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Circular and Linear Magnetic Birefringences in Xenon at =1064 Nm Downloaded from orbit.dtu.dk on: Oct 06, 2021 Circular and linear magnetic birefringences in xenon at =1064 nm Cadene, Agathe; Fouche, Mathilde; Rivere, Alice; Battesti, Remy; Coriani, Sonia; Rizzo, Antonio; Rizzo, Carlo Published in: Journal of Chemical Physics Link to article, DOI: 10.1063/1.4916049 Publication date: 2015 Document Version Publisher's PDF, also known as Version of record Link back to DTU Orbit Citation (APA): Cadene, A., Fouche, M., Rivere, A., Battesti, R., Coriani, S., Rizzo, A., & Rizzo, C. (2015). Circular and linear magnetic birefringences in xenon at =1064 nm. Journal of Chemical Physics, 142(12), [124313]. https://doi.org/10.1063/1.4916049 General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Circular and linear magnetic birefringences in xenon at λ = 1064 nm Agathe Cadène, Mathilde Fouché, Alice Rivère, Rémy Battesti, Sonia Coriani, Antonio Rizzo, and Carlo Rizzo Citation: The Journal of Chemical Physics 142, 124313 (2015); doi: 10.1063/1.4916049 View online: http://dx.doi.org/10.1063/1.4916049 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/142/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Periodic reversal of magneto-optic Faraday rotation on uniaxial birefringence crystal with ultrathin magnetic films AIP Advances 3, 072125 (2013); 10.1063/1.4816799 Comparison of standard and damped response formulations of magnetic circular dichroism J. Chem. Phys. 135, 024112 (2011); 10.1063/1.3607991 Interpreting magnetization from Faraday rotation in birefringent magnetic media J. Appl. Phys. 101, 053912 (2007); 10.1063/1.2437586 Theoretical studies on magnetic circular dichroism by the finite perturbation method with relativistic corrections J. Chem. Phys. 123, 164113 (2005); 10.1063/1.2080027 Four-component Hartree–Fock calculations of magnetic-field induced circular birefringence—Faraday effect—in noble gases and dihalogens J. Chem. Phys. 122, 074321 (2005); 10.1063/1.1849167 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 192.38.33.16 On: Wed, 29 Apr 2015 10:19:55 THE JOURNAL OF CHEMICAL PHYSICS 142, 124313 (2015) Circular and linear magnetic birefringences in xenon at λ = 1064 nm Agathe Cadène,1 Mathilde Fouché,1 Alice Rivère,1 Rémy Battesti,1 Sonia Coriani,2,3 Antonio Rizzo,4 and Carlo Rizzo1,a) 1Laboratoire National des Champs Magnétiques Intenses (UPR 3228, CNRS-UPS-UJF-INSA), 143 Avenue de Rangueil, 31400 Toulouse, France 2Dipartimento di Scienze Chimiche e Farmaceutiche, Università degli Studi di Trieste, via Giorgieri 1, 34127 Trieste, Italy 3Aarhus Institute of Advanced Studies, Aarhus University, DK-8000 Aarhus C, Denmark 4Istituto per i Processi Chimico-Fisici del Consiglio Nazionale delle Ricerche (IPCF-CNR), Area della Ricerca, via G. Moruzzi 1, I-56124 Pisa, Italy (Received 19 January 2015; accepted 11 March 2015; published online 30 March 2015) The circular and linear magnetic birefringences corresponding to the Faraday and the Cotton-Mouton effects, respectively, have been measured in xenon at λ = 1064 nm. The experimental setup is based on time dependent magnetic fields and a high finesse Fabry-Pérot cavity. Our value of the Faradayeffect is the first measurement at this wavelength. It is compared to theoretical predictions. Our uncertainty of a few percent yields an agreement at better than 1σ with the computational estimate when relativistic effects are taken into account. Concerning the Cotton-Mouton effect, our measurement, the second ever published at λ = 1064 nm, agrees at better than 1σ with theoretical predictions. We also compare our error budget with that established for other experimental published values. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4916049] I. INTRODUCTION where λ is the light wavelength. On the other hand, the Cotton- Mouton effect corresponds to a linear magnetic birefringence Magnetic birefringence corresponds to an anisotropy of induced by a transverse magnetic field B?. The field induces the (generally complex) refractive index induced in a medium a difference between the real parts of the refraction index by a magnetic field.1,2 A circular birefringence arises when the for light polarized parallel n with respect to that polarized ∥ magnetic field changes the angular velocity of the two eigen perpendicular to the magnetic field n?. The difference ∆nCM modes of polarization in which a linearly polarized beam is = n − n? is proportional to the square of the magnetic field, split, without deforming them. The net result is a rotation of ∥ 2 the plane of linear polarization, a phenomenon also seen in ∆nCM = kCMB?; (3) the absence of external fields in chiral samples (natural optical with k the linear magnetic birefringence per square unit rotation). When the presence of the external magnetic field CM magnetic field intensity. yields a different phase of two perpendicular components of For the Cotton-Mouton effect, k has two contributions, the linear polarization vector, the net result is the appearance CM the first one due to the distortion of the electronic structure of an ellipticity, and we are observing an example of linear while the second one corresponds to a partial orientation of birefringence. the molecules. When working in the conditions of constant Two well known examples of magnetic birefringences are volume, the orientational contribution is proportional to the the Faraday and the Cotton-Mouton effects. The former corre- inverse of the temperature T, and it usually dominates, often sponds to a circular birefringence induced by a longitudinal hiding the first temperature independent contribution. For axial magnetic field B (aligned parallel to the direction of propaga- molecules, for example, k is given by the expression3 tion of light). After∥ going through the birefringent medium, the CM real part of the index of refraction for left circularly polarized πNA ( 2 ) kCM = ∆η + ∆α∆ χ : (4) light n− is different from that for right circularly polarized light Vm4πϵ0 15kBT n+. The difference ∆nF = n− − n+ is proportional to B , ∥ Above NA is the Avogadro constant, Vm the molar volume, ∆nF = kFB ; (1) kB the Boltzmann constant, ϵ0 the electric constant, ∆η the ∥ frequency dependent hypermagnetizability anisotropy, ∆α the k being the circular magnetic birefringence per unit magnetic F optical electric dipole polarizability anisotropy, and ∆ χ the field intensity. For historical reason, the Faraday effect is usu- magnetic susceptibility anisotropy. For spherical molecules or ally given in terms of the Verdet constant, for atoms, such as xenon, however, the temperature depen- πk dent contribution vanishes. Measurements on noble gases, for V = F ; (2) λ example, allow to focus on the hypermagnetizability anisot- ropy ∆η term. On the other hand, since the Langevin-type orientational term vanishes, the magnetic birefringence is a)Electronic mail:[email protected] much lower than the one observed in nonspherical molecules. 0021-9606/2015/142(12)/124313/10/$30.00 142, 124313-1 © 2015 AIP Publishing LLC This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 192.38.33.16 On: Wed, 29 Apr 2015 10:19:55 124313-2 Cadène et al. J. Chem. Phys. 142, 124313 (2015) From an experimental point of view, measurements on such by the formula, gases require a very sensitive apparatus, with a ∆nCM of the −16 −14 order of 10 for helium and 10 for xenon at 1 atm and LB CM = π ∆nCM sin 2θP; (6) with a magnetic field of 1 T. In comparison, ∆nF is typically λ 105 bigger. The computational determination of the Verdet constant where θP is the angle between the light polarization and the and of the Cotton-Mouton effect requires the far-from-trivial magnetic field. calculation of higher-order response functions,2,3 and it has often served as a test bed for the validation of new electronic B. General setup structure methods. For atoms, in order to obtain accurate re- sults, one must properly account for the appropriate description The apparatus has already been described in detail else- of one-electron (basis set), N-electron (correlation), and rela- where.14,15 Briefly, light comes from a Nd:YAG laser at λ tivistic effects. As far as correlation is concerned, coupled clus- = 1064 nm (see Fig.1). It is linearly polarized by a first polar- ter (CC) methods are nowadays among the most accurate tools izer P,before going through either a transverse or a longitudinal in electronic structure theory.4,5 Both birefringences treated magnetic field. The polarization is then analyzed by a second here, and in particular, the Cotton-Mouton effect, require a polarizer A, crossed at maximum extinction compared to P. good description of the outer valence space of the system at The beam polarized parallel to the incident beam, reflected hand. Therefore, the presence of diffuse functions in the one- by the polarizer A as the ordinary ray, is collected by the 2,4 electron basis set is mandatory. Whereas for light atoms, photodiode Pht.
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