Magnetic skyrmions are “topologically protected” solitons, that have recently received increased attention due to their potential application as information carriers and for unconventional computing [1]. While the current-driven dynamics has been explored deeply, the theory of temperature gradient-induced dynamics - Skyrmion-Caloritronics [2] - is still at its early stages of development but it is particularly promising due to its low energy consumption.
In this work, we study the effects of thermal gradients on skyrmion motion in different systems (single-layer FM with interfacial Dzyaloshinskii-Moriya interaction (IDMI), multilayer, and synthetic antiferromagnets (SAFs)) inspired by the experimental results of Ref. [2] and from a fundamental point of view. We observe that, when driven by the entropic torque, skyrmions in single layers move from the cold to the hot region with a finite skyrmion Hall angle (Fig. 1), while in multilayers they move in the opposite direction (from hot to cold region) (Fig. 2). The latter is in qualitative agreement with the experimental observations (Fig. 3a in Ref. [2]). We demonstrate that this difference is due to the distinct scaling relations characterizing the two systems, and to the existence of a magnetostatic field gradient linked to the variation of saturation magnetization (MS) which cannot be neglected in magnetic multilayers. The numerical results are corroborated by a generalized Thiele’s equation developed for this scenario. Moreover, we show that the skyrmion Hall angle is completely suppressed in SAFs, similarly to the current-driven skyrmions [3,4].
Our results have fundamental implications in the future development of skyrmionic devices combining thermal gradients and SOTs where the proper temperature dependence of the parameters should be taken into account.
See Ref. [5] for founding statement. 
**References** [1] J. Zázvorka, et al., Nat. Nanotechnol. 14, 658 (2019).

[2] Z. Wang, et al., Nat. Electron. 3, 672 (2020).

[3] X. Zhang, et al., Nat. Commun. 7, 10293 (2016).

[4] R. Tomasello, et al., J. Phys. D. Appl. Phys. 50, 325302 (2017).

[5] This work was supported by the Project No. PRIN 2020LWPKH7 funded by the Italian Ministry of University and Research, and by the PETASPIN association (www.petaspin.com). JB acknowledges support from the Royal Society through a University Research Fellowship. E.R. acknowledges the economical support of the COST Action CA 17123 (MAGNETOFON) within the STSM program. We would like to acknowledge networking support from COST Action No. CA17123 “Ultrafast opto magneto electronics for nondissipative information technology.”

[6] W. Li, et al., Adv. Mater. 31, 1807683 (2019). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/5f492fdb99a4414723d8429930359fb7.png)

Skyrmion Caloritronics: a promising Strategy to manipulate Skyrmions

Spintronic diodes (STDs) are emerging as a technology for the realization of high-performance microwave detectors [1]. In this paper, we use their rectification properties to perform the analog multiplication between any two numbers. For this purpose, we introduce the concept of degree of rectification (DOR) and we confirm its applicability with micromagnetic and experimental data. The proposed method is suitable for highly integrated implementations and has promising perspectives for neural networks applications [2]. The multiplication can be obtained by measuring the response of a parabolic phenomenon to three well-determined inputs [3][4][5]. Therefore, we analyze the DOR of spintronic diodes, which is the output dc voltage measured for a variable input dc current in injection-locked devices. This Vdc/Idc curve can be well approximated to a parabola as shown in Fig. 1, the experimental data are taken from [6]. The voltage can be approximated by the following equation [6]: Vdc=[(RAP-RP )/4] Iac,MAX cos(φ(Idc)) √p (1) where RAP and RP are the device resistances in the antiparallel and parallel state, respectively, p is the power of the magnetoresistive signal, φ(Idc) is the intrinsic phase shift between the ac current and the magnetoresistive signal, and the cosine can be well approximated with a parable using Taylor’s second-order expansion. Moreover, Eq. 1 can be fully characterized knowing the physical parameters of the device and the values of Idc,MAX, Vdc,MAX (both represented in Fig. 1) and the second derivative of Vdc with respect to Idc evaluated in Idc=Idc,MAX. Fig. 2 shows the application of the presented method for 200 cases with random inputs, the red line shows the ideal result; the correlation coefficient found is r=99.83%. We will show how the proposed method can be used to implement the convolution for neural networks applications with excellent results for image recognition.

![](https://assets.underline.io/uploads/markdown_image/1/image/8be5d570eb2198667334d746191b22a6.jpg)

Fig. 1: Output dc voltage depending on the input dc current (data taken from [4]) for an injection-locked diode (blue circles) and parabolic fit (red line).

![](https://assets.underline.io/uploads/markdown_image/1/image/ef2d86778d75be9a7a2f863250048857.jpg)

Fig. 2: 200 multiplications obtained with the proposed method (black circles) compared with the ideal result (red line).

Analog multiplication implemented with spin-torque diodes for neural networks applications

Antiferromagnets (AFMs) are magnetically ordered materials without a macroscopic magnetization. There is accelerating interest in using them for memory applications, motivated by the possibility for electrically controlling AFM order via spin-orbit torques, and its read-out via magnetoresistive effects [1-2]. Here we show that micrometer-scale bits of the antiferromagnet PtMn, grown on a Ta or Pt heavy metal (HM) layer, can be switched reversibly between different magnetic states by electric currents, with readout through a second harmonic voltage technique [3]. The device exhibits multiple states, which can be set using different current amplitudes and may find application in neuromorphic computing. Micromagnetic simulations suggest that these metastable states consist of vortex and anti-vortex textures that move in response to current. We also demonstrate, using a modified device layout, direct voltage measurements to read out the electrically-induced switching of noncollinear PtMn3. The modified layout and measurement methodology, which was recently demonstrated using the IrMn3/Pt material system [4], is utilized here to distinguish current-induced magnetic and nonmagnetic switching signals in PtMn3/Pt devices. We also realize switching down to 10 µs pulse width, which shows the potential for fast device applications. The effect of temperature and external magnetic field (up to 15 T) are also studied. Our results pave the way towards practical PtMn and PtMn3 antiferromagnetic memories integrated on silicon, and indicate the importance of micromagnetic textures in the static and dynamic behavior of antiferromagnetic devices.

Electrical manipulation of antiferromagnetic order in PtMn and PtMn3 pillars

Antiferromagnetic materials (AFMs) provide a pathway to overcome the limitations of ferromagnet-based spintronics, enabling fast and high density memory devices, as well as terahertz detectors and sources. This has fueled intensive research on the electrical manipulation of metallic AFMs using interfacial spin-orbit torque (SOT) from a heavy metal (HM) layer [1-4]. However, the threshold current density in HM/AFM bilayers is typically large, thus creating non-magnetic contributions to resistive switching signals, complicating their interpretation. Here, we present a new device structure and measurement protocol based on differential voltage measurements, allowing in situ reference measurements and to systematically separate the switching signals originating in the AFM and HM layers of a HM/AFM heterostructure [5]. The proposed device consists of a double-cross HM structure with six terminals, where the AFM, patterned in a micropillar shape, is placed on one of the two crosses. We successfully use this method in devices formed by Pt and the non-collinear AFM IrMn3. The results provide clear evidence of electrical switching of the AFM order parameter in the IrMn3 pillar by SOT in the range of writing current densities from 36 to 50 MA/cm2 with no appreciable switching signal from the Pt layer. We discuss the role of different switching configurations (180° and 90° writing currents), as well as the role of thermal activation on the switching characteristics. Control experiments in Pt-only double-cross samples without an AFM pillar reveal HM-dominated switching at higher current densities ~60 MA/cm2. We discuss active readout of the switching signals using a differential amplifier, with large peak-to-peak output voltage ~100 mV. The structure allows for reliable electrical measurement of resistive signatures of AFM switching induced by SOT, which will be important not only for the fundamental understanding of current-induced AFM domain dynamics, but also as an electrical readout method for practical applications in memory and computing devices.

![](https://assets.underline.io/uploads/markdown_image/1/image/9f7b7e5713bbb79e6a1b7f3436e814c5.jpg)

Fig. 1. Design of double-cross device for differential voltage measurements and the measured differential voltage for the 180° switching configuration with 20 mA write pulses.

Observation of current-induced switching in non-collinear antiferromagnetic IrMn3 by differential voltage measurements

Microwave detectors based on the spin-torque diode effect are among the key emerging spintronic devices (see ref.[1] and references therein). By utilizing the spin of electrons in addition to their charge, they have the potential to overcome the theoretical performance limits of their semiconductor (Schottky) counterparts. Those devices realized with magnetic tunnel junctions and in active regime exhibit high-detection sensitivity &gt;200kV/W at room temperature and zero bias field, thanks to the injection locking mechanism, and for low-input power (micro-Watts or lower). Those performance can be improved with the bolometric effect or when coupled properly in arrays. Here, I will discuss our recent results in the field of microwave detectors based on spin diodes and possible implementations of THz detectors based on antiferromagnets working in linear and parametric excitation regime. I will point out how those devices can impact the IoT market and can be used for implement hardware multiplication by using the concept of degree of rectification and as dual band detectors in frequency shifting keying demodulation schemes in which the information is coded in two discrete values of the frequency in a carrier signal. In particular, the frequency response of spin-torque diodes and their current tunability can be also used as building blocks of the hardware realization of neurons and synapses in neuromorphic applications. Another application of spintronic diodes, when they have a broadband frequency response, is as electromagnetic energy harvesting, which offers an attractive energy source for applications in self-powered portable electronics in the “internet of things” era. Here I will show the development of a bias-field-free spin-torque diodes based on a magnetic tunnel junction having a canted magnetization in the free layer, and demonstrate that those devices could be an efficient harvester of broadband ambient RF radiation, capable to efficiently harvest microwave powers of microWatt and below and to power a black phosphorous nanodevice. I will also review recent idea on spintronic detectors in presence of nonuniform ground states such as skyrmions.

Challenges in microwave and THz spintronic diodes

Magnetic skyrmions are topologically-protected magnetization textures characterized by a non-trivial topology [1]. They have been observed in bulk materials [2] and asymmetric multilayers [3,4] in presence of a finite Dzyaloshinskii-Moriya interaction (DMI). The manipulation (nucleation, shifting, and detection) of skyrmions usually occurs via electrical currents [3], however, thermal effects have been also used to reshuffle skyrmions for low-power unconventional applications [5]. Recently, thermal gradients have been applied to magnetic multilayers where thermally-generated skyrmions unidirectionally diffuse from hot regions to cold regions [6]. This observation has been explained through the combination of repulsive forces between skyrmions, thermal spin-orbit torques, magnonic spin torques as well as entropic forces. Here, inspired by Ref. [6], we study, by means of micromagnetic simulations, the effect of thermal gradients on skyrmion motion from a fundamental point of view. We have previously demonstrated [7] that temperature induces a variation of the magnetic parameters (exchange, interfacial DMI, perpendicular anisotropy constants) which reduce with temperature following atomistically-computed scaling relations. The set of scaled values of those parameters can be used to deterministically simulate the effect of thermal fluctuations instead of a stochastic thermal field [7]. With this in mind, we consider a linear thermal gradient applied along the x-axis (Fig. 1) with the hot and cold regions placed on the left and right side, respectively. We firstly study a 1-repetition ferromagnetic sample with a number of cells Ncx=300, Ncy=300, and Ncz=1 where a Néel skyrmion is initially placed at the center of the sample. We analyze the effect of a linear gradient of only one parameter at time. The skyrmion exhibits two velocity components that follow the generalized Thiele equation [8], where the component parallel to the gradient direction depends on the parameter varied. In particular, the perpendicular anisotropy and exchange gradients move the skyrmion from the cold to the hot region, therefore to the region where those parameters are smaller. On the contrary, the saturation magnetization (magnetostatic field) and the DMI shift the skyrmion from the hot to the cold region, thus towards the region where those parameters are larger. Afterward, we study the effect of the gradients all at once, observing an overall skyrmion motion from the cold to the hot region (Fig. 1). Furthermore, we study the effect of the skyrmion profile on the thermal gradient-driven skyrmion motion. In magnetic multilayers, the skyrmion is characterized by a thickness-dependent profile which gives rise to the so-called hybrid skyrmion [4]. Therefore, we study the effect of the thermal gradients on a single hybrid skyrmion as a function of the number of ferromagnetic repetitions. Fig.1 shows a comparison of the skyrmion trajectories, where a dependence on the number of repetitions is observed. Our results can be useful for a deeper understanding of the effect of thermal gradients and therefore for the design of low-power thermally-driven skyrmion applications. This work was supported by the project “ThunderSKY,” funded by the Hellenic Foundation for Research and Innovation (HFRI) and the General Secretariat for Research and Technology (GSRT), under grant agreement No. 871.

**References:**

[1] G. Finocchio et al., J. Phys. D. Appl. Phys. 49, 423001 (2016). [2] X. Z. Yu et al., Nature 465, 901 (2010). [3] S. Woo et al., Nat. Mater. 15, 501 (2016). [4] W. Li et al., Adv. Mater. 1807683, 1 (2019). [5] J. Zázvorka et al., Nat. Nanotech. 14, 658 (2019). [6] Z. Wang et al., Nat. Electron. 3, 672 (2020). [7] R. Tomasello et al. Phys. Rev. B 97, 060402 (2018). [8] R. Tomasello et al. Phys. Rev. B 98, 024421 (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e7af58671e85206fb87cfe24d058a58f.jpg)
Figure 1: skyrmion trajectory under a thermal gradient (gradients of the parameters all at once) in a magnetic multilayer for different ferromagnetic repetitions, as obtained by micromagnetic simulations. The hot and cold regions are located on the left and right side, respectively.

 Micromagnetic study of thermal gradient-driven skyrmion motion in magnetic multilayers

Since the first experimental observation of electrical switching of antiferromagnet[1], the experiments on manipulation of antiferromagnetic order are exploded. However, the theoretical models are still very simplified (sigma model, macrospin approximation). This talk will discuss the recent developments of modeling antiferromagnets and ferromagnets considering a full numerical micromagnetic model. We benchmarked the approach with analytical theories for THz oscillator[2], domain wall and skyrmion dynamics[3], while predicting and describing some features for THz detectors, memories[4] and high speed DW motions [5]. Within this approach, it is possible to take into account three contributions for the exchange interactions (one homogeneous and two inhomogeneous) that are important to identify the two time scales of the antiferromagnetic dynamics. The first, at the THz range, that is related to relaxation processes from a misalignment of the antiferromagnetic state. The second one is related to the relaxation of domains and it is of the same order of the one of the ferromagnetic order. In the last part of the talk, It will discussed the origin of memristive behaviour [4] and the effect of grain sizes in the antiferomagnetic switching experiments.References: 1 P. Wadley, et al, Science, 351, 6273 (2016). 2 V. Puliafito, at al, Phys. Rev. B 99, 024405 (2019). 3 L. Sanchez-Tejerina, et al, Phys. Rev. B, 101, 014433, 2020. A. Salimath, et al Phys. Rev. B, 101, 024429, 2020. 4 S. Chen, G. Finocchio, et al, "Antiferromagnetic PtMn memory devices controlled by electric current" Nature Elettronics, 3, 92-98, 2020. 5 Heng-An Zhou, et al, " Compensated magnetic insulators for extremely fast spin-orbitronics", https://arxiv.org/abs/1912.01775.

Micromagnetic modeling of antiferromagnets INVITED

EOC: Skyrmions I

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.

<iframe width="560" height="315" src="https://s3.amazonaws.com/pf-user-files-01/u-59356/uploads/2022-11-02/un13zp7/MMM%20Welcome%20Video%20v5.mp4" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>

For tickets to the event, please register at the following link: https://magnetism.org/registration

Please register for the MMM 2022 conference to join the event.

MMM 2022

This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

**Session chair:** Denys Makarov, Helmholtz-Zentrum Dresden-Rossendorf


GOL - MRAM, Magnetic Logic and Related Devices II

The 15th Joint MMM-INTERMAG Conference (2022 Joint) 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 plenary session, and an evening session, with about 1500 presentations overall. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

The 2022 Joint Conference will offer both in-person and prerecorded on-demand content.

For tickets to the event, please register at the following link: https://magnetism.org/register

Please register for the Joint MMM-Intermag conference to join the event.

2022 Joint MMM-INTERMAG

**Session chairs:** Jean Anne Incorvia, University of Texas at Austin and Vincent Baltz, Spintec



GOO - Antiferromagnetic Spintronics I

**Session chair:** Romain Lebrun, Unité Mixte de Physique CNRS/Thales



GOP - Antiferromagnetic Spintronics II

**Session chairs:** Riccardo Tomasello, Politecnico di Bari and Mario Carpentieri, Politecnico of Bari



Symposium SB: Spintronic Diodes: Challenges and New Directions

symposium

*Session Chair: Chun-Yeol You, Daegu Gyeongbuk Institute of Science and Technology*

These on-demand presentations are available to view at your leisure.

HC: Skyrmions: DMI and Dynamics

INTERMAG 2021 Welcome Video



	
<figure class="video_container">
 <iframe src="https://screencast-o-matic.com/player/crflqFVnUpZ?v=6&ff=1&title=0&controls=1" width=640 height=360 frameborder="0" allowfullscreen="true"> </iframe>
</figure>

Want to buy a ticket? 

Register for INTERMAG 2021 here

[![](https://assets.underline.io/uploads/markdown_image/1/image/17ce76e7960db633258024eef8d6da7f.png)](https://intermag.org/register)

Got your ticket, but still can’t access the event?

Contact us and our team will look into it.

INTERMAG 2021

M1: Antiferromagnetic Spintronics III

The 65th Annual Conference on Magnetism and Magnetic Materials (MMM 2020) was held in a virtual form. The COVID-19 pandemic, with its associated uncertainty about international travel and the ability to gather in large groups, meant that the Steering Committee decided to cancel the face-to-face meeting that had been planned in Palm Beach, Florida November 2-6, 2020.

We were reluctant to give up the benefits of meeting face-to-face, and know that shifting to a virtual conference is a significant change for this community. Nevertheless, we are first and foremost concerned about the health and safety of all our Conference participants and their loved ones on returning home after travelling.

The MMM 2020 Steering Committee was working exceptionally hard, along with our sponsors, the IEEE Magnetics Society and AIP Publishing, to make this event serve the needs of our participants, who live in time zones all around the globe, in the best possible way. 

You need a ticket to explore this event.

If you have already registered for MMM 2020, and you have already created an account, then you
just need to login (above).

If you have already registered for MMM 2020, but you have not yet created an account, then you
need to click on &quot;create an account&quot; (above) and then login.

Forgot your password? Go to
https://www.underline.io/log-in

If you have not yet registered for MMM 2020 but would like to do so, go to
https://magnetism.org/register

Still need help? Contact our team!


Giovanni Finocchio

7

34

SHORT BIO

Presentations

Skyrmion Caloritronics: a promising Strategy to manipulate Skyrmions

Analog multiplication implemented with spin-torque diodes for neural networks applications

Electrical manipulation of antiferromagnetic order in PtMn and PtMn3 pillars

Observation of current-induced switching in non-collinear antiferromagnetic IrMn3 by differential voltage measurements

Challenges in microwave and THz spintronic diodes

Micromagnetic study of thermal gradient-driven skyrmion motion in magnetic multilayers

Micromagnetic modeling of antiferromagnets INVITED

Stay up to date with the latest Underline news!

PRESENTATIONS

CONFERENCES

COMPANY

RESOURCES