Vortices in ferromagnetic nanotubes

Imaging magnetic vortex configurations in ferromagnetic nanotubes.
M. Wyss, A. Mehlin, B. Gross, A. Buchter, A. Farhan, M. Buzzi, A. Kleibert, G. Tütüncüoglu, F. Heimbach, A. Fontcuberta i Morral, D. Grundler, and M. Poggio
Phys. Rev. B 96, 024423 (2017)

XMCD-PEEM images of a 6.9-$\mu m$-long Py NT with (a) $\hat{k}\perp \hat{n}$ and (b) $\hat{k}\parallel \hat{n}$ and of a 7.2-$\mu m$-long CoFeB NT with (c) $\hat{k}\perp \hat{n}$ and (d) $\hat{k}\parallel \hat{n}$. Dashed outlines indicate the positions of the NTs. Panels (e–h) represent 2-$\mu m$-long $I_{\text{XMCD}}$linecuts along the corresponding colored dashed lines in (a–d). In the linecuts, the background intensity is indicated by the level of the horizontal dashed lines and vertical dashed lines delineate the boundaries of the NT. Panels (i) and (j) show simulated remnant magnetic states for a NT with $l=2.1\mu m$ and $d=245$ nm. Both configurations are mixed states with an axial central domain and vortex ends of either (i) opposing circulation—consistent with (a) and (b)—or (j) matching circulation—consistent with (c) and (d). The color scale corresponds to normalized magnetization along $\hat{y}$. Arrowheads indicate the local magnetization direction.

Single crystalline cylindrical nanowires – toward dense 3D arrays of magnetic vortices : Scientific Reports

Single crystalline cylindrical nanowires – toward dense 3D arrays of magnetic vortices.
Yurii P. Ivanov, Andrey Chuvilin, Laura G. Vivas, Jurgen Kosel, Oksana Chubykalo-Fesenko & Manuel Vázquez
Scientific Reports 6, Article number: 23844 (2016)
Scientific Reports 6, 23844 (2016)

(a) Calculated dependence of the total energy of the vortex and non-vortex state on the length of NWs. (b) The nucleation field of the vortex and the switching field for the vortex core as a function of NW length after saturation in 1 T parallel to the NW axis. (c) Simulated magnetization of single-crystal hcp Co NW with a 75-nm diameter, depending on the length of the NW.

Vortex induced by impurity

Magnetic Vortex Induced by Nonmagnetic Impurity in Frustrated Magnets
Shi-Zeng Lin, Satoru Hayami, and Cristian D. Batista
Phys. Rev. Lett. 116, 187202 (2016)

Vortex solutions for $H_{\mathrm{sat}}<H<H_{\mathrm{sat}}^I$obtained from numerical simulations of $H$ in the classical limit ($S\to \infty$). (a) Vortex bound to a single-site nonmagnetic impurity for different field values. The vortex helicity is arbitrary due to the U(1) symmetry of $H$. (b) Giant vortex solution ($l=\pm 2$) obtained after removing the spins from the six sites indicated with black dots, for $J_3=-0.2777J_1$ and $Q=2\pi /12$. The saturation field is $H_{\mathrm{sat}}=0.02235\left|J_1\right|$ and $H_{\mathrm{sat}}^I=0.04725\left|J_1\right|$.

Non-Boolean computing with nanomagnets for computer vision applications : Nature Nanotechnology : Nature Publishing Group

Non-Boolean computing with nanomagnets for computer vision applications.
Sanjukta Bhanja, D. K. Karunaratne, Ravi Panchumarthy, Srinath Rajaram, Sudeep Sarkar

Nature Nanotechnology 11, 177 (2016)

Stages in object recognition:a, Grey-scale satellite image of an urban area. b, Edge image with extracted edge segments from a. c, Traditional approach to solving a quadratic optimization process using a CMOS-based arithmetic and logic unit (ALU). d, Proposed method to solve the quadratic optimization process using a magnetic coprocessor. e, Salient edge segments identified from b using the method in c. f, Objects identified using salient edges obtained from e.

Vortex core in a single NP

Switching the Magnetic Vortex Core in a Single Nanoparticle.
Elena Pinilla-Cienfuegos, Samuel Mañas-Valero, Alicia Forment-Aliaga, and Eugenio Coronado
ACS Nano 10, 1764 (2016)

Here we report the experimental observation of the vortex state formation and annihilation in individual 25 nm molecular-based magnetic nanoparticles measured by low-temperature variable-field magnetic force microscopy. Interestingly, in these nanoparticles the switching of the vortex core can be induced with very small values of the applied static magnetic field.

Spin configurations in a single Fe cube

Size-Specific Spin Configurations in Single Iron Nanomagnet: From Flower to Exotic Vortices.

Christophe Gatel, Francisco Javier Bonilla, Anca Meffre, Etienne Snoeck, Bénédicte Warot-Fonrose, Bruno Chaudret, Lise-Marie Lacroix, and Thomas Blon

Nano Letters 15, 6952 (2015)

Giant moving vortex mass

Giant moving vortex mass in thick magnetic nanodots.
K. Y. Guslienko, G. N. Kakazei, J. Ding, X. M. Liu & A. O. Adeyeye
Scientific Reports 5, 13881 (2015)

The frequency of the lowest vortex gyrotropic mode vs. dot thickness, ω₀(L) 2p: red squares – the experimental data, blue solid line – the simulated frequencies, green solid line – the calculations according to Eq. (4) accounting vortex mass, black dashed line – calculations without accounting for the vortex mass.

Vortex dynamics in arrays of nanomagnets

Observation of vortex dynamics in arrays of nanomagnets.
W. Yu, P. S. Keatley, P. Gangmei, M. K. Marcham, T. H. J. Loughran, R. J. Hicken, S. A. Cavill, G. van der Laan, J. R. Childress, and J. A. Katine
Phys. Rev. B 91, 174425 (2015)

TRSKM images, XPEEM images, and SEM images of arrays of 250-nm squares with separation of 500 nm in (a) and (b), and 50 nm in (c). After acquisition of the TRSKM images in (a), the equilibrium state was reinitialized before acquiring the TRSKM images in (b). In all TRSKM images the horizontal white bar has length of 1 μm. In (c) the white arrows in the TRSKM images denote regions of contrast with size comparable to, or larger than, that of a single element, while the dashed white rectangle in the XPEEM image highlights a cluster of elements with vortex equilibrium states. (d) Enlarged view of (c), in which the black grid position is a guide to the eye to show where the individual elements lie, and the white boxes highlight regions of contrast

Vortex state by electric measurements

Electrical determination of vortex state in submicron magnetic elements.

Ajay Gangwar, Hans G. Bauer, Jean-Yves Chauleau, Matthias Noske, Markus Weigand, Hermann Stoll, Gisela Schütz, and Christian H. Back 

Phys. Rev. B 91, 094407 (2015)

AMR spectra measured on a disk shaped sample for (a) up (p=+1) and (b) down (p=−1) polarization of the vortex core for an excitation current of 1.2 mA. The sample design is shown in the inset of (a). By applying a rotating current (counterclockwise or clockwise) the VC polarity can be switched selectively to up or down. A sign change of the AMR voltage signal can be observed for the two polarities. Note that a significant shift of the resonance frequency to higher frequencies is observed at larger bias fields. Also note that the fine structure observed in the spectra does not depend on the VC polarity.

Switching of magnetic skyrmion cores in nanodots

Microwave-induced dynamic switching of magnetic skyrmion cores in nanodots.
Bin Zhang, Weiwei Wang, Marijan Beg, Hans Fangohr and Wolfgang Kuch

Appl. Phys. Lett. 106, 102401 (2015)

Spin dynamics of the skyrmion excited by an AC magnetic field hωz=hω sin(ωt) with hω=2.4×10−3 up to time 25 000 (∼16.5 ns for J = 1 meV and S = 1). Selected time evolution of the magnetization distribution with two examples: (a) ωa  = 3.6 × 10⁻³, taoff=1750 and (b) ωb  = 1.4 × 10⁻², tboff=5600 . The color-coded mz (out-of-plane) and mx (in-plane) components of the magnetization are displayed in the first and third line, respectively, while the second line displays a perspective view (topography) with the color code of mz . (c) Time trace of the magnetization component mz (top graph), the AC magnetic field (dashed lines), and the skyrmion number (both in bottom graph). Black and red lines refer to the data of the two different examples, while the black circles and red prisms indicate the times corresponding to the snapshots shown in (a) and (b), respectively

Magnetic Vortex Nanorings: application to hysperthermia and simulations

Some recent articles related to the proposal of using Fe oxide nanorings for magnetic hyperthermia.

1) Magnetic Vortex Nanorings: A New Class of Hyperthermia Agent for Highly Efficient In Vivo Regression of Tumors.
Xiao Li Liu, Yong Yang, Cheng Teng Ng, Ling Yun Zhao, Ying Zhang, Boon Huat Bay, Hai Ming Fan, and Jun Ding
Advanced materials 27, 1939 (2015)

The unique magnetic vortex structure allows ferrimagnetic vortex-domain iron oxide nanorings to possess negligible remanence and large hysteresis loss, which not only promotes colloid stability but also maximizes the specific absorption rate. It overcomes the super-paramagnetic limitation and allows a new class of nanoparticle agent to be designed for high-performance thermal-based biomedical applications.

2) Innovative magnetic nanoparticle platform for magnetic resonance imaging and magnetic fluid hyperthermia applications
Xiao Li Liu, Hai Ming Fan
Current Opinion in Chemical Engineering 4, 38 (2014)

Illustration of representative NP agent comprised of magnetic core and shell coating for biorelated applications.

3) Stable vortex magnetite nanorings colloid: Micromagnetic simulation and experimental demonstration.
Yong Yang, Xiao-Li Liu, Jia-bao Yi, Yang Yang, Hai-Ming Fan, and Jun Ding
J. Appl. Phys. 111, 044303 (2012)

(a)-(c) The simulated ground states (F_out, vortex, and onion, respectively) of magnetite nanorings with different geometry. (d) Ground state phase diagram of magnetite nanorings as a function of T and D_out with β = 0.8 (black triangles), 0.6 (red squares), and 0.4 (blue circles). Solid symbols show the boundaries between the vortex, F_out (out-of-plane ferromagnetic) and F_in (in-plane ferromagnetic) configurations.

Vortices in nano objects

Stabilizing Vortices in Interacting Nano-Objects: A Chemical Approach.Lise-Marie Lacroix, Sébastien Lachaize, Florian Hue, Christophe Gatel, Thomas Blon, Reasmey P. Tan, Julian Carrey, Bénédicte Warot-Fonrose, and Bruno Chaudret
Nano Letters12, 3245 (2012)

We report a chemical method to prepare metallic Fe porous nanocubes. The presence of pores embedded inside the cubes was attested by electron tomography. Thanks to electronic holography and micromagnetic simulations, we show that the presence of these defects stabilizes the vortices in assembly of interacting cubes. These results open new perspectives toward magnetic vortex stabilization at relatively low cost for various applications (microelectronics, magnetic recording, or biological applications).

Logic operations using vortex networks

Logic Operations Based on Magnetic-Vortex-State Networks.
Hyunsung Jung, Youn-Seok Choi, Ki-Suk Lee, Dong-Soo Han, Young-Sang Yu, Mi-Young Im,
Peter Fischer, and Sang-Koog Kim
Nano Letters 6, 3712 (2012)

Experimental setup for the direct demonstration of XOR logic operation using the indicated vortex-state network
and full-field soft X-ray microscopy. Schematic layout of soft X-ray measurement setup for direct readout of output signals in disk 2, showing the sample (chain of three vortex-state Py disks) with electrodes on both end disks for application of input signals. Equal diameter 2R = 2.4 μm, thickness L = 50 nm, and center-to-center distance dint = 2.46 μm are used for the experimental sample. The right inset shows the initial ground vortex states measured by the microscope through XMCD
contrast (the same as those shown in Figure 1). Sinusoidal oscillating magnetic fields of 4.5 Oe amplitude and 160 MHz
frequency are applied to disk 1 and/or disk 3.

Phase diagram for vortex dynamics

Phase diagram of magnetic vortex dynamics.
T. Y. Chen, A. T. Galkiewicz, and P. A. Crowell
Phys. Rev. B 85, 180406 (2012)

Gyrotropic response as a function of excitation amplitude and frequency for (a) experiment and (b) numerical calculations. The experimental parameter space is above the horizontal dashed line in (b). The color scale is logarithmic. The contours are shown for increasing amplitude. The dashed curve in (b) shows the lower boundary of the region in which two gyrotropic
orbits exist.

Modeling vortices in nanodisks by simulations

I have compiled a collection of articles from the Brazilian group of B. V. Costa and collegues on the subject of simulation of vortex structures on nanodots. I hope they will be of interest to you:

Analytical and Monte Carlo study of two antidots in magnetic nanodisks
with vortex-like magnetization
A. R. Pereira, A. R. Moura, W. A. Moura-Melo, D. F. Carneiro, S. A. Leonel and P. Z. Coura
J. Appl. Phys. 101, 034310 (2007)

A model for vortex formation in magnetic nanodots
S. A. Leonel, I. A. Marques, P. Z. Coura, and B. V. Costa
J. Appl. Phys. 102, 104311 (2007)

Diagram for vortex formation in quasi-two-dimensional magnetic dots
J. C. S. Rocha, P. Z. Coura, S. A. Leonel, R. A. Dias, and B. V. Costa
J. Appl. Phys. 107, 053903 (2010)

Magnetic vortex formation and gyrotropic mode in nanodisks.
D. Toscano, S. A. Leonel, R. A. Dias, P. Z. Coura, J. C. S. Rocha  and B. V. Costa
J. Appl. Phys. 109, 014301 (2011)

Nonlinear gyration of a vortex

Nonlinear magnetic vortex gyration.
André Drews, Benjamin Krüger, Gunnar Selke, Thomas Kamionka, Andreas Vogel, Michael Martens, Ulrich Merkt, Dietmar Möller, and Guido Meier
Phys. Rev. B 85, 144417 (2012)

(a) Simulated trajectory (blue triangles) and trajectory obtained from Eq. (3) (solid line) in a permalloy square
with an edge length of 200 nm and a thickness of 10 nm. The dashed line denotes the solution for vanishing nonquadratic terms of the potential. The vortex is excited with j0 = 1 × 1011 Am−2 and gyrates resonantly at = 2.56 × 109 s−1 (2.71 × 109 s−1) for vanishing (nonvanishing) nonlinear terms. (b) Simulated magnetization patterns and corresponding isolines in the steady state at instants of time t = 0.57T , 0.74T , and 0.84T of one gyration period T.