystal structure with Pnma space group for all samples. The images acquired with a transmission electron microscope reveal the average particle sizes ranges from 32 nm to 65 nm. The temperature-dependent magnetization measurements, for 0.05 T external applied magnetic field, have revealed paramagnetic (PM) to ferromagnetic (FM) phase transition with transition temperatures (TC) ∼ 228 K, 219 K, and 233 K for x = 0, 0.05, and 0.1, respectively. The downward divergence of temperature dependence inverse susceptibility from the Curie-Weiss fit, indicates a pronounced Griffiths singularity in the samples. The positive slopes of Arrott plots for nanocrystalline La0.9−xBixBa0.1MnO3 (x = 0.05, 0.1) confirm the second-order magnetic phase transition. We have estimated the magnetic entropy change at different values of applied magnetic field for nanocrystalline La0.9−xBixBa0.1MnO3 (x = 0.05, 0.1) samples. Further, using this magnetic entropy data, we have also estimated the magnetic cooling capacity.

In English

The article discusses the use of KDP ferroelectric crystals (phosphates and arsenates of potassium, rubidium, cesium) and their deuterated analogues in various industries, including the creation of electro-optical devices and as hydrogen sorbents. The paper describes the physical properties of KDP crystals, changes in their properties near the phase transition temperature, as well as methods for obtaining KDP nanocrystals and their application in biomedicine. The paper also states that the phase transition in KDP crystals occurs near room temperature and manifests itself in a change in their physical properties, such as dielectric constant, optical properties, and heat capacity. In addition, approaching the phase transition temperature causes a change in the crystal lattice parameters, which can lead to the appearance of anomalous effects. The structure of the unit cell of potassium dihydrogen phosphate (KH2PO4) is considered. The plots of the temperature dependence of the order parameter of spontaneous polarization and the plots of the temperature dependence of the configurational heat capacity of the crystal in the phase transition region are calculated, and the plots of the temperature of the inverse and direct dielectric susceptibility are calculated. Graphs of the order parameter, which characterizes the degree of spontaneous polarization for different temperatures, depending on the strength of the external electric field, are also calculated.

Renormalized one-loop theory of correlations in disperse polymer blends.

Polymer blends are critical in many commercial products and industrial processes and their phase behavior is therefore of paramount importance. In most circumstances, such blends are formulated with samples of high dispersity, which have generally only been studied at the mean-field level. Here, we extend the renormalized one-loop theory of concentration fluctuations to account for blends of disperse polymers. Analyzing the short and long length-scale fluctuations in a consistent manner, various measures of polymer molecular weight and dispersity arise naturally in the free energy. Thermodynamic analysis in terms of moments of the molecular weight distribution(s) provides exact results for the inverse susceptibility and demonstrates that the theory is not formally renormalizable. However, physically motivated approximations allow for an "effective" renormalization, yielding (1) an effective interaction parameter, χe, which depends directly on the sample dispersities (i.e., Mw/Mn) and leaves the form of the mean-field spinodal unchanged, and (2) an apparent interaction parameter χa that depends on higher-order dispersity indices, for instance Mz/Mw, and characterizes the true limits of blend stability accounting for long-range off-critical fluctuations. We demonstrate the importance of dispersity on several example systems, including both "toy" models that may be realized in computer simulation and more realistic industrially relevant blends. We find that the effects of long-range fluctuations are particularly prominent in blends where the component dispersities are mismatched, especially when there is a small quantity of the high-dispersity species. This can be understood as a consequence of the shift in the critical concentration(s) from the monodisperse value(s).

An Effectively Uncoupled Gd8 Cluster Formed through Fixation of Atmospheric CO2 Showing Excellent Magnetocaloric Properties.

The [Gd8(opch)8(CO3)4(H2O)8]·4H2O·10MeCN coordination cluster (1) crystallises in P1¯. The Gd8 core is held together by four bridging carbonates derived from atmospheric CO2 as well as the carboxyhydrazonyl oxygens of the 2-hydroxy-3-methoxybenzylidenepyrazine-2-carbohydrazide (H2opch) Schiff base ligands. The magnetic measurements show that the GdIII ions are effectively uncoupled as seen from the low Weiss constant of 0.05 K needed to fit the inverse susceptibility to the Curie-Weiss law. Furthermore, the magnetisation data are consistent with the Brillouin function for eight independent GdIII ions. These features lead to a magnetocaloric effect with a high efficiency which is 89% of the theoretical maximum value.

ESR and magnetization studies of double perovskite Sr[formula omitted]FeNbO6

By pyrolysis of nitrate-organic mixtures, we synthesized double perovskite Sr2Fe0.6NbO5.4. We performed the study of the temperature dependencies of the EPR spectra, DC and AC magnetization, and magnetization isotherms in a wide temperature range of 4–300K. The EPR spectrum is described by the sum of two contributions below 125 K and indicates phase separation of the sample. The paramagnetic part of the inverse magnetic susceptibility is well approximated by the Curie–Weiss law with ΘCW≈−60K. The exchange integrals between iron spins, calculated from the temperature dependence of the ESR integral intensity and the Curie–Weiss temperature, coincide and are equal to J/kB≈10K. The negative sign of the Curie–Weiss temperature and the hysteresis loops indicate the antiferromagnetic canted nature of exchange interactions, which is further confirmed by the presence of a peak in the real part of the AC magnetization and its absence in the imaginary part.

Reentrant canonical spin-glass dynamics and tunable field-induced transitions in (GeMn)Co2O4 Kagomé lattice

We report on the reentrant canonical semi spin-glass characteristics and controllable field-induced transitions in distorted Kagomé symmetry of (GeMn)Co2O4. This B-site spinel exhibits complicated, yet interesting magnetic behaviour in which the longitudinal ferrimagnetic (FiM) order sets in below the Néel temperature T FN ∼ 77 K due to uneven moments of divalent Co (↑ 5.33 μ B) and tetravalent Mn (↓ 3.87 μ B) which coexists with transverse spin-glass state below 72.85 K. Such complicated magnetic behaviour is suggested to result from the competing anisotropic superexchange interactions (J AB/k B ∼ 4.3 K, J AA/k B ∼ −6.2 K and J BB/k B ∼ −3.3 K) between the cations, which is extracted following the Néel’s expression for the two-sublattice model of FiM. Dynamical susceptibility (χ ac (f, T)) and relaxation of thermoremanent magnetization, M TRM (t) data have been analysed by means of the empirical scaling-laws such as Vogel–Fulcher law and Power law of critical slowing down. Both of which reveal the reentrant spin-glass like character which evolves through a number of intermediate metastable states. The magnitude of Mydosh parameter (Ω ∼ 0.002), critical exponent zυ = (6.7 ± 0.07), spin relaxation time τ 0 = (2.33 ± 0.1) × 10−18 s, activation energy E a/k B = (69.8 ± 0.95) K and interparticle interaction strength (T 0 = 71.6 K) provide the experimental evidences for canonical spin-glass state below the spin freezing temperature T F = 72.85 K. The field dependence of T F obtained from χ ac (T) follows the irreversibility in terms of de Almeida–Thouless mean-field instability in which the magnitude of crossover scaling exponent Φ turns out to be ∼2.9 for the (Ge0.8Mn0.2)Co2O4. Isothermal magnetization plots reveal two field-induced transitions across 9.52 kOe (H SF1) and 45.6 kOe (H SF2) associated with the FiM domains and spin-flip transition, respectively. Analysis of the inverse paramagnetic susceptibility after subtracting the temperature independent diamagnetic term (=−3 × 10−3 emu mol−1 Oe−1) results in the effective magnetic moment = 7.654 μ B/f.u. This agrees well with the theoretically obtained = 7.58 μ B/f.u. resulting the cation distribution in support of the Hund’s ground state spin configuration and of Mn4+ and Co2+, respectively. The H–T phase diagram has been established by analysing all the parameters (T F(H), T FN(H), H SF1(T) and H SF2(T)) extracted from various magnetization measurements. This diagram enables clear differentiation among the different phases of the (GeMn)Co2O4 and also illustrates the demarcation between short-range and long-range ordered regions.

Improved magnetic properties of Fe substituted La2CoMnO6 for spintronic applications

A detailed study of magnetic behaviour of double perovskites was carried out by developing La2Co1-xFexMnO6; (x = 0.0, 0.2, 0.5, 0.8 and 1.0) via sol–gel technique. All samples showed single magnetic transition except pure LCMO (x = 0.0) and LCFMO2 (x = 0.5). Temperature dependent inverse magnetic susceptibility (χ-1) was fitted in accordance with Curie-Weiss law. μeff (effective magnetic moment) was determined for all the developed samples. Pure LCMO showed a downward divergence from Curie-Weiss law below 230 K but above transition temperature which indicates the characteristics of Griffiths phase. Saturation magnetization (Ms) increased initially and then decreased, whereas coercive field (Hc) was found to be monotonous decreased with increase in Fe content. LCFMO1 (x = 0.2) was noticed to have maximum Ms (38.87 emu/g) which indicated that the magnetic properties of pure LCMO were improved with Fe substitution, but for lower substitution only. Magnetization vs. field (M−H) curves were not well saturated even at a magnetic field of 60 kOe, therefore, values of Ms for all the samples were estimated using law of approach to saturation. With increase in Fe content, an increased anti-site disorder among Mn and Co strengthened antiferromagnetic (AFM) super exchange interactions and weakened ferromagnetism (FM). Therefore, substitution of Fe on Co-site was responsible for systematic decrease in saturation magnetization when × exceeded 0.2.

Effect of Al substitution at the Ga site on the structural and magnetic properties of GaFeO3

GaFeO3 compound figures among those orthoferrites that are potential candidates for multiferroics. However, GaFeO3 suffers from a relatively low Nèel temperature, TN ≈ 200 K, and magnetic moment. Based on the results of a detailed investigation of Raman-active modes, structural and magnetic properties of the Ga1-xAlxFeO3 (x = 0.0, 0.05, 0.10, 0.20, 0.30) samples, we show that Al substitution at the Ga sites remedies these shortcomings to a large extent. This work brings out clearly that Al preferentially occupies the tetrahedral (Ga1) sites rather than the octahedral (Ga2, Fe1 and Fe2) sites. The effect of Al substitution in Ga1-xAlxFeO3 is to (i) decrease the lattice parameters and cation-O bond lengths which results in a shift in the positions of Raman peaks towards higher wavenumbers, and (ii) increase (decrease) the cation-O-cation bond-angles such that the antiferromagnetic (ferromagnetic) superexchange interactions grow in strength. An enhancement in these interactions accounts for the observed increase in the Nèel temperature, TN, as well as in the saturation magnetization. The radically different temperature variations of the ‘zero-field-cooled’ and ‘field-cooled’ magnetizations below the irreversibility temperature can be qualitatively understood in terms of the Nèel molecular-field theory for ferrimagnetism. The temperature dependence of inverse susceptibility in the paramagnetic state provides evidence for the non-linear behavior at temperatures well above TN and hence for the persistence of short-range magnetic order to temperatures as high as 1.75 TN.

Revival of Ferromagnetic-Metallic Phase and Emergence of Griffiths Phase via Ni and Cr Substitution in Charged-Ordered Pr0.75Na0.25MnO3 Manganite

Polycrystalline samples of Pr0.75Na0.25Mn1-xAxO3 (A = Ni, Cr; x = 0, 0.03) were prepared using conventional solid-state method and their structural and magnetic properties were investigated. Monovalent-doped Pr0.75Na0.25MnO3 exhibits insulating behavior which is related to the strong localization of charge carriers due to the presence of charge ordering (CO). The substitution of different types of magnetic ions, A, which are Ni2+ and Cr3+, at a concentration of x = 0.03 at the Mn site in the CO Pr0.75Na0.25Mn1-xAxO3 manganite, has been found to dramatically modify its structural and magnetic properties. X-ray diffraction patterns showed that all samples were present in single phase and crystallized in orthorhombic structure with Pnma space group. The Rietveld refinement analysis showed that the unit cell volume increased due to Ni2+ substitution, while it decreased due to Cr3+ substitution, which may be attributed to the different ionic radii of both ions. The suppression of the CO state and the induction of the ferromagnetic-metallic state in the Ni-substituted and Cr-substituted samples are suggested to be due to the induction of double-exchange interaction involving Ni2+–O–Mn4+ and Mn3+–O–Cr3+, respectively. The variation in magnetic properties between the Ni-substituted and Cr-substituted samples is suggested to be due to the existence of different strengths of ferromagnetic interaction between Ni2+–O–Mn4+ and Mn3+–O–Cr3+. In addition, the deviation of the temperature dependence of the inverse magnetic susceptibility curves from the Curie-Weiss law suggests the existence of Griffith’s phase-like behaviour for both substitution samples. The Ni-substituted sample induced a greater GP effect than the Cr-substituted sample due to the larger difference of TC and TG value (TC-TG).

Retrieving the Intrinsic Microwave Permittivity and Permeability of Ni-Zn Ferrites

Mixing rules may be extremely useful for predicting the properties of composite materials and coatings. The paper is devoted to the study of the applicability of the mixing rules to permittivity and permeability and the possibility of retrieving the intrinsic properties of inclusions. Magnetically soft Ni-Zn ferrites are chosen as the object of the study due to their low permittivity and the negligible influence of the skin effect. Due to this, the microwave properties of bulk ferrites may be measured by standard techniques. It is suggested to perform the analysis of the microwave properties of composites filled with Ni-Zn ferrite powder in terms of the normalized inverse susceptibility defined as the volume fraction of inclusions divided by the effective dielectric or magnetic susceptibility of the composite. The measured properties of the bulk ferrite are compared with those obtained by mixing rules from composite materials. The experimental evidence for difference between the mixing rules for permittivity and permeability of a composite, which was previously predicted only theoretically, is obtained. The reason for the difference is considered to be the effect of non-ideal electrical contacts between neighboring inclusions. It is also experimentally shown that the measured permeability of the bulk material may differ from the retrieved one. The measured static permeability is 1400 and the retrieved one is 12. The reason for the discrepancy is the difference between the domain structures and demagnetizing fields of particles and bulk ferrite.

Surfactant-free synthesis and magnetic property evaluation of air-stable cobalt oxide nanostructures

We report the synthesis of metastable cobalt oxide (CoO) nanostructures via the low-temperature microwave-assisted solvothermal (MAS) process. An alcoholic solution of cobalt (II) acetylacetonate in a sealed vessel was irradiated with microwaves at a temperature <150 °C and a pressure below 100 psi. As-synthesized powder material was characterized in terms of its structure and morphology. X-ray diffractometry (XRD) indicates the formation of well-crystallized CoO nanoparticles without the need for post-synthesis annealing. The mean crystallite size of the nanoparticles was estimated to be 41 nm. The morphology of the as-prepared powder sample was evaluated by field-emission scanning electron microscopy (FESEM), which revealed the formation of densely packed nanospheres of diameter <100 nm. The CoO nanospheres were obtained without the need for any surfactants or capping agents; they were found to be quite resistant to oxidation in ambient air over several months. We attribute the stability of CoO nanospheres to their dense packing, the driving force being the minimization of surface energy and surface area. Fourier-transform infrared (FT-IR) spectroscopy and Raman spectroscopy confirm the formation of phase-pure CoO nanostructures. The deconvolution of the active modes in Raman spectra obtained at room temperature reveals the Oh symmetry in rock-salt CoO produced by the MAS route. We have analyzed its effect on the magnetic characteristics of the CoO nanostructures. Isothermal field-dependent magnetization (MH) and inverse magnetic susceptibility measurements show a phase transition from antiferromagnetic to ferromagnetic interactions in the CoO nanostructures at around 10 K. The results indicate that the phenomenon of magnetic phase transition as a function of temperature is unique to CoO nanoparticles. This finding reveals the magnetic behavior of CoO nanostructures and presents opportunities for its possible application as an anisotropy source for magnetic recording.

The significant magnetic attenuation with submicrometer scale magnetic phase separation in tensile-strained LaCoO3 films

It is well known that the epitaxial strain plays a vital role in tuning the magnetic states in transition metal oxide LaCoO3 films. Here, we reported a robust long-range ferromagnetic (FM) ground state in a tensile-strained perovskite LaCoO3 film on a SrTiO3 (STO) substrate, which has a very significant attenuation when the thickness ranges from 10 to 50 nm. It is speculated that such attenuation may be caused by the appearance of the cross-hatched grain boundary, which relaxes the tensile strain around the crosshatch, resulting in the local non-FM phases. Magnetic force microscope observation reveals non-FM patterns correlated with the structural crosshatches in the strain-relaxed film even down to a temperature of 2 K and up to a magnetic field of 7 T, suggesting the phase separation origin of magnetization attenuation. Furthermore, the investigations of the temperature-dependent inverse magnetic susceptibility show a deviation from the Curie–Weiss law above the transition temperature in a 50-nm-thick LaCoO3/STO film but not in the LaCoO3/LaAlO3 film, which is ascribed to the Griffiths phase due to the crosshatch-line grain boundaries. These results demonstrated that the local strain effect due to structural defects is important to affect the ferromagnetism in strain-engineered LaCoO3 films, which may have potential implications for future oxide-based spintronics.

Particle size-dependent structural and magnetic properties of Pr0.6-xBixSr0.4MnO3 (x = 0.10 and 0.25)

Nanoparticles of Pr0.6-xBixSr0.4MnO3 (x = 0.10 and 0.25) have been prepared using the swift and cost-effective top-down approach in a high-energy planetary ball mill without any chemical processing and environmental impacts resulting due to pollutants arising from nanoparticle synthesis. The work investigates the role of particle size reduction on the structural and magnetic properties. An increase in milling time from 0 to 240 min results in the drastic reduction of particle size which drops significantly in the initial phase of ball milling i.e., 0–60 min while the microstrain and dislocation densities show nearly monotonic increase. Interestingly the magnetism and size reduction demonstrate a clear one to one correspondence. In both compositions, the paramagnetic (PM) to ferromagnetic (FM) transition, TC decreases and the magnetic transitions broaden both as function Bi and size reduction. The Curie–Weiss analysis of the inverse magnetic susceptibility ({chi }^{-1}) shows a deviation from linearity indicating the presence of the short-range FM interactions above TC which has been understood as Griffith’s phase like singularity. The size reduction can effectively reduce TC, enabling a significant control over tuning of transition temperature and net magnetization. The field dependent magnetization for x = 0.10 demonstrate dominant FM state whereas for x = 0.25, metamagnetic magnetization highlights competitive coexistence of FM and antiferromagnetic (AFM) interactions in the system. With ball milling, the net magnetization decreases, and the metamagnetic behaviour is suppressed. The M–H loops of ball milled nanoparticles are highly unsaturated indicating the enhanced surface disorder in the nanoparticles which can be understood using the core–shell structure.

A possible phase and dynamical transition in a three-dimensional Electron Glass

Using mean-field approximations, this paper identifies a phase transition in a three-dimensional Electron Glass lattice model. The density of states of the eigenvalue distribution of the inverse susceptibility matrix is used to identify the possibility of a phase transition. In the thermodynamic limit, the eigenvalue spectrum appears to extend to zero as T≈Tc. To determine the dynamical relaxation laws near the transition temperature, we use the eigenvalue distribution of the linear dynamical matrix. Our analysis distinguishes between the phenomenon of phase transition and slow dynamics.

Exchange interactions in iron and nickel: DFT+DMFT study in paramagnetic phase

We analyze possible ways to calculate magnetic exchange interactions within the density functional theory plus dynamical mean-field theory (DFT+DMFT) approach in the paramagnetic phase. Using the susceptibilities obtained within the ladder DMFT approach together with the random phase approximation result for the Heisenberg model, we obtain bilinear exchange interactions. We show that the earlier obtained result of Stepanov et al. [Phys. Rev. Lett. 121, 037204 (2018); Phys. Rev. B 105, 155151 (2022)] corresponds to considering individual magnetic moments in each orbital in the leading-order approximation in the non-local correlations. We consider a more general approach and apply it to evaluate the effective magnetic parameters of iron and nickel. We show that the analysis, based on the inverse orbital-summed susceptibilities, yields reasonable results for both, weak and strong magnets. For iron we find, in the low-temperature limit, the exchange interaction $J_0\simeq 0.20$ eV, while for nickel we obtain $J_0\simeq 1.2$ eV. The considered method also allows one to describe the spin-wave dispersion at temperatures $T\sim T_C$, which is in agreement with the experimental data.