Importance of giant spin fluctuations in two-dimensional magnetic trilayers

Two ultrathin ferromagnetic films of Co and Ni separated by a nonmagnetic spacer of Cu are taken to study the spin-spin correlations of weakly coupled ferromagnets. The Ni film thickness ranging between $d_{\mathrm{Ni}}=2$ and 6 monolayers (ML) is chosen to study the two-dimensional $2\mathrm{D}\to 3\mathrm{D}$ crossover in ferromagnets. The spacer thickness ranges from $d_{\mathrm{Cu}}=2-8\mathrm{ML}$ to monitor the oscillatory behavior of the interlayer exchange coupling. The measured temperature-dependent magnetizations and the corresponding Curie temperatures are accompanied by a microscopic many-body Green’s function theory. Both experiment and theory give firm evidence that for nanostructured magnets a static mean field description is insufficient, higher order spin-spin correlations are important and explain the observed increase of the Curie temperature by up to $\sim 200\%$ due to the interlayer exchange coupling. The results are visualized in a three-dimensional diagram as a function of both the Ni thickness and the Cu spacer thickness.

Figure 1

Schematic illustration of a ferromagnetic two wedge trilayer. $\Delta T_{\mathrm{C},\mathrm{Ni}}$ is controlled by two independent parameters: (i) the IEC depending on $d_{\mathrm{NM}}$, and (ii) the thickness $d_{\mathrm{FM}1}$, while $d_{\mathrm{FM}2}$ is kept constant.

Figure 2

(Color online) Sketch of the investigated $\mathrm{Co}∕\mathrm{Cu}∕\mathrm{Ni}∕\mathrm{Cu}\left(100\right)$ trilayers and the underlying assumptions for the theoretical model. Magnetic moments are taken from experiments (Refs. 16, 17).

Figure 3

(Color online) Ni (circles) and Co (squares) sublayer magnetizations $M_{\mathrm{Ni}}\left(T\right)$ and $M_{\mathrm{Co}}\left(T\right)$ probed by XMCD. The influence of the IEC $J_{\mathrm{inter}}$ on the Ni magnetization is monitored by comparing $M_{\mathrm{Ni}}\left(T\right)$ before (open symbols) and after (closed symbols) the deposition of the Co film. The solid and dot-dashed lines are guides to the eye. A standard Ni magnetization curve (see text) is fitted to the Ni data points (dashed and dotted lines), yielding $T_{\mathrm{C},\mathrm{Ni}}$ and $T_{\mathrm{C},\mathrm{Ni}}^{*}$.

Figure 4

(Color online) Calculated Ni magnetization of a single Ni film (dashed line) and of a Ni film coupled to a Co film (solid line) as a function of the temperature with $J_{\mathrm{inter}}=86\mu \mathrm{eV}∕\text{bond}$, corresponding to the experiment shown in Fig. 3. The dot-dashed line refers to the Co magnetization. An external magnetic field of $H=3\mathrm{kA}∕\mathrm{m}$ causes the small tail in the Ni magnetization of the bilayer. By applying $M_{\mathrm{Ni}}(J_{\mathrm{inter}}=0)$, see text, we identify $T_{\mathrm{C},\mathrm{Ni}}^{*}$ (dotted line) and $\Delta T_{\mathrm{C},\mathrm{Ni}}=37\mathrm{K}$.

Figure 5

$T_{\mathrm{C},\mathrm{Ni}}$ and $T_{\mathrm{C},\mathrm{Ni}}^{*}$ as functions of the Ni film thickness $d_{\mathrm{Ni}}$ of bilayers and trilayers (experiment: open and full circles, theory: solid and dashed lines). The IEC is determined to be $J_{\mathrm{inter}}=310\mu \mathrm{eV}∕\text{bond}$. In the inset the relative temperature shift $\Delta T_{\mathrm{C},\mathrm{Ni}}∕T_{\mathrm{C},\mathrm{Ni}}\left(d_{\mathrm{Ni}}\right)$ is shown highlighting the difference between the calculations with (RPA) and without (MF) consideration of collective magnetic excitations.

Figure 6

Magnetization $M_{\mathrm{Ni}}\left(T\right)∕M_{\mathrm{Ni}}(T=0)$ as a function of the relative temperature $T∕T_{\mathrm{C},\mathrm{Ni}}\left(d_{\mathrm{Ni}}\right)$ scaled by the corresponding Curie temperature of the capped Ni films. For the calculations $J_{\mathrm{inter}}=310\mu \mathrm{eV}∕\text{bond}$ and $d_{\mathrm{Co}}=3\mathrm{ML}$ are used. The cases with Ni thicknesses of 2.1, 2.6, 3.1, and 4.2 ML and the corresponding Co and Cu thicknesses are given in Table . The top-down triangles $(d_{\mathrm{Ni}}=4.0\mathrm{ML})$ represent a case without IEC $(J_{\mathrm{inter}}=0)$.

Figure 7

Relative temperature shift $\Delta T_{\mathrm{C},\mathrm{Ni}}∕T_{\mathrm{C},\mathrm{Ni}}$ of the Ni magnetization as a function of the strength of the IEC $\mid J_{\mathrm{inter}}\mid$.

Figure 8

(Color online) Two-parameter plot of the relative temperature shift $\Delta T_{\mathrm{C},\mathrm{Ni}}∕T_{\mathrm{C},\mathrm{Ni}}(d_{\mathrm{Ni}},d_{\mathrm{Cu}})$ for $\mathrm{Co}∕\mathrm{Cu}∕\mathrm{Ni}∕\mathrm{Cu}\left(100\right)$ trilayers as a function of the Ni film thickness $d_{\mathrm{Ni}}$ and the thickness $d_{\mathrm{Cu}}$ of the Cu spacer layer. Two different thicknesses of the Co film are assumed: (a) $d_{\mathrm{Co}}=2\mathrm{ML}$ and (b) $d_{\mathrm{Co}}=3\mathrm{ML}$.

Figure 9

(Color online) Calculated phase diagram of the $\mathrm{Co}∕\mathrm{Cu}∕\mathrm{Ni}$ trilayer system. The Curie temperatures $T_{\mathrm{C}},T_{\mathrm{C},\mathrm{Ni}}$, and $T_{\mathrm{C},\mathrm{Co}}$, and the quasicritical temperatures $T_{\mathrm{C},\mathrm{Ni}}^{*}$ and $T_{\mathrm{C},\mathrm{Co}}^{*}$ are shown as a function of the exchange coupling $J_{\mathrm{Co}}$ in the Co film.