Reduction of the ordered magnetic moment in YMnO₃ with hydrostatic pressure

M Janoschek^1,2, B Roessli¹, L Keller¹, S N Gvasaliya^1,4, K Conder³ and E Pomjakushina^1,3

¹ Laboratory for Neutron Scattering ETHZ and Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
² Physik Department E21, TU München, 85748 Garching, Germany
³ Laboratory for Developments and Methods, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland

⁴ On leave from: Ioffe Physical Technical Institute, 26 Politekhnicheskaya, 194021, St Petersburg, Russia

Received 11 August 2005, in final form 16 September 2005
Published 7 October 2005

1. Introduction

Yttrium manganite belongs to the family of rare-earth manganites RMnO₃ (R  =  rare earth element) which have both ferroelectric and magnetic order. These compounds crystallize in the hexagonal space group P6₃cm below the paraelectric-ferroelectric phase transition (T_C~900 K). The six Mn^3 +  magnetic moments in the unit cell are located in planes separated by ~5.7 Å along the hexagonal axis. In the z  =  0 plane the Mn atoms are placed along the a, b and  - (a + b) axes, whereas in the z  =  1/2 plane they are along the axes  - a,  - b and (a + b). The Mn atoms are centred in triangular bi-pyramids whose vertices are oxygen atoms. Because of the large distance between adjacent triangular layers, YMnO₃ is a good candidate for a geometrically frustrated two-dimensional antiferromagnet al though small exchange interactions along the hexagonal axis drive magnetic ordering at T_N≈70 K. The magnetic structure of YMnO₃ was first studied by neutron diffraction by Bertaut [1], who found that two spin arrangements give similar agreement between observed and calculated powder diffraction patterns. Both models describe a triangular arrangement of the S  =  2 magnetic moments in the basal plane with the coupling between adjacent layers being either ferromagnetic or antiferromagnetic (further on labelled according to their irreducible representations Γ₃ and Γ₁ respectively; all representations are derived in [2]; see figure 1). Although both structures lead to very similar magnetic neutron intensities, Muñoz concluded from recent neutron diffraction studies that the probable magnetic structure of YMnO₃ corresponds to Γ₁ with the magnetic moment of the Mn ions being μ  =  2.9 μ_B at saturation [2]. The reduction of the value of the magnetic moment from the expected 4 μ_B of Mn^3 +  free spins is taken as evidence that even in the ordered phase strong spin fluctuations are present due to geometrical frustration [3].

The RMnO₃ ferroics have received renewed interest since anomalies in the dielectric constant are found at the magnetic ordering temperature T_N [4], indicating a strong coupling between ferroelectric and magnetic properties. The origin of the magnetoelectric (ME) effect in these compounds is still not fully understood but spin-lattice interaction might play an important role in these materials. For example, anomalies of the structural parameters were reported at T_N that yield evidence that coupling between spin and lattice degrees of freedom is at the origin of the ME effect in YMnO₃ [5, 6]. In order to get more insight into the coupling between spin and structural parameters and their possible relationship with the magnetic and dielectric properties of ferroic materials, we investigated the influence of hydrostatic pressure on the magnetic ordering in YMnO₃.

2. Experimental details

Polycrystalline YMnO₃ was prepared by a solid state reaction. Starting oxides of Y₂O₃ and MnO₂ with 99.99% purity were mixed and ground followed by sintering at 1000-1200 °C in air for 100 h with several intermediate grindings. The phase purity of the compound was checked with a conventional x-ray diffractometer (Siemens D500). The neutron measurements were performed at the neutron powder diffractometer DMC located at the cold source of the neutron spallation source SINQ. The instrument was operated with λ  =  2.566 Å and a PG filter was installed in the beam to remove higher-order harmonics. For measurements at ambient pressure, 13 g of polycrystalline YMnO₃ were filled in a standard vanadium container (  =  15 mm). For the pressure experiments a clamp-type pressure cell was used, that can attain a maximum pressure of 15 kbar. Hydrostatic pressure is obtained by mixing the powder sample with Fluorinert. The effective pressure was calculated from the known pressure dependence of the lattice parameters of NaCl [7] that was mixed with the YMnO₃ sample. The sample was cooled in a ⁴He cryostat of ILL type.

3. Results and discussion

A first series of measurements was made at ambient pressure in the temperature range 1.5 K<T<300 K. A typical neutron diffraction pattern is shown in figure 2(a), that was analysed with the Rietveld method [8] implemented in the program FULLPROF [9]. The structural parameters found at T  =  300 K are presented in table 1. The fit of the magnetic structure of YMnO₃ was found to yield a slightly better agreement with the Γ₁ type (magnetic R_Bragg  =  4.68, χ²  =  5.57) than the Γ₃ structure (magnetic R_Bragg  =  5.13, χ²  =  5.55). We note that the symmetry of the Γ₃ structure allows the magnetic moments to have a component out of the ab-plane. However, agreement factors between observed and calculated intensities do not improve when spins are canted and we conclude that the magnetic moments lie in the hexagonal plane. With the Γ₁ structure, the value of the magnetic moment at T  =  1.5 K is 3.09(2) μ_B, in good agreement with the results of Muñoz et al . The temperature dependence of the staggered magnetization is shown in figure 3.

Table 1. Results of the Rietveld refinement of neutron powder diffraction data for YMnO3 at 300 K for ambient pressure and 9.6 kbar. Atomic positions: Y1 and O3 at 2a (0,0,z); Y2 and O4 at 4b ; Mn, O1 and O2 at 6c (x,0,z) for Mn z  =  0.

Figure 2. Observed and calculated ( - ) neutron diffraction patterns of YMnO3 at T  =  20 K for (a) ambient pressure and (b) p  =  8 kbar. The bars below the patterns denote the position of nuclear (upper row) and magnetic Bragg reflections (lower row). The diffraction pattern for p  =  8 kbar contains additional reflections due to the NaCl powder (denoted by arrows). Bragg peaks originating from the pressure cell were excluded from the data. In addition, we note that the background is modulated around 2θ  =  28°, mainly due to the presence of Fluorinert in the neutron beam.

Although the maximum load was applied to the pressure cell, we found that the effective pressure was 7.8 kbar at T  =  1.5 K and increased to 9.6 kbar at T  =  300 K. However, the pressure increased only slightly from 7.8 to 8.3 kbar in the temperature range 1.5 K<T<80 K, where YMnO₃ is antiferromagnetically ordered. Figure 2(b) shows a typical neutron diffraction pattern measured at T  =  20 K and p  =  8 kbar. Apart from Bragg reflections of YMnO₃, the diffraction pattern now contains additional reflections due to the NaCl powder. In addition, the background is high mainly due to the presence of Fluorinert in the neutron beam. Therefore, the statistical quality of the data is much reduced when compared with the results obtained at ambient pressure. The applied hydrostatic pressure mainly altered the lattice constant a whereas c remained almost unchanged (Δa/Δc≈2.5). The volume of the unit cell changed from v  =  374.802(4) Å³ at ambient pressure to v  =  373.460(5) Å³ at p  =  9.6 kbar. Comparison of the structural parameters shown in table 1 indicates that only the z-coordinate of the O1 atom is significantly modified by application of pressure. The shift of the O1 atom decreases the length of the Mn-O1 bond from 1.84 to 1.68 Å. A preliminary analysis of the data at T  =  1.5 K showed that the neutron diffraction peaks of YMnO₃ have very similar relative intensities as observed at ambient pressure. Least-square refinements of the diffraction pattern yielded good agreement factors for the magnetic structure with Γ₁ and Γ₃ symmetry, namely (magnetic) R_Bragg  =  9.95 and χ²  =  4.73 for Γ₁ and (magnetic) R_Bragg  =  9.97 and χ²  =  4.78 for Γ₃ respectively. Hence, the spin arrangement of YMnO₃ is not modified by hydrostatic pressure up to p~8 kbar. However, the magnitude of the ordered magnetic moments is significantly reduced from μ~3 μ_B at ambient pressure to μ  =  2.50(5) μ_B at p~8 kbar for the Γ₁ symmetry. We note that the ordered moment is reduced to μ  =  2.44(5) μ_B for magnetic structure with Γ₃ symmetry. The temperature dependence of the ordered magnetic moment is shown in figure 3. Although from neutron powder measurements it is difficult to determine the value of T_N precisely, we conclude from our data that the difference of the temperature of the phase transition from the paramagnetic to the ordered antiferromagnetic state is less than ~5 K at p  =  8 kbar as compared to ambient pressure. A possible model to describe the magnetic and ferroelectric properties of ferroic materials was proposed by Gong et al [10] that includes antiferromagnetic Heisenberg exchange interactions and a double-well potential for the lattice displacements giving rise to ferroelectricity. The ME coupling is described by an interaction of the form and for the intraplane and for the interplane component respectively, where and are the intra- and interplane ME coupling constants, u_k is the lattice displacement at site k, S_ai is the Heisenberg spin operator, i and j denote the nearest neighbours to k and a and b represent the nearest planes. In the mean-field approximation, the ME coupling leads to a renormalization of the intra- and interplane exchange integrals and to and respectively, where . In this approach, the Néel temperature is reduced by the ME coupling, but the value of the magnetic moment in the ground state is essentially unaffected [11]. Although this is consistent with the observation that in HoMnO₃ thespin reorientation temperature T_SR of the manganese sublattice shifts to lower temperatures by about 1.5 K at p~8 kbar [12], the model does not explain the moment reduction observed in YMnO₃.

4. Conclusion

We investigated the influence of hydrostatic pressure on the properties of the magnetic ground state of YMnO₃. The magnetic structure of YMnO₃ is found to have Γ₁ symmetry at p  =  8 kbar. On the other hand, the ordered magnetic moment at saturation is significantly reduced by application of pressure. This suggests that coupling between the size of the magnetic moment and the volume of the unit cell is important in ferroic materials and that application of hydrostatic pressure leads to an increase of the spin fluctuations in YMnO₃ and enhances the two-dimensional character of the magnetic properties of this compound. We suggest that application of pressure leads to a renormalization of the temperature dependence of the staggered magnetization, i.e. the strain influences the sublattice magnetization [13].

We thank D Sheptyakov for help and advice with the pressure cell and P J Brown for fruitful discussions. This work was performed at the spallation neutron source SINQ and was partially supported by NCCR MaNEP.

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