(spinw-moment)=

# spinw.moment method

## 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)](http://iopscience.iop.org/article/10.1088/0953-8984/6/42/019/meta): $\langle S
\rangle = S - 0.261$ and 
[S. J. Miyake, J. Phys. Soc. Japan 61, 983 (1992)](http://journals.jps.jp/doi/abs/10.1143/JPSJ.61.983): $\langle S \rangle = S - 0.2613 +
0.0055/S$ ($1/S$ is a higher order term neglected here).
 
```matlab
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)](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.37.2380)
$\langle S \rangle = S - 0.197$.
 
```matlab
sq = sw_model('squareAF',1)
M = sq.moment('nRand',1e7)
dS = 1-M.moment
```
*Output*
```
dS =
    0.1966    0.1966    0.1966    0.1966
```
 
 
## Input Arguments
  
`obj`
: [spinw](#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](#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](#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`.
 
## See Also
  
[spinw](#spinw) \| [spinw.spinwave](#spinw-spinwave) \| [spinw.genmagstr](#spinw-genmagstr) \| [spinw.temperature](#spinw-temperature)