多铁性材料的磁电效应研究
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摘要
多铁性材料是指在一定温度范围内同时存在铁磁序和铁电序或铁弹序的体系。近些年来由于铁磁序和铁电序共存耦合而产生的某些新功能如磁电效应、磁介电效应,蕴含着的多种有序的耦合机制以及可预期的广阔应用前景而倍受人们的关注。在本论文中,我们主要就单相多铁性材料YMnO3的磁电耦合机理,复相纳米多铁性1-3型和准2-2型薄膜材料的磁电、逆磁电等效应分别运用基于密度泛函理论的第一性原理对非共线磁性结构的计算和朗道-德文希尔热力学理论与磁致伸缩理论结合的方法,进行了详细的研究和分析。主要内容如下:
1.六角钙钛矿YMnO3磁电耦合的第一性原理研究
基于第一性原理的共线磁性结构计算,人们已经对单相多铁性六角钙钛矿材料YMnO3的磁电耦合效应进行了较为全面的研究,但给出的结论仍然明显不能解释实验结果。在本文中,我们首次应用第一性原理的非共线磁性结构计算,并通过对不同磁性结构构型计算结果的比较,系统地研究了YMnO3材料中Mn离子的自旋三角阻挫作用、自旋-轨道耦合作用等对系统的能隙、磁矩、电子结构、轨道杂化和离子波恩有效电荷等的影响,从而对YMnO3中的多铁性起源提出了很好的第一性原理解释,并较好解释了相关实验结果。计算结果表明,由于自旋的三角阻挫排列和自旋-轨道耦合作用,晶体具有最稳定结构,费米面附近能隙加大,各离子位置和Mn离子的磁矩等都与实验值最为吻合。Y 4d-O 2p电子发生强烈轨道杂化,Mn 3d-O 2p轨道间的作用相对变弱,偏离中心的Y离子和O(3, 4)离子的波恩有效电荷异常增大,表明Y离子4d0轨道与O的2p轨道的重新杂化驱动了该材料中Y离子中心偏移,导致铁电极化。我们应用Heisenberg模型,拟合不同自旋构型的总能量,得到了锰离子间的自旋交换作用。发现由于强烈的层内Mn离子的反铁磁性耦合,使得平面内构成三角形网络结构的相邻Mn离子的自旋形成2π/3角的阻挫,而层间耦合是一种较弱的反铁磁作用,其强度小于层内电子自旋的次近邻耦合作用。此外,通过考虑电子强关联作用,我们还发现自旋阻挫导致费米面下电子态密度更加局域,Mn 3d和O 2p态杂化进一步减弱,基态能隙进一步打开,Mn离子磁矩增加。
2.1-3型纳米多铁复合薄膜中的磁电效应
对于1-3型纳米多铁性复合薄膜,虽然实验和理论已进行了大量的研究,并且发现室温下存在较大的磁场诱导的电极化和电场诱导的磁化,但对于其中不同方向的外磁场诱导的电极化、磁电耦合的基本形式以及电场诱导的磁化翻转等还缺乏系统的理论解释。本文中,我们首先将朗道-德文希尔热力学理论与磁致伸缩理论相结合,将薄膜和基底间、铁电和铁磁两相界面间的应变都分为晶格失配应变和磁致伸缩应变两部分,同时考虑晶格失配应变随薄膜厚度增加出现驰豫以及界面约束对薄膜性质如压电系数的修正,研究铁电相静态介电性质、压电性质和磁场诱导的电极化随厚度的变化等,重点研究了不同方向的外加磁场诱导的垂直于基平面方向的电极化随外磁场的变化,证明磁场诱导的电极化非常强烈依赖于薄膜中磁性纳米柱的各向异性磁致伸缩和两相界面的耦合情况。为了研究电场诱导的磁化翻转以及磁化翻转与电极化翻转的关联,我们对铁电和铁磁相均从朗道-德文希尔热力学唯象理论出发,考虑磁电薄膜与基片的机械边界条件,在两相界面处引入晶格相容条件,并与力学平衡态方程结合,两次重整介电和磁性作用系数后,首次得到了1-3型纳米多铁复合薄膜在朗道自由能函数下的磁电二次耦合的一般性形式。通过对不同温度和不同厚度下薄膜的电滞曲线和电场诱导的磁滞曲线比较,发现外加电场不仅能诱导极化场翻转,由于铁电和铁磁两相界面竖直方向的弹性耦合,导致磁化也随极化同步翻转,从而很好地解释了实验中观测到的电致磁化翻转行为。同时我们也定性地发现,由于位错导致的晶体缺陷使得薄膜内存在较大的剩余应力,这虽然有利于提高薄膜自发的铁电极化和磁化,然而却不利于外场诱导的电极化或磁化的提高,即缺陷的存在对磁电耦合效应的提高具有抑制作用。
3.准2-2型异质外延薄膜的磁电效应
异质外延铁电薄膜具有不同于体材料的物理性质,这主要取决于薄膜所处的应力状态。对于不同生长条件的薄膜,由于应力强度的不等,决定了其具有不同的介电、压电性质。通过外加磁场改变基底应变(应力),由于界面的耦合,调节薄膜受到的应力,也可控制薄膜的极化性质。这里为了研究准2-2型异质外延铁电薄膜中磁场诱导的电极化,我们将修正的压电、压磁的本构方程与朗道-金兹堡-德文希尔热力学理论相结合,对于一定厚度的薄膜,通过引入有效剩余应变和界面标度因子的概念,对极化、压电和介电系数等进行自洽求解,从而分析该薄膜中总的极化和磁场诱导的电极化。研究发现,横向磁场诱导的纵向电极化随着外加磁场的增加而非线性地增加,其非线性变化的趋势与磁性相的横向磁致伸缩变化相似。而由于磁场诱导的磁致伸缩在相变温度时最大,导致磁场诱导的电极化也是在磁相变温度时达到最大值,进一步证明了该薄膜中的磁电效应与磁致伸缩相关,定性地解释了实验结果。同时我们也计算了当外加磁场使磁性相处于饱和磁致伸缩时,磁电电压随温度的变化。我们选择了可与实验结果比较的本底稳恒磁场、交变场和一定厚度的薄膜,且假定界面标度因子为1,计算发现其在磁性相变温度时达到最大,理论结果与实验值基本定量一致,说明正是理想的界面耦合和磁性相大的磁致伸缩使得在这种构型的复合材料中实现磁电效应增强成为可能。
Multiferroic materials are defined as a kind of system, in which ferromagnetic ordering and ferroelectric ordering or ferroelastic ordering coexist spontaneously below a certain temperature. In recent years, because of some new functions such as magnetoelectric effect, magnetodielectric phenomena induced by strong coupling between two order parameters, implicate coupling mechanisms, as well as their wide and potential applications, multiferroic materials attract more and more attentions both in academic and engineering societies. In this thesis, using the first-principle based on density functional theory with noncollinear magnetic structure calculations and combining Landau-Devonshire thermody- namic theory with magnetostrictive thoery, we investigated in detail the magnetoelectric coupling mechanism of single phase multiferroic material YMnO3, and magnetoelectric effects of the 1-3 type nanocomposite thin films and epitaxial quasi 2-2 type hetero- structures including the magnetic field induced ferroelectric polarization (MIP), the electric field induced magnetization (EIP) reveral and magnetolectric enhancement and so on, respectively. The main results of our study are listed as follows:
1.The first-principles study on magnetoelectric couplings of hexagonal perovskite manganite YMnO3
Based on the collinear magnetic structure of the first-principles calculations, the comparatively overall research has been carried on the magnetoelectric coupling effects of hexagonal perovskite YMnO3, however, the results are obviously inconsistent with the X-ray diffraction ones. In first section of this thesis, we applied firstly and performed fully the noncollinear magnetic structure calculations of the first-principles based on density functional theory with generalied gradient approximation for hexagonal perovskite YMnO3. By comparing the cases calculated in different magnetic configurations, we investigated systematically the effects of the frustrated triangular spin of Mn3+ ions, spin-orbit coupling on the energy gap, magnetic moments, electronic structure, orbit hybridization and Born effective charges of YMnO3. Our conclusion provides a first-principle profound understanding of multiferroic origin in YMnO3, and the calculated results are in good agreement with the related experimental ones. We are surprised that, due to triangular spin frustration and spin-orbit coupling, the total energy of the supercell is reduced to the lowest, the energy gap is opened to the largest, the every ionic position and magnetic moment of Mn ions are most close to the experimental values. The interaction between the Y 4d and O(3,4) 2p orbits is obviusly increased, while ones between the Mn 3d and O(1,2) 2p states relatively decreased. The large anomalies in Born effective charges on off-centering Y and O ions manifest that the Y 4d0-ness with rehybridization is the driving force for the ferroeleectric of the YMnO3 along the c direction. We have also estimated the spin exchange integrals values of Mn3+ ions by mapping the calculated total energies of different spins configurations onto the Heisenberg spin model. It reveals a rather strong antiferromagnetic coupling exists between two nearest neighbor Mn ions spins, which leads to the spins frustration with 2π/3 angles between spins in plane triangular lattice, and a weaker antiferromagnetic coupling between nearest neighbor interplane. In addition, considering the strong electronic correction interaction, we also found that because of triangular spin frustration, the distributions of states densities are more localized below the Fermi level, the hybridization between Mn 3d and O 2p states is declined, the band-gap of ground state becomes wider, and the magnetic moment of Mn3+ ion increases.
2.Magnetoelectric effects in 1-3 type multiferroic nanocomposite thin fims
Although considerable research have been done through experimental and theoretical approaches on the MIP and the EIM in 1-3 type multiferroic nanocomposite thin fims, the polarization induced by appling different direction magnetic fields, the EIP reveral and so on have not been explained systematically in theory. In second section of this thesis, we investigated them by combining the Landau-Devonshire thermodynamic theory with magnetostrictive theory for ferroelectric and ferromagnetic phases, respectively. We divided each of strains from film/substrate and FE/FM interfaces into lattice mismatch strain and magnetostrictive strain, and considered film thickness dependence of epitaxial strains due to relaxation by misfit dislocation during film deposition as well as the coefficients modification of piezoelectric films due to interface constraint to study static dielectric, piezoelectric properties and MIP of thin films. Particularly, the MIP has also been mainly studied by appling the transversal and longitudinal external magnetic fields to the magnetostrictive phase, the results indicated the MIP is strong dependent on anisotropy magnetostriction of thin films and the interface coupling between two phases. On the other hands, in order to investigate the EIM reversal and the correlation between magnetization and polarization reversal, we applied Landau-Devonshire thermodynamic theory to ferroelectric and magnetic phases. After considering the mechanical boundary condition of the films/substrate and introducing the lattice compatible condition combined with the mechanical equation of equilibrium state at interface of two phases, we renormalized the dielectric and magnetic coefficients twice and obtained firstly quasi-intrinsic magneto- electric coupling in Landau free energy function of this multiferroic system. By comparing the electric hysteresis loops and EIM of thin films with different thickness and different temperature, we found that an applied electric field can result in the reversal of magnetization in step with switching of the electric polarization due to the out-of-plane elastic coupling between the interfaces of FE and FM phases. All those can excellently explained EIM reversal deeds obversed in the experiments. At the same time, we also find qualitatively that dislocation induced linear defect leads a large residual stress in thin films. Although this is beneficial to spontaneous polarization and magnetization of thin films, the MIP is depressed, that is, the existence of defect will depress the enhancement of the ME coupling in thin fims.
3.Magnetoelectric effects in epitaxial quasi 2-2 type heterostructure thin films
The properties of epitaxial heterostructure thin films are different from those of bulk, which mainly depend on the stress states in thin films. Due to the interface coupling of films/substrate, the applied magnetic field not only induces the strain of substrate but also controlls the dielectric, piezoelectric and polarization properties of thin films by adjusting the stress (strain). In this section, we introduced the effective residual strain and interface scale factor and combined the modified constitutive equations with the Landau- Ginsberg-Devonshine thermodynamic theory to investigate the MIP of the quasi 2-2 type heterostructure thin films. We analyzed the total electric polarization and MIP of this thin films by self-consistent calculation for polarization, piezoelectric and dielectric coefficients. The calculated results show that transverse magnetic-field-induced electric polarization of the multiferroic films increases nonlinearly with increasing external magnetic field. When the magnetostriction reaches its saturation at the higher magnetic field, the MIP begins to approach saturation, indicating large MIP could be produced in ferroelectric film due to a gigantic magnetically induced in-plane constraint. Moreover, because the magnetostriction of magnetic phase reaches a maximum at the magnetic transition temperature, the MIP will also get to a maximum value, further showing that the ME coupling is related to the magnetostriction. Next, we calculated the temperature dependence of magnetoelectric output voltage when the magnetostraction of magnetic phase was saturated. We chose the static, alternative magnetic field and the thickness of thin films comparable to experimental values and assumed the interface scale factor is 1, we found that the ME effect peaks at the ferromagnetic transition temperature of the manganite. Comparison with experimental data of multilayered samples reveals a good interface coupling of the films/substrate and a great magnetostriction of magnetic phase result in a large ME effect in this type of thin films.
1.六角钙钛矿YMnO3磁电耦合的第一性原理研究
基于第一性原理的共线磁性结构计算,人们已经对单相多铁性六角钙钛矿材料YMnO3的磁电耦合效应进行了较为全面的研究,但给出的结论仍然明显不能解释实验结果。在本文中,我们首次应用第一性原理的非共线磁性结构计算,并通过对不同磁性结构构型计算结果的比较,系统地研究了YMnO3材料中Mn离子的自旋三角阻挫作用、自旋-轨道耦合作用等对系统的能隙、磁矩、电子结构、轨道杂化和离子波恩有效电荷等的影响,从而对YMnO3中的多铁性起源提出了很好的第一性原理解释,并较好解释了相关实验结果。计算结果表明,由于自旋的三角阻挫排列和自旋-轨道耦合作用,晶体具有最稳定结构,费米面附近能隙加大,各离子位置和Mn离子的磁矩等都与实验值最为吻合。Y 4d-O 2p电子发生强烈轨道杂化,Mn 3d-O 2p轨道间的作用相对变弱,偏离中心的Y离子和O(3, 4)离子的波恩有效电荷异常增大,表明Y离子4d0轨道与O的2p轨道的重新杂化驱动了该材料中Y离子中心偏移,导致铁电极化。我们应用Heisenberg模型,拟合不同自旋构型的总能量,得到了锰离子间的自旋交换作用。发现由于强烈的层内Mn离子的反铁磁性耦合,使得平面内构成三角形网络结构的相邻Mn离子的自旋形成2π/3角的阻挫,而层间耦合是一种较弱的反铁磁作用,其强度小于层内电子自旋的次近邻耦合作用。此外,通过考虑电子强关联作用,我们还发现自旋阻挫导致费米面下电子态密度更加局域,Mn 3d和O 2p态杂化进一步减弱,基态能隙进一步打开,Mn离子磁矩增加。
2.1-3型纳米多铁复合薄膜中的磁电效应
对于1-3型纳米多铁性复合薄膜,虽然实验和理论已进行了大量的研究,并且发现室温下存在较大的磁场诱导的电极化和电场诱导的磁化,但对于其中不同方向的外磁场诱导的电极化、磁电耦合的基本形式以及电场诱导的磁化翻转等还缺乏系统的理论解释。本文中,我们首先将朗道-德文希尔热力学理论与磁致伸缩理论相结合,将薄膜和基底间、铁电和铁磁两相界面间的应变都分为晶格失配应变和磁致伸缩应变两部分,同时考虑晶格失配应变随薄膜厚度增加出现驰豫以及界面约束对薄膜性质如压电系数的修正,研究铁电相静态介电性质、压电性质和磁场诱导的电极化随厚度的变化等,重点研究了不同方向的外加磁场诱导的垂直于基平面方向的电极化随外磁场的变化,证明磁场诱导的电极化非常强烈依赖于薄膜中磁性纳米柱的各向异性磁致伸缩和两相界面的耦合情况。为了研究电场诱导的磁化翻转以及磁化翻转与电极化翻转的关联,我们对铁电和铁磁相均从朗道-德文希尔热力学唯象理论出发,考虑磁电薄膜与基片的机械边界条件,在两相界面处引入晶格相容条件,并与力学平衡态方程结合,两次重整介电和磁性作用系数后,首次得到了1-3型纳米多铁复合薄膜在朗道自由能函数下的磁电二次耦合的一般性形式。通过对不同温度和不同厚度下薄膜的电滞曲线和电场诱导的磁滞曲线比较,发现外加电场不仅能诱导极化场翻转,由于铁电和铁磁两相界面竖直方向的弹性耦合,导致磁化也随极化同步翻转,从而很好地解释了实验中观测到的电致磁化翻转行为。同时我们也定性地发现,由于位错导致的晶体缺陷使得薄膜内存在较大的剩余应力,这虽然有利于提高薄膜自发的铁电极化和磁化,然而却不利于外场诱导的电极化或磁化的提高,即缺陷的存在对磁电耦合效应的提高具有抑制作用。
3.准2-2型异质外延薄膜的磁电效应
异质外延铁电薄膜具有不同于体材料的物理性质,这主要取决于薄膜所处的应力状态。对于不同生长条件的薄膜,由于应力强度的不等,决定了其具有不同的介电、压电性质。通过外加磁场改变基底应变(应力),由于界面的耦合,调节薄膜受到的应力,也可控制薄膜的极化性质。这里为了研究准2-2型异质外延铁电薄膜中磁场诱导的电极化,我们将修正的压电、压磁的本构方程与朗道-金兹堡-德文希尔热力学理论相结合,对于一定厚度的薄膜,通过引入有效剩余应变和界面标度因子的概念,对极化、压电和介电系数等进行自洽求解,从而分析该薄膜中总的极化和磁场诱导的电极化。研究发现,横向磁场诱导的纵向电极化随着外加磁场的增加而非线性地增加,其非线性变化的趋势与磁性相的横向磁致伸缩变化相似。而由于磁场诱导的磁致伸缩在相变温度时最大,导致磁场诱导的电极化也是在磁相变温度时达到最大值,进一步证明了该薄膜中的磁电效应与磁致伸缩相关,定性地解释了实验结果。同时我们也计算了当外加磁场使磁性相处于饱和磁致伸缩时,磁电电压随温度的变化。我们选择了可与实验结果比较的本底稳恒磁场、交变场和一定厚度的薄膜,且假定界面标度因子为1,计算发现其在磁性相变温度时达到最大,理论结果与实验值基本定量一致,说明正是理想的界面耦合和磁性相大的磁致伸缩使得在这种构型的复合材料中实现磁电效应增强成为可能。
Multiferroic materials are defined as a kind of system, in which ferromagnetic ordering and ferroelectric ordering or ferroelastic ordering coexist spontaneously below a certain temperature. In recent years, because of some new functions such as magnetoelectric effect, magnetodielectric phenomena induced by strong coupling between two order parameters, implicate coupling mechanisms, as well as their wide and potential applications, multiferroic materials attract more and more attentions both in academic and engineering societies. In this thesis, using the first-principle based on density functional theory with noncollinear magnetic structure calculations and combining Landau-Devonshire thermody- namic theory with magnetostrictive thoery, we investigated in detail the magnetoelectric coupling mechanism of single phase multiferroic material YMnO3, and magnetoelectric effects of the 1-3 type nanocomposite thin films and epitaxial quasi 2-2 type hetero- structures including the magnetic field induced ferroelectric polarization (MIP), the electric field induced magnetization (EIP) reveral and magnetolectric enhancement and so on, respectively. The main results of our study are listed as follows:
1.The first-principles study on magnetoelectric couplings of hexagonal perovskite manganite YMnO3
Based on the collinear magnetic structure of the first-principles calculations, the comparatively overall research has been carried on the magnetoelectric coupling effects of hexagonal perovskite YMnO3, however, the results are obviously inconsistent with the X-ray diffraction ones. In first section of this thesis, we applied firstly and performed fully the noncollinear magnetic structure calculations of the first-principles based on density functional theory with generalied gradient approximation for hexagonal perovskite YMnO3. By comparing the cases calculated in different magnetic configurations, we investigated systematically the effects of the frustrated triangular spin of Mn3+ ions, spin-orbit coupling on the energy gap, magnetic moments, electronic structure, orbit hybridization and Born effective charges of YMnO3. Our conclusion provides a first-principle profound understanding of multiferroic origin in YMnO3, and the calculated results are in good agreement with the related experimental ones. We are surprised that, due to triangular spin frustration and spin-orbit coupling, the total energy of the supercell is reduced to the lowest, the energy gap is opened to the largest, the every ionic position and magnetic moment of Mn ions are most close to the experimental values. The interaction between the Y 4d and O(3,4) 2p orbits is obviusly increased, while ones between the Mn 3d and O(1,2) 2p states relatively decreased. The large anomalies in Born effective charges on off-centering Y and O ions manifest that the Y 4d0-ness with rehybridization is the driving force for the ferroeleectric of the YMnO3 along the c direction. We have also estimated the spin exchange integrals values of Mn3+ ions by mapping the calculated total energies of different spins configurations onto the Heisenberg spin model. It reveals a rather strong antiferromagnetic coupling exists between two nearest neighbor Mn ions spins, which leads to the spins frustration with 2π/3 angles between spins in plane triangular lattice, and a weaker antiferromagnetic coupling between nearest neighbor interplane. In addition, considering the strong electronic correction interaction, we also found that because of triangular spin frustration, the distributions of states densities are more localized below the Fermi level, the hybridization between Mn 3d and O 2p states is declined, the band-gap of ground state becomes wider, and the magnetic moment of Mn3+ ion increases.
2.Magnetoelectric effects in 1-3 type multiferroic nanocomposite thin fims
Although considerable research have been done through experimental and theoretical approaches on the MIP and the EIM in 1-3 type multiferroic nanocomposite thin fims, the polarization induced by appling different direction magnetic fields, the EIP reveral and so on have not been explained systematically in theory. In second section of this thesis, we investigated them by combining the Landau-Devonshire thermodynamic theory with magnetostrictive theory for ferroelectric and ferromagnetic phases, respectively. We divided each of strains from film/substrate and FE/FM interfaces into lattice mismatch strain and magnetostrictive strain, and considered film thickness dependence of epitaxial strains due to relaxation by misfit dislocation during film deposition as well as the coefficients modification of piezoelectric films due to interface constraint to study static dielectric, piezoelectric properties and MIP of thin films. Particularly, the MIP has also been mainly studied by appling the transversal and longitudinal external magnetic fields to the magnetostrictive phase, the results indicated the MIP is strong dependent on anisotropy magnetostriction of thin films and the interface coupling between two phases. On the other hands, in order to investigate the EIM reversal and the correlation between magnetization and polarization reversal, we applied Landau-Devonshire thermodynamic theory to ferroelectric and magnetic phases. After considering the mechanical boundary condition of the films/substrate and introducing the lattice compatible condition combined with the mechanical equation of equilibrium state at interface of two phases, we renormalized the dielectric and magnetic coefficients twice and obtained firstly quasi-intrinsic magneto- electric coupling in Landau free energy function of this multiferroic system. By comparing the electric hysteresis loops and EIM of thin films with different thickness and different temperature, we found that an applied electric field can result in the reversal of magnetization in step with switching of the electric polarization due to the out-of-plane elastic coupling between the interfaces of FE and FM phases. All those can excellently explained EIM reversal deeds obversed in the experiments. At the same time, we also find qualitatively that dislocation induced linear defect leads a large residual stress in thin films. Although this is beneficial to spontaneous polarization and magnetization of thin films, the MIP is depressed, that is, the existence of defect will depress the enhancement of the ME coupling in thin fims.
3.Magnetoelectric effects in epitaxial quasi 2-2 type heterostructure thin films
The properties of epitaxial heterostructure thin films are different from those of bulk, which mainly depend on the stress states in thin films. Due to the interface coupling of films/substrate, the applied magnetic field not only induces the strain of substrate but also controlls the dielectric, piezoelectric and polarization properties of thin films by adjusting the stress (strain). In this section, we introduced the effective residual strain and interface scale factor and combined the modified constitutive equations with the Landau- Ginsberg-Devonshine thermodynamic theory to investigate the MIP of the quasi 2-2 type heterostructure thin films. We analyzed the total electric polarization and MIP of this thin films by self-consistent calculation for polarization, piezoelectric and dielectric coefficients. The calculated results show that transverse magnetic-field-induced electric polarization of the multiferroic films increases nonlinearly with increasing external magnetic field. When the magnetostriction reaches its saturation at the higher magnetic field, the MIP begins to approach saturation, indicating large MIP could be produced in ferroelectric film due to a gigantic magnetically induced in-plane constraint. Moreover, because the magnetostriction of magnetic phase reaches a maximum at the magnetic transition temperature, the MIP will also get to a maximum value, further showing that the ME coupling is related to the magnetostriction. Next, we calculated the temperature dependence of magnetoelectric output voltage when the magnetostraction of magnetic phase was saturated. We chose the static, alternative magnetic field and the thickness of thin films comparable to experimental values and assumed the interface scale factor is 1, we found that the ME effect peaks at the ferromagnetic transition temperature of the manganite. Comparison with experimental data of multilayered samples reveals a good interface coupling of the films/substrate and a great magnetostriction of magnetic phase result in a large ME effect in this type of thin films.
引文
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