calculates the size of the reduced moment due to quantum and thermal fluctuations
M = MOMENT(obj, 'option1', value1 ...)
To calculate the reduced moment due to quantum and thermal fluctuations
the magnon poulation is calculated at temperature T over the full
Brillouin zone. To integrate numerically over the Brillouin zone random Q
points are generated and the magnon populations are summed over these
random Q points.
Input:
obj Input structure, sw class object.
Options:
nRand The number of random Q points in the Brillouin-zone,
default is 1000.
T Temperature, default is taken from obj.single_ion.T.
tol Tolerance of the incommensurability of the magnetic
ordering wavevector. Deviations from integer values of the
ordering wavevector smaller than the tolerance are
considered to be commensurate. Default value is 1e-4.
omega_tol Tolerance on the energy difference of degenerate modes when
diagonalising the quadratic form, default is 1e-5.
Output:
'M' is a structure, with the following fields:
moment Size of the reduced moments, dimensions are [1 nMagExt].
T Temperature.
nRand Number of random Q points.
obj The copy of the input obj.
Example 1:
tri = sw_model('triAF',1);
M = tri.moment('nRand',1e7);
The example calculates the moment expectation value at zero temperature
on the triangular lattice Heisenberg antiferromagnet. The function gives
the reduced moment (M=0.7385 for S=1 after nRand = 1e7, the reduction is
0.2615). The result can be compared with the following calculations:
[1] A. V Chubukov, S. Sachdev, and T. Senthil, J. Phys. Condens. Matter 6, 8891 (1994).
M = S - 0.261
[2] S. J. Miyake, J. Phys. Soc. Japan 61, 983 (1992).
M = S - 0.2613 + 0.0055/S (1/S is a higher order term neglected here)
Example 2:
sq = sw_model('squareAF',1);
M = sq.moment('nRand',1e7);
The reduced moment of the Heisenberg square lattice antiferromagnet at
zero temperature can be compared to the following published result:
[1] D. A. Huse, Phys. Rev. B 37, 2380 (1988).
M = S - 0.197
See also SW, SW.SPINWAVE, SW.GENMAGSTR, SW.TEMPERATURE.