United States

The spin splitting torque (SST) was theoretically proposed to combine advantages of conventional spin transfer torque (STT) and spin-orbit torque (SOT) as well as enable controllable spin current (1). This talk presents experimental evidences of SST and the inverse effect in collinear antiferromagnet RuO2 films. First, according to spin torque ferromagnetic resonance (ST-FMR) measurements of RuO2 films, we exhibit that spin current direction is correlated to the crystal orientation of RuO2 and spin polarization direction is dependent on (parallel to) the Néel vector, indicating the existence of SST in RuO2 (2). Second, based on spin Seebeck effect and THz emission measurements, we demonstrate that inverse SST effect can convert spin current polarized along Néel vector into charge current, which manifests as Néel vector-dependent spin Seebeck voltage signals and THz emission signal (3). These findings not only presents a new member for the spin torques besides traditional STT and SOT, but also proposes RuO2 for both promising spin source and spin sink for spintronics.&lt;br&gt;

**References:**&lt;br&gt;
(1) R. González-Hernández, et al., Phys. Rev. Lett. 126, 127701 (2021).&lt;br&gt;
(2) H. Bai, C. Song, et al. accpeted by Phys. Rev. Lett. 128, 197202 (2022).&lt;br&gt;
(3) H. Bai, C. Song, et al. In preparation.&lt;br&gt;

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MMM 2022

Observation of the spin splitting torque and its inverse effect in an antiferromagnet

The spin splitting torque (SST) was theoretically proposed to combine advantages of conventional spin transfer torque (STT) and spin-orbit torque (SOT) as well as enable controllable spin current (1). This talk presents experimental evidences of SST and the inverse effect in collinear antiferromagnet RuO2 films. First, according to spin torque ferromagnetic resonance (ST-FMR) measurements of RuO2 films, we exhibit that spin current direction is correlated to the crystal orientation of RuO2 and spin polarization direction is dependent on (parallel to) the Néel vector, indicating the existence of SST in RuO2 (2). Second, based on spin Seebeck effect and THz emission measurements, we demonstrate that inverse SST effect can convert spin current polarized along Néel vector into charge current, which manifests as Néel vector-dependent spin Seebeck voltage signals and THz emission signal (3). These findings not only presents a new member for the spin torques besides traditional STT and SOT, but also proposes RuO2 for both promising spin source and spin sink for spintronics. 

**References:** 
(1) R. González-Hernández, et al., Phys. Rev. Lett. 126, 127701 (2021). 
(2) H. Bai, C. Song, et al. accpeted by Phys. Rev. Lett. 128, 197202 (2022). 
(3) H. Bai, C. Song, et al. In preparation. 

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technical paper

#### Welcome to the 67th Annual Conference on Magnetism and Magnetic Materials, MMM 2022!

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Valley, as a new degree of freedom of electrons besides charge and spin, can be used to encode, transmit, store, and manipulate information [1-3]. By using various external methods, such as optical pumping, magnetic field, magnetic doping, and magnetic proximity effect, the valley polarization can be induced in materials for realizing practical valleytronic devices. Recently, ferrovalley materials, a system with intrinsic magnetic and valley characteristics, was proposed for 2H-VSe2 [4]. Compared to traditional valleytronic materials, the ferrovalley materials have potential to eliminate the limitations associated with external fields in inducing valley polarization. However, to date, most of the predicted ferrovalley materials possess in-plane magnetization, which impede the appearance of valley polarization in nature. The crucial challenge is to induce large perpendicular magnetic anisotropy to achieve spontaneous valley polarization in two-dimensional ferrovalley materials. The van der Waals heterostructure, constructed by isolated atomic layer by layer in a chosen sequence, can reveal unusual properties and phenomena. Here, using first-principles calculations, we find that A-type antiferromagnetic VSe2/CrI3 heterostructure can realize perpendicular magnetic anisotropy and spontaneous valley polarization for realizing anomalous valley Hall effect, while the magnetic anisotropy of VSe2 is in-plane. More interestingly, the electric-field-controlled valley states can be realized by capping a ferroelectric layer (In2Se3) on VSe2/CrI3. The half metal-to-semiconductor transition and turning off and on valley are achieved by switching the ferroelectric polarization. Our results of constructing ferrovalley/ferromagnetic and ferroelectric/ferrovalley/ferromagnetic two-dimensional van der Waals heterostrucutre to engineer electronic and valley states can be useful for developing low-dimensional spintronic and valleytronic devices.

Anomalous Valley Hall Effect in A type Antiferromagnetic Van der Waals Heterostructures

Recent spintronics revealed that the intrinsic anomalous Hall effect (AHE) emerged from an interplay between the Berry curvature and the spin-orbit coupling. Because the Berry phase theory does not require a spontaneous magnetization for AHE (1), AHE can be applied to antiferromagnetic (AFM) materials. Recently, we reported the hysteresis of AHE voltage as a function of magnetic field for the Pt/AFM-Cr2O3/Pt trilayer (2). The observed AHE should not be simply interpreted because Cr2O3 is an insulator, and we proposed the spin chiral texture in the energy bands as an origin (3). To address the insight of AHE, the correlation with the magnetization is helpful (1), which is difficult for Cr2O3 due to its AFM nature. To address this issue, the spontaneous magnetization is induced in the Cr2O3 thin film by Al doping (4) and investigated the correlation with AHE.
Pt(2 nm)/Al-doped Cr2O3(200 nm) bilayer was fabricated on α-Al2O3(0001) substrate by a DC magnetron sputtering. Al was doped by the cosputtering with Cr in the Ar and O2 mixed gas. Composition ratio was determined by XRF: Al/Cr = 4/96. Structural characterizations revealed that each layer grew in Pt(111)/(Al,Cr)2O3(0001). Magnetization was measured by VSM. AHE was measured using the Hall device fabricated by photolithography and Ar ion milling.
Fig.1 shows the M-H curve and the AHE loop at 200 K for the perpendicular magnetic field. The spontaneous magnetization, ~18 emu/cc is similar to the previous report (4). Loops show the rectangular hysteresis showing the perpendicular magnetic anisotropy. Reversal fields are similar for two loops. Temperature dependences of the remanent magnetization Mr and the remanent anomalous Hall resistivity σxy are shown in Fig.2. Although Mr monotonically decreases with increasing temperature, σxy first increase, show the maximum and decrease again. The similar temperature dependence of σxy was reported for other systems where the AHE is associated with the Berry phase. This similarity supports the Berry phase origin of AHE at the Pt/Cr2O3 interface. 

**References:** 
(1) N. Nagaosa, J. Sinova, S. Onoda, et al., Rev. Mod. Phys. 82, 1539 (2010). 
(2) X. Wang, K. Toyoki, R. Nakatani, Y. Shiratsuchi, AIP Advances, 12, 035216 (2022). 
(3) T. Moriyama, Y. Shiratsuchi, T. Ono et al., Phys. Rev. Appl. 13, 034052 (2020). 
(4) T. Nozaki, M. Al-Mahdawi, Y. Shiokawa, et al., Phys. Status Solidi RRL, 12, 180036 (2018). 

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Anomalous Hall effect in Pt/(Al0.04Cr0.96)2O3 epitaxial bilayer

Spin accumulation, which is created by an electrical current flowing in a nanomagnet, affects the strength of spin-orbit interaction (SO) and anisotropy field Hani in a nanomagnet. The reduction of Hani and SO by the current may cause a magnetization reversal. As a result, the data, which is encoded into the current, is memorized by means of two equilibrium magnetization directions of the nanomagnet. Recently, we have developed a high-precision measurement method of Hani and coefficient of spin-orbit interaction kso [1]. kso is a numerical parameter characterizing the SO strength.
Figure 1 shows kso vs. Hani measured in FeCoB nanomagnets.The SO strength is larger in nanomagnet, which contains several ferromagnetic layers (shown by stars) in comparison with nanomagnets containing only one ferromagnetic layer(shown by triangles). It means that the SO strength depends on the number of interfaces. The SO strength increases with an increase of the number of FeB layers up to 5 FeB layers. Further increase of the number of FeB layers causes a decrease of kso due to accumulated interface roughness.
Figure 2 compares current dependency of Hani for a single and multilayer nanomagnet. In the multilayer nanomagnet with a strong SO, the reduction of Hani is large of about 25 % and is nearly independent of current polarity. In contrast, in the single- layer nanomagnet with a weak SO, Hani changes almost linearly with the current only with a small symmetrical contribution due to heating, but the change is small of about 6%. Even such a small change of Hani is sufficient for magnetization reversal, when the conditions for the parametric resonance are met [2,3]. 
**References** [1] https://www.youtube.com/watch?v=LmvYN5hG-90
[2] V. Zayets, arXiv:2104.13008 (2021).
[3] V. Zayets, IOA-07, MMM (2021)
 
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Peculiarities of measured dependencies of strength of spin orbit interaction and anisotropy field on current density in FeCoB nanomagnet

Weyl semimetals can generate large current-induced spin-orbit torques (SOT) that can manipulate the magnetization dynamics in the ferromagnetic materials, and thus play an important role in spintronic devices. Due to their concomitant reduced symmetries, Weyl semimetals are also promising for generating SOTs with novel symmetries that may be able to switch perpendicular magnetic anisotropy thin films. Recently, the Td phase MoTe2, which is Weyl semimetal, has attracted a lot of attentions in the field of spintronics, due to its theoretically predicted SOT efficiencies that are even larger than those of WTe2 [1]. Here, we studied the effects of processing conditions on the stoichiometry and crystal structure of the magnetron-sputtered MoTe2 films by using Rutherford backscattering and X-ray diffraction. Furthermore, we identified different phases of the sputtered MoTe2 thin films using Raman spectroscopy, and we have observed a stable Td semimetal phase even at room temperature. The Td phase is generally considered to be a low-temperature phase and only appears at temperatures below 250 K, and at room temperatures, MoTe2 will be in the 1Tâ€™ monoclinic phase or the 2H hexagonal phase [2]. We have also observed dimensionality-dependent phase transitions from the Td to the 1Tâ€™ phase at room temperature for sputtered MoTe2 thin films as the characteristic peak for the Td phase MoTe2 gradually shifts from 264 cm-1 to 259 cm-1(the Raman peak position for the 1Tâ€™ phase), as the thickness of the sputtered films increases (shown in Figure 1). Finally, SOT efficiencies of the MoTe2 thin films were measured via spin-torque ferromagnetic resonance (ST-FMR) on MoTe2/Ni80Fe20 heterostructures and we observed a large novel SOT due to the spins with out-of-plane polarization directions in both the symmetric and anti-symmetric components of the homodyne mixing voltage signals (shown in Figure 2). The efficiencies of the novel damping-like and field-like SOT are estimated to be 16% and 27%, respectively.

Spin orbit Torques in Magnetron

In spintronics, the spin Hall effect is one of the most important mechanisms to generate and manipulate the spin current in an efficient way. Recent experimental study represented in [1] shows that anti-damping and the inverse spin Hall effect are observed simultaneously in the La0.67Sr0.33MnO3 (LSMO)/Pt heterostructure. Further, it has been observed that single layer LSMO films also exhibit significant amount of intrinsic spin Hall effect (ISHE) voltage (as seen in Fig. 1). Therefore, a series of LSMO films with varying thickness have been deposited via pulsed laser deposition technique to confirm the intrinsic ISHE in LSMO films. Polarity of measured voltage changes when we rotate our sample to 180 deg, which indicates the existence of intrinsic spin pumping in LSMO films. In order to elucidate the physical origin of experimental observations, we compute the spin Hall conductivity of LSMO using first principles calculations. First, the ground state electronic structure of LSMO is calculated using density functional theory (DFT), as implemented in Quantum Espresso package. Using Wannier90, the system was interpolated into maximally-localized Wannier functions (MLWF) basis. Then we employ the Kubo formula to compute the spin Hall conductivity tensors of LSMO to assess the generation of spin current for a given electric field.

Experimental study and first principles calculation of the spin Hall Effect in La0.67Sr0.33MnO3

Nowadays, magnetic nanoparticles may be arranged into highly ordered, crystal-like structures, so-called mesocrystals. Compared to their bulk counterpart, the
characteristics of mesocrystals are not only determined by the specific material employed, but also by the shape of its nanoscale constituents, their ordering on the meso- and on the
macroscale and the resulting mutual interactions between them. We use ferromagnetic resonance (FMR) experiments and Brillouin light scattering (BLS) microscopy in combination with micromagnetic simulations to investigate and characterize
dipolar interactions between magnetic nanoparticles (MNPs) within such mesocrystals. The MNPs investigated in this work consist of iron oxide (magnetite - Fe3O4
) and are coated with
non-magnetic polymers, forming highly ordered hexagonal monolayer crystals as shown in fig. 1 a.
The magnetic response of the regularly arranged hexagonal mesocrystals can be tuned in a controlled way by varying the thickness of the non-magnetic polymer coating of the MNPs and
thus the lattice constant of the mesocrystal. The spectral features reveal that the dipolar coupling strength between the MNPs decreases as the spacing between MNPs increases, as shown in
fig. 2 a.
Structuring the monolayer by employing electron beam lithography, well-defined, circularly shaped MNP assemblies can be fabricated as shown in fig. 1 b. Performing BLS experiments a
main signal accompanied by a satellite signal can be observed, showing distinct dependencies on the externally applied field. 2D-BLS-mapping of the circular assembly reveals the
associated active areas within the assembly for the two resonances. The experimental findings of the FMR and BLS experiments are fully corroborated by micromagnetic simulations. 
**References** 

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(a) Self-assembled, hexagonally arranged MNP monolayer. (b) Using electron beam lithography, well-defined MNP assemblies can be fabricated from monolayers as shown in (a). 

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(a) In FMR experiments on MNP monolayers (see fig. 1 (a)) of different spacing between the MNPs, but constant MNP size. (b) Investigations of structured MNP assemblies as shown in
fig. 1 (b) by BLS reveal two signals, both showing distinct dependencies on the externally applied field.

Dynamic properties of magnetic nanoparticles in highly ordered arrangements: distance and frequency dependent properties

Ultra-rapid annealing (URA) is an effective method to induce nano-crystallization in Fe-B based melt-spun amorphous precursors. The grain size after nano-crystallization depends on the heating rate employed for URA and thus, samples with a range of mean grain sizes can be prepared without altering the chemical composition. Such nanocrystalline samples are ideal for investigating the effect of mean grain size (D) on the core loss. In this study, we prepared a series of nanocrystalline Fe86B13Cu1 samples with grain sizes of 14.5, 21.7, 31.9 and 40.6 nm by varying heating rate between 10 and 104 K s-1. The core loss was measured on an Epstein frame in a frequency range between 10 Hz and 30 kHz. The measured core loss was separated into 3 parts, i.e. the hysteresis loss (Ph), classical eddy current loss (Pc) and the residual part, often referred to as the anomalous loss (Pa). Figure 1(a) shows an example of the relationship between Pa and the product of frequency (f) and the maximum polarization (Jm). The anomalous loss at Jm between 0.6 and 1.0 T is described universally by a simple power dependence with an exponent of about 1.4 over a wide frequency range between 10 Hz to 30 kHz. The grain size dependence of the coercivity (Hc) and the loss per cycle is shown in Fig. 1(b). Hc follows roughly a D3 dependence, suggesting that the samples contain large induced anisotropies. The hysteresis loss per cycle (Ph/f) reflects this steep D dependence while the anomalous loss at low frequencies appears almost independent of the grain size. Thus, the grain size effect on the total loss at low frequencies is attributable to the change in the hysteresis loss which reflects the static coercivity. However, the anomalous loss at 30 kHz shows a clear increase with an increase in D, indicating that the anomalous loss also becomes influential to the grain size dependence of the total core loss at high frequencies. 

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Fig. 1. (a) Anomalous loss versus Jm*f for a mean grain size (D) = 14.5 nm, and (b) changes in the coercivity and core loss per cycle as a function of D for nanocrystalline Fe86B13Cu1.

Effect of grain size on the core loss of nanocrystalline Fe86B13Cu1 prepared by ultra rapid annealing

Recently, there has been a growing interest in developing and using magneto-optical polymer nanocomposites (MO-PNCs) as efficient Faraday rotators [1,2]. A common
strategy to improve the Verdet constant, V, of MO-PNCs is by increasing the nanoparticle (NP) loading [3]. However, since the absorption coefficient, α, also increases with the loading,
the figure-of-merit, FOM = V/α, remains unchanged. In this work, we first showed that the FOM in Fe3O4-based MO-PNCs is independent of NP loading in the absence of aggregation and
decreases when NPs aggregate. Secondly, we demonstrated that the FOM is strongly sensitive to the NP size and composition via doping with terbium ions (Tb3+). In the loading study, we
used a polymerizable ligand to fabricate poly (methyl methacrylate) films containing 8 nm Fe3O4 NPs with high optical quality [4]. When the NP loading was increased from 3.5 to 12.8
wt%, the Verdet constant of the films improved from 4500 to 13500 °/Tm whereas the FOM remained constant at 2.9 °/T. This result confirms our expectation that increasing the loading
does not enhance the overall MO performance. When the NP diameter was increased from 8 to 17 nm, we observed a 7-fold enhancement in the FOM from 2.9 to 23.1 °/T (Fig. 1) which
can be attributed to the NPs reaching the critical size (~20 nm) at which their magnetic domains become stable against thermal fluctuations [5]. For larger sizes, however, the Verdet
constants saturated while FOMs declined due to increased aggregation. The FOM was further improved to ~70 °/T by doping with the highly MO-active Tb3+ ions (Fig. 2) [6]. The drop in
FOM at high Tb3+ doping is likely due to the increased lattice distortions and failure to incorporate the dopants inside the NPs [7]. At the optimal doping and size, the Verdet constant of
4wt% loaded MO-PNC film is 5.6×105 °/Tm which is among the highest reported in the literature, especially for moderately loaded films [1]. The MO-PNCs reported in this work are
promising candidates for compact room-temperature optical magnetometers that can be used for sensing and medical imaging. 


**References:** 

[1] K. Carothers et al., Chem. Mater., vol. 34, p.2531–2544, (2022) 
[2] N. Pavlopoulos et al., J. Mater. Chem. C, vol. 8, p.5417–5425, (2020) 
[3] K. Carothers et al., Chem. Mater., vol. 33, p.5010–5020, (2021) 
[4] Y. Jin et al., J. Mater. Chem. C, vol. 4, p.3654–3660, (2016) 
[5] A. Muxworthy et al., J. R. Soc. Interface, vol. 6, p.1207, (2009) 
[6] K. Miyamoto et al., J. Am. Chem. Soc., vol. 131, p.6328–6329, (2009) 
[7] K. Rice et al., Appl. Phys. Lett., vol. 106, p.062409, (2015) 

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Magneto Optical Figure

Magnetic hyperthermia with magnetic nanoparticles (MNPs) has been introduced to selective treatment of tumor [1,2] and the MNPs also has demonstrated diagnosis [3, 4].
For non-invasive treatment, a therapeutic system with a temperature monitoring that can avoid overheating in normal tissues is of vital importance. We have developed a temperature
monitoring/control system with an optical fiber temperature probe in vivo [2]. However, the optical fiber involves an invasive measurement due to the contact with the body.
In this study, we have developed a wireless temperature monitoring system by utilizing the combination of magnetic harmonic signals of the MNPs for clinical trials. Figure 1 shows the
developed wireless monitoring system with Resovist® (a clinically approved MNP). Under the application of alternating magnetic fields, the detected harmonics were analyzed to extract
only temperature-dependent signals. Figure 2 shows the measured temperature of Resovist® phantom. We achieved an accurate measurement with an error of 0.18°C (Fig. 2(a)). For
practical use on breast/oral cancer, a detectable distance of 10 mm is required. We measured the accurate temperature at a 10 mm distance (Fig. 2(b)). To demonstrate the feasibility toward
clinical trials, we investigated the dependency on the detectable distance and the amount of Resovist®. The error is less than 0.5°C in a 10 mm distance (Fig. 2(c)). Resovist® travels to the
whole body from the injection site via the lymphatic system, resulting in a decrement of the amount at the injection site. Our system can measure the correct temperature regardless of
Resovist® amount (Fig. 2(d)). The results indicate that our system can apply to clinical trials. We will pursue further study of a temperature monitoring system under magnetic
hyperthermia treatment. 

**References:** 

[1] D. Kouzoudis et al., frontiers in Materials 8, 638019 (2021) 
[2] A. Shikano et al., T. Magn. Soc. Jpn. (Special Issues) 6, 100-104 (2022). 
[3] M. Sekino et al., Scientific Reports 8, 1195 (2018) 
[4] K. Taruno et al., J. Surg. Oncol. 120, 1391 (2019) 

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Wireless temperature monitoring by using magnetic nanoparticles for clinical trials on magnetic hyperthermia treatment

Spin-orbit torque (SOT) arising from spin-orbit coupling promises efficient magnetization switching in spintronic devices. It is important for device applications that the SOT switches perpendicular magnetizations without an external magnetic field. In addition to field-free switching, reducing SOT switching current is another essential requirement for low energy consumption.
In this talk, we first demonstrate spin currents and associated SOT in ferromagnet/non-magnet/ferromagnet trilayers, in which the torque on the top magnetic layer can be controlled by changing the magnetization of the bottom ferromagnetic layer. In this structure, by aligning the magnetization of the bottom magnetization parallel to the current direction, spin current can carry out-of-plane spin polarization, enabling field-free SOT switching of the top perpendicular magnetization [1]. The out-of-plane SOT is generated by spin current precession at the interface due to the interfacial spin-orbit field. Second, we show that the spin current caused by the spin anomalous Hall effect can be additionally exploited in epitaxial Co-based magnetic trilayers (2). The large in-plane magnetic anisotropy of the epitaxial Co makes it possible to control the magnetic easy axis of the bottom magnetic layer away from the current direction. It is found that the critical current for field-free switching is reduced when the magnetization is at an angle between 30 and 45 degrees from the current direction where the spin anomalous Hall effect is non-negligible.
References (1) S-h. C. Baek, et al, Nat. Mater. 17, 509 (2018)
(2) J. Ryu, et al, Nat. Electron. 5, 217 (2022)

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Observation of the spin splitting torque and its inverse effect in an antiferromagnet

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Anomalous Valley Hall Effect in A type Antiferromagnetic Van der Waals Heterostructures

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