Vortex phase boundaries from ferromagnetic resonance measurements in a patterned disc array

Abstract

Using a recently developed broadband microwave measurement technique, we have studied the hysteretic appearance and disappearance with in-plane magnetic field of the uniform ferromagnetic resonance ͑FMR͒ mode of a patterned permalloy disk array. The observed features are consistent with our micromagnetic simulations ͑performed on an infinite array of such disks͒, which predict that on decreasing the magnetic field from a positively magnetized state at positive fields the array will: ͑i͒ pass continuously into a double-vortex state; ͑ii͒ followed by a discontinuous transition to a single-vortex state; and finally ͑iii͒ discontinuously into a negatively magnetized state at some negative field. The hysteretic counterpart occurs on reversing the field sweep and returning to positive fields. The FMR data are consistent with the hysteretic dc magnetization measurements performed earlier on samples patterned in an identical manner.There has recently been much interest in measuring the ferromagnetic resonance ͑FMR͒ spectrum of patterned nanostructured magnetic arrays. As an early example, measurements on square permalloy ͑Py͒ disk arrays showed the presence of multiple absorption lines, the structure of which changed with the in-plane field angle, clear evidence of a disk-disk interaction. 1,2 Measurements have also been carried out on a wide variety of other structures such as rings, 3 holes, 4 ellipsoidal holes, 5 etc. Evolving in parallel have been micromagnetic strategies to calculate the FMR spectrum of nanostructures. Two approaches have proved popular both of which are based on representing nanostructures as discrete dipoles positioned on a lattice each one of which precesses under the influence of static and dynamic, homogeneous or inhomogeneous, external applied fields as well as internal fields arising from exchange, magnetic anisotropy, and the field produced by the remaining dipoles, all evolving according to the Landau-Lifshitz ͑LL͒ equation. In the first of these approaches one carries out a brute-force time integration of the coupled LL equations subject to some initial conditions. The widely used NIST OOMMF code is freely available for this task; 6 alternatively there is the RKMAG code. 7 The first approach is necessarily slow running and does not yield mode frequencies directly, which must be obtained by analyzing the response; 8 however it has the virtue of being able to handle the full nonlinear behavior. The second approach linearizes the equations of motion thereby yielding an eigenvalue problem from which all the mode frequencies emerge at once; 9 codes utilizing this approach are also freely available. 7 Using the eigenvectors of the associated matrix one can directly calculate the absorption spectrum for an arbitrary harmonic driving field. 10 The approach was recently generalized to treat the static and dynamic properties of periodic nanostructures. 11In disk and ring nanostructures the lowest-energy state is a vortex in which the local magnetization vectors lie on concentric circles in the plane...

The wasp-waisted hysteresis loop and exchange bias in multiferroic BaNiF4

“…12 The wasp-waisted type M-H curves are often observed in those magnetic vortex system, where the spins tend to align circlewise at low magnetic fields and parallel to the magnetic field when the field is large enough. 13 It has also been pointed by Spaldin that the AFM aligned net spins due to spin canting are easy to be aligned. 7 Thus, we give a short explanation for the observed weak ferromagnetism in BaNiF 4 .…”

Magnon dispersion in thin magnetic films

“…Knowing the energy of the excited magnons, we can construct the dispersion by assigning wave vectors to every peak according to (1). Note, however, that some of the peaks do not come in pairs and are thus not related to magnetic excitations but to features in the density of states.…”

Ferromagnetic Resonance

“…Besides using FMR to characterize magnetic properties, it also allows one to study the fundamental excitations and technological applications of a magnetic system (Schmool, 1998;Voges, 1998;Zianni, 1998;Grünberg, 2000Grünberg, , 2001Vlasko-Vlasov, 2001;Zhai, 2003;Birkhäuser Verlag, 2007;Seib, 2009). The various thickness, disk array, half-metallic ferromagnetic electrodes, magnon scattering and other of some properties of samples have been studied using the FMR tehniques (Mazur, 1982;da Silva, 1993;Chikazumi, 1997;Song, 2003;Rameev, 2003Rameev, (a), 2003, 2004(a), 2004(b); Ramprasad, 2004;Xu, 2004;Wojtowicz, 2005;Zakeri, 2007;Tsai, 2009;Chen, 2009). The magnetic properties of single-crystalline (Kambe, 2005;Brustolon, 2009), polycrystalline (Singh, 2006;Fan, 2010), alloy films (Sihues, 2007), temperature dependence and similar qualities have been studied electromagnetic spectroscopy techniques (Özdemir, 1998;Fermin, 1999;Rameev, 2000;Aktaş, 2001;Budak, 2003;.…”