Magnetic structure driven by monoclinic distortions in the double perovskite Sr2YRuO6

The monoclinic double perovskite Sr2YRuO6 has recently gained a renewed interest in order to get a deeper insight into the exotic magnetic ground states associated with geometric frustration. Striking discrepancies between the spin order derived from the neutron diffraction refinements and the macroscopic magnetic and thermal responses is a major challenge that must be addressed. In this work, detailed neutron diffraction measurements as a function of temperature yield a completely different interpretation of the patterns. We show that at low temperatures a spin structure of the K2NiF4-type is an accessible configuration for the magnetic ground state. In the neighborhood of the magnetic transition, this configuration evolves into a canted superstructure. The deduced temperature dependence of the canting angle exhibits two closely spaced peaks, which are in excellent agreement with the double peaks in the magnetic contribution to the specific heat and in the thermal expansion coefficient. We explain these features in terms of reorientation of the net ferromagnetic moment of the noncollinear spin state, due to the local breaking of the inversion symmetry promoted by the monoclinic distortions, with structural changes acting as the driving force.


Introduction
Geometrically frustrated magnetic materials, such as double perovskites with chemical formula A 2 BB′O 6 , with B=Y, Ca, Na, or Li and B′=Ru, Mo, Os, or Re, exhibit a variety of fascinating magnetic structures comprising valence-bond glass [1], spin ice [2], spin liquid [3], and spin glass states [4], in addition to long-range ferromagnetic (FM) or antiferromagnetic (AFM) order [5]. A key point for this complex behavior is that the magnetic ions residing on the B′-sites present a face-centered-cubic (fcc) symmetry, which is a threedimensional lattice based on edge sharing tetrahedra, the simplest case of geometric frustration [6]. However, the fact that several isostructural materials with the same value of spin S of the magnetic ion show quite different magnetic responses reveals that a clear behavior pattern is not uniquely defined by frustration effects. Systematic studies of double perovskites with different S values [7][8][9] reveal that although S=1/2 quantum fluctuations are expected to be enhanced [7], several compounds of the family exhibit long-range ferromagnetism or antiferromagnetism [5], with minimal evidence of geometric frustration or a valence-bond glass state [1]. For S=1, a tuning of competitive superexchange interactions through slight structural changes leads either to lowdimensional short-range spin order or to a spin-frozen ground state [7,8], while for S=3/2, long-range order with very low variation in magnetic entropy emerges [9]. Therefore, a detailed understanding of these remarkable differences requires a careful correlation between the spin structure derived from neutron powder diffraction (NPD) refinements and results obtained from other techniques. A clear example comes from muonspin rotation and NPD measurements in La 2 LiMoO 6 [7], which yield contradictory results.
Despite the fundamental interest in understanding fcc antiferromagnets, in some cases, to the best of our knowledge, there is still a gap related to the validation of the NPD refinements using macroscopic measurements, and to the determination of whether geometric frustration indeed does have a leading role in the establishment of the magnetic ground state. In strongly distorted perovskites, crystallochemical details might introduce a significant contribution. The monoclinic double perovskite Sr 2 YRuO 6 , with a frustration index f∼15 [9], space group P2 1 /n, with pentavalent 4d 3 Ru 5+ ions in a high-spin state ( 4 A 2g ) with S=3/2, is a particularly suitable compound to address these topics. The collinear type-I AFM structure, derived from the only two NPD measurements reported [10,11], is inconsistent with magnetic measurements in single crystal [12] and polycrystalline samples [13][14][15], which conclusively show that this material is a weak ferromagnet. A crucial open issue is the nature of a double peak in the specific heat at T N1 =28 K and T N2 =24 K, just below the magnetic transition temperature, T M =32 K. Recently, this feature was interpreted in terms of a two-step model in which full long-range type-I AFM order at T N2 is preceded by two-dimensional (2D) magnetic fluctuations sandwiched between alternate parallel layers exhibiting partial long-range order at T N1 [11]. Following this approach, the ordered Ru moments in the layers are collinear for all temperatures and the coupling mechanism is completely based on geometric frustration considerations. Additional interest concerning Sr 2 YRuO 6 is that this compound might host an exotic type of high-T C superconductivity, when Ru ions are partially replaced by Cu (<15 at. %) [16]. It has been proposed that superconducting holes condensate in the nonmagnetic SrO layers [17]. This is still a controversial topic and a comprehensive knowledge of the magnetic ground state of the parent compound is of primary interest to understand how the superconducting order parameter would percolate through the pair-breaking effect of the Ru magnetic layers.
In this work, we present a detailed analysis of NPD patterns collected at various temperatures between 10 K and 300 K, with a fine temperature step of 1 K in the 20 KT33 K range. The emergence and subsequent disappearance of a forbidden line for the type-I AFM order as the temperature is varied in the interval between T N2 and T N1 allows us to refine the patterns using an alternative model, leading to a different interpretation of the nature of the double peak in the specific heat in terms of a noncollinear spin state accompanied by a reorientation of the associated net FM moment.

Experimental
The Sr 2 YRuO 6 sample was synthesized by a solid-state reaction. Stoichiometric amounts of high-purity RuO 2 , Y 2 O 3 , and SrCO 3 were ground together thoroughly in an agate mortar, placed in an alumina crucible, and fired first at 934°C for 24 h in air. The resulting powder was ground again, pressed into pellets, and heat treated in air at 1250°C, with intermediate regrindings, and finally sintered for 4 days with a 1°C min −1 cooling rate in an oxygen flow. NPD measurements were carried out on the time-of-flight diffractometer at the Powgen line of the Spallation Neutron Source Research Center at the Oak Ridge National Laboratory, USA, using a high-intensity pulsed beam. The sample was placed inside a vanadium can and held in a liquid helium cryostat. Neutron wavelengths λ=1.066 Å and λ=4.797 Å were used to scan a wide range of nuclear reflections and to measure in detail the Q region for magnetic peaks, respectively.
These vectors were automatically selected by the K-SEARCH subprogram in FullProf and confirmed by the Le Bail method according to the magnetic reflections. Refinements using K 0 and assuming a P2 1 /n space group for the magnetic reflections yield the reported type-I AFM order for TT N2 and T N1 T<T M , with good fit parameters, as shown in table 1 for selected temperatures. However, it was not possible to refine the patterns for the interval T N2 <T<T N1 using K 0 .
When using K 0 and the P2 1 /n space group for both nuclear and magnetic reflections, only collinear spin configurations can be generated from the corresponding base vectors of the irreducible representations. We recall that although the monoclinic symmetry of the Sr 2 YRuO 6 lattice is preserved on cooling, the bond distances and angles vary in a complex way [13], opening the possibility of noncollinear spin configurations as a consequence of unbalanced competitive FM and AFM interactions. These spin states would not necessarily exhibit the same periodicity of the lattice. Since Sr 2 YRuO 6 is a weak ferromagnet, in an attempt to allow a possible canted spin structure to emerge from the refinements, we use the triclinic P-1 space group for the magnetic reflections. In doing so, two Wyckoff positions for the Ru sites are considered and the corresponding Ru(1) and Ru(2) magnetic sublattices can be refined independently, with j 1 and j 2 being the azimuthal angles determining the respective orientation of the magnetic moments. Figure 1 shows the NPD pattern at T=10 K as a function of Q=(4π/λ)sinθ, with λ=4.797 Å (a) and λ=1.066) Å (b). In addition to the nuclear Bragg peaks, the magnetic diffraction reflections were clearly identified, since they appear just below T M . The intensity ratio of these magnetic reflections remains constant for T<T M . The calculated pattern after magnetic and crystal structure refinements using K 1/2 , the P-1 space group for the magnetic reflections, and keeping the P2 1 /n space group for the nuclear ones, yield a very good agreement with the experimental data, as shown in figure 1.
Weak reflections on both sides of the strong peak at ∼2.2 Å −1 correspond to a stray fraction of SrY 2 O 4 (<3%) that was identified and refined along with the Sr 2 YRuO 6 profile. The fit parameters are quite similar to those obtained using K 0 , as observed in table 1. However, the spin structure is of the K 2 NiF 4 -type [18], as shown in figure 2 for the elementary pseudocubic cell. In this configuration, the orientation of the Ru moments located at the center of the faces is reverted in relation to the type-I AFM structure. A small canting angle, within the error of the measurement, between spins located in neighboring cells was observed. We will return to this point in later sections. Therefore, the Ru moments in Sr 2 YRuO 6 at T=10 K have two accessible magnetic states, both with good fit statistics and meaningful physical parameters. For the K 1/2 case, the choice of the space group P-1 for the magnetic reflections, keeping the P2 1 /n space group for the nuclear ones, introduces a degree of freedom in the refinement that allows other spin configurations to be considered as possible ground states. Peak positions and relative intensities using K 0 and K 1/2 are not identical, but show only very slight differences within the corresponding refinement errors. Refinements at other temperatures in the intervals TT N2 and T N1 T<T M , using both K 0 and K 1/2 also show good matching.
The refinements for the interval T N2 <T<T N1 are more complex and interesting. Figure 3(b) shows a sequence of NPD patterns at closely spaced temperatures within this region. Profiles in a wide temperature range are shown in figure 3(a). This detailed temperature scanning allowed us to catch a remarkable feature: the emergence of a distinct magnetic reflection at T=27 K, quite close to T N1 =28 K. This additional peak, located Table 1. Fitting parameters of the Rietveld refinements of the Sr 2 YRuO 6 profiles for selected temperatures using the propagation vectors K 0 =(0, 0, 0) and K 1/2 =(1/2, 1/2, 0).  at Q=0.86 Å −1 , increases its intensity on cooling to T=26 K, diminishes for T=25 K, and disappears for TT N2 =24 K. It is a Gaussian symmetric reflection with line width given by instrumental resolution. Therefore, is not due to scattering from 2D fluctuations surviving below T M . Its intensity is similar or even slightly higher as compared to other magnetic peaks detected for all temperatures below T M . Most important, it was not possible to refine the NPD patterns for these three temperatures using K 0 , while a good refinement was achieved using K 1/2 . The fit parameters are presented in table 1. The resulting spin state is described by a canted magnetic superstructure along the c-axis, derived from the K 2 NiF 4 -type order previously obtained at low temperatures (see figure 2), and characterized by a canting angle η =|j 1 -j 2 -180°| that measures the deviation from the AFM orientation. The orientation of the Ru magnetic moments for this noncollinear state is shown in figure 4, which displays a top view from the c-axis of the pseudocubic cell. It is worth mentioning that the magnitude of the Ru magnetic moment shows a continuous and smooth decrease when crossing the  T N2 <T<T N1 region as T M is approached on warming, as shown in the inset of figure 5. Therefore, the use of K 1/2 as propagation vector yields physically meaningful results for the whole temperature range below T M. A remarkable feature of the temperature dependence of the canting angle η, which reaches a high value of 85°±5°, is a well-resolved double peak at temperatures quite close to T N1 and T N2 , as shown in figure 5. The two maxima observed for the thermal expansion coefficient, α, reported in [13] are also plotted for comparison. The excellent matching of the peaks unambiguously reveals that structural changes are involved in the rearrangement of the spin configuration just below T M , and clearly show the correspondence between the magnetic structure derived from the NPD refinements and the macroscopic properties. Additional support to the emergence of a canted spin state comes from the temperature dependence of the coercive field H C [14], which exhibits a maximum of ∼2 kOe close to T N1 followed by an abrupt decrease down to a few Oe near T N2 . We interpret this result as a consequence of reorientation of the net FM moment associated with the changes in the canted spin state detected by the variations in η. The collinear type-I AFM order cannot account for the H C (T) behavior.
The role of the structural changes as the dominant mechanism in determining the magnetic ground state is supported by the fact that the two maxima in C mag do not change when a magnetic field H=9 T is applied [14]. If, as proposed previously [11], the nature of these maxima was purely magnetic due to the transition from partial long-range spin order in alternate layers of the fcc Ru-sublattice at T N1 to full long-range order at T N2 , it would be expected that a high field would leave a signature in this process. This is indeed the case of the double perovskite Gd 2 YRuO 6 , for which the double peak in C mag due to the magnetic coupling between the Gd-and   figure 4, and the thermal expansion coefficient, α(T) (reprinted from [13]). Inset: temperature dependence of the magnitude of the magnetic moment of the Ru ions below the magnetic transition temperature T M =32 K after refinements of the NPD profiles using the propagation vector K 1/2 =(1/2, 1/2, 0). Ru-sublattices shifts and smears by applying a magnetic field of a few Tesla [19]. On the other hand, if the proposed coupling mechanism is actually an inherent property of the Ru fcc network, reflecting a general trend in fcc antiferromagnets [11], the double perovskite Ba 2 YRuO 6 must also present two maxima in the specific heat. However, only one λ-like sharp peak is observed [9,20]. In fact, Ba 2 YRuO 6 would be the ideal compound to exhibit this two-step mechanism, since the strength of the next-nearest-neighbors Ru-O-O-Ru interactions, assumed to be the key point for alternate layered coupling, is favored by the cubic structure of this compound. In contrast, the monoclinic Ca 2 YRuO 6 shows a broad peak for C mag with an unresolved structure that resembles the double peak observed for Sr 2 YRuO 6 [22]. The smearing of the doublet is probably due to 44% of partial disorder between the Ca/Y ions, generating slightly different local neighborhoods for Ru ions [21]. Other Rubased perovskites, such as monoclinic Ca 2 LaRuO 6 and cubic Ba 2 LaRuO 6 , with similar frustration index f∼18, exhibit type-I AFM and type-III AFM order, respectively, confirming that the structural distortions are relevant [22].

Conclusions
In summary, careful refinements of NPD measurements show that the low temperature magnetic ground state in Sr 2 YRuO 6 is of the K 2 NiF 4 -type, in contrast to previous studies. In the neighborhood of the magnetic transition temperature, the excellent matching between the double peaks in the canting angle of the Ru moments, the magnetic contribution to the specific heat, and the thermal expansion coefficient are interpreted in terms of a spin reorientation of the net FM moment associated with a noncollinear spin configuration. Comparison with the isospin compounds Ba 2 YRuO 6 and Ca 2 YRuO 6 supports that monoclinic distortions play a leading role in determining this canted structure, acting as the driving force of the magnetic response by unbalancing the fine equilibrium between FM and AFM interactions. Although geometric frustration is relevant, it cannot solely account for the observed features by simply considering the cancellation of the magnetic coupling between consecutive AFM square layers. Therefore, the magnetic and thermal responses of Sr 2 YRuO 6 do not reflect an inherent property of fcc magnets.