The 2<Superscript>1/3</Superscript> rule and other properties of ferromagnets near the temperature of the maximum of magnetic susceptibility

The behavior of the magnetization M and the magnetic susceptibility χ is theoretically analyzed for ferromagnets at the temperature T=T _m corresponding to the maximum of the function χ(T). Four new methods of determining the Curie temperature T_C with the use of the derived relationships are proposed. One of these methods is based on the relationship χ(T _m ) =2^1/3χ(T_C) (the 2^1/3 rule). The results are applied for processing experimental data obtained for lanthanum manganite of composition La_0.85Sr_0.15MnO₃.     

Experimental evidence of a two-phase magnetic state in thin epitaxial films of Re<Subscript>0.6</Subscript>Ba<Subscript>0.4</Subscript>MnO<Subscript>3</Subscript> (Re = La,Pr, Nd,Gd)

Thin epitaxial films of Re_0.6Ba_0.4MnO₃ (Re = La, Pr, Nd, Gd) on (001)-oriented single crystal SrTiO₃ and ZrO₂(Y₂O₃) substrates have been prepared and studied. All films possess a cubic perovskite structure, except for the film with Re = La, which exhibited a rhombohedral distortion of the perovskite lattice. The results show evidence for the presence of two magnetic phases, ferromagnetic (FM) and antiferromagnetic (AFM), in the films studied: (i) the magnetization isotherm M(H) appears as a superposition of a linear component (characteristic of antiferromagnets) and a small spontaneous magnetization component; (ii) the magnetic moment per formula unit is significantly reduced as compared to the value expected for the complete FM or ferrimagnetic ordering; (iii) there is a difference between magnetizations of the samples cooled with and without an applied magnetic field, which is preserved in the entire range of magnetic fields studied (50 kOe); (iv) the temperature dependence of the magnetization M(T) in strong magnetic fields is close to linear (for the composition with Re = Gd, M(T) is described by a Langevin function for superparamagnets with a cluster moment of 2μ_B); and (v) the magnetization hysteresis loops of the field-cooled samples are shifted along the field axis. The exchange integral (characterizing the Mn-O-Mn coupling via the FM-AFM phase boundary) estimated from the latter shift is | J|=10^?6 eV. This value is two orders of magnitude lower than the negative exchange integral between the FM layers in ReMnO₃, which makes the presence of a transition layer at the FM-AFM phase boundary unlikely. The temperature dependences of electrical resistance and magnetoresistance exhibit maxima at the Curie temperature (T_C), where the magnetoresistance reaches a colossal value. This behavior indicates that the two-phase magnetic state is caused by a strong s-d exchange.     

Calculations of paramagnetic susceptibility of rare-earth compounds based on contour integration and the green function method

The paramagnetic susceptibility of rare-earth metal compounds, such as Er_{1 ? x} Ho _x Rh₄B₄, is studied in terms of the microscopic theory of complex compounds. It is shown that the inverse statistical susceptibility of these systems obeys the Curie-Weiss law, with the Curie temperature being determined by the exchange interaction in the self-consistent approximation. The obtained results are compared with experimental data.     

Magnetic properties of Fe<Subscript>3</Subscript>C ferromagnetic nanoparticles encapsulated in carbon nanotubes

The low-temperature dependences of magnetic characteristics (namely, the coercive force H _c , the remanent magnetization M _r , local magnetic anisotropy fields H _a, and the saturation magnetization M _s ) determined from the irreversible and reversible parts of the magnetization curves for Fe₃C ferromagnetic nanoparticles encapsulated in carbon nanotubes are investigated experimentally. The behavior of the temperature dependences of the coercive force H _c (T) and the remanent magnetization M _r (T) indicates a single-domain structure of the particles under study and makes it possible to estimate their blocking temperature T _B = 420–450 K. It is found that the saturation magnetization M _s and the local magnetic anisotropy field H _a vary with temperature as ～T ^5/2.     

Magnetic Properties of Composite Materials Based on a Solid Solution of Type (CuInSe<Subscript>2</Subscript>)<Subscript>1 – <Emphasis Type="Italic">x</Emphasis></Subscript>(MeSe)<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> (Me = Mn,Fe) and Polyethylene

Basic magnetic characteristics (coercive force H_c, residual magnetization M_r, magnetization M, and saturation magnetization M_s) of solid solutions of type (CuInSe₂)_1–x(MeSe)_x (Me = Mn, Fe) have been investigated in a wide temperature interval (100–300 K). The existence of a magnetic phase transition has been established for all studied solid solutions at low temperatures, and the Néel temperatures have been determined from the temperature dependences of the magnetization. It is shown that the temperature dependences of coercive force H_c and of magnetization M can be described using the thermal relaxation (fluctuation) theory.     

Finite size and surface effects on the magnetic properties of cobalt ferrite nanoparticles

Cobalt ferrite, CoFe₂O₄, nanoparticles in the size range 2–15 nm have been prepared using a non-aqueous solvothermal method. The magnetic studies indicate a superparamagnetic behavior, showing an increase in the blocking temperatures (ranging from 215 to more than 340 K) with the particle size, D _TEM. Fitting M versus H isotherms to the saturation approach law, the anisotropy constant, K, and the saturation magnetization, M _S, are obtained. For all the samples, it is observed that decreasing the temperature gives rise to an increase in both magnetic properties. These increases are enhanced at low temperatures (below ~160 K) and they are related to surface effects (disordered magnetic moments at the surface). The fit of the saturation magnetization to the T ² law gives larger values of the Bloch constant than expected for the bulk, increasing with decreasing the particle size (larger specific surface area). The saturation magnetization shows a linear dependence with the reciprocal particle size, 1/D _TEM, and a thickness of 3.7 to 5.1 Å was obtained for the non-magnetic or disordered layer at the surface using the dead layer theory. The hysteresis loops show a complex behavior at low temperatures (T ≤ 160 K), observing a large hysteresis at magnetic fields H > ~1000 Oe compared to smaller ones (H ≤ ~1000 Oe). From the temperature dependence of the ac magnetic susceptibility, it can be concluded that the nanoparticles are in magnetic interaction with large values of the interaction parameter T ₀, as deduced by assuming a Vogel–Fulcher dependence of the superparamagnetic relaxation time. Another evidence of the presence of magnetic interactions is the almost nearly constant value below certain temperatures, lower than the blocking temperature T _b, observed in the FC magnetization curves.     

Magnetic and electrical properties of the ZnGeAs<Subscript>2</Subscript>: Mn chalcopyrite

Doping of the ZnGeAs₂ semiconductor with manganese has produced compositions with spontaneous magnetization and high Curie temperatures of up to 367 K for the composition 3.5 wt% Mn. Their magnetic properties are characteristic of spin glasses at temperatures T < T _S and magnetic fields H < 11 kOe. In stronger fields, the spin glass state transforms into a phase with a spontaneous magnetization 4–5 times weaker than that to be expected under ferromagnetic ordering of all Mn ions. This is obviously a singly-connected ferromagnetic phase containing regions with frustrated bonds. The frustrated regions and the spin glass phase have inclusions of noninteracting ferromagnetic clusters, because these regions and the spin glass phase at low temperatures exhibit a strong increase in the magnetization M, with the dependence M(T) being described by the Langevin function. Measurements of the electrical resistivity ρ and the Hall effect have revealed that, for T < 30 K, the resistivity ρ of compositions with 1.5 and 3.5 wt % Mn is higher that at 30 K, which makes superexchange dominant and gives rise to the onset of the spin glass state. The nonuniform distribution of Mn ions in the spin glass phase accounts for the existence of isolated ferromagnetic clusters, their ferromagnetism being generated by carrier-mediated exchange. As the temperature increases still more, the increase in the mobility occurs faster than the decrease in the concentration, thus promoting an enhancement of the carrier-mediated exchange and growth of the ferromagnetic clusters in size, which at T = T _S come in contact. This signifies a transition from a multiply-to a singly-connected ferromagnetic phase, which contains microregions with frustrated bonds.     

Crystal structure and magnetic susceptibility of (CuInSe<Subscript>2</Subscript>)<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>(2MnSe)<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>

The crystal structure of samples in the (CuInSe₂)_{1 ? x} (2MnSe) _x system at room temperature and their magnetic susceptibility in the temperature range 77–1000 K are investigated. It is established that compositions with concentrations 0≤ x ≤ 0.2 form solid solutions with a tetragonal structure, space group I \(\bar 4\)2d (122). The specific magnetic susceptibility χ of samples with 0.1 ≤ x ≤ 0.4 at 77 K lies in the range 9 × 10^?4?1.6 × 10^t-3cm³/g. The temperature dependence of the inverse magnetic susceptibility of the sample with x = 0.4 suggests the presence of a component with antiferromagnetic ordering and a reliably measured Néel temperature that is characteristic of MnSe. The dependences χ = f(T) of the compositions with x = 0.1, 0.2, 0.3, and 0.4 indicate the occurrence of magnetic phase transitions with a change in the spin state.     

Crystallographic,magnetic, and electrical properties of thin <Emphasis Type="Italic">Re</Emphasis><Subscript>0.6</Subscript>Ba<Subscript>0.4</Subscript>MnO<Subscript>3</Subscript> epitaxial films (<Emphasis Type="Italic">Re</Emphasis> = La,Pr, Nd,Gd)

Thin Re_0.6Ba_0.4MnO₃ epitaxial films (Re = La, Pr, Nd, Gd) grown on (001)SrTiO₃ and (001)ZrO₂(Y₂O₃) single crystal substrates have been prepared and studied. All the films were found to have a cubic perovskite structure, with the exception of the film with Re = La, which revealed rhombohedral distortion of the perovskite cell. The temperature dependences of the electrical resistivity and magnetoresistance pass through a maximum near the Curie point T_C, where the magnetoresistance reaches a colossal value. The magnetization isotherms M(H) are superpositions of a magnetization that is linear in field (like that of an antiferromagnet) and a weak spontaneous magnetization. The magnetic moment per formula unit is substantially smaller than that expected under complete ferro-or ferrimagnetic ordering. The magnetizations of samples cooled in a magnetic field (FC samples) and with no field applied (ZFC samples) differ by an amount that persists up to the highest measurement fields (50 kOe). The M(T) dependence obtained in strong magnetic fields is close to linear. Hysteresis loops of the FC samples are shifted along the field axis. The above magnetic and electric properties of thin films are explained in terms of two coexisting magnetic phases, which are due to strong s-d exchange coupling.     

The possibility of the “giant” isotope effect for ultrasound absorption in crystals

The Zeeman effect, magnetization M(H), and differential magnetic susceptibility dM/dH of ErVO₄ crystals in a pulsed magnetic field have been experimentally and theoretically studied. In magnetic fields H ∥ [001] and H ∥ [100], the energy levels of Er³⁺ ions exhibit mutual approach and crossing (the crossover effect), which results in the peaks in dM/dH and the jumps in M(H) curves at low temperatures. The anomalies in the magnetic properties related to the crossover in ErVO₄ for H ∥ [001] are highly sensitive to the electronic structure of Er³⁺ ion, which allows this effect to be used for refining the crystal field parameters. The influence of the temperature, field misorientation from the symmetry axis, parameters of pair interactions, and other factors on the magnitude and character of magnetic anomalies in ErVO₄ crystals is considered.     

Magnetization behavior and metamagnetic transitions in electron-doped manganites induced by a strong magnetic field

The behavior of magnetization M of the R_xA_1?xMnO₃ manganites (R=La, Pr, Nd, Sm, etc., A=Ca, Sr, Ba) in the electron doping region (x<0.4) is studied as a function of external magnetic field H. The M(H) relations for homogeneous magnetic structures are obtained by performing band calculations in the double-exchange model. Three different types of magnetization behavior corresponding to three electron concentration ranges (x<0.14, 0.14<x<0.27, x>0.27) are revealed. The M(H) relations are interpreted in terms of the phase diagram for the homogeneous ground state of the manganites calculated for H=0, and the results agree qualitatively with experimental data on the magnetization of Sm_xCa_1?xMnO₃.     

Anomalous magnetic properties of electron-irradiated antiferromagnetic copper monoxide

The influence of radiation defects on the magnetic properties of polycrystalline CuO and a high density nanoceramic with crystallite sizes d = 5 and 15 nm has been studied in the temperature range T = 77–300 K. Electron irradiation at fluences Φ = 5 × 10¹⁸ cm^?2 initiated an increase in the susceptibility χ ～ 1/T below 150 K, a feature anomalous for 3D antiferromagnets. The nonlinear behavior of magnetization in weak fields, the increase in the magnetic moment with decreasing temperature, and observation of the spontaneous magnetic moment at temperatures T < 150 K can be attributed to local changes in the exchange parameters and the formation of clusters with uncompensated magnetic moments in the antiferromagnetic matrix near point defects.     

Surface magnetism of nanocrystalline copper monoxide

The effect of the surface on the magnetic susceptibility of nanopowders of the CuO semiconducting antiferromagnet was studied. Single-phase nanopowders with nanoparticles 15, 45, and 60 nm in size were prepared through copper vapor condensation in an argon environment, with subsequent oxidation of the copper. The temperature dependences of the magnetic susceptibility of the nanopowders differ qualitatively from the χ (T) relations for bulk samples. In the region 80≤T≤600 K, the magnetic susceptibility of nanopowders is inversely proportional to temperature and is described by the sum of contributions due to the bulk part of CuO and to the Cu²⁺ paramagnetic ions localized in surface layers. The paramagnetic contribution to the total susceptibility is shown to increase with decreasing particle size and sample density. A comparison of the χ (T) relations is made for nanopowders and for a dense CuO nanoceramic with grain size 5≤d≤100 nm prepared using the shock wave technique.     

Magnetoresistance of a highly correlated electron liquid

The behavior in a magnetic field of a highly correlated electron liquid approaching the fermion condensation quantum phase transition from the disordered phase is considered. We show that, at sufficiently high temperatures T≥T*(x), the effective mass starts to depend on T, M* ∝T^?1/2. This T^?1/2 dependence of the effective mass at elevated temperatures leads to the non-Fermi liquid behavior of the resistivity, σ(T) ∝ T and at higher temperatures σ(T) ∝ T^3/2. The application of a magnetic field B restores the common T² behavior of the resistivity. The effective mass depends on the magnetic field, M*(B) ∝ B^?2/3, being approximately independent of the temperature at T≤T*(B) ∝ B^4/3. At T≥T*(B), the T^?1/2 dependence of the effective mass is reestablished. We demonstrate that this B-T phase diagram has a strong impact on the magnetoresistance (MR) of the highly correlated electron liquid. The MR as a function of the temperature exhibits a transition from negative values of MR at T→0 to positive values at T ∝ B^4/3. Thus, at T≥T*(B), MR as a function of the temperature possesses a node at T ∝ B^4/3.     

Magnetic susceptibility and thermal stability of particle size of nanocrystalline tungsten carbide WC

The magnetic susceptibility χ of coarse-grained and nanocrystalline tungsten carbides was studied in the temperature range 300–1250 K. The temperature dependence of the susceptibility χ(T) of coarse-grained carbide WC is typical of weak Pauli paramagnets and has no specific features. The χ(T) dependence of nanocrystalline carbide (n-WC) in the range 550–920 K exhibits features associated with annealing of microstrains, which leads to a decrease in the contribution of orbital paramagnetism to the magnetic susceptibility of n-WC and initiates precipitation of minor impurities of iron and cobalt as superparamagnetic particles. A nanocrystalline n-WC powder retains a stable particle size of ～55 nm after long annealing at temperatures of 300 to 1200 K, whereas microstrains relax at 550–920 K.     

Effect of low-temperature annealing on the magnetization curve of YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>6 + <Emphasis Type="Italic">x</Emphasis></Subscript> ceramics

The effect of low-temperature annealing on the magnetization curve of YBa₂Cu₃O_{6 + x} ceramics in the superconducting state (x ≈ 0.9) is investigated. When the annealing time is fairly long, the field dependence of magnetic moment M exhibits a feature in the form of a plateau, where the value of M remains almost constant. The evolution of this feature in the magnetization curves of annealed samples with annealing time and temperature is studied. It is assumed that low-temperature annealing gives rise to metastable ferromagnetic clusters in YBa₂Cu₃O_{6 + x} ceramics, the contribution of which to the magnetic moment accounts for the feature in the magnetization curves of the annealed samples.     

Magnetic characteristics of MgFe<Subscript>2</Subscript>O<Subscript>4</Subscript> nanoparticles obtained by glycine–nitrate synthesis

The magnetic properties of magnesium–iron spinel (MgFe₂O₄) powdered nanoparticles obtained by glycine–nitrate synthesis are investigated by X-ray phase analysis and the NMR method. According to the results of X-ray phase analysis, the average size of the crystalline part of nanoparticles of the powder under investigation is 45 ± 4 nm. Magnetization J is determined using the formula J = (B/μ0)–H, where B and H are the induction and strength of the magnetic field in the sample, which are measured by the NMR method. The magnetic characteristics of MgFe₂O₄ are as follows: specific saturation magnetization J_sat = 17.52 A m²/kg, specific residual magnetization J_r = 5.73 A m2/kg, coercive force H_c = 4600 A/m, and magnetic moment P_sat = 371 × 10^–20 A m² in the magnetic saturation state and P_r = 121 × 10^–20 A m² in the residual magnetization state.     

Propriétés magnétiques du thulium à l'état de sesquioxyde et de métal entre 0 et 110 kOe et de 2 à 1560°K

Tm₂O₃ obeys between 80 and 980°K the Curie-Weiss lawχA (T+25=7,08) withμ _eff=7.56 Bohr magnetons, the theoretical value for Tm³⁺(J=6,g=7/6). In the behavior of the metal,χΛ(T-14)=7.45 between 80 and 1540°K, a contribution of the non-localized electrons should be considered at high temperatures. The susceptibility of the metal is maximum at 53°K, minimum near 35°K, and the behavior is antiferromagnetic between these two temperatures, ferromagnetic below 35°K. An additional transition occurs near 10°K, vanishing by cooling in a magnetic field. The effect of this cryomagnetic treatment on the magnetization and the remanence has been measured in six different cooling fields. The magnetization reaches 1.0 and 5.0 magnetons in 26.7 and 110 kOe (pulsed field) respectively, whereas the saturation for the ground state³H₆ isgJ=7.     

Peculiarities of magnetic field-induced ferromagnetic ordering in narrow-band manganites

The temperature dependences of the residual magnetization in narrow-band manganites (Pr_0.67Ca_0.33MnO₃, Sm_0.55Sr_0.45Mn¹⁸O₃, Sm_0.55Sr_0.45Mn¹⁶O₃, and (NdEu)_0.55Sr_0.45Mn¹⁸O₃) have been studied. All compounds studied are characterized by a fairly high residual magnetization M _R (about 0.5 μ_B/Mn) at 4.2 K, which vanishes upon sample heating to the temperature T _RE ≈ 30–35 K, which is much lower than the temperature T _C of the ferromagnetic transition. However, upon magnetization of the samples at T _RE < T < T _C , the residual magnetization (smaller in magnitude) remains up to T _C . For the composition (NdEu)_0.55Sr_0.45Mn¹⁸O₃, the residual magnetization remains at T < T _C , independent of the temperature of magnetization. The disappearance of the residual magnetization found at intermediate temperatures is apparently related to the destruction of the magnetic field-induced ferromagnetic ordering (which contains an additional contribution of the rare-earth sublattice).