Coherent Precession Of Magnetization Research Articles

Direct observation of the transition from spin waves to the magnon Bose condensate

Bose-Einstein condensation occurs at an appropriate density of bosonic particles, depending on their mass and temperature. The transition from the semiclassical paradigm of spin waves to the magnon Bose-Einstein condensed state (mBEC) was obtained experimentally with increasing magnon density. We used the Faraday rotation effect to study the spatial distribution of the magnon density and phase far from their excitation region. A coherent magnetization precession was observed throughout the sample, which indicates the formation of a magnon BEC. It is shown that this result under experimental conditions goes beyond the applicability of the Landau-Lifshitz-Gilbert semiclassical theory.

Magneto-optical imaging of coherent spin dynamics in ferrites.

The explosive development of quantum magnonics is associated with the possibility of its use as macroscopic quantum systems. In particular, they can find an application for quantum computing processors and other devices. The recently discovered phenomenon of magnon Bose-Einstein condensation and coherent precession of magnetization can be used for these purposes. Our letter describes a method for the optical observation of the coherently precessing magnetization in conditions when the concentration of magnons reaches the value necessary for their quantum condensation. The investigations were conducted in the out-of-plane magnetized yttrium iron garnet films. The required magnon density was achieved by magnetic resonance technique. The magneto-optical imaging method provides such important parameters of the coherent spin dynamics as the amplitude and phase distributed all over the sample. It should become an indispensable read-out tool for the upcoming quantum technologies based on the magnon Bose-Einstein condensation.

Dynamical spin phenomena generated by longitudinal elastic waves traversing CoFe2O4 films and heterostructures

Electric-field control of spin dynamics in ferromagnetic films and heterostructures is crucial for the development of advanced spintronic devices with ultralow power consumption. Such control can be achieved via the magnetoelastic coupling between spins and strains created in a ferromagnet by the attached piezoelectric transducer. The efficiency of strain-mediated excitation and manipulation of spin phenomena is expected to increase drastically in materials with high magnetoelastic coefficients, such as cobalt ferrite. Here we report the state-of-the-art micromagnetic simulations of the spin dynamics arising in ${\mathrm{CoFe}}_{2}{\mathrm{O}}_{4}$ films and ${\mathrm{CoFe}}_{2}{\mathrm{O}}_{4}$/Pt bilayers traversed by longitudinal elastic waves. To fully allow for the magnetoelastic coupling, we numerically solve a system of differential equations involving the Landau-Lifshitz-Gilbert equation for the magnetization and the elastodynamic equation for the mechanical displacement. The simulations show that, despite high Gilbert damping characteristic of cobalt ferrite, the injected elastic waves with frequencies around the resonance frequency of coherent magnetization precession in unstrained ${\mathrm{CoFe}}_{2}{\mathrm{O}}_{4}$ film efficiently generate spin waves in this ferrimagnetic insulator. Furthermore, the generated spin wave, which has the wavelength of the driving acoustic wave, creates two secondary elastic waves due to the magnetoelastic feedback. In addition, it modifies the driving elastic wave, leading to the sound attenuation of magnetic origin with decay length about 70 $\ensuremath{\mu}\mathrm{m}$. In ${\mathrm{CoFe}}_{2}{\mathrm{O}}_{4}$/Pt bilayers, the magnetization precession at the interface gives rise to a spin current flowing in the Pt layer, which creates additional damping of the precession and generates a charge current via the inverse spin Hall effect. Remarkably, a circular charge flow is predicted for thick Pt layers, which leads to inhomogeneous potential distributions along their surfaces. The magnitude of the voltage between lateral sides of the Pt layer may exceed 1 nV, which can be measured experimentally.

Picosecond acoustic-excitation-driven ultrafast magnetization dynamics in dielectric Bi-substituted yttrium iron garnet

Using femtosecond optical pulses, we have investigated the ultrafast magnetization dynamics induced in a dielectric film of bismuth-substituted yttrium iron garnet (Bi-YIG) buried below a thick Cu/Pt metallic bilayer. We show that exciting the sample from Pt surface launches an acoustic strain pulse propagating into the garnet film. We discovered that this strain pulse induces a coherent magnetization precession in the Bi-YIG at the frequency of the ferromagnetic resonance. The observed phenomena can be explain by strain-induced changes of magnetocristalline anisotropy via the inverse magnetostriction effect. These findings open new perspectives toward the control of the magnetization in magnetic garnets embedded in complex heterostructure devices.

Nonlinear NMR and magnon BEC in antiferromagnetic materials with coupled electron and nuclear spin precession

We present a new study of nonlinear NMR and Bose-Einstein Condensation (BEC) of nuclear spin waves in antiferromagnetic MnCO3 with coupled electron and nuclear spins. In particular, we show that the observed behaviour of NMR signals strongly contradicts the conventional description of paramagnetic ensembles of noninteracting spins based on the phenomenological Bloch equations. We present a new theoretical description of the coupled electron-nuclear spin precession, which takes into account an indirect relaxation of nuclear spins via the electron subsystem. We show that the magnitude of the nuclear magnetization is conserved for arbitrary large excitation powers, which is drastically different from the conventional heating scenario derived from the Bloch equations. This provides strong evidence that the coherent precession of macroscopic nuclear magnetization observed experimentally can be identified with BEC of nuclear spin waves with k=0.

Coupled magnetic and elastic dynamics generated by a shear wave propagating in ferromagnetic heterostructure

Using advanced micromagnetic simulations, we describe the coupled elastic and magnetic dynamics induced in ferromagnet/normal metal bilayers by shear waves generated by the attached piezoelectric transducer. Our approach is based on the numerical solution of a system of differential equations, which comprises the Landau-Lifshitz-Gilbert equation and the elastodynamic equation of motion, both allowing for the magnetoelastic coupling between spins and lattice strains. The simulations have been performed for heterostructures involving a Fe81Ga19 layer with the thickness ranging from 100 to 892 nm and a few-micrometer-thick film of a normal metal (Au). We find that the traveling shear wave induces inhomogeneous magnetic dynamics in the ferromagnetic layer, which generally has an intermediate character between coherent magnetization precession and the pure spin wave. Owing to the magnetoelastic feedback, the magnetization precession generates two additional elastic waves (shear and longitudinal), which propagate into the normal metal. Despite such complex elastic dynamics and reflections of elastic waves at the Fe81Ga19|Au interface, periodic magnetization precession with the excitation frequency settles in the steady-state regime. The results obtained for the magnetization dynamics at the Fe81Ga19|Au interface are used to evaluate the spin current pumped into the Au layer and the accompanying charge current caused by the inverse spin Hall effect. The calculations show that the dc component of the charge current is high enough to be detected experimentally even at small strains ∼10−4 generated by the piezoelectric transducer.

The magnon BEC observation by switch off method

The Bose–Einstein condensation (BEC) corresponds to the formation of a collective quantum state in which macroscopic number of particles is governed by a single wave function. The magnon BEC forms by excited non-equilibrium magnons and manifests itself by coherent precession of magnetization even in an inhomogeneous magnetic field. The magnon BEC is very similar to an atomic BEC, but the potential of the interaction between magnons may variate very significantly. The superfluid phases of 3He are the best antiferromagnetic system for investigations of magnon BEC and spin superfluidity. The 6 different states of magon BEC were observed in 3He. Recently magnon BEC was observed in antiferromagnets with Suhl–Nakamura interaction and ferrites. Here we review for the first time the switch off NMR method, when magnon BEC forms during a long radiofrequency pulse. The new experimental results are discussed.

Effective Minkowski-to-Euclidean signature change of the magnon BEC pseudo-Goldstone mode in polar 3He

We discuss the effective metric experienced by the Nambu-Goldstone mode propagating in the broken symmetry spin-superfluid state of coherent precession of magnetization. This collective mode represents the phonon in the RF driven or pulsed out-of-equilibrium Bose-Einstein condensate (BEC) of optical magnons. We derive the effective BEC free energy and consider the phonon spectrum when the spin superfluid BEC is formed in the anisotropic polar phase of superfluid 3He, experimentally observed in uniaxial aerogel 3He-samples. The coherent precession of magnetization experiences an instability at a critical value of the tilting angle of external magnetic field with respect to the anisotropy axis. From the action of quadratic deviations around equilibrium, this instability is interpreted as a Minkowski-to-Euclidean signature change of the effective phonon metric. We also note the similarity between the magnon BEC in the unstable region and an effective vacuum scalar "ghost" condensate.

Double permeability peaks in Ce9Fe91films with in-plane uniaxial anisotropy

Ce9Fe91films were fabricated at different temperature by Rf magnetron sputtering. The static and dynamic magnetic properties of these films have been investigated in details. The results reveal that the two films prepared at 293K and 623K with the critical film thickness exhibit weak stripe domains and a small perpendicular anisotropy, and their correlated dynamic permeability spectra show one resonance peak, implying the coherent precession of magnetization at such critical thickness. However, the film prepared at 523K possesses an in-plane uniaxial anisotropy and lower coercive field. And the permeability spectrum displays two peaks, which can be ascribed to the coexistence of the rotatable anisotropy and in-plane uniaxial anisotropy.

Magnetization dynamics and spin pumping induced by standing elastic waves

The magnetization dynamics induced by standing elastic waves excited in a thin ferromagnetic film is described with the aid of micromagnetic simulations taking into account the magnetoelastic coupling between spins and lattice strains. The simulations have been performed for the 2 nm thick Fe81Ga19 film dynamically strained by longitudinal and transverse standing waves with various frequencies, which span a wide range around the resonance frequency nu_res of coherent magnetization precession in unstrained Fe81Ga19 film. It is found that standing elastic waves give rise to complex local magnetization dynamics and spatially inhomogeneous dynamic magnetic patterns. The spatio-temporal distributions of the magnetization oscillations in standing elastic waves have the form of standing spin waves with the same wavelength. Remarkably, the amplitude of magnetization precession does not go to zero at the nodes of these spin waves, which cannot be precisely described by simple analytical formulae. In the steady-state regime, the magnetization oscillates with the frequency of elastic wave, except for the case of longitudinal waves with frequencies well below nu_res, where the magnetization precesses with a variable frequency strongly exceeding the wave frequency. The precession amplitude at the antinodes of standing spin waves strongly increases when the frequency of elastic wave becomes close to nu_res. The results obtained for the magnetization dynamics driven by elastic waves are used to calculate the spin current pumped from the dynamically strained ferromagnet into adjacent paramagnetic metal. Importantly, the transverse charge current created by the spin current via the inverse spin Hall effect is high enough to be measured experimentally.

Magnon BEC Versus Atomic BEC

The Bose–Einstein condensation (BEC) corresponds to the formation of a collective quantum state in which macroscopic number of particles is governed by a single wave function. The magnon BEC, the coherent state of a macroscopic number of magnons, manifests itself by coherent precession of magnetization even in an inhomogeneous magnetic field. The magnon BEC has many similarities with the atomic BEC. But it shows a great variety of properties in different magnetic materials. Here we will classify the different types of magnonic BECs.

BEC of magnons in superfluid3He-Band symmetry breaking fields

States with a coherent precession of magnetization such as a homogeneously precessing domain or a persistently precessing domain created in the superfluid ${}^{3}$He-$B$ represent the macroscopic examples of the Bose-Einstein condensates of magnons. Once the magnons form one of these states, this many-magnon coherent quantum state is described by a ``single-magnon wave function'' (or an order parameter). A suitable external perturbation may cause the condensate to oscillate around the state of coherent precession, which demonstrates a collective rigidity of the condensate against scattering a single magnon out of it. The states corresponding to a free coherent precession of magnetization are degenerate in the phase of precession, so there exist oscillations around such states with a gapless dispersion relation, known as the Goldstone modes. Here, we present both experimental and theoretical results of the study of the spin density oscillations superposed on a homogeneously precessing domain in superfluid ${}^{3}$He-$B$ in the presence of a high-frequency excitation field ${B}_{\text{rf}}$. We show that the presence of this field lifts the degeneracy of the precessing state with respect to the phase of precession, that is, it violates the symmetry of the magnon condensate, and former Goldstone modes become non-Goldstone ones, as they acquire the energy gap in their spectrum.

Theory of magnetization precession induced by a picosecond strain pulse in ferromagnetic semiconductor (Ga,Mn)As

A theoretical model of the coherent precession of magnetization excited by a picosecond acoustic pulse in a ferromagnetic semiconductor layer of (Ga,Mn)As is developed. The short strain pulse injected into the ferromagnetic layer modifies the magnetocrystalline anisotropy resulting in a tilt of the equilibrium orientation of magnetization and subsequent magnetization precession. We derive a quantitative model of this effect using the Landau-Lifshitz equation for the magnetization that is precessing in the time-dependent effective magnetic field. After developing the general formalism, we then provide a numerical analysis for a certain structure and two typical experimental geometries in which an external magnetic field is applied either along the hard or the easy magnetization axis. As a result we identify three main factors, which determine the precession amplitude: the magnetocrystalline anisotropy of the ferromagnetic layer, its thickness, and the strain pulse parameters.

Coherent Magnetization Precession in Ferromagnetic (Ga,Mn)As Induced by Picosecond Acoustic Pulses

We show that the magnetization of a thin ferromagnetic (Ga,Mn)As layer can be modulated by picosecond acoustic pulses. In this approach a picosecond strain pulse injected into the structure induces a tilt of the magnetization vector M, followed by the precession of M around its equilibrium orientation. This effect can be understood in terms of changes in magnetocrystalline anisotropy induced by the pulse. A model where only one anisotropy constant is affected by the strain pulse provides a good description of the observed time-dependent response.

Magnon Bose–Einstein condensation and spin superfluidity

Bose–Einstein condensation (BEC) is a quantum phenomenon of formation of a collectivequantum state in which a macroscopic number of particles occupy the lowest energy stateand thus is governed by a single wavefunction. Here we highlight the BEC in a magneticsubsystem—the BEC of magnons, elementary magnetic excitations. The magnon BEC ismanifested as the spontaneously emerging state of the precessing spins, in whichall spins precess with the same frequency and phase even in an inhomogeneousmagnetic field. The coherent spin precession was observed first in superfluid 3He-B and this domain was called the homogeneously precessing domain (HPD).The main feature of the HPD is the induction decay signal, which ranges overmany orders of magnitude longer than is prescribed by the inhomogeneity ofmagnetic field. This means that spins precess not with a local Larmor frequency, butcoherently with a common frequency and phase. This BEC can also be created andstabilized by continuous NMR pumping. In this case the NMR frequency playsthe role of a magnon chemical potential, which determines the density of themagnon condensate. The interference between two condensates has also beendemonstrated. It was shown that HPD exhibits all the properties of spin superfluidity. Themain property is the existence of a spin supercurrent. This spin supercurrentflows separately from the mass current. Transfer of magnetization by the spinsupercurrent by a distance of more than 1 cm has been observed. Also related phenomenahave been observed: the spin current Josephson effect; the phase-slip processes atthe critical current; and the spin current vortex—a topological defect which isthe analog of a quantized vortex in superfluids and of an Abrikosov vortex insuperconductors; and so on. It is important to mention that the spin supercurrent is amagnetic phenomenon, which is not directly related to the mass superfluidity of 3He: it is the consequence of a specific antiferromagnetic ordering in superfluid 3He. Several different states of coherent precession have been observed in 3He-B: the homogeneously precessing domain (HPD); a persistent signal formed byQ-balls at very low temperatures; coherent precession with fractionalmagnetization; and two new modes of coherent precession in compressedaerogel. In compressed aerogel the coherent precession has been also found in 3He-A. We demonstrate that the coherent precession of magnetization is a true BEC ofmagnons, with the magnon interaction term in the Gross–Pitaevskii equation beingprovided by spin–orbit coupling which is different for different states of the magnonBEC.

Effect of dipole interaction on microwave assisted magnetization switching

Microwave assisted switching (MAS) of magnetization has attracted much attention as an alternative technique for future ultrahigh density magnetic recording. In this study, to elucidate the effect of magnetostatic interparticle interaction on MAS, we have calculated the switching behavior for a row of three uniaxial magnetic particles as a simplest case. When a dc field is applied only to one particle of the row in an ac field, MAS selectively occurs in the particle and not in the neighboring particles. This behavior may be very effective to realize narrow track recording without adjacent track erasure problem by downsizing a dc field source below an ac source. It has been also found that when both ac and dc fields are applied to all the particles, coherent magnetization precession is cooperatively induced in all the particles due to dipole-dipole interaction among neighboring particles, resulting in significant reduction of the switching field. This coherent magnetization precession is not only effective to reduce the switching field but also to suppress the effect of magnetic anisotropy dispersion, suggesting the effectiveness of MAS in granular recording media.

Coherent precession of magnetization in superfluid 3He A-phase in aerogel

The coherent precession in bulk 3He A-phase is unstable due to the positive feedback of spin supercurrent to the gradient of phase of precession. It was predicted that the homogeneous precession will be stable if the orbital momentum could be oriented along the magnetic field. [7] We have found that the orbital part of order parameter in 3He A-phase immersed in aerogel orients along the direction of aerogel axial squeezing. By this method we have oriented the orbital momentum of 3He A-phase along the magnetic field and studied non-linear NMR properties. By cw-NMR we have succeeded to form the state with Coherent Precession in 3He A-phase (CP-A), which is analog of Homogeneous Precession Domain (HPD) in 3He B-phase. We have found that the dissipation of CP-A and HPD in aerogel is much larger than in bulk superfluid 3He and depends from sample to sample. We propose a model to explain enhancement of the dissipation in CP-A, which takes into account the spin diffusion of inhomogeneous magnetization created by fluctuations of the condensation energy of Cooper pair in aerogel.

Coherent Precession of Magnetization in the SuperfluidHe3A-Phase

We report the first observation of coherent precession of magnetization in superfluid 3He A-like phase (CP-A) in aerogel. The coherent precession in bulk 3He A-phase is unstable due to the positive feedback of spin supercurrent to the gradient of phase of precession. It was predicted that the homogeneous precession will be stable if the orbital momentum of the 3He A-phase can be oriented along the magnetic field. We have succeeded to prepare this configuration by emerging 3He in uniaxially deformed anisotropic aerogel. The dissipation rate of coherent precession states in aerogel is much larger than that in bulk 3He B-phase. We propose a mechanism of this dissipation.

Control of coherent magnetization precession in GaMnAs by ultrafast optical excitation

AbstractWe report comprehensive temperature and photoexcitation intensity dependent studies of the photoinduced magnetization precession in Ga1–x Mnx As (x = 0.036) by time‐resolved Kerr rotation measurements. We observe coherent oscillations of local Mn spins triggered by an ultrafast photo‐induced reorientation of the easy axis due to changes in the magnetic anisotropy. The amplitude saturation of these oscillations above certain pump intensity is indicative of stabilization of the magnetic easy axis orientation on temperatures above ∼Tc/2. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Coherent magnetization precession in GaMnAs induced by ultrafast optical excitation

The authors use femtosecond optical pulses to induce, control, and monitor magnetization precession in ferromagnetic Ga0.965Mn0.035As. At temperatures below ∼40K, they observe coherent oscillations of the local Mn spins, triggered by an ultrafast photoinduced reorientation of the in-plane easy axis. The amplitude saturation of the oscillations above a certain pump intensity indicates that the easy axis remains unchanged above ∼TC∕2. The authors find that the observed magnetization precession damping (Gilbert damping) is strongly dependent on pump laser intensity, but independent of ambient temperature. They provide a physical interpretation of the observed light-induced collective Mn-spin precession and relaxation.