Join our Colloquia!

23. End-of-Year Mini-Workshop (Special)

Date: 18/12/2024

Time: 10:30 C.E.T.

Location: Conference Room Orio Zanetto, Alfa Building

Zoom Link → Password: seminar1

The Department of Molecular Sciences and Nanosystems (DSMN) is organizing an end-of-year mini-workshop for Physics Engineering students and researchers. The event offers a unique opportunity to explore the latest developments in the department’s engineering and physics research areas, as well as to learn about the educational and research opportunities provided by the Polytechnic Universities of Turin and Milan. The morning will conclude with a convivial networking moment, accompanied by traditional holiday treats.

22. Lara Benfatto, University or Rome “Sapienza” (Italy)

Date: 20/11/2024

Time: 11:00 C.E.T.

Title: Probing materials with strong THz light pulses: a theory perspective on experimental challenges”

Location: Conference Room Orio Zanetto, Alfa Building

Zoom Link → Password: seminar1

The recent experimental advances in generating intense and short-lived THz light pulses opened the way for a plethora of potential ground-breaking applications. Indeed, the THz spectral window corresponds to the timescale of several collective excitations in solids, ranging from lattice vibrations to collective modes of the electron system across a phase transitions, like e.g the superconducting one. From the theoretical point of view, facing with time-resolved spectroscopy with intense THz light pulses requires to address simultaneously two complementary problems: going beyond the linear-response regime, valid for weak perturbing fields, and describing a purely out-of-equilibrium process, where one probes relaxation out of a (possible) metastable state. While addressing the latter problem is still at its infancy, in the last decade several progresses have been done on the former aspect. In this talk I will review our contribution to the understanding of resonant and non-resonant excitations driven by strong THz fields in solids, with examples ranging from superconducting to lattice modes. I will show how a common theoretical framework can be efficiently used to interpret several experimental findings, making non-linear THz spectroscopy an extremely versatile tool to disentangle the microscopic processes at play in different systems.

21. Federico Levi, Springer Nature Publishing Group (United Kingdom)

Date: 24/10/2024

Time: 11:00 C.E.T.

Title: Inside Nature”

Location: Conference Room Orio Zanetto, Alfa Building

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Since its launch in 1869, Nature has seen its mission as two-fold: facilitating the prompt communication of the most important scientific developments to the relevant research communities, while at the same time fostering a greater appreciation of these great works of science amongst the wider public. In this talk, I will endeavour to explain how Nature editors apply these principles in practice, in particular by determining which few of the many excellent research submissions that we receive make it through to publication.

20. Hans Kleeman, Technische Universität Dresden (Germany)

Date: 19/09/2024

Time: 11:00 C.E.T.

Title: “Complexity in organic mixed ionic electronic conductors and its application in neuromorphic computing”

Location: Conference Room Orio Zanetto, Alfa Building

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Complexity is a decisive property enabling systems to work at the edge of chaos, which is necessary for resource-efficient computing and the design of intelligent machines. The complex behavior of a system originates from the nonlinear properties of all its components, resulting in a plethora of different signatures such as multi-state stability, stochastic oscillations, etc. These nonlinear properties and their couplings need to be understood and modeled to develop intelligent & energy-efficient computers.

Organic mixed ionic-electronic conductors (OMIECs) based on conjugated polymers open up a fascinating field of research where the ionic-electronic coupling, in combination with correlation effects at high charge carrier densities, enables the implementation of various paradigms of neuromorphic computing. In this contribution, I will discuss the various signatures of nonlinearity and complexity that have been observed in OMIECs in recent years and review the current understanding of these effects. Furthermore, I will discuss how phenomena such as hysteresis and bistability can be employed to design fundamental elements of asynchronous computing, such as spiking neurons or C-elements, providing the foundation for the efficient implementation of approaches of stochastic computing in hardware. Finally, I will present a technology platform that allows us to integrate such devices in all-printed, complementary circuits operating above 1kHz.

19. Caterina Vozzi, The Institute for Photonics and Nanotechnologies (IFN) – National Research Council (CNR) (Italy)

Date: 18/07/2024

Time: 11:00 C.E.T.

Title: Attosecond science for the study of electron dynamics in matter”

Location: Room Delta 1B, Delta Building

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Our knowledge of the microscopic world has been transformed by the study of matter on ultrafast time scales. The capacity to produce and apply light pulses with durations from the femtosecond (10-15 s) to the attosecond (10-18 s) scale has created new opportunities for watching and manipulating quantum mechanical processes in real-time. By revealing ultrafast processes in matter, attosecond science can unlock the secrets and potential of chemical reactions and enable technologies like ultrafast lasers and attosecond spectroscopy. It is a leading field in both fundamental research and technological innovation. Studying how electrons behave in ultrafast time scales with attosecond science is crucial for understanding and possibly influencing molecular transformations, impacting fields from medicine to materials science. This lecture will cover the subject of the 2023 Nobel Prize in Physics: the finding of a non-linear optical process called High-order Harmonic Generation (HHG) that has transformed the field of ultrafast science, allowing the creation of attosecond light pulses for investigating the briefest of events in the behaviour of matter.
18. Angelo Vulpiani, University or Rome “Sapienza” (Italy)

Date: 20/06/2024

Time: 11:00 C.E.T.

Title: Theory and data in model building: from Volterra to machine learning”

Location: Room Delta 2A, Delta Building

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It is not an exaggeration to say that models are unavoidable in scientific practice and that it is impossible to have real science without them. Even top theories (e.g. electromagnetism or quantum mechanics) are nothing but sophisticated models. The talk is devoted to ”true” models which do not pretend to offer a general description, in particular in the cases where the top theories are not very efficient and can be classified into 4 large classes: I- Oversimplified models; II- Models by analogy; III- Large scale models; IV- Models from data. In class I there is the celebrated Lorenz model; the Lotka-Volterra system is in class II, and it is at the origin of biomathematics. Among the models in class III, we have the effective equations used, e.g., in meteorology and engineering, where only ”relevant variables” are taken into account. In class IV we find the most interesting (and difficult) problem: the building of models just from data without a reference theoretical framework.

17. Miroslav Vozňák, VŠB-Technical University of Ostrava (Czech Republic)

Date: 24/05/2024

Time: 11:00 C.E.T.

Title: Emerging quantum key distribution networks”

Location: Conference Room Orio Zanetto, Alfa Building

Zoom Link → Password: seminar1

Conventional encryption algorithms are expected to be broken in a large-scale quantum computer. It is not a question of yes or no, we don’t know when it will happen, whether within this or the following decade. If you ask how we can deal with the coming threats to the cryptography currently in use, fortunately, we have a response. There are two ways, post-quantum cryptography (PQC) and quantum key distribution (QKD). The PQC standardization process began in 2016 and it’s still open, within the process, the world’s cryptographic experts were called to submit candidate algorithms, now we have selected four and we expect the next three this year. Another approach is not based on mathematical algorithms but on quantum physics principles, which is the idea of quantum key distribution (QKD). The speech will briefly introduce the principles of cryptography in the beginning, then will continue with the Open Quantum Safe project and the major part will be devoted to the QKD. A substantial part will be about issues of QKD networks and the speaker will share his experience from recently finished H2020 OpenQKD and NATO Quantum5 projects.

16. Nicola Marzari, École Polytechnique Fédérale de Lausanne (Switzerland)

Date: 23/04/2024

Time: 11:00 C.E.T.

Title: “The shape of things to come: first-principles simulations driving discovery and innovation”

Location: Conference Room Orio Zanetto, Alfa Building

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Computational science has benefited for many decades from the algorithms and the hardware that have made it one of the greatest accelerators of research, with results and impact that run deep in scientific discovery and technological innovation. This is particularly true for first-principles simulations, which address directly the quantum mechanics of interacting electrons and nuclei and have become one of the most widely used and widely misused tools in research.

I’ll first illustrate the key challenges and opportunities that this new kind of science faces: 1) of predictive accuracy, with simulations able to capture faithfully the quantum nature of electrons and nuclei; 2) of realistic complexity, aiming to describe ever more realistic systems; and 3) of materials informatics, leveraging the disruptive capabilities of machine learning and data mining, quantum computing, and artificial intelligence. 

I’ll then highlight some of the key efforts we are targeting: addressing the electronic structure of compounds with strongly localized electrons, developing mesoscopic equations and formulations that bring atomistic and quantum precision to the macroscopic scale, and delivering automated capabilities that can be externalized and then orchestrated by human and not-so-human players. Some case studies will cover the design and discovery of materials for energy (Li-ion cathodes and solid-state conductors) and materials for information-and-communication technologies (2D and 1D materials, topological insulators, and superconductors)

15. Janet Anders, University of Exeter (United Kingdom)

Date: 22/03/2024

Time: 11:00 C.E.T.

Title: “Quantum thermodynamic insights and their use for atomistic spin dynamics simulations and cold atom thermometry”

Location: Room Delta 1B, Delta Building

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Quantum thermodynamics is an emerging research field aiming to extend standard thermodynamics theory to nanoscale systems which do not fall within the thermodynamic limit, whose interaction with their environments becomes important, and where quantum effects can be present.  For example, the interaction of nanoscale and quantum systems with their environment can be relatively strong, and alter the equilibrium state. For open quantum systems, explicit expressions of these so-called mean force (MF) equilibrium states have been missing. I will first report on useful analytic expressions of these states, valid for a general quantum system in contact with a bosonic bath. These are illustrated for the well-known spin-boson model, for which we provide the first classification of coupling regimes, from weak to ultrastrong, and for both the quantum and classical setting. The utility of these theoretical concepts is demonstrated by predicting the equilibrium state’s magnetisation of a magnetic material (e.g. nickel) as a function of temperature. We show that including the environment-induced effects gives a much-improved match with experimental data, also in the low-temperature regime which has resisted accurate atomistic modelling. 

In the second part of my talk, I will briefly report on our recent results on optimal (global) quantum thermometry. This new framework is most relevant for small data sets, such as those in cold atom experiments where some scans for a single data point can take half a day. This theoretical framework, based on Bayesian principles, has successfully been used to reduce estimation errors in release-recapture experiments.

14. Andrea Droghetti, Trinity College Dublin (Ireland) and National Research Council CNR-SPIN (Italy)

Date: 22/02/2024

Time: 12:00 C.E.T.

Title: “Nano-magnetism and spintronic effects via first-principles computational methods”

Location: Room A, Zeta Building

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Magnetic materials are ubiquitous in electronic, sensing and power technologies. The modification in their electronic structure, due to interfaces and spatial confinement at the nanoscale, can induce new properties and emerging phenomena. In this talk, I will present some of these properties and phenomena, while describing how they can be predicted by means of quantum mechanical numerical simulations from first principles (i.e., without any empirical parameters). To begin with, I briefly introduce Density Functional Theory (DFT), used here to treat ferromagnetic metals within a single-particle picture, where electrons are non-interacting, but experience an effective magnetic field due to the other surrounding electrons.

Then, I discuss how this simple picture might break down in some cases because of electron correlations. To treat this problem, we have developed a computational approach, which combines DFT with Dynamical Mean Field Theory (DMFT) as a solver for many-body systems. DFT+DMFT calculations accurately describe the spin splitting and the appearance of satellite features in the electronic spectra of transition metal surfaces. More importantly, our results also indicate that electron correlations at surfaces can be tuned, for example, by adsorbing small atoms and molecules, leading to the formation of electron liquids with exotic properties. Finally, in the second part of the talk, I explain in detail how we have combined both DFT and DMFT with quantum transport schemes, based on the non-equilibrium Green’s function technique, to simulate spin transport (i.e., “spintronic”) phenomena and devices. Our approach is employed to estimate the giant and tunnel magnetoresistance in the prototypical and technologically-relevant Co/Cu and Fe/MgO nano-junctions as well as in van der Waals heterostructures comprising 2d ferromagnetic materials, such as Fe4GeTe2. Furthermore, it can also be applied to describe spin-charge conversion phenomena and spin torque effects. Overall, our methods and simulations provide an advanced description of magnetic and spintronic phenomena across the wide range of materials and devices of current interest for both fundamental science and technological applications.

13. Mattia Fanetti, University of Nova Gorica (Slovenia)

Date: 18/01/2024

Time: 11:00 C.E.T.

Title: “Basic concepts on topological insulators and their chemistry at the interface with metals”

Location: Room D, Zeta Building 

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Topological insulators (TIs) are materials with non-trivial band structure topology. Due to this, while they have a bandgap in the bulk, they also have conductive topological states at the surface (TSS), which are robust because they are symmetry protected. Further, TSS have other intriguing properties (e.g. spin-vs-k locking), which makes TIs widely investigated for spintronic and low-power electronic applications.

The interfaces between metals and TIs are present almost everywhere when TIs are used in prototypes and applications, from catalysis to spintronics, down to the fabrication of simple electric contacts. The interface structure is of crucial importance, since the special properties of TIs reside in the topological electronic states at their surface. However, in many cases such interface is far from being a stable and peaceful neighborhood between the metal and the TI crystal. In this presentation, a first part is dedicated to introduce the basic concept about topological insulators, while in the second part the results about our investigation (mostly by electron microscopy) on the interfacial properties of metal/TI system are presented.

12. End-of-Year Seminar (Special)

Date: 21/12/2023

Time: 12:00 C.E.T.

Title: “Engineering and physics research at DSMN: current work and future prospects”

Location: Conference Room Orio Zanetto, Alfa Building 

Zoom Link → Password: seminar1

This seminar brings together researchers at DSMN from diverse fields within physics and engineering to provide concise overviews of their ongoing work. Topics include theoretical physics, experimental condensed matter dynamics, complex networks, optoelectronics, telecommunication systems, and more! The presentations aim to offer a pragmatic view of current research strands, encouraging collaboration and discussion.

11. Giancarlo SoaviFriedrich Schiller University Jena (Germany)

Date: 17/11/2023

Time: 10:30 C.E.T.

Title: “Engineering nonlinear optics in atomically thin materials: ultrafast light modulators and nonlinear valleytronics”

Location: Conference Room Orio Zanetto, Alfa Building 

Zoom Link → Password: seminar1

Atomically thin materials and related layered structures are ideal candidates for ultrafast and nanoscale nonlinear devices, such as light modulators and frequency converters. In this seminar, I will discuss some of our recent works in two emerging fields that belong the realm of nonlinear optics. First, I will discuss the tuning and engineering of nonlinearities in graphene and TMDs by electrical and all-optical means. In graphene, ultra-broadband modulation of third harmonic generation can be obtained via an external gate voltage by tuning the Fermi Energy across multi-photon resonances occurring within the Dirac cone, while all-optical modulation can be ascribed to the combined effect of increased electronic temperature and Pauli blocking. In the second part of the talk, I will discuss the emerging field of nonlinear valleytronics. In monolayer TMDs, the K/K’ valleys can be selectively excited with circularly polarized light of opposite helicity, but the detection of a valley imbalance, either due to a real excited state population or simply induced by lifting the energy degeneracy between the valleys, has been limited to date to the realm of linear optics. I will show our new approach to valleytronics that allows to detect a valley polarization based on the ultrafast and non-invasive nonlinear process of second harmonic generation, in combination with a generation mechanism based on the ultrafast and coherent optical Stark effect.

10. Miriam VitielloNEST, National Research Council CNR-NANO and Scuola Normale Superiore (Italy)

Date: 17/10/2023

Time: 11:30 C.E.T.

Title: “Nano-photonic devices at terahertz frequencies employing scalable graphene heterostructures”

Location: Conference Room Orio Zanetto, Alfa Building 

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Bi-dimensional nano-materials and related heterostructures are establishing themselves as intriguing material systems for the development of a new class of electronic, photonic and plasmonic devices with ad hoc-properties, that can be engineered “from scratch”. Their peculiar band-structure and electron transport characteristics, which can be easily manipulated via layer thickness control, suggest they could also form the basis for a new generation of high-performance devices operating in the Terahertz frequency range (1-12 THz) of the electromagnetic spectrum.

This talk will review our latest achievements in the developments of state-of-the-art THz photodetectors, miniaturized metrological-grade THz frequency combs and mode-locked THz micro-sources all making use of graphene heterostructures, will discuss applications in near-field nanoscopy and will provide future perspectives of a vibrant and rapidly developing research field.

9. Manlio De Domenico, University of Padua (Italy) 

Date: 21/09/2023

Time: 12:15 C.E.T.

Title: “More is different in real-world multilayer networks: theory and applications”

Location: Conference Room Orio Zanetto, Alfa Building 

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Complex systems are characterized by constituents — from neurons in the brain to individuals in a social network — which exhibit special structural organization and nonlinear dynamics. As a consequence, a complex system can not be understood by studying its units separately because their interactions lead to unexpected emerging phenomena, from collective behavior to phase transitions.

In the last decade, we have discovered that a new level of complexity characterizes a variety of natural and artificial systems, where units interact, simultaneously, in distinct ways. For instance, this is the case of multimodal transportation systems (e.g., metro, bus and train networks) or of social networks, whose interactions might be of different type (e.g. trust, trade, virtual, etc.). The unprecedented newfound wealth of data allows to categorize system’s interdependency by defining distinct “layers”, each one encoding a different network representation of the system. The result is a multilayer network model.

In this talk we will discuss the most salient features of multilayer systems and how to determine their robustness, node versatility and mesoscale organization, with special attention to applications to empirical biological, socio-ecological and socio-technical networks.  

8. Raffaella Burioni, University of Parma (Italy) 

Date: 18/07/2023

Time: 12:15 C.E.T.

Title: “Statistical physics of brain networks”

Location: Room Delta 1A, Delta Building 

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The human brain is a highly complex dynamical system that operates across multiple spatiotemporal scales. It is an intricate network of many interconnected neurons, and its functionality emerges from the collective behavior of these complex interactions. Statistical physics provides a powerful framework to comprehend the emergent properties of large-scale brain networks, bridging the gap between microscopic neuronal dynamics and macroscopic brain function.

In this seminar, we delve into various aspects of brain networks, from the construction of structural and functional connectivity networks to the investigation of their collective dynamical regimes. We explore how statistical physics methods can be leveraged to uncover principles governing brain organization and dynamics, and to improve the design and performance of artificial neural networks.

7. Pierpaolo Palestri, University of Udine (Italy) 

Date: 26/06/2023

Time: 11:30 C.E.T.

Title: “Modeling and optimization of arrays for neuronal signal sensing and neuron stimulation based on ion release”

Location: Room Delta 1A, Delta Building 

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Micro- and nano-electrode arrays are widely employed in neuroscience for in-vitro, in-vivo and ex-vivo experiments. They allow the recoding and stimulation of single neurons and in some cases of specific areas of the neuron. The seminar presents our recent studies toward the development of simulation tools to describe the coupling between neurons and electrodes. The aims of this work are the analysis of the recorded neuronal signals and optimization of the electrode morphology as well as the proof-of-concept of a new stimulation methodology based on ionic release.

6. Maria Chiara Carrozza, Consiglio Nazionale delle Ricerche (Italy) 

Date: 15/05/2023

Time: 15:00 C.E.T.

Title: “l futuro della scienza è nel suo insegnamento” (Emmy Noether Lecture 2023)“E

Location: Auditorium Danilo Mainardi, Alfa Building 

5. Marina Piccioni, CDP Venture Capital (Italy) 

Date: 05/05/2023

Time: 14:00 C.E.T.

Title: “La finanza del default e i default della finanza”

Location: Room Delta 1A, Delta Building 

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4. Philippe Velha, University of Trento (Italy) 

Date: 20/04/2023

Time: 16:30 C.E.T.

Title: “Silicon photonics integrated circuits for future generation optical networks”

Location: Room Delta 1A, Delta Building 

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Silicon photonics integrated circuits offer economically advantageous manufacturing processes, such as the CMOS process, which makes them an attractive solution for industrial applications. This presentation will focus on two specific industrial use cases for silicon photonics: the first use case is in the context of 5G wireless networks, where integrated optics are used for radio communications, and the second use case is about the integration of an optical transponder aggregator. In the first use case, we will discuss the design and characterization of a photonic integrated circuit for Reconfiguration Optical Add-Drop Multiplexing data channels in 5G wireless networks. This circuit uses silicon-on-insulator (SOI) platform technology and enables low-power, dense integration, and low-cost operation. In the second use case, we will explore how silicon photonics can be used to integrate an optical transponder aggregator, which enables flexible and efficient aggregation of multiple optical transponders into a single line card. Through these use cases, we will demonstrate the significant potential of silicon photonics integrated circuits in industrial applications, particularly for improving the performance and efficiency of wireless networks and optical communication systems.

3. Mauro Moglianetti, Italian Institute of Technology (Italy) 

Date: 22/03/2023

Time: 10:30 C.E.T.

Title: “Highly engineered catalytic nanomaterials for sensors, energy, and cultural heritage applications: a scientific and entrepreneurial approach”

Location: Conference Room Orio Zanetto, Alfa Building 

Zoom Link → Password: seminar1

IIT CCT Genova: Noble metal nanoparticles have attracted great attention for their impressive catalytic properties and enormous potentiality as artificial enzymes (nanozymes). To fully uncover their potential, it is necessary to control the shape of nanomaterials whilst keeping the ultra-small characteristics in order to achieve superior efficiency, selectivity and enhanced activity in catalytic and enzymatic processes. For Pd nanoparticles, we have developed new methods to achieve different geometrical shapes like cubes, rods and wires whilst maintaining the thickness (in the case of rods and wires) and the size (in the case of cubes) below ten nanometers. These highly engineered nanomaterials achieve biocompatibility together with interesting enzymatic and catalytic properties due to the absence of sticky molecules, high quality of the surface and the removal of toxic reagents. For Pt nanocrystals, a “green” synthetic procedure has been developed to obtain ultra-small Pt nanocrystals by combining a strong and a weak reducing agent in aqueous environment in a single reaction vessel in only 10 minutes. Nanocrystals with size as low as 2.8 nm and high percentage of {111} surface domains have been achieved. These important characteristics are highly innovative and have proven ideal in hydrogen fuel cells application. IIT CCHT@Ca’ FoscariCatalytic, plasmonic and graphene-based nanomaterials represent ideal candidates for the development of the new generation of protective coatings in Cultural Heritage. The approach design and early results will be presented and discussed. Startup activity @HiQ-Nano: Thanks to the catalytic properties of Pt nanoparticles, iBlue, the first point-of-care, home-testing kit that enables measuring the total antioxidant level in saliva, in only 5 minutes has been launched on the market. More details can be found at the website: www.ibluelab.com. The idea of iBlue kit has been developed considering the importance of antioxidants for human health and the lack in the market of an easy solution for home testing measurements.

2. Alexander Balatsky, Nordita (Sweden) and UCONN (USA) 

Date: 16/02/2023

Time: 15:00 C.E.T.

Title: “Quantum dynamics and entangled orders”

Location: Conference Room Orio Zanetto, Alfa Building 

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Quantum matter out of equilibrium emerges as an important platform to induce correlations and transient orders. Modern techniques of coherent and fast light sources developed recently enable this evolution. Broad basic questions about orders that emerge dynamic have been addressed in the context of driven cold atoms, spins, magnetism and superconductivity.  I will discuss new orders that emerge in quantum matter due to dynamic drive, coherence and entanglement and discuss the concept of rectified quantum orders.  I will illustrate with old and new examples of dynamically induced quantum states.

1. Davide Bossini, University of Konstanz (Germany)

Date: 24/01/2023

Time: 14:00 C.E.T.

Title: “Femtosecond coherent magnonic manipulation of antiferromagnetism”

Location: Conference Room Orio Zanetto, Alfa Building 

Zoom Link → Password: seminar1

A future data-processing technology based on ultrafast optical manipulation of magnetically-ordered materials bears the potential to overcome limitations of nowadays computation schemes. In my talk I will first provide a brief introduction to the research field called “ultrafast magnetism”, predicated on the employment of femtosecond laser pulses aimed at manipulating the macroscopic magnetic order in solids. Such concept promises to scale the rates of operation from the low-GHz to the multi- THz regime due to the intrinsic nature of high energy modes in antiferromagnets (AF), i.e. magnetic materials lacking a net magnetisation in the ground state, even in the absence of major energy-dissipations. I will thus provide an exhausting review of the research activity concerning the femtosecond coherent spin dynamics in AFs, which constitutes the backbone of the antiferromagnetic spintronics field. In this framework, I will present extremely recent results, in the final part of my talk. I will outline the effects on a magnetic materials observed by resonantly driving high-energy magnons, near the edges of the Brillouin zone. The spin dynamics induced following this approach discloses unprecedented results: i) magnon modes in different regions of the Brillouin zone are photo-induced, ii) the eigeneigenfrequencies of magnons are modified, which demonstrates a modification of the magnon dispersion; iii) coupling between magnon modes that are conventionally believed to be orthogonal eigenstates of the magnetic Hamiltonian of the material is observed. Our observations are rationalised in view of a resonant impulsive stimulated Raman scattering mechanism. The perspective of our results in terms of femtosecond coherent magnonics will be discussed.