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Quantifying Power Flow Processes Mediated by Spin Currents

The power flow process mediated by spin current in the bilayer device consisting of ferromagnetic metal (FM) and nonmagnetic metal (NM) layers is examined by realizing experimental evaluations for each process from the microwave absorption to electromotive force (EMF) output. The absorption power by ferromagnetic resonance (FMR) of the thin FM layer during the EMF output is directly measured in operando using an antenna probe system. The transfer efficiency of the absorption power into the NM layer by spin pumping is estimated from strict linewidth evaluation of EMF spectra. The maximum transfer efficiency of the spin pumping power to the external load via the inverse spin Hall effect is determined to be 4.2 × 10–8 under 162 mW microwave irradiation using an analysis model assuming a parallel circuit. The main factors reducing the efficiency are found to be low resistivity of the NM layer and the interface loss. These quantifications are important as a first step to consider the efficient transfer of spin energy mediated by spin currents.

Strong interaction between light and electrons (4) "Transmission ESR/FMR measurement method"

Interaction between microwave photon and spins means in other words, interaction between resonating photon in a closing space and spins. Thus, measuring spectra using a non-resonant device can prevent the Purcell effect or strong coupling from distortion of intrinsic spectra. Figure 1(a) is a drawing expressing a typical spectroscopy. A light source irradiates light to a sample, and transmitted light is detected. A simple and non-resonant wave guide, as shown in Fig.1(b), can provide absorption spectra of para- and ferromagnetic samples which have a high spin density.

Strong interaction between light and electrons (2) "Four states of interaction between photon and spins"

A conventional ESR spectrometer uses a cavity for microwave irradiation and detection of ESR absorption. On the resonance state, it can be considered as a model that spins absorb energy of ℎ𝜈=𝑔𝜇𝐵𝐵 and then release it to the lattice system one way, where h: Planck constant, ν: frequency, g: g-value, μB: Bohr magneton, and B: magnetic flux density. However, the interaction between photon of microwave and spins of electrons is a little more complex in fact. Figure 1 is a modelized drawing that expresses energy flow of microwave photon and spins. The cavity resonates with angular frequency 𝜔c, relaxes with velocity of 𝜅𝑐=𝜔𝑐 / 𝑄𝑢 , which is inversely proportional to unloaded Q value of the cavity. On the other hand, spins do precess with an angular frequency of 𝜔𝑚= 𝛾𝑒 𝐵𝑚 under the static magnetic field 𝐵𝑚. When the resonant condition of 𝜔𝑐 = 𝜔𝑚 is satisfied, excited electron spins that absorbed microwave energy relax with the velocity of 𝛾𝑚 (half width: half width at half maximum (HWHM)), which corresponds to spectral line width. At this time, photon and electron spins exchange energy with a coupling constant 𝑔𝑚. The coupling constant 𝑔𝑚 is expressed as[1] 数式 where 𝜂𝑚𝑠𝑞𝑟𝑡 is the square root of the filling factor of the cavity, 𝛾𝑒 is gyromagnetic ratio of the electron, ℏ is reduced Planck constant (h/2π), 𝜇0 is vacuum permeability, 𝑉𝑐 is the volume of the cavity, N is number of magnetic ions, and S is spin quantum number.

Strong interaction between light and electrons (1) "Effect of excessive spins"

Typical electron spin resonance (ESR) spectrometer uses a microwave resonator, which is usually called a cavity, as a sensitive detector. A sample is usually set in the center of the cavity, and energy absorption by ESR phenomena is detected according to the degree of an impedance mismatching of the resonant circuit of the cavity. Absorption intensity in the ESR and FMR (Ferromagnetic Resonance) is proportional to the square root of the irradiated microwave power and the spin amount in the measured sample. Moreover, the spectral line width is proportional to the inverse of the transverse relaxation time of spins. The cavity is a device that stores only the light, of which the frequency is 𝜔𝑐=2𝜋𝑓𝑐, in the limited space. Electron spins lied in a static magnetic field are like spinning tops which are locked to specific Larmor frequency (𝜔𝑟=2𝜋𝑓𝑟). ESR/FMR spectrum is usually measured in the condition of 𝜔𝑐=𝜔𝑟. Recently, many attentions are gathering to the interaction between light (microwave) and spins in the cavity according to the development of quantum optics.

Strong interaction between light and electrons (3) "Strong coupling state of ferromagnetic thin film"

Coupling constant (𝑔𝑚) between microwave photon and electron spins is proportional to the square root of spin numbers as shown in eq.(1) of "Application Note ER200007E ". Therefore, FMR measurements using ferromagnets which include many spins and especially have narrow line widths do not work well, because spins in ferromagnets interact strongly with microwave photon, and achieve to "strong coupling" state larger than the state of "Purcell effect". Figure 1(a) is an example that shows the obtained unexpected spectrum in the strong coupling state. Normal FMR spectrum can be obtained as shown in Fig.1(d), if the filling factor is reduced and the system moves to a "weak coupling" state.

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February 22, 2020
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