Reduction of quantum fluctuations by anisotropy fields in Heisenberg ferro- and antiferromagnets

Abstract

The physical properties of quantum systems, which are described by the anisotropic Heisenberg model, are influenced by thermal as well as by quantum fluctuations. Such a quantum Heisenberg system can be profoundly changed towards a classical system by tuning two parameters, namely the total spin and the anisotropy field: Large easy-axis anisotropy fields, which drive the system towards the classical Ising model, as well as large spin quantum numbers suppress the quantum fluctuations and lead to a classical limit. We elucidate the incipience of this reduction of quantum fluctuations. In order to illustrate the resulting effects we determine the critical temperatures for ferro-and antiferromagnets and the ground state sublattice magnetization for antiferromagnets. The outcome depends on the dimension, the spin quantum number and the anisotropy field and is studied for a widespread range of these parameters. We compare the results obtained by: Classical Mean Field, Quantum Mean Field, Linear Spin Wave and Random Phase Approximation. Our findings are confirmed and quantitatively improved by numerical Quantum Monte Carlo simulations. The differences between the ferromagnet and antiferromagnet are investigated.We finally find a comprehensive picture of the classical trends and elucidate the suppression of quantum fluctuations in anisotropic spin systems. In particular, we find that the quantum fluctuations are extraordinarily sensitive to the presence of small anisotropy fields. This sensitivity can be quantified by introducing an "anisotropy susceptibility".

Two-dimensional quantum-spin-1/2 XXZ magnet in zero magnetic field: Global thermodynamics from renormalisation group theory

“…This asymmetry between FM and AFM critical temperatures is a pure quantum mechanical effect, and was indeed signaled by the specific heat peaks in d = 1: specific heat peak temperatures shift in opposite directions for AFM and FM models as the anisotropy gets stronger in d = 1. 48 As will be demonstrated in Section IV C 2, the quantum fluctuations at T = 0 are stronger in the AFM case compared to the FM case, as expected 94,105 . Hence, one expects the AFM order at low-temperatures to be washed out more easily (less thermal energy kT c is required) compared to FM order.…”

“…A possible explanation might be due to interrelated effects of entropy and density of states. 105 In Fig. 5, we plot the ratio of AFM and FM critical temperatures, T…”

Investigation of quantum and thermal fluctuations ferromagnetic spin chains with easy-plane anisotropy

“…The magnetization M reduces with decreasing chain length, which means that more and stronger quantum fluctuations occur. This behavior is logical because, with the reduction of the chain length, we further reduce the dimension of the system and this lead to the increase of the quantum fluctuations [50]. At this point an additional remark: inf.…”

Antiferromagnetic Dispersion Relations and Nature of Magnon Pressure

“…The impact of external magnetic fields on antiferromagnetic systems -both in two and three spatial dimensions -has been studied by various authors employing different techniques: (modified) spin-wave theory [1][2][3][4][5][6][7][8][9][10][11], Green's functions [12][13][14][15][16], series expansions [17][18][19][20], Monte Carlo simulations [21][22][23], exact diagonalization [24,25], and yet other methods [26][27][28][29][30][31][32][33][34][35][36][37].…”