Barton, who started for the SK Nove Mesto na Morave, appeared internationally for the first time in February 2007 at the European Youth Olympic Winter Festival 2007 in Jaca . There he took 30th place over 7.5 km classic and 19th place over 10 km freestyle. He completed his first race in the Slavic Cup in December 2008 in Horni Misecky , which he finished in 65th place over 10 km classic and 42nd place over 15 km freestyle. The following month he came in Wisla with the second place in the sprint for the first time in the Slavic Cup on the podium. In the 2010/11 season he won second place in the sprint in the Slavic Cup in Gerlachov and took his first victory in the Slavic Cup in the sprint in Nové Město . He finished ninth in the overall ranking. In December 2011 he made his debut in the cross-country skiing world cup in Düsseldorf . He came in 35th place in the sprint and 18th in the team sprint. In the 2012/13 season he won the Slavic Cup in Wisla in the sprint and took third place in the sprint in Kremnica . At the Nordic World Ski Championships in 2013 in Fiemme Valley , he achieved 55th place in the sprint. At the end of the season he was eighth in the overall ranking of the Slavic Cup. In February 2015 he finished 32nd in the sprint at the Nordic World Ski Championships 2015 in Falun and took his third victory in the Slavic Cup in the sprint in Kremnica. In the 2015/16 season he reached three top ten placings in the Slavic Cup, including second place in the sprint in Kremnica and first place in the sprint in Štrbské Pleso and thus finished fourth in the overall ranking of the Slavic Cup. He scored his first World Cup points at the Tour de Ski 2016/17 with 27th place in the sprint. At the Nordic World Ski Championships 2017 in Lahti , he came 42nd in the sprint.