PDF Magnetic phase transition and multiferroic phase separation in Ho1-xGdxMnO3

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Ceramics International

journal homepage:www.elsevier.com/locate/ceramint

Magnetic phase transition and multiferroic phase separation in Ho

_1-

x

Gd

_x

MnO

₃

N. Zhang

^a,b,∗

, Y.P. Wang

^a

, X. Li

^b,c

, M.F. Liu

^b,c,∗∗

, X.N. Liu

^a

, N. Li

^a

, Y.J. Qiu

^a

, R.Y. Dong

^a

, Z.M. Fu

^a

, Y.Y. Guo

^d

, P.X. Zhou

^b

, J.-M. Liu

^b

aCollege of Physics and Materials Science, Henan Key Laboratory of Photovoltaic Materials, Henan Normal University, Xinxiang, 453007, China

bLaboratory of Solid State Microstructures, Nanjing University, Nanjing, 210093, China

cInstitute for Advanced Materials, Hubei Normal University, Huangshi, 435002, China

dCollege of Electronic Science and Engineering, Nanjing University of Posts and Telecommunications, Nanjing, 210003, China

A R T I C L E I N F O

Keywords:

Multiferroic

Magnetic phase transition Phase separation

A B S T R A C T

In the orthorhombic (o) RMnO₃compound, it is known that the magnetic state can change from the A-type antiferromagnetic (A-AFM) through a spiral spin order (SSO) into the E-AFM state with the decrease in the R ionic radius (r_R). The magnetic phase transition from the E-AFM state to the A-AFM state is expected, but no experimental realization has been reported. In this study, this process in o-Ho_1-xGd_xMnO₃(x: 0–0.6) is reported.

A substitution of Ho with Gd enables the transition of the multiferroic ground state from the E-AFM order (at x≤0.1) to the SSO (atx> 0.4). Accompanied by the quenched disorder, a multiferroic phase separation state is demonstrated in the intermediate composition range of 0.1 <x< 0.4 near the phase boundary between the E-AFM and SSO. This phase-separated state is believed to enhance the ferroelectric polarization and magnetoelectric coupling. Our results demonstrate the dependences of the multiferroic properties of RMnO₃onr_Rand conﬁrm that the multiferroic phase separation is an eﬀective approach to enhance the multiferroic properties of RMnO3.

1. Introduction

The type-II multiferroic manganites RMnO3(R is a rare-earth ele- ment), in which the ferroelectric polarization originates intrinsically from speciﬁc frustrated magnetic structures, have attracted signiﬁcant attention owing to their challenging physical mechanisms for strongly correlated systems and potential technological applications [1–7]. In the orthorhombic (o) RMnO3 with a smaller R ionic radius rR (R:

Gd–Lu), owing to the combination of a signiﬁcant GdFeO3distortion and staggered orbital ordering, the next-nearest-neighbor Mn³⁺antiferromagnetic (AFM) coupling is comparable with the nearest-neighbor ferromagnetic (FM) coupling. The frustration of Mn³⁺spins transforms the magnetic structure into a noncollinear spiral spin order (SSO) (R:

Gd–Dy) and E-type antiferromagnetic (E-AFM) (R: Ho–Lu) order, de- pending on the R ions. The two orders break the spatial inversion symmetry leading to ferroelectric polarization (P) [1,8].

Systematic investigations revealed two generation mechanisms for ferroelectricity in these manganites. For a cycloidal spin structure, spin

chirality induces ferroelectric polarization based on the inverse Dzyaloshinskii–Moriya (DM) mechanism P∼eij× (Si×Sj), where eij

represents the unit vector connecting the interacting spinsSi andSj

[9,10]. For the E-AFM with a commensurate collinear spin structure, the symmetric exchange striction (ES) between Mn³⁺spins leads to a ﬁnite ferroelectricityP∼(Si·Sj), probably larger than that from the DM mechanism [4,11,12]. Furthermore, it has recently been demonstrated that these two mechanisms can coexist in some special multiferroic RMnO3 [13–18]. The coexistence and intercoupling between the Mn³⁺–Mn³⁺DM interaction and Dy³⁺–Mn³⁺ES in DyMnO3lead to a very large polarization and colossal magnetocapacitance eﬀect [2,13,15]. This also demonstrates that the R³⁺–Mn³⁺coupling is es- sential for the multiferroicity in RMnO3.

Similar to DyMnO3, o-HoMnO3exhibits a very peculiar evolution of the magnetic structure against the temperatureTand magneticﬁeldH.

Besides the incommensurate (IC) to commensurate transition of the Mn spins around Tc= 26 K, owing to the direct Ho³⁺–O^2-–Ho³⁺ superexchange interactions, the Ho spins order into a noncollinear structure

https://doi.org/10.1016/j.ceramint.2019.01.140

Received 16 July 2018; Received in revised form 21 January 2019; Accepted 21 January 2019

∗Corresponding author. College of Physics and Materials Science, Henan Key Laboratory of Photovoltaic Materials, Henan Normal University, Xinxiang, 453007, China.

∗∗Corresponding author. Institute for Advanced Materials, Hubei Normal University, Huangshi, 435002, China.

E-mail addresses:[email protected](N. Zhang),[email protected](M.F. Liu).

Ceramics International 45 (2019) 8325–8332

Available online 02 February 2019

T

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below THo= 9 K, with the same periodicity as that of the Mn spin structure [19,20]. Recent investigations revealed that the Ho³⁺–Mn³⁺

ES, rather than the Mn³⁺–Mn³⁺ES, has a predominant contribution to the large P(∼0.15μC/cm²) and considerable magnetoelectric (ME) coupling in HoMnO3[16,17]. In addition, unlike in DyMnO3, where the ferroelectric polarization can beflopped by a magneticfield [3], the polarization direction in o-HoMnO3can be rotated from thea-axis to thec-axis by temperature cooling, as the Ho³⁺–Mn³⁺ES may become dominant over the Mn³⁺–Mn³⁺ES in the low-Trange [17]. It is considered that the two different mechanisms coexisting in o-HoMnO3

could enable distinctive ME control, which makes HoMnO3the most promising candidate for subsequent investigations of complex multiferroic behaviors in these magnetism-induced ferroelectrics.

Measured data indicate that the polarization Pin an o-HoMnO3

single-crystal is signiﬁcantly smaller than the predicted value [11,12]

and that the ME coupling is even weaker than that of DyMnO3. The difference between the theoretical prediction and experimental result is still unexplained. In order to address this issue, a straightforward route is to introduce a multiferroic phase separation in HoMnO3. Previous studies suggested that the magnetic state of RMnO3can be successfully tuned from the SSO to the E-AFM structure through an A-site substitution using smaller rare-earth ions [21,22]. Considering the size mismatch between the substituent and host ions, a random potential or quenched disorder is introduced into the perovskite lattice constituting the R1-xR′xMnO3system. The random potential significantly modulates the magnetic interactions on a local scale; near the boundary between the SSO phase and E-AFM phase, a multiferroic phase separation may be expected [21–24]. The coexistence and competition between the two ordered phases trigger the cross-correlation between different magnetic interactions and change the coupling between magnetic and ferroelectric orders, which could enable to enhance the polarizationPand ME coupling [21,22].

Intrinsically, the competition between the two ordered states in the presence of quenched disorder is the origin of novel eﬀects of phase- separated manganites with proper substitutions [23,24]. In this regard, Gd substitution of Ho is a suitable approach to evaluate the possibility of multiferroic phase separation in HoMnO3. The Gd³⁺ion has a sig- niﬁcantly larger ionic radius,rGd3+∼1.107 Å, than that of the Ho³⁺

ion,rHo3+∼1.072 Å (for a coordination number (CN) of 9) [25]. Or- thorhombic GdMnO3is located on the boundary between the A-AFM phase and SSO phase [8]; therefore, it is expected that the substitution may lead to appearance of the SSO phase from the E-AFM structure of o- HoMnO3. Furthermore, the large ionic size diﬀerence between Gd³⁺

and Ho³⁺ inevitably introduces quenched disorder. Therefore, it is plausible to obtain the desired enhancements inPand ME coupling in a proper substitution range. In contrast to the previously widely studied Eu1-xYxMnO3 and Nb1-xYxMnO3 [21–23,26], where the substitution using small ions drives the A-AFM phase into the SSO phase, in this study, we analyze the magnetic phase transition from the E-AFM to the SSO phase. Moreover, the coexistence of three mechanisms for ferroelectricity generation in Ho1-xGdxMnO3, i.e., the Mn³⁺–Mn³⁺ ES, Ho³⁺–Mn³⁺ES, and Mn³⁺–Mn³⁺DM interaction, may lead to novel phenomena.

2. Experimental details

A series of polycrystalline Ho1-xGdxMnO3 (HGMO) samples (x:

0–0.6) were synthesized by the standard solid-state sintering method.

Stoichiometric amounts of high-purity Ho2O3 (99.99%), Gd2O3

(99.99%), and Mn2O3 (99.9%) were used as reagents and were well ground by ball milling. The mixtures were then calcined in air at 800–900 °C for 24 h (each of them), with several intermittent heating and grinding sequences. Finally, the obtained powders were pressed into pellets and sintered at 1050 °C for 24 h in air.

The phase purities and crystalline structures of the as-prepared samples were analyzed using X-ray diﬀraction (XRD) with Cu Kα

radiation at room temperature. A simulation of the crystal structure based on the measured XRD pattern was carried out using the General Structure Analysis System (GSAS) Rietveld crystal structure reﬁnement software. Raman scattering spectra were measured at room temperature using a Laser Micro Raman spectrometer with an excitation source wavelength of 632.8 nm.

The speciﬁc heat measurement was carried out employing the Quantum Design Physical Properties Measurement System (PPMS).

Magnetization (M) measurements were performed using a Quantum Design superconducting quantum interference device (SQUID) mag- netometer with a DCﬁeld of 1000 Oe in the range of 2–50 K. Magnetic hysteresis measurements were carried out at 3, 7, 10, 15, 20, and 42 K, with a full hysteresis loop in the range of 70 to−70 kOe starting from zeroﬁeld with steps of 100 Oe.

For electrical measurements, gold electrodes were sputtered onto the disk-like samples. The dielectric permittivity was measured on a capacity bridge at 100 kHz in the temperature range of 2–50 K. The ferroelectric polarizationPwas obtained by measuring the pyroelectric current with a Keithley 6514A electrometer while the sample heating was carried out at a rate of 2 K/min. The measurement procedure and validity of this procedure were reported previously [16,27]. The cryo- genic environment and magneticﬁeld during the pyroelectric current and dielectric measurements were provided by the PPMS.

3. Results and discussion

The measured XRD patterns of several representative HGMO samples are shown inFig. 1(a). The observed peaks can be indexed to the orthorhombic structure with a space group ofPnma, indicating the high qualities of the samples withx up to 0.6. Peak down-shift with the increase inx is observed in the inset ofFig. 1(a), suggesting lattice expansion. In order to obtain more details on the structure variation, a high-precision Rietveld profile refinement of the XRD data was performed. As an example, the refined results for the sample withx= 0.3 are plotted inFig. 1(b). The reliability parameters areRwp= 5.06% and Rp= 3.96%. For all of the other samples, the obtainedRwpandRpare at similar levels, suggesting the high purities of the phase structures and chemical homogeneities.

The obtained lattice parameters (a, b/√2, c) and volume V are plotted as a function ofxin Fig. 1(c). The monotonous dependences indicate the high reliability of the dataﬁtting. The lattice parameters follow the relationshipb/√2 <c<a, characteristic of the so-called O′ structure [28]. The lattice constants and volumeVgradually increase withx. In particular, the roughly linear dependence ofV(x), according to the Vergard's law, suggests that Gd³⁺substitutes Ho³⁺. These dependences are reasonable as the Gd³⁺ionic radius is larger than that of Ho³⁺ [25]. For an extensive discussion, we may scale x with the average ionic radii of the R sites, i.e., <rR> =rHo(1 -x) + (rGdx), which changes fromrHo3+to the Tb³⁺ionic radius atx= 0.6. In addition, the spontaneous orthorhombic strain, deﬁned ass= 2(a−c)/(a +c) in thePnmanotation as a measure of the octahedral tilting and distortion, gradually decreases, fromx= 0 to 0.6, as shown inFig. 1(d), suggesting opening of the MneOeMn angles. This leads to a less distorted perovskite structure with a larger tolerance factor f = (<rR> +rO)/√2(rMn+rO) [28]. As the magnetic state of RMnO3is closely correlated with the octahedral titling and distortion, the magnetic structure changes with the increase inx.

The variation in <rR> reflecting the lattice distortion and magnetic structure can be probed by phonon parameters [29]. Unpolarized Raman scattering spectra of the as-prepared samples were measured at ambient conditions. Various active Raman modes exist in such a com- plicated orthorhombic structure; however, some of the measured features are to some extent overlapped profiles of several modes. There- fore, the spectra were fitted and deconvoluted into individual Lorentzian components to obtain the peak of each Raman mode. The enumeration and assignment were carried out according to a previous

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report from Iliev et al., who assumed 24 Raman active modes, ΓRaman= 7Ag + 5B1g+ 7B2g + 5B3g, in orthorhombic perovskites [29,30]. Theﬁtted Raman spectra of selected samples (x= 0 and 0.3) are shown inFig. 2(a). Owing to the polycrystalline structures of the samples, all of the Raman active modes, Ag, B2g, and B3g, are observed;

the mode intermixing is a common phenomenon in the RMnO3family [30].

A detailed analysis of these modes for the sample withx= 0.3, with respect to those of the sample withx= 0, provides valuable insights.

First, the Ag(1) and Ag(3) modes are more convoluted and cannot be clearly separated, which implies a reduced orthorhombic distortion.

Second, the Raman scattering intensity is smaller and the Raman frequencies are softened, consistent with the well-established relationship between the evolution of Raman active modes and variation inrRof RMnO3[30]. The softening of these peaks is due to the tensile strains leading to the lattice expansion. The dependences of the representative phonon frequencies Ag(4) and B2g(1) onxare plotted inFig. 2(b). The Ag(4) mode experiences a larger shift than the B2g(1) mode. It should be noted that the Ag(4) mode represents the out-of-phase MnO6rotation, activated by the [101] rotations, while the B2g(1) mode is assigned to the in-plane O2 symmetric stretching, activated by the Jahn–Teller distortion [30], as illustrated in the inset ofFig. 2(b). As the Jahn–Teller distortions of RMnO3 with R = Tb and Ho are similar [28,30], the

relatively weak phonon frequencyﬂuctuations of the B2g(1) mode with xare reasonable. On the other hand, the phonon frequency of the Ag(4) mode is considered to scale with the tilt angle of MneO1eMn [30–32].

Consequently, the reduced phonon frequency of the Ag(4) mode withx implies a reduction in the out-of-phase tilting of the MnO6octahedra. It should be mentioned that the impact of the local disorder induced by the substitution can be excluded, as the possible disorder mainly exists at the R sites [31,33].

3.1. Magnetic behaviors

Further, we discuss the magnetic effects of the Gd substitution. We collected a sufficient amount of data on theTandHdependences of the magnetizationMin the zero-field cooling (ZFC) andfield cooling (FC) modes with a measurementfield of 1000 Oe. The measuredM–Tdata for several selected samples are plotted inFig. 3(a)–(c), where the dM/

dT (M ′) data in the FC mode are shown as insets. In general, the measured data in the two modes are roughly overlapped, and no anomaly regarding the AFM transitions of the Mn³⁺spins is detected owing to the masking effect from the Ho³⁺/Gd³⁺large paramagnetic moment. For the sample with x= 0, i.e., HoMnO3, the only visible anomaly in the ZFCM–Tcurve is the peak aroundTR= 7 K from the Ho³⁺ AFM ordering [34], which implies that the magnetization of Fig. 1.(a) Measured X-ray diffraction spectra of samples HGMO (x: 0–0.6) at room temperature. (b) The Rietveld refinement for the HGMO sample withx= 0.3. (c) Evaluated lattice parametersa,b/√2,c, and the volumeVas a function of Gd contentx. (d) Evolution of the calculated strain(s) and tolerance factor (f) with the average R³⁺ ionic radius <rR> . The inset of (a) shows the dominant diffraction peaks for the samples withx= 0, 0.1, 0.3 and 0.6 from bottom to up, respectively.

Fig. 2.(a)Unpolarized Raman spectra of HGMO compounds withx= 0 and 0.3 at ambient conditions. (b) Shift of the phonon frequencies of the A_g(4) and B_2g(1) modes with respect to the Gd contentx. The out-of-phase MnO6rotation mode [Ag(4)] and the in-plane O2 symmetric stretching mode [B_2g(1)] are labeled in thisﬁgure. The atoms with purple, green and red color represent Mn, O1 and O2, respectively.

The sketches show the atomic motions involved in these modes.

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HoMnO3 is determined mainly by the Ho³⁺ spin moment. The Gd substitution could weaken the Ho³⁺AFM order, gradually removing the anomaly atTR, as reﬂected by the reduced negative peak in the dM/

dTcurves.

We also present M–H data for several samples at various T in Fig. 3(d)–(f). It is worth noting that no hysteresis is observed even for a cyclingfield up to 70 kOe, a feature of the robust AFM structure with a strong frustration below TN. However, the metamagnetic transition feature is observed in the data belowTR= 7 K [19], due to the abrupt rotation of the Ho³⁺moment at a certain criticalfield, which leads to a peak in dM/dH at HHo∼1.0 T, shown in the insets. This feature is suppressed forx> 0; the peak positionHHoinitially shifts toward high fields atx≤0.3 and then shifts back to lowfields. The maximumHRis

∼1.6 T; the corresponding criticalﬁeld for DyMnO3is approximately 1.8 T [34]. This consistence suggests that the sample with x= 0.3 is similar to DyMnO3in terms of magnetic structure and multiferroic response.

The measured speciﬁc heat data of HGMO (x: 0–0.6) are plotted as C/T–Tcurves inFig. 4to reveal the plausible magnetic phase transition.

For x= 0 (Fig. 4(a)), two anomalies are identified. The anomaly at TN≈41 K corresponds to the onset of the (Cx, 0, 0)-type IC AFM structure of the Mn spins [19]. The other anomaly around TR= 7 K indicates the magnetic ordering of the Ho spins, consistent with the peak position in the M–T curve. On the other hand, the dielectric constantεris regarded as another indicator of the magnetic state of RMnO3. For the sample withx= 0, the IC AFM order of the Mn spins is identified by the upturn ofεraroundTN≈41 K. The IC-AFM to commensurate E-AFM transition, which triggers the ferroelectricity in HoMnO3, is reflected by the marked peak atTC= 24 K. The spiral order of the Ho³⁺spins is identified by the broad anomaly aroundTR≈7 K [16,19]. The good coincidence between the magnetic transitions and dielectric anomalies suggests the substantial ME coupling in HoMnO3. The C/T–T andεr–T plots identify two distinctive features, even

though the IC AFM structure of the Mn spins seems to be independent of the Gd substitution up tox= 0.6 [4]. As shown by theεr–Tcurves, the onset point of ferroelectricity (TC) shifts from the initial value of 24 K (x= 0) down to 18 K at x≥0.2; this point is also the lock-in temperature for Mn cycloidal ordering. Furthermore, according to the magnetoelectric phase diagram of RMnO3, the averageR-site radii <

rR> of HGMO (x≥0.2) coincide with rR of these RMnO3, whose magnetic state is thebc-cycloidal order belowTC∼20 K [35]. Conse- quently, we can infer that the E-AFM coexists with the SSO in HGMO (x≥0.2). In addition, the anomaly corresponding to TRof HGMO is slightly down-shifted to a lowTwhenx≤0.2, but cannot be detected in the compounds withx= 0.3 and 0.4, suggesting the strong disorder eﬀect on the R site. These two features provide explicit evidences that the expected multiferroic phase separation is realized in the HGMO compound with a Gd content aroundx= 0.3.

3.2. Ferroelectric behaviors and multiferroic phase separation

The hypothesis of the multiferroic phase separation in HGMO can be conﬁrmed by the measurements of theT andHdependences of the ferroelectric polarizationsPof the HGMO samples (x: 0–0.6), as shown inFig. 5(a)–(f). Forx= 0, a nonzeroPemerges belowTC∼24 K, owing to the symmetry breaking induced by the Mn³⁺–Mn³⁺symmetric ES. A rapid increase inPis observed belowTNC≈13 K, where a noncollinear (NC) magnetic arrangement of Ho spins with the same wave vector of the Mn spins has been reported [19], demonstrating the signiﬁcant contribution of the symmetric ES between Ho³⁺–Mn³⁺spin pairs toP of HoMnO3. For simplicity, the polarization of HoMnO3 can be expressed as:P_total₁= P_{ES Mn Mn}₍ ₋ ₎+ P_{ES Ho Mn}₍ ₋ ₎.

Upon the Gd partial substitution (x= 0.1), the stability of the E- AFM Mn spins and NC magnetic arrangement of the Ho spins are dis- turbed, leading to a slight decrease in P, compared with that of HoMnO3. With the further increase in the Gd content to x= 0.2, a Fig. 3.(a)–(c) Measured magnetization as a function of temperature under zerofield cooling andfield cooling sequences for the HGMO samples withx= 0, 0.3 and 0.6. The inset shows the M′(T) curve of HGMO. (d)–(f) Measured magnetization as a function of the magneticfield at selected temperatures for the HGMO samples withx= 0, 0.3 and 0.6.

The inset shows thedM/dHcurve atT= 3 K.

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nonzeroPis observed aroundTC= 18 K, conﬁrming that the E-AFM Mn order is partially replaced by the SSO of the Mn spins. Surprisingly, instead of decrease, atT= 2 K,Pof the sample withx= 0.2 is larger than that of HoMnO3, as shown inFig. 5(a) and (b). A plausible contribution to the enhancement inPof the sample withx= 0.2 are the

coexistence and competition between the SSO and remaining E-AFM.

The polarization of the sample withx= 0.2 can be then expressed as:

= ₋ + ₋ + ₋ + ₋

P_total₂ P_{ES Mn Mn}₍ ₎ P_{ES Ho Mn}₍ ₎ P_{DM ES} P_{DM Mn Mn}₍ ₎. This result indicates that although the E-AFM is predominant in the sample with x= 0.2,ﬂuctuations of another order are present. Theseﬂuctuations Fig. 4.(a)–(f) Temperature dependence ofC/Tand dielectric constants (εr) for the HGMO samples withx= 0–0.6.

Fig. 5.(a)–(c) Temperature dependence of ferroelectric polarization for the HGMO samples withx= 0–0.6. (d)–(f) showP(T)curves under various magneticﬁelds for the samples withx= 0, 0.3 and 0.6, respectively.

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are strengthened in the sample withx= 0.3. As shown by theC/T–T andεr–Tcurves of the sample withx= 0.3, the anomaly corresponding to the low-temperature magnetic ordering of the Ho spins cannot be detected, which is attributed to the strong A-site disorder. This local disorder eﬀect intensiﬁes the phase competition between E-AFM and SSO, leading toPof the sample withx= 0.3 twice larger than that of the sample withx= 0. It should be noted that even if the sample with x= 0.3 has a similar <rR> to that of DyMnO3[28], the most promi- nent feature of the ferroelectric polarization of DyMnO3is not observed in the sample withx= 0.3. In DyMnO3, the spontaneousPis generated by the DM interaction between the SSO Mn spins and is enhanced by the ES between the Dy³⁺–Mn³⁺ spin pairs [15,36], but is severely suppressed belowTDy= 6.5 K, due to the emergence of an independent collinear AFM order of the Dy³⁺spins, which decouple the Dy³⁺–Mn³⁺

spin pairs leading to the typical kink feature in the P–T curve of DyMnO3[13,22]. The absence of the kink feature in theP–Tcurve of the sample withx= 0.3 and disappearance of the independent R spin order at low temperatures imply that the R³⁺–Mn³⁺coupling is not involved inPof the sample withx= 0.3. Therefore, the polarization at x= 0.3 should be simpliﬁed as: Ptotal3 =

+ +

− − −

P_{ES Mn Mn}₍ ₎ P_{DM ES} P_{DM Mn Mn}₍ ₎. It should be mentioned that the weights of the three items are diﬀerent from those of the sample with x= 0.2. On the other hand, the mismatch between <rR> atx= 0.3 and that of DyMnO3indicates deviation from the trends established for the RMnO3series, which was also observed in the Nd1-xYxMnO3and Eu1-xYxMnO3systems, attributed to the ionic radius diﬀerence between the substituent and host ions [23,26].

Surprisingly, even the A-site disorder eﬀect is identiﬁed atx= 0.4;

a slight decrease inPcompared to that of HoMnO3is determined, im- plying that the magnetic structure is dominated by the SSO. This is conﬁrmed by theP–Tplot atx= 0.6. As shown inFig. 5(c),Pemerges aroundTC= 17 K and is severely suppressed belowTR= 7 K, yielding a kink feature in the P–T curve at x= 0.6, indicating the onset of a second magnetic component superposition on the established cycloidal ordering of Mn spins, inducing thePdecrease at low temperatures. This behavior is similar to that in the well-studied multiferroic DyMnO3, suggesting a complete transformation of the E-AFM order into the cycloidal order. The ferroelectricity is generated by the DM interaction from the Mn cycloidal magnetic order and ES between R and Mn spins.

In this compound, P can be expressed as:

= ₋ + ₋

P_total₄ P_{DM Mn Mn}₍ ₎ P_{ES R Mn}₍ ₎.

Another evidence for the multiferroic phase separation in HGMO is

the ME effect [21,22]. Detailed measurements of the responses ofPto an external magnetic field (H) were carried out; the results for representative samples are presented in Fig. 5(d)–(f). As shown in Fig. 5(d),Patx= 0 exhibits a major decrease aboveH= 1 T, where a metamagnetic transition alignment of the Ho moments with thefield is observed in theM–Hcurve of HoMnO3. Thefield-induced reorientation of the Ho spins weakens the Ho³⁺–Mn³⁺ES, which leads to the decrease inP, confirming the strong correlation of the polarization with the Ho magnetic order. Atx= 0.3, owing to the complex competition between E-AFM and SSO, the frustration of the magnetic structure of the Mn spins is intensified, making the polarization fragile, which is thus modified by the external magneticfield. The ME coefficient, de- fined as (P(0) -P(H))/P(0) atT= 2 K andH= 5 T, is significantly enhanced, from 31% (x= 0) to 75% (x= 0.3). It is worth noting that the magneticfield response ofPatx= 0.6 is distinct. As shown inFig. 5(f), upon the application of the external magnetic field of H= 1 T, the R³⁺–Mn³⁺ spin coupling seems to be suppressed as an obvious decrease inPis observed belowT= 15 K [34], but the independent R spin ordering is preserved to some extent, as reflected by the residual kink in theP–Tcurve aroundTR. The independent R spin ordering is destroyed by the stronger magneticfield (H= 5 T), leading to a slight increase in Pat a low temperature. This phenomenon further verifies the influence of the R³⁺–Mn³⁺ spin coupling on the ferroelectric polarization at x= 0.6.

3.3. The multiferroic phase diagram of HGMO

Based on the observedTCandPof the HGMO samples withxof 0–0.6, the multiferroic phase diagram is presented in the left side of Fig. 6.TCdecreases from 24 K (x= 0) to 18 K (x≥0.2), indicating the formation of the cycloidal spin order at x≥0.2. According to the measurements ofC/T,εr, andPof HGMO, the E-AFM order is preserved atx= 0.1, while a noncollinear cycloidal order is conﬁrmed atx= 0.6.

During this magnetic phase transition process, signiﬁcant enhancements inPand ME coupling are obtained atx= 0.3. In order to reveal the underlining mechanism, we should consider the relationship between the structural distortion and complex magnetic interactions in the RMnO3compound.

The crystal structure and spin ordering of o-RMnO3are shown in the right side ofFig. 6. It is widely accepted that the predominated mechanism for the magnetic phase transition from the SSO (R = Dy) to the E-AFM (R = Ho) is the GdFeO3-type distortion [8,28]. Therefore, in Fig. 6.The left side display the multiferroic phase diagram of HGMO. T_C and P are determined from the dielectric and ferroelectric measurement, respectively. SSO and E-AFM de- note the spiral spin order and E-type antiferromagnetic spin orders, respectively. The dash lines indicate the possible phase separation area. The crystal structure and spin ordered feature of HoMnO3 are illustrated in the right side. The J_FM(NN) and J_FM(NNN) represent the ferromagnetic superexchange interactions between the nearest-neighbor (NN) and the next-nearest-neighbor (NNN)egspins.JAFM(NNN)de- notes the antiferromagnetic superexchange interactions between the next-nearest-neighbor (NNN)egspins. The stack of spin order along thebaxis is staggered and uniform order.

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order to reveal the driving force for the magnetic phase transition from the E-AFM to the SSO, we should analyze the variation in the GdFeO3- type distortion with the structural tuning of HGMO. According to our analysis about the Raman spectra of HGMO (x: 0–0.6), the GdFeO3-type distortion is released upon the Gd substitution due to the structural available space for replacement of the Ho ions by the larger Gd ions.

Accompanied by the reduction in the structural distortion, the spin frustration induced by the competition between the nearest-neighbor FM superexchange and next-nearest-neighbor AFM superexchange interactions is mitigated, which enables the magnetic structure to restore from the E-AFM to the SSO, as conﬁrmed by the ferroelectric behaviors of the HGMO compounds.

The magnetic phase transition from the E-AFM phase to the ferroelectric cycloidal phase was realized in the Ho1-xGdxMnO3(x: 0–0.6) system. Furthermore, owing to the significant ionic radius difference between Ho³⁺and Gd³⁺, a random potential is introduced into the HGMO perovskite lattice, which in turn significantly modulates the magnetic interactions on the local scale, close to the E-AFM to SSO phase boundary as a function of x [23]. Such random potential or quenched disorder is considered to lead to the phase separation at the boundary between the two competing phases, E-AFM and SSO [24], which then leads to the significant increases inPand ME coupling in the HGMO system. Based on the responses ofPof HGMO toTandH, we can infer that the multiferroic phase separation state emerges around x= 0.3.

4. Conclusion

In summary, the multiferroic behaviors of HGMO (x: 0–0.6) were systematically investigated. The refinement of the XRD data of HGMO confirmed the O′structures in all of the compounds, originating from the strong cooperative Jahn–Teller effect. Along with the almost un- changed orbital ordering associated with the Jahn–Teller effect, the Gd- substitution-induced reduction in the MnO6octahedral tilt was revealed through the Raman spectrum measurement of HGMO (x: 0–0.6). The released frustration of the Mn spins enabled the change in the magnetic structure of HGMO from the original E-AFM to the SSO, further demonstrating that the magnetic phase transition of RMnO3was strongly coupled with the changes in the MnO6distortion accompanied by the variation in <rA> . Furthermore, the size mismatch between Ho³⁺

and Gd³⁺ introduced the local quenched disorder into the HGMO compounds, which led to the multiferroic phase separation near the phase boundary between the E-AFM and SSO, leading to the remarkable enhancements in ferroelectric polarization and ME coupling in the HGMO system. The multiferroic phase separation may be realized in a wider region around x= 0.3, which is an eﬀective approach to opti- mize the multiferroic properties of the orthorhombic RMnO3. Author contributions

N. Z., M. F. L. and J.-M. L. conceived and designed the experiments.

Y. P. W., X. L., X. N. L., N. L., Y. J. Q. and R.Y. D. carried out the experiments. N. Z., M. F. L. and J.-M. L. wrote the paper. Z. M. F., Y. Y.

G. and P. X. Z. reviewed and commented on the paper. All the authors discussed the results and commented on the manuscript.

Conﬂicts of interest

There are no conﬂicts of interest to declare.

Acknowledgement

This work was supported by the Natural Science Foundation of China (Grant No. 11504093, 11604164, U1204111, and 51332006, 11704109), the National Key Research Projects of China (2016YFA0300101), the High Performance Computing Centre of Henan

Normal University, and the Research Project of Hubei Provincial Department of Education (Grant No. Q20172501).

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