Thermal Hall effect of spins in a paramagnet

Abstract

Theory of Hall transport of spins in a correlated paramagnetic phase is developed. By identifying the thermal Hall current operator in the spin language, which turns out to equal the spin chirality in the pure Heisenberg model, various response functions can be derived straightforwardly. Subsequent reduction to the Schwinger boson representation of spins allows a convenient calculation of thermal and spin Hall coefficients in the paramagnetic regime using self-consistent mean-field theory. Comparison is made to results from the Holstein-Primakoff reduction of spin operators appropriate for ordered phases.

Magnetic transitions in the topological magnon insulator Cu(1,3-bdc)

“…For example, due to the kagome geometry 18 , one of the topologically notrivial magnon bands is also nearly dispersionless. Additionally, magnons in this material display a magnon Hall e↵ect 19,20 , as confirmed by thermal Hall measurements 21 . The magnon Hall e↵ect may find applications in the field of spintronics 22 , as has been proposed for a number of pyrochlore ferrogmanets that also display a magnon Hall e↵ect 23,24 .…”

Topological magnetic excitations on the distorted kagomé antiferromagnets: Applications to volborthite, vesignieite, and edwardsite

“…For quantum magnets with magnetic long-range order the thermal Hall effect has been realized in the collinear kagomé ferromagnet Cu(1-3, bdc) [35] and a number of collinear pyrochlore ferromagnets [36,37]. In this case the transverse thermal Hall conductivity (κ xy ) can be explained in terms of Berry curvature induced by the DM spin-orbit interaction [38][39][40] leading to topological magnons [41][42][43][44][45][46][47][48][49] and Weyl magnons [50,51] similar to spin-orbit coupling electronic systems [52][53][54][55][56]. In a recent experiment [57], a nonzero κ xy has been observed in a frustrated distorted kagomé volborthite at a strong magnetic field of 15 T with no signs of the DM spin-orbit interaction and no discernible thermal Hall signal was observed at zero magnetic field [58].…”

Thermal Hall Effect in a Phonon-Glass Ba3CuSb2O9

“…Among them, the most studied case is the magnon THE which has been observed in ferromagnetic insulators [12][13][14] and is understood in terms of the Berry phase associated with the magnon bands [2,3]. The THEs of spin excitations in paramagnetic states have also been studied theoretically [2,4,5]; these THEs were reported recently in a spin ice compound Tb 2 Ti 2 O 7 [15], a ferromagnetic kagomé lattice system [14], and a frustrated kagomé lattice system [16].…”

“…Among them, the most studied case is the magnon THE which has been observed in ferromagnetic insulators [12][13][14] and is understood in terms of the Berry phase associated with the magnon bands [2,3]. The THEs of spin excitations in paramagnetic states have also been studied theoretically [2,4,5]; these THEs were reported recently in a spin ice compound Tb 2 Ti 2 O 7 [15], a ferromagnetic kagomé lattice system [14], and a frustrated kagomé lattice system [16].In contrast, reports on the THE of phonons have been limited to studies on a dielectric garnet Tb 3 Ga 5 O 12 (TbGG) [17,18]. The theoretical origin of the phonon THE has been discussed as a Raman-type interaction between phonons and large spins [6,7], a Berry curvature of phonon bands [8,9], and a resonant skew scattering of phonons by superstoichiometric Tb 3+ ions [10].…”

“…On the other hand, no Hall effect is expected in insulators because the Hall effect originates from conduction electrons. However, a Hall effect of charge-neutral excitations, which is observed as a thermal Hall effect (THE), has been predicted to occur in magnetic and non-magnetic insulators [2][3][4][5][6][7][8][9][10][11], thereby providing new insights into the research on quantum spin liquids and other frustrated materials. So far, three kinds of THEs have been reported in insulators: THEs of magnons in ordered magnets [12][13][14], spin excitations in disordered magnets [14][15][16], and phonon THEs [17,18].…”