Curie Law Research Articles

On the Form of the Functional Dependence of the Magnetic Susceptibility of a Magnetic Liquid on the Temperature

The fulfilment of the Curie and Curie–Weiss laws for a magnetic dispersive nanosystem is critically discussed. Results of investigations into the temperature dependences of the magnetic susceptibility of these media are presented for a wide range of dispersive phase concentrations. Based on the results of these investigations, the validity of these laws for the χ/μ and χ–1 is checked. A conclusion is drawn that the Curie law is valid only for colloids with a certain limited range of magnetic nanoparticle concentrations due to difference in magnitudes of the external magnetic field and the field acting on an individual nanoparticle (effective field). The effective field parameter is calculated in the context of the effective field theory. It is indicated that the value of the effective field parameter is not a constant and depends on the concentration of magnetic nanoparticles and on the temperature of the disperse medium as a whole.

A historical introduction to the symmetries of magnetic structures. Part 1. Early quantum theory, neutron powder diffraction and the coloured space groups

This paper introduces the historical development of the symmetries for describing magnetic structures culminating in the derivation of the black and white and coloured space groups. Beginning from the Langevin model of the Curie law, it aims to show the challenges that magnetic ordering presented and how different symmetry frameworks were developed to meet them. As well as explaining core ideas, later papers will show how the different schemes are connected. With these goals in mind, the maths related is kept to the minimum required for clarity. Those wishing to learn more details are invited to engage with the references. As well as looking back and reviewing the development of magnetic symmetry over time, particular attention is spent on explaining where the concept oftime-reversalhas been applied. That time-reversal has different meaning in classical and quantum mechanical situations, has created confusions which continue to propagate.

Defect-induced magnetism in SiC probed by nuclear magnetic resonance

We give evidence for intrinsic defect-induced bulk paramagnetism in SiC by means of $^{13}\mathrm{C}$ and $^{29}\mathrm{Si}$ nuclear magnetic resonance (NMR) spectroscopy. The temperature dependence of the internal dipole-field distribution, probed by the spin part of the NMR Knight shift and the spectral linewidth, follows the Curie law and scales very well with the macroscopic dc susceptibility. In order to quantitatively analyze the NMR spectra, a microscopic model based on dipole-dipole interactions was developed. The very good agreement between these simulations and the NMR data establishes a direct relation between the frequency distribution of the spectral intensity and the corresponding real-space volumes of nuclear spins. The presented approach by NMR can be applied to a variety of similar materials and, thus, opens a new avenue for the microscopic exploration and exploitation of diluted bulk magnetism in semiconductors.

Magnetic Properties of Liquid Gd–TM (TM = Mn, Fe, Co, Ni) Alloys

Liquid Gd–TM (TM = Mn, Fe, Ni) alloys on the TM-rich side have relatively small and negative temperature coefficients of the magnetic susceptibility χ, which become large and negative with increasing Gd content. The large and negative temperature coefficient of χ for liquid Co gradually weakens at up to 70 at. % Co with the addition of Gd. Liquid Gd and GdcCo1−c alloys with c ≥ 0.5 also have a relatively large and negative temperature coefficient of χ. Liquid Gd–TM alloys on the Gd-rich side obey the Curie law. The magnetic susceptibilities of liquid Gd–Fe and Gd–Co alloys exhibit Curie–Weiss behavior on the TM-rich side. The dependence of χ on the composition for liquid Gd–TM (TM = Mn, Fe, Ni) alloys gradually increases with the Gd content, and that for liquid Gd–Co alloys has a minimum at the composition of 20 at. % Gd. The dependences of χ3d and χ4f on the composition due to the 3d- and 4f-electrons were analyzed by subtracting the corresponding data for liquid La–TM alloys from χ for the liquid Gd–TM ...

The Langevin formula for describing the magnetization curve of a magnetic liquid

It has been shown that, at the initial stage of the magnetization curve, the magnetic susceptibility of magnetic liquid determined as χ = Mμ0/B (M is the magnetization, B is the magnetic induction in a sample) obeys the Curie law, and the magnetic susceptibility determined as χ = M/H (H is the magnetic field intensity in a sample) obeys the Curie–Weiss law. Since the Curie law is a particular case of the Langevin dependence, it is assumed that an experimental magnetization curve is described by the Langevin formula with a Langevin parameter ξ = PB/kT, where P is the magnetic moment of a particle and T is the temperature. Experimental verification has shown that, at parameter ξ, the mean relative deviation between the values of M measured and calculated by the Langevin formula is 5%. This deviation can be accounted for by the influence of dispersion of the magnetic moments of nanoparticles.

Surface magnetism of strontium titanate

SrTiO3 plays a central role in oxide electronics. It is the substrate of choice for functional oxide heterostructures based on perovskite-structure thin-film stacks, and its surface or interface with a polar oxide such as LaAlO3 can become a 2D conductor because of electronic reconstruction or the presence of oxygen defects. Inconsistent reports of magnetic order in SrTiO3 abound in the literature. Here, we report a systematic experimental study aimed at establishing how and when SrTiO3 can develop a magnetic moment at room temperature. Polished (1 0 0), (1 1 0) or (1 1 1) crystal slices from four different suppliers are characterized before and after vacuum annealing at 750 °C, both in single-crystal and powdered form. Impurity content is analysed at the surface and in the bulk. Besides the underlying intrinsic diamagnetism of SrTiO3, magnetic signals are of three types—a Curie law susceptibility due to dilute magnetic impurities at the ppm level, a hysteretic temperature-dependent ferromagnetic impurity contribution, and a practically anhysteretic defect-related temperature-independent component that saturates in about 200 mT. The latter component is intrinsic. It is often the largest, reaching 10 μB nm−2 of the surface area or more and dominating the magnetic response in low fields at room temperature. It is associated with defects near the surface, and can be destroyed by treatment with Tiron (C6H4Na2O8S2), an electron donor molecule that forms a strong complex with titanium at the surface. The origin of this unusual high-temperature ferromagnetic-like response is discussed.

Magnetized liquid 3He at finite temperature: A variational calculation approach

Using the spin-dependent (SD) and spin-independent (SI) correlation functions, we have investigated the properties of liquid [Formula: see text] in the presence of magnetic field at finite temperature. Our calculations have been done using the variational method based on cluster expansion of the energy functional. Our results show that the low field magnetic susceptibility obeys Curie law at high temperatures. This behavior is in a good agreement with the experimental data as well as the molecular field theory results in which the spin dependency has been introduced in correlation function. Reduced susceptibility as a function of temperature as well as reduced temperature has been also investigated, and again we have seen that the spin-dependent correlation function leads to a good agreement with the experimental data. The Landau parameter, [Formula: see text], has been calculated, and for this parameter, a value about [Formula: see text] has been found in the case of spin–spin correlation. In the case of spin-independent correlation function, this value is about [Formula: see text]. Therefore, inclusion of spin dependency in the correlation function leads to a more compatible value of [Formula: see text] with experimental data. The magnetization and susceptibility of liquid [Formula: see text] have also been investigated as a function of magnetic field. Our results show a downward curvature in magnetization of system with spin-dependent correlation for all densities and relevant temperatures. A metamagnetic behavior has been observed as a maximum in susceptibility versus magnetic field, when the spin–spin correlation has been considered. This maximum occurs at [Formula: see text] for all densities and temperatures. This behavior has not been observed in the case of spin-independent correlation function.

Classical impurities and boundary Majorana zero modes in quantum chains

We study the response of classical impurities in quantum Ising chains. The Z2 degeneracy they entail renders the existence of two decoupled Majorana modes at zero energy, an exact property of a finite system at arbitrary values of its bulk parameters. We trace the evolution of these modes across the transition from the disordered phase to the ordered one and analyze the concomitant qualitative changes of local magnetic properties of an isolated impurity. In the disordered phase, the two ground states differ only close to the impurity, and they are related by the action of an explicitly constructed quasi-local operator. In this phase the local transverse spin susceptibility follows a Curie law. The critical response of a boundary impurity is logarithmically divergent and maps to the two-channel Kondo problem, while it saturates for critical bulk impurities, as well as in the ordered phase. The results for the Ising chain translate to the related problem of a resonant level coupled to a 1d p-wave superconductor or a Peierls chain, whereby the magnetic order is mapped to topological order. We find that the topological phase always exhibits a continuous impurity response to local fields as a result of the level repulsion of local levels from the boundary Majorana zero mode. In contrast, the disordered phase generically features a discontinuous magnetization or charging response. This difference constitutes a general thermodynamic fingerprint of topological order in phases with a bulk gap.

Reentrance of disorder in the anisotropic shuriken Ising model

For a material to order upon cooling is common sense. What is more seldom is for disorder to reappear at lower temperature, which is known as reentrant behavior. Such resurgence of disorder has been observed in a variety of systems, ranging from Rochelle salts to nematic phases in liquid crystals. Frustration is often a key ingredient for reentrance mechanisms. Here we shall study a frustrated model, namely the anisotropic shuriken lattice, which offers a natural setting to explore an extension of the notion of reentrance between magnetic disordered phases. By tuning the anisotropy of the lattice, we open a window in the phase diagram where magnetic disorder prevails down to zero temperature. In this region, the competition between multiple disordered ground states gives rise to a double crossover where both the low- and high-temperature regimes are less correlated than the intervening classical spin liquid. This reentrance of disorder is characterized by an entropy plateau, a multi-step Curie law crossover and a rather complex diffuse scattering in the static structure factor. Those results are confirmed by complementary numerical and analytical methods: Monte Carlo simulations, Husimi-tree calculations and an exact decoration-iteration transformation.

Linking Curie constant and phase transition temperature with fundamental ion properties

ABSTRACTThe Curie Law and Curie – Weiss Law, empirically determined relations, with experimentally determined Curie constant(s) and Curie temperature(s), Tc, are related, through correlation, to the permittivity. The Clausius – Mossotti relation, a fundamental equation that links: permittivity; index of refraction through the Lorentz – Lorenz equation; and, conductivity through Maxwell's formula; is here shown to incorporate both the ferroelectric Curie Law and Curie – Weiss Law. In light of recent developments with regard to coordination and temperature dependent ion properties, radii and polarizabilities, of Perovskites, it is now possible to model and design temperature dependent properties: lattice parameters and volumes; permittivity; as well as the temperature of polarization induced structural phase transitions; of at least Perovskites through the Clausius – Mossotti equation using fundamental ion properties which also form the foundational basis upon which the indices of refraction, through the Lorentz – Lorenz equation, and, conductivity, through Maxwell's formula, depend.

On the possibility of determining the thermodynamic temperature of colloid solutions by the nuclear magnetic resonance method

A new method of determining the thermodynamic temperature of colloid solutions placed onto a sealed glass vessel is considered; the method is based on measurements of the magnetic susceptibility in flowing liquid by the magnetic nuclear resonance method. Experimental results show that the Curie law holds for colloid solutions in the temperature range of 278–333 K, in which ferrofluid cells prepared based on these solutions are used.

Nonuniform paramagnetic state in nonstoichiometric lanthanum manganites La1–x Mn1–y O3

The magnetic properties of nonstoichiometric lanthanum manganites La1–x Mn1–y O3 have been studied in the temperature range 80 K < T < 650 K. The Curie temperature T C changes nonmonotonically as the number of Mn4+ ions increases. In the paramagnetic region, there exist isolated Mn ions and magnetic polarons which can be conserved to T ⩽ 4T C, independent of the lattice symmetry. In the T C < T < T pol region, the temperature dependences of the magnetic susceptibility are nonlinear and can be described by the Curie law with a temperature-dependent Curie constant C. The sample has been prepared having a composition near the O′ → O structural transition; the spontaneous magnetization of the sample at T ⩽ 1.6T C is associated to correlated polarons forming due to the double exchange in chains of the E-type antiferromagnetic phase.

Finite block pseudo-spin approach of proton glass

Abstract We herein propose an alternative phenomenology to explain the phase of proton glass by reference to finite block spin theory in magnetism, in which the phase may be considered as being a short-range ferroelectric ordering of block pseudo-spins comprised of random pseudo-spins that have a majority of individual pseudo-spins in a given sense. By making use of the Curie law of block pseudo-spins, we obtained the dielectric susceptibility for the lower and higher temperature approximations of the Brillouin function . The experimental results for the susceptibility in hydrogen-bonded mixed crystals of ferroelectric RbH 2 P(As)O 4 and antiferroelectric NH 4 H 2 P(As)O 4 were thus fitted fairly well at low temperatures in the proton glass phase whereas some deviation from our formulation was seen at high temperatures in the paraelectric phase.

Magnetic properties of point defects in proton irradiated diamond

We investigate the magnetic properties of ultra-pure type-IIa diamond following irradiation with proton beams of ≈1–2MeV energy. SQUID magnetometry indicate the formation of Curie type paramagnetism according to the Curie law. Raman and Photoluminescence spectroscopy measurements show that the primary structural features created by proton irradiation are the centers: GR1, ND1, TR12 and 3H. The Stopping and Range of Ions in Matter (SRIM) Monte Carlo simulations together with SQUID observations show a strong correlation between vacancy production, proton fluence and the paramagnetic factor. At an average surface vacancy spacing of ≈1–1.6nm and bulk (peak) vacancy spacing of ≈0.3-0.5nm Curie paramagnetism is induced by formation of ND1 centres with an effective magnetic moment μeff~(0.1–0.2)μB. No evidence of long range magnetic ordering is observed in the temperature range 4.2-300K.

Size effects in electrical and magnetic properties of quasi-one-dimensional tin wires in asbestos

Bulk composites have been prepared based on one-dimensional fibers of natural chrisothil-asbestos with various internal diameters (d = 6–2.5 nm) filled with tin. The electrical and magnetic properties of quasi-one-dimensional Sn wires have been studied at low temperatures. The electrical properties have been measured at T = 300 K at a pressure P = 10 kbar. It has been found that the superconducting (SC) characteristics of the nanocomposites (critical temperature T c and critical magnetic field H c) increase as the Sn filament diameter decreases. The temperature spreading of the resistive SC transition also increases as the Sn filament diameter decreases, which is explained by the SC order parameter fluctuations. The size effects (the increase in critical temperature T c and transition width ΔT c) in Sn nanofilaments are well described by the independent Aslamazov–Larkin and Langer–Ambegaokara fluctuation theories, which makes it possible to find the dependence of T c of the diffuse SC transition on the nanowire diameter. Using the temperature and magnetic-field dependences of the magnetic moment M(T, H), it has been found that the superconductor–normal metal phase diagram of the Sn–asbestos nanocomposite has a wider region of the SC state in T and H as compared to the data for bulk Sn. The magnetic properties of chrisotil-asbestos fibers unfilled with Sn have been studied. It has been found that the Curie law is fulfilled and that the superparamagnetism is absent in such samples. The obtained results indicate the absence of magnetically ordered impurities (magnetite) in the chrisotil-asbestos matrix, which allowed one to not consider the problem of the interaction of the magnetic subsystem of the asbestos matrix and the superconducting subsystem of Sn nanowires.

Curie law for systems described by kappa distributions

We derive the magnetization of a system, Pierre Curie's law, for paramagnetic particles out of thermal equilibrium described by kappa distributions. The analysis uses the theory and formulation of the kappa distributions that describe particle systems with a non-zero potential energy. Among other results, emphasis is placed on the effect of kappa distribution on the phenomenon of having strong magnetization at high temperatures. At thermal equilibrium, high temperature leads to weak magnetization. Out of thermal equilibrium, however, strong magnetization at high temperatures is rather possible, if the paramagnetic particle systems reside far from thermal equilibrium, i.e., at small values of kappa. The application of the theory to the space plasma at the outer boundaries of our heliosphere, the inner heliosheath, leads to an estimation of the ion magnetic moment for this space plasma, that is, .

Magneto-structural versatility of copper(II)-3-phenylpropionate coordination polymers with N-donor coligands.

A novel series of copper(II) coordination polymers [Cu2(O2CC8H9)4(pyz)]n (1), [Cu2(O2CC8H9)4(dps)]n (2), {[Cu(O2CC8H9)2(dps)(H2O)]·H2O}n (3), {[NaCu(O2CC8H9)2(bpm)(NO3)]·H2O}n (4), and [Cu4(O2CC8H9)6(OH)2(bpp)2]n (5) [O2CC8H9− = 3-phenylpropionate anion, pyz = pyrazine, dps = di(4-pyridyl)sulfide, bpm = 2,2′-bipyrimidine, and bpp = 1,3-bis(4-pyridyl)propane] have been synthesized and magneto-structurally investigated. Compounds 1 and 2 belong to a large group of copper(II) carboxylates where bis-monodentate pyz (1) and dps (2) ligands connect the paddle-wheel [CuII2(μ-O2CC8H9)4] units leading to alternating copper(II) chains. The structure of 3 consists of uniform chains of trans-[CuII(O2CC8H9)2] units linked by the bis-monodentate dps ligand. Compound 4 consists of heterobimetallic chains where [NaI2CuII2(μ-O2CC8H9)4(NO3)2] units are doubly bridged by bis-bidentate bpm ligands. Compound 5 is also a chain compound whose structure is made up by tetranuclear [CuII4(μ3-OH)2(μ-O2CC8H9)4(O2CC8H9)2] units which are doubly bridged by bis-monodentate bpp ligands. The magnetic properties were investigated in the temperature range 1.8–300 K. Strong antiferromagnetic interactions across the quadruple syn–syn carboxylate are observed in 1 and 2 [J = −378 (1) and −348 cm−1 (2)] whereas a weak ferromagnetic coupling through the double out-of-plane oxo(carboxylate) bridge occurs in 4 [J = +2.66 cm−1], the spin Hamiltonian being defined as H = −JS1·S2 with S1 = S2 = SCu = 1/2. A quasi Curie law is observed for 3 (θ = −0.36 cm−1), the bis-monodentate dps ligand being a very poor mediator of magnetic interactions. The analysis of the magnetic properties of 5 is quite complex because of the presence of two crystallographically independent tetracopper(II) units with single-μ-hydroxo, di-μ-hydroxo, μ3-hydroxo and single-μ-hydroxo plus double syn,syn carboxylate bridges in each one. The nature and values of the magnetic couplings for 5 obtained by fitting (intermediate, strong and weak antiferromagnetic interactions for the three former exchange pathways respectively, and intermediate ferromagnetic interactions for the latter one) were substantiated by DFT type calculations.

Influence of anisotropic magnetoelectric interaction on the spontaneous magnetocapacitance in TbMnO3

The spontaneous magnetocapacitance (i.e., the temperature dependence of dielectric constant in the absence of a magnetic field) of the orthorhombic ferroelectromagnet TbMnO3 in the incommensurable antiferromagnetic states is phenomenologically and numerically analyzed. It is shown that both the inhomogeneous magnetoelectric (ME) energy of the third order, which creates the electric polarization, and the ME anisotropy of the fourth order must be considered to get qualitative agreement with the experiment. The inhomogeneous ME energy induces the peak on the εzz(T) which satisfies the Curie law, and a small peak on the εxx(T) at the vicinity of the temperature of the ferroelectric (FE) ordering. The anisotropic ME energy of the fourth order is responsible for the appearance and character of the breaks on the εzz and εxx temperature dependences at the Néel temperature, namely, a decrease in εzz and an increase in εxx in the event of antiferromagnetic ordering. It is shown that the competition of the anisotropic ME energies of the fourth and third orders leads to the minimum on εzz(T) near the FE-transition temperature. The numerical calculation of spontaneous magnetocapacitance with the use of experimental data was performed. The signs and the orders of the constants of anisotropic ME-interactions in TbMnO3 were determined.

Ion induced modifications of Mn-doped ZnO films

We have studied ion impact effects on atomic structure in terms of X-ray diffraction (XRD), optical absorption and electrical resistivity of Mn(6%)-doped ZnO films under 100MeV Xe ion impact at room temperature. We find the monotonic reduction of the XRD intensity to 1/50 of that of unirradiated film at 5×1014cm−2 and the lattice compaction of 0.6% for the ion fluence >1013cm−2, little bandgap change (<0.02eV) and decrease of the resistivity by 4 order of magnitude. The resistivity modification has been compared with that by irradiations of low energy ions such as 100keV Ne and N, which show more effective decrease of resistivity. We also find that temperature (T) dependence of the magnetic susceptibility (χ) of Mn-doped ZnO follows the Curie law: χ=χo+C/T (i.e., paramagnetic) and the Curie constant C decreases to a half of that before irradiation (CO=0.012emucm−3K) at 100MeV Xe ion fluence of 1012cm−2. Relationship is discussed between modifications of the magnetic property and change in the valence of Mn, using a simple and crude argument.

The Radiation Effect on the Thermo-Magnetic Convection in Participating Paramagnetic Medium under Microgravity Condition

The radiation effect on the thermo-magnetic convection which occurs in participating paramagnetic medium under microgravity (g = 0) condition is numerically investigated. Different from the electrically conducting fluid, the paramagnetic fluid is driven by Kelvin force which is proportional to the product of magnetic susceptibility and the gradient of the square of the magnetic induction and is introduced into the source term of the Navier-Stokes equation. In order to realize the fluid flow, an external magnetic field with uniform or non-uniform magnetic gradient is imposed. Further, the thermo-magnetic convection is carried out in high temperature field, in which the magnetic susceptibility varies greatly with absolute temperature according to Curie's law, and the radiation field is also modified by the absorbing-emitting paramagnetic medium. In the present study, the effects of magnetic Rayleigh number and optical thickness are investigated. The results show that radiative heat transfer plays a significant role in thermo-magnetic convection.