Magnetization reversal and soft modes in nanorings: Transitions between onion and vortex states studied by Brillouin light scattering

F. Montoncello, L. Giovannini, F. Nizzoli, H. Tanigawa, T. Ono, G. Gubbiotti, M. Madami, S. Tacchi, and G. Carlotti

Phys. Rev. B 78, 104421 – Published 26 September 2008

Abstract

We present a joint experimental and theoretical investigation of the magnetization reversal process in an array of circular permalloy nanorings. The longitudinal hysteresis loop measured by magneto-optic Kerr effect exhibits the typical two-step switching behavior corresponding to transition from the onion to the vortex state and vice versa with plateaux in each loop branch. The frequencies of the spin excitations in these configurations calculated by means of the dynamical matrix approach are in good agreement with those measured by Brillouin light scattering. Several types of spin modes are found localized in different regions of the rings. It is found that the onion-to-vortex and the vortex-to-onion transitions are triggered by soft spin modes. The shape and symmetry of the dynamic magnetization profile of these soft modes provide the initial modifications of the magnetization at the onset of the transitions.

Received 30 April 2008

DOI:https://doi.org/10.1103/PhysRevB.78.104421

Authors & Affiliations

F. Montoncello¹, L. Giovannini¹, F. Nizzoli¹, H. Tanigawa², T. Ono², G. Gubbiotti³, M. Madami³, S. Tacchi³, and G. Carlotti^3,4

¹Dipartimento di Fisica, Università di Ferrara and CNISM, Via Saragat 1, I-44100 Ferrara, Italy
²Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan
³CNISM, Dipartimento di Fisica, Università di Perugia, Via A. Pascoli, I-06123 Perugia, Italy
⁴Research Center INFM-CNR S3, I-44100 Modena, Italy

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Issue

Vol. 78, Iss. 10 — 1 September 2008

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Images

Figure 1
Experimental longitudinal Kerr hysteresis loop (symbols). Calculated loop in the micromagnetic approach: solid line refers to increasing applied field, dotted line to decreasing field. $M_{y} / M_{s}$ is the component of the magnetization in the direction of the applied field in unit of the saturation magnetization $M_{s}$ . Five configurations of the equilibrium magnetization are sketched and labeled by Roman numbers: onion state (phase I), distorted onion states (II and III), vortex state (IV), and reversed-onion state (V). The inset shows the reference system.Reuse & Permissions
Figure 2
BLS measured frequencies of the spin modes (symbols) starting from negative to positive applied field values. The calculated frequency dispersions of the modes (lines) are labeled according to the character of the modes. $(m, n)$ are vortex modes. DE, BA, F, and EM are Damon-Eshbach-type, backwardlike, fundamental, and end modes, respectively. The two thin vertical lines mark the critical fields $H_{c 1} = 110 Oe$ (onion-to-vortex transition) and $H_{c 2} = 417 Oe$ (vortex-to-onion transition).Reuse & Permissions
Figure 3
The $y$ component $H_{i y}$ of the internal magnetic field represented in grayscale (Oe). Left-hand side: onion state for an applied field $H = - 440 Oe$ . Right-hand side: vortex state for $H = 417 Oe$ . The $y$ axis points upward.Reuse & Permissions
Figure 4
Calculated (normal) $z$ component of the dynamic magnetization of the (a) antisymmetric and (b) symmetric F-loc modes localized in the upper and lower sectors of the ring. The dynamic magnetization is represented in grayscale (arbitrary units). The dot is in the onion state and $H = - 440 Oe$ (directed downwards).Reuse & Permissions
Figure 5
Calculated (normal) $z$ component of the dynamic magnetization of the four end modes. (a) AS outer EM, (b) S outer EM, (c) AS inner EM, and (d) S inner EM. The dynamic magnetization is represented in grayscale (arbitrary units). The dot is in the onion state and $H = - 440 Oe$ (directed downwards). “Outer” modes are mainly localized close to the external border of the ring. “Inner” modes are mainly localized close to the internal border with a V-shape pattern.Reuse & Permissions
Figure 6
Magnetic equilibrium configuration [(a) and (c)] and $x$ component of the dynamic magnetization of the corresponding soft modes [(b) and (d)] just before the phase transitions. The upper row refers to $H = 110 Oe$ (before the onion-to-vortex transition), the lower row refers to $H = 417 Oe$ (before the vortex-to-onion transition). The dynamic magnetization is represented in grayscale (arbitrary units). The applied field $H$ is directed upwards.Reuse & Permissions

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