$\beta$-NMR Investigation of the Depth-Dependent Magnetic Properties of an Antiferromagnetic Surface

By measuring the prototypical antiferromagnet $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$, we show that it is possible to determine the static spin orientation and dynamic spin correlations within nanometers from an antiferromagnetic surface using the nuclear spin polarization of implanted ${}^8{\mathrm{Li}}^{+}$ ions detected with $\beta$-NMR. Remarkably, the first-order Morin spin reorientation in single crystal $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$ occurs at the same temperature at all depths between 1 and 100 nm from the (110) surface; however, the implanted nuclear spin experiences an increased $1/T_1$ relaxation rate at shallow depths revealing soft-surface magnons. The surface-localized dynamics decay towards the bulk with a characteristic length of $\epsilon =11\pm 1\mathrm{nm}$, closely matching the finite-size thresholds of hematite nanostructures.

Figure 1

Spin-lattice-relaxation measurements of ${{}^8\mathrm{Li}}^{+}$ implanted at 20 keV into an $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$ crystal show a step in the observable nuclear polarization at the SR transition ($T_M=260\mathrm{K}$) for two rotations of the crystal such that (a) $\overrightarrow{P}\parallel (001)$ and (b) $\overrightarrow{P}\parallel (\overline{1}10)$. The curves have not been offset or scaled. The kink at 4 s in (a) and (b) is the end of the incoming ${{}^8\mathrm{Li}}^{+}$ pulse. The antiferromagnetic spin reorientation is evident in (c) as a step in the initial asymmetry $A_0$ as a function of temperature.

Figure 2

(a) Stopping profile of ${{}^8\mathrm{Li}}^{+}$ ions as a function of beam energy calculated with srim. (b) Initial experimental asymmetry $A_0$ as a function of temperature for several beam energies. The steplike decrease signifies the SR transition. (c) Sample $\beta$-NMR SLR data as a function of beam energy below the Morin transition showing modified spin-lattice relaxation for ions stopping near the $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$ (110) surface.

Figure 3

(a) The nuclear relaxation rate $1/T_1$ is depth dependent near the (110) $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$ surface, with a characteristic decay length of 11 nm. (b) Data-mined experimental results for spherical $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$ nanoparticles taken from the previously published references showing the finite-size threshold for the Néel and Morin phase transition are approximately 2.3 and 11 nm, respectively. (c) Temperature dependence of the $\beta$-NMR $1/T_1$ rate at the surface of the $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$ crystal at different depths, implying that the relaxation is caused by soft-surface magnons, described by the model encapsulated in Eqs. (3) and (2).