Low-energy magnetic excitations in Co/CoO core/shell nanoparticles

We have used inelastic neutron scattering measurements to study the magnetic excitations of Co core/CoO shell nanoparticles for energies from 0 to 50 meV. Above the blocking temperature $T_B$, broad quasielastic scattering is observed, corresponding to the reorientation of the Co core moments and to paramagnetic CoO scattering. Below $T_B$, two nearly dispersionless inelastic peaks are found, whose energies increase with decreasing temperature as order parameters, controlled by the nanoparticle Néel temperature $T_N=235$ K, and saturating as $T\to 0$ at 2.7 and 6.7 meV, respectively. Similar excitations were observed in a powdered single crystal of CoO, indicating that both are intrinsic excitations of CoO, resulting from the exchange splitting of single-ion states for $T⩽T_N$. Pronounced finite-size effects are observed for the scattering from the CoO nanoparticle shells, whose thicknesses range from 1.7 to 4.5 nm. These include an enhanced excitation linewidth, as well as a response that is not only spread over a much wider range of wave vectors, but is also significantly more intense in the nanoparticles than in bulk CoO.

Figure 1

(a) The $q$-integrated scattered intensity $I(E)$ at different temperatures for Co/CoO nanoparticles (sample Co/CoO no. 4). Dashed lines indicate the onset of antiferromagnetic order at $T_N$ and the dynamical blocking of the Co cores at the blocking temperature $T_B$. (b) Energy dependence of ${\chi }^{″}(E)$ for a constant wave-vector cut 0.12 Å${}^{-1}$ wide and centered at $q=1.27$ Å${}^{-1}$ for Co/CoO nanoparticle sample no. 4 at different temperatures, as indicated. Solid lines are the fits, described in the text. (c) The scattered intensity $I(q,E)$ at 150 K for Co/CoO nanoparticles (sample Co/CoO no. 4). Dark curved lines are shadows from the radial collimator.

Figure 2

(a) Scattered intensity $I(q,E)$ for sample Co/CoO no. 4 at 300 K for a constant wave-vector cut 0.3 Å${}^{-1}$ wide, centered at $q=2.45$ Å${}^{-1}$. Solid line is the fit, consisting of a broad Lorentzian $I_{\text{broad}}$ (bold dashed line) and a narrow Lorentzian $I_{\text{narrow}}$ (dashed line), and a resolution broadened $\delta$ function (dotted line), representing the elastic scattering. (b) An alternate presentation of the same data as (a), but with the narrow Lorentzian component omitted from the fit. Note the excess scattered intensity at low energies that is not captured by the new fit, indicated by the solid line, consisting here of a broad Lorentzian $I_{\text{broad}}$ (bold dashed line) and a resolution broadened $\delta$ function (dotted line), representing the elastic scattering. (c) Left panel: the temperature dependencies of the core-reversal linewidths ${\Gamma }_{\text{narrow}}$ ($\square =\text{Co}/\text{CoO}$ no. 3, $ˆ=\text{Co/CoO}$ no. 4). Solid lines are fits to an Arrhenius expression, horizontal dotted line is DCS resolution. Right panel: temperature dependencies of the linewidths ${\Gamma }_{\text{broad}}$ ($\blacksquare =\text{Co/CoO}$ no. 3, $•=\text{Co/CoO}$ no. 4). Solid lines are guides for the eye.

Figure 3

(a) Energy dependence of ${\chi }^{″}(E)$ for sample Co/CoO no. 4 at 50 K for a constant wave-vector cut with a width of 0.12 Å${}^{-1}$ centered at $q=1.27$ Å${}^{-1}$. Solid line is the fit, consisting of two pairs of inelastic Lorentzians, the first centered at $E_1\approx \pm$3 meV (long dashed line) and the second at $E_2\approx \pm$6 meV (short dashed line), and a resolution broadened $\delta$ function (dotted line), representing the elastic scattering. (b) The wave-vector dependence of the inelastic excitation energies $E_1$ (left panel) and $E_2$ (right panel) at 150 K, measured for Co/CoO no. 4 ($\oplus$) and powdered bulk CoO ($♦$). Solid lines are the best fits to nanoparticle $E_1(q)$ and $E_2(q)$, described in the text, dashed lines are for powdered bulk CoO. (c) Temperature dependencies of the wave vector averaged value of $\overline{E_1}$ in our different samples ($\square =\text{Co/CoO}$ no. 1, $ˆ=\text{Co/CoO}$ no. 2, $◊=\text{Co/CoO}$ no. 3, $▵=\text{Co/CoO}$ no. 4, $▿=\text{Co/CoO}$ no. 5, and $•=\text{powdered}$ bulk CoO). Solid lines are mean-field fits with $T_N=235$ K (nanoparticle samples) and $T_N=293$ K (bulk CoO powder). (d) The $q$ dependence of the intensity of the inelastic peak at $E_1\approx 3$ meV at 150 K for Co/CoO no. 4 nanoparticles ($○$) and powdered bulk CoO ($\blacksquare$, multiplied by 450 for comparison). The solid line is the fit of Co/CoO no. 4 with the following function: $I(q)=I_0+{\text{Aq}}^2$. The dashed line is a guide for the eye.

Figure 4

(a) The scattered intensity $I(q,E)$ at 50 K for powdered bulk CoO. (b) An expanded view of the outlined area in (a), demonstrating enhanced scattering near the antiferromagnetic wave vector $q_{\text{AF}}=1.27$ Å${}^{-1}$ of bulk CoO.

Figure 5

(a) The scattered intensity $I(q,E)$ at 300 K for a constant wave-vector cut with a width of 0.12 Å${}^{-1}$ centered at $q_{\text{AF}}=1.27$ Å${}^{-1}$ for powdered bulk CoO. Solid line shows the fit, described in the text and consisting of a quasielastic Lorentzian (dashed line), a broad background (dotted-dashed line), and a resolution broadened $\delta$ function (dotted line), representing the elastic scattering. (b) The scattered intensity $I(q,E)$ at 50 K for a constant wave vector cut with a width of 0.12 Å${}^{-1}$ centered at $q_{\text{AF}}=1.27$ Å${}^{-1}$ for powdered bulk CoO. Solid line shows the fit, described in the text, consisting of two inelastic Lorentzians (dashed lines) centered near $E_1\approx 3$ meV and $E_2\approx 5.7$ meV, as well as a broad background function (dotted-dashed line) and a resolution broadened $\delta$ function (dotted line) representing the elastic scattering.

Figure 6

(a) The scattered intensity $I(q,E)$ for powdered bulk CoO at 50 K, for constant wave-vector cuts with widths of 0.12 Å${}^{-1}$ centered at 0.73 Å${}^{-1}$ ($\blacksquare$), $q_{\text{AF}}=1.27$ Å${}^{-1}$($•$), and 1.65 Å${}^{-1}$ ($▴$). Solid lines are fits described in text. (b) The wave-vector dependencies of the integrated intensity of the fitted $E_1\approx 3$ meV inelastic peaks of powdered bulk CoO, measured at different temperatures, as indicated. Solid lines are guides for the eye.

Figure 7

(a) The scattered intensities $I(q,E)$, normalized to the CoO mass, for powdered bulk CoO ($\blacksquare$, multiplied by 150 for ease of comparison) and Co/CoO no. 4 ($○$) at 50 K, for constant wave-vector cuts with widths of 0.12 Å${}^{-1}$, centered at $q_{\text{AF}}=1.27$ Å${}^{-1}$. Solid lines are fits described in the text. The Lorentzian functions associated with the inelastic excitations at $E_1\approx 3$ meV and $E_2\approx 6$ meV are shown for Co/CoO no. 4 as solid lines, and for powdered bulk CoO as dashed lines. (b) Same as (a), but for 150 K, and with larger energy transfers ($\lambda =1.22$ Å). Here the fitted inelastic peaks for Co/CoO no. 4 (left axis) are given as solid lines, and dashed lines for powdered bulk CoO (right axis). (c) Same as (b) but with background scattering removed.

Figure 8

The wave-vector dependencies of the $E_1\approx 3$ meV inelastic peak in Co/CoO no. 4 ($○$, 4.5 nm CoO thickness), Co/CoO no. 1 ($•$, 1.7 nm CoO thickness), and powdered bulk CoO ($\blacksquare$), multiplied by 3 for comparison. Solid lines are guides for the eye.