以第一原理計算研究Ca3Mn2O7的磁學、電子及聲子性質

Abstract

因為室溫下可由外加電場調控磁性的特性，多鐵過度金屬氧化物近年來被廣泛地研究。最近提出的一種混合非正規鐵電性(hybridimproper ferroelectricity, HIF)，其自發極化來自於混合兩個布里淵區邊界的非極性晶格不穩定性。做為HIF的原型材料，Ca3Mn2O7原本被認為是X+2和X−3聲子模混合凝聚的連續相變，但實驗卻發現了與對稱性違背的過渡態，因此其相變機制仍然不確定。 本文利用基於第一原理的密度泛函理論以及平面波贋勢法，計算Ca3Mn2O7的磁學、電子以及聲子特性。透過計算不同磁結構下的系統總能量，我們發現G型反鐵磁結構具有最低能量。根據海森堡模型，我們計算了交換耦合係數，並且用其估計Néel 溫度，得到了與實驗相當符合的結果。我們也計算了Ca3Mn2O7不同磁性結構下的電子結構，其中G型反鐵磁的電子結構顯示其具有弱鐵磁特性，因此我們再加入自旋軌道耦合效應，結果發現在G型反鐵磁下Ca3Mn2O7 會因為自旋傾斜出現淨總磁矩。進一步探討，發現自旋傾斜是源自於X−3聲子模造成的MnO6八面體傾斜。根據聲子色散關係的聲子軟化現象，我們發現X−3聲子模的軟化程度不及X−1聲子模，阻礙了X−3和X+2聲子模的混合凝聚，導致了與對稱性違背的相變路徑。布里淵區中心的聲子頻率顯示磁性會導致過度態的X−3聲子模軟化，驅動其發生往基態結構的相變。我們證明了Ca3Mn2O7的鐵電極化是由X+2和X−3所誘導，並透過計算得到極化強度為3.50 μC/cm2。

Because of the possibility of electric-field control of magnetism at room temperature, multiferroic transition metal oxides have been widely studied in recent years. Recently, hybrid improper ferroelectricity (HIF) have been reported as a new type of ferroelectricity. The spontaneous polarization of HIF originates from combining two nonpolar zone-boundary lattice instabilities. As a prototype of HIF materials, Ca3Mn2O7 considered to undergo continuous phase transition by hybrid condensation of X−3 and X+2 mode. However, a symmetry incompatible intermediate phase have been found, and thus the precise phase transition mechanism is still not determined. In this thesis, ab initio calculations of phononic, magnetic and electronic properties have been performed within density functional theory and projected augmented-wave method. From calculating total energies of different magnetic configurations, we found G-type antiferromagnetic configuration have the lowest energy. By Heisenberg model, we have calculated the exchange coupling constants, and estimate the Néel temperature, the results agree with experiments. In order to study the electronic properties, we have calculated the density of states of NM, FM, A-AF and G-AF state. The results indicate G-AF state exhibits weak-ferromagnetism. By including spin-orbit coupling, we found there exists net magnetic moment in G-AF Ca3Mn2O7. A further study reveals that the spin-canted moment is due to X−3 tilt mode. According to soft phonon in phonon dispersion, we found that X−1 mode is softer than X−3 mode, impeding the hybrid condensation of X−2 and X−3 soft mode, thus transits in a symmetry incompatible pathway. The phonon frequencies calculated at Brillouin zone center indicate that magnetic ordering soften the X−3 tilt mode in the intermediate state, driving it to structural ground state. We have shown the ferroelectric polarization is induced by X−2 and X−3 mode, and the calculated polarization is 3.50 μC/cm2.