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Field demagnetization protocols may be employed to bring athermal, artificial spin systems into an arrested, low-energy magnetic configuration. Such protocols, applied to systems in which thermal fluctuations are absent, are intrinsically deterministic: if the field history and the sample properties were known, the final configuration would be completely determined. Here, we study the response of a given athermal, artificial square ice submitted to successive, albeit similar, field demagnetization protocols. We show that each resulting arrested state differs from the previous one. Analyzing these magnetic states, we demonstrate that our artificial ice magnet behaves as a stochastic system. We propose a mechanism by which stochasticity can be induced.

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INTERMAG 2021

 Are field demagnetized, athermal, artificial square ice magnets stochastic systems?

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5d metals are used in electronic architectures because of their high spin-orbit coupling (SOC) leading to efficient spin ↔ electric conversion and strong magnetic interactions. When C60 is grown on a metal, the electronic structure is altered due to hybridisation and charge transfer. Previously, it has been shown that this can lead to the emergence of spin ordering [1]. This interfacial effect is also critical in spin filtering and spin transport effects [2]. We have studied the spin Hall magnetoresistance (SHMR) for YIG/Pt/C60 and YIG/Ta/C60. [3]. The SHMR at room temperature are up to a factor 6 higher than for the pristine metals, with the spin Hall angle increased by 20-60%. Here we studied YIG/PtMn with without C60. PtMn is an antiferromagnet that has been shown to have a strong spin Hall effect [4]. This will allow us to determine if the molecular orientation can play a role in the enhanced SOC observed in Pt. We aim to: investigate the mechanisms that generate spin orbit scattering at the hybrid conducting interface and maximise the effect. By fitting the SHMR data, we can extract the spin Hall angle which is significantly higher with the molecular overlayer. The SHMR saturates once the applied field saturates the magnetisation out-of-plane, at 0.1-0.15 T for a YIG film, and no higher than 0.5 T for any measured condition. However, above this field range, other contributions such as Koehler MR, localisation and the Hanle effect can result in significant linear contributions to the MR that would artificially enhance the SHMR ratio and spin hall angle [Fig1]. Thus, the spin Hall angle ΘSH is bigger for PtMn/C60 than PtMn, which we attribute to an enhancement of the spin orbit coupling (SOC) by the C60. Figure 2 shows the maximum SHMR measured as a function of the PtMn thickness for both pure metal and PtMn covered on molecules. Also, the PtMn/C60 SHMR value is increased after annealing the sample at 200 C.

**References:**

References: 1. F. Al ma’mari, et al., Nature. 524, 69—73 (2015) 2. M. Cinchetti, et al., Nature materials. 16, 507 (2017) 3. S. Alotibi, et al., arXiv preprint: 1912. 02712, 2020. 4. Y. Ou, Phys. Rev. B 93, 220405(R) (2016).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/081f905ccccdb5556742fbf743fdc34e.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/5ec866da85e77a56bbedc861a638dbe0.jpg)

 Effects of a Molecular C60 Interfaces on the Spin Hall Magnetoresistance of YIG/PtMn

Topological chiral semi-metal CoSi exhibit unusual quasi-particles excitations near the band crossing point, which have spin-1 and charge-2 chiral charge [1]. Like Dirac and Weyl semimetals, these semimetals also show some unusual electrical transport behavior, such as large magneto-resistance, mobility, and anomalous Hall effects. Therefore, we have performed temperature and magnetic field dependent electrical transport measurements on the topological chiral semimetal CoSi poly-crystals. We observed that while χ versus T indicates the paramagnetic nature of poly-crystals (inset of image1), 1/χ versus T behavior indicates that there is the presence of some weak antiferromagnetic exchange interaction at low temperature [2]. These poly-crystals show anomalous behavior in resistivity versus temperature measurements in the vicinity of such magnetic exchange interaction. The temperature and angle-dependent magneto-resistance (MR) measurements show negative behavior at low temperature, which is in contrast to the single crystal counterpart of CoSi, probably due to the presence of weak exchange interaction [3,4].

**References:**

 1. D. Takane, and T. Sato, Phys. Rev. Lett. 122, 076402, (2019). 2. Banik, S. et al. Phys. Rev. B 77, 224417 (2008). 3. X. Xu and S. Jia, Phys. Rev. B 100, 045104 (2019). 4. S.S Samatham, D Venkateshwarlu, and V Ganesan, Mater. Res. Express 1 026503, (2014).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b58415af3c3b708d66c150d5bdbaeaab.jpg)
Temperature dependence of 1/χ showing the presence of exchange interaction at low temperature. Inset shows the temperature dependence of χ

![](https://assets.underline.io/uploads/markdown_image/1/image/18e6611ba53e53bfc851fc126014ccff.jpg)
Temperature-dependent magnetoresistance(MR) showing a change in MR from negative to positive as the temperature is increased

 Magneto-Transport Study on Topological Chiral Semimetal CoSi

Heusler alloys are materials with the composition X2YZ, where X and Y are transition metals and Z is the p-element. By the change of an element in the composition, new properties, e. g. the magnetocaloric effect, spin-polarization, or coexistence of ferromagnetism and superconductivity can be achieved. Those properties can be combined to achieve multifunctional Heusler alloys. Nowadays, new superconducting materials are being explored, such as HTC superconductors, superconducting magnets, and also as mentioned, ferromagnetic superconductors. Heusler alloy Ni2NbSn represents the superconductor with the ferromagnetic behaviour under the critical temperature of superconductivity. It would be difficult for the alloy Ni2NbSn to find practical usage since the critical temperature is 3.4 K at zero external magnetic field. One of the possibilities to increase the critical temperature can be the doping with various p-elements, to modify the lattice constant. In this topic, we decided to study the doped series of alloys Ni50Nb25Sn25-xZx, where Z is Ga, Ge, or Sb and x = 1, 2. Their structural, magnetic, and electric properties were analyzed to show the effect of modifying the lattice constant on the critical temperature of the Ni2NbSn Heusler alloy. This research was supported by the projects APVV-16-0079 and Slovak VEGA grant. No. 1/0053/19.

**References:**

T. Graf, C. Felser and S. S.P. Parkin, Progress in Solid State Chemistry, Vol. 39, p.1-50 (2011) T. Klimczuk, C. H. Wang and K. Gofryk, PHYSICAL REVIEW B, Vol. 85, p.174505 (2012)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/9aa3b7f404eada4a41ac7bf2a0b0b864.jpg)
Hysteresis loops of alloys with 1% doping.

 Effect of doping on ferromagnetic and superconducting properties of Ni2NbSnZ (Z = Ga, Ge, and Sb) Heusler alloy

Frustrated systems with two or more competing interactions have a wide variety of phases with unconventional properties and complex symmetry. The pseudospin formalism is a powerful method to study complex magnetic systems with various degrees of freedom. Pseudospin models of anisotropic magnets are widely used to describe the properties of binary alloys, classical and quantum liquids, dilute magnets, superconductors, and many other physical systems [1]. In addition, disorder caused by introduction of impurities and defects into the system significantly affects the critical behavior and phase states of magnets [2]. This work is devoted to modelling and theoretical description of phase and critical properties of a low-dimensional site-dilute magnet with frustration caused by the competitive charge and spin orders. We consider the Blume-Emery-Griffiths-type spin-pseudospin model, which was initially proposed [3] to consider the competition between spin and charge orders in underdoped high-Tc cuprates like La2-xSrxCuO4 in the normal state. The model considers the CuO2 planes as a system of charge triplets consisting of three many-electron mixed-valence centers [CuO4]7-;6-;5- (corresponding nominally to the copper ion states Cu1+;2+;3+). Two charge states Cu1+;3+ are associated with two components of the pseudospin S=1 triplet with MS=±1. The Cu2+ state associated with the MS=0 component is magnetic and has a conventional spin σ=1/2. Within this pseudospin formalism, the Hamiltonian of the static spin-pseudospin model includes Ising spin exchange coupling (J), on-site (Δ) and inter-site (V) density-density correlations, which have the form of single-ion pseudospin anisotropy and Ising exchange coupling in the language of pseudospin operators. The chemical potential μ is necessary to take into account the constant charge density doped in the CuO2 plane, which gives the concentration of doped charged impurities n. The properties of the spin-pseudospin model in the ground state were studied with the mean-field approximation [3,4], and the temperature phase diagrams were obtained with the Bethe approximation [5]. We performed a computer simulation of a spin-pseudospin model using the classical Monte Carlo method and a modified Metropolis algorithm on a 2D square lattice with periodic boundary conditions. Phase transitions and critical properties of a dilute magnet with frustration were investigated in the framework of the theory of finite-size scaling. The system demonstrates the 2D Ising universality class as it is far from frustration, while as the system approaches the frustrated state, significant changes are observed in the critical behavior of the system: spin (charge) metastable phase states are formed, first-order phase transitions occur, and the critical exponents for second-order phase transitions depend on the parameters of the model, i.e. the critical behavior of the system becomes non-universal (for example, see Fig. 1) [6]. Also, the critical behavior becomes non-universal with an increase in the density of the doped charge n in the non-frustrated state. In addition, temperature and ground state phase diagrams were obtained, and the features of the formation of phase states with an increase in the density of doped impurities in frustration were revealed. There is a wide variety of phase states with different properties in the ground state. If the spin exchange coupling is greater than the one for pseudospin (V/J≤1), there are actually two phases in the ground state, namely the charge order (CO) and the antiferromagnetic (AFM) order, which is unstable with respect to the phase separation into charge and spin subsystems that behave like immiscible quantum liquids. Various configurations of phase separation are formed depending on the value of n, viz., a charge/AFM droplet or a charge/AFM stripe. There are 5 phases in the ground state for V/J&gt;1: AFM and “ferromagnetic” orders, and three types of CO. Analysis of the system in frustration has shown that the ground state of the system turns out to be degenerate not at one specific point, but in a whole range of parameters. Under identical calculation conditions, both AFM order and CO can form with a certain probability. Charge doping in a frustrated state leads to unusual effects. When the spin exchange coupling is strong (V/J≤1), AFM order changes to CO with decreasing temperature (or vice versa, depending on the value of n), as well as reentrant order-order phase transitions [7] occur, which is shown in Fig. 2. Thus, the competition between charge and magnetic orders, leading to frustration of the system, as well as charged impurities, significantly affect the properties of a two-dimensional Ising magnet. This work was prepared with the financial support of Competitiveness Enhancement Program - CEP 3.1.1.1-20.

**References:**

[1] Hovhannisyan V. V. et al., Physical Review E., Vol. 96, p. 062103 (2017) [2] Giacomin G., Springer, Vol. 2025 (2011) [3] Y. D. Panov et al., J. Supercond. Novel Magn., Vol. 29, p. 1077 (2016). [4] Y. D. Panov et al., J. Low Temp. Phys, Vol. 187, p. 646 (2017). [5] Y. D. Panov et al., JMMM, Vol. 477, p. 162 (2019). [6] D. N. Yasinskaya et al., Acta Phys. Pol. A., Vol. 137, p. 979 (2020) [7] D. N. Yasinskaya, V. A. Ulitko, Y. D. Panov, Phys. Solid State, Vol. 62, p. 1713 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/fc9010fa0e9f0f0bf9f53632bb55fb8e.jpg)
Dependence of critical exponents for heat capacity and susceptibility on single-ion anisotropy Δ/J for V/J=0.2, n=0. Dark gray corresponds to the universality class of the 2D Ising model, light gray corresponds to non-universal critical behavior. White color corresponds to first-order phase transitions

![](https://assets.underline.io/uploads/markdown_image/1/image/33dac2d32c21ee256bf53ecc248d2123.jpg)
Temperature phase diagram for n = 0.15, V/J=1 near the frustration. The order type changes twice when the temperature decreases, i.e. the reentrant phase transition to AFM takes place

 Phase States and Critical Properties of a Dilute Magnet with Frustration

The study of quantum critical effects and more generally of the physical properties of “strange metals” is currently of high interest in condensed-matter physics [1]. In rare-earth based intermetallics, heavy-fermion behaviors and quantum criticality are mainly investigated in materials where Ce or Yb are alloyed with non-magnetic elements [2]. Quantum critical effects are then generally perceived at low temperature near the magnetic instability of almost trivalent 4f element. Recently, we showed that the situation is somewhat different in YbMn6Ge6-xSnx where intermediate valent Yb is alloyed with a ferromagnetic Mn sublattice. In this series of compounds, several very unusual phenomena have been evidenced using magnetic measurements, neutron diffraction and electronic spectroscopies [3-6]. That includes an abnormal thermal variation of the Yb valence [3,4], a record value for the Yb magnetic ordering temperature (up to TYb = 125 K [4,5]), a Yb magnetic instability occurring for far from trivalent Yb (υ ~ 2.73) and signatures of quantum criticality up to room temperature [6]. These unusual phenomena have been tentatively ascribed to the strong Mn-Yb exchange interactions. For a further understanding of the YbMn6Ge6-xSnx series of compounds (x ≥ 4.0), we have performed specific heat (Cp) measurements. Our results indicate that these alloys are heavy-fermion materials (γ &gt; 50 mJ.mol-1.K-2) and that the electronic specific heat coefficient reaches a maximum value γ ~ 280 mJ.mol-1.K-2 for compositions close to the Yb magnetic instability near x ~ 5.20 (Figure 1). Details about the analysis of the data will be presented on the poster together with a discussion of the results.

**References:**

[1] H. Zhao, et al., Nat. Phys. 15, 1261-1266 (2019). [2] H. V. Löhneysen, et al., Rev. Mod. Phys. 79, 1015 (2007). [3] T. Mazet, et al., Phys. Rev. Lett. 11, 096402 (2013). [4] T. Mazet, et al., Phys. Rev. B. 92, 075105 (2015). [5] L. Eichenberger, et al., Phys. Rev. B. 96, 155129 (2017). [6] L. Eichenberger, et al., Phys. Rev. B. 101, 020408 (R) (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f438e8a96f89b2fa974fad75794646cb.jpg)
Fig. 1: Composition dependence of the electronic specific heat 
coefficient γ in YbMn6Ge6-xSnx (x ≥ 4.0)

 Specific Heat of YbMn6Ge6-xSnx Compounds



A common feature of many organic-based molecular magnets is that inter-molecular magnetic interactions are extremely weak compared to intra-molecular ones. As a result a bulk sample can be described in terms of independent individual molecular magnets made up of a finite cluster of coupled magnetic spins. Because of the large value of individual spins of several molecular magnetic compounds it turns out that such systems can be described to very high accuracy, at sufficiently high temperatures, by a classical Heisenberg spin model. Only for sufficiently low temperatures need one incorporate the quantum character of the spins. In this work we focus on the exact spin dynamics of small nanoscale molecular magnetic clusters of classical Heisenberg spins. The present study permits us to obtain analytical solutions for the time-dependent spin-spin autocorrelation function for certain clusters of classical Heisenberg spins coupled through exchange interaction. This study underscores the potential utility of a classical spin treatment of nanoscale magnetic clusters and provides results useful to interpret data obtained from neutron scattering experiments.

**References:**



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 Exact Spin Dynamics of High Spin Nanoscale Molecular Magnetic Clusters

INTRODUCTION Phosphate fluoride-based cathode material is attracting great interest in secondary batteries due to its superior properties compared to phosphate-based cathode [1, 2]. The theoretical discharge capacity and redox voltage of LiFePO4F are 152 mAh/g and 2.75 V. In the case of LiFePO4F, unlike other intercalation cathode materials, stars in a state of charge and then discharge to form Li2FePO4F. In this paper, we synthesized the tavorite-structured LiFePO4F by two-step solid state reaction method with different molar ratios of LiF. We report on the structural and magnetic properties of LiFePO4F, especially as studied by Mössbauer spectroscopy. EXPERIMENT PROCEDURES The tavorite LiFePO4F cathode was synthesized by two-step solid state reaction method. First, the FePO4 was obtained using stoichiometric mixture of Fe2O3 and (NH4)2HPO4 as starting materials. The mixture was calcined at 300 oC for 7 h in air and sintered at 870 oC for 8 h in air. After that, the obtained FePO4 and LiF were mixed at different mole ratios of 1:1, 1:1.05, and 1:1.1, respectively. The mixture pressed into pellets and sintered at 625 oC for 1.5 h. The crystal structure of sample was determined with X-ray diffraction measurements (XRD) using Rigaku Ultima IV using Cu/Kα radiation. The magnetic properties of sample was measured by using a vibrating sample magnetometer (VSM) at various temperature. Mössbauer spectra were recorded from 4.2 and 295 K using a in transmission geometry employing a 57Co source and fitted by a least square fit programmed assuming Lorentzian line shapes. RESULTS AND DISCUSSION The XRD patterns of FePO4, which was pre-synthesized to make LiFePO4F, were confirmed the formation of hexagonal structure with P3121. The XRD patterns of LiFePO4F synthesized from above FePO4 and excess LiF were measured. Secondary phases from XRD patterns were found in the sample synthesized with LiF mole ratios of 1 and 1.1. The crystal structure of the refined LiFePO4F (LiF-excess 5 %) was determined to be triclinic with P space group and the lattice constants were a = 5.2973 Å, b = 7.2539 Å, c = 5.1506 Å, α = 107.92 °, β = 98.52 °, and γ = 107.36 ° (Fig. 1). The temperature dependent zero-field-cooled (ZFC) and field-cooled (FC) magnetization susceptibility χ(T) curves were measured at 100 Oe in the temperature range from 4.2 to 295 K. From ZFC-FC curve, the magnetic property of LiFePO4F showed antiferromagnetic behavior below the Néel temperature. The Mössbauer spectra of the LiFePO4F were obtained at various temperatures ranging from 4.2 to 295 K. The Mössbauer spectrum at 295 K was analyzed symmetric doublet with the electric quadrupole splitting of 1.10 mm/s and the isomer shift of 0.31 mm/s and, which is Fe3+ state (Fig. 2). Since LiFePO4F has two crystallographically unique Fe sites, Mössbauer for each temperature was measured to investigate detailed magnetic properties. The spectrum at 4.2 K were confirmed had two set of eight asymmetric line indicating that they have both magnetic dipole interaction and electric quadrupole interaction. The value of isomer shift at all temperature was analyzed as Fe3+ ions.

**References:**

[1] Y. Zhang, Q. Liang, C. Huang, et al., J. Solid State Electr., Vol. 22, p.1995 (2018). [2] N. Goubard-Bretesché, E. Kemnitz, and Nicola Pinna, Chem. Eur. J., Vol. 25, p.6189 (2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e039bb5160e298b54b22d9ae7af11ced.jpg)
Fig. 1. Refined XRD patterns of tavorite LiFePO4F.

![](https://assets.underline.io/uploads/markdown_image/1/image/16da341514aafef163ff9faa21efe26d.jpg)
Fig. 2. Mössbauer spectrum of tavorite LiFePO4F at 295 K.

 Synthesis, structural, and Mössbauer studies of tavorite LiFePO4F cathode material

At present, the study of physical properties of magnetic quasi-low-dimensional compounds intensively developed. Oxyborates with ludwigites structure are the members of such type of compounds due to the presence of quasi-two-dimensional elements in their structure. The unit cell of ludwigites includes 4 non-equivalent positions which can be occupied by magnetic cations. The magnetization reversal is occur in (Ni,Mn)3BO5 [1]. The exchange bias effects is occur in Ni5GeB2O10[2]. In this work, single crystals of (Ni,Cu)2MnBO5 with ludwigites structures were synthesized by flux method, using the fluxes based on bismuth trimolybdat. Structural and magnetic characterization of the samples was carried out. Magnetic transition occurs at the temperature at around 75 K (Fig. 1). M-H curves measured at 10 K are presented on Figure 2. Indirect exchange interactions calculation was held for the compound (Ni,Cu)2MnBO5 in frameworks of the Anderson-Zavadskiy indirect exchange interactions model. Calculation results showed that ferromagnetic and atiferromagnetic interaction competition presents between ions in plane and ions connected planes. Acknowledgments The research was funded by RFBR, Krasnoyarsk Territory and Krasnoyarsk Regional Fund of Science, project number 20-42-240011

**References:**

[1] L.N. Bezmaternykh, E.M. Kolesnikova, E.V. Eremin, et al. J. Magn. Magn. Mater. 364,55 (2014) [2] S.N. Sofronova, L.N. Bezmaternykh, E.V. Eremin,et al. J. Magn. Magn. Mater. 401, 217 (2016)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ffa2a493700f5078c7de96b9ab59e675.jpg)
Fig.1. The magnetization in the zero-field-cooled (ZFC), field-cooled (FC), and field-cooled-heating (FH) conditions measured at H=1 kOe.

![](https://assets.underline.io/uploads/markdown_image/1/image/2cfe810f1d7cb15d0679f2c6f1f3c436.jpg)
Fig. 2. M-H hysteresis loops measured at 10 K.

 Magnetic Properties of Quasi-Two-Dimensional Oxyborates (Ni,Cu)2MnBO5 with Ludwigite Structure



Analyzing the magnetic structure factor of a field demagnetized artificial square ice, qualitative deviations from what would predict the square ice model are observed. Combining micromagnetic and Monte Carlo simulations, we demonstrate that these deviations signal the presence of interactions between nanomagnets that extend beyond nearest neighbors. Including further neighbor, dipolar-like couplings in the square ice model, we find that the first seven or eight coupling strengths are needed to reproduce semi-quantitatively the main features of the magnetic structure factor measured experimentally. An alternative, more realistic numerical scenario is also proposed in which the ice condition is slightly detuned. In that case as well, the features evidenced in the experimental magnetic structure factor are only well-described when further neighbor couplings are taken into account. Our results show that long range dipolar interactions are not totally washed out in a field demagnetized artificial square ice, and cannot be neglected as they impact the magnetic correlations within the ice manifold.

**References:**



**Images:**





 Signatures of long range dipolar interactions in artificial square ice

The dynamics of spin waves propagating in thin magnetic films has been studied intensively for several decades, and is relatively well-understood [1,2]. However, investigations have been mainly focused on the cases of either perpendicular or in-plane magnetization, where forward volume, backward volume, and surface magnetostatic (or dipolar) long-wavelength wave modes have been identified [1]. A more general dipole-exchange theory of the spin wave spectrum in magnetic films applicable also to the short-wavelength spin waves has been later developed by the research group of B.A. Kalinikos [2]. The conventional theory led to the understanding that a spin wave in a magnetic film with spin-sink-free surfaces is a non-uniform travelling wave having a stationary distribution of the variable magnetization along the film thickness, and can transfer energy and angular momentum only along the in-plane direction of the spin wave propagation. It turned out, that the situation becomes substantially more complicated in the case when the magnetic film is magnetized obliquely (see Fig.1), and short-wavelength dipole-exchange spin waves are considered. The results of recent experiments [3], performed using Brillouin light-scattering spectroscopy, in combination with the numerical results, based on the theory of dipole-exchange spin-wave spectra [2], have shown two effects: (i) thickness profiles of the propagating spin waves (both in in-plane and obliquely magnetized films) are strongly dependent on the in-plane wavenumber k due to the strong dipolar hybridization between the modes having different thickness profiles, and demonstrate “dipolar pinning” [4] with the increase on the in-plane wavenumber (see Fig.2, top panel); (ii) transverse (thickness) profiles of the spin waves propagating in the film plane in an obliquely magnetized film are non-stationary , i.e. are changing with time in the process of the wave propagation (see Fig.2, bottom panel). This last phenomenon might mean that there could be a transverse (along the film thickness) transfer of spin angular momentum without corresponding transverse transfer of energy. In the end, this issue of transverse spin transport is related to the boundary conditions at the surfaces of the magnetic film. In our simple system Fig. 1, we consider a magnetic film with spin-sink-free surfaces. However, if there is a spin-sink formed by a layer of a heavy metal, such as Pt, present at the film surface, it may be possible to experimentally detect the transfer of spin angular momentum along the film thickness in an obliquely magnetized magnetic film supporting the unidirectional spin wave propagation in the film plane. Further experimental studies are necessary to clarify the issue of possible transverse spin angular momentum transfer in obliquely magnetized magnetic films.

**References:**

[1] R. Damon and J. Eshbach, J. Phys. Chem. Solids, vol. 19, p.308 (1960). [2] B. Kalinikos and A. Slavin, J. Phys. C, vol. 19, p.7013 (1986). [3] D. Bozhko, H. Musiienko-Shmarova, V. Tiberkevich, et al., Phys. Rev. Research, vol. 2, p.023324 (2020). [4] K.Yu. Guslienko, S.O. Demokritov, B. Hillebrands, and A.N. Slavin, Phys. Rev. B , vol.66, 132402 (2002).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d2c295c636a8de1bab19ac4b6cee516b.jpg)
Fig. 1. Geometry of an obliquely magnetized (by an internal magnetic field Hi directed at an angle θ to the surface) spin-sink-free magnetic film of the thickness L carrying a propagating spin wave having a wavenumber k. An example of a transverse profile of the dynamic magnetization in a propagating spin wave is shown along the film thickness.

![](https://assets.underline.io/uploads/markdown_image/1/image/81be77679a816fef838e8f4e5180f41f.jpg)
Fig. 2. Numerically calculated transverse dynamic magnetization profiles of spin wave modes propagating in a 5.6 μm thick yttrium-iron garnet (YIG) film. Top panel: profiles in an in-plane magnetized ( θ =0) film , corresponding to three different values of the in-plane wavenumber, and demonstrating the effect of “dipolar pinning”. Bottom panel: profiles of the wave having in-plane wavenumber k =1 rad μm-1 in an obliquely magnetized ( θ =π/4 ) film at three different time moments, demonstrating that the transverse spin wave profile is non-stationary. 
T - is the period of the spin wave frequency.

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Effects of a Molecular C60 Interfaces on the Spin Hall Magnetoresistance of YIG/PtMn