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Long and short range magnetism in the frustrated double perovskite Ba2MnWO6

The structural and magnetic properties of the face-centered cubic double perovskite Ba2MnWO6 were investigated using neutron powder diffraction, DC-magnetometry, muon spin relaxation and inelastic neutron scattering. Ba2MnWO6 undergoes Type II long-range antiferromagnetic ordering at a Neel temperature of 8(1) K with a frustration index, f = 8. Inelastic neutron scattering was used to identify the magnetic coupling constants J1 and J2, which were found to equal -0.080 meV and -0.076 meV respectively. This indicated that both of the magnetic coupling constants were antiferromagnetic with similar magnitudes, which is in contrast to other known 3d metal double perovskites Ba2MWO6. Above the Neel temperature, muon spin relaxation measurements and inelastic neutron scattering techniques identify a short-range correlated magnetic state that is similar to that observed in the archetypical face-centered cubic lattice antiferromagnet MnO.


I. INTRODUCTION
Geometrical frustration is a phenomenon which can prevent antiferromagnetic systems from achieving a unique ground state. This is driven purely by the structure of the material and 2 primarily affects lattices which consist of connecting triangular plaquettes, such as planar kagome lattices, pyrochlores and the face-centred cubic (fcc) structure [1]. Geometrical frustration can result in a number of novel states such as spin glass [2,3], spin ice [4,5] spin liquids [6,7] and other complex states such as the valence bond glass [8,9]. Frustration has also been shown to cause unexpected behaviour above the Néel temperature (TN), where short range correlations can take place [10,11]. Many of these novel spin states are found when magnetic cations are arranged in the fcc lattice and we have undertaken an extensive study of these frustration effects.
Magnetism in fcc lattice compounds can often be described using a simple J1-J2 Heisenberg model: where J1 is the nearest neighbour (NN) interaction, J2 is the next nearest neighbour (NNN) interaction, Si is spin at site i, and the sums are taken over all NN (J1) and NNN (J2) interactions respectively. Using the above equation, antiferromagnetic interactions are denoted using J < 0 whilst J > 0 for ferromagnetic interactions. Three distinct antiferromagnetically ordered ground states are possible depending on the relative strengths of the J1 and J2 interactions: Type I, Type II and Type III. Type II antiferromagnetic order is the most commonly observed magnetic structure in fcc lattices. The Type II structure occurs when J2 is dominant and antiferromagnetic, and as a result all next nearest neighbour magnetic cations couple antiferromagnetically. In this instance, magnetic frustration arises from the weaker J1 interaction as not all nearest neighbour magnetic cations are able to couple antiferromagnetically [12,13].
MnO is an archetypal Type II fcc antiferromagnet and has been shown to experience frustration effects. In 1949, Shull and Smart reported the detection of antiferromagnetic peaks at 80 K using neutron diffraction in this material. This was the first time this signature of antiferromagnetism was directly observed and MnO was correctly identified to possess the propagation vector of k = (1/2 1/2 1/2) corresponding to Type II order [14]. Since this was reported MnO has been keenly investigated and was initially reported to experience a structural phase transition from cubic to rhombohedral at its magnetic transition temperature of 118 K.
This transition was stated to enable long range antiferromagnetic order to take place within MnO, where Mn 2+ ions are arranged in a parallel configuration in (111) planes and any 3 perpendicular (111) planes are arranged in an antiparallel manner [15,16]. However, this is now known to be the result of a monoclinic distortion to space group C2, rather than a rhombohedral distortion [17]. More recently, MnO has also been reported to exhibit a shortrange correlated state above its transition temperature, which is thought to be the result of magnetic frustration within the system [18].  [19]. Further studies completed on Ba2MnWO6, correlated fairly well with this initial assessment, also indicating a type-II AFM structure [20]. However, the possibility of short-range magnetic correlations similar to those present in MnO has not been investigated nor are the magnetic interactions J1 and J2 known.
This study presents a comprehensive investigation of the magnetic behaviour observed in Ba2MnWO6 utilising neutron powder diffraction, DC-magnetometry, muon spin relaxation and inelastic neutron scattering. Using this range of techniques, Ba2MnWO6 we have characterised the Type II antiferromagnetic order below a transition temperature of 8(1) K. Above this transition temperature, a short range correlated state, similar to that described in MnO [18], was detected using muon spin relaxation in conjunction with inelastic neutron scattering.
Inelastic neutron scattering shows that the magnetic interactions J1 and J2 are both antiferromagnetic with almost equal magnitude, with J1 the slightly stronger coupling constant.
This is an unexpected trait of Ba2MnWO6 which is not observed in other similar double perovskites and is interesting as J2 interactions remain unfrustrated within the magnetic lattice.

II. EXPERIMENTAL
A powder sample of Ba2MnWO6 was prepared via solid state synthesis using stoichiometric quantities of BaCO3, MnO2 and WO3. The reagents were mixed with extensive grinding and 4 calcined in air at 800 °C. The powder was then thoroughly ground, pressed into 13 mm diameter pellets and subsequently heated to 1250 °C in a reducing atmosphere of 5% H2 in N2 for approximately 96 hours. These grinding and heating steps were repeated out until phase purity was achieved. A Panalytical X'Pert Pro diffractometer with a Cu Kα X-ray source was used to determine the phase purity of the samples.
Time of flight neutron powder diffraction experiments observed the low temperature nuclear structure and the long-range magnetic structure. This was completed on GEM, the General Materials diffractometer at the ISIS Neutron and Muon Source, Didcot, Oxfordshire, UK [21].
Approximately 6 g of powder was placed in an 8 mm cylindrical vanadium can and the data were corrected for absorption. The collected data set can be found at the following reference [22]. Structural refinements against these data used the General Structure Analysis System (GSAS), and a convolution of the Ikeda-Carpenter and pseudo-Voigt functions to describe the peak shapes [23]. The background was modelled using a shifted Chebyshev function. The magnetic form factor of the Mn 2+ ions was taken from the neutron data booklet [24].
Magnetic susceptibility measurements were carried out using a Quantum Design MPMS3 based at the Materials Characterisation Laboratory at the ISIS Neutron and Muon Source.
Temperature dependent magnetic susceptibility was measured between 2 K and 300 K under zero field cool (ZFC) and field cool (FC) conditions in an applied field of 1000 G.
Approximately 100 mg of Ba2MnWO6 was placed in a gelatine capsule and held tightly in place using a small quantity of PTFE tape. The filled capsule was then inserted into a plastic straw for measurement.
Muon spin relaxation measurements were carried out on EMU at the ISIS Neutron and Muon Source, where zero, transverse and longitudinal fields were applied to the sample [25]. Around 5 g of Ba2MnWO6 was densely packed into silver foil and placed on a silver sample holder.
Zero-field measurements were completed between 2 K and 30 K. A transverse field of 100 G was applied between 2 K and 30 K to observe the transition temperature. Longitudinal field measurements were carried out to study the decoupling of muon spins from the internal magnetic field. The measured data can be observed using the referenced DOI [26]. The data was analysed using the Mantid software [27].
Inelastic neutron scattering measurements were performed on the LET time-of-flight direct geometry spectrometer at the ISIS facility of the Rutherford Appleton Laboratory [28]. The sample was contained in a cylindrical aluminium can of diameter 10 mm and height 30 mm, which also contained helium exchange gas. The sample can was cooled by a helium cryostat.
Data were collected using neutrons with incident energies of 3.7 meV at temperatures between 2 and 100 K for ~3h each, these measured data sets can be found using the following reference [29]. The data were reduced using the MantidPlot software package [27]. The raw data were corrected for detector efficiency and time independent background following standard procedures [30].

A. Diffraction
Laboratory X-ray diffraction data indicate that the single phase double perovskite Ba2MnWO6 had been synthesised, with the fcc structure arising from Mn 2+ /W 6+ cation ordering over the octahedral sites of the perovskite structure as previously described [19,20].
Neutron powder diffraction was utilised to determine both the low temperature nuclear structure and to analyse the magnetic structure of Ba2MnWO6. This was carried out between temperatures of 2 K and 69 K. Throughout the temperature range there was no peak broadening or splitting and the nuclear phase could be accurately fitted using the fcc space group, Fm3 m, indicating no phase transition in the crystal structure down to 2 K. Conventional thermal expansion properties were exhibited by the material however a change in the slope of the lattice parameter could be observed around 9(1) K which is indicative of magnetostrictive behaviour [31]. A representative fitted diffraction pattern, collected at 2 K, and the thermal evaluation of the lattice parameters are presented in Figure 1.
In data sets collected at T ≤ 9 K, a number of additional Bragg peaks were evident at higher dspacings, whilst the data at shorter d-spacings remain unchanged, indicative of the onset longrange antiferromagnetic order. These peaks were readily indexed using a doubling of the crystallographic cell along each axis corresponding to a magnetic propagation vector k = (1/2 1/2 1/2). As the direction of magnetic moments in cubic materials like Ba2MnWO6 cannot be determined precisely using powder diffraction, different potential magnetic structures were used to identify which best described the magnetic structure of Ba2MnWO6 [32]. This was completed using the model building in GSAS with a simultaneous checking approach using the FULLPROF code [33,34]. The neutron data sets were initially fitted using the established Ising spin model as outlined for Ba2MnMoO6, [35] followed by the non-collinear model described for Ba2Nd0.10Mn0.90MoO6, [36] but neither approach provided a good match to the data.
Subsequently the magnetic structure of MnO was trialled. Despite the structural distortion observed in MnO below 118 K, this compound was considered to be a likely candidate due to the pseudo-fcc nature of the lattice and the presence of high spin Mn 2+ cations. In this model, the Mn 2+ magnetic moments within (111) planes are aligned in a parallel configuration but are aligned antiparallel to this in adjacent (111) planes. The direction of the magnetic moments alternate in parallel and antiparallel fashion along the (112 ) axes [18]. Rietveld refinements were completed using each of these models, which were identical bar the magnetic structure utilised. From this analysis the magnetic structure of MnO, gave the best fit to the observed data with Rwp = 4.52 and χ 2 = 4.73, the output from this refinement is shown in Table I. This refinement yielded an effective magnetic moment of 4.5(1) μB, the thermal evolution of which can be observed in Figure 2(a).

C. Muon spin rotation and relaxation
The local nature of the muon spin relaxation measurements on Ba2MnWO6 was used to complement the bulk techniques outlined previously. Initially, an external transverse field (TF-µSR) of 100 G was applied to the system and measurements were carried out between 1.6 K and 70 K to identify the transition temperature accurately. When the sample is in a paramagnetic state, the muon spins couple to the applied transverse field resulting in a large oscillating signal as depicted in Figure 4(a). In the magnetically ordered state, the static internal fields are much stronger than the weak applied transverse field and the oscillation is no longer 10 observed. Thus, the asymmetry of the oscillating signal in TF-µSR can be used to determine the transition temperature. Furthermore, the paramagnetic fraction of the sample at a given temperature can be estimated from the normalised magnitude of the oscillatory term relative to that observed in the paramagnetic regime at a high temperature of 70 K.
All of these data sets could be fitted using the sum of an oscillating decay, an exponential decay and a flat background. This is described by the following function: where Aosc, A2 and A3 correspond to the asymmetries of the oscillating decay, the exponential decay and the constant signal respectively, λ corresponds to the relaxation rate, f is the frequency of the oscillation (which is dependent on the applied transverse field) and φ is the phase of this oscillation. The decaying functions were related to any possible relaxation within the system, arising due to unpaired electrons whilst the flat background can be attributed to large static magnetic fields along the muon's initial spin direction. K, no asymmetry should be observed as the internal magnetic field is significantly greater than the applied transverse field. However, a small oscillation is observed which is attributed to muons implanted in the silver sample holder. As the temperature increases the fraction remains small until 8.25(8) K where the relaxing proportion of the material begins to increase, therefore this was identified as the transition temperature of the material. A further increase in the temperature shows a gradual increase in this relaxing proportion, and this was attributed to potential short-range magnetic correlations within the material. This gradual increase did not reach a plateau over the measured range up to 30 K.
Zero-field measurements were carried out between 1.6 K and 30 K. These showed characteristic low asymmetry below the ordering temperature which was found to increase with temperature. Between 1.6 K and 20 K the ZF-data sets could be fitted using:

3
This again corresponds to both relaxing and static behaviour present within Ba2MnWO6. This leads to two separate relaxations, where A1 corresponds to a slow relaxation and A2 corresponds to a faster relaxation, with relaxation rates of λ1 and λ2 respectively. The persistence of relaxation above the transition suggests that short-range correlations exist within the system.
At 30 K, the function reduces to: 11 4 At which point the short correlations are no longer detected by the implanted muons. initially low between 2 and ~8 K before a sharp rise at the transition temperature, this is followed by a more gradual increase between 8.5 K and 30 K, which is attributed to short range correlations. (d) ZF measurements carried out at a range of temperatures, above the transition the relaxation has a high asymmetry, whilst below TN the initial asymmetry is damped. (e) ZFmeasurement carried out at 20 K, fit using F = (A1exp(-λ1x)) + (A2exp(-λ2x)) + A3. This fit is indicative of potential short range correlations as two separate relaxation rates are able to persist above this transition temperature. (f) The longitudinal field data sets collected at 30 K, this is significantly above the transition temperature and from this it is clear that any magnetic behaviour is not decoupled by the external field, not even at 4000 G. This could suggest short range correlations between the Mn 2+ ions.
Longitudinal field measurements carried out above the transition temperature also support the presence of short-range magnetic correlations. Above TN, a full decoupling of the relaxation was not achieved when a longitudinal field of 4000 G was applied to the sample, as shown in Figure 4(f). If no magnetic interactions were taking place within Ba2MnWO6, then a full decoupling of the relaxation curve would be expected.

D. Inelastic neutron scattering
Inelastic neutron scattering measurements were carried out at a range of temperatures both below and above the transition temperature. Below TN these could be used to quantify the magnetic coupling constants within the system. Above TN, these could be used to give firm evidence of short range excitations taking place within Ba2MnWO6.
Initially, inelastic neutron scattering was carried out at 2 K, where distinct spin waves were observed within the system. This pattern was then compared to a SpinW simulation, based on the Hamiltonian presented in equation (1), to extract the values of the coupling constant using linear spin wave theory [37]. The spin wave spectra were well described by the J1-J2 Heisenberg model with NN J1 and NNN J2 interactions. From this practice it was found that J1 = -0.080 meV, whilst J2 = -0.076 meV. Figure 5 shows the level of agreement between the measured and simulated inelastic neutron scattering data. This results in a J2/J1 ratio of 0.95, indicating that both are of similar strength. Despite J1 being stronger than J2, this J2/J1 ratio corresponds to Type II magnetic order in the fcc J1-J2 model [12]. This is because in the fcc model all antiferromagnetic J2 interactions can be satisfied simultaneously but that is not the case for J1 interactions. When testing this model, a dominant J2 was also investigated using J1 = -0.010 meV and J2 = -0.146 meV, however, it was clear that this did not correlate with what was observed within the system. This is most clearly demonstrated by taking vertical cuts through the data as a function of energy transfer, integrating between |Q|=0.9 and 1.1 Å -1 , and comparing these with cuts through the SpinW simulations for the two different models. As depicted in Figure 5 interactions, as the fcc structure does not allow all NN spins to align antiferromagnetically.
Since J1 is stronger than J2, Ba2MnWO6 is relatively frustrated with f = 8. A number of parallels may be drawn between Ba2MnWO6 and MnO. Both materials possess Mn 2+ ions, and therefore a 3d 5 electronic configuration corresponding to S = 5/2. These are present in a high spin state and therefore experience no orbital contribution to their magnetic behaviour. Both Ba2MnWO6 and MnO have Type II antiferromagnetic order with TN = 8(1) K and 160 K, respectively. The materials are relatively frustrated with frustration indexes f = 8 for Ba2MnWO6 and f = 5 for MnO. Similar values have been reported for the J2/J1 ratio of both materials (~1), although the magnitude of J1 is smaller than J2 in MnO, whilst the opposite is true in Ba2MnWO6. A lower J2/J1 ratio corresponds to a greater degree of frustration in the Type II magnetic structure, which explains the higher frustration index experienced by Ba2MnWO6 compared to MnO. MnO has also recently been reported to experience short range magnetic correlations above its transition temperature which was evidenced by diffuse neutron scattering alongside reverse Monte-Carlo simulations. [18] One large difference between the two materials is that MnO experiences a combined magnetic and structural transition at TN, 16 whilst Ba2MnWO6 remains cubic down to 2 K with no structural transitions. This suggests that magnetoelastic coupling is weaker in Ba2MnWO6.

V. CONCLUSIONS
Neutron powder diffraction, DC-magnetometry, muon spin relaxation spectroscopy and inelastic neutron scattering were used to investigate the magnetic nature of Ba2MnWO6. Type-II long range magnetic order was observed by all of these techniques, which indicated a transition temperature of 8(1) K. The magnetic structure was characterised and found to have propagation vector, k = (1/2 1/2 1/2), although the direction of the magnetic moments cannot be accurately determined by powder diffraction, the magnetic structure was found to be best described by one related to another fcc lattice, MnO. Inelastic neutron scattering showed that