Phase transitions in a ferromagnetic semiconductor. I

An analysis is given of the conditions for ferromagnetic phase transitions in an idealised semiconductor model containing magnetic ions. The system is described by a constant interaction — 2J/N between the magnetic ions (Spin I) and the electrons, by the energy gapΔ between two infinitely narrow bands and by the concentrationc of the magnetic ions. We find a great variety of ferromagnetic behavior. In particular there exists the possibility for the magnetization to disappear with a first or second order transition as the temperature decreases or increases. Some magnetization curves are evaluated numerically.     

Dependence of the anhysteretic magnetization on the demagnetization factor

A method is presented to measure the dependence of the anhysteretic magnetization curve (the anhysteretic magnetization as a function of the internal field after degaussing) on the demagnetization factor N without physically varying N. The relation between the Preisach distribution and the N dependence of the anhysteretic magnetization curve is discussed in a way that is very close to the work of Bertotti. Classes of (moving) Preisach models are identified for which the anhysteretic magnetization curve is independent of the demagnetization factor. It is proven that the anhysteretic magnetization increases with N at fixed internal field, if the Preisach distribution decreases monotonically with increasing H_cent, the internal field value of a Preisach domain. It is shown that the Moving Preisach model may lead to a negative anhysteretic permeability.     

Metamagnetic transition and magnetocaloric effect in antiferromagnetic TbPdAl compound

Magnetic properties and the magnetocaloric effect of the compound TbPdAl are investigated. The compound exhibits a weak antiferromagnetic (AFM) coupling, and undergoes two successive AFM transitions at T_N=43 K and T_t=22 K. A field-induced metamagnetic transition from AFM to ferromagnetic (FM) state is observed below T_N, and a small magnetic field can destroy the AFM structure of TbPdAl, inducing an FM-like state. The maximal value of magnetic entropy change is −11.4 J/kg K with a refrigerant capacity of 350 J/kg around T_N for a field change of 0-5 T. Good magnetocaloric properties of TbPdAl result from the high saturation magnetization caused by the field-induced AFM-FM transition.     

Low-temperature quasi-adiabatic magnetization reversal of rare-earth Ising metamagnets

The magnetization and magnetically induced elastic strains of rare-earth Ising antiferromagnets DyAlO₃ and TbAlO₃ are shown to exhibit an unusual behavior associated with low-temperature metamagnetic phase transitions. As an external magnetic field is applied and then removed slowly, the state of the magnetic system in these compounds follows quite different paths on the H-T diagram. Small alternating-sign variations in the field magnitude cause the magnetic system to switch reversibly from one path to another, which is accompanied by sharp changes in the magnetization and elastic strains. The observed anomalies are shown to be due to the magnetization process being quasi-adiabatic in character in the compounds under study. This fact should be taken into account in interpreting the data on the magnetization and magnetostriction in Ising antiferromagnets undergoing metamagnetic transitions at low temperatures. Experimentally, quasi-adiabatic magnetization makes it possible to determine the critical fields for metamagnetic transitions very exactly and to investigate the H-T phase diagram at temperatures that are far below the minimum temperature of a helium bath and are unattainable under strictly isothermal conditions.     

Exchange energy for conduction electrons in (ZnMn)Se derived from spin-flip Raman scattering and magnetization

Spin-flip Raman scattering, magnetization, and susceptibility data for Zn_0.97Mn_0.03Se are reported. The exchange energy N_oα = 243 ± 10 meV for the conduction electrons is obtained from an analysis of the Raman and magnetization data. At large magnetic fields (H > 60 kOe), the spin-flip energy ΔE saturates at 14 meV. At low fields ΔE does not extrapolate to zero as H → 0, which is characteristic of scattering from donor-bound electrons. The low temperature magnetization curves are fit to a modified Brillouin function. The fit gives $\text{x}\text{?}\text{/x}\text{= 0.67}$ as the fraction of active magnetic ions, and an effective temperature T_eff = T + T_o with T_o = 1.1 K. The magnetic susceptibility follows a Curie-Weiss law between T = 150 and 280 K with a Curie-Weiss temperature θ = ?33 K.     

One-dimensional Ising chain with generalized molecular field

The behavior of a spin-$\text{1}\text{2}$ one-dimensional nearest-neighbor Ising chain coupled to a generalized internal molecular field is considered. The internal field is shown to be equivalent to long-range spin-spin interactions. An assumed expansion of the internal field in powers of the magnetization results in the possibility of first- or second-order phase transitions and softening in the spontaneous magnetization and specific heat near the transition temperature. The internal energy and magnetic susceptibility are also discussed.     

Magnetic phase transitions in Nd7Rh3 single crystal

Magnetic phase transitions in rare earth intermetallic compound Nd₇Rh₃ have been investigated using a single crystal. Measurement results of magnetization, magnetic susceptibility, specific heat, and electrical resistivity reveal that Nd₇Rh₃ has two magnetic phase transitions at T_N=34 K, T_t2=9.1 K and a change of the magnetic feature at T_t1=6.8 K in the absence of an external magnetic field. Antiferromagnetic orderings exist in all the three magnetic states; a large magnetic anisotropy between the c-axis and the c-plane is observed. In the magnetic phase below T_t2, an irreversible field-induced magnetic phase transition takes place in the c-plane; after removing external magnetic field, a coexistence state of ferro- and antiferromagnetic ordering or a ferrimagnetic state having a remanent magnetization M_R is stabilized. The M_R decays to a certain value for several hours after the first process; a magnetic field cooling effect was also observed in the c-plane below T_t2. In the antiferromagentic state above T_t2, the irreversibility disappears and an ordinary antiferromagnetic state takes place. As the origin of this phenomenon, a kind of martensitic structural transition that is observed in Gd₅Ge₄ can be considered.     

Ultra-sharp metamagnetic transition in manganite Pr0.6Na0.4MnO3

We report the magnetic and electrical transport properties of manganite Pr_0.6Na_0.4MnO₃. At the temperature of 2 K, a field-induced steplike magnetization and resistivity transition are observed. The step transitions of magnetization and resistivity are shifted to higher fields as a result of field cooling, and transformed to a smooth broad one when the cooling field is higher than 20 kOe. Moreover, in a magnetic field slightly below the critical field, the magnetic and resistive relaxation exhibits a spontaneous step after a long incubation time when both the temperature and magnetic field are constant. Such steplike transitions are discussed in terms of a martensiticlike transformation associated with phase separation.     

Magnetization and spin-flip energy in Cd0.9Mn0.1Se

Magnetization and spin-flip Raman measurements are reported for Cd_1?xMn_xSe, x = 0.106, at 1.9 < T < 4.2 K and magnetic fields H up to 80 kOe. The high-field results are combined to determine the exchange energy between donor electrons and Mn⁺⁺ spins, αN₀=261±13 meV. Empirical fits to the magnetization data are described.     

Magnetic and electrical properties of Gd7Rh3 single crystal

Magnetic and electrical properties of hexagonal Gd₇Rh₃ single crystals have been studied by measuring magnetization, magnetic susceptibility, and electrical resistivity. Gd₇Rh₃ shows antiferromagnetic order below T_N=141 K as reported by Loebich et al; magnetic anisotropy is small in paramagnetic region. Metamagnetic transitions were observed at 4 K in the external magnetic field up to 130 kOe along the c-axis and in the c-plane. Electrical resistivity shows a characteristic hump just below T_N due to the super-zone gap formation along the new Brillouin zone boundaries. High-temperature resistivity indicates that Gd₇Rh₃ has a semi-metallic band structure; the band gap energy 4.9 meV was obtained.     

Size effect on magnetic properties of a nano-graphene bilayer structure: A Monte Carlo study

In this paper we use the Monte Carlo simulations to investigate the magnetic properties of an Ising ferromagnetic–antiferromagnetic model. The system is based on a nano-graphene structure-like bilayer with two bloc sizes: N=24 and 42 spins. For each size N, the upper layer A is formed with spin −3/2, whereas the lower layer B is composed of spin −5/2. We only consider the first nearest-neighbor interactions between the sites i and j. The magnetic properties are studied, in the absence as well as in the presence of a crystal magnetic field, and an external magnetic field. The increasing temperature and crystal field as well as the inter-layer coupling constant, are also studied for this system sizes N=24 and 42 spins. The zero-field-cooled and the field cooled magnetization behaviors are investigated for different values of external magnetic field and a fixed value of exchange interaction between the two blocs. The magnetizations as well as the magnetic susceptibilities versus the temperature are used in order to obtain blocking temperature.     

Effect of surface chemisorption on the spin reorientation transition in magnetic ultrathin Fe film on Ag(0 0 1)

We have investigated the effect of surface chemisorption on the spin reorientation transitions in magnetic ultrathin Fe films on Ag(0 0 1) by means of the polar and longitudinal magneto-optical Kerr effect (MOKE) and X-ray magnetic circular dichroism (XMCD) measurements. It is found by the MOKE that adsorption of O₂ and NO induces the shift of the critical thickness for the transitions to a thinner side, together with the suppression of the remanent magnetization and the coercive field of the Fe film. This implies destabilization of the perpendicular magnetic anisotropy. On the other hand, H₂ adsorption is found not to change the magnetic anisotropy, though the enhancement of the coercive field is observed. The XMCD reveals that although both the spin and orbital magnetic moments along the surface normal are noticeably reduced upon O₂ and NO adsorption, the reduction of the orbital magnetic moments are more significant. This indicates that the destabilization of the perpendicular magnetic anisotropy upon chemisorption of O₂ and NO originates from the change of the spin-orbit interaction at the surface.     

Impurity effects on the magnetization and magnetic susceptibility of an electron confined in a quantum ring under the presence of an external magnetic field

The magnetization and the magnetic susceptibility of a single electron confined in a two-dimensional (2D) parabolic quantum ring under the effect of external uniform magnetic field and in the presence of an acceptor impurity have been studied. The shifted 1/N expansion method was used to solve the Hamiltonian quantum ring within the effective mass approximation. The computed energy spectra, the magnetization and magnetic susceptibility have been displayed as a function of the quantum ring parameters: confinement strength ω₀, magnetic field strength (ω_c), and temperature (T). The obtained energy results show level-crossings, in the absence and presence of acceptor impurity, which are manifested as oscillations in the magnetization and magnetic susceptibility curves.     

Determination of the g-factor of electrons in N-type silicon surface inversion layers

The g-factor of conduction electrons in the surface inversion layer on a silicon (100) surface has been determined using the tilted magnetic field method developed by Fang and Stiles.The value of (m¹/m₀)·g at the fixed magnetic field was independent of surface carrier density n_s, whereas it had a sharp peak at about 97 koe. At strong magnetic field limit the value was constant and 0.4. If we take the effective mass of conduction electrons in the inversion layer on the (100) surface as 0.2m₀, the g-factor is about two which is the same as that for conduction electrons in bulk silicon.     

Heat capacity and entropy of two electrons quantum dot in a magnetic field with parabolic interaction

The thermodynamic properties of two electrons in two dimensional parabolic GaAs quantum dot are studied where both the magnetic field and the e–e interaction are fully considered. The e–e interaction has been treated by a model potential which makes the Hamiltonian exactly solvable. The energy spectrum is used to calculate the canonical partition function, and then we obtain the thermodynamic properties; mean energy, heat capacity and entropy as a function of temperature (T) and magnetic field (B).A steep transition from zero to 4k_B is observed in the heat capacity as a function of temperature for small values of magnetic field and saturates within a small temperature range, also the heat capacity has a peak-like structure at low temperature, while for high magnetic field heat capacity develops a shoulder at 2k_B then it approaches the saturation value with further increase in temperature. The entropy increases with increasing temperature, but at higher temperature, it remains almost independent of the magnetic field. It is shown that, at low magnetic field values, the effect of magnetic field on heat capacity is tangible and it attains a constant value with further increase in magnetic field. Entropy is almost linearly proportional with increasing magnetic field strength.     

Optical properties of donor electrons in semimagnetic semiconductors

The cross section of the spin-flip Raman scattering and the absorption coefficient of the electric-dipole spin-resonance of donor electrons in Cd_1?x Mn_xSe are calculated. The exchange induced spin-splitting of a donor level is described taking into account three sources of a local magnetization: external magnetic field, thermodynamical fluctuations of magnetization and molecular field of the donor electron (bound magnetic polaron). The theory takes into account the selection rules appropriate for the hexagonal CdMnSe. The role played by fluctuations of composition is considered. It is suggested that a spin-flip line is inhomogeneously broadened by thermodynamical fluctuations of magnetization and additionally, in high fields, by fluctuations of the composition.     

Requirements for soft magnetic underlayer (SUL)—Micromagnetic simulations of single-pole-type write heads and SUL systems

Landau-Lifshitz-Gilbert micromagnetic models were used to analyze the head field distributions and high-frequency responses for various soft magnetic underlayer thicknesses (t-SUL) and saturation magnetization flux densities (B_s) of single-pole-type (SPT) head-SUL systems. It was found that B_s of 10-12 kG and t-SUL of 30-45 nm would be sufficient for the examined head and perhaps for most next generation head-SUL systems. Antiferromagnetic coupling in the SUL affects the head and SUL magnetization and, eventually, the head field. With regard to the head magnetization response, it was found that the magnetization under the coil responded first, while the response at the main pole tip was quite slow, even compared with the head field. The main pole tip of the head was fully saturated and the main pole yoke was almost saturated, while the SUL was not saturated in the examined head-SUL system.     

Delayed demagnetization jumps in (NdDy)(FeCo)B magnets in a steady-state magnetic field

Spontaneous demagnetization jumps are observed in sintered magnets (Nd_0.6Dy_0.4)₁₆(Fe_0.77Co_0.23)₇₈B₆ in a constant magnetic field after a sharp decrease in an external magnetic field from the value corresponding to the saturation to a value close to the coercive force. It is shown that the number of the magnetization jumps is proportional to their amplitudes. A low value of the autocorrelation coefficient between the jump amplitude and the time of its appearance (R < 0.1) demonstrate the stochasticity of the jumps. It is found that the spectral jump density is independent of the frequency, i.e., a white magnetic noise is observed. The distribution of the magnetic field gradient has been obtained near the sample surface that makes it possible to distinguish domains and the grain magnetization in the dependence on the direction of the texturing of the sintered magnet.

     

Monte Carlo study of small magnetic particles

In earlier computer simulation small magnetic particles with nearest neighbor Heisenberg interactions in zero magnetic field have been studied. We now continue these investigations including next nearest neighbor exchange and non zero magnetic fieldsH. The particles treated have spherical shape with a number of spinsN in the range from 33 to 3071. It is shown that the spontaneous magnetization of the particles is rather different from the bulk magnetization. The magnetization process can be accounted for by the Néel theory, if the correct spontaneous magnetization of the particle is used. The distribution of local magnetizations (the magnetic “profile”) was also obtained in various cases. It is shown that the magnetization of very small particles is much more depressed than predicted by the mean field approximation. We introduce an “effective magnetic radius” \(\hat R\) accounting for the reduction of the local magnetization. This magnetic radius is important for the interpretation of experimental results. A distinct dependence of \(\hat R\) on the magnetic field, temperature and the fraction of next nearest neighbor exchange is found. Finally a brief comparison is made with the recent study of magnetic surface properties by Binder and Hohenberg.