MagNanoLab

Multiferroics are materials that exhibit two or more ferroic behaviors, including magnetoelectricity, piezoelectricity, and piezomagneticity.^1-5 One of the potential applications of multiferroics is to be a next-generation memory storage.⁵ Various types of memory devices using BiFeO₃, RMnO_3,or RMn₂O₅(R = rare earth) compounds, have been developed.^6-8 For example, Zavaliche et al. demonstrated a electrically assisted magnetic recording method for BiFeO₃-CoFe₂O₄ multiferroic nanostructure.⁹ Bibes and Barthélémy designed a potential structure for memory device usage called “MERAM” using magnetoelectric materials.¹⁰ Yu-Ting Tsai et al. reported the performance of resistance-switching Pt/DyMn₂O₅/TiN memory device.⁸ These studies indicate the feasibility of designing real memory using multiferroic materials with the advantages of stackability and rapid electronic access. However, some elementary physical limitations must be clarified. General magnets lose their permanent magnetism when they are smaller than the superparamagnetic limit.¹¹ This effect is also evident in multiferroics, and puts a lower limit on their functional size. In sandwich structure designs, the information in each bit is preserved magnetically and accessed electronically.¹⁰ Any improper response of the magnetic or electric signal because of small size will cause the loss of valuable information. Therefore, the determination of the magnetically and electrically critical sizes is crucial for practical applications. Another consideration is that the recording density of these new designs that use multiferroics must be comparable with those already used. Recently, the commercial perpendicular magnetic recording (PMR) technique has improved hard disk recording density by as much as 500-600 Gbits/in², and further reduced the size of the magnetic clusters of recording unit close to the superparamagnetic limit.¹² To overcome this limit, three-dimensional and stackable designs are superior to planar disks.

RMn₂O₅ (R = rare earth) compounds are multiferroics with magnetoelectric properties.^5,13-15 Based on electronic configurations, the difference of magnetic moment between gadolinium and its neighboring elements (Eu = 0 μ_B, Gd = 7.94 μ_B, and Tb = 9.72 μ_B) are very large. Hence, any variation of the valence electron will cause a large change in the magnetic moment, especially in a small sample that has large bounding defects at its surface. Moreover, although an external field can induce magnetic or electric ordering by the magnetoelectric effect, in practice, both orderings must occur spontaneously and simultaneously to preserve informations.¹⁰ This study determines the maximal recording density that is set by the critical size associated with the multiferroicity of GdMn₂O₅nanorods. The importance of the size effect in structural, magnetic and electric properties is elucidated.

GdMn₂O₅ nanorods were synthesized using a hydrothermal method.^16,17The obtained powder was divided into five parts, and sintered in an electrical furnace at annealing temperatures (T_a) of 400, 600, 800, 1000, and 1200 °C, respectively. To compare its multiferroicity with those of nanorods, a bulk sample was also made by the conventional solid state reaction method.

The composition and purity of the sample were determined using a Philips X’pert powder X-ray diffractometer with a CuKα wavelength. The diffraction patterns were analyzed using the General Structure Analysis System (GSAS) program following the Rietveld refinement method.¹⁸ Figure 1(a) presents the patterns thus obtained, which reveal that the nanorods maintain the same crystal structure as that of the bulk when the annealing temperatures are equal or less than 1000 °C. Structural refinement revealed that the GdMn₂O₅nanorods and bulk are formed with orthorhombic Pbam symmetry.^19,20 As T_a increased to 1200 °C, GdMn₂O₅decomposed into two major compounds, GdMnO₃and Mn₃O₄, in a molar ratio of approximately 71% to 29%.¹⁹ The size of the nanorods was observed to be correlated with annealing temperature. The width (FWHM) of the {112} single peak at 2θ = 35.6° decreased with increasing T_a, indicating that the size of the samples increased with annealing temperature.

Figure 1. (Color online) (a) X-ray diffraction patterns of GdMn₂O₅ bulk and nanorods at various annealing temperatures T_a of 400 °C, 600 °C, 800 °C, 1000 °C, and 1200 °C. (b) TEM image of <L_C> = 198 nm GdMn₂O₅ nanorods. Selected area electron diffraction (SAED) pattern and high-resolution electron microscopic images are inset.

To quantify the sizes of four types of single-phase GdMn₂O₅ nanorod, a JEOL JEM-2100 field emission transmission electron microscope (FE-TEM) and selection area electron diffraction (SAED) were utilized to determine the axial/radial lengths and their directions.²¹ Figure 1(b) shows one of the obtained images of the T_a = 1000 °C sample. Clearly, the high-resolution images and SAED pattern reveal that the c axis of the crystal is parallel to the axial direction of the nanorod.¹⁶ This phenomenon is also observed in those nanorods that were annealed T_a = 400, 600, 800, and 1000 °C. Similar observation of the radial direction with a specified orientation is not found. In contrast, the mean measured values of the products “axial length (error bar)×radial length (error bar)” for the samples with T_a equal to 400, 600, 800, and 1000 °C are 55(10) nm×26(7) nm, 66(10) nm×31(6) nm, 79(12) nm×31(5) nm, and 198(43) nm×99(26) nm, respectively. For brevity and to provide crystal orientation, the samples are referred to by their mean axial lengths, “<L_C>”, rather than their annealing temperature, T_a.

Ac magnetic susceptibility measurements were made using a “Physical Property Measurement System” (PPMS) from Quantum Design with the standard setup. The sample was subjected to a weak driving ac magnetic field at 10 Oe with a frequency of 10³ Hz (f_m). Figure 2(a) shows the collected temperature profiles of the in-phase component c' of bulk, <L_C> = 198, 79, 66, and 55 nm. The c'-T curve of the bulk revealed a magnetic susceptibility raise at 43 K (T*), which is associated with the starting of the incommensurate antiferromagnetic (ICAFM) ordering of Mn ions.²⁰ Simultaneously, a small distinct feature that is related with the transition from incommensurate to commensurate antiferromagnetic (CAFM) ordering was observed at 41.5 K (T_CAF).²⁰ For <L_C> = 198 and 79 nm samples, the values of T* and T_CAF are 2 K and 1 K lower, respectively, than those of the bulk. In the contrast, no such antiferromagnetic (AFM) peaks were observed when <L_C> was reduced to 66 and 55 nm. Above 80 K, all samples were in the paramagnetic phase. The effective magnetic moment (m_eff) and Néel temperature (T_N) in Fig. 2(b) are obtained by curve fitting using the Curie-Weiss law. Both m_eff and T_N decreased with <L_C>. An abrupt drop in both parameters also occurs between <L_C> = 79 and 66 nm, which corresponds the disappearance of the AFM peak in Fig. 2(a). Clearly, as <L_C> decreased, both T* and T_N shifted to lower temperatures, implying that the size effect weakens magnetic coupling between Mn ions. Both figures reveal that the critical length of magnetic ordering is between <L_C> = 66 and 79 nm. Notably, the radial lengths of <L_C> = 55 , 66 , and 79 nm are all near 30 nm to within the statistical error, indicating that the critical length of AFM magnetic ordering may not be obviously correlated with the radial length, but governed by the correlation length along the c axis of the crystal (<L_C> length).

Figure 2. (Color online) (a) χ-T curves of bulk, <L_C>= 198 nm, 79 nm, 66 nm, and 55 nm nanorods. (b) Fitted effective magnetic moment μ_eff and Néel temperature T_N of four nanorod and one bulk samples.

The effects of size on the dielectric properties of the nanorods were also investigated. Samples were packed, wired, and placed in a closed-cycle refrigerator with precise temperature maintenance using a Lakeshore 325 temperature controller. An Agilent E4980A LCR meter was utilized to measure the capacitance of the samples in exciting ac electric fields of various frequencies (f_e). The in-phase relative dielectric constant e' is calculated from the measured capacitance. Here, the porosity (P) of each sample was in the range 33~35 %, which can be utilized to correct the measurements.²² Figure 3(a) presents the e' of bulk, <L_C> = 79, 66, and 55 nm samples at f_e =10³ Hz. The corresponding ferroelectric (FE) ordering temperatures (T_c) were around 38 K, 42 K, 43 K, and unavailable, respectively. Obviously, T_c increased as the size larger than 55 nm. Moreover, the saturated dielectric constant (e_s') of FE ordering at approximately 14 K was decreased as the size decreased. The critical size of FE ordering is between <L_C> = 66 and 55 nm, which is smaller than AFM one. These observations imply that the FE domains are smaller than the AFM ones, and confined by axial lengths of nanorods. Otherwise, the FE domain is also sensitive to the frequency of the ac electric field. To study this effect, Figs. 3(b), (c), and (d) presents the relative dielectric constants of the <L_C> = 79, 66, and 55 nm samples at frequencies from 10³ to 10⁶ Hz. The e_s' of all three samples were decreased as the frequency increased. By comparison with the reduction of e', Δe', at f_e = 10⁶ Hz between the <L_C> = 79 and 66 nm samples, the Δe' between 14 K (e_s') and 45 K (above T_c) of the <L_C> = 79 nm sample is finite. In contrast, the Δe' of the <L_C> = 66 nm sample is almost zero. This finding reveals the frequencies of applied electric field strongly affect the FE ordering near critical size.

Figure 3. (Color online) (a) Measured relative dielectric constants of bulk, <L_C>= 79 nm, 66 nm, and 55 nm samples excited at ac frequency of 10³ Hz. (b) <L_C> = 79 nm and (c) <L_C> = 66 nm (d) <L_C> = 55 nm samples at various ac frequencies are also shown.

Many groups have reported that the polarization of the AFM domain in multiferroic materials is govern by FE domain, which originate from the coupling between FE and AFM domain walls (DWs) and provide tunability by varying the external electric field.^23-25 In contrast, the polarization of some AFM domains at structural defects is not easily changed, causing the freezing of coupled FE DWs. This behavior results in a poor response at high frequencies. Moreover, the structural defects are usually existed at the surface of the sample (where the bonds are abnormal), and they are especially important in nanorods with a large surface-to-volume ratio. Hence, a smaller <L_C> is associated with a lower e'. Figure 3(a) shows this effect. Comparison with magnetism, the difference between the values of m_eff of the nanorods and the bulk can be simply used to estimate the fraction of AFM DWs that are located at structural defects. Magnetic moments that are at surface may not respond to an exciting ac magnetic field, and make less contribution to m_eff. The reduction of m_eff of the bulk by this effect can be neglected, so that m_eff of the bulk ( ) can be used as a standard for comparison. In this conception, the ratio of the surface defects of <L_C> = 66 to 79 nm is estimated to be ( - ) / ( - ) = 0.68±0.06 / 0.18±0.05 = 3.8±1.9 (from the table in Fig. 2(b)), which is close to the reduction ratio of ( - ) / ( - ) = 4.3 / 1 = 4.3 (from Figs. 3(b) and (c)). Clearly, these calculations verify the previous inference, and reveal the consistency between magnetic and electric properties.

The mechanism of magnetoelectric coupling involves simultaneous magnetic and electric ordering, and governs by the structural distortions.²⁰ The size effect is known to be responsible for these distortions. To investigate the relationship between structural distortions and the size effect, in situ X-ray diffraction experiments were carried out on <L_C> = 66 and 79 nm samples, whose lengths were close to critical, at various temperatures from 10 K to 55 K at intervals of 5 K.²⁶ Figure 4(a) displays the results of refinement of the <L_C> = 79 nm at 25 K. An additional peak at 2θ = 27.3°, which is not indexed by orthorhombic Pbam symmetry, is observed.²⁰ Many space groups, including Pb2₁m symmetry, have also been tested in the refinement, but no one is matching the peak.²⁷The <L_C> = 66 nm sample does not yield this peak in the range of temperatures of interest. To trace the evolution of the peak, experiments were conducted again between 15 K and 30 K using intervals for 1 K with 2q in the range 25° to 30°. Figure 4(b) shows the temperature profile of the <L_C> = 79 nm sample, which develops an additional peak at approximately 18 K, and suddenly disappears at 27 K. Two local maxima were also observed at 19 K and 24 K. No similar observations are made of <L_C> = 66 nm in Fig. 4(c). Figure 4(d) shows the cell volume and the Mn³⁺-O-Mn⁴⁺ bond angles of both samples, and indicates that the variation of the <L_C> = 79 nm is larger than that of the <L_C> = 66 nm sample. Two local cell volume minima are associated with two local maxima intensities of the additional peak in Fig. 4(b). Moreover, the Mn⁴⁺-O^2-(4)-Mn³⁺-O^2-(3)-Mn⁴⁺ chain is roughly extended in the direction, and confined by the radial length. The inset in Fig. 4(a) schematically depicts the relative Mn and O positions at pyramid and the plane through the middle of an octahedron. Again, the fact that the radial lengths of the two samples are almost equal implies that the only differences between the two samples are mean axial length. The experiment in this study reveals that increasing the axial length reduced cell volume and created distortions inside the unit cell, resulting in periodic charge ordering. The evidence is that the charge ordering peak at 27.3° can be indexed as {2 1 ½}, and its intensity varies with distortions. Giovannetti et al. reported theoretical calculations concerning similar phenomena that involve the transfer of charges between Mn and oxygen ions, and proposed a relationship between distortion and bond lengths.²⁷

Figure 4. (Color online) (a) Refinement results from X-ray diffraction pattern of <L_C> = 79 nm at 25 K. Figure shows observed (red crosses) and calculated (green solid line) with estimated peak positions (black dash). Diffraction patterns obtained at various temperatures for (b) <L_C> = 79 nm and (c) <L_C> = 66 nm nanorods are also plotted. (d) Refined cell volume and Mn³⁺-O-Mn⁴⁺ angles of <L_C> = 79 nm and <L_C> = 66 nm.

In conclusion, the magnetic, electric, and structural properties of nanorods with various axial lengths <L_C> were investigated. Multiferroicity is broken by the disappearance of AFM ordering as <L_C> reduced to 66 nm. The FE ordering is further suppressed as <L_C> is reduced to 55 nm. A smaller <L_C> is associated with a larger surface-to-volume ratio and greater freezing of the motion of FE DWs. Therefore, e' is reduced as the size reducing, worsening the response to higher frequencies. X-ray diffraction experiments on the <L_C> = 79 nm sample between 18 and 26 K yield a charge ordering peak at 27.3°, which is indexed as {2 1 ½} and the appearance is correlated with the <L_C> length. Obviously, the magnetic, electric, and structural properties are governed by the axial lengths of nanorods. In applications, the memory capacity of GdMn₂O₅ nanorods can be calculated by minimizing their functional size (AFM and FE must occur spontaneously and simultaneously) as upstanding pillars, which have a cross-sectional area of (31 nm)². Hence, the estimated maximal capacity is approximately 650 Gbits/in².

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