Transfer of magnetic order and anisotropy through epitaxial integration of 3$d$ and 4$f$ spin systems

TL;DR

This study demonstrates how magnetic order and anisotropy can be transferred through epitaxial interfaces in 3d-4f spin systems, revealing controllable magnetic states in oxide heterostructures.

Contribution

It provides new insights into the manipulation of spin structures via tailored exchange interactions in epitaxial oxide superlattices.

Findings

Development of a commensurate spiral state in Ni spins below 100 K.

Induction of Dy magnetic order and Ni spin reorientation below 18 K.

Reversible magnetic transition induced by an external 3 T magnetic field.

Abstract

Resonant x-ray scattering at the Dy $M_5$ and Ni $L_3$ absorption edges was used to probe the temperature and magnetic field dependence of magnetic order in epitaxial LaNiO$_3$-DyScO$_3$ superlattices. For superlattices with 2 unit cell thick LaNiO$_3$ layers, a commensurate spiral state develops in the Ni spin system below 100 K. Upon cooling below $T_{ind} = 18$ K, Dy-Ni exchange interactions across the LaNiO$_3$-DyScO$_3$ interfaces induce collinear magnetic order of interfacial Dy moments as well as a reorientation of the Ni spins to a direction dictated by the strong magneto-crystalline anisotropy of Dy. This transition is reversible by an external magnetic field of 3 T. Tailored exchange interactions between rare-earth and transition-metal ions thus open up new perspectives for the manipulation of spin structures in metal-oxide heterostructures and devices.

Figures

Equations

$$I_{\mu \nu }=|\sum _i{e}^{ı\mathbf{q}\cdot {\mathbf{r}}_i}{F}_i(E){\epsilon }_{\mu }\times {\epsilon }_{\nu }^{\ast }\cdot {\hat{\mathbf{m}}}_i){|}^2,$$

Full text

Exchange interactions between the localized $4f$ electrons in rare earths and the more itinerant $3d$ electrons in transition metals are of key importance in a wide spectrum of materials ranging from permanent magnets McCallum et al. (2014) to multiferroics Matsukura et al. (2015). The transition-metal subsystems in such materials typically exhibit magnetic order at high temperatures. Coupling to the rare-earth moments with large spin-orbit coupling pins the order parameter to the crystal lattice and greatly enhances the magneto-crystalline anisotropy that is central to the functionality of many magnetic materials. Progress in understanding and tailoring $3d-4f$ interactions is currently limited by the ability to efficiently integrate both subsystems in multinary compounds McCallum et al. (2014); Matsukura et al. (2015).

Metal-oxide heterostructures and superlattices have recently emerged as a powerful platform for the investigation and control of spin, charge, and orbital order Hwang et al. (2012). In field-effect devices built from such structures, gate electric fields can efficiently counteract built-in polarization fields and thus elicit large changes in the carrier density and transport properties. Manipulation of antiferromagnetic structures through external magnetic fields would open up many additional perspectives for electronic devices, but the large fields required to counteract the exchange interactions between transition metal ions prohibit most experimental investigations along these lines. Here we show that $3d-4f$ interactions in metal-oxide heterostructures can pin the orientation of the 3$d$ moments to directions determined by the anisotropy of the rare earth ions across the epitaxial interface. As a function of temperature, this pinning results in a spin reorientation transition within the transition metal layer. This transition is fully reversible by magnetic fields of a few Tesla, which couple to the 3$d$ moments indirectly via the large Dy moments. Rare-earth moments can thus serve as “anchors” for the magnetic-field-induced manipulation of magnetic order in metal-oxide heterostructures. In this way, the $3d$-electron system is disturbed only at the boundary, contrary to bulk multinary compounds where $4f$ elements inextricably influence both the magnetic interactions and the lattice structure.

The multilayer system we have chosen comprises two compounds, LaNiO3 and DyScO3, that have already been studied individually as components of metal-oxide heterostructures. Both compounds share the same pseudocubic perovskite structure with similar lattice parameters, and are therefore well suited for epitaxial integration. LaNiO3 is metallic and paramagnetic in its bulk form Goodenough and Raccah (1965); Demazeau et al. (1971); Lacorre et al. (1991), but non-collinear antiferromagnetism of the Ni ions appears below $T_{N}\sim 100$ K when 2 pseudocubic unit cells (u.c.) thin LaNiO3 layers are confined between insulators Boris et al. (2011); Frano et al. (2013). DyScO3 is commonly used as a substrate for metal-oxide heterostructures. It is a paramagnetic insulator and is known to exhibit magnetic order driven by Dy-Dy exchange interactions below 3.1 K Ke et al. (2009); Raekers et al. (2009), but the magnetic structure and anisotropy have not yet been investigated in detail. The trivalent La and Sc ions in the compounds constituting the superlattice have closed electronic shells and are nonmagnetic.

We have used pulsed laser deposition to grow superlattices of LaNiO3 and DyScO3, using a previously established protocol Sup . Three different superlattices have been studied: a) 2 u.c. LaNiO3 + 2 u.c. DyScO3 ($2||2$) repeated 15 times, b) 2 u.c. LaNiO3 + 4 u.c. DyScO3 ($2||4$) repeated 11 times, and c) 4 u.c. LaNiO3 + 4 u.c. DyScO3 ($4||4$) repeated 12 times. The superlattices were grown on DyScO3 substrates oriented in the (110) direction of their orthorhombic structure (space group $Pbnm$). The $Pbnm$ setting of the substrate is used throughout this article to index the reciprocal space of the superlattice. To develop a detailed, element- and layer-specific description of the magnetic structure of the superlattices, we have used a combination of magnetometry and resonant x-ray scattering (RXS) Fink et al. (2013). The RXS experiments were performed at the BESSY II undulator beamline UE46-PGM1 with photon energies tuned to the Ni $L_{3}$ edge (photon energy $E=853.4$ eV) or to the Dy $M_{5}$ edge ($E=1293.8$ eV), using a three-circle ultra-high-vacuum diffractometer. The magnetization was measured with a Quantum Design VSM magnetometer.

Before discussing the results of the RXS experiments, we describe measurements of the macroscopic magnetization of bulk DyScO3 which will be important to understand the x-ray data. Figure 1(a) shows the saturation magnetization measured at $T=$ 2 K as a function of angle in the $a$-$b$ plane, along with the results of an Ising model inspired by prior work on the isostructural compounds DyAlO3, TbAlO3, and DyCoO3 Holmes et al. (1972, 1968); Velleaud and Mercier (1975). The magnetic Dy3+ ions in the orthorhombically distorted perovskite structure are coordinated by 12 neighboring oxygens, which produce a crystal field of point-group symmetry $C_{1h}$. The crystal field splits the ${}^{6}H_{15/2}$ manifold of the free ion into 8 Kramers doublets, with a magnetic moment of 10 $\mu_{B}$ in the $M_{J}=\pm 15/2$ ground-state doublet. The low-symmetry crystal field produces a strong Ising anisotropy, with two inequivalent Ising axes (related by a mirror reflection in the $b$-$c$ plane) that alternate from site to site (Fig. 1(b)) Schuchert et al. (1969); Holmes et al. (1972). Since both Ising axes lie in the $a$-$b$ plane, the angular dependence of the saturation magnetization in this plane can be described by the sum of the absolute values of two cosine functions $\propto|cos(\alpha)|+|cos(-\alpha)|$ i.e., the projection of the full moments onto the direction of the applied field (black line in Fig. 1(a)). The Ising axes are found to lie at $\alpha=29^{\circ}$ from the $b$ axis. From the anisotropy of the Dy moments’ saturation (measured up to 7 T) it can be concluded that in this field and temperature regime the exchange energy $<<$ Zeeman energy $<<$ crystal field and spin-orbit energies.

We now discuss the RXS data which provide insight into the microscopic arrangement of the Dy and Ni magnetic moments in the LaNiO3-DyScO3 superlattices Scagnoli et al. (2006, 2008). Previous Ni $L_{3}$-edge RXS experiments on a ($2||2$) LaNiO3-DyScO3 superlattice grown on DyScO3 revealed a commensurate spiral state with magnetic Bragg reflections at momentum transfer $\mathbf{q}=$ ($\frac{1}{2}$ 0 $\frac{1}{2}$) [$\mathbf{q}=$ ($\frac{1}{4}$ $\frac{1}{4}$ $\frac{1}{4}$) in pseudocubic notation] below $T_{N}\sim 100$ K Frano et al. (2013). Here we report the observation of a magnetic Bragg reflection at the same momentum transfer $\mathbf{q}$, but for photons tuned to the Dy $M_{5}$ edge (Fig. 2(a)). This reflection is not observed in bulk DyScO3. It appears in the superlattice at low temperatures (Fig. 2(c), red diamonds), and exhibits an energy dependence characteristic of resonant scattering from the first order magnetic Bragg reflection of ordered Dy3+ moments (inset in Fig. 2(a)), with two peaks corresponding approximately to transitions of the type $\Delta M_{J}=\pm 1$ Schierle et al. (2010); Ott et al. (2006).

The magnetic Bragg reflection is also detectable at the Dy edge for a ($2||4$) superlattice (4 u.c. of DyScO3 per bilayer), but no longer for a ($4||4$) superlattice. Figure 2(a) provides a comparison of rocking curves around momentum transfer ($\frac{1}{2}$ 0 $\frac{1}{2}$) for the three samples, where the scattered intensity is normalized to the total number of DyScO3 layers. The weaker intensity recorded for the ($2||4$) superlattice indicates that the magnetic order is induced only in the interfacial DyScO3 layers. Since superlattices with 4 u.c. of LaNiO3 per bilayer do not exhibit antiferromagnetic order in the nickelate layers, the lack of magnetic scattering at the Dy $M_{5}$ edge for the ($4||4$) sample demonstrates that the magnetic order at the Dy sites does not result from confinement of the DyScO3 layers, but is rather induced in proximity to antiferromagnetic LaNiO3 by Ni-Dy exchange interactions across the epitaxial interface.

The direction of the magnetic moments in the superlattice can be inferred from the photon polarization dependence of the RXS cross section. In a magnetic RXS experiment, the scattered intensity is given by

[TABLE]

to first order in the magnetic moment $\mathbf{\hat{m}}_{i}$ of the ion located at $\mathbf{r}_{i}$. $\varepsilon_{\mu(\nu)}$ is the polarization of the incoming (outgoing) light, and $F_{i}$ is the photon energy ($E$) dependent scattering tensor Hill and McMorrow (1996). By rotating the sample about $\mathbf{q}$, the Bragg condition defined by the phase factor $e^{\imath\mathbf{q}\cdot\mathbf{r}_{i}}$ in equation 1 is preserved, but the scattered intensity is modulated as the projection of $\varepsilon_{\mu}$ onto $\mathbf{\hat{m}}_{i}$ changes. Rotation about $\mathbf{q}$ is parameterized by the azimuthal angle $\psi$ which is defined independently for each $\mathbf{q}$. For $\mathbf{q}$=($\frac{1}{2}$ 0 $\overline{\frac{1}{2}}$) we set $\psi=0$ when the scattering plane is spanned by ($\frac{1}{2}$ 0 $\overline{\frac{1}{2}}$) and $(1\,\overline{1}\,2)$, and the projection of the latter onto $\mathbf{k}_{in}$ is positive. $\psi$ increases for left handed rotation of the crystal about $\mathbf{q}$.

We recorded the integrated magnetic intensity (i.e., the area of a rocking curve about the magnetic Bragg peak) at $\mathbf{q}=$($\frac{1}{2}$ 0 $\overline{\frac{1}{2}}$) as a function of $\psi$, for both $\pi$ and $\sigma$ polarization of the incoming light (i.e., $\varepsilon_{\mu}$ perpendicular and parallel to the scattering plane, respectively). The polarization of the scattered light is not analyzed, so that $I_{\pi}\equiv I_{\pi\pi}+I_{\pi\sigma}$ and $I_{\sigma}\equiv I_{\sigma\sigma}+I_{\sigma\pi}$. Figure 2(b) shows the ratio $I_{\pi}$/$I_{\sigma}$ of integrated intensities measured at the Dy $M_{5}$ edge together with a model calculation of the $\psi$-dependence of $I_{\pi}$/$I_{\sigma}$ based on a collinear antiferromagnetic model, with the two angles specifying the Dy moment direction as free parameters. The best agreement was found for a structure in which the Dy moments form an angle of $25^{\circ}\pm 4^{\circ}$ with the $Pbnm$ $b$-axis in the $a$-$b$ plane (right panel of Fig. 3).

Interestingly, the crystallographic axis along which the ordered dysprosium moments are oriented agrees closely with one of the two Ising axes determined for bulk DyScO3 (Fig. 1). A magnetic structure that singles out one of the two moment directions of bulk DyScO3 is indeed expected in this situation, because the LaNiO3-DyScO3 interface is oriented such that the two Dy sites become crystallographically inequivalent (Fig. 1(b)). The RXS experiment cannot distinguish between structures of the form “up-up-down-down” and “up-zero-down-zero” (or linear combinations thereof). We note, however, that collinear structures with moments on all sites are strongly disfavored by the alternating Ising anisotropy of DyScO3 (Fig. 1), and that the RXS data rule out any non-collinear structure consistent with the alternating anisotropy. An “up-zero-down-zero” sequence of ordered moments, on the other hand, is physically plausible, because bulk DyScO3 is paramagnetic in the temperature range covered by our experiments ($T\geq 4$ K). The antiparallel orientation of next-nearest-neighbor Dy moments in the “up-zero-down-zero” structure is well matched to the commensurate spiral state of LaNiO3 (Fig. 3). The small or vanishing amplitude of the ordered moment on the other Dy site can then be ascribed to a reduced Ising anisotropy under the altered crystal-field conditions at the interface and/or competition between the Ising anisotropy and the exchange field. Both mechanisms weaken the effective field acting on the Dy moments such that it is insufficient to quench the magnetic fluctuations. Microscopic model calculations are required to quantitatively determine the magnetic Hamiltonian at the interface.

We now turn our attention to the magnetic structure of the Ni sublattice. In previous work on spiral order in tensile-strained PrNiO3 and LaNiO3 films/superlattices, the Ni spins were found to tilt symmetrically $28^{\circ}$ from the pseudocubic $c$ axis, with in-plane projections lying symmetrically between the pseudocubic $a$- and $b$-axes Frano et al. (2013). For $T\geq T_{ind}\sim 18$ K, the Ni $L_{3}$ edge data on our superlattices agree with this result (red line in Fig. 2(b)). Upon cooling below $T_{ind}$, however, we observe pronounced intensity changes of the Ni $L_{3}$ Bragg reflections, heralding a temperature dependent spin reorientation concomitant with the onset of induced magnetic order in the DyScO3 layers (Fig. 2(c)).

Figure 2(b) shows that the azimuthal dependence of $I_{\pi}$/$I_{\sigma}$ at the Ni $L_{3}$ edge for $T<T_{ind}$ differs from the one for $T\geq T_{ind}$, confirming a reorientation of the Ni spins. The blue line in Fig. 2(b) represents the results of a model calculation for the magnetic structure depicted in Fig. 3, which yields the best agreement with the experimental data collected at 4 K Sup . The interaction across the interface generates two inequivalent Ni sites, depending on whether the two adjacent ordered Dy moments are (1) parallel or (2) antiparallel to one another (see Fig. 3, right panel). Ni spins which see two parallel Dy moments reorient almost exactly antiparallel to these moments (in the $a$-$b$ plane, 18${}^{\circ}\pm 4^{\circ}$ from [010]), thereby gaining Ni-Dy exchange energy at the expense of the magneto-crystalline anisotropy energy resulting from the weak intra-atomic spin-orbit interaction of Ni. For Ni spins which see two antiparallel Dy moments, the Ni-Dy coupling is frustrated, and their orientation is determined exclusively by Ni-Ni exchange interactions in the spiral state (almost directly perpendicular to the surface at 8${}^{\circ}\pm 5^{\circ}$ from [110] and rotated in the sample plane 28${}^{\circ}\pm 20^{\circ}$ from [$\overline{1}$10] towards [001]).

Finally we address the response of the system to an external magnetic field $H$. In x-ray magnetic circular dichroism (XMCD) measurements at the Dy $M_{5}$ edge for $H$ along the [1 0 $\overline{1}$] direction at $T=4.4$ K, we observed a magnetic field-induced net Dy moment with 88$\%$ saturation at $H=3$ T (data not shown). It is expected that such a field induced breaking of the ($\frac{1}{2}$ 0 $\frac{1}{2}$) Dy magnetic structure renders the Ni-Dy exchange interaction ineffective, and that the temperature-induced reorientation of the spin spiral is thus reversed for sufficiently high $H$. RXS experiments at the Ni $L_{3}$ edge indeed reveal the expected $H$-induced spin-flop transition. The inset of Fig. 2(c) shows $I_{\pi}$/$I_{\sigma}$ at the Ni $L_{3}$ edge for $\psi=30^{\circ}$ as a function of applied field. The reorientation transition manifests itself as an upturn in $I_{\pi}$/$I_{\sigma}$ that saturates around 3 T, consistent with the Dy XMCD data. The $H$-induced spin reorientation is fully reversed upon removal of the field.

In summary, our comprehensive Dy $M_{5}$ and Ni $L_{3}$ edge RXS experiments have revealed an unusual magnetic ground state generated by $3d-4f$ exchange interactions across LaNiO3-DyScO3 interfaces. Whereas the Ni spin system imposes the periodicity of its magnetic order on the interfacial Dy moments, these moments in turn, rigid due to their large magneto-crystalline anisotropy, pin the Ni spins and induce a reorientation transition in the two-unit-cell thick LaNiO3 layer. With their 10 $\mu_{B}$ amplitude, the Dy moments provide “anchoring points” for external magnetic fields, which enable field-induced transitions for moderate field strengths. In contrast, applying magnetic fields of up to 5 T to LaNiO3-LaAlO3 superlattices, where no rare earth magnetic moment is present, induces only a slight canting of the Ni spin spiral Wu_ . The insertion of layers containing “anchor spins” could enable the control of the relative orientation of antiferromagnetic structures in spintronic devices and thus facilitate previously infeasible spin transport experiments.

Related effects have been investigated in the bulk multiferroic manganites TbMnO3 and DyMnO3, where magnetic-field-induced spin reorientations induce an electric polarization flop Kimura et al. (2003, 2005); Mochizuki and Furukawa (2009); Cuartero et al. (2015); Prokhnenko et al. (2007a, b); Kenzelmann et al. (2005). We emphasize, however, that the superlattice approach we have introduced here is quite distinct from the effect of chemical substitution in perovskites with electronically active transition metals. For instance, replacing La in LaNiO3 with the smaller Dy ion reduces the Ni-O-Ni bond angle and the electronic band width, and thus drives a phase transition into a charge-ordered insulating state. In contrast, the lattice structure and chemical bonding pattern in our superlattices are only minimally disturbed by the adjacent DyScO3 layers, and LaNiO3 can maintain its high electrical conductivity. Tailored $3d-4f$ exchange interactions in metal-oxide heterostructures and devices thus open up new perspectives for the manipulation of spin structures by external magnetic fields, complementary to the manipulation of the carrier density by gate electric fields.

We thank the German Science Foundation (DFG) for financial support under grant No. SFB/TRR 80.