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The magneto-optical response of Fe and Ni during ultrafast demagnetization is studied experimentally and theoretically. We have performed pump-probe experiments in the transverse magneto-optical Kerr effect (T-MOKE) geometry using photon energies that cover the M-absorption edges of Fe and Ni between 40 to 72 eV. The asymmetry was detected by measuring the reflection of light for two different orientations of the sample magnetization. Density functional theory (DFT) wasused to calculate the magneto-optical response of different magnetic configurations, representing different types of excitations: long-wavelength magnons, short wavelength magnons, and Stoner excitations. In the case of Fe, we find that the calculated asymmetry is strongly dependent on the specific type of magnetic excitation. Our modelling also reveals that during remagnetization Fe is, to a reasonable approximation, described by magnons, even though small non-linear contributions could indicate some degree of Stoner excitations as well. In contrast, we find that the calculated asymmetry in Ni is rather insensitive to the type of magnetic excitations. However, there is a weak non-linearity in the relation between asymmetry and the off-diagonal component of the dielectric tensor, which does not originate from the modifications of the electronic structure. Our experimental and theoretical results thus emphasize the need of considering a coupling between asymmetry and magnetization that may be more complex that a simple linear relationship. This insight is crucial for the microscopic interpretation of ultrafast magnetization experiments.

Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) approach, we discuss mainly the fermionic (i.e. off-shell nilpotent) (anti-)BRST, (anti-)co-BRST and some discrete dual-symmetries of the appropriate Lagrangian densities for a two (1+1)-dimensional (2D) modified Proca (i.e. a massive Abelian 1-form) theory without any interaction with matter fields. One of the novel observations of our present investigation is the existence of some kinds of restrictions in the case of our present St\"{u}ckelberg-modified version of the 2D Proca theory which is not like the standard Curci-Ferrari (CF)-condition of a non-Abelian 1-form gauge theory. Some kinds of similarities and a few differences between them have been pointed out in our present investigation. To establish the sanctity of the above off-shell nilpotent (anti-)BRST and (anti-)co-BRST symmetries, we derive them by using our newly proposed (anti-)chiral superfield formalism where a few specific and appropriate sets of invariant quantities play a decisive role. We express the (anti-)BRST and (anti-)co-BRST conserved charges in terms of the superfields that are obtained after the applications of (anti-)BRST and (anti-)co-BRST invariant restrictions and prove their off-shell nilpotency and absolute anticommutativity properties, too. Finally, we make some comments on (i) the novelty of our restrictions/obstructions, and (ii) the physics behind the negative kinetic term associated with the pseudo-scalar field of our present theory., Comment: LaTeX file, 58 pages, Journal reference given

Ni$_{0.8}$Fe$_{0.2}$ (Py) and Py alloyed with Cu exhibit intriguing ultrafast demagnetization behavior, where the Ni magnetic moment shows a delayed response relative to the Fe, an effect which is strongly enhanced by Cu alloying. We have studied a broad range of Cu concentrations to elucidate the effects of Cu alloying in Py. The orbital/spin magnetic moment ratios are largely unaffected by Cu alloying, signifying that Cu-induced changes in the ultrafast demagnetization are not related to spin-orbit interactions. We show that magnon diffusion can explain the delayed Ni response, which we attribute to an enhanced magnon generation rate in the Fe sublattice relative to the Ni sublattice. Furthermore, Py exhibits prominent RKKY-like exchange interactions, which are strongly enhanced between Fe atoms and diminished between Ni atoms by Cu alloying. An increased Fe magnon scattering rate is expected to occur concurrently with this increased Fe-Fe exchange interaction, supporting the results obtained from the magnon diffusion model.

Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism, we show that the four $(3+1)$-dimensional (4D) massive Abelian 2-form gauge theory (without any interaction with matter fields) is a model for the Hodge theory because its discrete and continuous symmetry transformations (and their corresponding Noether conserved charges) provide the physical realizations of the de Rham cohomological operators of differential geometry at the algebraic level. For this purpose, we incorporate the pseudo-scalar and axial-vector fields which appear in the theory with negative kinetic terms (but with proper definition of mass). The negative kinetic terms, for the above fields, are essential so that our theory could respect the discrete symmetry transformations which provide the physical realizations of the Hodge duality operation in the domain of differential geometry. Thus, our present endeavour, not only provides the physical realizations of all the mathematical ingredients connected with the de Rham cohomological operators of differential geometry, it also sheds light on the existence and emergence of fields with negative kinetic terms. We discuss the implications and relevance of the latter fields in the context of current models of dark matter and dark energy as well as the bouncing models of Universe., Comment: LaTeX file, 42 pages, two figures, journal reference is given

We exploit the potential and power of the Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST invariant restrictions on the (anti-)chiral supervariables to derive the proper (anti-)BRST symmetries for the reparameterization invariant one (0+1)-dimensional (1D) toy models of the free relativistic particle as well as free spinning (i.e. supersymmetric) relativistic particle within the framework of (anti-)chiral supervariable approach to BRST formalism. Despite the (anti-)chiral super expansions of the (anti-)chiral supervariables, we observe that the (anti-)BRST charges, for the above toy models, turn out to be absolutely anticommuting in nature. This is one of the novel observations of our present endeavor. For this proof, we utilize the beauty and strength of Curci-Ferrari (CF) type restriction in the case of spinning relativistic particle but no such restriction is required in the case of the free scalar relativistic particle. We have also captured the nilpotency property of the conserved charges as well as the (anti-)BRST invariance of the appropriate Lagrangian(s) of our present toy models within the framework of (anti-)chiral supervariable approach., Comment: LaTeX file, 32 pages, journal version

We exploit the power and potential of the (anti-)chiral superfield approach (ACSA) to Becchi-Rouet-Stora-Tyutin (BRST) formalism to derive the nilpotent (anti-)BRST symmetry transformations for any arbitrary D-dimensional interacting non-Abelian 1-form gauge theory where there is a SU(N) gauge invariant coupling between the gauge field and the Dirac fields. We derive the conserved and nilpotent (anti-)BRST charges and establish their nilpotency and absolute anticommutativity properties within the framework of ACSA to BRST formalism. The clinching proof of the absolute anticommutativity property of the conserved and nilpotent (anti-)BRST charges is a novel result in view of the fact that we consider, in our present endeavor, only the (anti-)chiral super expansions of the superfields that are defined on the (D, 1)-dimensional super-submanifolds of the general (D, 2)-dimensional supermanifold on which our D-dimensional ordinary interacting non-Abelian 1-form gauge theory is generalized. To corroborate the novelty of the above result, we apply the ACSA to an N = 2 supersymmetric (SUSY) quantum mechanical (QM) model of a harmonic oscillator and show that the nilpotent and conserved N = 2 supercharges of this system do not absolutely anticommute., Comment: LaTeX file, 27 pages, journal version

We derive the off-shell nilpotent (fermionic) (anti-)BRST symmetry transformations by exploiting the (anti-)chiral superfield approach (ACSA) to Becchi-Rouet-Stora-Tyutin (BRST) formalism for the interacting Abelian 1-form gauge theories where there is a coupling between the U(1) Abelian 1-form gauge field and Dirac as well as complex scalar fields. We exploit the (anti-)BRST invariant restrictions on the (anti-)chiral superfields to derive the fermionic symmetries of our present D-dimensional Abelian 1-form gauge theories. The novel observation of our present investigation is the derivation of the absolute anticommutativity of the nilpotent (anti-)BRST charges despite the fact that our ordinary D-dimensional theories are generalized onto the (D, 1)-dimensional (anti-)chiral super submanifolds (of the general (D, 2)-dimensional supermanifold) where only the (anti-)chiral expansions of the (anti-)chiral superfields have been taken into account. We also discuss the nilpotency of the (anti-)BRST charges and (anti-)BRST invariance of the Lagrangian densities of our present theories within the framework of ACSA to BRST formalism., Comment: LaTeX file, 20 pages, journal version

We exploit the theoretical strength of augmented version of superfield approach (AVSA) to Becchi-Rouet-Stora-Tyutin (BRST) formalism to express the nilpotency and absolute anticommutativity properties of the (anti-)BRST and (anti-)co-BRST conserved charges for the two $(1+1)$-dimensional (2D) non-Abelian 1-form gauge theory (without any interaction with matter fields) in the language of superspace variables, their derivatives and suitable superfields. In the proof of absolute anticommutativity property, we invoke the strength of Curci-Ferrari (CF) condition for the (anti-)BRST charges. No such outside condition/restriction is required in the proof of absolute anticommutativity of the (anti-)co-BRST conserved charges. The latter observation (as well as other observations) connected with (anti-)co-BRST symmetries and corresponding conserved charges are novel results of our present investigation. We also discuss the (anti-)BRST and (anti-)co-BRST symmetry invariance of the appropriate Lagrangian densities within the framework of AVSA. In addition, we dwell a bit on the derivation of the above fermionic (nilpotent) symmetries by applying the AVSA to BRST formaism where only the (anti-)chiral superfields are used., Comment: LaTeX file, 33 pages, journal reference

We discuss the nilpotent Becchi-Rouet-Stora-Tyutin (BRST), anti-BRST and (anti-)co-BRST symmetry transformations and derive their corresponding conserved charges in the case of a two (1+1)-dimensional (2D) self-interacting non-Abelian gauge theory (without any interaction with matter fields). We point out a set of novel features that emerge out in the BRST and co-BRST analysis of the above 2D gauge theory. The algebraic structures of the symmetry operators (and corresponding conserved charges) and their relationship with the cohomological operators of differential geometry are established, too. To be more precise, we demonstrate the existence of a single Lagrangian density that respects the continuous symmetries which obey proper algebraic structure of the cohomological operators of differential geometry. In literature, such observations have been made for the coupled (but equivalent) Lagrangian densities of the 4D non-Abelian gauge theory. We lay emphasis on the existence and properties of the Curci-Ferrari (CF) type restrictions in the context of (anti-)BRST and (anti-)co-BRST symmetry transformations and pinpoint their key differences and similarities. All the observations, connected with the (anti-)co-BRST symmetries, are completely novel., Comment: LaTeX file, 27 pages, minor changes in the text, journal reference given

We derive the off-shell nilpotent symmetries of the two (1+1)-dimensional (2D) non-Abelian 1-form gauge theory by using the theoretical techniques of the geometrical superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism. For this purpose, we exploit the augmented version of superfield approach (AVSA) and derive theoretically useful nilpotent (anti-)BRST, (anti-)co-BRST symmetries and Curci-Ferrari (CF) type restrictions for the self-interacting 2D non-Abelian 1-form gauge theory (where there is no interaction with matter fields). The derivation of the (anti-)co-BRST symmetries and all possible CF-type restrictions are completely novel results within the framework of AVSA to BRST formalism where the ordinary 2D non-Abelian theory is generalized onto an appropriately chosen (2, 2)-dimensional supermanifold. The latter is parameterized by the superspace coordinates Z^{M} = (x^{\mu}, \theta, \bar\theta) where x^{\mu } (with \mu = 0,1) are the bosonic coordinates and a pair of Grassmannian variables (\theta, \bar\theta) obey the relationships: \theta^{2} = \bar\theta^{2} = 0, \theta\bar\theta + \bar\theta\theta = 0., Comment: LaTeX file, 20 pages, journal version

Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism, we discuss the full set of proper BRST and anti-BRST transformations for a 2D diffeomorphism invariant theory which is described by the Lagrangian density of a standard bosonic string. The above (anti-)BRST transformations are off-shell nilpotent and absolutely anticommuting. The latter property is valid on a submanifold of the space of the quantum fields where the 2D version of the universal (anti-)BRST invariant Curci-Ferrari (CF) type of restrictions are satisfied. We derive the precise forms of the BRST and anti-BRST invariant Lagrangian densities as well as the exact expressions for the conserved (anti-)BRST and ghost charges. The lucid derivation of the proper anti-BRST symmetry transformations and the emergence of the CF-type restrictions are completely novel results for our present bosonic string which has already been discussed earlier in literature where only the BRST symmetry transformations have been pointed out. We briefly mention the derivation of the CF-type restrictions from the modified version of Bonora-Tonin superfield approach, too., Comment: LaTeX file, 22 pages, version to appear in AHEP

Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism, we discuss some novel features of a two (1+1)-dimensional (2D) non-Abelian 1-form gauge theory (without any interaction with matter fields). Besides the usual off-shell nilpotent and absolutely anticommutating (anti-)BRST symmetry transformations, we discuss the off-shell nilpotent and absolutely anticommutating (anti-)co-BRST symmetry transformations. Particularly, we lay emphasis on the existence of the coupled (but equivalent) Lagrangian densities of the 2D non-Abelian theory in view of the presence of (anti-)co-BRST symmetry transformations where we pin-point some novel features associated with the Curci-Ferrari (CF) type restrictions. We demonstrate that these CF-type restrictions can be incorporated into the (anti-)co-BRST invariant Lagrangian densities through the fermionic Lagrange multipliers which carry specific ghost numbers. The modified versions of the Lagrangian densities (where we get rid of the new CF-type restrictions) respect some precise symmetries as well as a couple of symmetries with CF-type constraints. These observations are completely novel as far as the BRST formalism, with proper (anti-)co-BRST symmetries, is concerned., Comment: LaTeX file, 14 pages, journal version

We exploit the key concepts of the augmented version of superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism to derive the superspace (SUSP) dual unitary operator (and its Hermitian conjugate) and demonstrate their utility in the derivation of the nilpotent and absolutely anticommuting (anti-)dual BRST symmetry transformations for a set of interesting models of the Abelian 1-form gauge theories. These models are the one (0+1)-dimensional (1D) rigid rotor, modified versions of the two (1+1)-dimensional (2D) Proca as well as anomalous gauge theories and 2D model of a self-dual bosonic field theory. We show the universality of the SUSP dual unitary operator and its Hermitian conjugate in the cases of all the Abelian models under consideration. These SUSP dual unitary operators, besides maintaining the explicit group structure, provide the alternatives to the dual-horizontality condition (DHC) and dual-gauge invariant restrictions (DGIRs) of the superfield formalism. The derivation of the dual unitary operators and corresponding (anti-)dual BRST symmetries are completely novel results in our present investigation., Comment: LaTeX file, 25 pages, journal reference is given