A nonfrustrated magnetoelectric with incommensurate magnetic order in magnetic field
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RDER, DISORDER, AND PHASE TRANSITION IN CONDENSED SYSTEMS
A Nonfrustrated Magnetoelectric with Incommensurate Magnetic Order in Magnetic Field1 A. V. Syromyatnikov Petersburg Nuclear Physics Institute, Gatchina, St. Petersburg, 188300 Russia e-mail: [email protected] Received February 19, 2007
Abstract—We discuss a model nonfrustrated magnetoelectric in which a sufficiently strong magnetoelectric coupling produces an incommensurate magnetic order leading to ferroelectricity. Properties of the magnetoelectric in the magnetic field directed perpendicular to the wave vector describing the spin helix are considered in detail. Analysis of the classical energy shows that in contrast to the naive expectation, the onset of ferroelectricity occurs at a field Hc1 that is lower than the saturation field Hc2. We have Hc1 = Hc2 at large enough magnetoelectric coupling. We show that at H = 0, ferroelectricity occurs at T = TFE < TN. A qualitative discussion of the phase diagram in the H–T plane is presented within the mean-field approach. PACS numbers: 75.80.+q, 71.70.Ej, 77.80.-e DOI: 10.1134/S1063776107090154 1
1. INTRODUCTION In recent years, there has been a revival of interest in magnetic ferroelectrics in which magnetic and ferroelectric orders coexist (magnetoelectrics) [1, 2]. Systems in which the ferroelectric and spiral magnetic order occur simultaneously attract particular interest presently because the role of such materials in fabricating novel magnetoelectric (ME) devices has been recognized [3]. A number of such compounds have been obtained recently: RMnO3 with R = Gd, Tb, Dy [4–6]; RMn2O5 with R = Ho, Y, Tb, Dy [7–9]; Ni3V2O8 [10, 11]; spinel oxides RCr2O4 with R = Co, Fe, Mn [12]; MnWO4 [13], etc. In the majority of these materials, the paraelectric phase with a collinear spin structure (sinusoidal spin density wave) appears below the Néel temperature, TN. Upon further cooling, at T = TFE < TN, a transition occurs to the phase in which the ferroelectric order coexists with an incommensurate elliptical (conical in RCr2O4) magnetic spiral. Some of such ferroelectric phases (e.g., RMnO3 and RCr2O4) are stable down to very small temperatures; in others, transitions to collinear paraelectric phases occur below TFE. All experiments point to the key role of the noncollinear spin configurations induced by frustrated exchange interactions in producing the electric polarization [2]. Due to the frustration, TN and TFE are quite small in all compounds found up to now, with only one exception, Ba0.5Sr1.5Zn2Fe12O22 [14], in which TFE is greater than room temperature. A “giant” ME effect is observed in these materials as a very high sensitivity of the electric polarization to the magnetic field: the spin-flop transition in the magnetic field is accompanied by rotation of 1 The
text was submitted by the author in English.
the polarization through 90° and by an anomaly in the dielectric constant. The value of the electric polarization was found to be two to three orders smaller than in typical ferroelectrics; there is
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