Theoretical models of ferromagnetic III–V semiconductors

Recent materials research has advanced the maximum ferromagnetic transition temperature in semiconductors containing magnetic elements toward room temperature. Reaching this goal would make information technology applications of these materials likely. In this article we briefly review the status of work over the past five years which has attempted to achieve a theoretical understanding of these complex magnetic systems. The basic microscopic origins of ferromagnetism in the (III,Mn)V compounds that have the highest transition temperatures appear to be well understood, and efficient computation methods have been developed which are able to model their magnetic, transport, and optical properties. However many questions remain.     

Relaxation in Ni–Mn–Ga ferromagnetic shape memory alloys

Evidence of relaxation has been observed in ferromagnetic Ni–Mn–Ga single crystals. The relaxation may be explained by a change in symmetry-conforming short-range ordering according to Ren and Otsuka in this off-stoichimetric ordered alloy. Martensite stabilization has also been found after martensite ageing.     

Unusual metal–insulator transition in disordered ferromagnetic films

We present a theoretical interpretation of recent data on the conductance near and farther away from the metal–insulator transition in thin ferromagnetic Gd films of thickness b≈2$b\approx 2$–10 nm. For increasing sheet resistances a dimensional crossover takes place from d=2 to d  =3 dimensions, since the large phase relaxation rate caused by scattering of quasiparticles off spin wave excitations renders the dephasing length L_??b$L_{?}?b$ at strong disorder. The conductivity data in the various regimes obey fractional power-law or logarithmic temperature dependence. One observes weak localization and interaction induced corrections at weaker disorder. At strong disorder, near the metal–insulator transition, the data show scaling and collapse onto two scaling curves for the metallic and insulating regimes. We interpret this unusual behavior as proof of two distinctly different correlation length exponents on both sides of the transition.     

Bose–Einstein condensation of magnons in ferromagnetic thin films

Experimental evidence for Bose–Einstein condensation (BEC) of magnons at room temperature in a thin film of yttrium iron garnet (YIG) excited by parallel pumping is already available and different features of the experimental results have been explained qualitatively [Nature 443, 430 (2006)]. In the present work, we explain quantitatively different aspects of this experimental observation through spin wave treatment. In the case of parallel pumping field, we have developed a formula for the time required for the formation of magnon BEC in a thin film of ferromagnetic material. This relation is found to be in good agreement with known experimental results. In a similar treatment we predict the condition for the formation of BEC of magnons in the case of perpendicular pumping.     

Ab initio calculations of the ferromagnetic shape memory alloy Ni–Mn–Al

Results of the first-principles calculations of the magnetic shape-memory alloy NiMnAl are presented. The properties of a series of alloys in the composition range Ni₅₀Mn _x Al_{50? x} with 0 ≤ x ≤ 50 were deduced from the ab initio simulations. One essential result is that the alloy is ferromagnetic in the range from 14 to 31?at.% Mn. Furthermore, the martensitic phases 2?M, 10?M, and 14?M with long-periodic structure were calculated. They are metastable in the stoichiometric Ni₂MnAl alloy due to additional bonding between specific atomic sites. Their properties are discussed in terms of the density of states and their charge distribution.     

Neutron-diffraction studies of the antiferromagnetic–ferromagnetic transition in anion-deficient cobaltites

Anion-deficient La_0.5Ba_0.5CoO_2.8 and Y_0.25Ca_0.25Sr_0.5CoO_2.62 cobaltites are studied under pressures up to 6.5 GPa in the temperature range of 5?300 K by neutron powder diffraction. Under ambient pressure both compounds are antiferromagnetic with T _N = 250 K. The applied pressure induces in the first compound a gradual transition from the antiferromagnetic to ferromagnetic state through a mixed magnetic state, whereas the second compound remains antiferromagnetic in the whole pressure range. We suggest that the magnetic ground state depends on the unit-cell volume and the magnetic transition is associated with the transition of cobalt ions from the mixed high-spin/low-spin state to the intermediate-spin/low-spin state.     

Magnetic and mechanical properties of Ni–Mn–Ga/Fe–Ga ferromagnetic shape memory composite

A ferromagnetic shape memory composite of Ni–Mn–Ga and Fe–Ga was fabricated by using spark plasma sintering method. The magnetic and mechanical properties of the composite were investigated. Compared to the Ni–Mn–Ga alloy,the threshold field for magnetic-field-induced strain in the composite is clearly reduced owing to the assistance of internal stress generated from Fe–Ga. Meanwhile, the ductility has been significantly improved in the composite. A fracture strain of 26% and a compressive strength of 1600 MPa were achieved.     

Enhanced exchange bias in magnetron-sputtered Ni–Mn–Sb–Al ferromagnetic shape memory alloy thin films

In the present study, the influence of aluminium (Al) addition on the martensite-austenite phase transformation and exchange bias of Ni–Mn–Sb films have been investigated. Ni–Mn–Sb–Al films with different Al concentration (∼0–5.6%) were deposited by co-sputtering of Ni–Mn–Sb and Al targets. Experimental results revealed the decrease in martensitic transformation temperature with increasing Al content upto a certain extent (3.3%) beyond which martensitic transformation was suppressed. Paramagnetic to ferromagnetic transition temperature (T_C) also decreased with increasing Al concentration. Ni₅₀Mn_36.3Sb_10.4Al_3.3 thin film showed significant improvement in exchange bias field as compared to pure Ni_50.3Mn_36.9Sb_12.8 thin film. This enhancement in the exchange bias field H_EB = 611 Oe at 10 K is attributed to the increase of AFM-FM interactions that result from the decrease of Mn–Mn distance due to the incorporation of Al atoms. This behaviour is an additional property of the FSMA thin films apart from various other multifunctional properties and therefore, is of technological importance for their applications in magnetic storage devices.     

Chemical order in off-stoichiometric Ni–Mn–Ga ferromagnetic shape-memory alloys studied with neutron diffraction

The chemical order of three off-stoichiometry Ni–Mn–Ga compositions has been measured in the austenitic phase using powder and single-crystal neutron diffraction. The compositions studied, 48–52 at.% nickel, having excess manganese and deficient in gallium, are of technical interest due to the observed large room-temperature, magnetic-field-induced strain. It has been determined that compositions with less than 50% nickel have the excess Mn atoms occupying Ni and Ga sites. Compositions enriched in nickel are best fit with Ni atoms in excess of 50% occupying Mn sites while the excess and displaced Mn occupy Ga sites. The saturation magnetic moments calculated from the site occupations determined here and using Ni and Mn moments reported for Ni₂MnGa, agree within 4% with the low-temperature measured moments.     

Exact soliton solutions in anisotropic ferromagnetic wires with Dzyaloshinskii–Moriya interaction

We theoretically investigate the exact soliton solutions of anisotropic ferromagnetic wires with Dzyaloshinskii–Moriya interaction. For example, we give the bright and black soliton solutions. From these results we find that the Dzyaloshinskii–Moriya interaction affects the existence region of soliton, spin-wave transport, and soliton dynamic properties. As the Dzyaloshinskii–Moriya interaction grows, the soliton width is widened, which provides a way to control the soliton dynamics.     

Relaxation of the magnetic state of a ferromagnetic–superconducting layered structure

We have proposed a real-time method of neutron reflectometry. The magnetic state of the Ta/V/FM/Nb/Si ferromagnetic–superconducting system has been analyzed. Relaxation of the inhomogeneous magnetic state with a characteristic time of several hours, which depends on the magnetic field magnitude and temperature, has been observed. The relaxation of the domain structure has changed upon a transition of the V and Nb layers to the superconducting state. It has been concluded that real-time reflectometry data for polarized neutrons are important for determining the origin of magnetism in ferromagnetic–superconducting layered structures.     

Annealing effect on phase transformation in nano structured Ni–Mn–Ga ferromagnetic shape memory alloy

Nano structured Ni_52.6Mn_23.7Ga_24.3 alloy was prepared using the ball milling technique. High martensitic transition temperatures are observed in the range between 336 and 367 K. The X-ray diffraction profile revealed that annealed Ni–Mn–Ga powder at 1073 K displays mixture phases of austenite and martensite. Annealing at 1173 K induces phase transformation from mixture phase to Heusler L2₁ structure, which confirms the high-temperature shape memory effect. On the contrary, the milled sample shows no evidence of shape memory effect. Furthermore, annealing at higher temperature (1273 K) shows the accumulation of oxidation, which leads to the loss of shape memory effect. The grain size increases with increasing annealing temperature and causes deterioration in the soft magnetic properties.     

Effect of chemical ordering annealing on superelasticity of Ni–Mn–Ga–Fe ferromagnetic shape memory alloy microwires

Ni_(50)Mn_(25)Ga_(20)Fe_5 ferromagnetic shape memory alloy microwires with diameters of ～ 30–50 μm and grain sizes of ～ 2–5 μm were prepared by melt-extraction technique. A step-wise chemical ordering annealing was carried out to improve the superelasticity strain and recovery ratio which were hampered by the internal stress, compositional inhomogeneity,and high-density defects in the as-extracted Ni_(50)Mn_(25)Ga_(20)Fe_5 microwires. The annealed microwires exhibited enhanced atomic ordering degree, narrow thermal hysteresis, and high saturation magnetization under a low magnetic field. As a result, the annealed microwire showed decreased superelastic critical stress, improved reversibility, and a high superelastic strain(1.9%) with a large recovery ratio(96%). This kind of filamentous material with superior superelastic effects may be promising materials for minor-devices.     

Thickness dependent phase transformation of magnetron-sputtered Ni–Mn–Sn ferromagnetic shape memory alloy thin films

In this study, the influence of film thickness on the first-order martensite–austenite phase transformation of Ni–Mn–Sn ferromagnetic shape memory alloy thin films has been systematically investigated. Different thicknesses of the Ni–Mn–Sn films (from ~100 to 2,500 nm) were deposited by DC magnetron sputtering on Si (100) substrates at 550 °C. X-ray analysis reveals that all the films exhibit austenitic phase with the L2₁ cubic crystal structure at room temperature. The grain size and crystallization extent increase with the increase in film thickness, but the films with thickness above ~1,400 nm show structural deterioration due to the formation of MnSn₂ and Ni₃Sn₄ precipitates. The improvement in the crystallinity of the film with thickness is attributed to the decrease in film–substrate interfacial strain resulting in preferred oriented growth of the films. Temperature-dependent magnetization measurements as well as electrical measurements demonstrate the complete absence of phase transformation for the film of thickness of ~120 nm. For thickness greater than 400 nm, film exhibits the structural transformation, and it occurs at higher temperature with better hysteresis as film thickness is increased up to ~1,400 nm, after which degradation of phase transformation phenomenon is observed. This degradation is attributed to the disorders present in the films at higher thicknesses. Film with thickness ~1,400 nm possesses the highest magnetization with the smallest thermal hysteresis among all the films and therefore best suited for the actuators based on first-order structural phase transformation. Nanoindentation measurements reveal that the higher values of hardness and elastic modulus of about 5.5 and 215.0 GPa obtained in film of 1,014 nm thickness can considerably improve the ductility of ferromagnetic shape memory alloys (FSMA) and their applicability for MEMS applications. The exchange bias phenomenon is also found to be present in the films of thickness 1014, 1412, and 2022 nm exhibiting prominent martensitic transformation. Film of thickness 2,022 nm exhibits maximum exchange bias of ~50 Oe and higher exchange bias blocking temperature of 70 K as compared to other films.     

Phase transformation in Ni–Mn–Sn ferromagnetic shape memory alloy thin films induced by dense ionization

The effects of 200 MeV Au ions irradiation on the structural and magnetic properties of Ni–Mn–Sn ferromagnetic shape memory alloy (FSMA) thin films have been systematically investigated. In order to understand the role of initial microstructure and phase of the film with respect to high energy irradiation, the two types of Ni–Mn–Sn FSMA films having different phases at room temperature were irradiated, one in martensite phase (Ni_58.9Mn_28.0Sn_13.1) and other in austenite phase (Ni₅₀Mn_35.6Sn_14.4). Transmission electron microscope (TEM) and scanning electron microscope (SEM) images along with the diffraction patterns of X-rays and electrons confirm that martensite phase transforms to austenite phase at a fluence of 6×10¹² ions/cm² and a complete amorphization occurs at a fluence of 3×10¹³ ions/cm², whereas ion irradiation has a minimal effect on the austenitic structure (Ni₅₀Mn_35.6Sn_14.4). Thermo-magnetic measurements also support the above mentioned behaviour of Ni–Mn–Sn FSMA films with increasing fluence of 200 MeV Au ions. The results are explained on the basis of thermal spike model considering the core and halo regions of ion tracks in FSMA materials.     

Relaxation process and ferromagnetic resonance investigation of ferrofluids with Mn–Zn and Mn–Fe mixed ferrite particles

The magnetic relaxation processes in two ferrofluids with Mn_0.4Zn_0.6Fe₂O₄ (sample F1) and Mn_0.6Fe_0.4Fe₂O₄ (sample F2) mixed ferrite particles, dispersed in n-decan and kerosene, respectively, are investigated through the determination of components χ′ and χ′′ of the complex magnetic susceptibility in the range of (2–30) MHz. The values of the saturation magnetization of the two ferrofluids are M_∞=5.28 kA/m for sample F1 and M_∞=10.99 kA/m for sample F2. A maximum of the imaginary component χ′′ was observed for both samples at frequencies of tens MHz. This maximum was assigned to relaxation processes of Néel type.The effective anisotropy constant K of the particles from the studied samples was evaluated, using both static and dynamic measurements and the values were found to be K₁=6.12×10³ J m⁻³ for the ferrofluid F1, and K₂=5.60×10³ J m⁻³ for the ferrofluid F2. From ferromagnetic resonance measurements, and based on the theoretical values computed for the Lande factor (g), the effective anisotropy constants for the mixed ferrite particles in the studied ferrofluids and the anisotropy field values were determined using a new method. The values obtained in this way for the anisotropy constants K₁ and K₂ are compared to the ones determined from magnetic relaxation measurements.     

Goos–H?nchen-like shift related to spin and valley polarization in ferromagnetic silicene

We study the Goos–H?nchen-like shift of single silicene barrier under the external perpendicular electric field, offresonant circularly polarized light and the exchange field modulation using the stationary-phase method. The results show that the Goos–H?nchen-like shift of silicene resulting from the external perpendicular electric field does not have the characteristics of spin or valley polarization, while that from off-resonant circularly polarized light or the exchange field is spin-polarized. More importantly, the combined effect of the external perpendicular electric field and the exchange field or off-resonant circularly polarized light can cause the Goos–H?nchen-like shift of the system to be spin and valley polarized.It is particularly worth noting that when the three modulations are considered at the same time, as the exchange field changes, the system will have a positive or negative Goos–H?nchen-like shift.     

Nb diffusion in ferromagnetic α-Fe

The effect of the magnetic ordering on the diffusion of Nb in α-Fe was investigated. Measurements were made in the 673–1073 K temperature range using secondary ion mass spectrometry as analysis tool. By expanding the temperature range with respect to the previous works, the Arrhenius plot shows the variation of the slope at the Curie temperature and a soft-upward curvature in the ferromagnetic region. The curvature observed is well fitted by the model developed by Ruch et al. The parameter that takes into account the influence of the magnetic order in the vacancy formation and mobility during the Nb diffusion process is quite similar to that observed in other non-magnetic diffusers. A possible explanation for such an effect is given, supported by ab initio calculations. PACS  66.30.-h; 66.30.J-; 67.80.dk; 85.40.Ry