Magnetic order of tetragonal CuO ultrathin films

We present a detailed low-energy muon spin rotation and x-ray magnetic circular dichroism (XMCD) investigation of the magnetic structure in ultrathin tetragonal (T)-CuO films. The measured muon-spin polarization decay indicates an antiferromagnetic (AFM) order with a transition temperature higher than 200 K. The XMCD signal obtained around the $\mathrm{Cu}{L}_{2,3}$ edges indicates the presence of pinned ${\mathrm{Cu}}^{2+}$ moments that are parallel to the sample surface, and additionally, isotropic paramagnetic moments. The pinning of some of the Cu moments is caused by an AFM ordering consisting of moments that lie most likely in plane of the film. Moreover, pinned moments show a larger orbital magnetic moment contribution with an approximate ratio of $m_{\mathrm{orb}}/m_{\mathrm{spin}}=1.5$, indicating that these spins are located at sites with reduced symmetry. Some fractions of the pinned moments remain pinned from an AFM background even at 360 K, indicating that $T_{\mathrm{N}}>360\mathrm{K}$. We propose a simple model that explains these experimental findings, showing that the magnetic order of the $T$-CuO ultrathin films differs from the theoretical predictions.

Figure 1

(a) Crystal structure of T-CuO. (b) Top view of the edge- and corner-sharing Cu-O square lattices that are interconnected. The O ions are in red and the Cu ions in blue. The orange square indicates the chemical unit cell.

Figure 2

Results of Trim.SP simulation to calculate the stopping distribution of muons in C/T-CuO/STO. (a) Stopping profile as a function of depth for different implantation energies. (b) Stopped fraction of muons, for each layer, as a function of implantation energy.

Figure 3

(a) Temperature dependence of the asymmetry for three different muon implantation energies for C/T-CuO-STO sample. (b) Measured asymmetry as a function of implantation energy of C/STO at 200 K and C/T-CuO/STO at 200 and 150 K (lines are guides to the eye). (c) Asymmetry, (d) field, and (e) damping rate extracted from fits of the data measured as a function of temperature in the two specimens, C/STO and C/T-CuO/STO, at 1.5 keV. The uncertainty range of the measurements has been defined from statistical error analysis.

Figure 4

XAS and XMCD signals at 3 K for positive FC (6.5 T) and applied magnetic field of (a),(b) 6.5 T and (c),(d) −6.5 T, respectively. Data have been collected at 30 ° incident angle. The dashed green lines indicate the background subtracted from the XAS signals. The integrated XAS is calculated as $\int \mathit{XAS}$-step function.

Figure 5

Comparison of the experimental and calculated XLD signal for the C/T-CuO/STO sample. The XLD signal has been collected at 300 K, with 30 ° incident angle in zero field.

Figure 6

XAS and XMCD signals at 3 K for negative FC (−6.5 T) and applied magnetic field of 6.5 T in (a),(b) and −6.5 T in (c),(d), respectively. Data have been collected at 30 ° incident angle. The dashed green lines indicate the background subtracted from the XAS signals. The integrated XAS is calculated as $\int \mathit{XAS}$-step function.

Figure 7

XMCD signal at the maxima of the $\mathrm{Cu}{L}_3$ edge as a function of ramped magnetic field measured at 3 K following (a) +FC in +6.5 T and (b) −FC in −6.5 T. $M_{\mathrm{pin}}$ and $M_{\mathrm{rot}}$ indicate the contribution of pinned and rotated moments, respectively. The dashed line in (a) represents the Brillouin function for spin ½. Data collected at a 30 ° incident angle.

Figure 8

Experimental data of the XMCD signal at the maximum of $\mathrm{Cu}{L}_3$ edge as a function of temperature (dark squares) and the partition function $Z$ of a paramagnetic system with spin ½ (red line). Data collected at a 30 ° incident angle. The error bars of the experimental data obtained from statistical error analysis are below the size of the marker.

Figure 9

XMCD as a function of applied field at normal incidence angle. FC of −6.5 T. The arrow indicates the contribution of rotated moments ($M_{\mathrm{rot}}$).

Figure 10

XAS (top) and XMCD (bottom) data measured at $\mathrm{Cu}{L}_{2,3}$ edges. FC in −6.5 T from 360 to 3 K and data taken in zero field at 3 K. Data taken at an incident angle of 30 °. The dashed green line indicates the background subtracted from the XAS signals. The integrated XAS is calculated as $\int \mathit{XAS}$-step function.

Figure 11

XAS (top) and XMCD (bottom) signal taken at the $\mathrm{Ti}{L}_{2,3}$ edges with +FC, in an applied magnetic field of 6.5 T and $T=3\mathrm{K}$.

Figure 12

Sketch of the proposed model for T-CuO. Part (a) represents the + FC case, and (b) represents the −FC case. The blue layer highlights the paramagnetic moments, the green layer corresponds to the pinned moments, and the orange layer corresponds to the antiferromagnetic moments. Note that in (a) the pinned moment layer is enhanced because the pinned moment and paramagnetic moments (PM) have the same orientation.