Enhanced magnetism-generated ferroelectricity in highly frustrated Fe-doped Ho

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Enhanced magnetism-generated ferroelectricity in highly frustrated Fe-doped Ho

₂

Ti

₂

O

₇

L.Lin,^1,2Y. L.Xie,²Z. Y.Zhao,²J. J.Wen,³Z. B.Yan,²S.Dong,^1,a)and J.-M.Liu^2,b)

1Department of Physics, Southeast University, Nanjing 211189, China

2Laboratory of Solid State Microstructures and Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China

3Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA

(Presented 7 November 2014; received 1 September 2014; accepted 12 December 2014; published online 14 April 2015)

We present careful experiments on the ferroelectric (FE), dielectric, and magnetic behaviors of Ho_2xFe_xTi₂O₇with Fe^3þsubstitution for Ho^3þ. A remarkable enhancement of polarization up to 235lC/m²is obtained at a low level x¼0.08, accompanied with the FE transition up to80 K.

Theacsusceptibility under magnetic fields shows an expected saturated maximum in the real part v⁰, along with an unexpected frequency-dependent peak in the imaginary partv⁰⁰, indicating unusual slow spin relaxation. The coupled correlated spin domains through dipolar interaction are argued to give rise to nonzero electric-dipole via Dzyaloshinskii-Moriya interaction. V^C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4918334]

I. INTRODUCTION

In the past decade, multiferroics have been receiving con- tinuous attention because of their fascinating physical phenom- ena and promising prospection for multi-functional devices based on the mutual modulation of magnetic order and electric-dipole order.^1–4 The pioneering work on rare-earth manganite TbMnO₃ led to a unique branch of multiferroics (the so-called the type-II multiferroics), in which the ferroelectricity was directly generated and thus intrinsically controlled by spin orders.^3,4 In some of these type-II multiferroics, the spontaneous polarization (P) is driven by the spiral spin order, via the inverse Dzyaloshinskii-Moriya (DM) interaction.^5–7To pursuit the utilization of the intrinsic mutual control between the magnetic and ferroelectric (FE) orders, more research efforts on the type-II multiferroics remain needed, e.g., to explore new materials with better performance.

Interestingly, almost all type-II multiferroics can be catego- rized into the spin-frustrated systems, in which the energies of competing interactions cannot be entirely minimized.^8–10Even though, as far as we know, only very few works have touched the multiferroicity of pyrochlore magnet Re₂B₂O₇(Re¼rare- earth ion and B¼Ti, Sn, Mo, and Ru) in which the rich noncollinear spin structures may hide plenty opportunities for novel multiferroics.^11–14In fact, the so-called spin ice discovered in some of these frustrated magnets has received particular attention, in which the spins of rare earth ions at low temperatures (T) precisely mimic the protons’ behavior in water ice, giving nonzero entropy even down to the absolute zero-Tlimit.^15,16

As a typical spin ice, Ho₂Ti₂O₇(HTO) is composed of corner-shared TiO₆ octahedron and Ho₄O tetrahedron (Fig.

1(a)), in which the four Ho^3þspins staying on the corners of each tetrahedron satisfy the “two-in-two-out” ice rule with macroscopic degeneracy.¹¹Along theh111iaxis, every spin

FIG. 1. (a) A schematic crystal structure of Ho2Ti2O7. (b) Sketch of spin con- figurations in the spin ice state of Ho2Ti2O7, projected onto theaaxis. The

“þ” and “” signs indicate the parallel and antiparallel component of spins to theaaxis, respectively. The pink arrow presents the generated local polarization between the neighbor spinsSiandSjby inverse DM interaction. (c) Non- zero polarization may survive upon partial Fe-substitution. (d) The measured XRD pattern of the prepared polycrystalline samples Ho_2xFexTi2O7(HFTO).

a)Electronic mail: [email protected].

b)Electronic mail: [email protected].

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chain shows noncollinear spin configuration, and thus, the inverse DM interaction may take effect for these Ho^3þ-O²- Ho^3þ pairs, generating local electric dipoles, as shown in Fig.1(b). However, it should be noted that any of the ground states following the “ice rule” would not allow macroscopic polarization, since neighboring electric dipoles would cancel each other. Even though, the latest theoretical work predicted that the elementary excitation in spin ice materials (the so- called magnetic monopole^17–20) not only carries magnetic charge but also electric-dipole, which manifests another type of intrinsic coupling between magnetic and electric properties.²¹ If a long-range order can be established for these electric- dipoles, a macroscopic electric polarization may be expected.

Indeed, the ferroelectricity has already been evidenced in both the single crystal and polycrystalline Ho₂Ti₂O₇ samples,^22,23while the measured polarization is very small. Along this line, to pursuit better multiferroic performance, any modulation of the magnetic monopole excitation is meaningful. For example, it may be possible to tune the magnetic monopole excitation and thus, its multiferroicity by substitution of other magnetic species with large disparity in moment and ionic radius, e.g., Fe^3þ. Fig.1(c)presents the schematic diagram of the spin configuration with Fe-substitution to the spin ice state, which may allow particular modulation in magnetic interactions and dynamics of magnetic monopoles, as well as the polarization.

II. EXPERIMENTAL DETAILS

A series of Ho_2xFe_xTi₂O₇ (HFTO) was prepared by standard solid-state reaction method. In detail, the stoichio- metric starting material Ho₂O₃, Fe₂O₃, and TiO₂were first thoroughly ground and sintered at 1200C–1400C with several intermittent heating and grinding steps until high quality single phase was obtained. The measured XRD pattern for a series of HFTO samples are shown in Fig.1(d). It can be seen that all the samples are well crystallized and indexed by single phase cubic pyrochlore structure, without any detectable impurity phase. Theacmagnetic susceptibility (v⁰andv⁰⁰) was measured with the corresponding powder sample using the physical properties measurement system (PPMS) (Quantum Design, Inc.) with the ACMS option (fre- quencyf¼10 Hz–10 kHz). TheT-dependence of the dielectric constant (e) was measured using the HP4294A impedance analyzer integrated with PPMS. The measurement of specific heat (Cp) was carried out using the PPMS in the standard procedure. To probe the polarization, pyroelectric current method was used, and other extrinsic contribu- tions, such as the de-trapped charges, were carefully excluded.^24,25 The T-dependent P under magnetic field (H) was collected at a warming rate of 4 K/min with a fixed magnetic field during the whole process. The poling field (E) before the pyroelectric measurement is 7.69 kV/cm.

III. RESULTS AND DISCUSSION

First, the ferroelectric and dielectric properties of the Fe- substituted Ho₂Ti₂O₇ (HFTO) samples are presented. For example, let us take the substitution concentration x¼0.10.

Fig.2(a)shows theT-dependence of the pyroelectric current (Ip) under different ramping rates of 2, 4, and 6 K/min. It can

be seen that two clear peaks show up. No obvious deviation of these peaks is observed with different warming scan rates, implying that the measured pyroelectric current is intrinsic.

Also, it should be noted that there is a dim anomaly around 40 K, which is not well understood yet due to the limited knowledge of magnetic structure. To simplify the discussion below, we only focus on the main features, leaving this open question to future studies. In addition, we also measured the Ip–Tcurve after a negative poling electric field with 6 K/min warming rate, as shown in Fig. 2(b). The two curves of 67.69 kV/cm poling fields are almost antisymmetric, which implies that the polarity can be fully reversed by external electric field, further confirming the existence of ferroelectricity.

Fig.2(c)shows theT-dependentPover the wholeT-range from 2 K to 100 K, in which two FE phase transitions at Tc80 K andTc130 K, are observed. The inset of Fig.2(c) shows the enlarged P-T curve of x¼0.10, in which the FE transitionTccan be clearly clarified. For comparison, the meas- uredP(T) curve of pure polycrystalline Ho2Ti₂O₇is also presented in Fig.2(c). Two striking changes in our Fe-substituted samples are detected. First, a remarkable enhancement of polarization up to 135lC/m²was obtained at the low substitution levelx¼0.10, accompanied with the FE phase transition (Tc) up to 80 K, while the low-T Pand Tc in HTO is only 0.6lC/m², and60 K, respectively. Second, the value ofP in pure HTO almost reaches saturation below 50 K, whereas in the Fe-substituted sample continues to increase with decreas- ingT, until the saturated value at15 K. These two significant differences indicate that Fe-substitution can substantially tune

FIG. 2. (a) Temperature (T) dependence of pyroelectric current (Ip) at different warming ramp rates (2, 4, and 6 K/min) for samplex¼0.1. (b) MeasuredIp(T) under a positive and negative poling electric field E (67.69 kV/cm). (c) MeasuredT-dependence of polarization for samplex¼0.1 and HTO. Note the polarization of HTO has been enlarged 150 times for a clear comparison. The inset shows the enlargedP-Tcurve forx¼0.10 near 80 K. (d) The measured dielectric constanteas a function ofTat different frequencies. (e) Measured P(T) curves for selected samples and the inset showsP-xrelation atT¼2 K. (b) MeasuredP-Tcurves for samplex¼0.1 underH¼5 T and 9 T, respectively.

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the multiferroicity of HTO. In addition, there is a kink around 50 K for the samplex¼0.10, which might be the feature of pure HTO. The dielectric constant (e) also show changes upon Fe-substitution, which first increases with decreasingT, reaching a broad bump roughly atTcas shown in Fig.2(d). Besides, the frequency (f) dispersion behavior is also observed for the dielectric constant. Both the broad bump and f-dispersion reflect the characteristic behavior of a ferroelectric relaxor.²⁶

The enhancement of ferroelectricity upon Fe’s partial substitution is not limited to thex¼0.10 sample. The correspond- ingP-Tdata of a series of HFTO samples with various xare presented in Fig.2(e). It can be seen that all samples show clear ferroelectricity, with two ferroelectric transition points, although the values of P and Tc depend on x. The detailed x-dependence ofPatT¼2 K is shown in the inset of Fig.2(e).

The value ofP at 2 K first increases with the Fe-substitution levelx, reaching the maximum235lC/m²atx¼0.08, while further substitution leads to suppression. Meanwhile, the criti- cal pointTcalso shows similar behavior, which increases first but decreases rapidly atx>0.08, e.g.,Tc¼40 K forx¼0.15.

To uncover the intrinsic correlation between magnetic and ferroelectric properties, the magnetoelectric (ME) responses of HFTO samples are investigated under selected magnetic fields. Still taking thex¼0.10 sample, for example, Fig. 2(f) shows that the external magnetic field sup- presses P in the whole FE phase region, implying the significant response ofPtoH. The reduced value ofPunder H¼9 T can reach up to20lC/m²at lowT, confirming the intrinsic type-II multiferroicity.

To shed light on the mechanism of multiferroicity, we turn to investigate the magnetism and specific heat of HFTO sample. Aforementioned HFTO samples show similar P-T behavior and ME response, suggesting a common mechanism for variousx. In the following, the substitution concentration x¼0.04 is shown as an example. Fig.3(a)shows that the real part of the ac susceptibility (v) at f¼1 kHz monotonically rises with decreasingTunder zero magnetic field, closely following the canonical paramagnetic behavior.²⁷ However, as shown in Figs.3(a)and 3(b), the corresponding real partv⁰ and imaginary part (v⁰⁰) ofacsusceptibility taken atH¼3 T demonstrate an expected freezing temperature Tf28 K for

the v⁰, together with an unexpectedf-dependent peak for the imaginary partv⁰⁰. In particular, the magnitude of the peak of v⁰⁰(T) gradually grows with decreasing frequency at lower f range (f<1 kHz), and the application of magnetic field can enhance the value ofTf. This abnormal freezing phenomenon reminds us that an unusual slow spin relaxation occurs in the highly spin polarized state, similar to that of Tb₂Ti₂O₇.²⁸ Besides, it should be noted that the prominentf-dependence of v⁰⁰(T) behave more like spin ice.^29–31 In other words, a low level substitution dramatically changes the dynamic of spin relaxation process, with the coexistence of spin-ice freezing and Tb₂Ti₂O₇-like relaxation. Such a relaxation process in this highly polarized cooperative paramagnetic system is argued to be originated with the development of correlated regions of spins coupled through dipolar interactions.²⁸

To uncover more information of the magnetism of HFTO, both the specific heat data of HFTO (x¼0.04) (CHFTO) and Y₂Ti₂O₇(YTO) (CYTO) were obtained. As YTO is structurally analogous to HTO but without magnetism, the lattice vibration contribution term (Clatt) of specific heat of HTO can be approximated by measuring the nonmagnetic YTO. Consequently, the magnetic term (Cmag) of specific heat can be evaluated by deducting the lattice vibration contribution: CHFTO–CYTO. As shown in Fig.3(c),Cmag gradually rises with decreasing T, and subsequently turns into a broad platform below 60 K, which indicates that there are still spin fluctuations within the system. In this context, the timescale of the dynamic response is long enough to allow the system to respond to the varying magnetic field. Hence, the correlated T-dependentCmag,v, andPimply close rela- tionship between magnetism and ferroelectricity.

Finally, the possible origin of enhanced ferroelectricity in HFTO is discussed. As mentioned in the Introduction, Khomskii’s theory based on the magnetic monopole of spin ice proposes the new possibility to mutual control of magnetic monopoles and electric dipoles.²¹Of course, convincing experimental evidences are still scarce, as far as we know, due to the complexity of magnetism in these spin ice systems. Thus, here our discussion is only for qualitative and preliminary reference.

First, let us start with the discussion of FE mechanism of pure HTO. A schematic diagram of Ho^3þspin configura- tions at Tc1<T<Tc and T<Tc1 for HTO is presented in Figs.4(a)and4(b), respectively. It is known that HTO shows paramagnetic (PM) behavior at Tc1<T<Tc, and thus, the FE Pcannot be driven by specific spin order. The measured polarization shown in Fig. 2(c)is likely to be caused by the ion-displacement associated with the Ti-O octahedral distor- tion.²² When the system enters into the low temperature (T<Tc1) region, a number of magnetic monopoles as labeled by the dashed rectangles are activated, which thus give rise to the electric dipoles. However, the macroscopic polarization driven by magnetic monopoles should be very limited,²¹ since the electric dipole alignment driven by electric field can be more complicated. The electric field driven dipole flip is actually realized by the motion of the associated monopoles, e.g., the local creation and annihilation of magnetic monopoles by the manipulation field.

However, the above explanation appears not plausible for the Fe-doped HTO, since the change of magnetic

FIG. 3. (a) and (b) Measuredacsusceptibility of the samplex¼0.04 versus temperature for several frequencies at H¼3 T. (a) Real part v⁰. (b) Imaginary partv⁰⁰.Thev⁰(T) without magnetic field atf¼1 kHz is also presented in Fig.3(a)(right axis). (c) TheT-dependence of magnetic contribution termCmagof specific heat for samplex¼0.04.

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monopoles should not be so dramatic upon such tiny substi- tutions.²¹As demonstrated by theacsusceptibility, the original dynamics of typical spin ice is significantly weakened;

instead, highly correlated cooperative paramagnetic (CCPM) behavior is dominated in the Fe-substituted samples. In this context, all spins should be immensely correlated, where or- dered noncollinear spin pattern is highly possible to be formed, e.g., propagating alongh001idirection as illustrated in Figs.4(c) and 4(d). It is believed that there is a strong competition between spin fluctuations and dipolar interaction. Hence, with the coupled correlated regions through dipolar interactions, a macroscopic P is gradually established. However, excess Fe-substitution will weaken the dipolar interactions between Ho^3þ-Ho^3þpairs, leading to the decreasingP andTc,as shown in Fig.2(e). In addition, the observation of theacsusceptibility shown in Fig.3(a)can be explained as the formation of correlated magnetic domains, in most of which the spins are polarized along the field and in a few of which the spins are polarized antiparallel to the field.²⁸Switching these oppositely polarized domains needs a large energy barrier, making the spin relaxation becoming much slow. Therefore, accompanied by the switching of domains, the long-range spiral spin order may be partially broken, leading to the suppressed P by the application of magnetic field. Of course, an unambiguous clarification of the underlying microscopic mechanism, as well as the dynamics of creation and annihilation of magnetic monopoles by electric field, desires further experimental and theoretical investigations.

IV. CONCLUSION

In conclusion, we have demonstrated a remarkable enhancement of polarization in Fe-doped Ho₂Ti₂O₇. Theac susceptibility indicates that the original typical spin ice behavior changes into unusual slow spin relaxation. We argue that the competition between correlated spins and dipolar interactions gives rise to the finite electric dipoles via the inverse DM interaction. Our experimental measurements indicate a magnetic multiferroic behavior in such a pyrochlore oxide, which extends the scope and deepens the

understanding of exotic magnetically induced ferroelectricity in frustrated magnets.

ACKNOWLEDGMENTS

This work was supported by the 973 Projects of China (Grant No. 2011CB922101), the Natural Science Foundation of China (Grant Nos. 11234005, 11374147, 51332006, and 51322206), and the Priority Academic Program Development of Jiangsu Higher Education Institutions, China.

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FIG. 4. The sketch map of the spin snapshots of HTO at (a)Tc1<T<Tcand (b)T<Tc1and HFTO at (c)Tc1<T<Tcand (d)T<Tc1. The magnitude and orientation of these spin arrows are drawn only for guide of eyes. Here, Tcis not a special temperature for HTO, but only for comparison between HTO and HFTO.

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