Magnetization compensation and spin reorientation transition in ferrimagnetic ${\mathrm{DyCo}}_5$: Multiscale modeling and element-specific measurements

We use a multiscale approach linking ab initio calculations for the parametrization of an atomistic spin model with spin dynamics simulations based on the stochastic Landau-Lifshitz-Gilbert equation to investigate the thermal magnetic properties of the ferrimagnetic rare-earth transition-metal intermetallic ${\mathrm{DyCo}}_5$. Our theoretical findings are compared to elemental resolved measurements on ${\mathrm{DyCo}}_5$ thin films using the x-ray magnetic circular dichroism technique. With our model, we are able to accurately compute the complex temperature dependence of the magnetization. The simulations yield a Curie temperature of $T_{\mathrm{C}}=1030\text{K}$ and a compensation point of $T_{\mathrm{comp}}=164\text{K}$, which is in a good agreement with our experimental result of $T_{\mathrm{comp}}=120\text{K}$. The spin reorientation transition is a consequence of competing elemental magnetocrystalline anisotropies in connection with different degrees of thermal demagnetization in the Dy and Co sublattices. Experimentally, we find this spin reorientation in a region from $T_{\mathrm{SR}1,2}=320$ to $360\text{K}$, whereas in our simulations the Co anisotropy appears to be underestimated, shifting the spin reorientation to higher temperatures.

Figure 1

(a) ${\mathrm{CaCu}}_5$-type structure ($P6/mmm$) of ferrimagnetic ${\mathrm{DyCo}}_5$, with EBP (left) and EA (right) magnetization, corresponding to the low- and high-temperature configurations, respectively. (b) Measurements geometry and sample composition. The $c$ axis of the structure lies in the sample plane, which is the $\left[1\overline{1}00\right]$ plane; thus EBP (EA) magnetization is out of sample plane (in sample plane).

Figure 2

(a) X-ray absorption spectroscopy data of ${\mathrm{DyCo}}_5$ measured at Co and Dy edges for opposite magnetic fields (top red and blue curves) at room temperature. The resulting XMCD signal for Co and Dy is shown at the bottom. (b) Spin and orbital magnetic moments of Dy and Co vs temperature as deduced upon applying the magneto-optical sum rules [33, 34, 35, 36, 37]. The lowest frames show the orbital/spin moments ratios for both elements. The dashed lines are guides to the eye. (c) Stoichiometry-weighted (spin+orbital) magnetic moment of Dy and Co vs temperature; the curve's inflection point determines the magnetization compensation temperature region. For comparison, the coercive field is shown, with its divergence at the compensation point $T_{\text{comp}}$.

Figure 3

(a) Temperature dependence of coercive field and out-of-plane remanent magnetization (upper panel inset) measured at Co $L_3$ and Dy $M_5$ edges. (b) Representative hysteresis loops (Dy $M_5$ edge) measured along the out-of-plane direction below and above the compensation temperature as well as above the spin reorientation temperature. (c) Schematic display of the Dy and Co magnetic moments' alignment as a function of temperature; incoming x-ray beam and the external applied magnetic field are depicted on the right-hand side.

Figure 4

Sublattice-resolved magnetization as a function of temperature from atomistic simulations. The solid vertical line shows the magnetization compensation point $T_{\mathrm{comp}}=164\text{K}$. The SRT region is indicated by the dashed lines, with starting point $T_{\mathrm{SR}1}=432\text{K}$ and end point $T_{\mathrm{SR}2}=460\text{K}$, clearly visible by the steep slope of the magnetization in this temperature range. A Curie temperature of 1030 K is found in the simulations, in reasonable agreement with previous experiments [5, 25].

Figure 5

(a) Simulation results for direction of the easy axis of ${\mathrm{DyCo}}_5$ with respect to the $c$ axis. With increasing temperature, the magnetization rotates from the EBP direction (${90}^{\circ }$) to the EA direction ($0^{\circ }/{180}^{\circ }$). (b) Within the reorientation region $T_{\mathrm{SR}1}<T<T_{\mathrm{SR}2}$, i.e., for the EC magnetization, the Dy and Co spins are no longer aligned perfectly antiparallel, but show a finite canting of up to $5^{\circ }$. Co orientation has been mirrored for better comparison.