Collinear magnetic structure and multiferroicity in the polar magnet Co
2Mo
3O
8Y. S. Tang,1S. M. Wang,1L. Lin,1,*Cheng Li,2,3S. H. Zheng,1C. F. Li,1 J. H. Zhang,1Z. B. Yan,1X. P. Jiang,4and J.-M. Liu1
1Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China
2Forschungszentrum Jülich GmbH, Jülich Centre for Neutron Science Outstation at SNS, Germany
3Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
4School of Materials Science and Engineering, Jingdezhen Ceramic Institute, Jingdezhen 333403, China
(Received 31 May 2019; revised manuscript received 29 September 2019; published 30 October 2019) Among numerous multiferroic phenomena observed in spin frustrated lattice, giant magnetoelectricity in honeycomb lattice (Fe, Mn)2Mo3O8has stimulated great interest and substantial effort in searching for novel members in this 238 family. In this work, we synthesize successfully compound Co2Mo3O8, a structural analogue of Fe2Mo3O8, and present a series of characterizations on its structural, magnetic, and electric properties.
An antiferromagnetic transition takes place at the Neel temperature TN=39 K with appearance of electric polarization and dielectric anomaly, which provides clear evidence of simultaneous magnetic and ferroelectric transitions. The neutron powder diffraction (NPD) and magnetic susceptibility data confirm thec-axis collinear antiferromagnetic orders and emergent ferroelectric polarization. In particular, such antiferromagnetic order is relatively robust against magnetic field up to 9 T, different from Fe2Mo3O8 with ferrimagnetic transition or Mn2Mo3O8 with spin flop in the low-field region. Our data on single crystals demonstrate the second-order magnetoelectric effect in terms of magnetic field dependence of ferroelectric polarization response, while no linear magnetoelectric response is allowed. It is suggested that Co2Mo3O8provides a unique platform on which rich multiferroic physics in the presence of collinear magnetic order can be explored.
DOI:10.1103/PhysRevB.100.134112
I. INTRODUCTION
Multiferroic materials exhibiting more than one primary ferroic order in a single phase have driven significant research activity [1,2]. The mutual control and coupling between these ferroic orders, especially magnetoelectric (ME) coupling be- tween magnetization (M) and ferroelectric polarization (P), offer new routes to device architectures [3–7]. From the fundamental point of view, it is highly concerned that some noncollinear antiferromagnetic (AFM) ordering may lead to the inversion symmetry breaking, as evidenced in a number of so-called type-II multiferroics (spin order driven ferroelectric- ity). Nevertheless, in these compounds, the ferroelectric Curie temperature and ME signal are seriously limited [8–11]. In spite of great improvement in understanding the ME effect in such compounds, searching for room-temperature multi- ferroic candidates and colossal ME effect has been difficult, hindering device applications.
Along this line, one class of promising candidates includes those systems with linear ME effects, in which the remarkable tunability of ME coefficients is achieved by chemical modifi- cation [12–15]. Recent breakthroughs in Fe2Mo3O8 [12,16–
19], Co4Nb2O9 [20], CaBaCo4O7 [21], GaFeO3 [22], and Ni3TeO6 [23] have stimulated a flurry of research on these new multiferroics. Among them, the family ofA2Mo3O8(A= Fe, Mn, Co and Ni) belongs to the noncentrosymmetric space groupP63mc with A2+ ions occupying both the octahedral
*Corresponding author: [email protected]
(OCT) and tetrahedral (TET) sites, as shown in Fig. 1(a).
The crystal structure can be viewed as the stacking of hon- eycomblike A2O12−8 layers and sheets of Mo4+ ions along thecaxis. Here the Mo4+ ions form the unique spin-singlet trimers and do not contribute to magnetism [24]. The spin frustration inherent to such honeycomb lattice arises due to the competing long-range magnetic interactions and anisotropic magnetic exchanges. Therefore the magnetic properties of this family are different from one and another [25,26], as exam- pled by Figs.1(b)and1(c)where the collinear AFM order of Fe2Mo3O8 and ferrimagnetic (FIM) order of Mn2Mo3O8 by taking into account the Mn/Fe - O coordination are illustrated.
Recently, large linear ME coupling reported in Fe2Mo3O8
[12,16] triggered more efforts in the search for large linear ME systems. An interesting feature of Fe2Mo3O8 is the tunability between the distinct magnetic ground states by Zn doping, which leads to the varied ME coefficient from−142 to 107 ps/m [12]. Similar linear ME susceptibility was also observed in Mn2Mo3O8, and large manipulation of ME coef- ficient by Fe-doping was found [17]. These emergent effects suggest that the A2Mo3O8 family is a rich source for large linear ME effects and indeed a number of works regarding this issue have been reported [18,19]. It is also interested to check for species substitution because different d-orbital filling strategies make the magnetic and ME properties of this family distinctly different. It was suggested that the nonfilling of 3d orbitals of the Aions and strong magnetic anisotropy govern the Neel temperature (TN): TN=59.5, 41.5, 40.8, and 6 K forA2+=Fe2+(S=2), Mn2+(S=5/2), Co2+(S= 3/2), and Ni2+(S=1), respectively [27,28]. One case is
c
a b
(a)
A (OCT) Mo A (TET)
(b) (c)
AFM FIM
Fe2Mo3O8 Mn2Mo3O8
FIG. 1. (a) Crystal structure ofA2Mo3O8 (A: Mn, Fe, Co, and Ni). A (OCT) and A (TET) represent the octahedral and tetrahedral coordination of magnetic atoms, respectively. (b) The schematic diagram of antiferromagnetic order in Fe2Mo3O8. (c) Ferrimagnetic order in Mn2Mo3O8.
Ni2Mo3O8, which was previously reported to remain param- agnetic untilT =2 K [27], whereas an AFM ordering with a mixture of stripy and zigzag character was discovered most recently [28]. Nonetheless, little about the 3d7Co2+ isotype oxides is known.
The first-principles calculations show that exchange stric- tion is the leading mechanism responsible for the observed ME effects in Fe2Mo3O8 [16]. It was suggested that the ground state allows the oxygen ion displacement so that the magnetic energy gains in the AFM and FIM states is maximized, illuminating the underlying mechanism for the observed giant ME coefficients. However, so far, no direct experimental evidence has been presented and all these claims are based on theoretical predictions. Despites powder neutron scattering of A2Mo3O8 compounds where A=Mn, Fe, Co, or 1/2(FexZn2-x) was performed as early as the 1970s [29], the ground magnetic structures of these compounds were proposed based on data with narrowd-value range, without detailed atom positions due to the low resolution of the data [27]. Furthermore, investigation of lattice phase transition is still missing. Therefore systematic neutron scattering investi- gations on these compounds are highly desired to unveil the ME mechanism.
Motivated by these facts, we here report an investigation of dielectric, ferroelectric, ME coupling, magnetic order, and specific heat of polycrystalline and single crystal Co2Mo3O8,
one member of the A2Mo3O8 family. An AFM transition at TN=39 K, accompanied with a dielectric anomaly and a jump in electric polarization is revealed, which provides a clear evidence for simultaneous magnetic and ferroelectric transitions. Furthermore, a magnetic field, induced suppres- sion of the electric polarization and a shifting of the ferro- electric Curie temperature (TFE) below TN, is identified. To more precisely capture the intrinsic physics, measurements on single crystals reveal that ferroelectric polarization is indeed aligned along the caxis, and nonlinear ME coupling effect (Pis quadratic to magnetic fieldH) is also evidenced, which is distinct from that identified in Fe2Mo3O8and Mn2Mo3O8. The neutron scattering data suggest a layered collinear AFM magnetic structure along the c-axis, and detailed ions dis- placement upon transition from PM to AFM state are ex- plicitly obtained. All these results point towards Co2Mo3O8
as a new and unusual multiferroic member in thisA2Mo3O8
family.
II. EXPERIMENTAL DETAILS
The polycrystalline Co2Mo3O8 samples were synthetized by the standard solid-state reaction method [30,31]. The sin- tering procedure has been optimized by repeated experiments.
Stoichiometric amounts of CoO and MoO2 powder were ground with a molar ratio 2:3 in an agator mortar, and sealed in evacuated silica tubes at 1000 °C for 48 h. The obtained power was compressed into a rod under hydrostatic pressure, and heated at 600 °C for 40 min under a pressure of 5.0 GPa. Then the rod was cut into plates, and each plate was polished into a thin disk of∼3.0 mm in diameter and∼0.2 mm in thickness.
Sufficient plates were again broken into a large amount of powder for subsequent neutron scattering experiments. The single crystals were grown by chemical vapor transport reac- tion method as described in Ref. [27].
The crystallinity of the as-prepared samples was checked using x-ray diffraction (XRD, D8 Advanced, Bruker) in the θ-2θ mode with Cu Kα source (λ=1.5406 Å). The neutron powder diffraction (NPD) experiment was performed on the BL-11A powder diffractometer at the Oak Ridge National Laboratory. Approximately 4.93 g powder was loaded into an 8-mm vanadium can, which was then backfilled with Helium before the loading. The data were collected using POWGEN auto changer in the high-resolution mode, with a center wavelength of 1.5 Å. Approximately 2 hours gathering time was used for each temperature (300, 50, and 10 K). The crystal and magnetic structures were refined using theTOPAS
v5 andJANA2006 software [32,33].
The dc magnetization was measured using the Quantum Design superconducting quantum interference device magne- tometer (SQUID) with a measuring magnetic field of 1000 Oe in the zero field-cooling (ZFC) and field-cooling (FC) modes.
At the same time, the specific heat (CP) was measured using the Quantum Design Physical Property measurement system (PPMS) in the standard procedure.
For the electrical measurements, each of the disklike sam- ples was coated with the bottom and top Au electrodes for dielectric and ferroelectric probing. The dielectric constant (ε) as a function of temperature (T) was measured using the HP4294A impedance analyzer integrated with PPMS. For the
FIG. 2. (a) Temperature dependence of the magnetic susceptibil- ityχ(T) and Curie-Weiss fitting (1/χ). (b) Magnetic field depen- dence of the magnetizationM(H) under selected temperatures.
spontaneous polarizationP, the pyroelectric current method was used in the standard mode, as described in Ref. [34].
The pyroelectric currentIpyin the warming sequence with the sample warming rate of 2, 4, and 6 K/min was collected using Keithely 6517 programmable electrometer.
III. RESULTS AND DISCUSSION A. Magnetization and specific heat
TheT dependence of magnetic susceptibilityχ(T) curves with the measuring magnetic field of 1000 Oe under the ZFC and FC modes are plotted Fig.2(a). In agreement with previ- ous results,χ(T) shows a cusp atTN∼ 39 K, suggesting the antiferromagnetic ordering. In addition, the Curie-Weiss law fitting of the inverse magnetic susceptibility above 40 K yields the Weiss temperatureθcw∼ −138.9 K, indicative of strong antiferromagnetic interactions. The effective paramagnetic magnetic moment μeff =4.250 μB/Co is derived, close to the expected spin-only moment of 3.873μB/Co for high-spin Co2+(S=3/2).
Here, it should be pointed out that a small tip in addition to the relatively broad bumplike peak aroundTN in theχ(T) curve can be seen. Such a small tip remains to be an issue although it was also observed in some earlier experiment [27] where the measured χ on single crystals for theH⊥c mode exhibited such a small tip but no such tip in theH//c
mode can be seen. It is reasonable to understand the different details in the magnetic susceptibility near TN between dif- ferent samples. Of course, there may be other possibilities, e.g., ferromagnetic impurities, which are difficult to be distin- guished by conventional XRD actually, and even by neutron measurement (only tiny amount of MoO2impurity phase was found). As species Fe is often an impurity in the Co-based samples, the small peak near the magnetic transition might be attributed to the impurity effect as reported in Co1/3TaS2[35].
Nevertheless, no clear evidence of this is available because it does not affect the subsequent determination of the magnetic structure as well as the ME response measurement.
In Fig. 2(b), we plot the magnetic field (H) dependent magnetization (M) under several selected temperatures (T).
The magnetization increases monotonically with H, a typ- ical AFM feature. No field-induced magnetic transition or spin flop has been observed up to H=9 T, implying that Co2Mo3O8 slightly differs from other members of this 238 family. Certainly, it is expected that such a transition would occur if higher magnetic field is applied, and it is highly desir- able to measure the ultrahigh-field data (e.g., 50 T) to unveil the possible magnetic transition in Co2Mo3O8. Unfortunately, such a measurement is not accessible to us but its absence does not change the main conclusion we shall reach.
Subsequently, we switch our attention to the specific heat CP. A large anomaly in the specific heat is present at the mag- netic transition point, as seen in Fig.3(a). To uncover the mag- netic contribution to the specific heat, we measured the spe- cific heat of nonmagnetic compound Zn2Mo3O8, structurally analogous to Co2Mo3O8. The magnetic contributionCMas a function ofT can be approximated by subtracting the value of Zn2Mo3O8(phonon term). One sees clearly an enhancement of the specific heat occurring at TN, is ∼30 J mol−1K−1, which can be seen as the magnetic contribution term to the specific heat, i.e., CM. This term is smaller than the value deduced from the mean-field theory. As the first-order approx- imation, we assume that all the Co2+ions are in the high-spin (S=3/2) state. The magnetic contributionCMcan be written as
CM=5R 2S(S+1)
S2+(S+1)2 ∼36.7 J mol−1K−1, (1) where R is the gas constant. Here, the slight difference be- tween the measured value and evaluated value from Eq. (1) suggests the presence of short-range magnetic correlation at higher temperature in Co2Mo3O8. Besides, the measuredCM
data at low temperature are well fitted with the power law CM∼T3, which is consistent with the power-law expression for a three-dimensional antiferromagnet [36].
The T dependence of magnetic entropy SM(T) is also shown in Fig. 3(b). Strikingly, the entropy loss occurs at TN with a saturation value SM(T =50 K)
∼11.50 J mol−1K−1, just half of the saturated value. This phenomenon is similar to recent reports on sister compounds Fe2Mo3O8 and Ni2Mo3O8 [16,28]. It is worthwhile to point out that application of magnetic field up to 9 T does not cause obvious peak shifts as shown in Fig.3(c), suggesting a robust antiferromagnetic coupling, coincident with the magnetiza- tion behaviors.
FIG. 3. (a) T dependence of specific heatCP(T) of magnetic Co2Mo3O8 and nonmagnetic Zn2Mo3O8. Red curve represents magnetic specific heat (CM), calculated by subtracting theCP of Zn2Mo3O8 from that of Co2Mo3O8. (b) Temperature dependence of magnetic entropySM(T). (c) TheCM-T curves under different magnetic fields.
B. Magnetic structure determination
The NPD data were collected at T =300, 50, and 10 K, and the Rietveld refinement results are presented in Fig.4. About 2.4 wt% of MoO2 impurity phase was found in the sample, therefore the Mo occupancy was initially
FIG. 4. Rietveld fit of the NPD patterns measured at (a) 300, (b) 50, and (c) 10 K, respectively. The inset shows the zoomed view of a selected reflection (100) atT =50 and 10 K.
released. However, the refined value does not differ from the stoichiometric compound, and thus the occupancy of Mo site is fixed for the subsequent refinement. At room temperature, the refined structure of Co2Mo3O8 exhibits the
TABLE I. Refined structure parameters of polycrystalline Co2Mo3O8from powder neutron diffraction data measured at 300 K.
Cell parameters a(Å) b(Å) c(Å) α β γ Space group
5.7698(1) 5.7698(1) 9.9134(1) 90 90 120 P63mc
Atom x y z Occ. Biso
Co1 0.33333 0.66667 0.9478(3) 1 0.29(3)
Co2 0.33333 0.66667 0.5116(2) 1 0.01(3)
Mo1 0.1460(1) 0.8540(1) 0.2494(1) 1 0.099(6)
O1 0.00000 0.00000 0.3913(1) 1 0.227(16)
O2 0.33333 0.66667 0.1457(1) 1 0.181(17)
O3 0.4879(1) 0.5121(6) 0.3649(1) 1 0.231(8)
O4 0.1673(1) 0.8327(1) 0.6331(1) 1 0.306(8)
TABLE II. Refined structure parameters of polycrystalline Co2Mo3O8from powder neutron diffraction data measured at 10 K.
Cell parameters a(Å) b(Å) c(Å) α β γ Space group
5.7658(3) 5.7658(3) 9.9053(0) 90 90 120 P63mc
Atom x y z Occ. Biso
Co1 0.33333 0.66667 0.9488(1) 1 0.010a
Co2 0.33333 0.66667 0.5122(4) 1 0.010a
Mo1 0.1461(1) 0.8538(9) 0.2496(3) 1 0.010a
O1 0.00000 0.00000 0.3918(3) 1 0.098
O2 0.33333 0.66667 0.1455(3) 1 0.083
O3 0.4876(8) 0.5123(2) 0.3654(2) 1 0.050
O4 0.16730 0.83270 0.6331(3) 1 0.105
aThe displacement parameters were fixed at 0.01 Å2during the refinement.
noncentrosymmetric P63mc space group with unit cell pa- rameters a=b=5.7698(1) Å, and c=9.9134(1) Å, well consistent with earlier reported data [27]. The detailed refined atomic parameters at 300 and 10 K are given in Table I and TableII, respectively. These data allow us to discuss the magnetic structure of Co2Mo3O8.
It is noted that earlier investigation of magnetic ordering in A2Mo3O8 systems was pioneered by McAlister and Strobel [27,30]. Most recently, Morey et al. reported the magnetic structure of Ni2Mo3O8 atT =1.6 K and found that the dou- bling along the abplane with wave vectork=(1/2, 0, 0) is required to fully index the magnetic reflections [28]. Con- sequently, a quite complex magnetic ordering, consisting of the stripyab-plane moment and zigzag AFM ordering along the c axis was reported. When it comes to Co2Mo3O8, we first identify the magnetic Bragg peaks by subtracting the neutron powder diffraction pattern measured atT >TN from that atT <TN, as shown in the inset of Fig.4(c). The highest magnetic peak is located atQ∼0.792 Å−1. AtT =10 K, all the magnetic reflections could be indexed using the nuclear cell, and thus a search for the magnetic structure with k= (0, 0, 0) was conducted using theISODISTORTpackage [37].
Choosing the Wycoff position of Co, 2b, as the magnetic sites, the search returns four irreducible representations (IRs) that have a single order parameter direction (OPD), namely, mGM2, mGM3, mGM5, and mGM6, and contain eight mag- netic space groups (S.G.), listed in TableIII. Previous mag- netic measurement identified thec-axis as the easy axis for AFM ordering [31], and thus we focus on the space groups
that produce the AFM ordering along the c-axis. Here, the
“+” or “−” signs denote the direction of magnetic moment alongcat the tetrahedral (T) and octahedral (O) sites, in the adjacent chain in the order of TTOO.
In our fitting, all the six space groups were tested, and the+ − + −configuration in general produces better fitting results than the+ + − −sets: an improved fitting withRwp= 7.1% toRwp=5.1% was obtained if one switches from S.G.
186.207 to 186.205. However, lowering the symmetry to S.G.
36.174 to include the in-plane contribution leads to a minor improvement in the fitting quality (Rwp=5.0%), which is not sufficient strong to support the existence ofab-plane moment.
Therefore the S.G. 186.205 is considered an accurate depic- tion of the magnetic structure. Finally, the refined magnetic structure exhibits the Ising-type AFM order along thec-axis (see Fig.5), the same as that in Fe2Mo3O8.
It is worth noting that the refined moments on the tetrahe- dral and octahedral sites are highly correlated and the refined moment was 3.44(1)μBfor Co1, and 3.35(1)μBfor Co2 site, respectively. In Fe2Mo3O8, the octahedral site of Fe (Feo) has larger spin than the tetrahedral site (Fet) with the magnitude of moment 4.21μBand 4.83μB. Thus the comparable difference between Feo and Fet results in the ferrimagnetic transition with application of magnetic field. Therefore the magnetic order of Co2Mo3O8is essentially different from that identified for Fe2Mo3O8 and Mn2Mo3O8, and thus different response to magnetic field, namely, no ferrimagnetic transition or spin flop, is rationalized in Co2Mo3O8, as shown in the M-H data. From this point of view, it is highly recommended to further explore the ferroelectricity and possible ME coupling
TABLE III. List of the magnetic space groups generated using the ISODISTORT, using parent space groupP63mcwithk=(0, 0, 0), for the 10 K dataset of Co2Mo3O8.
IR Magnetic S.G S.G. number moment alongc(in the order of TTOO) in-plane moment allowed?
mGM2 P63mc 186.207 ++−− No
mGM3 P63mc 186.205 +−+− No
Cmc21 36.172 0000 Yes
mGM5 Cmc21 36.176 ++−− Yes
P21 4.7 ++−− Yes
Cmc21 36.175 0000 Yes
mGM6 Cmc21 36.174 +−+− Yes
P21 4.9 +−+− Yes
FIG. 5. The sketch of collinear magnetic order refined from the NPD data. The red and green colored arrows denote the magnetic moment on Co1 and Co2 sites.
underneath the collinear magnetic order in Co2Mo3O8, to be discussed below.
C. Dielectric, ferroelectric, and multiferroic properties Along this line, we first discuss the dielectric response as a function of T. The measured dielectric constant ε(T) at several frequencies are plotted in Fig.6(a). Clearly, these curves reveal an anomaly occurring atT ∼TN, indicating the simultaneous magnetic and structural transitions. In particular,
FIG. 6. (a) Temperature dependence of dielectric constantε(T) for selected frequencies. (b)ε(T) curves under applying magnetic fields with f =63 kHz.
the anomaly is somehow frequency independent, but the peak strength is frequency dependent, indicating that this dielectric anomaly is related to the spin-induced ferroelectric phase transition rather than from relaxation [38–40]. However, the ε(T) data at a fixed frequency shift upward with increasing magnetic field and the dielectric anomaly also shifts towards the high-T side as shown in Fig. 6(b). These behaviors are understandable since the dielectric anomaly is associated with the magnetic transition atTNand the magnetic field enhances ferromagnetic correlation in Co2Mo3O8.
We then investigate the ferroelectricity and magnetoelec- tric response of Co2Mo3O8 by probing the pyroelectric cur- rent, to probe magnetism-induced ferroelectrics. Given that the lattice structure is polar, it is more interested to investigate the magnetic-induced polarization. Therefore the pyroelectric currentIpy(T) on the sample upon cooling fromT =60 to 2 K under a poling electric field of 10 kV/cm was measured under magnetic field strength from 0 T to 6 T (note thatTN ∼40 K).
This scheme ensures that the measuredIpy(T) is purely mag- netically generated and the integration ofIpy(T) data from the high-T side corresponds to a variation of polarization. Here, we still usedPfor characterizing the ferroelectric polarization to distinguish the variation of polarization (P) vs. ramping magnetic field.
We first look at the Ipy(T) curves measured at three different warming rates at 2, 4, and 6 K/min to verify the reliability of our methodology. No distinct shifting of the Ipy(T) peaks is observed, and the polarization was re- versed by applying a reverse voltage, as shown in Fig. 7(a) and the inset, suggesting that the detected current does come from the pyroelectric effect. The data revealed the simultaneous magnetic ordering and appearance of ferro- electric polarization. The saturated value of P in the low- T side is ∼40μC/m2, much smaller than the values ob- served in single crystals Fe2Mo3O8 (∼1400μC/m2) and Mn2Mo3O8(∼2000μC/m2). This difference is ascribed to the sample nature, noting that the measured polarization in polycrystalline samples is usually much smaller than that in single crystals for multiferroics. We shall return to this issue below when we discuss the ferroelectric polarization direction from our preliminary data on single crystal samples.
The most important issue is the linear ME (LME) effect to be checked for Co2Mo3O8. We employed two modes to check the ME effect. First, we collected theIpy(T) data under a constant magnetic fieldH, as plotted in Fig.7(b). It can be found that the peak height has only weak shift downwards with increasing H, and a shifting of the ferroelectric Curie temperature (TFE) below TN is identified, suggesting weak suppression of ferroelectric polarization by magnetic field.
The as-evaluatedP(T) curves under theseHvalues are shown in Fig. 7(c), indicating that the polarization suppression is indeed minor if any. Second, we also measured the isothermal magnetoelectric current as a function of H during the H cycling between 5.0 and−5.0 T. Our measurements failed to observe remarkable ME response as shown in Fig.7(d), and the detected current was on the similar level as the background current noise∼0.1 pA. We shall come back to this issue once more below.
Due to the polycrystalline nature of the samples, the ME coupling measured in these samples is often elusive and might
FIG. 7. (a) Temperature dependence of pyroelectric currents Ipy(T) measured under different heating rates. The inset shows the electric polarization (P) under positive and negative pooling electric field under 4 K/min heating rate. (b) The relationship ofT depen- dence ofIpy(T) under different H. (c) The time-integrated change of electric polarizationP(T) under differentH. (d) The measured H-dependent pyrocurrentIunderT =30 K.
escape detection if the signal is intrinsically low, or if the mag- netic energy gain is not sufficient to overcome the energy bar- rier between multiple grains. From such perspective, a single crystal is much more favorable to investigate the underlying multiferroic property. While the ME effect in this system is one of the core issues addressed in this work, substantial effort has been made to synthesize single crystal samples. In spite of
FIG. 8. The XRD pattern of as-grown single crystal (hexagonal plate). The inset shows the image and Laue spots of the crystal.
challenges, we eventually grew successfully some very small single crystal plates. Fortunately, these small crystals allow us to perform some additional measurements on the c-axis ferroelectric polarization if any.
The slow-scan XRD pattern focusing on the naturally developed hexagonal plane is plotted in Fig. 8. Comparing with the standard XRD diffraction pattern, the plane is well indexed by (00l). In addition, the crystal was aligned by Back-Reflection Laue Detector (The MWL120, Multiwire Laboratories, Ltd.), and this hexagonal plane shows perfect diffraction spots from the [001] direction (Fig.8 inset), and no other sets of spots are found, demonstrating good quality of our crystal. Here we note that our as-grown crystals are basi- cally with diameter of∼0.5 mm and thickness of 10–100μm as shown in the inset, that it is difficult to cut a piece ofab plane to conduct the electric measurement owing to the small thickness. Therefore only the ferroelectric polarization along thecaxis will be discussed below. To probe the ME effect, the magnetoelectric current (Ic) along thecaxis was measured at ramping magnetic field with 100 Oe/s by the scan from+H to−H, and then−Hback to+H, forming a swamping cycle.
Figure9(a)displays the pyroelectric currentIcand electric polarization Pc as a function of T. In contrast to the data from polycrystalline samples, the Ic data here show rapid increasing near the transition pointTN, then slowly decrease with further decreasing T, and finally drop down to zero below 15 K. The Ic variation near TN is noticeably sharper than that in polycrystalline samples. In addition, as we have claimed earlier, the magnitude of polarization in the single crystals is indeed much larger (∼1160μC/m2 atT =2 K) than that in the polycrystalline samples (40μC/m2). This value is still smaller than but comparable on the order of magnitude with the polarizations observed in Fe2Mo3O8and Mn2Mo3O8, implying that the as-grown crystals, in spite of very small in size, may be useful for unveiling some issues uncovered in polycrystalline samples.
First, to explore the possible ME effect stemming from the collinear spin order, we examined the T dependence of magnetic susceptibility in theH//candH⊥cgeometries, and found the same behaviors as previously reported by Mcalister
FIG. 9. (a) TheT-dependent pyroelectric currentIcand polariza- tionPcalong thec-axis for the single crystal. (b)Hdependence ofM alongc-axis underH//candH⊥c. (c)Hdependence of polarization Pcmeasured at different temperatures underH//c. The dashed line is the fit to thePc-Hcurve with the function ofP=βH2, where βis constant. (d) TheT dependence ofβunderH//c.
et al.[27] (not shown here). Here we present theH depen- dence ofMthe two modes, measured atT =5 K in Fig.9(b).
Clearly, theM-Hdata along the two different crystallographic directions suggest absence of any magnetic transition or spin flop belowH=9 T, as observed in polycrystalline samples.
In particular, the linear increase of magnetization versus field bears some resemblance to the response of polarization in the H//cmode, as shown in Fig.9(c). The term of magnetic field driven polarization,Pc, as a function ofH, is obtained by scanning from+H to−H, and then from−H back to+H. In the low-T range,Pc remains nearly the same, and then increases quickly at T ∼30 K up to ∼9 times larger than that atT =2 K, keeping in mind that the largest variation of Pcin Fe2Mo3O8also appears at intermediateT range, e.g., T =45 K [12].
In addition, it is worth noting that all the ME effect and M-H curves were measured in the relatively low-field range (H9 T). It is suggested that the magnetic transition and inherent ME response in the ultrahigh magnetic field range, e.g., up to 50 T, cannot be neglected. These high magnetic field measurements would be useful for revealing the spin dynamics in Co2Mo3O8, which is beyond the scope of this work and unfortunately not accessible at this moment.
Second, one is allowed to formulate the ME response from the phenomenological viewpoint and discuss the relevant microscopic mechanisms associated with the magnetic point group 63mc. In general,Pis given as a function ofHup to the second order as follows:
P=Pc+Ps+αH+βH2, (2) where Pc and Ps are the crystallographic and spin-induced spontaneous polarization, which are finite even under zero
field [17]. The coefficients αand β correspond to the first- order and second-order ME coefficients, respectively. Here, we exemplify thePc−H curves measured atT =30 K in the H//cmode and the fitting is plotted as dashed lines in Fig.9(c). It is clearly seen that the data show perfect fitting by introducing the second-order ME term. The Pc term is quadratic to H with the second-order ME coefficient β= 29.59×10−19s/A in theH//cmode. This result is consistent with the fact that the magnetic space group for the antiferro- magnetic order (P63mc) allows only the second-order ME effect, while the linear ME effect is forbidden.
Nonetheless, these results contrast to the previous ME coefficients in Fe2Mo3O8 and Mn2Mo3O8, in which the lin- ear ME coupling plays an important role. In particular, the second-order ME susceptibilityβ of Co2Mo3O8 is consider- ably larger than that of Fe2Mo3O8(1.81×10−28 s/A) which manifests the same magnetic ground state [12]. Therefore Co2Mo3O8 seems to be a peculiar new multiferroic member that is distinctly different from the other two well recognized linear magnetoelectric members in this 238 family.
D. Ionic displacement
Finally, we would like to discuss the possible structural distortion associated with the magnetic transition atTN from the macroscopic point of view based on the NPD data. To evaluate the distortion, we need to extract the ionic coor- dinates of the lattice unit from the structural fitting so that the ionic displacements can be obtained. In proceeding, the lattice structure was expanded to be commensurate with the magnetic cell (space groupP63mc, 186.205). Overall, minor change in the nuclear structure was found after the transition.
Nevertheless, we can obtain the ionic displacement for each ion associated with the paramagnetic (PM) to AFM transition atTN, while the nuclear structure in the original space group (P63mc, S.G. 186) is kept.
We then compare the structure parameter between the 50-K and 10-K data by using the same S.G. (P63mc). Based on the symmetry operation, all the displacements alongxandywill be canceled out, and the ionic shifts alongcdirections during the paramagnetic to AFM transition are obtained. In fact, symmetry operations of the space group limit the ferroelectric polarization to align with the c-axis, whereas the in-plane polarization component is not allowed [41].
For the 238 family, it is well recognized that the exchange striction, where the lattice deforms to gain the exchange energy, contributes to the ferroelectric polarization. The first- principle calculations demonstrate that the main ionic shift comes from O3 and O4 as schematically illustrated in Fig.10 [16]. The Fe-O-Fe angle (θ) between the nearest Fe2+ in- creases from 109◦ to ∼111◦ upon the transition from the PM to the AFM state due to the oxygen shifts. Hence, we believe that the exchange striction should equally apply to Co2Mo3O8, taking the collinear magnetic order into account.
However, it is surprised that the Co-O-Co angle is essentially unchanged at all for the Co2Mo3O8case as shown in Fig.10, in which all the ionic displacements are illustrated. The main displacement comes from Co1 and O2, and Co2 ions are nearly unchanged, while displacements of Fe1 and Fe2 ions
FIG. 10. Schematics of all ionic displacement in a unit cell upon transition from PM to AFM state in Co2Mo3O8.
in Fe2Mo3O8 are comparative in the PM to AFM states according to the calculations.
IV. CONCLUSION
In conclusion, we have systematically investigated the magnetic structure and multiferroic property in polar anti- ferromagnet Co2Mo3O8. The antiferromagnetic moment and
associated ferroelectric polarization generation along the c axis are well evidenced by neutron scattering. Remarkable ME coupling has been observed in the single crystals but very weak in the polycrystalline samples. The previously recognized linear magnetoelectric effect in other members of this 238 family is not observed in Co2Mo3O8, suggesting some specific characteristics with this system. More impor- tantly, the second-order ME coupling, which is stronger than those observed in Fe2Mo3O8 is significant for Co2Mo3O8. In particular, the antiferromagnetic order remains relatively robust against magnetic field up to 9 T, making it distinctive among this 238 multiferroic family. The neutron scattering data suggest the collective displacement of Co1 and O2 ions to gain the exchange energy, giving rise to thec-axis ferroelectric polarization. Further ultra-high magnetic field measurements would be highly required to quantify possible magnetic transi- tion to unveil the hidden magnetic order as well as the inherent ME coupling in Co2Mo3O8.
ACKNOWLEDGMENTS
This work was financially supported by the National Key Research Program of China (Grants No. 2016YFA0300101) and the National Science Foundation of China (Grants No.
11874031, 11834002, 11774106, 51431006, 51721001, and 11974167). A portion of this research used resources at Spal- lation Neutron Source, a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory.
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