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General Magnetic Transition Dipole Moments for Electron ...

General Magnetic Transition Dipole Moments for Electron paramagnetic ResonanceJoscha Nehrkorn,1, Alexander Schnegg,1 Karsten Holldack,2and Stefan Stoll3, 1 Berlin Joint EPR Laboratory, Institut f ur Silizium-Photovoltaik,Helmholtz-Zentrum Berlin f ur Materialen und Energie, Berlin, Germany2 Institut f ur Methoden und Instrumentierung der Forschung mit Synchrotronstrahlung,Helmholtz-Zentrum Berlin f ur Materialen und Energie, Berlin, Germany3 Department of Chemistry, University of Washington, Seattle, USA(Dated: November 27, 2014)We present General expressions for the Magnetic Transition rates in beam Electron ParamagneticResonance (EPR) experiments of anisotropic spin systems in the solid state.

Electron paramagnetic resonance (EPR) is a spectro-scopic technique that yields unique information on struc-tural [1{7], magnetic [8{10] and electronic properties [11{13] of paramagnetic states in material systems ranging ... scribed by time-dependent perturbation theory (Fermi’s

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Transcription of General Magnetic Transition Dipole Moments for Electron ...

1 General Magnetic Transition Dipole Moments for Electron paramagnetic ResonanceJoscha Nehrkorn,1, Alexander Schnegg,1 Karsten Holldack,2and Stefan Stoll3, 1 Berlin Joint EPR Laboratory, Institut f ur Silizium-Photovoltaik,Helmholtz-Zentrum Berlin f ur Materialen und Energie, Berlin, Germany2 Institut f ur Methoden und Instrumentierung der Forschung mit Synchrotronstrahlung,Helmholtz-Zentrum Berlin f ur Materialen und Energie, Berlin, Germany3 Department of Chemistry, University of Washington, Seattle, USA(Dated: November 27, 2014)We present General expressions for the Magnetic Transition rates in beam Electron ParamagneticResonance (EPR) experiments of anisotropic spin systems in the solid state.

2 The expressions applyto General spin centers and arbitrary excitation geometry (Voigt, Faraday, and intermediate). Theywork for linear and circular polarized as well as unpolarized excitation, and for crystals and expressions are based on the concept of the (complex) Magnetic Transition Dipole momentvector. Using the new theory , we determine the parities of ground and excited spin states of high-spin (S= 5/2) FeIIIin hemin from the polarization dependence of experimental ground state EPRline numbers: ; ; ; paramagnetic resonance (EPR) is a spectro-scopic technique that yields unique information on struc-tural [1 7], Magnetic [8 10] and electronic properties [11 13] of paramagnetic states in material systems rangingfrom proteins to nanomagnets and semiconductors.

3 Inaddition, EPR methods are increasingly used for con-trolled manipulation of spin systems, which may formthe basis of spin quantum computing [14 17]. Experi-mental design, interpretation, prediction and control ofthe latter require General theoretical tools to calculateEPR Transition energies and probabilities. These prop-erties are determined by the spin center under study andthe choice of the experimental a standard EPR experiment, linearly polarized low-frequency microwave (mw) radiation is coupled into a res-onator exposed to a static Magnetic fieldB0such that theradiation Magnetic field componentB1(t) of the ensuingstanding wave is perpendicular toB0.

4 With a lineardetector, the measured EPR spectral intensity is propor-tional to the power absorbed by the sample, which inturn is proportional to the quantum mechanical transi-tion rate. For this standard geometry, compact expres-sions for the EPR Transition rate can be found in the lit-erature [18, 19]. Analytical expressions for a single spinwithout fine or hyperfine interactions are known [20 25].However, the limitation to a resonator, linear mwpolarization and orthogonal orientation between staticand oscillating Magnetic fields restricts the versatility ofEPR experiments.

5 Recently, experimental setups thatgo beyond these limitations have become more non-resonant beam EPR setups explore very broadfield (up to 30 T) and frequency (up to THz) high field/high frequency EPR experiments arebased on a range of excitation sources, ranging from lab-based semiconductors, lasers and tube sources [26 29] tosynchrotrons [30 33] and free Electron lasers [34, 35]. De-spite the variety of source technology, these approachesare all based on quasioptical techniques that transmit mwor THz radiation in open space instead of wave guides orcoaxial cables.

6 This provides much larger freedom for thealignment of the radiation beam relative to the externalmagnetic , entirely new EPR experiments became possi-ble. These include experiments in Faraday geometry [36],and the employment of split ring resonator arrays as THzmetamaterials for selective EPR excitation [37, 38]. Un-like with resonators, in non-resonant setups circular orunpolarized radiation can be employed. Circularly po-larized radiation can be used to determine the sign ofg factors [25, 39 42] and is a possible selection tool inEPR based quantum computing [43].

7 Depending on thehandedness of the circularly polarized radiation, differentsets of EPR transitions can be adressed in single-moleculemagnets [36]. For dynamic nuclear polarization, it wasrecently shown that the enhancement depends on thehandedness of the circular polarized mw radiation [44].Unpolarized radiation, or radiation that is extracted frombeam paths which do not conserve the polarization of theradiation, are used in high-field cw EPR [27, 29, 45 48],for frequency-swept cw EPR [33, 49, 50] as well as forfree- Electron laser based cw EPR experiments [34].

8 Spectral intensities from these new experimental de-signs cannot be described by current theory , which islimited to perpendicular and parallel excitation geome-tries with linear polarization. Here, we derive compactand General expressions for EPR Magnetic Transition in-tensities that cover all excitation geometries and polar-izations. We show that the Transition intensities can bedescribed in an elegant way using a General magnetictransition Dipole moment (mtdm) vector . The mtdmis the Magnetic analog of the electric Transition dipolemoment vector widely used in optical , we treat a solid-state sample containing iso-lated identically oriented spin centers, each [ ] 26 Nov 20142 FIG.

9 1. Sketches of magneto-optical excitation geometriesdescribed in the text. Electric (E1) and Magnetic (B1) fieldcomponents of the mw/THz radiation are depicted by redand green oscillating lines, (yellow arrow) de-notes the propagation direction of the radiation. The staticmagnetic fieldB0is indicated by the gray arrow. Magnetcoils are shown as gray tori. (a) EPR excitation of a sam-ple (blue box) inside a mw resonator (pale yellow box withblack ceiling). The standing wave in the resonator ensuresmaximumB1and minimumE1at the sample position.

10 Inthe present caseB1is aligned perpendicular toB0. (b) and(c) depict travelling wave excitation in Voigt geometry (b),wherek B0, and Faraday geometry (c), wherek spins (electrons and/or nuclei) with arbitraryanisotropic interactions. We then extend the treatmentto dilute powder samples, where isolated spin centers oc-cur in a random uniform orientational distribution. Next,we treat the special case of isolated Electron spins with-out fine or hyperfine interactions. All cases cover lin-ear, circular, and unpolarized radiation. The associatedderivations are given in the supplemental material (SM).


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