Coherent Two-Dimensional Terahertz Magnetic Resonance Spectroscopy of Collective Spin Waves

Abstract

We report a demonstration of two-dimensional (2D) terahertz (THz) magnetic resonance spectroscopy using the magnetic fields of two time-delayed THz pulses. We apply the methodology to directly reveal the nonlinear responses of collective spin waves (magnons) in a canted antiferromagnetic crystal. The 2D THz spectra show all of the third-order nonlinear magnon signals including magnon spin echoes, and 2-quantum signals that reveal pairwise correlations between magnons at the Brillouin zone center. We also observe second-order nonlinear magnon signals showing resonance-enhanced second-harmonic and difference-frequency generation. Numerical simulations of the spin dynamics reproduce all of the spectral features in excellent agreement with the experimental 2D THz spectra. DOI: 10.1103/PhysRevLett.118.207204 Nonlinear manipulation of spins is the basis for all advanced methods in magnetic resonance including multidimensional nuclear magnetic resonance and electron spin resonance (ESR) spectroscopies [1,2], magnetic resonance imaging, and, in recent years, quantum control over individual spins [3]. The methodology is facilitated by the ease with which the regime of strong coupling can be reached between radio frequency or microwave magnetic fields and nuclear or electron spins, respectively, typified by sequences of magnetic pulses that control the magnetic moment directions [1][2][3]. The capabilities meet a bottleneck, however, for far-infrared magnetic resonances characteristic of correlated electron materials, molecular magnets, and metalloproteins.ESR in the terahertz (THz) frequency region can reveal rich information content in chemistry, biology, and materials science [1,2,[4][5][6][7]. In molecular complexes and metalloproteins, THz-frequency zero-field splittings (ZFS) of high-spin transition-metal and rare-earth ions show exquisite sensitivity to ligand geometries, providing mechanistic insight into molecular magnetic properties [4] and protein catalytic function [5]. With strong applied magnetic fields (∼10 T), resonances of unpaired electron spins in molecular complexes can be shifted from the usual microwave regime into the THz range, drastically improving the resolution due to enhanced spectral splittings [2,6,7]. In many ferromagnetic (FM) and antiferromagnetic (AFM) materials, intrinsic magnetic fields in the same range put collective spin waves (magnons) in the THz range. Current ESR spectroscopy remains limited at THz frequencies because the weak sources used only permit measurements of free-induction decay (FID) signals that are linearly proportional to the excitation magnetic field strength. In some cases, including most proteins, even linear THz-frequency ESR signals may not be measurable because the THz spectrum includes much stronger absorption features due to low-frequency motions of polar segments [8]. However, the fast dephasing of such motions ensures that they would not compete with nonlinear spin echo signals [9]. Two-dimensional (2D) THz ESR spectroscopy, like 2D ESR at lower frequenci...

Resolving Continua of Fractional Excitations by Spinon Echo in THz 2D Coherent Spectroscopy

“…This results in a diffusive, barely discernible signal in the first frequency quadrant ( Fig. 2b,g), which is similar to the non-rephasing (NR) signal usually found in χ (3) [29]. See SM [32] for detailed discussion of these features.…”

“…dio frequency range [24][25][26][27] 2DCS is an established technique that probes nonlinear susceptibilities. Thanks to recent technical advances that enable table-top high intensity THz sources, it has been extended recently to the THz range to study graphene and quantum wells [22,23], molecular rotations [28], and spin waves in the conventional magnet YFeO 3 [29]. THz 2DCS uses two pulses in a collinear geometry to excite a system at one frequency and detect at another, thus producing a 2D spectrum.…”

“…We consider a setup similar to that used in Ref. [29]. Two linearly polarized magnetic field pulses A and B arrive at the sample at time 0 and τ > 0 ( Fig.…”

“…Note that in the PM phase the streak-like rephasing signal that is characteristic of fractional excitations is absent. χ (3) yyyy instead shows sharp isolated peaks [32] that are typical of nonlinear spin waves [12,29].…”

Temporal and spectral fingerprints of ultrafast all-coherent spin switching

“…Understanding strongly nonequilibrium spin dynamics triggered by THz pulses, however, is still in its infancy. In antiferromagnets, magnons feature resonance energies in the meV range 20 and can be directly addressed by the magnetic field component of intense THz pulses [21][22][23] . Since the underlying Zeeman interaction is relatively weak, magnetic field amplitudes, which allow for a complete spin reversal have only been reached in linear accelerators 9 , where the spin dynamics have not been accessible on the intrinsic femtosecond scale.…”