Influence of Randomness and Localization on RKKY Interactions in Diluted Magnetic Semiconductors

We show that the spatially random distribution of magnetic moments of dopants in diluted magnetic semiconductors can partially localize the itinerant carriers and change the carrier-mediated indirect RKKY interaction. From numerical calculations of the electron states taking into account the interaction with magnetic impurities which are random both in spatial positions and in orientations of magnetic moments, we obtain the electron states and the RKKY interaction as a function of the distance between magnetic dopants L and of the sp - d exchange integral J. With the increase of disorder, the localization of itinerant electrons become stronger and the long-range regular oscillatory behaviour of the RKKY interaction gradually disappears and is replaced by severe fluctuations. The randomness and localization may enhance the RKKY interaction between dopants with short and middle distances and in favour of the ferromagnetism.     

Phase diagram of the disordered RKKY model in dilute magnetic semiconductors

We consider ferromagnetism in spatially randomly located magnetic moments, as in a diluted magnetic semiconductor, coupled via the carrier-mediated indirect exchange RKKY interaction. We obtain, via Monte Carlo calculations, the magnetic phase diagram as a function of the impurity moment density n(i) and the relative carrier concentration n(c)/n(i). As evidenced by the diverging correlation length and magnetic susceptibility, the boundary between ferromagnetic and nonferromagnetic phases constitutes a line of zero temperature critical points which can be viewed as a magnetic percolation transition. In the dilute limit, we find that bulk ferromagnetism vanishes for n(c)/n(i) >0.1. We also incorporate the local antiferromagnetic direct superexchange interaction between nearest neighbor impurities and examine the impact of a damping factor in the RKKY range function.     

Ferromagnetism in dilute magnetic semiconductors and new materials for spintronics

Spintronics materials may be classified under concentrated magnetic semiconductors, semimetals and half-metals, semimagnetic semiconductors, and dilute magnetic semiconductors (DMS). The nature of ferromagnetism, that occurs in p-type DMS with an increase in the transition metal content, is governed by the proposed kinematic exchange involving the kinetic energy gain of the heavy hole carriers caused by their hybridization with 3d electrons of impurities. The synthesis of DMS (In,Mn)Sb is proposed on the basis of hint at its T_C from kinematic mechanism. The effect of the dimensionality-driven T_C increase is derived for spintronics materials such as delta-doped DMS (DDMS) and DMS heterostructures. The state-of-the-art in the field of synthesis and research of “new” DMS with announced “high T_C” is also outlined with particular attention to chalcopyrite-based systems.     

Concentration dependence of the transition temperature in spin glasses

The transition temperature T_f of randomly distributed spins interacting via the RKKY interaction (spin glasses) has been calculated numerically within the spherical approximation. The dependence of T_f on the concentration c of magnetic impurities and on the damping of the interaction due to a finite mean free path of the conduction electrons is investigated for 10^?5 < c < 10^?1.     

High-temperature ferromagnetism in laser-deposited layers of silicon and germanium doped with manganese or iron impurities

The paper reports on the results of a study of the synthesis conditions effects on magnetic and transport properties of nanosized layers of high-T_c diluted magnetic semiconductors (DMS), such as Ge:Mn, Si:Mn and Si:Fe, fabricated by laser-plasma deposition over a wide range of the growth temperature, T_g=(20-550) °C on single-crystal GaAs or Al₂O₃ substrates. Ferromagnetism of the layers was detected by measurement data of the magneto-optical Kerr effect, anomalous Hall effect, negative magnetoresistance and ferromagnetic resonance (FMR) at 5-500 K. The optimum growth temperature, T_g, for Si:Mn/GaAs layers with T_c≈400 K is shown to be about 400 °C. The Si:Mn/Al₂O₃ layers with 35% of Mn have the metal-type of conductivity with manifestation of magnetization up to room temperature. Different types of uniformly doped structures and digital alloys have been investigated. In contrast to GaSb:Mn films, Si-based ferromagnetic layers have strongly different magnetic and electric properties in case of uniformly doped structures and digital alloys. Positive results of the Fermi level variation effect on the improvement of Si- and Ge-based DMS layers have been gained on the use of additional doping with shallow acceptor Al impurity which contributes to the increase of the hole concentration and the RKKY exchange interaction of 3d-ions. The Ge:(Mn, Al)/GaAs or Ge (Mn, Al)/Si layers grown at 20 °C feature surprising extraordinary angular dependence of FMR.     

稀磁合金中“电阻极大”现象的双杂质散射理论

本文基于s-d相互作用,考虑杂质之间存在RKKY相互作用,提出了一种新的双杂质散射模型。按照这个模型,当一个杂质作自旋翻转散射时,由于杂质之间存在着RKKY关联,它的自旋作为内部自由度会受到限制。由于这种关联,抑制了杂质的自旋翻转散射,结合Kondo的logT项,能形成电阻极大。本文计算了所有可能的“DIS”图(双杂质自能图),在Kondo电阻公式中加入了A/(T₀²—T²)这样的项。其中A是一个正常数。T₀是一个临界温度。当T≤T₀时,这个公式不再有意义。这个理论和已有的分子场理论在本质上是不同的.因为它并不依赖于合金中的磁有序.因此当T≥T_c时(T_c是磁有序转变温度),这种机制仍起作用,但分子场理论则不行.这是一种顺磁效应.我们和Cd-Mn(杂质浓度从0.01到0.1at./0)的实验曲线进行了比较,发现符合得很好.最后,我们认为即使在极低浓度下这种机制也是消除Kondo logT发散的主要原因. 关键词：     

Relations between the Ruderman-Kittel-Kasuya-Yosida interaction electron concentration and crystal structure

The Ruderman-Kittel-Kasuya-Yosida interaction between localized magnetic spins on the basis of perfectly free conduction electron is calculated as a function of the Fermi wave vector of the conduction electrons. The expression of the interaction according to us converges rapidly, furthermore is strongly related to the detailed crystal structure. The q-dependence of exchange interaction j(q) between conduction- and localized magnetic electron is also taken into account. The result of the calculation is compared successfully with the change of magnetic structures, with θ_p and T_c or T_N of compounds having the CsCl structure, but less successfully with gadolinium compounds having the NaCl structure. These facts are discussed in conjunction with the difference of the RKKY interaction in the cscl and the NaCl structure.     

Magnetic impurity interactions in a quantum well on the base of IV-VI semiconductors

We study the indirect exchange interaction of magnetic impurities via 2D excitations in a quantum well on the base of IV-VI narrow-gap semiconductors. The energy spectrum of 2D excitations takes into account the nonparabolicity of dispersion as well as the strong spin-orbit interaction. The calculations are performed for the case when the main mechanism is an exchange by virtual electron-hole pairs. It means that we assume the Fermi level to lie inside the energy gap, and the temperature to be small, T << ϵ₀. It is shown that at large distances. R >> ν/ϵ₀ (2ϵ₀ is the excitation energy for nearest size-quantized subbands, ϵ the interband interaction parameter), the antiferromagnetic interaction of pairs dominates, so that the impurity spins tend to be directed along the heterojunction plane perpendicular to the vector connecting the impurities. The interaction contains both the Heisenberg and pseudodipole terms.     

Antiferromagnetic exchange coupling in amorphous Fe–Sc alloys

Results of ⁵⁷Fe Mössbauer, AC and DC susceptibility, grazing incidence X-ray diffraction, resistivity and Rutherford-backscattering measurements on the amorphous alloys ${\text{Fe}}_{100 - x} {\text{Sc}}_x (8 \leqslant x \leqslant 70)$ give for the first time convincing evidence for the antiferromagnetic exchange coupling between Fe-moments. The antiferromagnetic coupling between Fe-moments is for $(8 \leqslant x \leqslant 70)$ limited to certain regions (magnetic clusters) of the sample. The nature of the coupling is of the Heisenberg type. For $8 \leqslant x < 20$ , the magnetic coupling between Fe-moments is across nonmagnetic Sc-atoms. The conduction electrons mediate an indirect magnetic interaction between the Fe-moments. The magnetic exchange coupling between Fe-moments across Sc-atoms is negative. The antiferromagnetic coupling between Fe-moments can be explained by the Ruderman-Kittel-Kasuya-Yosida, RKKY, interaction by taking into account the damped oscillatory behavior of the RKKY interactions.     

Checkerboard patterns and magnetic resonance peak in cuprate superconductors

We investigate a kind of spin-Peierls transition (SP) in high T_c superconductivity. It is found the antiferromagnetic exchange integral of SP corresponds to the magnetic resonance peak. The kind of spin-Peierls transition applied to cuprate superconductors is that without dimerization of lattice ions and with dimerization of localized hole h_Cu attached to the ion. Absence of the magnetic resonance peak in La-Sr-Cu-O results from the dimerized state of localized hole, h_Cu below T_c into tetramerized phase above T_c in SP transition without dimerization of copper-ion. The checkerboard patterns with four unit cell period originate from the SP of electronic part without ion-dimerization and from charge occupation probability of oxygen-atom around Cu.     

From bubble to Skyrmion: Dynamic transformation mediated by a strong magnetic tip

Skyrmions in thin metallic ferromagnetic films are stable due to competition between the RKKY interaction and uniaxial magnetic anisotropy. We study static nonlinear excitations in magnetic film in the presence of strong cylindrical magnetic tip of nanometer size. We mimic the RKKY interaction by the next-nearest-neighbors ferromagnetic and antiferromagnetic exchange interactions. We demonstrate analytically and numerically dissipative transformation of a bubble created by a strong magnetic tip into a stable Skyrmion.     

Kondo effect in the presence of magnetic impurities

We measure transport through gold grain quantum dots fabricated using electromigration, with magnetic impurities in the leads. A Kondo interaction is observed between dot and leads, but the presence of magnetic impurities results in a gate-dependent zero-bias conductance peak that is split due to a RKKY interaction between the spin of the dot and the static spins of the impurities. A magnetic field restores the single Kondo peak in the case of an antiferromagnetic RKKY interaction. This system provides a new platform to study Kondo and RKKY interactions in metals at the level of a single spin.     

Influence of impurities on the band ferromagnetism

The influence of non-magnetic impurities on band ferromagnetism for an electron gas withδ-function interaction is investigated in the framework of the quantum field theory applied to phase transitions. The Hartree-Fock approximation is used for non-zero temperatures. An equation for the magnetizationM and the critical temperatureT F_c is obtained. It is found that the transition temperature is lowered by increasing impurity concentration. There exists a critical concentration which vanishes the ferromagnetism.     

Magnetic hyperfine interactions in GdAl3

We have studied the magnetic hyperfine interactions in GdAl₃ using¹⁵⁵Gd Mössbauer spectroscopy between the temperatures of 4K and 90K. Previous studies on GdAl₃ have shown that antiferromagnetic ordering occurs at 18K, and that a fit of the susceptibility to 1/(T-θ_p) yields a θ_p value of ?89K. The large ratio of θ_p to T_N is indicative of magnetic frustration between competing ferro-and antiferromagnetic interactions, which may be due to a combination of the oscillatory nature of the RKKY interaction and the geometry of the hexagonal lattice. Our studies show that the saturation magnetic hyperfine field at the Gd site is ?24.0 T, with the moments lying in the basal plane. The efg at the gadolinium site is 2.55(1)×10¹⁷V cm^?2 which is considerably larger than the value predicted by a point charge calculation. This difference may indicate that there is a conduction electron contribution. A helical magnetic structure has been calculated from RKKY theory.     

On the magnetic ordering implemented by the s–d exchange interaction

The RKKY perturbation scheme for the spin s–d exchange model is reexamined in the case of a finite number of electrons per impurity. The distribution of impurities is assumed to be random. The free electron gas representing the unperturbed system in the RKKY approach is replaced by a mean-field system h_r asymptotically equivalent to the reduced s–d model H_r which includes part of the s–d exchange. Below the transition temperature T_c of h_r the lowest energy levels of the s–d exchange Hamiltonian H_K resulting from second-order perturbation theory prove to be ordered in the same manner as those of h_r in the limit of weak s–d exchange, favouring the same definite parallel alignment of any pair of impurity spins. It follows therefore that in the low temperature, weak coupling regime, the s–d model exhibits ferromagnetic ordering of impurities. At temperatures above T_c there is no ordering and impurity–impurity exchange has the RKKY form. These observations are consistent with the presence of a low-temperature ferromagnetic phase in numerous compounds with s–d exchange interaction.     

Influence of the Fe2+ ion triple clusters on the magnetic susceptibility of Fe-based diluted magnetic semiconductors

Low lying energy levels of Fe²⁺ ion triples in the cubic-structure iron-based diluted magnetic semiconductors are calculated on the basis of a model which includes crystal field, spin–orbit interaction, Zeeman interaction and Heisenberg-type exchange interaction. Using this energy level diagram the magnetic susceptibility of a crystal is calculated in the nearest-neighbour (NN) and in the extended NN pair approximation. We find that the Fe²⁺ ion triples contribute to the temperature dependent susceptibility up to the lowest temperatures investigated, T⩾1 K. It appears that the triple Fe²⁺ ion clusters may explain at least a part of the low-temperature increase of the magnetic susceptibility which is observed in these magnetic materials.     

Another approach to mechanism of ferromagnetic superconductor UGe2

We study the ferromagnetic superconductor of UGe₂ applying our previous model [Phys. Rev. B 61 (2000), 4289] for the high transition temperature superconductivity (HTSC). The Coulomb interaction for triplet electron pairs is reduced by a difference of the exchange interaction. In the case of UGe₂ including other heavy fermion superconductors, coexistence of triplet superconductivity and ferromagnetism is possible in the case of our scheme. We also investigate the pressure-dependence of Curie temperature, T_c and superconducting temperature, T_sc.     

Effect of electron-beam irradiation on the magnetic properties of Ga1−xMnxAs thin films grown on GaAs (100) substrates

The effect of electron-beam irradiation on the magnetic properties of (Ga_1−xMn_x)As thin films grown on GaAs (100) substrates by using molecular beam epitaxy was investigated. The ferromagnetic transition temperature (T_c) of the annealed (Ga_0.933Mn_0.067)As thin films was 160 K. The T_c value for the as-grown (Ga_0.933Mn_0.067)As thin films drastically decreased with increasing electron-beam current. This significant decrease in the T_c value due to electron-beam irradiation originated from the transformation of Mn substituted atoms, which contributed to the ferromagnetism, into Mn interstitials or Mn-related clusters. These results indicate that the magnetic properties of (Ga_1−xMn_x)As thin films grown on GaAs (100) substrates are significantly affected by electron-beam irradiation.     

Green function theory of Curie and order—order transitions in ferromagnetic systems

Dipolar critical temperatures in ferromagnetic systems with isotropic bilinear and biquadratic exchange are investigated by means of the Green function technique. Expressions are found for both the familiar Curie temperature, T_c, and the less well known order-order transition temperature, T_o, at which, under appropriate conditions, the magnetic ordering undergoes a change between fully aligned and canted ferromagnetism. At T = 0, a fully aligned state has <s_i^z = s for spin s and all lattice sites i, while a canted state has 〈s_i^z〉<s. It is shown independently of the Green function analysis that the T = 0 ground state is fully aligned if α, the ratio of biquadratic to bilinear exchange integrals, obeys ?[2s(s?1)]^?1<α< [2s²?2s+1]^?1. The region below the lower limit is identified as the range in which canted ferromagnetism can occur and is a range that does not appear to have been considered previously via the Green function formalism.The temperature dependence of the magnetic ordering is investigated by means of the double-time temperature-dependent Green function formalism. A new decoupling scheme is derived and used to reduce higher order Green functions to lowest order. It is found that a canted state, occuring at low temperatures, undergoes a transition to a fully aligned state at a temperature T₀ and subsequently becomes disordered at temperature T_c. Transitions to paramagnetism are found to be second order for α<α_c and first order for α?α_c where α_c is a critical value that depends on the atomic spin and weakly on the lattice structure. A phase diagram is given to illustrate the results, and a comparison is made with the corresponding results found in mean field theory.     

Unusual directional dependence of exchange energies in GaAs diluted with Mn: is the RKKY description relevant?

Ferromagnetism in Mn-doped GaAs, the prototypical dilute magnetic semiconductor (DMS), has so far been attributed to hole mediated RKKY-type interactions. First-principles calculations reveal a strong direction dependence of the ferromagnetic (FM) stabilization energy for Mn pairs, a dependence that cannot be explained within RKKY. In the limit of a hostlike hole engineered here where the RKKY model is applicable, the exchange energies are strongly reduced, suggesting that this limit cannot explain the observed ferromagnetism. The dominant contribution stabilizing the FM state is found to be maximal for 110-oriented Mn pairs and minimal for 100-oriented Mn pairs, providing an alternate explanation for magnetism in such materials in terms of energy lowering due to p-d hopping interactions, and offering a new design degree of freedom to enhance FM.