Increasing the Phase-Transition Temperatures in Spin-Frustrated

Article pubs.acs.org/cm

Increasing the Phase-Transition Temperatures in Spin-Frustrated Multiferroic MnWO4 by Mo Doping Lynda Meddar,† Michael̈ Josse,‡ Mario Maglione,‡ Amandine Guiet,† Carole La,† Philippe Deniard,† Rodolphe Decourt,‡ Changhoon Lee,§ Chuan Tian,§ Stéphane Jobic,† Myung-Hwan Whangbo,*,§ and Christophe Payen*,† †

Institut des Matériaux Jean Rouxel (IMN), Université de Nantes, CNRS, Nantes, France CNRS, Université de Bordeaux, ICMCB, Bordeaux, France § Department of Chemistry, North Carolina State University, Raleigh, North Carolina 27695-8204, United States ‡

S Supporting Information *

ABSTRACT: Ceramic samples of MnW1−xMoxO4 (x ≤ 0.3) solid solution were prepared by a solid-state route with the goal of increasing the magnitude of the spin-exchange couplings among the Mn2+ ions in the spin spiral multiferroic MnWO4. Samples were characterized by X-ray diffraction, optical spectroscopy, magnetization, and dielectric permittivity measurements. It was observed that the Néel temperature TN, the spin spiral ordering temperature TM2, and the ferroelectric phase-transition temperature TFE2 of MnWO4 increased upon the nonmagnetic substitution of Mo6+ for W6+. Like pure MnWO4, the ferroelectric critical temperature TFE2(x) coincides with the magnetic ordering temperature TM2(x). A density functional analysis of the spin-exchange interactions for a hypothetical MnMoO4 that is isostructural with MnWO4 suggests that Mo substitution increases the strength of the spin-exchange couplings among Mn2+ in the vicinity of a Mo6+ ion. Our study shows that the Mo-doped MnW1−xMoxO4 (x ≤ 0.3) compounds are spin-frustrated materials that have higher magnetic and ferroelectric phase-transition temperatures than does pure MnWO4. KEYWORDS: MnWO4, multiferroic, spin frustration, magnetic exchange, inductive effect

1. INTRODUCTION Multiferroic materials, in which ferroelectric and magnetic orders coexist in the same phase, can be classified into two groups.1 In type I multiferroics, ferroelectricity and long-range magnetic order have different origins and can set in at different critical temperatures. As a result, the coupling between magnetic and ferroelectric properties, that is, the magnetoelectric coupling, is generally weak. High ferroelectric critical temperatures and polarizations can be experimentally observed. In type II multiferroics, ferroelectricity is driven by a chiral magnetic order, which removes inversion symmetry. Therefore, the magnetoelectric coupling can be strong so that these materials are interesting from a fundamental point of view and are potentially useful. However, most of them exhibit weak spontaneous ferroelectric polarizations and suffer from low critical temperatures because they are spin-frustrated antiferromagnets. Any strategy aimed at increasing critical temperatures or ferroelectric polarization in type II magnetoelectric multiferroics would be of interest. The principal objective of this work is to examine whether the critical temperatures of MnWO4 can be increased by chemical substitution. Among the reported type II multiferroics, MnWO4 stands out due to its rather simple crystal structure,2,3 strong magnetoelectric coupling,4−6 interesting domain effects,7,8 and possible chemical substitutions at the Mn site.9−12 As will be described in section 3, the monoclinic wolframite crystal © 2012 American Chemical Society

structure of MnWO4 contains zigzag chains of Jahn−Tellerinactive Mn2+ (d5, S = 5/2) ions along the c axis. MnWO4 undergoes three successive magnetic transitions at TN = 13.5 K, TM2 = 12.3 K, and TM1 = 7.5 K.13 These transitions separate different magnetic structures termed AF1, AF2, and AF3. Below TM1, the AF1 structure has a collinear ↑↑↓↓ spin arrangement along the chains. In the AF2 state between TM1 and TM2, an incommensurate (IC) helical spin spiral propagates along the chain direction. A partially ordered collinear structure (AF3) with IC sinusoidal spin modulation along the c axis is observed between TM2 and TN. These magnetic structures emerge as a consequence of competing intrachain and interchain exchange interactions in the presence of weak local magnetic anisotropy.14,15 Spin frustration occurs not only within each zigzag chain along the c direction but also between the chains in the a direction. The AF2 spin spiral magnetic phase observed between TM1 and TM2 shows spontaneous electric polarization, with ferroelectric critical temperatures TFE1 and TFE2 equal to TM1 and TM2, respectively.16−18 In the present work we examine how the critical temperatures of MnWO4 are affected by the substitution of Mo for W. Ceramic samples of the MnW1−xMoxO4 (x ≤ 0.3) solid Received: October 23, 2011 Revised: December 12, 2011 Published: January 6, 2012 353

dx.doi.org/10.1021/cm2031653 | Chem. Mater. 2012, 24, 353−360

Chemistry of Materials

Article

3. CRYSTAL STRUCTURE CONSIDERATIONS AND COMPUTATIONAL DETAILS Wolframite-type MnWO4 crystallizes in the monoclinic P2/c space group.2,3 The building blocks are MnO6 octahedra containing Mn2+ ions and WO6 octahedra containing diamagnetic W6+ (d0) ions. The distorted MnO6 (WO6) octahedra share edges to form zigzag MnO4 (WO4) chains running along the c-direction (Figure 1). The three-dimensional (3D) structure of

solution were synthesized and characterized for the first time. We choose to replace W6+ with Mo6+ for the following reasons. Both ions have the same nonmagnetic d0 configuration and have almost the same ionic radius, which facilitates the substitution with little change in the crystal lattice for low x values. For a sufficiently high nominal starting Mo composition, a two-phase system is expected because MnWO4 and MnMoO4 do not have the same crystal structure when the synthesis reactions are carried out at ambient pressure.19,20 Furthermore, Mo is slightly less electronegative than W (i.e., 2.16 versus 2.36 according to the Pauling electronegativity scale), so that Mo doping is expected to induce changes in the local electronic structure. Since the Mo−O bond is expected to be more ionic than the W−O bond, the Mn−O should become more covalent according to the inductive effect.21,22 Thus, Mo doping is anticipated to increase the strength of the Mn−O−Mn superexchange interactions, and hence the magnetic phase transitions are expected to increase upon Mo doping. Indeed, we show in the present work that Mo doping in MnWO4 increases both the magnetic ordering and ferroelectric critical temperatures, and that the spin-exchange interactions of a hypothetical wolframite-type MnMoO4 are stronger than those of MnWO4.

2. EXPERIMENTAL DETAILS Ceramic samples of MnW1−xMoxO4 (0 ≤ x ≤ 0.3) were prepared via a solid-state reaction method. Stoichiometric amounts of high-purity MnO, MoO3, and WO3 powder materials were ball-milled, and the resulting mixtures were pelletized and heated at 850 °C for 30 h in air with several intermediate grindings. Pellets (0.5 g) were then sintered at temperature above 1100 °C in air after their sintering behavior was studied by use of a dilatometer. The relative density of all sintered samples was higher than 90%. The chemical homogeneity and cation stoichiometries were checked by means of energy-dispersive X-ray spectroscopy (EDS) at different positions on the sample surfaces. Within the experimental accuracy of a few percent, the results agreed with the nominal starting concentrations of the metal atoms (i.e., Mn, W, and Mo). The ceramic samples and the starting materials were also examined by X-ray powder diffraction (XRD) on a Bruker D8 diffractometer with Cu KLII.III radiation. Diffuse reflectance spectra were recorded in the range of 200−1250 nm (i.e., 1.0−6.2 eV) at room temperature with a UV−visible−near-infrared spectrometer (Lambda 1050, PerkinElmer). A mirror sample was used as the reference for 100% reflectance. Direct current (dc) magnetization measurements were made on a superconducting quantum interference device (SQUID) magnetometer (MPMS, Quantum Design) with heating or cooling rates of 0.03 K/min. No sign of ferro- or ferrimagnetic impurity phase (e.g., Mn3O4) was seen in fieldand temperature-dependent magnetizations, M(H) and M(T), respectively. Dielectric measurements were performed on sintered discs by use of an HP4194a impedance bridge. Samples were loaded in a Quantum Design physical properties measurement system (PPMS), and measurements were taken in the frequency (f) range 102−103 kHz and in the temperature range 2−20 K. All capacitances and loss data were collected at heating and cooling rates of 0.2 K/min and at magnetic field up to 9 T. All samples displayed very small capacitances. At T = 5 K and f = 788 kHz, for instance, the capacitance lies in the range 6.9−8.1 pF in the absence of magnetic field and 7.1−8.0 pF in a magnetic field H = 9 T. The ferroelectric transitions were associated with even smaller variations of the capacitance.

Figure 1. Perspective views of the three-dimensional arrangement of MnO4 and WO4 chains in wolframite-type MnWO4, viewed perpendicularly to the bc plane (top) and perpendicularly to the ab plane (bottom). O atoms are represented by small red spheres. MnO6 and WO6 octahedra are represented in magenta and gray, respectively.

MnWO4 is obtained from these MnO4 and WO4 chains on sharing their octahedral corners. In this structure, layers of magnetic Mn2+ ions parallel to the bc plane alternate with layers of diamagnetic W6+ ions along the a-direction. To evaluate the effect of Mo doping on the spin-exchange interactions of MnWO4, it is necessary to evaluate the spinexchange interactions of a hypothetical MnMoO4 that is isostructural with MnWO4 (hereafter w-MnMoO4). Although they crystallize in the same monoclinic system, MnWO4 and MnMoO4 do not have the same structure when they are prepared at ambient pressure.19,20 In the ambient-pressure molybdate α-MnMoO4, the Mn and Mo atoms occupy sixand four-coordinate positions, respectively.19 A wolframite-type MnMoO4 that is isostructural with MnWO4 has been synthesized at high pressure.23,24 Heating this high-pressure phase in air (at atmospheric pressure) to elevated temperatures, that is, above 500 °C, converts it to the α-MnMoO4 phase,23 showing that wolframite-type MnMoO4 is metastable under 354



Article

ambient conditions. We therefore constructed the structure of w-MnMoO4 by employing the space group P2/c and the unit cell parameters of MnWO4 (i.e., a = 4.8226 Å, b = 5.7533 Å, c = 4.9923 Å, α = 90°, β = 91.075°, γ = 90°)13 because the doping-induced change in cell parameters is extremely small for low Mo doping rate (see section 4A). We then optimized the atom positions on the basis of first-principles density functional theory (DFT) calculations, which we carried out by employing the Vienna ab initio simulation package (VASP), the generalized gradient approximations (GGA) for the exchange and correlation corrections, with a plane-wave cutoff energy of 400 eV, a set of 196 k-points for the irreducible Brillouin zone, and a threshold of 10−6 eV for the self-consistent-field convergence of the total electronic energy. To account for the electron correlation of the Mn 3d states, the GGA plus on-site repulsion U (GGA+U) method25 was employed with an effective U = 4 eV on the Mn atom. The resulting crystal structure of w-MnMoO4 is summarized in Table 1. All optimized atom positions are similar to those of MnWO4.

Figure 2. Room-temperature powder XRD patterns of MnW1−xMoxO4 ceramic samples taken with Cu KLII.III radiation. Patterns are vertically shifted for the sake of clarity. The upper pattern, which was recorded for a sample with nominal starting composition x = 0.4, shows extra peaks, marked with arrows, attributed to α-MnMoO4. The inserted graph shows the cell volume of MnW1−xMoxO4 as a function of x (error bars are slightly smaller than the size of the symbols).

Table 1. Atom Positions of w-MnMoO4a atom

Wyckoff position

x

Mn

2f

1/2

Mo (W)

2e

0

O1

4g

O2

4g

0.2178 [0.2108(3)] 0.2715 (0.250(2))

y 0.6070 [0.6853(4)] 0.1516 [0.1795(4)] 0.1318 [0.1024(2)] 0.37289 [0.375(2)]

z 1/4

At room temperature, the relative change of the cell volume for x = 0.3, [V(x = 0.3) − V(x = 0)]/V(x = 0) = −3 × 10−3, is very small. Indeed, the same relative change of the cell volume would be observed for a pure MnWO4 sample if a MnWO4 sample were cooled from 300 to about 150 K, assuming that the thermal expansion coefficient of pure MnWO4 is the same as that of wolframite-type ZnWO4,29 as has been suggested by theoretical calculations30 (To our knowledge, details of lattice expansion of MnWO4 in a broad temperature range have not been reported so far.) From this, it can be concluded that lattice contraction cannot explain the principal effects of Mo substitution on the electronic and physical properties. B. Optical Properties. In order to describe some effects of Mo substitution on the electronic structure, optical properties were investigated by means of diffuse reflectance measurements. Figure 3 shows Kubelka−Munk transformed reflectance spectra (i.e., the equivalent of the absorption spectra); KM = (1 − R)2/2R, where R is the reflectance.31 The spectrum for

1/4 0.9225 [0.9419(2)] 0.4115 [0.392(2)]

a

Atom positions were determined by GGA+U calculations (U = 4 eV) with space group P2/c and cell parameters (a = 4.8226 Å, b = 5.7533 Å, c = 4.9923 Å, α = 90°, β = 91.075°, γ = 90°) of MnWO4. Atom positions of the published crystal structure of MnWO413 are given in brackets.

4. RESULTS AND DISCUSSION A. Crystal Structure of MnW1−xMoxO4. We first describe the influence of Mo doping on the crystal structure of MnWO4. Figure 2 presents the room-temperature XRD patterns of some MnW1−xMoxO4 samples. All patterns show very narrow diffraction peaks. For nominal starting compositions with x > 0.3, a few diffraction peaks attributed to α-MnMoO4 show up in the patterns, consistent with the existence of limited solid solubilities in the MnWO4−MnMoO4 system at ambient pressure.26 For x ≤ 0.3, the data were analyzed with the Rietveld method, using the published P2/c wolframite crystal structure of MnWO4 as a starting model and a random distribution of the Mo and W ions on the Wyckoff 2e position. Prompted by EDS analysis, the fractional occupancy for Mo at the W site was held fixed to the Mo content x. With this model, all patterns were successfully refined by use of the JANA program.27 The Mn−O and W/Mo−O bond lengths calculated from the refined lattice parameters and atomic coordinates compare well with those observed for MnWO4. Both the Mn and W environments are not significantly impacted by the Mo substitution. As shown in Figure 2, the cell volume linearly decreases with increasing Mo content, at a very small rate of −0.0125 Å3 per 1 mol % of Mo doping, because Mo6+ ion is slightly smaller in size than W6+ (ionic radii of Mo6+ and W6+ ions at an octahedral site are 0.59 and 0.6 Å, respectively28).

Figure 3. Room-temperature Kubelka−Munk transformed reflectance spectra [KM = (1 − R)2/2R, where R is the reflectance] of MnW1−xMoxO4 ceramic samples (0 ≤ x ≤ 0.2). 355



Article

MnWO4 agrees well with published data.32−34 The broad absorption band peaking at about 2.2 eV has been associated with intra-atomic Mn2+ d−d transitions, while the absorption threshold at 2.7 eV has been assigned to a charge transfer (CT) transition from the O 2p to the Mn 3d and W 5d states.32,33 As can be seen in Figure 3, this CT absorption shifts to lower energies with increasing Mo content, consistent with change in color from yellow-green to red-orange. This is due to a decrease in the band gap induced by Mo doping (see section 4E). A similar trend has been observed in the K3P(Mo(1−x)Wx)12O40 (0 ≤ x ≤ 1) series.35 C. Magnetic Properties. We now turn to the effect of Mo doping on the bulk magnetic properties. Across the 30−300 K temperature range, the paramagnetic susceptibility of MnW1−xMoxO4 obeys a Curie−Weiss law, χ(x, T) = C(x)/ [T − θ(x)], with negative θ(x) for all x, showing that the principal magnetic interactions remain antiferromagnetic in the Mo-doped samples. The effective moments per Mn atom, calculated from the Curie constant C(x), are in the range 5.8− 5.9μB, consistent with the spin-only value of 5.92μB expected for the high-spin Mn2+ (S = 5/2) ion. Increasing the Mo content leads to a moderate increase in the absolute θ(x), from |θ(0)| = 70(1) K to |θ(0.3)| = 74(1) K. Within the mean-field model, in which the Weiss temperature is given by θ = [S(S + 1)/3kB] ∑i ziJi, where Ji is the exchange coupling between a central spin and the zi spins linked by Ji, this increase indicates the strengthening of some or all the spin-exchange couplings Ji between Mn2+ spins upon the Mo substitution. For all x values, the Curie− Weiss law is observed down to temperatures significantly lower than the absolute Weiss temperature, indicating that the spin frustration in MnWO4 survives the Mo substitution. The same trend was observed for the Mn1−x(Mg,Zn)xWO4 solid solutions where Mn2+ ions are replaced with nonmagnetic Mg2+ or Zn2+ ions.12 The magnetic susceptibility data obtained below T = 20 K are shown in Figure 4. The Néel temperature TN, noticed

dependences of the magnetic heat capacity for antiferromagnetic systems.37 As can be seen in Figure 5, TM2 and TN increase with

Figure 5. Derivative of the temperature-dependent magnetic susceptibility of MnW1−xMoxO4 ceramic samples (x ≤ 0.3). Vertical lines indicate the magnetic phase-transition temperatures of MnWO4.13

Mo content at almost the same rate of 0.063 K per 1 mol % Mo. While the AF1-to-AF2 transition shows up as a sharp hysteretic peak at TM1 ≈ 7.5 K in dχ/dT for pure MnWO4,12,13 a broad steplike anomaly in dχ/dT is observed without any sign of thermal hysteresis or magnetic irreversibility at low Mo concentrations (Figure 5). This anomaly becomes invisible for x ≥ 0.20. This feature does not necessarily indicate that Mo doping stabilizes the AF2 helical magnetic structure seen in MnWO4. Neutron diffraction studies on single crystals are needed to find how the Mo substitution impacts the three different magnetic structures of MnWO4. TM2 and TN are plotted as a function of x in Figure 6. As both the Néel

Figure 6. Phase-transition temperatures in MnW1−xMoxO4 ceramic samples plotted as a function of Mo concentration x. TN(x) and TM2(x) were determined from magnetic susceptibility. TFE1(x) and TFE2(x) were determined from our dielectric measurements, except for TFE1(0), which was previously determined from singlecrystal data.16,17 The dashed lines are guides for the eyes.

Figure 4. Temperature dependence of the zero-field-cooled magnetic susceptibility of MnW1−xMoxO4 ceramic samples (x ≤ 0.3) obtained at H = 1 kOe. Vertical lines indicate the magnetic phase-transition temperatures for MnWO4.13

temperature and absolute Weiss temperature increase with x at approximately the same rate, the Mo substitution does not significantly impact the frustration parameter |θ|/TN, so the Mo-doped samples exhibit the same degree of spin frustration as in the pure system, that is, |θ|/TN ≈ 6. This, along with the observation of a doping-induced increase in TM2, suggests that the Mo-doped phases MnW1−xMoxO4 should also exhibit magnetically induced ferroelectricity with critical temperatures higher than in pure MnWO4.

as a decrease in χ(x, T), clearly increases with increasing Mo content. The changes in the two magnetic transition temperatures TM1 and TM2 are more difficult to follow in the dc susceptibility data because these transitions may be associated with tiny slope changes in χ(x, T). As previously done for pure and doped MnWO4,11,13,36 TM1 and TM2 were identified as the temperatures of peaklike anomalies in the dχ/dT versus T curves. Identical values were obtained from the d(χT)/dT versus T curves (not shown here), which mimic the temperature 356



Article

D. Dielectric Properties. Low-temperature dielectric responses were then investigated between 100 kHz and 1 MHz. No dielectric dispersion was observed in either the capacitance or loss factor, indicating that the ferroelectric nature of the observed dielectric anomalies is retained upon Mo doping. Figure 7 shows representative temperature-dependent data for the

The x dependences of TFE1 and TFE2 are compared with those of the magnetic phase transitions TN and TM2 in Figure 6. Given the experimental uncertainties and differences in warming rates, it is clear from Figure 6 that TFE2 is equal to TM2 for all x values. This finding shows that the MnW1−xMoxO4 materials are magnetic multiferroic with a critical temperature higher than that of pure MnWO4. As can be seen from Figure 6, all phase-transition temperatures increase with increasing x, at approximately the same rate, suggesting a common origin to the x dependence of these transition temperatures. If a wolframite form of MnMoO4 were thermodynamically stable at ambient pressure, the linearly extrapolated values of TFE2 = TM2 and TN would be about 19 and 20 K, respectively. We also measured the dielectric responses under applied magnetic fields up to 9 T. Figure 8 shows representative data

Figure 7. Temperature dependence of the capacitance, C(T) − C(5 K), and the loss factor, tan δ(T) − tan δ(16 K), of MnW1−xMoxO4 ceramic samples (x ≤ 0.3), measured in the absence of magnetic field at 788 kHz during the cooling run.

capacitance and loss tangent of MnW1−xMoxO4 in zero magnetic field. For pure MnWO4, sharp peaks are observed at TFE2(x = 0) ≈ 12 K in both the capacitance and loss tangent, in agreement with published data.16−18 There is also a broad steplike anomaly in the capacitance that corresponds to the stepwise transition previously seen at TFE1(x = 0) ≈ 7.5 K on single crystals.17 The two peaks at TFE2 shift to higher temperature with increasing extent of Mo doping for all operating frequencies. For each Mo content x, the peak in the loss factor coincides with the peak in the capacitance, which confirms that the ferroelectric nature of the transition at TFE2 is retained. A weaker but well-defined peak in the capacitance is also seen above TFE1(x = 0) ≈ 7.5 K, and its position, TFE1(x > 0), increases with increasing x. Because there is a progressive disappearance of the slope change in magnetic susceptibility at TFE1 with increasing Mo doping (see section 4C), we cannot say that these anomalies are associated with a AF2-toAF1 transition, as in pure MnWO4. In Mn1−xMgxWO4 with x = 0.05, 0.10, and 0.15, additional low-temperature dielectric anomalies were also detected without any corresponding anomalies in the magnetization.12,38 A recent study of the pyroelectric properties of a ceramic sample of Mn0.85Mg0.15WO4 showed that this Mg-doped sample remains ferroelectric below TFE1.38

Figure 8. Temperature dependence of the capacitance, C(T) − C(5 K), and the loss factor, tan δ(T) − tan δ(16 K), of MnW1−xMoxO4 ceramic samples (x ≤ 0.3), measured in an external magnetic field of 9 T at 788 kHz during the cooling run.

obtained for an external field of 9 T. For our polycrystalline sample of MnWO4, double peaklike anomalies are observed at TFE2 in both the capacitance and loss tangent, consistent with published single-crystal data obtained for magnetic fields applied along different crystal directions.17 As in zero magnetic field, these peaks at TFE2 shift to higher temperature with increasing Mo content x at approximately the same rate. Very weak anomalies, which may correspond to the transition observed at TFE1 in zero magnetic field, are visible in capacitance for low doping up to x = 0.15. Single crystals are clearly needed to further explore how the phase transitions and magnetoelectric properties of the MnW1−xMoxO4 series are affected by the Mo doping. 357



Article

Figure 9. TDOS and PDOS plots obtained for the AF4 state14 of (a) MnWO4 and (b) w-MnMoO4 from the GGA+U calculations.

Figure 10. (a) Four spin-exchange paths (J1−J4) in wolframite-type MnMoO4 within each bc layer of Mn2+ ions. (b) Five spin-exchange paths (J5−J9) between adjacent bc layers of Mn2+ ions in hypothetical wolframite MnMoO4. The numbers 1−9 refer to the spin-exchange paths J1−J9, respectively.

J1−J9, defined in Figure 10, were evaluated by performing GGA+U calculations for the 10 ordered spin states of w-MnMoO4, which were used for MnWO4. The relative energies of these states determined from our GGA+U calculations are summarized in Table S1 in Supporting Information. To extract the values of the spin-exchange parameters J1−J9, we express the total spin-exchange interaction energies of the 10 ordered spin states in terms of the spin Hamiltonian:

E. Electronic Structure, Spin-Exchange Interactions, and Magnetic Phase-Transition Temperatures of wMnMoO4 and MnWO4. The total density of states (TDOS) and the partial density of states (PDOS) plots calculated for the magnetic ground state (i.e., the AF4 state in ref 14) of MnWO4 and w-MnMoO4 are presented in Figure 9. Both MnWO4 and w-MnMoO4 have a band gap, but w-MnMoO4 has a considerably smaller one. In both compounds the valence band maximum (VBM) is represented by the top of the Mn 3d bands. The conduction band minimum (CBM) is represented by the bottom of the W 5d bands in MnWO4 and by the bottom of the Mo 4d bands in w-MnMoO4. The CBM is substantially lower in energy for w-MnMoO4 than for MnWO4, hence leading to a smaller band gap for w-MnMoO4. This means that the W 5d−O 2p antibonding in the CBM of MnWO4 is much stronger than the Mo 4d−O 2p antibonding in the CBM of w-MnMoO4. The latter results from the fact that the W 5d orbitals, being more diffuse than the Mo 4d orbitals, overlap better with the O 2p orbitals than do the Mo 4d orbitals. In essence, the Mo doping in MnWO4 has the effect of reducing the band gap, as found experimentally (see section 4B). The spin-exchange interactions between Mn2+ ions of w-MnMoO4 were evaluated by the approach previously employed for MnWO4.14 The nine spin-exchange parameters,

Ĥ = −

∑ Jij Sî Sĵ i

Increasing the Phase-Transition Temperatures in Spin-Frustrated

Recommend Documents