Magnon dressing by orbital excitations in ferromagnetic planes of K₂CuF₄ and LaMnO₃

Abstract

We show that even when spins and orbitals disentangle in the ground state, spin excitations are renormalized by the local tuning of e g orbitals in ferromagnetic planes ofK 2 CuF 4 and LaMnO 3 . As a result, dressed spin excitations (magnons) obtained within the electronic model propagate as quasiparticles and their energy renormalization depends on momentum  k . Therefore magnons in spin-orbital systems go beyond the paradigm of the effective Heisenberg model with nearest neighbor spin exchange derived from the ground state-spin-orbital entanglement in excited states predicts large magnon softening at the Brillouin zone boundary, and in case of LaMnO 3 the magnon energy at the M=(π, π) point may be reduced by ∼45%. In contrast, simultaneously the stiffness constant near the Goldstone mode is almost unaffected. We elucidate physics behind magnon renormalization in spin-orbital systems and explain why long wavelength magnons are unrenormalized while simultaneously energies of short wavelength magnons are reduced by orbital fluctuations. In fact, the  k -dependence of the magnon energy is modified mainly by dispersion which originates from spin exchange between second neighbors along the cubic axes a and b. OPEN ACCESS RECEIVED LaMnO 3 (S=2) [10], with three {ˆ} H n terms explained below. The positive coefficients {c 1 , c 2 , c 3 } depend on the multiplet structure of excited 3d 8 Cu 3+ states [48] (3d 5 Mn 2+ states [10]) via Hund's exchange J H /U [13]. In the ground state an e g hole at a Cu 2+ ion in K 2 CuF 4 (an e g electron at a Mn 3+ ion in LaMnO 3 ) occupies a linear combination of two orbital states (1) at site i [1] New J. Phys. 21 (2019) 023018 M Snamina and A M OleśThe fitted value of the nearest neighbor exchange spin constant =´-J J 6.34 10 1 3 is much smaller than the value =à -J J 11.56 10 3 obtained in the frozen orbital approach, actually by´-J 5.22 10 3 , i.e. by~à J 0.45 . This reduction of J 1 may be rationalized and was also calculated analytically using our SVA, see the appendix. Expanding the obtained dispersion w  k in the range of small   k 0, we derived thatThis explains why:(i) the overall magnon bandwidth of J S 8 1 is here strongly reduced from w  ( ) J 0.185 M 0 to w  J 0.101 M , but simultaneously (ii) the stiffness constant determined by + J J 4 1 3 (by à J for frozen orbitals) remains unrenormalized [56], see equation (10). z obtained: (a) in various approximations, i.e. the frozen orbital approach, the VA, and the SVA (black, green, and red line), and the NA (purple dots), and (b) in the VA (green line) and fitted using the Heisenberg model with nearest neighbor =´-J J 6.34 10 1 3 interaction only (orange line), and with both the above nearest neighbor J 1 and third nearest neighbor =´-J J 1.35 10 3 3 interactions (dark blue line). Gray shading highlights the difference between the frozen orbital approach and the VA. Parameter: J H /U=0.1725 [10].where the second term captures the deviation form the frozen orbital description.In order to rationalize the reported va...

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