Sublattice Magnetization Research Articles

Synthesis, thermal X-ray, neutron diffraction, Mössbauer spectroscopy and magnetic properties investigation of Al doped barium hexaferrite BaFe11AlO19

Polycrystalline aluminum substituted barium hexaferrite BaFe11AlO19 synthesized by the ceramic technique. The results of energy dispersive X-ray analysis, thermal X-ray diffraction (XRD), neutron diffraction, Mössbauer spectroscopy, magnet properties measurements were measured. XRD analysis demonstrated P63/mmc hexagonal structure of BaFe11AlO19. The magnetic sublattice of barium hexaferrite BaFe11AlO19 was obtained using neutron diffraction data. The distribution of aluminum in barium hexaferrite matrix at positions 2a and 12k was obtained with Mössbauer spectroscopy. A comparison of the calculated intensities of the neutronograms and the actual ones allowed us to establish that in position 2a the aluminum ion occupied a position with the coordinate (1;1;0), and the position of the substituent ion in position 12k (0.83333; 0.66667; 0.10810). According to neutron diffraction data, it was found that the actual Curie temperature is lower than that measured by differential scanning calorimetry.

Enhancing temperature stability of Ce: RIG films Faraday rotation through magnetic sublattice control

Cerium doped rare-earth iron garnet (Ce: RIG) film is a promising candidate for magneto-optical devices in laser systems with giant Faraday effect; nevertheless, devices fail nonreciprocally with increasing temperature due to a negative Faraday rotation angle temperature coefficient. To mitigate this effect, the relationship between the magnetic moments of three distinct magnetic sublattices and the temperature coefficients of the Faraday rotation angle was investigated. Cerium doped holmium iron garnet (Ce: HoIG) film, where magnetic Ho3+ occupied the dodecahedrons, exhibited an enhanced Faraday rotation angle retention at a temperature of 400 K. However, the nonmagnetic ion doping in tetrahedral and octahedral sites yielded a negligible effect. The mechanism behind this occurrence is attributed to the magnetic compensation effect, which results in a small magnetic moment temperature coefficient within the range of 300–400 K. The study not only offers strategies for designing Ce: RIG components with reduced temperature coefficient, but also presents the development of a Ce: HoIG film exhibiting promising stability in Faraday rotation angle as a function of temperature.

Spin reorientation in GdMn2(Ge1-xSix)2 compounds

Structure and magnetic properties of layered GdMn2(Ge1-xSix)2 (0 ≤ x ≤ 1) compounds were studied. All the compounds crystallize in the tetragonal ThCr2Si2-type structure. It was shown by magnetization measurements at low temperature on quasi-single crystals that, with increasing Si concentration, the easy magnetization direction reorients from the c-axis to the basal plane. The spin reorientation occurs via an angular phase. A model of three magnetic sublattices coupled by negative intersublattice exchange interactions was used to describe the field dependences of the magnetization. For GdMn2Ge2 and GdMn2(Ge0.9Si0.1)2 in the fields applied along the c-axis, seven different magnetic structures were predicted, including two angular structures considered for the first time. The model explains formation of angular magnetic structures in zero field in GdMn2(Ge1-xSix)2 system by taking into account magnetic anisotropy of Mn sublattices with a positive anisotropy constant K1 and negative K2.

Surface-Symmetry-Driven Dzyaloshinskii-Moriya Interaction and Canted Ferrimagnetism in Collinear Magnetoelectric Antiferromagnet Cr_{2}O_{3}.

Antiferromagnets are normally thought of as materials with compensated magnetic sublattices. This adds to their technological advantages but complicates readout of the antiferromagnetic state. We demonstrate theoretically the existence of a Dzyaloshinskii-Moriya interaction (DMI), which is determined by the magnetic symmetry classes of Cr_{2}O_{3} surfaces with an in-plane magnetic easy axis. The DMI explains a previously predicted out-of-plane magnetization at the nominally compensated surfaces of chromia, leading to a surface-localized canted ferrimagnetism. This is in agreement with magnetotransport measurements and with density functional theory predictions that further allow us to quantify the strength of DMI. The temperature dependence of the transversal resistance for these planes shows distinct behavior in comparison with that of the Cr_{2}O_{3} c plane, which we attribute to the influence of DMI. Our Letter provides a framework to analyze surface-driven phenomena in antiferromagnets, and motivates the use of nominally compensated chromia surfaces for antiferromagnetic spintronics and magnonics.

Double Helix of Icosahedra Structure and Spin Glass Magnetism of the δ-Co2.5Zn17.5-xMnx (x = 0.4-3.5) Pseudo-Binary Alloys.

We have synthesized δ-Co2.5Zn17.5-xMnx (x = 0.4-3.5) pseudo-binary alloys of 10 different compositions by a high-temperature solid-state synthetic route, determined their crystal structures and the Mn substitution pattern, and estimated the existence range of the δ-phase. The alloys crystallize in two chiral enantiomorphic space groups P62 and P64, where the basic atomic polyhedron of the chiral structure is an icosahedron and the neighboring icosahedra share vertices to form an infinitely long double helix along the hexagonal axis (like in the δ-Co2.5Zn17.5 parent binary phase). The alloys are pure δ-phase up to the Mn content x ≈ 3.5. The Mn atoms partially substitute Zn atoms at particular crystallographic sites located on the icosahedra. The study of magnetism was performed on the Co2.5Zn17.1Mn0.4 alloy with the lowest Mn content. Contrary to the expectation that structural chirality may induce the formation of a nontrivial magnetic state, a spin glass state with no relation to the structural chirality was found. The magnetic sublattice contains all of the necessary ingredients (randomness and frustration) for the formation of a spin glass state. Typical out-of-equilibrium dynamic phenomena of a spin system with broken ergodicity were detected below the spin freezing temperature Tf ≈ 8 K.

Алгоритм определения намагниченностей подрешеток двухподрешеточного ферримагнетика с точкой компенсации. Часть 1. Фазовая диаграмма

The calculation algorithm of sublattice magnetizations in two-lattice ferromagnet with compensation point is proposed. On the basis of preceding works review it is put the task about calculation of sublattices in individuality. It is investigated the general scheme of whole ferrimagnet magnetization forming which contains two magnetic sublattices both connected by exchange interaction. In geometry of axis symmetry along constant field direction it is investigated the orientational dependence of sublattices magnetization from applied field. It is found the forming conditions of anti-parallel and parallel collinear phases and corner phase between its. It is proposed the model presentation of magnetization dependence from temperature which contain the degree index dependence of general temperature to Curie temperature relation for each sublattice individual. For the simplicity and clear appearance of presentation the power index was choose. It is established the conditions which are necessary for forming the temperature compensation point. It is found the dependencies of deflection corners of each sublattices magnetization from field direction in accounting the given temperature. The decision of proposed excitation for magnetic field allows to find the boundaries of sublattice system transition between phases. On the basis of proposed temperature dependencies of critical transition fields it is drawing the phase diagram of two-sublattice ferrimagnet. It is found two settled on field one above other branches. The lower branch correspond to anti-parallel phase and upper branch correspond to parallel phase. It is found that lower branch contain sufficient quantity of information for to determine the individual both sublattice magnetization. It is proposed the methodic for calculation the individual sublattice magnetization based on the character temperature values and summary magnetizations. On the lower branch marked four character points which correspond to four temperatures and two values of summary magnetization. With using these points it is founded the equation system which allows to determinate the individual magnetizations values. It is proposed some recommendations for further development of investigations.

Growth-associated emergence of spontaneous magnetization in Al-doped Cr2O3 thin film

Development of antiferromagnetic/ferrimagnetic materials has been an area of active pursuit to advance the antiferromagnetic/ferrimagnetic spintronics. In this paper, we investigated the emergence of the spontaneous magnetization MS in the antiferromagnetic Cr2O3 thin film by the Al substitution. In the case of the (Cr1-xAlx)2O3(0001) thin films, MS increases with increasing Al composition x up to x ∼0.21. The magnitude of MS decreases abruptly for x > 0.22, accompanied with the collapse of the crystal formation. We found that the induction of the spontaneous magnetization was highly associated with the growth process. The magnitude of MS depends on the growth direction of the film: MS at 10 K for x = 0.13±0.01 is 80 kA/m, 30 kA/m and 0 kA/m for (0001), (011¯2) and (112¯0) films, respectively. The difference in MS with the growth direction is relevant to the magnetic sublattice selective substitution of Al during the thin film growth. This specific substitution occurs in the growth plane having the layer-by-layer stacking of the magnetic sublattice, which was verified by the direct observations using the scanning transmission electron microscope.

Алгоритм определения намагниченностей подрешеток двухподрешеточного ферримагнетика с точкой компенсации. Часть 2. Степенное приближение

The calculation algorithm of sublattice magnetizations in two-sublattice ferrimagnet with compensation point is proposed. On the consideration of magnetic as the combination of spin with two orientations it is found the dependence of magnetization from the temperature in the firm of transcendent equation. The calculated decision of this equation make the coincidence the calculated dependence with experiment in precision about 10%. For the analytic presentation of magnetization temperature dependence in obviously view it is proposed the power index approximation which consist of relation magnetic temperature to curie temperature in six power index. On the basis of power index approximation the phase diagram of two-sublattice ferrimagnet with compensation point is constructed. It is shown the scheme of sublattice magnetization determination on the basis of using meanings by temperature character points of phase diagram lower branch. It is found the equation system which connects the character points parameters with magnetizations in initial point and in the point of maximum of diagram in the temperature more than compensation. By solving this equation system it is found the enough simple analytical expressions which determine the saturation magnetizations both sublattices through parameters of character points on lower brunch of phase diagram. The proposed methods is applied to determination of sublattice magnetizations in experiments by measuring summary magnetization which are curried out on the films of two different compositions using the vibration magnetometer. For the examination of determined meanings the comparison with constructed on its basis phase diagram with the diagram determined in experiment was carried out. The examination shows the coincidence calculated data with experiment in limits from 8 to 40%. The analysis of correspondence determined diagram data with experimental data. It is found the good (to part of percent) coincidence of whole magnetization meaning in the beginning of diagram and also the coincidence of compensation temperature and Curie temperature. For the interpretation of visible deflections it is proposed the hypothesis about influence of third sublattice which changes the magnetizations of main sublattices. It is proposed some recommendations for further development of investigations.

Origins of multi-sublattice magnetism and superexchange interactions in double–double perovskite CaMnCrSbO6

The multi-sublattice magnetism and electronic structure in double–double perovskite compound CaMnCrSbO6 is explored using density functional theory. The bulk magnetization and neutron diffraction suggest a ferrimagnetic order ( TC∼ 49 K) between between Mn2+ and Cr3+ spins. Due to the non-equivalent Mn atoms (labelled as Mn(1) and Mn(2) which have tetrahedral and planar oxygen coordinations, respectively) and the Cr atom in the centre of distorted oxygen octahedron in the unit cell, the exchange interactions are more complex than that expected from a two sublattice magnetic system. The separations between the on-site energies of the d-orbitals of Mn(1), Mn(2) and Cr obtained from Wannier function analysis are in agreement with their expected crystal field splitting. While the DOS obtained from non spin-polarized calculations show a metallic character, starting from Hubbard U = 0 eV the spin-polarized electronic structure calculations yield a ferrimagnetic insulating ground state. The band gap increases with Ueff (U − J), thereby showing a Mott–Hubbard nature of the system. The inclusion of anti-site disorder in the calculations show decrease in band-gap and also reduction in the total magnetic moment. Due to the ∼90∘ superexchange, nearest neighbour exchange constants obtained from DFT are an order of magnitude smaller than those reported for various magnetic perovskite and double-perovskite compounds. The Mn(1)–O–Mn(2) (out of plane and in-plane), Mn(1)–O–Cr and Mn(2)–O–Cr superexchange interactions are found to be anti-ferromagnetic, while the Cr–O–O–Cr super-superexchange is found to be ferromagnetic. The Mn(2)–O–Cr superexchange is weaker than the Mn(1)–O–Cr super-exchange, thus effectively resulting in ferrimagnetism. From a simple 3-site Hubbard model, we derived expressions for the antiferromagnetic superexchange strength JAFM and also for the weaker ferromagnetic JFM . The relative strengths of JAFM for the various superexchange interactions are in agreement with those obtained from DFT. The expression for Cr–O–O–Cr super-superexchange strength ( J~SS ), which has been derived considering a 4-site Hubbard model, predicts a ferromagnetic exchange in agreement with DFT. Finally, our mean field calculations reveal that assuming a set of four magnetic sub-lattices for Mn2+ spins and a single magnetic sublattice for Cr3+ spins yields a much improved T C , while a simple two magnetic sublattice model yields a much higher T C .

Magnetic properties of the spin-1 J 1 − J 3 Heisenberg model on a triangular lattice

We study the spin-1 J 1 − J 3 Heisenberg model with antiferromagnetic nearest neighbors J 1 > 0 and the ferromagnetic third nearest neighbor J 3 < 0 for a triangular lattice. The ground-state and thermodynamic properties are evaluated under the Popov-Fedotov functional integral method and the Luttinger-Tisza procedure. Perturbation expansion of the auxiliary field around mean-field theory was carried out to investigate the effect of thermal fluctuations on ground state energy and sublattice magnetization. The results are compared with those of the spin wave approximation and other methods.

Magnetothermal properties including magnetocaloric performance of the ternary rhombohedral Laves phase of Pr2Rh3Ge

The article presents the study of the magnetocaloric effect (MCE) for the rhombohedral Laves phase of Pr2Rh3Ge, which shows a magnetic order below TC=8.5 K. We have established that the compound exhibits a continuous second-order type of transition which was demonstrated and confirmed by several different techniques, mainly by analyzing universal curves of normalized entropy change as a function of scaled temperature. The observed MCE, in our opinion, is a consequence of an indirect exchange coupling between the magnetic sublattices of the rare earth ions, which, however, does not exclude the potential contribution of sublattice-containing transition metals. In this paper, the procedure to evaluate the MCE from magnetization and specific heat data is described. As a result, important parameters such as the isothermal magnetic entropy change (ΔSM), adiabatic temperature change (ΔTad), relative cooling power (RCP), and the temperature averaged entropy change (TEC) were determined. The highest values of −ΔSM, ΔTad, and RCP for a field change (Δμ0H) of 5 T at TC are 5.96 J/kgK, 3.87 K, and 72.62 J/kg, respectively. These results obtained for Pr2Rh3Ge seem to be, however, low compared to the values obtained for the rhombohedral Laves phases, belonging to the group of ternary germanides RE2Rh3Ge containing heavy rare earth metals (RE = Gd, Tb, Ho, and Er). Nevertheless, we believe that the results presented in this work extend and complement the current knowledge on the magnetocaloric properties of this family of materials.

Antiferromagnetic and nutation resonance frequencies of antiferromagnets at an arbitrary strength of the applied dc field

Nutation and precession resonances in an antiferromagnet subjected to a dc magnetic field are investigated by employing coupled linearized inertial Landau–Lifshitz–Gilbert equations describing the dynamics of magnetizations of antiferromagnet sublattices with uniaxial magnetocrystalline anisotropy. Analytical expressions for the eigenfrequencies of such an antiferromagnet are obtained for the longitudinal and transverse directions of the external dc field and for different ranges of its strength. The effect of inertia on the values of the resonant frequencies is shown for all possible states of the antiferromagnet in both the longitudinal and transverse directions of the external field. The estimated resonant frequencies are compared with those obtained from the numerical solution of the system of undamped inertial Landau–Lifshitz–Gilbert equations for closed trajectories of sublattice magnetizations. The good agreement of both independent estimations is demonstrated.

Magnetotransport of Sm2Ir2O7 across the pressure-induced quantum-critical phase boundary

Rare-earth pyrochlore iridates host two interlocking magnetic sublattices of corner-sharing tetrahedra and can harbour a unique combination of frustrated moments, exotic excitations and highly correlated electrons. They are also the first systems predicted to display both topological Weyl semimetal and axion insulator phases. We have measured the transport and magnetotransport properties of single-crystal Sm2Ir2O7 up to and beyond the pressure-induced quantum critical point for all-in-all-out (AIAO) Ir order at pc = 63 kbar previously identified by resonant X-ray scattering and close to which Weyl semimetallic behavior has been previously predicted. Our findings overturn the accepted expectation that the suppression of AIAO order should lead to metallic conduction persisting down to zero temperature. Instead, the resistivity-minimum temperature, which tracks the decrease in the AIAO ordering temperature for pressures up to 30 kbar, begins to increase under further application of pressure, pointing to the presence of a second as-yet unidentified mechanism leading to non-metallic behavior. The magnetotransport does track the suppression of Ir magnetism, however, with a strong hysteresis observed only within the AIAO phase boundary, similar to that found for Ho2Ir2O7 and attributed to plastic deformation of Ir domains. Around pc we find the emergence of a new type of electronic phase, characterized by a negative magnetoresistance with small hysteresis at the lowest temperatures, and hysteresis-free positive magnetoresistance above approximately 5 K. The temperature dependence of our low-temperature transport data are found to be best described by a model consistent with a Weyl semimetal across the entire pressure range.

Electric-Field Control of Perpendicularly Magnetized Ferrimagnetic Order and Giant Magnetoresistance in Multiferroic Heterostructures.

Electrical control of magnetism is highly desirable for energy-efficient spintronic applications. Realizing electric-field-driven perpendicular magnetization switching has been a long-standing goal, which, however, remains a major challenge. Here, electric-field control of perpendicularly magnetized ferrimagnetic order via strain-mediated magnetoelectric coupling is reported. We show that the gate voltages isothermally toggle the dominant magnetic sublattice of the compensated ferrimagnet FeTb at room temperature, showing high reversibility and good endurance under ambient conditions. By implementing this strategy in FeTb/Pt/Co spin valves with giant magnetoresistance (GMR), we demonstrate that the distinct high and low resistance states can be selectively controlled by the gate voltages with assisting magnetic fields. Our results provide a promising route to use ferrimagnets for developing electric-field-controlled, low-power memory and logic devices.

Interplay of two magnetic sublattices in related compounds Sm2Mn1-xGa6-yGey (x = 0.1-0.3, y = 0.6-1.0) and Sm4MnGa12-yGey (y = 3.0-3.5) with different ordering of empty and filled (Ga,Ge)6 octahedra.

Single crystals of two new intermetallic phases Sm2Mn1-xGa6-yGey (x = 0.1-0.3, y = 0.6-1.0) and Sm4MnGa12-yGey (y = 3.0-3.5) were grown using a self-flux technique. According to single crystal X-ray diffraction data, Sm4MnGa12-yGey is characterised by the Y4PdGa12 structure type (a ∼ 8.65 Å; Im3̄m), while Sm2Mn1-xGa6-yGey formally adopts the K2PtCl6 structure type (a ∼ 8.71 Å; Fm3̄m). The general features of both compounds with rather similar crystal structures are represented by the alternation of empty and Mn-filled p-element octahedra, the order of which is determined by the Mn concentration. The diffraction data for Sm2Mn1-xGa6-yGey reveal a large concentration of Mn vacancies (x ∼ 0.3), which affects adjacent Ga/Ge atoms leading to their shift towards the vacancy. Both compounds demonstrate two ferromagnetic-like transitions and the presence of two interacting Mn and Sm magnetic sublattices. The Mn sublattice orders at TC1 of 143 K and 318 K, while the Sm one orders at lower temperatures at TC2 of 50 K and 280 K for Sm4MnGa8.6Ge3.4 and Sm2Mn0.74Ga5.1Ge0.9, respectively. The increase in Mn content not only increases the ordering temperatures, but also dramatically decreases the coercivity μ0HC from 230 mT to just 6.5 mT at 2 K. Despite the presence of two magnetically active sublattices in Sm2Mn0.74Ga5.1Ge0.9, the magnetic entropy change is quite low and only reaches 0.3 J kg-1 K-1 at T = 300 K and μ0H = 5 T, while the estimated relative cooling power (RCP) is about 36 J kg-1 at 5 T.

Spin-phonon coupling driven magnetodielectric effect in low-dimensional complex magnetic BaGdFeO4 system

In this report, we have investigated the detailed magnetodielectric properties associated with spin-phonon coupling in the BaGdFeO4 polycrystalline compound, X-ray diffraction study confirms the orthorhombic crystal structure with a space group of Pnma. The DC magnetization measurements indicate the complex magnetic behavior with multiple magnetic transitions at TN1 = 62 K and TN2 = 31 K. In the field-dependent magnetization study, field-induced metamagnetic transitions and their temperature dependence have been attributed to the competing magnetic interactions of two magnetic sub-lattices with rare-earth (Gd3+) and Fe3+ magnetic spins. Dielectric measurements have revealed the correlation of observed dielectric anomalies with the magnetic transitions. The frequency-independent and magnetic field-dependent dielectric anomalies, along with the corresponding magnetic transitions, thus corroborate the subtle magnetodielectric coupling studied by temperature-dependent magnetodielectric measurements. We discuss possible origins for the magnetodielectric behavior in terms of weak spin-phonon interactions, as confirmed by the temperature-dependent Raman spectra measurements.

Antiferromagnitnyy eksitonnyy dielektrik

The effective the two-band Hamiltonian is obtained for iridium oxides with account for strong electron correlations (SEC) and the spin–orbit interaction. The intraatomic electron correlations in iridium ions induce the formation of Hubbard fermions (HF) filling the states in the valence band. Another consequence of SEC is associated with the emergence of the antiferromagnetic (AFM) exchange interaction between HF in accordance with the Anderson mechanism. As a result, a long-range antiferromagnetic order is established in the system, and in the conditions of band overlapping, the intersite Coulomb interaction induces a phase transition to the excitonic insulator (EI) state with a long-range AFM order. The system of integral self-consistent equations, the solution to which determines the excitonic order parameter components Δi, j(k), sublattice magnetization M, Hubbard fermion concentration nd, and chemical potential μ, is obtained using the atomic representation, the method of two-time temperature Green’s functions, and the Zwanzig–Mori projection technique. The symmetry classification of AFM EI phases is performed, and it is shown that in the nearest neighbor approximation, state Δi, j(k) with the s-type symmetry corresponds to the ground state, while the phases with the d- and p-symmetries are metastable.

Моделирование внешнего воздействия на резонансные свойства объемного антиферромагнетика α − Fe2O3 при спин-переориентационном переходе

This paper presents a model that explains the influence of external pressure on the resonant frequency of a bulk crystal a–Fe2O3 in an external magnetic field. The dynamics of vectors l and m before and after the Morin temperature TM are considered. The dependences of the resonant frequency on pressure and external magnetic field for the cases H║(HA ║ z) and H┴(HA ║ z) are obtained, and the dependences of the magnetic field on pressure are obtained for the lower and upper modes. It was found that when external pressure is applied to the structure, the natural frequency of vibrations of the magnetic sublattices of the antiferromagnet increases significantly. The results obtained can be used in the development of devices for generating and processing signals in the gigahertz and terahertz frequency ranges.

Exchange bias effect and compensation point in the bulk ferrimagnet Fe2CrSe4

Polycrystalline samples of the Fe2CrSe4 compound have been synthesized and studied by means of x-ray diffraction and magnetization measurements. The as-synthesized Fe2CrSe4 sample shows ferrimagnetic ordering below TN ∼ 300 K with a compensation point Tcomp ∼ 140 K. This compound is found to exhibit a large coercive field (half-width of the hysteresis loop reaches 15 kOe at 2 K) and a significant exchange bias (EB) effect below 50 K (HEB up to 6.6 kOe) after cooling in an applied field and after zero-field cooling. The exchange bias in Fe2CrSe4 is suggested to result from the presence of regions (clusters) with short-range correlations in the ferrimagnetic matrix due to the inhomogeneous distribution of iron and chromium atoms over the lattice. Additional heat treatment and subsequent rapid cooling lead to an increase in magnetic ordering temperature, the disappearance of compensation for sublattice magnetizations and a decrease in the exchange bias, thus showing the possibility of controlling the exchange bias and magnetic characteristics in the system.

Optically controlling the competition between spin flips and intersite spin transfer in a Heusler half-metal on sub-100-fs time scales.

The direct manipulation of spins via light may provide a path toward ultrafast energy-efficient devices. However, distinguishing the microscopic processes that can occur during ultrafast laser excitation in magnetic alloys is challenging. Here, we study the Heusler compound Co2MnGa, a material that exhibits very strong light-induced spin transfers across the entire M-edge. By combining the element specificity of extreme ultraviolet high-harmonic probes with time-dependent density functional theory, we disentangle the competition between three ultrafast light-induced processes that occur in Co2MnGa: same-site Co-Co spin transfer, intersite Co-Mn spin transfer, and ultrafast spin flips mediated by spin-orbit coupling. By measuring the dynamic magnetic asymmetry across the entire M-edges of the two magnetic sublattices involved, we uncover the relative dominance of these processes at different probe energy regions and times during the laser pulse. Our combined approach enables a comprehensive microscopic interpretation of laser-induced magnetization dynamics on time scales shorter than 100 femtoseconds.