### Syntax

M = moment(obj,Name,Value)

### Description

M = moment(obj,Name,Value) calculates the spin expectation value including the leading quantum and thermal fluctuations ($$S^{-1}$$ terms). The magnon poulation is calculated at a given temperature $$T$$ integrated over the Brillouin zone. To calculate the numerical integral the Brillouin zone is sampled using Monte Carlo technique.

### Example

#### Triangular lattice antiferromagnet

The example calculates the spin expectation value at zero temperature on the triangular lattice Heisenberg antiferromagnet. The result can be compared with the following calculations: A. V Chubukov, S. Sachdev, and T. Senthil, J. Phys. Condens. Matter 6, 8891 (1994): $$\langle S \rangle = S - 0.261$$ and S. J. Miyake, J. Phys. Soc. Japan 61, 983 (1992): $$\langle S \rangle = S - 0.2613 + 0.0055/S$$ ($$1/S$$ is a higher order term neglected here).

tri = sw_model('triAF',1)
M = tri.moment('nRand',1e7)
dS = 1-M.moment

Output

dS =
0.2612

#### Square lattice antiferromagnet

The reduced moment of the Heisenberg square lattice antiferromagnet at zero temperature can be compared to the published result of D. A. Huse, Phys. Rev. B 37, 2380 (1988) $$\langle S \rangle = S - 0.197$$.

sq = sw_model('squareAF',1)
M = sq.moment('nRand',1e7)
dS = 1-M.moment

Output

dS =
0.1966    0.1966    0.1966    0.1966

obj
spinw object.

### Name-Value Pair Arguments

'nRand'
The number of random $$Q$$ points in the Brillouin-zone, default value is 1000.
'T'
Temperature, default value is taken from obj.single_ion.T and the unit is stored in spinw.unit with the default being K.
'tol'
Tolerance of the incommensurability of the magnetic propagation wavevector. Deviations from integer values of the propagation vector smaller than the tolerance are considered to be commensurate. Default value is $$10^{-4}$$.
'omega_tol'
Tolerance on the energy difference of degenerate modes when diagonalising the quadratic form, default value is $$10^{-5}$$.
'fid'
Defines whether to provide text output. The default value is determined by the fid preference stored in swpref. The possible values are:
• 0 No text output is generated.
• 1 Text output in the MATLAB Command Window.
• fid File ID provided by the fopen command, the output is written into the opened file stream.

### Output Arguments

M
structure, with the following fields:
• moment Size of the reduced moments in a row vector with $$n_{magExt}$$ number of elements.
• T Temperature.
• nRand Number of random $$Q$$ points.
• obj The clone of the input obj.