Following enhanced Sm spin projection in Gd_xSm_1-xN

The lanthanides are the series of the periodic table across which the $4f$ shell is sequentially filled, imbuing them with the strongest angular momentum and magnetic moments among all stable elements. The strong spin-orbit coupling within the 4$f$ shell ties the orbital moment firmly to the spin so that the net magnetic moment is of mixed spin and orbital character. Furthermore, the limited extent of the $4f$ wave function reduces the orbital angular momentum quenching that is a feature of transition metal compounds; indeed the orbital moment can dominate the net magnetic moment.

The rare-earth nitrides (RN, with R a lanthanide element) form in the very simple NaCl structure which provides a fertile ground to investigate the spin/orbit magnetism that stems from the partially full $4f$ electron levels [1]. The chemical similarity of the lanthanides and the well-matched lattice constants in their nitrides invites studies in the mixed-cation environments offered by multilayers and solid solutions. Multilayer structures of GdN/SmN and of GdN/NdN have already shown a striking competition between the exchange and Zeeman interactions across interfaces [2, 3, 4, 5]. The present report investigates the effects of that competition among randomly-sited Gd³⁺/Sm³⁺ ions in the solid solution Gd_xSm_1-xN using x-ray magnetic circular dichroism (XMCD).

The magnetism of the parent materials, GdN ($x=1$) and SmN ($x=0$) illustrates the range of magnetism in the RN series. Both are ferromagnetic, with Curie temperatures (T_C) of $\sim 70$ and $\sim 30$ K, respectively, resulting from an indirect exchange mechanism that links the $4f$ alignments via the R $5d$ and N $2p$ states [6, 1, 7, 8]. The Gd³⁺ ions in GdN have a half-filled $4f$ shell ([Xe]$4f^{7}$), and in the ground state all seven spins align giving a spin-number, $S~{}=~{}7/2$. The half-full shell further features zero orbital angular momentum ($L=0$) so that the material behaves as a spin-only ferromagnet with $\langle M_{z}\rangle=2\mu_{B}\langle S_{z}\rangle=7~{}\mu_{B}$ per Gd³⁺ ion. In contrast, the Sm³⁺ ions in SmN possess two fewer electrons giving an electronic configuration of [Xe]$4f^{5}$. Inter-ion exchange aligns the $4f$ spins, but opposing magnetic contributions from the spin and orbital angular momenta very nearly cancel to yield a net magnetisation of $\approx$ 0.035 $\mu_{B}$ per Sm³⁺ ion in the ferromagnetic ground state [9, 8]. Crucially, the magnetic moment $\langle M_{z}\rangle=\mu_{B}(\langle L_{z}\rangle+2\langle S_{z}\rangle)$ is weakly orbital dominated, with $\langle L_{z}\rangle/2\langle S_{z}\rangle<-1$ [10], so that the spin contribution to the magnetic moment is opposed to an applied field. It is this opposition of the spin magnetic moment ($\mu_{S}$) to the applied field that provides a competition between the Zeeman and exchange interactions when SmN and GdN are paired in multilayers [10, 3].

Similarly to multilayer structures, the Gd-Sm exchange interaction in Gd_xSm_1-xN disrupts the tendency of the Zeeman interaction to align the Sm³⁺ orbital magnetic moment ($\mu_{L}$) with an applied field. The alignment (anti-alignment) of the Gd³⁺ (Sm³⁺) spin magnetic moments with an applied magnetic field (Figure 1a) is in direct competition with the ferromagnetic inter-ion exchange attempting to align the Gd³⁺ and Sm³⁺ spins (Figure 1b). Because the Gd³⁺ magnetic moment is two orders of magnitude the larger, most values of $x$ show the alignment of the the Gd³⁺ spin-moment with the applied field. Yet, for extremely dilute concentrations of Gd in solution (that is, $x\approx 0$) it must be that the net Sm³⁺ magnetic moments align with the applied field, rather than the Gd³⁺, due to the same exchange.

The simplest model for the magnetic state of Gd_xSm_1-xN would treat the Sm³⁺ and Gd³⁺ ion moments as fixed at their values in SmN and GdN. This model suggests that under full ferromagnetic order the saturation magnetisation is linear in $x$ and for some appropriate composition there exists a net zero magnetisation, a magnetisation compensation point. Within that model the net magnetisation ($\bar{M}$) ranges from $-0.035~{}\mu_{B}$ to $7~{}\mu_{B}$ per R ion (with respect to the spin-moment direction in the solid solution) with the compensation point occurring at $x~{}=~{}0.005$ (Figure 1c). The XMCD results in this paper indicate that the Sm³⁺ spin-alignment does $not$ remain as adopted in SmN, but nearly doubles in Gd-rich films.

Furthermore, the same behaviour seen for the net magnetic moment must also manifest for the net angular momentum, $\bar{J}$, meaning that under full FM order $\bar{J}$ $must$ also pass through zero as $x$ varies from $0$ to $1$, giving an angular momentum compensation point (Figure 1c). Here again the simplest model uses a linear interpolation between the ground state angular momenta of GdN and SmN, but unlike the magnetisation there is no simple measurement of the angular momenta of the parent materials. The spin-only magnetism in GdN clearly indicates that $J=S=7/2$, and Hund’s rules suggest that $J=L-S=5/2$ in SmN. However, an atom-centred treatment of the magnetism of SmN based on realistic crystal-field and exchange interactions and reproducing the orbital-dominant ground state moment of $0.035~{}\mu_{B}$ per Sm³⁺ ion yields an eigenstate of neither $L_{z}$ or $S_{z}$ [11]. Rather, it shows projections $\langle L_{z}\rangle\approx 2\hbar$ and $\langle S_{z}\rangle\approx-\hbar$, substantially smaller than the maximum possible values provided by Hund’s rules ($\langle L_{z}\rangle=5\hbar$ and $\langle S_{z}\rangle~{}=-5\hbar/2$, treating the spin moment direction as positive, once more). Importantly, the spin-orbit coupling is still strong enough that the spin and orbital angular momenta remain opposed.

This description of the magnetism of the Sm³⁺ ion, in which the $4f$ spins are ferromagnetically aligned in the ground state, but without their maximum potential magnitudes, accommodates the factor of $\approx$ 2 increase in the Sm spin polarisation that is seen in XMCD measurements performed on GdN/SmN superlattices [2, 11]. We thus introduce a parameter $\alpha=\langle S_{z}\rangle/(5\hbar/2)$, which indicates the expectation value of the spin-alignment $\langle S_{z}\rangle$ in the $4f$ shell of the Sm³⁺ ion. Appealing to the ion-based model of McNulty et al. [11], in homogeneous SmN $\alpha~{}\approx~{}0.4$, while at the SmN/GdN interface $\alpha~{}\approx~{}0.6$. One might then anticipate, as seen below, that that $\alpha$ increases with Gd concentration $x$. The simple model shown in Figure 1 illustrates the dependence of the net magnetic moment and angular momentum on $x$, but assumes that $\alpha$ is independent of $x$. In the upcoming discussion we show the equivalent diagram with $\alpha(x)$ as implied by the XMCD results (Figure 7).

Gd_xSm_1-xN films were grown in a Riber 32p molecular beam epitaxy (MBE) system on 100 nm thick (0001) AlN buffered Si, heated during growth to between $450$ and $700^{\circ}$ C depending on the composition. The growth rate was held to $100$ nm/h. High purity rare-earth metals were evaporated from conventional effusion cells to achieve the desired composition under nitrogen rich conditions ($P_{N_{2}}\approx 2.1\times 10^{-5}$ Torr). The composition of the solid-solutions was measured to within $x\pm 0.04$ using X-ray fluorescence (XRF) spectroscopy. X-ray diffraction confirmed (111)-oriented FCC NaCl structure, typical of the rare-earth nitride series.

Field in-plane SQUID magnetometry was performed in a Quantum Design Magnetic Property Measurements System (MPMS) capable of temperatures as low as 5 Kelvin and fields up to 7 Tesla. These measurements determine the temperature- and hysteretic field-dependent net magnetic moment across the para- to ferro-magnetic transition. In the present system that net magnetic moment is overwhelmingly dominated by the Gd ions, motivating support of the ionic-species resolution capability of XMCD to investigate the Sm³⁺ alignment separately. That alignment relates specifically to the 4$f$-shell spin and orbital states, suggesting the use of XMCD at the M_4,5 edge, which interrogates alignment in the 4$f$ shell. However, the surface sensitivity of XAS at the $\sim 1$ keV M-edge renders it unsuitable for the present study, and we have used instead XMCD at the L_2,3 edges of Gd and Sm. The hard-x-ray lanthanide L edge measurements probed the full $\approx$ 100 nm thickness of the films.

The L edge involves excitation into the $5d$ band, coupled to the $4f$ spin alignment by the strong $5d$-$4f$ exchange interaction. Thus, we report here the results of XMCD at the Gd and Sm L_2,3 edges to probe separately the alignment on the two cations. The measurements were performed at temperatures down to $5$ K and fields up to $6$ T at the BL39XU beamline at the SPring-8 synchrotron in Japan. All XMCD was performed at $10^{\circ}$ from grazing incidence.

XMCD at the two edges, L_2,3, separated by the spin-orbit interaction in the $2p$ core-hole state, can in principle yield information about the spin and orbital alignments in the final $5d$ state, though the failure of the XMCD sum rules for the L_2,3 edges prevent their use in the present case [12]. Furthermore, the Sm L₂ edge in these materials is masked by magnetic EXAFS from the Gd L₃ edge [13]. We thus focus the present discussion on the relatively weak L₃ edge of Sm and the stronger L₂ edge of Gd, interpreted in terms of the temperature- and composition-dependent spin alignments.

We have probed the alignment of the moments in Gd_xSm_1-xN by L-edge XMCD tracing out the spin alignments $\langle S_{z}\rangle$ independently on the Sm³⁺ and Gd³⁺ ions. Special care was taken to follow the XMCD signal amplitudes and the spin alignments $\langle S_{z}\rangle$ of the two ionic species as a function of the composition across the GdN/SmN solid solutions.

The XMCD study was supported by thorough magnetisation studies of the films. It is noted that the magnetisation is overwhelmingly dominated by the Gd³⁺ spin alignment, since the magnetic moment on the Sm³⁺ is more than two orders of magnitude the smaller. Magnetic measurements revealed the temperature-dependent magnetisation as well and complete hysteresis curves in the ferromagnetic phase that were used to inform XMCD measurements and limit those to magnetic fields adequate to ensure saturated magnetisation. There was excellent agreement between the magnetisation and Gd $\langle S_{z}\rangle$, but it is only XMCD that is capable of revealing the spin alignment $\langle S_{z}\rangle$ on the Sm³⁺ ions, the primary outcome of the study.

The sign of the Sm XMCD, opposite to that in SmN, immediately identifies that the alignment of the Sm and Gd spins by the Sm-Gd exchange interaction dominates the Sm³⁺ Zeeman interaction, which on its own acts to align the orbital magnetic moment in SmN [10, 2]. The data further show that the exchange dominance strengthens the Sm³⁺ spin alignment in the presence of Gd³⁺ ions; the projection $\langle S_{z}\rangle\approx\hbar$ in SmN, rising to $\langle S_{z}\rangle\approx 3\hbar/2$ for isolated Sm³⁺ ions in a predominantly GdN host. The composition-dependent alignment specifies that the composition at which an angular-momentum compensation can be expected is at higher values of $x$ than implied by measurements of pure SmN films.