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MMM 2020

Measurements Dynamics

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Magnetic characterization is an undeniable scheme for the identification of magnetic and mechanical properties of materials [1] [2]. More pertinent is the unavoidable urge for localized magnetic monitoring schemes in line with the current growing industrial expectations [3] [4]. Herein, the adequacy and consistency of the magnetic needle probe (MNP) method over the conventional search coil method were concealed by the instrumentation prerequisite coupled to very weak levels of the sensor signals and the limited theoretical investigation on the method, generally considered quite blurry. The first hindrance taken care of by technological upgrades, studies on the basis of the electromagnetic theory from eddy-current distribution in magnetic materials has advanced the interpretation of the MNP method for local magnetic measurements [5] [6]. The objectives of this paper are twofold; it presents an electromagnetic modelling of the MNP method in a rectangular bar from a micro-magnetic perspective and exploits the model to derive the magnetic anhysteretic behaviour of the ferromagnetic materials. In the first objective, the advance theoretical background of the MNP method is modelled for anti-parallel domain structure using Finite Difference (FD) approach and compared to the analytical approach in [5]. Then, the model is used to simulate the reversible stochastic motion of domain walls for a hysteresis free magnetic material. The dependence of the anhysteretic model on the domain width (d) and the ratio of domain width to the thickness (d/c) of a Fe-3%Si sheet tells of the sensitivity of the magnetic microstructure on the magnetic signature. Noticeable hysteresis losses were however observed at smaller domain width translating to a state of high magneto-crystallographic anisotropy where closure domain effects add the resultant magnetization in the magnetic material. A complete account of the domain constituency is envisaged for future studies.References: [1] Y. A. Tene, P. Tsafack, B. Ducharne and al, IEEE Trans. Mag., vol. 55, no. 7, 2019. [2] B. Ducharne, B. Gupta and al, IEEE Trans. on Mag., vol. 54, no. 11, 6202606, Nov. 2018. [3] A. Pulnikov, V. Permiakov and al, J. Magn. Magn. Mater., vol. 47, no. 9, p. 254–255, 2003. [4] K. S. H. Nguedjang, D. Y. A. Tene and al, J. Magn. Magn. Mater., pp. 1-10, 505, 166767, March 2020. [5] T. Yamaguchi, K. Senda and al, J. Physique IV, vol. 8, p. 717–20, 1998. [6] K. Senda, M. Ishida and al, Electr. Eng. Japan, vol. 126, p. 942–9, 1999.

Electromagnetic Modelling of the Magnetic Needle Probe Method from Parallel Domain Structure by FD Approximation

A technique to measure the full magnetic torque vector (three orthogonal torque components) on micro- and nano-scale magnetic materials is introduced. Measurements of a single axis or component of torque are most common and are very useful for hysteresis measurements of thin film structures in particular, where high shape anisotropy yields a near-proportionality of in-plane magnetic moment and the magnetic torque along the perpendicular in-plane axis. More generally, any component of cross-product torque involves a linear combination of perpendicular moment and magnetic susceptibility, yielding the rotational magnetic anisotropy or stiffness of the spin texture in response to torque. The method is demonstrated using a modified, single-paddle silicon-on-insulator resonant torque sensor [1]. The torsion mechanical susceptibilities to x- and z-torques are maximized by clamping the sensor at a single point. Figure 1 shows a completed device supporting a permalloy / cobalt oxide bilayer disk, deposited on a silicon paddle which is supported by a single beam. Mechanically-resonant AC torques are driven by an RF field containing a frequency component for each fundamental torsional mode of the device, and the resulting displacements read out through optical position-sensitive detection. A typical hysteresis measurement obtained as an in-plane DC bias field is swept is shown in Figure 2. The measurements are compared with micromagnetic simulations of the mechanical torque to verify the interpretation of the signals. As an application example, simultaneous observations of hysteresis in the net magnetization along with the field-dependent in-plane anisotropy is highly beneficial for studies of exchange bias.References: [1] Z. Diao et al., J. Vac. Sci. Technol. B., Vol. 31, p.051805 (2013)

Mechanical Torque Vector Measurements for Micromagnets

Among several advantageous, additive manufacturing facilitates rapid prototyping and the realization of objects that cannot be made with traditional manufacturing methods. Recently, additive manufacturing of magnetic structures is being investigated including the inkjet [1], Fused Filament Modelling (FFM) [2], and UV Assisted Direct Write methods [3]. Soft or hard magnetic particles are included in polymer binder to realize objects interesting for magnetic shielding, magnetic flux guiding, or for their permanent magnetic properties. Magnetic characterization of 3D printed samples with a Vibrating Sample Magnetometer (VSM) however is not straightforward, particularly when larger samples are characterized that have a non-zero infill percentage. Determination of the saturation magnetization is difficult because of the lack of calibration standards for such inhomogeneous samples. Therefore, we modeled the sensitivity of a biaxial VSM for different 3D printed samples produced by FFM. The magnetic potential of a distributed coil with finite dimensions was approximated from the first 3 Legendre polynomial terms and used to determine the point dipole sensitivity of a MicroSense VSM employing a Mallinson pickup coil set using an approach similar as described in [4]. The obtained point sensitivity function was used to calculate the sample signal of various 3D printed samples with different infill orientations and infill percentages using Mathematica. The calculations show that the measured signal is strongly affected by the infill percentage and orientation. For 2D shaped samples (1x1x0.05 cm3) with low infill percentages, the signal differs by up to a factor 2 depending on the sample orientation. The calculated signal of cubed samples (1x1x1 cm3) can vary as much as 30% with infill percentage. A Mathematica spreadsheet was developed that allows one to calculate the signal produced by any specific 3D printed sample in a biaxial VSM that employs a Mallinson coil set configuration. This work was supported in part by NSF through an DMR-MRI Grant under Award 1726970.References: [1] M.P. Paranthaman, C.S. Shafer, M. Elliot, JOM 68 (2017) 1978. [2] C. Huber, C. Abert, F. Bruckner, et al., App. Phys. Lett. 109 (2016) 162401. [3] Alan Shen, Xiaoguang Peng, Callum P. Bailey et al., Mater. and Des.183 (2019) 108133. [4] Co-Cr layers for perpendicular magnetic recording, J.P.C. Bernard, C.P.G. Schrauwen, PhD. Thesis University of Twente, ISBN 90-9003454-4.

Effect of Field Orientation and Infill Percentage on the VSM calibration factor of FFM 3D printed samples

Modern inductive magnetometry is very widely used for bulk samples and thin films alike. SQUID-based, superconducting second-order gradiometer magnetometry has become the de facto standard, worldwide. While a decade ago, it was dominated by primarily extraction-style systems, where the sample is moved at relatively long distances (~ base of the gradiometer) and at low frequencies (~ 1 Hz); nowadays, higher frequency (many 10ns of Hz), shorter translation length systems, rapidly gain popularity. The benefits of faster measurements must be paid by a compromise of capability elsewhere: increased sample geometry- and position-dependent systematic errors are two just two examples. Here, the influence of the dominating radial sample offset and radial projection systematic uncertainties is analysed [1] and a new data processing algorithm is advised, which allows for the determination of the radial sample offset, minimizing its impact. The normalized point spread functions (PSF) of the MPMS3 and its predecessor, the MPMS system [2], are shown on Fig. 1. The PSF of the MPMS3 is sharper, larger in amplitude. [3] The change of shape and magnitude of the PSF of the MPMS3 as a function of radial sample offset is also shown on Fig. 1. There is a pronounced amplitude increment and a narrowing of the z-axis carrier, with radial offset. [4] The normalized response as a function of oscillation amplitude is shown on Fig. 2. With our algorithm, it is possible to fit it and extract the radial offset, by means of generalized non-linear least squares regression, with an uncertainty of about 10 %, as illustrated using Monte-Carlo simulated data, on Fig. 2. [5] It is hoped that this algorithm will be utilized by the magnetic community and will help reduce the spread of data in very many experimental situations.References: [1] Based on a direct quadrature integration approach for the computation of the coupled flux. [2] Quantum Design, San Diego, CA, USA. [3] The MPMS3 gradiometer is more sensitive to radial offsets or spread of the moment distribution. [4] This results in a very substantial increase in the second harmonic pickup, > 200 % in the worse case scenario: millimetric radial errors result in systematic errors of 10ns of percent. [5] This leads to a relative uncertainty of about 2-3 % in a general experimental scenario – a rather substantial and welcome error containment.

An Algorithm for Radial Offset Systematic Error Correction in Second-Order Gradiometer-Based Vibrating Sample Magnetometers

The lifetime of magnetic excitations in metals is governed by scattering rates between magnons and electrons. Recent investigations [1, 2] document how magnetization dynamics vary with composition in magnetic metal alloys due to changes in their electronic band structures; e.g. Co0.25Fe0.75 thin-films display low magnetic damping (α ~ 10-4). In my talk, I will present experimental measurements of magnetic damping, ultrafast magnetization dynamics, and thermal transport properties of CoFe magnetic alloys, varying with alloy composition. To explore the magnetization dynamics, I use a time-resolved MOKE set-up to observe ultrafast demagnetization in a few hundred femtoseconds followed by precessional dynamics. Through TDTR measurements, I check if lower electron-magnon scattering rates lead to improved thermal transport. My investigation sheds light on how magnon-electron scattering rates govern dynamics on femtosecond (ultrafast demagnetization), nanosecond (magnetic precession and damping), and microsecond time-scales (thermal transport of energy). *This work was supported by the U.S. Army Research Laboratory and the U.S. Army Research Office under grant # W911NF-18-1-0364.References: [1] Qin, H. J., et al. Nature communications 6 (2015): 6126. [2] Schoen, Martin AW, et al. Nature Physics 12.9 (2016): 839.

Effects of CoFe Alloy Composition on Magnetization Dynamics and Magnetic Thermal Transport

Engineering of magnetic materials for developing better spintronic applications relies on the control of two key parameters: the spin polarization and the Gilbert damping responsible for the spin angular momentum dissipation. Both of them are expected to affect the ultrafast magnetization dynamics occurring on the femtosecond time scale. Here, we use engineered Co2MnAlxSi1-x Heusler compounds grown by molecular beam epitaxy to adjust the degree of spin polarization at the Fermi energy P and investigate how it correlates with the damping. We first demonstrate experimentally that substituting Si by Al in Co2MnAlxSi1-x Heusler compounds allows us to get a tunable spin polarization at EF from ~60% in Co2MnAl to 100% in Co2MnSi, indicating the transition from metallic to half metallic behaviors. Second, a strong correlation between the spin polarization and the Gilbert magnetic damping is established in these films. The damping decreases when increasing the spin polarization from 1.1 10-3 for Co2MnAl (with 63% spin polarization) to an ultra-low value of 4.10-4 for the half-metallic ferromagnet Co2MnSi [1]. This allows us investigating the relation between these two parameters and the ultrafast demagnetization time characterizing the loss of magnetization occurring after femtosecond laser pulse excitation. The demagnetization time is observed to be inversely proportional to 1-P and as a consequence to the magnetic damping, which can be attributed to the similarity of the spin angular momentum dissipation processes responsible for these two effects. Altogether, our high quality Heusler compounds allow controlling the band structure and therefore the channel for spin angular momentum dissipation [2].References: [1] C. Guillemard et al, Phys. Rev. Appl.. 11, 064009 (2019) [2], W. Zhang, C. Guillemard, et al, Advanced Materials, 1908357 (2020)

Engineering Co2MnAlxSi1-x Heusler compounds as a model system to correlate spin polarization, intrinsic Gilbert damping and ultrafast demagnetization

After the first observation of the ultrafast demagnetization process, a huge experimental and theoretical effort was devoted to reveal the microscopic mechanism governing the ultrafast optically induced loss of magnetic order in ferromagnetic materials. Almost all experimental fs-demagnetization studies so far employed fs light pulses of 1.55 eV to trigger the magnetization-dynamics. Hence, the role of the photon energy of the exciting light pulse has been largely neglected so far. Therefore, we have implemented an all-optical time-resolved MOKE setup with variable pump photon energy in the range of 1.55 to 3.10 eV. As prototypical system, we investigated the ultrafast demagnetization dynamics of thin Ni films on insulating and conducting substrates. The characteristic parameters of the demagnetization process, i.e., the demagnetization time for various excitation photon energies are compared with simulations applying a temperature-based model. These simulations consider the density of states of Nickel and interface effects to describe the non-equilibrium dynamics of the spin-carrying excited electrons. For metallic substrates, we further discuss the magnitude and timescale of the optically injected spin carriers across the magnetic/non-magnetic interface.References: M. Hofherr, et al., Physical Review B 96, 100403 (2017) U. Bierbrauer, et al., J. Phys.: Condens. Matter 29, 244002 (2017) B.Y. Mueller and B. Rethfeld, Phys. Rev. B 90, 144420 (2014)

Photon energy dependent fs-demagnetization dynamics of thin Nickel films

The observation of ultrafast manipulation and coherent control of spins in magnetic materials at room temperature [1-2] has prompted the intense experimental and theoretical efforts to understand the underlying microscopic mechanisms and relevant interactions (exchange, spin-lattice, electron-phonon, coulomb etc.) driving such magnetic phenomena at sub-picosecond timescales. Stoichiometric B2 ordered epitaxial (001) FeRh undergoes a first order magnetic phase transition from antiferromagnetic (AFM) to ferromagnetic (FM) at ≈ 380K. In the AFM phase of FeRh, only Fe has net magnetic moment, whereas in the FM phase both Fe and Rh carry net moments. The phase transition is also accompanied by a ≈ 1% isotropic lattice expansion in the bulk BCC structure, and changes in electronic structure, see [3-5] and refs. therein.Since magnetic and structural dynamics occur at different timescales, it makes FeRh an ideal candidate for disentangling relevant interaction mechanisms at different timescales. The phase transition has been extensively studied theoretically and experimentally[6-8], in thermal equilibrium and in the time domain, but a precise understanding of the roles of the electronic, phononic and spin sub-systems remains elusive. We have studied the laser-driven AFM to FM phase transition in FeRh with small angle X-ray scattering (tr-SAXS) and X-ray absorption spectroscopy (tr-XAS) around the Fe L3 edge. The experiments were performed at the SCS Instrument of the European XFEL. We also performed the time-dependent density functional theory(TD-DFT) calculations to simulate the XAS spectra at different time delays. In this contribution, we will discuss the changes of the electronic structure of FeRh on the femto- and picosecond timescales, derived from the XAS and scattering measurements at the Fe L3 absorption edge performed at European XFEL, and compare them with the theoretical simulations (see the figure) , in order to show the relation between them and the first order AFM-FM phase transition in FeRh.References: [1] E. Beaurepaire et al., Phys. Rev. Lett. 76, 4250 (1996) [2] J.-Y. Bigot et al., Nature Physics 5, 515 (2009) [3] J.-U. Thiele et al. Appl. Phys. Lett. 82, 2859 (2003) [4] A.X. Gray et al., Phys. Rev. Lett. 108, 257208 (2012). [5] C. Baldasseroni et al., Appl. Phys. Lett. 100, 262401 (2012). [6] J.-U. Thiele, M. Buess, C.H. Back, Appl. Phys. Lett 85, 2857 (2004). [7] G. Ju et al., Phys. Rev. Lett. 93, 197403 (2004) [8] I. Radu et al., PRB 81, 104415 (2010)

Probing the Laser-driven Antiferromagnetic to Ferromagnetic Phase Transition of FeRh with Femtosecond Time-resolved Small Angle X-ray Scattering (tr-SAXS) and X-ray Absorption Spectroscopy (tr-XAS)

Antiferromagnetically coupled ferromagnetic thin films have recently attracted significant attention in magnonics because of the possibility to tune the spin-wave dispersion by altering the interlayer exchange coupling, which would help to achieve the spin-wave nonreciprocity [1]. To implement such coupled films in magnonic devices, a detailed understanding of the precessional dynamics of magnetization in such systems is required. Here, we present a systematic characterization of the precessional dynamics for systems with the layer magnetization going from nearly antiparallel to parallel alignment on application of a magnetic field. Experimentally, we have measured the ultrafast-laser-induced magnetization precession in samples with different interlayer exchange coupling strengths using the time-resolved magneto-optical Kerr effect. In addition to the acoustic and optical modes, an extra mode is observed that is due to the laser-induced decoupling of the two ferromagnetic layers. The observed precessional dynamics is in good agreement with our theoretical model based on the Landau-Lifshitz-Gilbert equation, and can be separated into three different field regions determined by the relationship between the Zeeman energy and the energy associated with the interlayer exchange coupling, as shown in Fig. 1 [2]. This work gives a detailed insigth of how the interlayer exchange coupling and Zeeman energy influence the precessional dynamics, and provides an important guide to implement antiferromagnetically coupled films in functional magnonic devices.References: [1] R. A. Gallardo, et al. Phys. Rev. Appl. 12, 034012 (2019) [2] J. Zhou, et al. Phys. Rev. B, 101, 214434 (2020)

Ultrafast Laser Induced Precessional Dynamics in Antiferromagnetically Coupled Ferromagnetic Films

A thorough understanding of femtosecond magnetism will address the important questions of how fast the magnetization can be reoriented in a material and what physical processes present fundamental limits to this speed. Ultimately, light represents the fastest means to alter the state of a material since laser pulses can now be generated with extremely short temporal duration down to a few tens of attoseconds. One particularly interesting and novel scheme for the ultrafast manipulation of spins using light takes advantage of the optically-induced spin transfer (OISTR), which was recently introduced by Dewhurst et al. [1]. This microscopic mechanism is driven by a spin-selective direct optical excitation from one magnetic sublattice to another. Guided by time dependent density functional theory calculations, we are able to monitor the optically induced transient changes in the model systems FeNi in real time by time-resolved magneto-optical Kerr spectroscopy using high-harmonic generation (HHG TMOKE) [2]. Exploiting the spectral sensitivity of this measurement technique we are able to follow the ultrafast spin transfer from Fe to Ni during the optical excitation. OISTR, therefore, opens up a new avenue towards manipulating solids on timescales only limited by the duration of the exciting light pulse, which forecasts a control of the spin dynamics on the attosecond time scale. How far this spin manipulation via OISTR is a general phenomenon or restricted to a subset of materials with specific properties is an open experimental and theoretical question. In order to opens up a systematic path for coherent manipulation of spin dynamics by direct light-matter interaction we started to investigate OISTR in a variety of different compounds with higher complexity [3]. We reveal for example that the half-Heusler materials NiMnSb and CoMnSb exhibit strong signatures of OISTR, whereas this is less pronounced in the full-Heusler compounds Co2MnSi, Co2FeSi, and Co2FeAl in agreement with ab initio calculations [4].References: [1] J.K. Dewhurst et al, Nano Lett. 18 1842 (2018) [2] M. Hofherr et al. Sci. Adv. 6 eaay8717 (2020) [3] P. Tengdin et al , Sci. Adv. 6 eaaz1100 (2020) [4] D. Steil et al, Phys. Rev. Research 2, 023199 (2020)

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