United States

The bonding strength between adsorbates and substrate is related to the degree of anti-bonding sates filling during the adsorbates-substrate interaction, which is an important descriptor of electrochemical performance.[1,2] Based on first-principles calculations, the Gibbs free energy (ΔGH) of transition metal doped WSe2 (TM-WSe2, TM=Ti, Mn, Fe, Co, Ni and Cu) are decreased, especially for the Ni-WSe2 and Cu-WSe2 which are -0.20 and 0.06 eV, respectively. By analyzing the partial density of states (PDOS) and integrated-crystal orbital Hamilton population (ICOHP), the decreased ICOHPspin up values of TM-WSe2 improve the interaction of Se-H, thereby the H atom is easier to be adsorbed on the Se active site. While ICOHPspin down values of TM-WSe2 are increased, this indicates the weak interaction of Se-H, which promotes desorption of H2 molecule (i.e. Tafel/Heyrovsky reaction step). Therefore, the synergistic effect of spin up and spin down anti-bonding states filling makes TM-WSe2 possess an enhanced HER performance.
This work was supported by the National Natural Science Foundation of China (22161142002).&lt;br&gt;&lt;br&gt;

**References** [1] M. D. Hossain, Z. Liu, M. Zhuang, et al. Adv. Energy Mater. 9, 1803689 (2019).
[2] X. Ai, X. Zou, H. Chen, et al. Angew. Chem. Int. Edit. 59, 3961-3965 (2020).&lt;br&gt;
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MMM 2022

Role of Spin resolved Anti

The bonding strength between adsorbates and substrate is related to the degree of anti-bonding sates filling during the adsorbates-substrate interaction, which is an important descriptor of electrochemical performance.[1,2] Based on first-principles calculations, the Gibbs free energy (ΔGH) of transition metal doped WSe2 (TM-WSe2, TM=Ti, Mn, Fe, Co, Ni and Cu) are decreased, especially for the Ni-WSe2 and Cu-WSe2 which are -0.20 and 0.06 eV, respectively. By analyzing the partial density of states (PDOS) and integrated-crystal orbital Hamilton population (ICOHP), the decreased ICOHPspin up values of TM-WSe2 improve the interaction of Se-H, thereby the H atom is easier to be adsorbed on the Se active site. While ICOHPspin down values of TM-WSe2 are increased, this indicates the weak interaction of Se-H, which promotes desorption of H2 molecule (i.e. Tafel/Heyrovsky reaction step). Therefore, the synergistic effect of spin up and spin down anti-bonding states filling makes TM-WSe2 possess an enhanced HER performance.
This work was supported by the National Natural Science Foundation of China (22161142002). 

**References** [1] M. D. Hossain, Z. Liu, M. Zhuang, et al. Adv. Energy Mater. 9, 1803689 (2019).
[2] X. Ai, X. Zou, H. Chen, et al. Angew. Chem. Int. Edit. 59, 3961-3965 (2020). 
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technical paper

#### Welcome to the 67th Annual Conference on Magnetism and Magnetic Materials, MMM 2022!

The Conference was held from October 31 to November 4 and offers both in-person and on-demand content.

MMM 2022 is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a tutorial, and several special sessions. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

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Manganites are one of the promising materials due to their great diversity in physical properties [1-4]. These properties can be tuned by varying probability occupancy as well as ionic size of A-site cations, such as long range ordering observed in RBaMn2O6 (R=Rare earth ions) can be suppressed by cationic disorder [5-6]. We made a comparative study of structure, magnetic (M) properties and magneto-resistance (MR) in A-site ordered NdBaMn2O6 (O-NB) and A-site disordered NdBaMn2O6 (D-NB), NdCaMn2O6 (D-NC). Experimental results from T dependent synchrotron PXRD (fig.1.a-c) concluded that structural symmetry strongly depends on A-site cationic distribution and their ionic sizes resulting in intriguing magnetic ground states. Moreover, MR (fig.2) is considerably large in disordered systems as compared to ordered one. Refinement of PXRD data showed that the A-site cations (Nd3+ & Ba2+) are completely ordered in O-NB. Lowering the T is accompanied with structural transition (ST) (fig.1.a) to lower space group. Whereas, there is no ST in disorder system, D-NB down to 120K. However, ST has been restored again in D-NC disordered system due to similar A-site cationic sizes, Nd3+ and Ca2+ ions. At the same time, M-T data show AFM ground state due to lower structural symmetry in O-NB and the ground state becomes FM in case of D-NB system due to the retainment of higher symmetric structure upto lowest T. Interestingly, AFM state has been restored in D-NC similar to that of O-NB due to presence of cationic disorder of similar sizes (fig.1.d-f). So, it can be argued that crystal structure and magnetic degrees of freedoms are strongly correlated with each other. Further, MR studies depict 3 times higher value of MR in both disorder compounds to that of order one (fig.2). However, behaviour of MR with H is different for D-NB and D-NC implying a different origin of this large MR in these compounds. We believe that the presence of phase separation in D-NC and AFM fluctuation in D-NB might be possible origin of their large MR with respect to O-NB system. 
**References** 
[1] V.N. Smolyaninova, S.E. Lofland, C. Hill , R.C. Budhani, Z. Serpil Gonen, B.W. Eichhorn, and R.L. Green, Effect of A-site cation disorder on charge ordering and ferromagnetism of La0.5Ca0.5-yBayMnO3, J. Magn. Magn. Mater.248 (2002) 348. 
[2] T. Nakajima, H. Kageyama, H. Yoshizawa, K. Ohoyama, and Y. Ueda, Ground State Properties of the A-site Ordered Manganites, RBaMn2O6 (R = La, Pr and Nd), J. Phys. Soc. Jpn. 72 (2003) 3237. 
[3] J. Blasco, G. Subías, M. L. Sanjuán, J. L. García-Muñoz, F. Fauth, and J. García, Structure and phase transitions in A-site ordered RBaMn2O6 (R=Pr,Nd) perovskites with a polar ground state, Phys. Rev. B 103 (2021), 064105. 
[4] S. Yamada, H. Sagayama, K. Higuchi, T. Sasaki, K. Sugimoto, and T. Arima, Physical properties and crystal structure analysis of double-perovskite NdBaMn2O6 by using single crystals, Phys. Rev. B 95 (2017) 035101. 
[5] D. Akahoshi, M. Uchida, Y. Tomioka, T. Arima, Y. Matsui, and Y. Tokura, Random Potential Effect near the Bicritical Region in Perovskite Manganites as Revealed by Comparison with the Ordered Perovskite Analogs, Phys. Rev. Lett. 90 (2003) 177203. 
[6] T. Nakajima, H. Yoshizawa, and Y. Ueda, A-site Randomness Effect on Structural and Physical Properties of Ba-based Perovskite Manganites, J. Phys. Soc. Jpn. 73 (2004) 2283. 

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Role of Cationic Size Mismatch to Control the Effect of A site Disorder

Electrical manipulation of spin textures inside antiferromagnets represents a new opportunity for developing spintronics with superior speed and high device density. Injecting spin currents into antiferromagnets and realizing efficient spin-orbit-torque-induced switching is however still challenging. Because of the diminishing magnetic susceptibility, the nature and the magnitude of current-induced magnetic dynamics remain poorly characterized in antiferromagnets, whereas spurious effects further complicate experimental interpretations (1-4). In this work (5), by growing a thin film antiferromagnetic insulator, α-Fe2O3, along its non-basal plane orientation, we realize a configuration where an injected spin current can robustly rotate the Néel vector within the tilted easy plane, with an efficiency comparable to that of classical ferromagnets. The spin-orbit torque effect stands out among other competing mechanisms and leads to clear switching dynamics. Thanks to this new mechanism, in contrast to the usually employed orthogonal switching geometry, we achieve bipolar antiferromagnetic switching by applying positive and negative currents along the same channel, a geometry that is more practical for device applications. By enabling efficient spin-orbit torque control on the antiferromagnetic ordering, the tilted easy plane geometry introduces a new platform for quantitatively understanding switching and oscillation dynamics in antiferromagnets. 

**References:** 
(1) P. Zhang, J. Finley, T. Safi, et al., Phys. Rev. Lett. Vol. 123, p. 247206 (2019). 
(2) Y. Cheng, S. Yu, M. Zhu, et al., Phys. Rev. Lett. Vol. 124, p. 027202 (2020). 
(3) C. C. Chiang, S. Y. Huang, D. Qu, et al., Phys. Rev. Lett. Vol. 123, p. 227203 (2019). 
(4) H. Meer, F. Schreiber, C. Schmitt, et al., Nano Lett. Vol. 21, p. 114 (2021). 
(5) P. Zhang, C.-T. Chou, H. Yun, et al., arXiv:2201.04732 (2022), accepted by Phys. Rev. Lett.. 

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Control of Néel Vector with Spin Orbit Torques in an Antiferromagnetic Insulator with Tilted Easy Plane

We study the spin Hall effect (SHE) and the orbital Hall effect (OHE) in magnetic materials using automatic high-throughput calculation scheme. The SHE is a phenomenon in which an applied electric field induces a spin current. This effect plays a key role in various spintronics devices. Although the SHE has been researched mainly in nonmagnetic materials, SHE in magnetic materials has gained a considerable attention recently as they can exhibit a large SHE[1]. The OHE, a phenomenon in which electric field generates a flow of orbital angular momentum, has also been attracting attention as a new driving mechanism of devices [2]. For future application, exploring materials with large SHE or OHE is demanded.

In this study, we perform a systematic evaluation of the spin Hall conductivity (SHC) and the orbital Hall conductivity (OHC) of select materials from MAGNDATA[3], a database of magnetic materials. We target collinear materials both ferromagnets and antiferromagnets, and evaluate their intrinsic contributions of SHC and OHC based on Kubo-formula.

Figure 1 shows the results of SHC and OHC of 84 materials. The OHCs in most materials are nearly ten times larger than the SHCs. Interestingly, the Mn3Pt has a colossal OHC reaching about 14000 (hbar/e)S/cm, which is higher than either OHC of Mn (~10000) and Pt (~2000) [4], suggesting the importance of the material structure. Further analysis of both theoretical aspect and data science will be presented at the conference. 
**References** [1] C. Qin, et al., Phys. Rev. B 96, 134418 (2017); Y. Zhang et al., New J. Phys. 20, 7 (2018).
[2] H. Kontani, et al., J. Phys. Soc. Jpn., 76, 103702 (2007).
[3] S.V. Gallego et al., J. Appl. Crystallogr. 49, 1750 (2016).
[4] D. Jo, D. Go, and H-W. Lee, Phys. Rev. B 98, 214405 (2018).
 
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High throughput study of spin and orbital transport in magnetic materials

Spin-wave band structures can be engineered by varying the crystal geometries and this is important to facilitate the realization of many functional magnonic devices [1],
such as band stop filters and magnonic transistors. Recently, we have shown [2] the magnetostatic mode formation in an artificial magnetic structure, going beyond the crystal geometry to
a fractal structure, where the mode formation is related to the geometric scaling of the fractal structure. Fractals [3] are composed of self-similar structures across different length scales,
which look similar under different magnifications. This property is commonly referred to as dilation symmetry. Snowflakes, Romanesco broccoli, and coastlines are popular examples of
fractals observed in nature. We have determined the evolution of the magnetostatic spin-wave modes from a simple geometric structure toward a Sierpinski carpet and Sierpinski triangle by imaging the precessional
dynamics using time resolved scanning Kerr microscope as shown in Fig. 1. The experimentally observed evolution of the precessional motion could be linked to the progression in the
geometric structures that results in a modification of the demagnetizing field. Furthermore, we have found sets of modes at the ferromagnetic resonance frequency that form a scaled spatial
distribution following the geometric scaling. Based on this, we have determined the two conditions for such mode formation to occur. One condition is that the associated magnetic
boundaries must scale accordingly, and the other condition is that the region where the mode occurs must not coincide with the regions for the edge modes. This established relationship
between the fractal geometry and the mode formation in magnetic fractals provides guiding principles for their use in magnonics applications. 
**References:** M. Krawczyk and D. Grundler, J. Phys.: Condens. Matter 26, 123202 (2014).
J. Zhou, M. Zelent, Z. Luo, V. Scagnoli, M. Krawczyk, L. J. Heyderman, S. Saha, Phys. Rev. B 105, 174415 (2022)
C. Swoboda, M. Martens, and G. Meier, Phys. Rev. B 91, 064416 (2015). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/24a9a1dd46c44dd22e7bdb62c2ca9011.png) 
Fig. 1: SEM and scanning Kerr images of (a) Sierpinski triangles (b) Sierpinski squares with iteration number 3.

Precessional dynamics of geometrically scaled magnetostatic spin waves in two dimensional magnonic fractals

Within this talk we show the importance of accurate implementations of the RKKY interactions for antiferromagnetically coupled ferromagnetic layers with thicknesses exceeding the exchange length. In order to evaluate the performance of different implementations of RKKY interaction, we develop a benchmark problem by deriving the analytical formula for the saturation field of two infinitely thick magnetic layers that are antiparallelly coupled (Fig. 1). Without external field, the magnetization in the layers is parallel to the easy axis (y-direction) in the +y and -y direction. When a field in the x-direction is applied, a partial domain wall is formed (Fig. 1). We find that there exists a critical field that fully saturates the structure in the x-direction which is given by, Hx,crit = 2 K1/Js [1+Jrkky2/(AK1)], where Jrkky is the RKKY coupling strength, K1 the anisotropy constant and A exchange constant [1]. This benchmark problem shows that state-of-the-art implementations in commonly used finite-difference codes lead to errors of the saturation field that amount to more than 20% for mesh sizes of 2 nm which is well below the exchange length of the material. In order to improve the accuracy, we develop higher order cell based (see Fig. 2 - paper, cell O1 and O2) and nodal based finite-difference codes (see Fig. 2 - paper, node) that significantly reduce the error compared to state-of-the-art implementations (see Fig. 2 - mumax) [2]. For the second order cell based and first order nodal based finite element approach, the error of the saturation field is reduced by about a factor of 10 (2% error) for the same mesh size of 2 nm. 

**References** 
[1] D. Suess, S. Koraltan, F. Slanovc, F. Bruckner, C. Abert, "Accurate finite-difference micromagnetics of magnets including RKKY interaction -- analytical solution and
comparison to standard micromagnetic codes", https://arxiv.org/abs/2206.11063 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/5b0630c6640f4a9ee05ac6fd7125be33.png) 

Fig. 1: Analytic benchmark problem of two infinitely extended layers, that are antiferromagentically coupled via Jrkky.

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Fig. 2: Convergence towards the analytic solution of Hx =5 x 2 K1/Js for different micromagnetic codes as function of discretization length dz. It is shown that standard finite difference
codes (e.g. mumax) that uses zero order methods for the RKKY interaction show significant errors. The developed method (paper,cell O2) shows significantly better convergence.

Accurate finite difference micromagnetics of magnets including RKKY interaction

Accurate calculation of the hysteresis characteristics of magnetic materials is of great significance for the optimal design of electrical equipment. In previous studies, the Preisach model based on the centered cycle method is widely used for the simulation of hysteresis characteristics as this method uses data that can be easily obtained [1]. However, the existing centered cycle method model cannot correctly consider the influence of reversible magnetization and leads to a large error when calculating the small major hysteresis loops [2]. In this paper, an improved centered cycle method for identifying the Preisach distribution function (PDF) considering the reversible magnetization is proposed, which can improve the accuracy of predicting the symmetrical minor loops. II Method and Discussion As shown in Figure 1, an improved PDF identification method considering the reversible magnetization is proposed, which is consistent with the principle of the magnetization process. The reversible relative permeability is obtained by derivation at the reversal points of the centered cycles with different measured magnetic flux densities and obtained parametric equation, which is integrated to obtain the reversible magnetization. Four centered cycles of different magnetic flux densities are used to discretize the Preisach plane, and the values of the PDF are calculated through the modified magnetic flux densities. The irreversible magnetization is obtained by accumulating the values of the PDF. The final output value is obtained by superposing the irreversible magnetization and the reversible magnetization. The simulation results of grain-oriented silicon steel based on B30P105 are shown in Fig. 2, and the expected accuracy can be achieved. III Conclusion In this paper, a modified Preisach model with centered cycle method under the magnetization principle is developed. Obtained results show that the accuracy of the simulated symmetrical minor loops can be improved. 

**References** 
[1] Bernard Y, Mendes E, Ren Z. Determination of the distribution function of Preisach’s model using centred cycles[J]. COMPEL: The International Journal for Computation
and Mathematics in Electrical and Electronic Engineering, 2000.
[2] Peng D, Sima W, Ming Y, et al. An Improved Centered Cycle Method for Identifying the Preisach Distribution Function[J]. IEEE Transactions on Magnetics, 2018, PP(11):1-5. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/8452cc04d3ef3c8756ca45abe73b8393.png) 

Fig.1. (a) Discretized Preisach Plane.
(b) Numerical discrete calculation process of improved Preisach Model. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/cece0b04c75fbf57da22b132e9edf631.png) 

Fig.2. Comparison of simulation results of B30P105 silicon steel.
(a) Bp=0.2T. (b) Bp=0.5T. (c) Bp=0.7T. (d) Bp=1.1T.

An improved Preisach distribution function identification method considering reversible magnetization effect

Recently, multifunctional composite materials with magnetic wire inclusions for non-destructive and non-contact stress and temperature monitoring have been proposed [1]. Therefore, studies of temperature dependence of the Giant magnetoimpedance, GMI, effect become essentially relevant. There are only very few studies on temperature dependence of GMI and most of them were performed in thick amorphous wires without glass coating and in very limited temperature range [2,3,4]. Although usually the highest GMI effect is observed in Co-rich magnetic wires, GMI effect of Fe-rich glass-coated microwires can be substantially improved by stress-annealing induced magnetic anisotropy [5]. 
GMI effect and magnetic properties under temperature influence of as-prepared and stress annealed (annealing temperature Tann= 325 oC, stress applied during the annealing σ= 190MPa) thin amorphous Fe75B9Si12C4 glass-coated microwires produced by the Taylor Ulitovsky technique are analyzed. Remarkable change in the hysteresis loops and GMI effect is observed for both samples upon heating. For as-prepared FeBSiC microwire a beneficial influence of temperature on the GMI ratio is observed and hysteresis loops change of character from almost rectangular shape to inclined one (Fig.1). On the other hand, although GMI ratio improvement after stress-annealing decreases with the temperature increasing (Fig.2), temperature dependence can be tuned by the stress annealing conditions. Additionally, almost complete reversibility of the changes induced by the temperature is observed. 
Temperature dependence of the hysteresis loops and GMI effect of studied microwires is explained considering the heating effect on the internal stresses relaxation, the modification of the thermal expansion coefficients of the metallic nucleus and the glass coating and in terms of the Hopkinson effect. 
**References:** [1] A. Allue et al., Compos. Part A Appl. Sci. and Manuf., Vol. 120, p.12 (2019). 
[2] J. Nabias, A. Asfour and J. Yonnet, IEEE Trans. Magn., Vol. 53(4), p.4001005 (2017). 
[3] J.D. Santos, R. Varga, B. Hernando and A. Zhukov, J. Magn. Magn. Mater. 321, p.3875 (2009). 
[4] M. Kurniawan et al., J. Electron. Mater., Vol. 43, p.4576 (2014). 
[5] V. Zhukova et al., Scr. Mater., Vol. 142, p.10 (2018). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/4bac301404213f54c4bb4adca5d0984b.png) 
Fig.1. Hysteresis loops (a) and GMI ratio at f= 50 MHz (b) of as-prepared sample, measured at different temperature. 
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/2cf9acf5640bce6a1403026372c49c55.png) 
Fig.2. Hysteresis loops (a) and GMI ratio at f= 50 MHz (b) of stress annealed sample at 325 oC during 15 min (applied stress σ= 190 MPa), measured at different temperature.

Effect of temperature on magnetic properties and magnetoimpedance effect in Fe rich microwires

Artificial spin ices (ASIs) are arrays of Ising-like magnetic nanoislands that are of interest for investigating fundamental physics as well as designing information processing devices. Recent efforts have pushed ASIs beyond the Ising model by using systems capable of possessing both Ising and complex spin textures (CSTs) such as vortices, which alters the nature of dipolar coupling and gives rise to exotic physics in existing ASI lattices [1-3]. CST-Ising studies in metal-based ASIs have primarily focused on field-dependent properties, as temperature-dependent experiments present challenges for metal-based systems. However, we have found that ASIs fabricated from the epitaxial complex oxide La0.7Sr0.3MnO3 (LSMO) can facilitate studies of CST-Ising formations in thermally active ASIs. CST-Ising formations in thermalized LSMO ASIs occurs through a careful balance of inter- and intra-island energetics enabled by the LSMO magnetic parameters [1]. Using x-ray photoemission electron microscopy (XPEEM) to perform magnetic domain imaging, we studied the thermal evolution of ex situ magnetized LSMO-based brickwork ASIs using a series of short (~5 min) annealing steps at 350 K (near LSMO bulk Tc ~ 370 K). We observed that the spin texture evolution can be tuned through the ASI lattice parameter, a. While ASIs with a = 600 nm formed only Ising states and experienced a few spin flips (~1 % of nanoislands) between annealing steps, ~20% of initially Ising nanoislands transformed into CSTs after the first annealing step for ASIs with a = 638 nm. Furthermore, we observed that thermal fluctuations in nanoisland domain states can occur through several different routes including Ising spin flips and transformations in magnetization topology (i.e., Ising-to-CST, CST-to-Ising, and CST-to-CST states). These results suggest the potential to introduce exotic kinetics in existing ASI lattices and would provide further insights into designing magnetically-reconfigurable computing architectures.

Imaging thermally induced Ising

Magnetic multilayers constitute a rich class of material systems with a number of precisely tunable parameters (e.g., layer thickness and repeat number) that determine both their magnetic and electronic properties [1]. We present a comprehensive characterization of structural and magnetic properties of the novel system Pt/Co/Mn, which extends the group of Pt/Co/X (X = metal) multilayers that have been investigated thus far. The structural properties of the sputter-deposited Pt/Co/Mn stacks were determined from X-ray reflectometry and scanning transmission electron microscopy experiments. Subsequently, we performed magnetometry measurements in order to study hysteresis loops as a function of varying layer thickness values. We demonstrate that an increasing Co layer thickness changes the magnetic anisotropy from out of plane to in plane, whereas the deposition of thicker Mn layers leads to a decrease in the saturation magnetization, see Fig. 1. Temperature-dependent magnetometry measurements reinforce the hypothesis of antiferromagnetic coupling at the Co/Mn interfaces being responsible for the observed Mn thickness dependence of the magnetization reversal. Moreover, magneto-optical imaging experiments indicate systematic changes in magnetic domain patterns as a function of the Co and Mn layer thickness and suggest the existence of bubblelike domainsâ€”potentially even magnetic skyrmionsâ€”in the case of sufficiently thick Mn layers, which are expected to contribute to a sizable Dzyaloshinskii-Moriya interaction in the multilayer stacks. We identify Pt/Co/Mn as a highly complex multilayer system with strong potential for further fundamental studies and possible applications [2]. This work is supported by the Deutsche Forschungsgemeinschaft (DFG) through the research fellowship LO 2584/1-1, the NSF through I-MRSEC Grant No. DMR-1720633 and US DOE, Office of Science, MSED under Contract No. DE-SC002260.

Structural and Magnetic Properties of Pt/Co/Mn Multilayers

I will provide an overview on our work to experimentally quantify and verify the presence of spin-mixed states in ferromagnetic 3d transition metals via the precise
measurement of the orbital moment. [1] While central to phenomena such as Elliot-Yafet scattering, quantification of the spin-mixing parameter <'b'2> has hitherto been confined to
theoretical calculations. We demonstrate that this information is also available by experimental means. Comparison of ferromagnetic resonance (FMR) spectroscopy with x-ray magnetic
circular dichroism (XMCD) results show that Kittel’s original derivation [2] of the spectroscopic g-factor requires modification, to include second order terms in spin-mixing of valence
band states. Such modification can have a large effect on the measured value of the spectroscopic g-factor in these materials. Not only does it explain discrepancies between XMCD and
FMR, but provides the means to quantify <'b'2>. Our results are supported by ab-initio relativistic electronic structure theory, which show good agreement between the measured and predicted values of <'b'2>. 
**References** 
[1] J. M. Shaw, R. Knut, A. Armstrong, S. Bhandary, Y. Kvashnin, D. Thonig, E. K. Delczeg-Czirjak, O. Karis, T. J. Silva, E. Weschke, H. T. Nembach, O. Eriksson, and D.
A. Arena, Phys. Rev. Lett. 127, 207201 (2021).
[2] C. Kittel, Phys. Rev. 76, 743 (1949). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/c78e22817d83e5b27034d803930513ce.png) 
Figure 1: Experimental values of '/s obtained from XMCD and FMR for a 10 nm thick Ni80Fe20
sample. The value obtained from XMCD is indicated as the horizontal dashed line. In the
case of FMR (solid line), µL / µS is calculated from the experimentally determined g-factor and application of the modified equation for the g-factor for various values of b2. The value of b2= 0.02 for this material can be graphically determined by the intersection of the two lines.

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