Effect of inhomogeneous magnetization in optical second harmonic generation from layered nanostructures

Abstract

Magnetic nanostructures reveal unique interface induced properties that differ from those of bulk materials, thus magnetization distributions in interface regions are of high interest. Meanwhile, direct measurement of magnetization distribution in layered nanostructures is a complicated task. Here we study magnetic field induced effects in optical second harmonic generation (SHG) in three-layer ferromagnetic / heavy metals nano films. For a certain experimental geometry, which excludes the appearance of magnetooptical effects for homogeneously magnetized structures, magnetization induced SHG intensity variation is observed. Symmetry analysis of the SHG intensity dependencies on external magnetic field shows that the nonlinear source terms proportional to the out-of-plane gradient component of magnetization govern the observed effect.

Interface Driven Effects in Magnetization-Induced Optical Second Harmonic Generation in Layered Films Composed of Ferromagnetic and Heavy Metals

“…If considering multilayer films, the strongest magnetic field induced effect in the SHG response is observed only in the case of non-equivalent magnetic interfaces, i.e., Pt/Co and Co/W, coexist in the same structure, while for symmetric ones like Co/Pt/Co or Pt/Co/Pt it is within the experimental error. Strong MOKE-SHG effect for asymmetric three-layer films was reported recently for the transmission geometry [19], while only two structures were analyzed. Here we show that the order of the magnetic interfaces, as well as the integral thickness of the ferromagnetic materials in the film is not important, which also confirms that the main source of the MOKE-SHG is located at magnetic interfaces.…”

“…This is valid as well in the case of magnetic field induced terms of the non-linear susceptibility that determine magnetooptical effects at the SHG wavelength. Following the description presented in [18,19], the i−th component of the non-linear polarization at the SHG wavelength, which is the source of the SHG wave, can be presented through the so called crystallographic (non-magnetic) and a set of magnetization-sensitive components of non-linear susceptibility as:…”

“…This contradicts with the results of the experiment, as non-zero SHG magnetic contrast ρ is observed in the case of Co/heavy-metal interfaces present in the two-layer structures and in asymmetric Pt/Co/W film. So it was suggested that gradient in magnetization terms like χ (3),∇M and χ (4),∇M can provide the modulation of the SHG intensity [16,19]. At the same time, it stems from the symmetry analysis that odd in longitudinal magnetization terms for in-plane isotropic films can appear only due to χ (4),∇M contributions, as shown in [18,19].…”

“…So it was suggested that gradient in magnetization terms like χ (3),∇M and χ (4),∇M can provide the modulation of the SHG intensity [16,19]. At the same time, it stems from the symmetry analysis that odd in longitudinal magnetization terms for in-plane isotropic films can appear only due to χ (4),∇M contributions, as shown in [18,19]. One can suppose that ∇M term in the direction perpendicular to the film, which determines the efficiency of χ (4),∇M contribution to the SHG polarization, increases if the Co layer is squeezed between two non-equivalent heavy metals.…”

Магнитоиндуцированный нелинейно-оптический отклик плeнок на основе нанослоeв тяжeлых и ферромагнитного металлов

“…При этом был обнаружен нечeтный интенсивностный магнитооптический эффект на частоте ВГ, запрещeнный по соображениям симметрии для границ раздела однородно намагниченных сред ( " запрещeнный" эффект) [6]; наибольшее значение этого эффекта в двухслойных плeнках на основе кобальта достигалось в структуре на основе Co/Pt [7,8]. Более того, в случае несимметричной трeхслойной структуры Pt/Co/W данный эффект усиливался, относительная модуляция интенсивности ВГ при смене направления меридионального магнитного поля превышала 10% [9]. В продолжение этих исследований представляет несомненный интерес изучение данного эффекта для случая других видов магнитных наноструктур на основе ферромагнитного и тяжeлого металлов.…”