##### Quantifying the spin mixing conductance of EuO/W heterostructures by spin Hall magnetoresistance experiments

P. Rosenberger, M. Opel, S. Geprägs, H. Huebl, R. Gross, M. Müller, M. Althammer

Applied Physics Letters 118, 192401 (2021).

The spin Hall magnetoresistance (SMR) allows to investigate the magnetic textures of magnetically ordered insulators in heterostructures with normal metals by magnetotransport experiments. We here report the observation of the SMR in in situ prepared ferromagnetic EuO/W thin film bilayers with magnetically and chemically well-defined interfaces. We characterize the magnetoresistance effects utilizing angle-dependent and field-dependent magnetotransport measurements as a function of temperature. Applying the established SMR model, we derive and quantify the real and imaginary parts of the complex spin mixing interface conductance. We find that the imaginary part is by one order of magnitude larger than the real part. Both decrease with increasing temperature. This reduction is in agreement with thermal fluctuations in the ferromagnet.

##### Design of an optomagnonic crystal: Towards optimal magnon-photon mode matching at the microscale

J. Graf, S. Sharma, H. Huebl, S.V. Kusminskiy

Physical Review Research 3 (1), 013277 (2021).

We put forward the concept of an optomagnonic crystal: a periodically patterned structure at the microscale based on a magnetic dielectric, which can co-localize magnon and photon modes. The co-localization in small volumes can result in large values of the photon-magnon coupling at the single quanta level, which opens perspectives for quantum information processing and quantum conversion schemes with these systems. We study theoretically a simple geometry consisting of a one-dimensional array of holes with an abrupt defect, considering the ferrimagnet yttrium iron garnet (YIG) as the basis material. We show that both magnon and photon modes can be localized at the defect, and use symmetry arguments to select an optimal pair of modes in order to maximize the coupling. We show that an optomagnonic coupling in the kHz range is achievable in this geometry, and discuss possible optimization routes in order to improve both coupling strengths and optical losses.

##### All-electrical detection of skyrmion lattice state and chiral surface twists

A. Aqeel, M. Azhar, N. Vlietstra, A. Pozzi, J. Sahliger, H. Huebl, T.T.M. Palstra, C.H. Back, M. Mostovoy

Physical Review B 103 (10), L100410 (2021).

We study the high-temperature phase diagram of the chiral magnetic insulator Cu2OSeO3 by measuring the spin-Hall magnetoresistance (SMR) in a thin Pt electrode. We find distinct changes in the phase and amplitude of the SMR signal at critical lines separating different magnetic phases of bulk Cu2OSeO3. The skyrmion lattice state appears as a strong dip in the SMR phase. A strong enhancement of the SMR amplitude is observed in the conical spiral state, which we explain by an additional symmetry-allowed contribution to the SMR present in noncollinear magnets. We demonstrate that the SMR can be used as an all-electrical probe of chiral surface twists and skyrmions in magnetic insulators.

##### Spin to charge conversion in Si/Cu/ferromagnet systems investigated by ac inductive measurements

E. Shigematsu, L. Liensberger, M. Weiler, R. Ohshima, Y. Ando, T. Shinjo, H. Huebl, M. Shiraishi

Physical Review B 103, 094430 (2021).

Semiconductor/ferromagnet hybrid systems are attractive platforms for investigation of spin conversion physics, such as the (inverse) spin Hall effect. However, the superimposed rectification currents originating from anisotropic magnetoresistance have been a serious problem preventing unambiguous detection of dc spin Hall electric signals in semiconductors. In this study, we applied a microwave frequency inductive technique immune to such rectification effects to investigate the spin to charge conversion in heterostructures based on Si, one of the primitive semiconductors. The Si doping dependence of the spin-orbit torque conductivity was obtained for the Si/Cu/NiFe trilayer system. A monotonous modulation of the spin-orbit torque conductivity by doping and relative sign change of spin to charge conversion between the degenerate n- and p-type Si samples were observed. These results unveil spin to charge conversion mechanisms in semiconductor/metal heterostructures and show a pathway for further exploration of spin-conversion physics in metal/semiconductor heterostructures.

##### Temperature-Dependent Spin Transport and Current-Induced Torques in Superconductor-Ferromagnet Heterostructures

M. Mueller, L. Liensberger, L. Flacke, H. Huebl, A. Kamra, W. Belzig, R. Gross, M. Weiler, M. Althammer

Physical Review Letters 126 (8), 087201 (2021).

We investigate the injection of quasiparticle spin currents into a superconductor via spin pumping from an adjacent ferromagnetic metal layer. To this end, we use NbN-Ni80Fe20(Py) heterostructures with a Pt spin sink layer and excite ferromagnetic resonance in the Permalloy layer by placing the samples onto a coplanar waveguide. A phase sensitive detection of the microwave transmission signal is used to quantitatively extract the inductive coupling strength between the sample and the coplanar waveguide, interpreted in terms of inverse current-induced torques, in our heterostructures as a function of temperature. Below the superconducting transition temperature T-c, we observe a suppression of the dampinglike torque generated in the Pt layer by the inverse spin Hall effect, which can be understood by the changes in spin current transport in the superconducting NbN layer. Moreover, below T-c we find a large fieldlike current-induced torque.

##### Sideband-resolved resonator electromechanics based on a nonlinear Josephson inductance probed on the single-photon level

P. Schmidt, M.T. Amawi, S. Pogorzalek, F. Deppe, A. Marx, R. Gross, H. Huebl

Communication Physics 3 (1), 233 (2020).

Light-matter interaction in optomechanical systems is the foundation for ultra-sensitive detection schemes as well as the generation of phononic and photonic quantum states. Electromechanical systems realize this optomechanical interaction in the microwave regime. In this context, capacitive coupling arrangements demonstrated interaction rates of up to 280Hz. Complementary, early proposals and experiments suggest that inductive coupling schemes are tunable and have the potential to reach the single-photon strong-coupling regime. Here, we follow the latter approach by integrating a partly suspended superconducting quantum interference device (SQUID) into a microwave resonator. The mechanical displacement translates into a time varying flux in the SQUID loop, thereby providing an inductive electromechanical coupling. We demonstrate a sideband-resolved electromechanical system with a tunable vacuum coupling rate of up to 1.62kHz, realizing sub-aNHz(-1/2) force sensitivities. The presented inductive coupling scheme shows the high potential of SQUID-based electromechanics for targeting the full wealth of the intrinsically nonlinear optomechanics Hamiltonian. Recently, inductively-coupled optomechanical systems have been realized. They represent an important step forward towards achieving strong light-matter interaction, offer extreme sensitivity to mechanical displacement, and allow to study quantum phenomena on a single quantum level. In this work, a superconducting device is inductively coupled to a microwave resonator forming an electromechanical system operating at the single-photon level.

##### Observation of Antiferromagnetic Magnon Pseudospin Dynamics and the Hanle Effect

T. Wimmer, A. Kamra, J. Gueckelhorn, M. Opel, S. Gepraegs, R. Gross, H. Huebl, M. Althammer

Physical Review Letters 125 (24), 247204 (2020).

We report on experiments demonstrating coherent control of magnon spin transport and pseudospin dynamics in a thin film of the antiferromagnetic insulator hematite utilizing two Pt strips for all-electrical magnon injection and detection. The measured magnon spin signal at the detector reveals an oscillation of its polarity as a function of the externally applied magnetic field. We quantitatively explain our experiments in terms of diffusive magnon transport and a coherent precession of the magnon pseudospin caused by the easy-plane anisotropy and the Dzyaloshinskii-Moriya interaction. This experimental observation can be viewed as the magnonic analog of the electronic Hanle effect and the Datta-Das transistor, unlocking the high potential of antiferromagnetic magnonics toward the realization of rich electronics-inspired phenomena.

##### Antiferromagnetic magnon pseudospin: Dynamics and diffusive transport

A. Kamra, T. Wimmer, H. Huebl, M. Althammer

Physical Review B 102 (17), 174445 (2020).

We formulate a theoretical description of antiferromagnetic magnons and their transport in terms of an associated pseudospin. The need and strength of this formulation emerges from the antiferromagnetic eigenmodes being formed from superpositions of spin-up and -down magnons, depending on the material anisotropies. Consequently, a description analogous to that of spin-1/2 electrons is demonstrated while accounting for the bosonic nature of the antiferromagnetic eigenmodes. Introducing the concepts of a pseudospin chemical potential together with a pseudofield and relating magnon spin to pseudospin allows a consistent description of diffusive spin transport in antiferromagnetic insulators with any given anisotropies and interactions. Employing the formalism developed, we elucidate the general features of recent nonlocal spin transport experiments in antiferromagnetic insulators hosting magnons with different polarizations. The pseudospin formalism developed herein is valid for any pair of coupled bosons and is likely to be useful in other systems comprising interacting bosonic modes.

##### Quantitative comparison of magnon transport experiments in three-terminal YIG/Pt nanostructures acquired via dc and ac detection techniques

J. Gueckelhorn, T. Wimmer, S. Gepraegs, H. Huebl, R. Gross, M. Althammer

Applied Physics Letters 117 (18), 182401 (2020).

All-electrical generation and detection of pure spin currents are promising ways toward controlling the diffusive magnon transport in magnetically ordered insulators. We quantitatively compare two measurement schemes, which allow us to measure the magnon spin transport in a three-terminal device based on a yttrium iron garnet thin film. We demonstrate that the dc charge current method based on the current reversal technique and the ac charge current method utilizing first and second harmonic lock-in detection can both efficiently distinguish between electrically and thermally injected magnons. In addition, both measurement schemes allow us to investigate the modulation of magnon transport induced by an additional dc charge current applied to the center modulator strip. However, while at a low modulator charge current both schemes yield identical results, we find clear differences above a certain threshold current. This difference originates from nonlinear effects of the modulator current on the magnon conductance.

##### Echo Trains in Pulsed Electron Spin Resonance of a Strongly Coupled Spin Ensemble

S. Weichselbaumer, M. Zens, C.W. Zollitsch, M.S. Brandt, S. Rotter, R. Gross, H. Huebl.

Physical Review Letters 125, 137701 (2020).

We report on a novel dynamical phenomenon in electron spin resonance experiments of phosphorus donors. When strongly coupling the paramagnetic ensemble to a superconducting lumped element resonator, the coherent exchange between these two subsystems leads to a train of periodic, self-stimulated echoes after a conventional Hahn echo pulse sequence. The presence of these multiecho signatures is explained using a simple model based on spins rotating on the Bloch sphere, backed up by numerical calculations using the inhomogeneous Tavis-Cummings Hamiltonian.

##### Effect of interfacial oxidation layer in spin pumping experiments on Ni80Fe20/SrIrO3 heterostructures

T.S. Suraj, M. Mueller, S. Gelder, S. Gepraegs, M. Opel, M. Weiler, K. Sethupathi, H. Huebl, R. Gross, M.S.R. Rao, M. ALthammer

Journal of Applied Physics 128 (8), 083903 (2020).

SrIrO3 with its large spin-orbit coupling and low charge conductivity has emerged as a potential candidate for efficient spin-orbit torque magnetization control in spintronic devices. Here we report on the influence of an interfacial oxide layer on spin pumping experiments in Ni80Fe20 (NiFe)/SrIrO3 bilayer heterostructures. To investigate this scenario, we have carried out broadband ferromagnetic resonance (BBFMR) measurements, which indicate the presence of an interfacial antiferromagnetic oxide layer. We performed in-plane BBFMR experiments at cryogenic temperatures, which allowed us to simultaneously study dynamic spin pumping properties (Gilbert damping) and static magnetic properties (such as the effective magnetization and magnetic anisotropy). The results for NiFe/SrIrO3 bilayer thin films were analyzed and compared to those from a NiFe/NbN/SrIrO3 trilayer reference sample, where a spin-transparent, ultra-thin NbN layer was inserted to prevent the oxidation of NiFe. At low temperatures, we observe substantial differences in the magnetization dynamics parameters of these samples. In particular, the Gilbert damping in the NiFe/SrIrO3 bilayer sample drastically increases below 50 K, which can be well explained by enhanced spin fluctuations at the antiferromagnetic ordering temperature of the interfacial oxide layer. Our results emphasize that this interfacial oxide layer plays an important role for the spin current transport across the NiFe/SrIrO3 interface.

##### Spin Hall magnetoresistance in antiferromagnetic insulators

S. Gepraegs, M. Opel, J. Fischer, O. Gomonay, P. Schwenke, M. Althammer, H. Huebl, R. Gross

Journal of Applied Physics 127 (24), (2020).

Antiferromagnetic materials promise improved performance for spintronic applications as they are robust against external magnetic field perturbations and allow for faster magnetization dynamics compared to ferromagnets. The direct observation of the antiferromagnetic state, however, is challenging due to the absence of a macroscopic magnetization. Here, we show that the spin Hall magnetoresistance (SMR) is a versatile tool to probe the antiferromagnetic spin structure via simple electrical transport experiments by investigating the easy-plane antiferromagnetic insulators

alpha -

Fe 2

O 3 (hematite) and NiO in bilayer heterostructures with a Pt heavy-metal top electrode. While rotating an external magnetic field in three orthogonal planes, we record the longitudinal and the transverse resistivities of Pt and observe characteristic resistivity modulations consistent with the SMR effect. We analyze both their amplitude and phase and compare the data to the results from a prototypical collinear ferrimagnetic

Y 3

Fe 5

O 12/Pt bilayer. The observed magnetic field dependence is explained in a comprehensive model, based on two magnetic sublattices and taking into account magnetic field-induced modifications of the domain structure. Our results show that the SMR allows us to understand the spin configuration and to investigate magnetoelastic effects in antiferromagnetic multi-domain materials. Furthermore, in

alpha

- Fe 2

O 3/Pt bilayers, we find an unexpectedly large SMR amplitude of

2.5 x

10

- 3, twice as high as for prototype

Y 3

Fe 5

O 12/Pt bilayers, making the system particularly interesting for room-temperature antiferromagnetic spintronic applications.

##### Large Spin Hall Magnetoresistance in Antiferromagnetic alpha-Fe2O3/Pt Heterostructures

J. Fischer, M. Althammer, N. Vlietstra, H. Huebl, S.T.B. Goennenwein, R. Gross, S. Gepraegs, M. Opel

Physical Review Applied 13 (1), 014019 (2020).

We investigate the spin Hall magnetoresistance (SMR) at room temperature in thin-film heterostructures of antiferromagnetic insulating (0001)-oriented alpha-Fe2O3 (hematite) and Pt. We measure their longitudinal and transverse resistivities while rotating an applied magnetic field of up to 17 T in three orthogonal planes. For out-of-plane magnetotransport measurements, we find indications for a multidomain antiferromagnetic configuration whenever the field is aligned along the film normal. For in-plane field rotations, we clearly observe a sinusoidal resistivity oscillation characteristic for the SMR due to a coherent rotation of the Neel vector. The maximum SMR amplitude of 0.25% is, surprisingly, twice as high as for prototypical ferrimagnetic Y3Fe5O12/Pt heterostructures. The SMR effect saturates at much smaller magnetic fields than in comparable antiferromagnets, making the alpha-Fe2O3/Pt system particularly interesting for roomtemperature antiferromagnetic spintronic applications.

##### Spin Transport in a Magnetic Insulator with Zero Effective Damping

T. Wimmer, M. Althammer, L. Liensberger, N. Vlietstra, S. Geprägs, M. Weiler, R. Gross, H. Huebl

Physical Review Letters 123 (25), 257201 (2019).

Applications based on spin currents strongly rely on the control and reduction of their effective damping and their transport properties. We here experimentally observe magnon mediated transport of spin (angular) momentum through a 13.4-nm thin yttrium iron garnet film with full control of the magnetic damping via spin-orbit torque. Above a critical spin-orbit torque, the fully compensated damping manifests itself as an increase of magnon conductivity by almost 2 orders of magnitude. We compare our results to theoretical expectations based on recently predicted current induced magnon condensates and discuss other possible origins of the observed critical behavior.

##### High spin-wave propagation length consistent with low damping in a metallic ferromagnet

L. Flacke, L. Liensberger, M. Althammer, H. Huebl, S. Geprags, K. Schultheiss, A. Buzdakov, T. Hula, H. Schultheiss, E.R.J. Edwards, H.T. Nembach, J.M. Shaw, R. Gross, M. Weiler

Applied Physics Letters 115 (12), 122402 (2019).

We report ultralow intrinsic magnetic damping in Co25Fe75 heterostructures, reaching the low 10(-4) regime at room temperature. By using a broadband ferromagnetic resonance technique in out-of-plane geometry, we extracted the dynamic magnetic properties of several Co25Fe75-based heterostructures with varying ferromagnetic layer thicknesses. By measuring radiative damping and spin pumping effects, we found the intrinsic damping of a 26 nm thick sample to be alpha 0 less than or similar to 3.18x10-4. Furthermore, using Brillouin light scattering microscopy, we measured spin-wave propagation lengths of up to (21 +/- 1) mu m in a 26 nm thick Co25Fe75 heterostructure at room temperature, which is in excellent agreement with the measured damping.

##### Magnetoelasticity of Co25Fe75 thin films

D. Schwienbacher, M. Pernpeintner, L. Liensberger, E.R.J. Edwards, H.T. Nembach, J.M. Shaw, M. Weiler, R. Gross, H. Huebl

Journal of Applied Physics 126 (10), 103902 (2019).

We investigate the magnetoelastic properties of Co25Fe75 and Co10Fe90 thin films by measuring the mechanical properties of a doubly clamped string resonator covered with multilayer stacks containing these films. For the magnetostrictive constants, we find lambda Co25Fe75=(-20.68 +/- 0.25)x10-6 and lambda Co10Fe90=(-9.80 +/- 0.12)x10-6 at room temperature, in contrast to the positive magnetostriction previously found in bulk CoFe crystals. Co25Fe75 thin films unite low damping and sizable magnetostriction and are thus a prime candidate for micromechanical magnonic applications, such as sensors and hybrid phonon-magnon systems.

##### Exchange-Enhanced Ultrastrong Magnon-Magnon Coupling in a Compensated Ferrimagnet

L. Liensberger, A. Kamra, H. Maier-Flaig, S. Geprags, A. Erb, S.T.B. Goennenwein, R. Gross, W. Belzig, H. Huebl, M. Weiler

Physical Review Letters 123 (11), 117204 (2019).

We experimentally study the spin dynamics in a gadolinium iron garnet single crystal using broadband ferromagnetic resonance. Close to the ferrimagnetic compensation temperature, we observe ultrastrong coupling of clockwise and counterclockwise magnon modes. The magnon-magnon coupling strength reaches almost 40% of the mode frequency and can be tuned by varying the direction of the external magnetic field. We theoretically explain the observed mode coupling as arising from the broken rotational symmetry due to a weak magnetocrystalline anisotropy. The effect of this anisotropy is exchange enhanced around the ferrimagnetic compensation point.

##### Anomalous spin Hall angle of a metallic ferromagnet determined by a multiterminal spin injection/detection device

T. Wimmer, B. Coester, S. Geprags, R. Gross, S.T.B. Goennenwein, H. Huebl, M. Althammer

Applied Physics Letters 115 (9), 092404 (2019).

We report on the determination of the anomalous spin Hall angle in the ferromagnetic metal alloy cobalt-iron (Co25Fe75, CoFe). This is accomplished by measuring the spin injection/detection efficiency in a multiterminal device with nanowires of platinum (Pt) and CoFe deposited onto the magnetic insulator yttrium iron garnet (Y3Fe5O12, YIG). Applying a spin-resistor model to our multiterminal spin transport data, we determine the magnon conductivity in YIG, the spin conductance at the YIG/CoFe interface, and finally the anomalous spin Hall angle of CoFe as a function of its spin diffusion length in a single device. Our experiments clearly reveal a negative anomalous spin Hall angle of the ferromagnetic metal CoFe, but a vanishing ordinary spin Hall angle. This work, therefore, adds new observations to the results reported in Tian et al. [Phys. Rev. B 94, 020403 (2016)] and Das et al. [Phys. Rev. B 96, 220408(R) (2017)] , where the authors found finite contributions of the ordinary spin Hall angle in the ferromagnetic metals Co and Permalloy. Published under license by AIP Publishing.

##### Measurements and atomistic theory of electron g-factor anisotropy for phosphorus donors in strained silicon

M. Usman, H. Huebl, A.R. Stegner, C.D. Hill, M.S. Brandt, L.C.L. Hollenberg

Physical Review B 98, 35432 (2018).

This work reports the measurement of electron g-factor anisotropy (|Δg|=|g001−g1¯10|) for phosphorous donor qubits in strained silicon (sSi = Si/Si1−xGex) environments. Multimillion-atom tight-binding simulations are performed to understand the measured decrease in |Δg| as a function of x, which is attributed to a reduction in the interface-related anisotropy. For x<7%, the variation in |Δg| is linear and can be described by ηxx, where ηx≈1.62×10−3. At x=20%, the measured |Δg| is 1.2±0.04×10−3, which is in good agreement with the computed value of 1×10−3. When strain and electric fields are applied simultaneously, the strain effect is predicted to play a dominant role on |Δg|. Our results provide useful insights on the spin properties of sSi:P for spin qubits, and more generally for devices in spintronics and valleytronics areas of research.