Weakly coupled motion of individual layers in ferromagnetic resonance

We demonstrate a layer- and time-resolved measurement of ferromagnetic resonance (FMR) in a ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}∕\mathrm{Cu}∕{\mathrm{Co}}_{93}{\mathrm{Zr}}_7$ trilayer structure. Time-resolved x-ray magnetic circular dichroism has been developed in transmission, with resonant field excitation at a FMR frequency of $2.3\mathrm{GHz}$. Small-angle (to 0.2°), time-domain magnetization precession could be observed directly, and resolved to individual layers through elemental contrast at Ni, Fe, and Co edges. The phase sensitivity allowed direct measurement of relative phase lags in the precessional oscillations of individual elements and layers. A weak ferromagnetic coupling, difficult to ascertain in conventional FMR measurements, is revealed in the phase and amplitude response of individual layers across resonance.

Figure 1

(Color online) (a) side view of precession cones for ${\mathbf{M}}_{\mathrm{Fe},\mathrm{Ni}}$ and ${\mathbf{M}}_{\mathrm{Co}}$ showing the different cone angles and top view of phase difference, $\Delta \psi$, between the two vectors. (b) top view indicating out-of-phase difference. (c) top view indicating in-phase condition. (d) Diagram of measurement geometry. The sample is oriented vertically in the $x\text{−}y$ plane with the sample normal parallel to $z$. Photons are incident along the horizontal (in the $y\text{−}z$ plane), rotated 38° away from the $z$ axis. Orthogonal Helmholtz coils provide a magnetic field parallel to the film plane along $x$ (bias field ${\mathbf{H}}_{\mathbf{B}}$) or parallel to the incident photon direction (transverse field ${\mathbf{H}}_{\mathbf{T}}$). Transmitted photons are detected with a photodiode.

Figure 2

Block diagram electronics used to generate phase-locked, $2.3\mathrm{GHz}$ excitation for conventional FMR and ETR-FMR measurements. (b) Top view of experimental geometry.

Figure 3

(Color online) XMCD spectra and element specific hysteresis measurements of the ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}∕\mathrm{Cu}∕{\mathrm{Co}}_{93}{\mathrm{Zr}}_7$/trilayer. The hysteresis curves and ETR-FMR were measured at the photon energies indicated by the arrows ($707.5\mathrm{eV}$ for Fe, $851.5\mathrm{eV}$ for Ni, and $778\mathrm{eV}$ for Co). The XMCD signal levels at saturation in the hysteresis curves provide an angular calibration for ETR-FMR measurements.

Figure 4

(Color online) (a) In situ FMR measurement at $2.3\mathrm{GHz}$. The rf excitation used in the measurement is phase-locked with the synchrotron photon bunch clock at $88\mathrm{MHz}$. Note the main resonance indicated by the zero crossing point at ${\mathbf{H}}_{\mathbf{B}}\sim 40\mathrm{Oe}$ and a weaker resonance at near zero bias. ETR-FMR measurements were acquired at the field values indicated by the arrows. (b) Position of resonance field ${\mathbf{H}}_{\mathbf{B},\mathbf{res}}$, measured with ex situ, variable frequency FMR. Two resonances are observed in the trilayer, derived primarily from the ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ layer (red squares) and the ${\mathrm{Co}}_{93}{\mathrm{Zr}}_7$ layer (blue circles). See text for description of dashed/solid lines.

Figure 5

(Color online) ETR-FMR measurements for Fe, Ni, and Co in the ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}∕\mathrm{Cu}∕{\mathrm{Co}}_{93}{\mathrm{Zr}}_7$ magnetic trilayer. The open symbols are the measured points and the solid black lines are sinusoidal fits to the data. For clarity, the data have been offset vertically.

Figure 6

(Color online) Measured values for the precession cone angle (left panel) and phase of oscillation (right panel) for the Fe (solid red triangles) and Co (open blue circles) moments in the ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}∕\mathrm{Cu}∕{\mathrm{Co}}_{93}{\mathrm{Zr}}_7$ trilayer. The dashed lines are calculated values for the amplitude and phase assuming no coupling $(A_{\mathit{ex}}=0)$ between the layers. Solid lines are model calculations that assume weak coupling $(A_{\mathit{ex}}=0.01\mathrm{ergs}∕{\mathrm{cm}}^2)$ between the two FM layers. Estimated errors are indicated by vertical lines; note that some estimated errors are smaller than the size of the symbols.