electrons in Mn-Tb coupling of multiferroic TbMnO

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Role of t

_2g

electrons in Mn-Tb coupling of multiferroic TbMnO

₃

Y. Y. Guo,¹Y. L. Wang,²J.-M. Liu,^2,a)and T. Wei³

1College of Electronic Science and Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210003, China

2Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China

3College of Science, Civil Aviation University of China, Tianjin 300300, China

(Received 11 July 2014; accepted 2 August 2014; published online 13 August 2014)

We investigate the effect of Cr-doping in polycrystalline TbMn_1xCr_xO₃(x6%) ceramics on the magnetism, ferroelectricity, and dielectricity. The Cr substitution gradually suppresses the ferroelectricity induced by the Mn spiral spin ordering, and results in a stronger modulation of polarization by magnetic field with increasingx. However, the transition temperatureTTbcorresponding to onset of Tb magnetic ordering has barely shifted with Cr doping. In other words, although the Cr-doping obviously disrupts the Mn spiral spin ordering, the exchange fieldJMn-Tbacting on the Tb moments from the Mn-spin structure is hardly impacted. Our work demonstrates that theeg

electron of Mn^3þplays an important role in forming the Mn spiral spin order, but thef-dexchange interaction between the Mn 3d spins and the Tb 4f moments in multiferroic TbMnO₃ almost involves only thet2gelectrons.V^C 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4893018]

I. INTRODUCTION

Multiferroic manganites RMnO3(R¼Gd, Tb, Dy, and Ho) with orthorhombic structure have been intensively investigated since the discovery of magnetoelectric (ME) effect. The strong coupling between spin, charge, orbital, and lattice degrees of freedom gives rise to many competing phases in manganites, with rich physical properties.^1–3 TbMnO₃ (TMO) is a typical example of magnetoelectric multiferroics, which exhibits gigantic magnetoelectric response. According to neutron diffraction studies,⁴the Mn magnetic moments in TbMnO₃undergo an antiferromagnetic transition at TN (41–42 K). When the spin structure trans- forms into a cycloidal spiral structure with decreasing temperature (T) down to TC (26–28 K), the ferroelectric order gradually develops. Upon further decreases in T, Tb magnetic moments show long-range ordering at TTb (7 K).

Theoretical and experimental studies^5–7reveal that the ferroelectricity in TbMnO₃and many other cycloidal-spin mag- nets is induced by the noncollinear Mn spiral spin order with inverse Dzyaloshinskii-Moriya (DM) interaction, which is the driving force of oxygen atom displacements.

Extensive studies have demonstrated that the electric polarizationPcan be rotated in TbMnO₃by applying a magnetic field.^2,3,8,9The Mn-Tb coupling was found to play an important role in the electric polarization flop. The involved physics mechanism is that the arrangement of Tb moments is modified by sweeping a magnetic field, thus resulting in the change of Mn spin configuration under the influence of thef- d interaction between the Mn 3d spins and the Tb 4f moments.^2,3

Moreover, recent reports on multiferroic TbMnO₃reveal a complex coupling between Tb- and Mn-magnetic orders down to the lowestT, and the effective exchange fieldHMn- Tbgenerated by the Mn spins has a significant influence on

the Tb-magnetic ordering via thef-dcoupling.^10–12But some details on their respective roles of t2gelectrons and egelec- trons of Mn^3þin thef-dcoupling between Tb and Mn spins are still unclear up to now.

Because the whole ordering scheme of Tb in multiferroic TbMnO₃is strongly dependent on competingJMn-Tband JTb-Tbexchange interactions.^10–12Thus, one can easily speculate the Tb-magnetic ordering should be very sensitive to any variation inJMn-Tb, when the exchange interactionJTb-Tb

remains unchanged. With this in mind, to ascertain whether the eg electrons of Mn^3þ are essential in the f-d exchange interaction between the Mn 3dspins and the Tb 4fmoments, we shall visit the magnetic and ferroelectric behaviors in TbMnO₃by a slight Cr^3þsubstitution for Mn^3þ. The choice of Cr^3þis based on the unoccupied egorbital and the very tiny difference between ionic sizes of ²⁴Cr^3þ (ionic radius r0.0615 nm) and²⁵Mn^3þ(r0.0645 nm).¹³

II. EXPERIMENTAL DETAILS

Along this line, we prepared a series of polycrystalline TbMn_1xCr_xO₃ (x¼0%, 2%, 4%, 6%) samples using the conventional solid-state reaction route. The phase purity and crystallinity at room temperature were checked by X-ray diffraction (XRD) using Cu Karadiation. The diffraction data were structurally refined using the general structure analysis system (GSAS) program. The magnetic measurement was performed using the superconducting quantum interference device (SQUID) magnetometer (Quantum Design, Inc). In order to probe the spin ordering sequence, the specific heat measurement was carried out using the Quantum Design physical properties measurements system (PPMS). The dielectric data e(T) were measured withTramp rate of 2 K/

min using the HP4294A impedance analyzer. For measuring polarizationP, we detected the pyroelectric current using an electrometer (Keithley 6514), integrated with PPMS. The

a)E-mail: [email protected]

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poling electric field isE¼15 kV/cm. For these electric measurements, gold electrodes were sputtered on sample surfaces.

III. RESULTS AND DISCUSSION

Fig. 1(a) shows the XRD h–2h patterns of all the as- prepared samples. All the reflections can be indexed with a

single orthorhombic structure (space group Pbnm) and no identifiable second phase was observed within the apparatus resolution. The sharp diffraction peak indicates the high crys- talline quality. The high-precision Rietveld refinements of the XRD data were performed. A representative Rietveld refining is plotted in Fig.1(b)forx¼2%. The difference between the measured spectrum and the calculated one is small, indicating they agree very well (Rp¼6.84%, Rwp¼9.32%). For the other samples, the obtained Rp and Rwp are in the similar level. Furthermore, one can evaluate the Mn-O-Mn bond angle from the structure refinement data, and the evaluated variation of the Mn-O₁-Mn bond angle with the Cr content obtained from the diffraction data is presented in the inset of Fig. 1(a). We notice that Cr for Mn substitution leads to a slight increase of the Mn-O₁-Mn bond angle. This is reasona- ble owing to the tiny difference between ionic sizes of²⁴Cr^3þ (r0.0615 nm) and²⁵Mn^3þ(r0.0645 nm).¹³

Based on the understanding of multiferroic behaviors, we pay attention to the magnetic ordering and the corre- spondingP-generation. First, we consult the specific heat (C/

T) data in Fig.2(a), which are sensitive to each phase transition. For the x¼0% (TbMnO₃) sample, theC/Tdata exhibit three anomalies at T41 K, 26 K, and 7 K, consistent with earlier reports.^1–4The anomaly atT¼TN41 K corre- sponds to the onset of a Mn collinear sinusoidal spin ordering with an incommensurate wavevector. A second anomaly atT¼TC26 K attributes to the Mn noncollinear spiral spin ordering, where a nonzeroPensues (Fig.2(d)) and which is accompanied with a pronounced k-type peak of e(T) (Fig.

2(c)). Upon further cooling down to T¼TTb7 K, a third anomaly of C/T associated with the long-range ordering of Tb^3þmoments can be identified, at whiche(T) also exhibits a small anomaly featured with a slow decaying. These above behaviors of thex¼0% (TbMnO₃) sample are in agreement with previous reports.^1–4

Now, we focus on the evolution of the measured data with varyingx. The specific heat (C/T) data in Fig.2(a)show

FIG. 1. (a) Room temperature X-ray diffraction patterns for all TbMn1xCrxO3polycrystalline samples, and the inset shows the evaluated Mn-O1-Mn bond angle as a function of Cr content. (b) The Rietveld refinement for thex¼2% sample.

FIG. 2. Temperature profiles of (a) specific heat divided by temperature C/T, (b) magnetizationM, (c) dielectric constanteat 100 kHz, and (d) electric polarization P for all TbMn1xCrxO3

samples. The poling field is 15 kV/cm.

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that with increasingx, the above mentioned two transition temperatures (TN,TC) of the Mn magnetic sublattice exhibit gradual downshifting and, in particular, the second anomaly, which reflects the ferroelectric transition has already become ambiguous forx¼4% andx¼6% samples. The decrease in TN is a direct evidence of the effective reduction in the strength of Mn-Mn interactions JMn-Mn. Consequently, TC

also falls down with increasing Cr content,¹² indicating that the ferroelectric state becomes unstable upon the Cr-doping.

These identifications can be further confirmed by the effect of Cr-doping on the dielectric constanteand the electric polarizationP, as shown in Figs.2(c)and2(d). It should be noted that theeandPof thex¼6% sample are very small in comparison with those of thex4% samples. Thus, for the sake of clarity, Figs. 2(c) and 2(d) only present the dielectric and ferroelectric data for TbMn_1xCr_xO3 with x4%. Thex-dependence ofe(T) in Fig. 2(c) is character- ized by the downward shifting ofTC, the suppressed peak heighte(TC), and the broadened peak width ofe(T) as a function of doping levelx. It is seen from Fig.2(d)that the polar- izationPand transition temperature TC reduce dramatically with increasingx. With increasingxup to 2%, the polariza- tionPhas fallen by almost half, and the polarization value of thex¼4% sample has slumped to less than 10lC/m², indicating significant suppression ofPupon such a doping.

All these results suggest that the Cr-doping disrupts the Mn spiral spin ordering and thereby suppresses the ferroelectric phase induced by the Mn spiral spin ordering. To understand these features, one may consult to those possible underlying mechanisms.

In previous reports,^14–17the origin of the Mn spiral spin order (SSO) in perovskite multiferroic manganites RMnO3

(R¼Tb or Dy) was investigated by incorporating a next- nearest-neighbor (NNN) super-exchange (SE) interaction and a Jahn-Teller distortion into a pure two eg-orbital double-exchange (DE) model, which included only the DE and nearest-neighbor (NN) SE interactions. The whole Hamiltonian takes the following form:

H¼–Xab

hijit^ab_r Xijc^þ_iacjbþJAF

X

hijiSiSjþX

½ikJ2cSiSk

þkX

i½Q2;isx;iþQ3;isz;i;

(1) where the first term was the standard DE of itinerantegelec- trons, andtrabwas the DE hopping integral. The second and third terms in the Hamiltonian were the NN and NNN SE couplings between t2g spins, respectively. The fourth term was the electronic-phonon coupling of Jahn-Teller (JT) distortion. The experimentally observed SSO and ferroelectric transition can be obtained by considering four pairs of couplings.

The substitution of Cr^3þwithoutegelectrons for Mn^3þ will lead to a net decline in the DE hopping integral trab. Consequently, the DE interaction of eg electrons in the Hamiltonian will obviously reduce with increasing Cr content. Meanwhile, however, owing to the close atomic number and ionic radius between²⁴Cr^3þand²⁵Mn^3þand the slightly increased Mn-O-Mn bond angle induced by the Cr

substitution,¹³ the SE couplings between t2g spins and the Jahn-Teller (JT) distortion only change a little. Early studies have already identified that despite its smaller value than those of other interactions, the DE interaction ofegelectrons plays an important role in forming the Mn spiral spin order in RMnO3 (R¼Tb or Dy).^14–16 Thus, the substitution of Cr^3þwithoutegelectrons for Mn^3þwill cause a dramatically decrease in the coherence length of the Mn spin spiral structure, or to short-range ordering. Consequently, the ferroelectric phase induced by the Mn spiral spin ordering is significantly suppressed.

In order to deeply understand the effect of Cr doping on the Mn spiral spin order, we performed the magnetic field modulation of polarization (Magnetoelectric response). The T-dependence ofPmeasured under various magnetic fieldH for some samples are presented in Figs. 3(a)–3(c). Fig.3(a) shows that for the x¼0% (TbMnO₃) sample, the ferroelectric transition TCis not sensitive to the application of magnetic fields, consistent with earlier reports,^3,18 and a small change of P under Hassociated with the multiple domains can be identified. After doping 2% Cr, a slight reduction of TCis observed andPtends to decrease with increasingH, as seen in Fig. 3(b). With increasing xup to 4%,P is rapidly suppressed andTCis significantly reduced by H(Fig.3(c)).

TheH-dependence ofTCfor thex¼4% sample is presented in the inset of Fig. 3(c). The magnetoelectric coefficient, defined as aME¼(P(0)P(H))/P(0), atT¼3 K andH¼8 T is found to be enhanced from 7% for sample withx¼0%

to89% for sample withx¼4%, as shown in Fig.3(d). The mechanism of this enhancement is that the stability of the Mn spiral spin order is disturbed by the Cr substitution, which facilitates the breaking of the Mn spiral spin order configuration by magnetic field, resulting in a stronger modulation ofPbyH. Thus, one can conclude that the Cr substitution improves the magnetic field modulation of the ferroelectric polarization.

Having observed magnetic phase transition behavior of the Mn sublattice and the induced ferroelectricity and dielectricity in all compounds, we come to address the effect of the Cr substitution on the Mn-Tb coupling. We present, in Fig.

2(b), the T-dependence of magnetization (M) for TbMn_1xCr_xO₃withx¼0%, 2%, 4%, and 6% under a field H100 Oe. No clear signature of TN and TC of Mn spins can be observed in these polycrystalline samples, due to the dominating paramagnetic susceptibility of the Tb spins, which have a much larger moment than the Mn spins. The most surprising effect is that the transition temperature TTb

corresponding to onset of Tb magnetic ordering has barely shifted with increasingx. In other words, the Cr for Mn substitution has not influenced theTTb.

An understanding of the underlying physical picture will be attractive. Early extensive studies had suggested that the whole ordering scheme of Tb in multiferroic TbMnO₃ is strongly dependent on competingJMn-TbandJTb-Tbexchange interactions.^10–12Thus, according to the above experimental results, one can easily speculate that the effective fieldJMn- Tbacting on the Tb moments from the Mn-spin structure via the f-dcoupling has nearly no change upon Cr substitution, when keeping JTb-Tbconstant. Therefore, one can conclude

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that thef-dexchange interaction is actually between the t2g

electrons of Mn^3þ and the 4f electrons of Tb^3þ. In other words, theegelectron of Mn^3þis nearly not involved in the f-dexchange interaction between the Mn 3dspins and the Tb 4fmoments in multiferroic TbMnO₃.

IV. CONCLUSION

In conclusion, we have performed investigations on the magnetic and ferroelectric behaviors of Cr-doped TbMnO₃. The substitution of Cr^3þ with unoccupied eg orbital for Mn^3þleads to significant reduction in the strength of Mn-Mn interactions JMn-Mn, and thereby results in a dramatically decrease in the coherence length of the Mn-spin-spiral structure, or to short-range ordering. Consequently, the ferroelectricity induced by the Mn spiral spin ordering is significantly suppressed and easily modulated by magnetic field.

However, the transition temperature TTb corresponding to onset of Tb magnetic ordering has barely shifted with Cr doping, which implies that the exchange fieldJMn-Tb acting on the Tb moments from the Mn-spin structure via the f-d coupling is not changed. Thus, our work proves that thef-d exchange interaction between the Mn 3dspins and the Tb 4f moments in multiferroic TbMnO₃almost involves only the t2gelectrons of Mn^3þ.

ACKNOWLEDGMENTS

This work was supported by the Natural Science Foundation of China (Nos. 11304158, 11374147, and 51102277), the National Key Projects for Basic Research of China (No. 2011CB922101), the Natural Science Youth

Foundation of Jiangsu Province (No. BK20130865), and the Scientific Research Foundation of Nanjing University of Posts and Telecommunications of China (No. NY213020).

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FIG. 3. Magnetic field modulation of polarization as a function of T for TbMn1xCrxO3 samples with (a) x¼0%, (b) 2%, and (c) 4%. (d) The measured a_ME-H relations at T¼3 K for all TbMn1xCrxO3 samples. The inset shows the measuredTCas a function ofHfor sample withx¼4%.

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