  We calculate the magnetic dipole $\gamma$-ray strength functions in a chain
of even-mass neodymium isotopes $^{144-152}$Nd in the framework of the
configuration-interaction (CI) shell model. We infer the strength function by
applying the maximum entropy method (MEM) to the exact imaginary-time response
function calculated with the shell-model Monte Carlo (SMMC) method. The success
of the MEM depends on the choice of a good strength function as a prior
distribution. We investigate two choices for the prior strength function: the
static path approximation (SPA) and the quasiparticle random-phase
approximation (QRPA). We find that the QRPA is a better approximation at low
temperatures (i.e., near the ground state), while the SPA is a better choice at
finite temperatures. We identify a low-energy enhancement (LEE) in the MEM
deexcitation $M1$ strength functions of the even-mass neodymium isotopes and
compare with recent experimental results for the total deexcitation
$\gamma$-ray strength functions. The LEE is already seen in the SPA strength
function but not in the QRPA strength function, indicating the importance of
large-amplitude static fluctuations around the mean field in reproducing the
LEE. Our method is currently the only one which can reproduce LEE in heavy
open-shell nuclei where conventional CI shell model calculations are
prohibited. With the onset of deformation as number of neutrons increases along
the chain of neodymium isotopes, we observe that some of the LEE strength
transfers to a low-energy excitation, which we interpret as a
finite-temperature "scissors" mode. We also observe a finite-temperature
spin-flip mode.
