Output Files - mcphas.qvc,phs,sps,mf,fum,j1...,xyt,hkl

(in directory ./results/ after a simulation run)

mcphas.qvc

the set of test q-vectors used for calculation of free energy. Components of these q vectors refer to the reciprocal lattice $\vec a^*,\vec b^*,\vec c^*$.

mcphas.phs

spin-configuration table of different types of spin-configurations.

Note: there is no natural criteria for deciding, if one spin-configuration is different from another one. Therefore the list of ”different” spin-configurations is dependent on the meaning of ”different”.

The program McPhase decides whether a spin-configuration is different from another by a simple criteria, namely by the angle between the spins. Comparing two spin configurations it calculates the angle between corresponding spins and if for one spin the angle is not small, the configuration is treated as a different configuration. Therefore for example a ferromagnet with moments in $a$ has a different spin configuration than a ferromagnet with moments in $b$ direction.

mcphas.sps

$T-H$ dependence of spin-configuration. The spin configurations stored in this file may be displayed using the program spins, an example is given in figure 25. The expectation values $\langle \hat I_{\alpha} \rangle$ ( $\alpha=1,\dots,{\rm nofcomponents}$, note that for the single ion module so1ion $\hat I_1=\hat J_x,\hat I_2=\hat J_y,\hat I_3=\hat J_z,\hat I_4=\hat O_2^{-2},\hat I_5=\hat O_2^{-1}, \dots$, for the complete list see appendix G) are stored in this file for i=1,2,...,number of spins in magnetic unit cell.

mcphas.mf

$T-H$ dependence of exchange field configuration, stored as $H_{xc}(i)$(unit is in meV) for i=1,2,...,number of spins in magnetic unit cell.

mcphas.fum

free energy $f$ according to equation (19), magnetic energy per site $u$

  $$u=f+Ts=f-T\partial f/\partial T=\frac{1}{N_b}\sum_{s,i} \epsilon^s_i \frac{e^{-\epsilon^s_i/kT}}{z^s}+\frac{E_{corr}}{N_b}$$ (21)

Note, that form the numerical derivative of $u$ with respect to temperature the specific heat per site in mean field approximation can be calculated $c_V=\partial u/\partial T$. Finally, mcphas.fum contains the calculated magnetisation (only if a mcalc function is present in the single ion module). As an example for the information contained in this file the calculated magnetisation of NdCu$_2$ is shown in fig 9. Note, in case of non-orthogonal axes the convention for applied field $Ha, Hb, Hc$ and also for the magnetisation components $ma,mb,mc$ in these tables is $Hb\vert\vert\vec b$, $Hc\vert\vert(\vec a \times \vec b)$ and $Ha$ perpendicular to $Hb$ and $Hc$.

mcphas1.j1 .j1 .j2 ...

spin-spin correlation functions for sub-lattice 1 neighbour 1 2 ... (linear combination is proportional to magnetostriction) The spin-spin correlation functions for neighbour $k$ are defined by the following sum of dyadic products:

  $$\frac{1}{N_b}\sum_{s=1}^{N_b} <{\hat \mathbf I}^s> \otimes <{\hat \mathbf I}^{s+k}>$$ (22)

with $N_b$ being the number of magnetic atoms in the magnetic unit cell. For example for the single ion module so1ion $\hat I_1=\hat J_x,\hat I_2=\hat J_y,\hat I_3=\hat J_z,\hat I_4=\hat O_2^{-2},\hat I_5=\hat O_2^{-1}, \dots$, for the complete list see appendix G. Single ion and two-ion magnetostriction can be calculated using the $<\hat I_{\alpha}>$ from mcphas.xyt and the spin-spin correlation functions from mcphas1.j1 .j1 .j2 .... As an example the magnetostriction analysis of NdCu$_2$ is shown in figure 10. For details please refer to [19]. Note, in case of non-orthogonal axes the convention for applied field $Ha, Hb, Hc$ and also for the moment components in these tables is $Hb\vert\vert\vec b$, $Hc\vert\vert(\vec a \times \vec b)$ and $Ha$ perpendicular to $Hb$ and $Hc$.

mcphas.xyt

phase diagram as x,y,T, H, phase-number j according to spin-configuration table given in mcphas.phs, a periodicity key, thermal expectationvalues $\langle \hat I_{\alpha} \rangle$ (averaged over the unit cell). Figure 28 shows the phase diagram of NdCu$_2$ for magnetic fields parallel to the orthorhombic $b$-direction. Note, in case of non-orthogonal axes the convention for applied field $Ha, Hb, Hc$ in these tables is $Hb\vert\vert\vec b$, $Hc\vert\vert(\vec a \times \vec b)$ and $Ha$ perpendicular to $Hb$ and $Hc$. Note that the phase-number is not necessarily a unique number for each phase in the phase diagram, because the program numbers phases according to their similarity in the moments. For example, any tetragonal easy plane magnet will have domains with moments parallel to $a$ and $b$. The program will generate both domains and find equal energy for both. It will give each domain a separate phase number, because spin directions are completely different. Because both domains have the same free energy at every temperature, the phase-index will vary in a random manner. In order to generate a beautiful phase diagram figure, such equivalent domains have to be identified and phase numbers have to be substituted.

mcphas.hkl

calculated (unpolarised) neutron diffraction data (the calculated magnetic intensities correspond to the magnetic structure + Polarisation factor + magnetic Formfactor (dipole approx). The Lorentz-factor and instrumental corrections are not calculated.). The single ion module function mcalc is used to evaluate the magnetic moment on each site. As an example figure 27 shows the calculated temperature dependence of magnetic amplitudes for NdCu$_2$. $h,k,l$ refer to the reciprocal lattice $\vec a^*,\vec b^*,\vec c^*$. Note, in case of non-orthogonal axes the convention for applied field $Ha, Hb, Hc$ in these tables is $Hb\vert\vert\vec b$, $Hc\vert\vert(\vec a \times \vec b)$ and $Ha$ perpendicular to $Hb$ and $Hc$.

mcphasa.hkl

Fourier Transform of the $a$-component of the magnetic Moments. $h,k,l$ refer to the reciprocal lattice $\vec a^*,\vec b^*,\vec c^*$. The single ion module function mcalc is used to evaluate the magnetic moment on each site. Note, in case of non-orthogonal axes the convention for applied field $Ha, Hb, Hc$ and the magnetic moment component in these tables is $Hb\vert\vert\vec b$, $Hc\vert\vert(\vec a \times \vec b)$ and $Ha$ perpendicular to $Hb$ and $Hc$.

mcphasb.hkl

Fourier Transform of the $b$-component of the magnetic Moments. The single ion module function mcalc is used to evaluate the magnetic moment on each site. $h,k,l$ refer to the reciprocal lattice $\vec a^*,\vec b^*,\vec c^*$. Note, in case of non-orthogonal axes the convention for applied field $Ha, Hb, Hc$ and the magnetic moment component in these tables is $Hb\vert\vert\vec b$, $Hc\vert\vert(\vec a \times \vec b)$ and $Ha$ perpendicular to $Hb$ and $Hc$.

mcphasc.hkl

Fourier Transform of the $c$-component of the magnetic Moments. The single ion module function mcalc is used to evaluate the magnetic moment on each site. $h,k,l$ refer to the reciprocal lattice $\vec a^*,\vec b^*,\vec c^*$. Note, in case of non-orthogonal axes the convention for applied field $Ha, Hb, Hc$ and the magnetic moment component in these tables is $Hb\vert\vert\vec b$, $Hc\vert\vert(\vec a \times \vec b)$ and $Ha$ perpendicular to $Hb$ and $Hc$.

Exercises:

• Look at the output files of McPhase in the directory examples/ndcu2b_new/results. At which magnetic field the ferromagnetically aligned state is achieved (at $T=$2 K)?
• What is the propagation vector in the different antiferromagnetic phases at $T=$2 K ?