Enhancement of domain-wall mobility detected by NMR at the angular momentum compensation temperature

The angular momentum compensation temperature $T_{\mathrm{A}}$ of ferrimagnets has attracted much attention because of high-speed magnetic dynamics near $T_{\mathrm{A}}$. We show that NMR can be used to investigate domain-wall dynamics near $T_{\mathrm{A}}$ in ferrimagnets. We performed ${}^{57}\mathrm{Fe}\text{−}\mathrm{NMR}$ measurements on the ferrimagnet ${\mathrm{Ho}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$ with $T_{\mathrm{A}}=245$ K. In a multidomain state, the NMR signal is enhanced by domain-wall motion. We found that the NMR signal enhancement shows a maximum at $T_{\mathrm{A}}$ in the multidomain state. The NMR signal enhancement occurs due to increasing domain-wall mobility toward $T_{\mathrm{A}}$. We develop the NMR signal enhancement model involves domain-wall mobility. Our study shows that NMR in multidomain state is a powerful tool to determine $T_{\mathrm{A}}$, even from a powder sample and it expands the possibility of searching for angular momentum-compensated materials.

Figure 1

Schematic illustration of enhancement of the NMR signal in a domain wall. (a) An input RF magnetic field $H_1$ causes the domain wall to move. The electron spins in the domain wall rotate, exciting the nuclear resonance through the hyperfine coupling. As a result, $H_1$ appears to be ${\eta }_{\mathrm{in}}$ times for the nuclear spins. (b) The domain wall moves in accordance with the precession of nuclear spins, and the bulk magnetization oscillates with NMR frequency. The NMR signal becomes ${\eta }_{\mathrm{out}}$ times.

Figure 2

The ${}^{57}\mathrm{Fe}$ NMR results for the $d$ site and the magnetic properties in ${\mathrm{Ho}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$. (a) Temperature dependence of the NMR spectra. (b) In the upper panel, the red open and filled circles show the bare integrated signal intensity and calibrated intensity by multiplying by $T{\nu }^{-2}exp(2\tau /T_2)$, respectively. In the bottom panel, the blue cross shows $M_{\mathrm{\Omega }}$ obtained by the Barnett effect. The blue curve is a guide to the eye. The orange curve shows the magnetization obtained under the magnetic field of 1000 [Oe]. In both panels, the black solid and dashed lines show the magnetization and angular momentum compensation temperatures of ${\mathrm{Ho}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$, respectively. (c) Temperature dependence of resonance frequency (top), $1/T_1$, and $1/T_2$ (bottom).

Figure 3

The NMR results in the magnetic fields ranging from 0 to 1 T at 300 K. The top panel shows the field dependence of the resonance frequency. The solid line shows the slope of the gyromagnetic ratio of a ${}^{57}\mathrm{Fe}$ nucleus. The bottom panel shows the field dependence of optimized RF power.

Figure 4

(a) The temperature dependence of the NMR intensity in the magnetic fields ranging from 0 to 1 T. The NMR intensity of 0 and 0.3 T is calibrated by multiplying by $T{\nu }^{-2}exp(2\tau /T_2)$. The NMR intensity of 0.5 and 1 T is calibrated by multiplying by $T{\nu }^{-3}exp(2\tau /T_2)$. The solid and dashed lines show the magnetization and angular momentum compensation temperatures, respectively. (b) Schematic illustration of the domain-wall motion induced by an effective RF magnetic field $H_{\mathrm{eff}}$ through the hyperfine coupling. Here, $R, d$, and $x$ are a particle radius, a domain-wall thickness, and domain-wall displacement, respectively. The domain wall moves $l=4x$ in one cycle of $t=1/\nu$.